test_torch.py

import sys
import io
import os
import math
import random
import re
import copy
import shutil
import torch
import torch.cuda
import torch.backends.cuda
import tempfile
import unittest
import warnings
import pickle
import gzip
import types
import textwrap
import zipfile
from torch._utils_internal import get_file_path_2
from torch.utils.dlpack import from_dlpack, to_dlpack
from torch._utils import _rebuild_tensor
from torch._six import inf, nan, string_classes, istuple
from itertools import product, combinations, combinations_with_replacement, permutations
from functools import reduce
from random import randrange
from torch import multiprocessing as mp
from common_methods_invocations import tri_tests_args, run_additional_tri_tests, \
    _compare_trilu_indices
from common_utils import TestCase, iter_indices, TEST_NUMPY, TEST_SCIPY, TEST_MKL, \
    TEST_LIBROSA, run_tests, download_file, skipIfNoLapack, suppress_warnings, \
    IS_WINDOWS, PY3, NO_MULTIPROCESSING_SPAWN, do_test_dtypes, do_test_empty_full, \
    IS_SANDCASTLE, load_tests, brute_pdist, brute_cdist, slowTest, \
    skipCUDANonDefaultStreamIf, skipCUDAMemoryLeakCheckIf
from multiprocessing.reduction import ForkingPickler
from common_device_type import instantiate_device_type_tests, \
    skipCPUIfNoLapack, skipCUDAIfNoMagma, skipCUDAIfRocm, onlyCUDA, onlyCPU, \
    dtypes, dtypesIfCUDA, deviceCountAtLeast
import torch.backends.quantized


# load_tests from common_utils is used to automatically filter tests for
# sharding on sandcastle. This line silences flake warnings
load_tests = load_tests

if TEST_NUMPY:
    import numpy as np

if TEST_SCIPY:
    from scipy import signal

if TEST_LIBROSA:
    import librosa

SIZE = 100

can_retrieve_source = True
with warnings.catch_warnings(record=True) as warns:
    with tempfile.NamedTemporaryFile() as checkpoint:
        x = torch.save(torch.nn.Module(), checkpoint)
        for warn in warns:
            if "Couldn't retrieve source code" in warn.message.args[0]:
                can_retrieve_source = False
                break


class FilelikeMock(object):
    def __init__(self, data, has_fileno=True, has_readinto=False):
        if has_readinto:
            self.readinto = self.readinto_opt
        if has_fileno:
            # Python 2's StringIO.StringIO has no fileno attribute.
            # This is used to test that.
            self.fileno = self.fileno_opt

        self.calls = set()
        self.bytesio = io.BytesIO(data)

        def trace(fn, name):
            def result(*args, **kwargs):
                self.calls.add(name)
                return fn(*args, **kwargs)
            return result

        for attr in ['read', 'readline', 'seek', 'tell', 'write', 'flush']:
            traced_fn = trace(getattr(self.bytesio, attr), attr)
            setattr(self, attr, traced_fn)

    def fileno_opt(self):
        raise io.UnsupportedOperation('Not a real file')

    def readinto_opt(self, view):
        self.calls.add('readinto')
        return self.bytesio.readinto(view)

    def was_called(self, name):
        return name in self.calls


class BytesIOContext(io.BytesIO):
    def __enter__(self):
        return self

    def __exit__(self, *args):
        pass


# This is intentionally prefixed by an underscore. Otherwise pytest will try to
# run its methods as test cases.
class _TestTorchMixin(object):
    def _make_tensors(self, shape, val_range=(-100, 100), use_floating=True, use_integral=True):
        float_types = [torch.double,
                       torch.float]
        int_types = [torch.int64,
                     torch.int32,
                     torch.int16]

        def make_contiguous(shape, dtype):
            if dtype in float_types:
                val = torch.randn(shape, dtype=dtype)
                val = val * ((val_range[1] - val_range[0]) / (math.pi * 2.0))
                val = val + ((val_range[1] - val_range[0]) / 2.0)
                val = torch.clamp(val, min=val_range[0], max=val_range[1])
                return val
            result = torch.zeros(shape, dtype=dtype)
            result.apply_(lambda x: random.randint(val_range[0], val_range[1]))
            return result

        def make_non_contiguous(shape, dtype):
            contig = make_contiguous(shape, dtype)
            non_contig = torch.empty(shape + (2, 2), dtype=dtype)[..., 0]
            non_contig = non_contig.select(-1, -1)
            non_contig.copy_(contig)
            self.assertFalse(non_contig.is_contiguous())
            return non_contig

        def make_contiguous_slice(size, dtype):
            contig = make_contiguous((1, size), dtype)
            non_contig = contig[:1, 1:size - 1]
            self.assertTrue(non_contig.is_contiguous())
            return contig

        types = []
        if use_floating:
            types += float_types
        if use_integral:
            types += int_types
        tensors = {"cont": [], "noncont": [], "slice": []}
        for dtype in types:
            tensors["cont"].append(make_contiguous(shape, dtype))
            tensors["noncont"].append(make_non_contiguous(shape, dtype))
            tensors["slice"].append(make_contiguous_slice(sum(list(shape)), dtype))

        return tensors

    def test_dir(self):
        dir(torch)

    def test_type_conversion_via_dtype_name(self):
        x = torch.tensor([1])
        self.assertEqual(x.byte().dtype, torch.uint8)
        self.assertEqual(x.bool().dtype, torch.bool)
        self.assertEqual(x.char().dtype, torch.int8)
        self.assertEqual(x.double().dtype, torch.float64)
        self.assertEqual(x.float().dtype, torch.float32)
        self.assertEqual(x.half().dtype, torch.float16)
        self.assertEqual(x.int().dtype, torch.int32)
        self.assertEqual(x.bfloat16().dtype, torch.bfloat16)

    def test_doc_template(self):
        from torch._torch_docs import __file__ as doc_file
        from torch._torch_docs import multi_dim_common, single_dim_common, factory_common_args, factory_like_common_args

        with open(doc_file, "r") as f:
            doc_strs = f.read()

        for doc_str in re.findall(r'add_docstr\((.*?),.*?("""|\'\'\')(.*?)("""|\'\'\')\)', doc_strs, re.MULTILINE | re.DOTALL):
            for common_args in [multi_dim_common, single_dim_common, factory_common_args, factory_like_common_args]:
                for k, v in common_args.items():
                    self.assertNotIn(v, doc_str[2], 'The argument description "{}" in {} can be '
                                                    'replaced by {{{}}}'.format(v, doc_str[0], k))

    def test_doc(self):
        checked_types = (types.MethodType, types.FunctionType,
                         types.BuiltinFunctionType, types.BuiltinMethodType)

        def test_namespace(ns, *skips):
            if isinstance(ns, object):
                ns_name = ns.__class__.__name__
            else:
                ns_name = ns.__name__
            skip_regexes = []
            for r in skips:
                if isinstance(r, string_classes):
                    skip_regexes.append(re.compile('^{}$'.format(re.escape(r))))
                else:
                    skip_regexes.append(r)
            for name in dir(ns):
                if name.startswith('_'):
                    continue
                var = getattr(ns, name)
                if not isinstance(var, checked_types):
                    continue
                doc = var.__doc__
                has_doc = doc is not None and len(doc.strip()) > 0
                full_name = ns_name + '.' + name
                if any(r.match(name) for r in skip_regexes):
                    self.assertFalse(has_doc,
                                     'New docs have been added for {}, please remove '
                                     'it from the skipped list in TestTorch.test_doc'.format(full_name))
                else:
                    self.assertTrue(has_doc, '{} is missing documentation'.format(full_name))

        # FIXME: All of the following should be marked as expected failures
        # so that it is easier to tell when missing has been added.
        # FIXME: fix all the skipped ones below!
        test_namespace(torch.randn(1),
                       'as_strided_',
                       re.compile('^clamp_(min|max)_?$'),
                       'coalesce',
                       'is_coalesced',
                       'is_distributed',
                       'is_complex',
                       'is_nonzero',
                       'is_same_size',
                       'isclose',
                       'log_softmax',
                       'map2_',
                       'new',
                       'reinforce',
                       'relu',
                       'relu_',
                       'prelu',
                       'resize',
                       'resize_as',
                       'smm',
                       'softmax',
                       'split_with_sizes',
                       'sspaddmm',
                       'to_dense',
                       'sparse_resize_',
                       'sparse_resize_and_clear_',
                       )
        test_namespace(torch.nn)
        test_namespace(torch.nn.functional, 'assert_int_or_pair', 'feature_alpha_dropout')
        # TODO: add torch.* tests when we have proper namespacing on ATen functions
        # test_namespace(torch)

    def test_dot(self):
        types = {
            'torch.DoubleTensor',
            'torch.FloatTensor',
        }
        for tname in types:
            v1 = torch.randn(100).type(tname)
            v2 = torch.randn(100).type(tname)
            res1 = torch.dot(v1, v2)
            res2 = 0
            for i, j in zip(v1, v2):
                res2 += i * j
            self.assertEqual(res1, res2)
            out = torch.randn(()).type(tname)
            torch.dot(v1, v2, out=out)
            self.assertEqual(res1, out)

        # Test 0-strided
        for tname in types:
            v1 = torch.randn(1).type(tname).expand(100)
            v2 = torch.randn(100).type(tname)
            res1 = torch.dot(v1, v2)
            res2 = 0
            for i, j in zip(v1, v2):
                res2 += i * j
            self.assertEqual(res1, res2)
            out = torch.randn(()).type(tname)
            torch.dot(v1, v2, out=out)
            self.assertEqual(res1, out)

    def test_ger(self):
        types = {
            'torch.DoubleTensor',
            'torch.FloatTensor',
            'torch.BFloat16Tensor',
        }
        for tname in types:
            v1 = torch.randn(100).type(tname)
            v2 = torch.randn(100).type(tname)
            res1 = torch.ger(v1, v2)
            res2 = torch.zeros(100, 100).type(tname)
            for i in range(100):
                for j in range(100):
                    res2[i, j] = v1[i] * v2[j]
            self.assertEqual(res1, res2)

        # Test 0-strided
        for tname in types:
            v1 = torch.randn(1).type(tname).expand(100)
            v2 = torch.randn(100).type(tname)
            res1 = torch.ger(v1, v2)
            res2 = torch.zeros(100, 100).type(tname)
            for i in range(100):
                for j in range(100):
                    res2[i, j] = v1[i] * v2[j]
            self.assertEqual(res1, res2)

    def test_addr(self):
        types = {
            'torch.DoubleTensor',
            'torch.FloatTensor',
            'torch.BFloat16Tensor',
        }

        def run_test(m, v1, v2, m_transform=lambda x: x):
            m = m_transform(m.clone())
            ref = m.clone()
            torch.addr(m, v1, v2, out=m)
            for i in range(m.size(0)):
                for j in range(m.size(1)):
                    ref[i, j] += v1[i] * v2[j]
            self.assertEqual(m, ref)

        for tname in types:
            for h, w in [(100, 110), (1, 20), (200, 2)]:
                m = torch.randn(h, w).type(tname)
                v1 = torch.randn(h).type(tname)
                v2 = torch.randn(w).type(tname)
                run_test(m, v1, v2)
                # test transpose
                run_test(m, v2, v1, lambda x: x.transpose(0, 1))
                # test 0 strided
                v1 = torch.randn(1).type(tname).expand(h)
                run_test(m, v1, v2)
                run_test(m, v2, v1, lambda x: x.transpose(0, 1))

    def test_addmv(self):
        types = {
            'torch.DoubleTensor': 1e-8,
            'torch.FloatTensor': 1e-4,
            'torch.BFloat16Tensor': 1e-0,
        }
        for tname, prec in types.items():
            t = torch.randn(10).type(tname)
            m = torch.randn(10, 100).type(tname)
            v = torch.randn(100).type(tname)
            res1 = torch.addmv(t, m, v)
            res2 = torch.zeros(10).type(tname)
            res2 += t
            for i in range(10):
                for j in range(100):
                    res2[i] += m[i, j] * v[j]

            self.assertEqual(res1, res2, prec)

        # Test 0-strided
        for tname, prec in types.items():
            t = torch.randn(1).type(tname).expand(10)
            m = torch.randn(10, 1).type(tname).expand(10, 100)
            v = torch.randn(100).type(tname)
            res1 = torch.addmv(t, m, v)
            res2 = torch.zeros(10).type(tname)
            res2 += t
            for i in range(10):
                for j in range(100):
                    res2[i] += m[i, j] * v[j]

            self.assertEqual(res1, res2, prec)

    def test_addmm(self):
        types = {
            'torch.DoubleTensor': 1e-8,
            'torch.FloatTensor': 1e-4,
            'torch.BFloat16Tensor': 1e-1,
        }
        for tname, prec in types.items():
            M = torch.randn(10, 25).type(tname)
            m1 = torch.randn(10, 50).type(tname)
            m2 = torch.randn(50, 25).type(tname)
            res1 = torch.addmm(M, m1, m2)
            res2 = torch.zeros(10, 25).type(tname)
            res2 += M
            for i in range(10):
                for j in range(25):
                    for k in range(50):
                        res2[i, j] += m1[i, k] * m2[k, j]
            self.assertEqual(res1, res2, prec)

        # Test 0-strided
        for tname, prec in types.items():
            M = torch.randn(10, 1).type(tname).expand(10, 25)
            m1 = torch.randn(10, 1).type(tname).expand(10, 50)
            m2 = torch.randn(50, 25).type(tname)
            res1 = torch.addmm(M, m1, m2)
            res2 = torch.zeros(10, 25).type(tname)
            res2 += M
            for i in range(10):
                for j in range(25):
                    for k in range(50):
                        res2[i, j] += m1[i, k] * m2[k, j]
            self.assertEqual(res1, res2, prec)

    def test_allclose(self):
        x = torch.tensor([1.0, 2.0, 3.0])
        y = torch.tensor([1.01, 2.01, 3.01])
        self.assertTrue(torch.allclose(x, y, rtol=0, atol=0.02))
        self.assertTrue(torch.allclose(x, y, rtol=0.01, atol=0.0))
        self.assertFalse(torch.allclose(x, y))
        self.assertTrue(torch.allclose(torch.tensor([0.0]), torch.tensor([1e-8])))
        x = torch.tensor([2.0, 3.0, nan])
        y = torch.tensor([2.01, 3.01, nan])
        self.assertFalse(torch.allclose(x, y, rtol=1e-2))
        self.assertTrue(torch.allclose(x, y, rtol=1e-2, equal_nan=True))
        self.assertFalse(torch.allclose(x, y, rtol=1e-3, equal_nan=True))
        inf_t = torch.tensor([inf])
        self.assertTrue(torch.allclose(inf_t, inf_t))
        self.assertTrue(torch.allclose(-inf_t, -inf_t))
        self.assertFalse(torch.allclose(inf_t, -inf_t))
        self.assertFalse(torch.allclose(inf_t, torch.tensor([1e20])))
        self.assertFalse(torch.allclose(-inf_t, torch.tensor([-1e20])))

    def test_linear_algebra_scalar_raises(self):
        m = torch.randn(5, 5)
        v = torch.randn(5)
        s = torch.tensor(7)
        self.assertRaises(RuntimeError, lambda: torch.mv(m, s))
        self.assertRaises(RuntimeError, lambda: torch.addmv(v, m, s))
        self.assertRaises(RuntimeError, lambda: torch.ger(v, s))
        self.assertRaises(RuntimeError, lambda: torch.ger(s, v))
        self.assertRaises(RuntimeError, lambda: torch.addr(m, v, s))
        self.assertRaises(RuntimeError, lambda: torch.addr(m, s, v))

    def _test_math(self, torchfn, mathfn, input=None, test_expand=False):
        if input is None:
            input = []
            input.append(list(range(-5, 5)))
            input.append([0 for x in range(-5, 5)])
            input.append([x + 1e-6 for x in range(-5, 5)])
            # Some vectorized implementations don't support large ranges
            input.append([x + 1e10 for x in range(-5, 5)])
            input.append([x - 1e10 for x in range(-5, 5)])
            input.append(torch.randn(10).tolist())
            input.append((torch.randn(10) + 1e6).tolist())
            input.append([math.pi * (x / 2) for x in range(-5, 5)])

        def compare_reference(input, dtype):
            input = torch.tensor(input, dtype=dtype)
            res1 = torchfn(input.clone())
            res2 = input.clone().apply_(mathfn)
            torch.testing.assert_allclose(res1, res2)

        # compare against the reference math function
        compare_reference(input, torch.double)
        compare_reference(input, torch.float)

        def check_non_contiguous(shape, dtype):
            contig = torch.randn(shape, dtype=dtype)
            non_contig = torch.empty(shape + (2,), dtype=dtype)[..., 0]
            non_contig.copy_(contig)
            self.assertFalse(non_contig.is_contiguous())
            self.assertEqual(torchfn(contig), torchfn(non_contig), 'non-contiguous')

        # compare application against contiguous vs. non-contiguous
        check_non_contiguous((5, 7), torch.double)
        check_non_contiguous((1024,), torch.double)
        check_non_contiguous((5, 7), torch.float)
        check_non_contiguous((1024,), torch.float)

        def check_non_contiguous_index(dtype):
            contig = torch.randn((2, 2, 1, 2), dtype=dtype)
            non_contig = contig[:, 1, ...]
            contig = non_contig.clone()
            self.assertFalse(non_contig.is_contiguous())
            self.assertEqual(torchfn(contig), torchfn(non_contig), 'non-contiguous index')

        check_non_contiguous_index(torch.float)
        check_non_contiguous_index(torch.double)

        def check_non_contiguous_expand(shape, dtype):
            contig = torch.randn(shape, dtype=dtype)
            non_contig = contig.clone().expand(3, -1, -1)
            self.assertFalse(non_contig.is_contiguous())
            contig = torchfn(contig)
            non_contig = torchfn(non_contig)
            for i in range(3):
                self.assertEqual(contig, non_contig[i], 'non-contiguous expand[' + str(i) + ']')

        # Expand is not defined for in-place operations
        if test_expand:
            # The size 1 case is special as it leads to 0 stride and needs to persists
            check_non_contiguous_expand((1, 3), torch.double)
            check_non_contiguous_expand((1, 7), torch.double)
            check_non_contiguous_expand((5, 7), torch.float)

        # If size(dim) == 1, stride(dim) is not defined.
        # The code needs to be able to handle this
        def check_contiguous_size1(dtype):
            contig = torch.randn((5, 100), dtype=dtype)
            contig = contig[:1, :50]
            contig2 = torch.empty(contig.size(), dtype=dtype)
            contig2.copy_(contig)
            self.assertTrue(contig.is_contiguous())
            self.assertTrue(contig2.is_contiguous())
            self.assertEqual(torchfn(contig), torchfn(contig2), 'contiguous size1')

        check_contiguous_size1(torch.double)
        check_contiguous_size1(torch.float)

        def check_contiguous_size1_largedim(dtype):
            contig = torch.randn((5, 2, 3, 1, 4, 5, 3, 2, 1, 2, 3, 4), dtype=dtype)
            contig = contig[:1, :, :, :, :, :, :, :, :, :, :, :]
            contig2 = torch.empty(contig.size(), dtype=dtype)
            contig2.copy_(contig)
            self.assertTrue(contig.is_contiguous())
            self.assertTrue(contig2.is_contiguous())
            self.assertEqual(torchfn(contig), torchfn(contig2), 'contiguous size1')

        check_contiguous_size1_largedim(torch.double)
        check_contiguous_size1_largedim(torch.float)

        def check_large(dtype):
            input = torch.randn(1024, 512, dtype=dtype)
            actual = torchfn(input)
            expected = torch.stack([torchfn(slice) for slice in input])
            self.assertEqual(actual, expected, 'large')

        # compare large tensor vs. repeated small applications to expose
        # possible parallelism bugs.
        check_large(torch.double)
        check_large(torch.float)

    def __test_math_by_name(self, function_name, mathfn, selffn):
        mathfn = getattr(math, mathfn)
        if selffn:
            def torchfn(x):
                return getattr(x, function_name)()
        else:
            torchfn = getattr(torch, function_name)
        self._test_math(torchfn, mathfn, test_expand=(not selffn))

    def _test_math_by_name(self, function_name, test_self=True):
        if test_self:
            self.__test_math_by_name(function_name + "_", function_name, True)
        self.__test_math_by_name(function_name, function_name, False)

    def test_sin(self):
        self._test_math_by_name('sin')

    def test_sinh(self):
        def sinh(x):
            try:
                return math.sinh(x)
            except OverflowError:
                return inf if x > 0 else -inf
        self._test_math(torch.sinh, sinh)

    def test_lgamma(self):
        def lgamma(x):
            if x <= 0 and x == int(x):
                return inf
            return math.lgamma(x)
        self._test_math(torch.lgamma, lgamma)

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_mvlgamma(self):
        from scipy.special import multigammaln
        for d in range(1, 5):
            input = torch.empty(10).uniform_(d, 10)
            res_torch = torch.mvlgamma(input, d)
            res_scipy = multigammaln(input.numpy(), d)
            self.assertEqual(res_torch.numpy(), res_scipy)

    def test_mvlgamma_argcheck(self):
        def run_test(d):
            input = torch.linspace((d - 2) / 2, 10, 10)
            torch.mvlgamma(input, d)

        with self.assertRaisesRegex(RuntimeError, "Condition for computing multivariate log-gamma not met"):
            run_test(3)

    def _digamma_input(self, test_poles=True):
        input = []
        input.append((torch.randn(10).abs() + 1e-4).tolist())
        input.append((torch.randn(10).abs() + 1e6).tolist())
        zeros = torch.linspace(-9.5, -0.5, 10)
        input.append(zeros.tolist())
        input.append((zeros - 0.49).tolist())
        input.append((zeros + 0.49).tolist())
        input.append((zeros + (torch.rand(10) * 0.99) - 0.5).tolist())

        if test_poles:
            input.append([-0.999999994, -1.999999994, -2.0000000111,
                          -100.99999994, -1931.99999994, 0.000000111,
                          -0.000000111, 0, -2, -329])
        return input

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_digamma(self):
        from scipy.special import digamma

        # scipy 1.1.0 changed when it returns +/-inf vs. NaN
        def torch_digamma_without_inf(inp):
            res = torch.digamma(inp)
            res[(res == -inf) | (res == inf)] = nan
            return res

        def scipy_digamma_without_inf(inp):
            res = digamma(inp)
            if np.isscalar(res):
                return res if np.isfinite(res) else nan
            res[np.isinf(res)] = nan
            return res

        self._test_math(torch_digamma_without_inf, scipy_digamma_without_inf, self._digamma_input())

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_polygamma(self):
        from scipy.special import polygamma
        for n in [0, 1]:
            self._test_math(lambda x: torch.polygamma(n, x),
                            lambda x: polygamma(n, x).item(),
                            self._digamma_input(test_poles=False))

        with self.assertRaisesRegex(RuntimeError, r'polygamma\(n, x\) does not support negative n\.'):
            torch.polygamma(-1, torch.tensor([1.0, 2.0]))

    def test_asin(self):
        self._test_math(torch.asin, lambda x: math.asin(x) if abs(x) <= 1 else nan)

    def test_cos(self):
        self._test_math_by_name('cos')

    def test_cosh(self):
        def cosh(x):
            try:
                return math.cosh(x)
            except OverflowError:
                # Return inf on overflow.
                # See http://en.cppreference.com/w/cpp/numeric/math/cosh
                return inf
        self._test_math(torch.cosh, cosh)

    def test_acos(self):
        self._test_math(torch.acos, lambda x: math.acos(x) if abs(x) <= 1 else nan)

    def test_tan(self):
        self._test_math_by_name('tan')

    def test_tanh(self):
        self._test_math_by_name('tanh')

    def test_atan(self):
        self._test_math_by_name('atan')

    def test_log(self):
        def log(x):
            if x == 0:
                return -inf
            elif x < 0:
                return nan
            return math.log(x)
        self._test_math(torch.log, log)

    def test_log10(self):
        def log10(x):
            if x == 0:
                return -inf
            elif x < 0:
                return nan
            return math.log10(x)
        self._test_math(torch.log10, log10)

    def test_log1p(self):
        def log1p(x):
            if x == -1:
                return -inf
            elif x < -1:
                return nan
            return math.log1p(x)
        self._test_math(torch.log1p, log1p)

    def test_log2(self):
        def log2(x):
            if x == 0:
                return -inf
            elif x < 0:
                return nan
            try:
                return math.log2(x)
            except AttributeError:
                return math.log(x, 2)
        self._test_math(torch.log2, log2)

    def test_sqrt(self):
        self._test_math(torch.sqrt, lambda x: math.sqrt(x) if x >= 0 else nan)

    def test_erf(self):
        self._test_math_by_name('erf')

    def test_erfc(self):
        self._test_math_by_name('erfc')

    def test_exp(self):
        def exp(x):
            try:
                return math.exp(x)
            except OverflowError:
                return inf
        self._test_math(torch.exp, exp)

    @slowTest
    def test_exp_slow(self):
        # Test for https://github.com/pytorch/pytorch/issues/17271
        # This is pretty slow on my Macbook but it only takes a few
        # seconds on a beefy Xeon server
        a = torch.exp(torch.ones(2 ** 31, dtype=torch.float32))
        b = torch.exp(torch.ones(1, dtype=torch.float32))
        self.assertEqual(a, b.expand(2 ** 31))

    def test_expm1(self):
        def expm1(x):
            try:
                return math.expm1(x)
            except OverflowError:
                return inf
        self._test_math(torch.expm1, expm1)

    def test_floor(self):
        self._test_math_by_name('floor')

    def test_ceil(self):
        self._test_math_by_name('ceil')

    def test_rsqrt(self):
        def rsqrt(x):
            if x == 0:
                return inf
            elif x < 0:
                return nan
            return 1.0 / math.sqrt(x)

        self._test_math(torch.rsqrt, rsqrt)

    def test_sigmoid(self):
        # TODO: why not simulate math.sigmoid like with rsqrt?
        inputValues = [-1000, -1, 0, 0.5, 1, 2, 1000]
        expectedOutput = [0.0000, 0.2689, 0.5, 0.6225, 0.7311, 0.8808, 1.000]
        precision_4dps = 0.0002

        def checkType(tensor):
            self.assertEqual(tensor(inputValues).sigmoid(), tensor(expectedOutput), precision_4dps)

        checkType(torch.FloatTensor)
        checkType(torch.DoubleTensor)

    def test_frac(self):
        self._test_math(torch.frac, lambda x: math.fmod(x, 1))

    def test_trunc(self):
        self._test_math(torch.trunc, lambda x: x - math.fmod(x, 1))

    def test_round(self):
        self._test_math(torch.round, round)

    def test_has_storage(self):
        self.assertIsNotNone(torch.Tensor().storage())
        self.assertIsNotNone(torch.Tensor(0).storage())
        self.assertIsNotNone(torch.Tensor([]).storage())
        self.assertIsNotNone(torch.Tensor().clone().storage())
        self.assertIsNotNone(torch.Tensor([0, 0, 0]).nonzero().storage())
        self.assertIsNotNone(torch.Tensor().new().storage())

    def _testSelection(self, torchfn, mathfn):
        # contiguous
        m1 = torch.randn(100, 100)
        res1 = torchfn(m1)
        res2 = m1[0, 0]
        for i, j in iter_indices(m1):
            res2 = mathfn(res2, m1[i, j])
        self.assertEqual(res1, res2)

        # non-contiguous
        m1 = torch.randn(10, 10, 10)
        m2 = m1[:, 4]
        res1 = torchfn(m2)
        res2 = m2[0, 0]
        for i, j in iter_indices(m2):
            res2 = mathfn(res2, m2[i][j])
        self.assertEqual(res1, res2)

        # with indices
        m1 = torch.randn(100, 100)
        res1val, res1ind = torchfn(m1, 1, False)
        res2val = m1[:, 0:1].clone().squeeze()
        res2ind = res1ind.clone().fill_(0)
        for i, j in iter_indices(m1):
            if mathfn(res2val[i], m1[i, j]) != res2val[i]:
                res2val[i] = m1[i, j]
                res2ind[i] = j

        maxerr = 0
        for i in range(res1val.size(0)):
            maxerr = max(maxerr, abs(res1val[i] - res2val[i]))
            self.assertEqual(res1ind[i], res2ind[i])
        self.assertLessEqual(abs(maxerr), 1e-5)

        # NaNs
        for index in (0, 4, 99):
            m1 = torch.randn(100)
            m1[index] = nan
            res1val, res1ind = torch.max(m1, 0)
            self.assertTrue(math.isnan(res1val))
            self.assertEqual(res1ind, index)
            res1val = torchfn(m1)
            self.assertTrue(math.isnan(res1val))

        # Bool
        m1 = torch.tensor([True, False, True], dtype=torch.bool)
        res1 = torchfn(m1)
        res2 = m1[0]
        for i in iter_indices(m1):
            res2 = mathfn(res2, m1[i])
        self.assertEqual(res1, res2)

    def test_max(self):
        self._testSelection(torch.max, max)

    @staticmethod
    def _test_max_with_inf(self, dtypes=(torch.float, torch.double), device='cpu'):
        for dtype in dtypes:
            a = torch.tensor([[-inf, -inf, inf, 3], [inf, inf, -inf, -1]], dtype=dtype, device=device)
            self.assertTrue(torch.all(torch.max(a, dim=1)[0] == inf).item())
            self.assertTrue(torch.max(a).item() == inf)

    def test_max_with_inf(self):
        self._test_max_with_inf(self)

    def test_min(self):
        self._testSelection(torch.min, min)

    @staticmethod
    def _test_min_with_inf(self, dtypes=(torch.float, torch.double), device='cpu'):
        for dtype in dtypes:
            a = torch.tensor([[-inf, -inf, inf, 3], [inf, inf, -inf, -1]], dtype=dtype, device=device)
            self.assertTrue(torch.all(torch.min(a, dim=1)[0] == (-inf)).item())
            self.assertTrue(torch.min(a).item() == -inf)

    def test_min_with_inf(self):
        self._test_min_with_inf(self)

    def test_dim_reduction_uint8_overflow(self):
        example = [[-1, 2, 1], [5, 3, 6]]
        x = torch.tensor(example, dtype=torch.uint8)
        self.assertEqual(x.sum(dtype=torch.uint8).item(), 16)
        self.assertEqual(x.sum(0, dtype=torch.uint8), torch.FloatTensor([4, 5, 7]))
        self.assertEqual(x.sum(1, dtype=torch.uint8), torch.FloatTensor([2, 14]))
        y = torch.tensor(example, dtype=torch.uint8)
        torch.sum(x, 0, out=y)
        self.assertEqual(x.sum(0, dtype=torch.uint8), y)

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_logsumexp(self):
        from scipy.special import logsumexp
        a = torch.randn(5, 4)
        a[0, 0] = inf
        a[1, :] = -inf
        actual = a.logsumexp(1)
        expected = logsumexp(a.numpy(), 1)
        self.assertEqual(expected.shape, actual.shape)
        self.assertTrue(np.allclose(expected, actual.numpy()))
        # check that out is actually inplace
        b = torch.zeros(5, 2)
        c = b[:, 0]
        torch.logsumexp(a, 1, out=c)
        self.assertTrue(np.allclose(expected, b[:, 0].numpy()))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_cpu_parallel(self):
        # To use parallel branches we'll need to compare on tensors
        # that are relatively large. Even if this is run on a single
        # core machine these tests will still give you signal on
        # the correctness

        def _run_test(size):
            for dim in range(len(size) + 1):
                nv = np.round(np.random.rand(*size))  # 0s and 1s
                tv = torch.from_numpy(nv)
                # Parallelisim is only used if numel is
                # larger than grainsize defined in Parallel.h
                self.assertTrue(tv.numel() > 32768)
                if dim == len(size):
                    nvs = nv.sum()
                    tvs = tv.sum()
                else:
                    nvs = nv.sum(dim)
                    tvs = tv.sum(dim)
                diff = np.abs(nvs - tvs.numpy()).sum()
                self.assertEqual(diff, 0)

        _run_test([2, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3])
        _run_test([4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
        _run_test([1, 32 * 8 * 32 * 8])
        _run_test([1, 32770])

    def _testCSelection(self, torchfn, mathfn):
        # Two tensors
        size = (100, 100)
        a = torch.rand(*size)
        b = torch.rand(*size)
        c = torchfn(a, b)
        expected_c = torch.zeros(*size)
        expected_c.map2_(a, b, lambda _, a, b: mathfn(a, b))
        self.assertEqual(expected_c, c, 0)

    def test_max_elementwise(self):
        self._testCSelection(torch.max, max)

    def test_min_elementwise(self):
        self._testCSelection(torch.min, min)

    def test_all_any(self):
        def test(size):
            x = torch.ones(*size).byte()
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x[3] = 0
            self.assertFalse(x.all())
            self.assertTrue(x.any())

            x.zero_()
            self.assertFalse(x.all())
            self.assertFalse(x.any())

            x.fill_(2)
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x = torch.ones(*size).bool()
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x[3] = False
            self.assertFalse(x.all())
            self.assertTrue(x.any())

        test((10,))
        test((5, 5))

    def test_where_bool_tensor(self):
        for d in torch.testing.get_all_device_types():
            a = torch.tensor([True, False], device=d)
            res = torch.where(a > 0)
            self.assertEqual(1, len(res))

    def test_where_tensor(self):
        def rand_tensor(size, dtype, device):
            if dtype.is_floating_point:
                return torch.rand(size=size, dtype=dtype, device=device)
            elif dtype == torch.uint8:
                return torch.randint(1, 5, size=size, dtype=dtype, device=device)
            elif dtype == torch.bool:
                return torch.randint(0, 1, size=size, dtype=dtype, device=device).bool()
            else:
                return torch.randint(-5, 5, size=size, dtype=dtype, device=device)

        def get_tensor(size, dtype, device, contiguous):
            if not contiguous and len(size) < 2:
                raise RuntimeError("Unable to generate non contiguous tensor with size < 2")
            t = rand_tensor(size, dtype, device)
            if contiguous:
                return t
            else:
                return t.transpose(0, 1)

        height = 5
        width = 5
        for device in torch.testing.get_all_device_types():
            for dt1 in torch.testing.get_all_math_dtypes(device):
                for dt2 in torch.testing.get_all_math_dtypes(device):
                    for contiguous in [True, False]:
                        x1 = get_tensor((height, width), dt1, device, contiguous)
                        x2 = get_tensor((height, width), dt2, device, contiguous)
                        if dt1 != dt2:
                            self.assertRaisesRegex(RuntimeError, "expected scalar type", lambda: torch.where(x1 == 1, x1, x2))
                        else:
                            if x1.is_floating_point():
                                condition = (x1 < 0.5)
                            else:
                                condition = (x1 == 1)
                            expected = condition.to(x1.dtype) * x1 + (~condition).to(x2.dtype) * x2
                            result = torch.where(condition, x1, x2)
                            self.assertEqual(expected, result)

    def test_all_any_with_dim(self):
        def test(x):
            r1 = x.prod(dim=0, keepdim=False).byte()
            r2 = x.all(dim=0, keepdim=False)
            self.assertEqual(r1.shape, r2.shape)
            self.assertTrue((r1 == r2).all())

            r3 = x.sum(dim=1, keepdim=True).clamp(0, 1).byte()
            r4 = x.any(dim=1, keepdim=True)
            self.assertEqual(r3.shape, r4.shape)
            self.assertTrue((r3 == r4).all())

        test(torch.ByteTensor([[0, 0, 0],
                               [0, 0, 1],
                               [0, 1, 1],
                               [1, 1, 1]]))

    def test_mv(self):
        def _test_mv(m1, v1):
            res1 = torch.mv(m1, v1)
            res2 = res1.clone().zero_()
            for i, j in iter_indices(m1):
                res2[i] += m1[i][j] * v1[j]

            self.assertEqual(res1, res2)

        _test_mv(torch.randn(100, 100, dtype=torch.float32), torch.randn(100, dtype=torch.float32))
        _test_mv(torch.randn(100, 100, dtype=torch.float64), torch.randn(100, dtype=torch.float64))
        _test_mv(torch.randint(0, 100, (100, 100), dtype=torch.int32), torch.randint(0, 100, (100, ), dtype=torch.int32))
        _test_mv(torch.randint(0, 100, (100, 100), dtype=torch.int64), torch.randint(0, 100, (100, ), dtype=torch.int64))
        _test_mv(torch.randn(100, 100, dtype=torch.float32).bfloat16(), torch.randn(100, dtype=torch.float32).bfloat16())

    def test_numpy_args(self):
        x1 = torch.randn(10)
        x2 = torch.randn(10)
        res1 = torch.add(input=x1, other=x2)
        res2 = torch.add(x1=x1, x2=x2)
        self.assertEqual(res1, res2)

        x1 = torch.randn(10, 10, 10)
        res1 = x1.sum(dim=(0, 2), keepdim=True)
        res2 = x1.sum(axis=(0, 2), keepdims=True)
        self.assertEqual(res1, res2)

    def test_sub(self):
        for dtype in torch.testing.get_all_dtypes():
            m1 = torch.tensor([2.34, 4.44], dtype=dtype)
            m2 = torch.tensor([1.23, 2.33], dtype=dtype)

            if (dtype == torch.half or dtype == torch.bool):
                self.assertRaises(RuntimeError, lambda: m1 - m2)
            elif (dtype == torch.bfloat16):
                # bfloat16 has a lower precision so we have to have a separate check for it
                self.assertEqual(m1 - m2, torch.tensor([1.11, 2.11], dtype=dtype), 0.01)
            else:
                self.assertEqual(m1 - m2, torch.tensor([1.11, 2.11], dtype=dtype))

    def test_csub(self):
        # with a tensor
        a = torch.randn(100, 90)
        b = a.clone().normal_()

        res_add = torch.add(a, -1, b)
        res_csub = a.clone()
        res_csub.sub_(b)
        self.assertEqual(res_add, res_csub)

        # with a scalar
        a = torch.randn(100, 100)

        scalar = 123.5
        res_add = torch.add(a, -scalar)
        res_csub = a.clone()
        res_csub.sub_(scalar)
        self.assertEqual(res_add, res_csub)

    def test_threshold(self):
        for dtype in torch.testing.get_all_math_dtypes('cpu'):
            if dtype != torch.uint8 and dtype != torch.float16:
                # 100 is wide enough to use AVX2 instructions for all types
                x = torch.randn(100).sign().to(dtype=dtype)
                y = torch.threshold(x, 0, 0)
                self.assertTrue(y.le(0).any())

    def test_reciprocal(self):
        for dtype in [torch.float, torch.double]:
            a = torch.randn(100, 89, dtype=dtype)
            res_div = 1 / a
            res_reciprocal = a.clone()
            res_reciprocal.reciprocal_()
            self.assertEqual(res_reciprocal, res_div)

    def test_div(self):
        m1 = torch.randn(10, 10)
        res1 = m1.clone()
        res1[:, 3].div_(2)
        res2 = m1.clone()
        for i in range(m1.size(0)):
            res2[i, 3] = res2[i, 3] / 2
        self.assertEqual(res1, res2)

        a1 = torch.tensor([4.2, 6.2], dtype=torch.bfloat16)
        a2 = torch.tensor([2., 2.], dtype=torch.bfloat16)
        self.assertEqual(a1 / a2, torch.tensor([2.1, 3.1], dtype=torch.bfloat16), 0.01)
        self.assertEqual(a1.div(a2), a1 / a2)

    def test_floordiv(self):
        for dtype in torch.testing.get_all_math_dtypes('cpu'):
            if dtype is torch.float16:
                continue
            x = torch.randn(100).mul(10).to(dtype)
            y = x // 3
            self.assertEqual(y.dtype, x.dtype)
            z = torch.tensor([math.trunc(v.item() / 3.) for v in x], dtype=y.dtype)
            self.assertEqual(y, z)

    def test_rdiv(self):
        for dtype in torch.testing.get_all_math_dtypes('cpu'):
            if dtype is torch.float16:
                continue
            x = torch.rand(100).add(1).mul(4).to(dtype)
            y = 30 / x
            if dtype.is_floating_point:
                z = torch.tensor([30 / v.item() for v in x], dtype=dtype)
            else:
                z = torch.tensor([math.trunc(30. / v.item()) for v in x], dtype=dtype)
            self.assertEqual(y, z)

    def test_fmod(self):
        m1 = torch.Tensor(10, 10).uniform_(-10., 10.)
        res1 = m1.clone()
        q = 2.1
        res1[:, 3].fmod_(q)
        res2 = m1.clone()
        for i in range(m1.size(1)):
            res2[i, 3] = math.fmod(res2[i, 3], q)
        self.assertEqual(res1, res2)

    def test_remainder(self):
        # Check the Floating point case, both tensor and scalar overloads
        for use_item in [True, False]:
            m1 = torch.Tensor(10, 10).uniform_(-10., 10.)
            res1 = m1.clone()
            res2 = m1.clone()
            qs = torch.arange(-5.1, 4.1)
            # Check the case where the divisor is a simple float
            for col_idx, q in enumerate(qs):
                # Reference
                for i in range(m1.size(0)):
                    res2[i, col_idx] = res2[i, col_idx] % q
                # To test
                res1[:, col_idx].remainder_(q if not use_item else q.item())
            self.assertEqual(res1, res2)
            # Check the case where the divisor is a tensor
            res1 = m1.clone()
            res1.remainder_(qs.unsqueeze(0).expand_as(res1))
            self.assertEqual(res1, res2)

        # Check the LongTensor case, both tensor and scalar overloads
        for use_item in [True, False]:
            long_m1 = torch.LongTensor(10, 10).random_(-10, 10)
            long_res1 = long_m1.clone()
            long_res2 = long_m1.clone()
            long_qs = torch.arange(-5, 5)
            long_qs[5] = 5  # Can't handle the divisor=0 case
            for col_idx, long_q in enumerate(long_qs):
                # Reference
                for i in range(long_m1.size(0)):
                    long_res2[i, col_idx] = long_res2[i, col_idx] % long_q
                # To test
                long_res1[:, col_idx].remainder_(long_q if not use_item else long_q.item())
            self.assertEqual(long_res1, long_res2)
            # Divisor is a tensor case
            long_res1 = long_m1.clone()
            long_res1.remainder_(long_qs.unsqueeze(0).expand_as(long_res1))

    def test_mm(self):
        def _test_mm(n, m, p, dtype, genf):
            # helper function
            def matrixmultiply(mat1, mat2):
                n = mat1.size(0)
                m = mat1.size(1)
                p = mat2.size(1)
                res = torch.zeros(n, p, dtype=dtype)
                for i, j in iter_indices(res):
                    res[i, j] = sum(mat1[i, k] * mat2[k, j] for k in range(m))
                return res

            # contiguous case
            mat1 = genf(n, m)
            mat2 = genf(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 1
            mat1 = genf(n, m)
            mat2 = genf(p, m).t()
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 2
            mat1 = genf(m, n).t()
            mat2 = genf(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 3
            mat1 = genf(m, n).t()
            mat2 = genf(p, m).t()
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # test with zero stride
            mat1 = genf(n, m)
            mat2 = genf(m, 1).expand(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # explicitly exercise the _out variant in torch.mm().
            # contiguous case
            mat1 = genf(n, m)
            mat2 = genf(m, p)
            res = genf(n, p)
            torch.mm(mat1, mat2, out=res)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # explicitly exercise the _out variant in torch.mm().
            # non contiguous case 3
            mat1 = genf(m, n).t()
            mat2 = genf(p, m).t()
            res = genf(n, p)
            torch.mm(mat1, mat2, out=res)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

        for (n, m, p) in [(20, 10, 5), (15, 5, 10), (5, 18, 10)]:
            _test_mm(n, m, p, torch.float32, lambda x, y: torch.randn(x, y, dtype=torch.float32))
            _test_mm(n, m, p, torch.float64, lambda x, y: torch.randn(x, y, dtype=torch.float64))
            _test_mm(n, m, p, torch.int32, lambda x, y: torch.randint(0, 100, (x, y), dtype=torch.int32))
            _test_mm(n, m, p, torch.int64, lambda x, y: torch.randint(0, 100, (x, y), dtype=torch.int64))
            _test_mm(n, m, p, torch.bfloat16, lambda x, y: torch.randn(x, y, dtype=torch.float32).bfloat16())

    @staticmethod
    def _test_lu_solve(self, cast, pivot=True):
        from common_utils import lu_solve_test_helper
        for k, n in zip([2, 3, 5], [3, 5, 7]):
            b, A, LU_data, LU_pivots = lu_solve_test_helper(self, (n,), (n, k), cast, pivot)
            x = torch.lu_solve(b, LU_data, LU_pivots)
            self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

    @skipIfNoLapack
    def test_lu_solve(self):
        self._test_lu_solve(self, lambda t: t)

    @staticmethod
    def _test_lu_solve_batched(self, cast, pivot=True):
        from common_utils import lu_solve_test_helper

        def lu_solve_batch_test_helper(A_dims, b_dims, cast, pivot):
            b, A, LU_data, LU_pivots = lu_solve_test_helper(self, A_dims, b_dims, cast, pivot)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.lu_solve(b[i], LU_data[i], LU_pivots[i]))
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.lu_solve(b, LU_data, LU_pivots)  # Actual output
            self.assertEqual(x_exp, x_act)  # Equality check
            self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 1e-12)  # Correctness check

        for batchsize in [1, 3, 4]:
            lu_solve_batch_test_helper((5, batchsize), (batchsize, 5, 10), cast, pivot)

        # tensors with 0 elements
        b = cast(torch.randn(3, 0, 3))
        A = cast(torch.randn(3, 0, 0))
        LU_data, LU_pivots = torch.lu(A)
        self.assertEqual(torch.empty_like(b), b.lu_solve(LU_data, LU_pivots))

    @skipIfNoLapack
    def test_lu_solve_batched(self):
        self._test_lu_solve_batched(self, lambda t: t)

    @staticmethod
    def _test_lu_unpack(self, cast, pivot=True):
        def run_test(shape, cast):
            a = cast(torch.randn(*shape))
            a_lu, p = torch.lu(a, pivot=pivot)
            p_ref, l_ref, u_ref = torch.lu_unpack(a_lu, p)
            self.assertEqual(p_ref.matmul(l_ref.matmul(u_ref)), a)

        run_test((3, 3), cast)
        run_test((5, 3, 3), cast)
        run_test((7, 3, 5, 5), cast)
        run_test((7, 5, 3, 3, 3), cast)

    @skipIfNoLapack
    def test_lu_unpack(self):
        self._test_lu_unpack(self, lambda t: t)

    def test_bmm(self):
        num_batches = 10
        M, N, O = 23, 8, 12
        b1 = torch.randn(num_batches, M, N)
        b2 = torch.randn(num_batches, N, O)
        res = torch.bmm(b1, b2)
        for i in range(num_batches):
            r = torch.mm(b1[i], b2[i])
            self.assertEqual(r, res[i])
        if torch.cuda.is_available():
            # check that mixed arguments are rejected
            self.assertRaises(RuntimeError, lambda: torch.bmm(b1, b2.cuda()))
            self.assertRaises(RuntimeError, lambda: torch.bmm(b1.cuda(), b2))

    def test_addbmm(self):
        # num_batches = 10
        # M, N, O = 12, 8, 5
        num_batches = 2
        M, N, O = 2, 3, 4
        b1 = torch.randn(num_batches, M, N)
        b2 = torch.randn(num_batches, N, O)
        res = torch.bmm(b1, b2)
        res2 = torch.Tensor().resize_as_(res[0]).zero_()

        res2.addbmm_(b1, b2)
        self.assertEqual(res2, res.sum(0, False))

        res2.addbmm_(1, b1, b2)
        self.assertEqual(res2, res.sum(0, False) * 2)

        res2.addbmm_(1., .5, b1, b2)
        self.assertEqual(res2, res.sum(0, False) * 2.5)

        res3 = torch.addbmm(1, res2, 0, b1, b2)
        self.assertEqual(res3, res2)

        res4 = torch.addbmm(1, res2, .5, b1, b2)
        self.assertEqual(res4, res.sum(0, False) * 3)

        res5 = torch.addbmm(0, res2, 1, b1, b2)
        self.assertEqual(res5, res.sum(0, False))

        res6 = torch.addbmm(.1, res2, .5, b1, b2)
        self.assertEqual(res6, res2 * .1 + (res.sum(0) * .5))

    def test_baddbmm(self):
        num_batches = 10
        M, N, O = 12, 8, 5
        b1 = torch.randn(num_batches, M, N)
        b2 = torch.randn(num_batches, N, O)
        res = torch.bmm(b1, b2)
        res2 = torch.Tensor().resize_as_(res).zero_()

        res2.baddbmm_(b1, b2)
        self.assertEqual(res2, res)

        res2.baddbmm_(1, b1, b2)
        self.assertEqual(res2, res * 2)

        res2.baddbmm_(1, .5, b1, b2)
        self.assertEqual(res2, res * 2.5)

        res3 = torch.baddbmm(1, res2, 0, b1, b2)
        self.assertEqual(res3, res2)

        res4 = torch.baddbmm(1, res2, .5, b1, b2)
        self.assertEqual(res4, res * 3)

        res5 = torch.baddbmm(0, res2, 1, b1, b2)
        self.assertEqual(res5, res)

        res6 = torch.baddbmm(.1, res2, .5, b1, b2)
        self.assertEqual(res6, res2 * .1 + res * .5)

    def _test_cop(self, torchfn, mathfn):
        def reference_implementation(res2):
            for i, j in iter_indices(sm1):
                idx1d = i * sm1.size(0) + j
                res2[i, j] = mathfn(sm1[i, j], sm2[idx1d])
            return res2

        # contiguous
        m1 = torch.randn(10, 10, 10)
        m2 = torch.randn(10, 10 * 10)
        sm1 = m1[4]
        sm2 = m2[4]

        res1 = torchfn(sm1, sm2.view(10, 10))
        res2 = reference_implementation(res1.clone())
        self.assertEqual(res1, res2)

        # non-contiguous
        m1 = torch.randn(10, 10, 10)
        m2 = torch.randn(10 * 10, 10 * 10)
        sm1 = m1[:, 4]
        sm2 = m2[:, 4]
        # view as sm1.size()
        sm2.set_(sm2.storage(), sm2.storage_offset(), sm1.size(), (sm2.stride()[0] * 10, sm2.stride()[0]))
        res1 = torchfn(sm1, sm2)
        # reference_implementation assumes 1-d sm2
        sm2.set_(sm2.storage(), sm2.storage_offset(), m2[:, 4].size(), m2[:, 4].stride())
        res2 = reference_implementation(res1.clone())
        self.assertEqual(res1, res2)

    def test_cdiv(self):
        self._test_cop(torch.div, lambda x, y: x / y)

    def test_cfmod(self):
        self._test_cop(torch.fmod, math.fmod)

    def test_cremainder(self):
        self._test_cop(torch.remainder, lambda x, y: x % y)

    def test_cmul(self):
        self._test_cop(torch.mul, lambda x, y: x * y)

    def test_cpow(self):
        self._test_cop(torch.pow, lambda x, y: nan if x < 0 else math.pow(x, y))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_einsum(self):
        # test cases taken from https://gist.github.com/rockt/15ee013889d65342088e9260a377dc8f
        x = torch.randn(5)
        y = torch.randn(7)
        A = torch.randn(3, 5)
        B = torch.randn(2, 5)
        C = torch.randn(2, 3, 5)
        D = torch.randn(2, 5, 7)
        E = torch.randn(7, 9)
        F = torch.randn(2, 3, 5, 7)
        G = torch.randn(7, 11, 13)
        H = torch.randn(4, 4)
        I = torch.randn(3, 4, 4)
        l = torch.randn(5, 10)
        r = torch.randn(5, 20)
        w = torch.randn(30, 10, 20)
        test_list = [
            # -- Vector
            ("i->", x),                 # sum
            ("i,i->", x, x),            # dot
            ("i,i->i", x, x),           # vector element-wise mul
            ("i,j->ij", x, y),          # outer
            # -- Matrix
            ("ij->ji", A),              # transpose
            ("ij->j", A),               # row sum
            ("ij->i", A),               # col sum
            ("ij,ij->ij", A, A),        # matrix element-wise mul
            ("ij,j->i", A, x),          # matrix vector multiplication
            ("ij,kj->ik", A, B),        # matmul
            ("ij,ab->ijab", A, E),      # matrix outer product
            # -- Tensor
            ("aij,ajk->aik", C, D),     # batch matmul
            ("ijk,jk->i", C, A),        # tensor matrix contraction
            ("aij,jk->aik", D, E),      # tensor matrix contraction
            ("abcd,dfg->abcfg", F, G),  # tensor tensor contraction
            ("ijk,jk->ik", C, A),       # tensor matrix contraction with double indices
            ("ijk,jk->ij", C, A),       # tensor matrix contraction with double indices
            ("ijk,ik->j", C, B),        # non contiguous
            ("ijk,ik->jk", C, B),       # non contiguous with double indices
            # -- Diagonal
            ("ii", H),                 # trace
            ("ii->i", H),              # diagonal
            # -- Ellipsis
            ("i...->...", H),
            ("ki,...k->i...", A.t(), B),
            ("k...,jk", A.t(), B),
            ("...ii->...i", I),       # batch diagonal
            # -- Other
            ("bn,anm,bm->ba", l, w, r),  # as torch.bilinear
            ("... ii->...i  ", I),       # batch diagonal with spaces
        ]
        for test in test_list:
            actual = torch.einsum(test[0], test[1:])
            expected = np.einsum(test[0], *[t.numpy() for t in test[1:]])
            self.assertEqual(expected.shape, actual.shape, test[0])
            self.assertTrue(np.allclose(expected, actual.numpy()), test[0])
            # test vararg
            actual2 = torch.einsum(test[0], *test[1:])
            self.assertEqual(expected.shape, actual2.shape, test[0])
            self.assertTrue(np.allclose(expected, actual2.numpy()), test[0])

            def do_einsum(*args):
                return torch.einsum(test[0], args)
            # FIXME: following test cases fail gradcheck
            if test[0] not in {"i,i->", "i,i->i", "ij,ij->ij"}:
                gradcheck_inps = tuple(t.detach().requires_grad_() for t in test[1:])
                self.assertTrue(torch.autograd.gradcheck(do_einsum, gradcheck_inps))
            self.assertTrue(A._version == 0)  # check that we do not use inplace ops

    def test_sum_all(self):
        def check_sum_all(tensor):
            pylist = tensor.reshape(-1).tolist()
            self.assertEqual(tensor.sum(), sum(pylist))

        check_sum_all(torch.tensor([1, 2, 3, 4, 5]))
        check_sum_all(torch.randn(200000))
        check_sum_all(torch.randn(2000, 2)[:, 0])
        check_sum_all(torch.tensor([True, False, True], dtype=torch.bool))

    def _assert_matches_numpy(self, t, n):
        self.assertEqual(n.shape, t.shape)
        if t.dtype == torch.float:
            self.assertTrue(np.allclose(n, t.numpy(), rtol=1e-03, atol=1e-05,
                            equal_nan=True))
        else:
            self.assertTrue(np.allclose(n, t.numpy(), equal_nan=True))

    def _test_dim_ops(self, pytorch_op, numpy_op,
                      use_floating=True, use_integral=True):
        def do_one(tensors_dict, dim):
            for category, tensors in tensors_dict.items():
                if category == "slice":
                    dim = 0
                for tensor in tensors:
                    # we have no control over NumPy warnings...
                    with warnings.catch_warnings():
                        warnings.simplefilter("ignore")
                        expected = numpy_op(tensor.numpy(), dim)
                    actual = pytorch_op(tensor, dim)
                    self._assert_matches_numpy(actual, expected)
                    if torch.cuda.is_available():
                        self._assert_matches_numpy(pytorch_op(tensor.cuda(),
                                                              dim).cpu(),
                                                   expected)
        do_one(self._make_tensors((5, 400000), use_floating=use_floating,
               use_integral=use_integral), 1)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
               use_integral=use_integral), 0)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
               use_integral=use_integral), 1)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
               use_integral=use_integral), 2)
        do_one(self._make_tensors((100000, ), use_floating=use_floating,
               use_integral=use_integral), -1)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), 0)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), 1)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), 2)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), (1, 2))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), (1, -1))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), (0, 2))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
               use_integral=use_integral), (0, 2, 1))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_sum_dim(self):
        self._test_dim_ops(
            lambda t, d: t.sum(d),
            lambda n, d: n.sum(d))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_mean_dim(self):
        self._test_dim_ops(
            lambda t, d: t.mean(d),
            lambda n, d: n.mean(d),
            use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_std_dim(self):
        for unbiased in [False, True]:
            self._test_dim_ops(
                lambda t, d: t.std(d, unbiased=unbiased),
                lambda n, d: n.std(d, ddof=1 if unbiased else 0),
                use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_var_dim(self):
        for unbiased in [False, True]:
            self._test_dim_ops(
                lambda t, d: t.var(d, unbiased=unbiased),
                lambda n, d: n.var(d, ddof=1 if unbiased else 0),
                use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    @unittest.skipIf(not TEST_SCIPY, 'Scipy not found')
    def test_logsumexp_dim(self):
        from scipy.special import logsumexp
        self._test_dim_ops(
            lambda t, d: t.logsumexp(d),
            lambda n, d: logsumexp(n, d),
            use_integral=False)

    def test_sum_out(self):
        x = torch.rand(100, 100)
        res1 = torch.sum(x, 1)
        res2 = torch.Tensor()
        torch.sum(x, 1, out=res2)
        self.assertEqual(res1, res2)
        x = torch.rand(100, 100, 100)
        res1 = x.sum(2).sum(1)
        res2 = torch.Tensor()
        torch.sum(x, (2, 1), out=res2)
        self.assertEqual(res1, res2)

    # TODO: these tests only check if it's possible to pass a return value
    # it'd be good to expand them
    def test_prod(self):
        x = torch.rand(100, 100)
        res1 = torch.prod(x, 1)
        res2 = torch.Tensor()
        torch.prod(x, 1, out=res2)
        self.assertEqual(res1, res2)

    def _test_reduce_integer_upcast(self, fn, has_out=True):
        shape = (3, 4, 5)
        reduced_shape = fn(torch.ones(shape)).shape

        def _test_out(dtype, other_dtype):
            out = torch.ones(reduced_shape, dtype=dtype)
            result = fn(x, out=out)
            self.assertIs(out.dtype, result.dtype)
            self.assertEqual(fn(x.type(dtype)), result)
            result = fn(x, out=out, dtype=dtype)
            self.assertIs(out.dtype, result.dtype)
            self.assertEqual(fn(x.type(dtype)), result)
            # 'out' is favored over dtype, check error
            self.assertRaises(RuntimeError, lambda: fn(x, out=out, dtype=other_dtype))

        for dtype in [dtype for dtype in torch.testing.get_all_math_dtypes('cpu') if dtype != torch.float16]:
            x = torch.ones(shape, dtype=dtype)
            expected_dtype = dtype if dtype.is_floating_point else torch.int64
            self.assertIs(expected_dtype, fn(x).dtype)
            self.assertEqual(fn(x.type(expected_dtype)), fn(x))

            if dtype.is_floating_point:
                other_dtype = torch.float32 if dtype == torch.float64 else torch.float64
            else:
                other_dtype = torch.int32 if dtype != torch.int32 else torch.int16
            self.assertIs(other_dtype, fn(x, dtype=other_dtype).dtype)
            self.assertEqual(fn(x.type(other_dtype)), fn(x, dtype=other_dtype))

            # test mixed int/float
            mixed_dtype = torch.int32 if dtype.is_floating_point else torch.float32
            self.assertIs(mixed_dtype, fn(x, dtype=mixed_dtype).dtype)
            self.assertEqual(fn(x.type(mixed_dtype)), fn(x, dtype=mixed_dtype))

            if has_out:
                _test_out(dtype, other_dtype)
                _test_out(dtype, mixed_dtype)

    def test_sum_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.sum(x, **kwargs), False)
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.sum(x, 0, **kwargs))

    def test_prod_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.prod(x, **kwargs), False)
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.prod(x, 0, **kwargs))

    def test_cumsum_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.cumsum(x, 0, **kwargs))

    def test_cumprod_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.cumprod(x, 0, **kwargs))

    def test_cross(self):
        x = torch.rand(100, 3, 100)
        y = torch.rand(100, 3, 100)
        res1 = torch.cross(x, y)
        res2 = torch.Tensor()
        torch.cross(x, y, out=res2)
        self.assertEqual(res1, res2)

    def test_cross_with_and_without_dim(self):
        x = torch.rand(100, 3)
        y = torch.rand(100, 3)
        res1 = torch.cross(x, y, dim=1)
        res2 = torch.cross(x, y, dim=-1)
        res3 = torch.cross(x, y)
        self.assertEqual(res1, res2)
        self.assertEqual(res1, res3)

    def test_cross_validation(self):
        self.assertRaisesRegex(
            RuntimeError, "inconsistent tensors dimensions",
            lambda: torch.cross(torch.rand(100, 3), torch.rand(100, 3, 10)))
        self.assertRaisesRegex(
            RuntimeError, "inconsistent tensors sizes",
            lambda: torch.cross(torch.rand(5, 3), torch.rand(3, 5)))
        self.assertRaisesRegex(
            RuntimeError, "no dimension of size 3 in input",
            lambda: torch.cross(torch.rand(5, 4), torch.rand(5, 4)))
        self.assertRaisesRegex(
            RuntimeError, "dimension 0 does not have size 3",
            lambda: torch.cross(torch.rand(5, 4, 3), torch.rand(5, 4, 3), dim=0))
        self.assertRaisesRegex(
            RuntimeError, "dimension -1 does not have size 3",
            lambda: torch.cross(torch.rand(5, 3, 4), torch.rand(5, 3, 4), dim=-1))
        self.assertRaisesRegex(
            IndexError, "Dimension out of range",
            lambda: torch.cross(torch.rand(5, 3, 4), torch.rand(5, 3, 4), dim=-5))

    def test_zeros(self):
        res1 = torch.zeros(100, 100)
        res2 = torch.Tensor()
        torch.zeros(100, 100, out=res2)
        self.assertEqual(res1, res2)

        boolTensor = torch.zeros(2, 2, dtype=torch.bool)
        expected = torch.tensor([[False, False], [False, False]], dtype=torch.bool)
        self.assertEqual(boolTensor, expected)

        halfTensor = torch.zeros(1, 1, dtype=torch.half)
        expected = torch.tensor([[0.]], dtype=torch.float16)
        self.assertEqual(halfTensor, expected)

        bfloat16Tensor = torch.zeros(1, 1, dtype=torch.bfloat16)
        expected = torch.tensor([[0.]], dtype=torch.bfloat16)
        self.assertEqual(bfloat16Tensor, expected)

    def test_zeros_out(self):
        shape = (3, 4)
        out = torch.zeros(shape)
        torch.zeros(shape, out=out)

        # change the dtype, layout, device
        self.assertRaises(RuntimeError, lambda: torch.zeros(shape, dtype=torch.int64, out=out))
        self.assertRaises(RuntimeError, lambda: torch.zeros(shape, layout=torch.sparse_coo, out=out))
        if torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: torch.zeros(shape, device='cuda', out=out))

        # leave them the same
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, dtype=out.dtype, out=out))
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, layout=torch.strided, out=out))
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, device='cpu', out=out))

    def test_ones(self):
        res1 = torch.ones(100, 100)
        res2 = torch.Tensor()
        torch.ones(100, 100, out=res2)
        self.assertEqual(res1, res2)

        # test boolean tensor
        res1 = torch.ones(1, 2, dtype=torch.bool)
        expected = torch.tensor([[True, True]], dtype=torch.bool)
        self.assertEqual(res1, expected)

    def test_ones_like(self):
        expected = torch.ones(100, 100)

        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

        # test boolean tensor
        expected = torch.tensor([True, True], dtype=torch.bool)
        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

    def test_dtypes(self):
        all_dtypes = torch.testing.get_all_dtypes()
        do_test_dtypes(self, all_dtypes, torch.strided, torch.device('cpu'))
        if torch.cuda.is_available():
            all_dtypes.remove(torch.bfloat16)  # Remove once _th_zero_ is enabled on cuda for bfloat16
            do_test_dtypes(self, all_dtypes, torch.strided, torch.device('cuda:0'))

    def test_copy_dtypes(self):
        all_dtypes = torch.testing.get_all_dtypes()
        for dtype in all_dtypes:
            copied_dtype = copy.deepcopy(dtype)
            self.assertIs(dtype, copied_dtype)

    def test_copy_transpose(self):
        x = torch.arange(100 * 100, dtype=torch.float).reshape(100, 100).t()
        y = torch.empty(100, 100, dtype=torch.float)
        y.copy_(x)
        self.assertEqual(y[:, 0], range(100))
        self.assertEqual(y[:, 40], range(4000, 4100))

        y = torch.empty(100, 100, dtype=torch.double)
        y.copy_(x)
        self.assertEqual(y[:, 0], range(100))
        self.assertEqual(y[:, 40], range(4000, 4100))

    def test_device(self):
        cpu = torch.device('cpu')
        self.assertEqual('cpu', str(cpu))
        self.assertEqual('cpu', cpu.type)
        self.assertEqual(None, cpu.index)

        cpu0 = torch.device('cpu:0')
        self.assertEqual('cpu:0', str(cpu0))
        self.assertEqual('cpu', cpu0.type)
        self.assertEqual(0, cpu0.index)

        cpu0 = torch.device('cpu', 0)
        self.assertEqual('cpu:0', str(cpu0))
        self.assertEqual('cpu', cpu0.type)
        self.assertEqual(0, cpu0.index)

        cuda = torch.device('cuda')
        self.assertEqual('cuda', str(cuda))
        self.assertEqual('cuda', cuda.type)
        self.assertEqual(None, cuda.index)

        cuda1 = torch.device('cuda:1')
        self.assertEqual('cuda:1', str(cuda1))
        self.assertEqual('cuda', cuda1.type)
        self.assertEqual(1, cuda1.index)

        cuda1 = torch.device('cuda', 1)
        self.assertEqual('cuda:1', str(cuda1))
        self.assertEqual('cuda', cuda1.type)
        self.assertEqual(1, cuda1.index)

        self.assertRaises(RuntimeError, lambda: torch.device('cpu:-1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu:1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu', -1))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu', 1))
        self.assertRaises(RuntimeError, lambda: torch.device('cuda:-1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cuda', -1))
        self.assertRaises(RuntimeError, lambda: torch.device(-1))

        self.assertRaises(RuntimeError, lambda: torch.device('other'))
        self.assertRaises(RuntimeError, lambda: torch.device('other:0'))

        device_set = {'cpu', 'cpu:0', 'cuda', 'cuda:0', 'cuda:1', 'cuda:10', 'cuda:100'}
        device_hash_set = set()
        for device in list(device_set):
            device_hash_set.add(hash(torch.device(device)))
        self.assertEqual(len(device_set), len(device_hash_set))

    def test_tensor_device(self):
        def assertEqual(device_str, fn):
            self.assertEqual(torch.device(device_str), fn().device)
            self.assertEqual(device_str, str(fn().device))

        assertEqual('cpu', lambda: torch.tensor(5))
        assertEqual('cpu', lambda: torch.ones((2, 3), dtype=torch.float32, device='cpu'))
        # NOTE: 'cpu' is the canonical representation of 'cpu:0', but 'cuda:X' is the canonical
        # representation of cuda devices.
        assertEqual('cpu', lambda: torch.ones((2, 3), dtype=torch.float32, device='cpu:0'))
        assertEqual('cpu', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cpu:0'))
        if TEST_NUMPY:
            assertEqual('cpu', lambda: torch.tensor(np.random.randn(2, 3), device='cpu'))

        if torch.cuda.is_available():
            assertEqual('cuda:0', lambda: torch.tensor(5).cuda(0))
            assertEqual('cuda:0', lambda: torch.tensor(5).cuda('cuda:0'))
            self.assertRaises(RuntimeError, lambda: torch.tensor(5).cuda('cpu'))
            self.assertRaises(RuntimeError, lambda: torch.tensor(5).cuda('cpu:0'))
            assertEqual('cuda:0', lambda: torch.tensor(5, dtype=torch.int64, device=0))
            assertEqual('cuda:0', lambda: torch.tensor(5, dtype=torch.int64, device='cuda:0'))
            assertEqual('cuda:' + str(torch.cuda.current_device()),
                        lambda: torch.tensor(5, dtype=torch.int64, device='cuda'))
            assertEqual('cuda:0', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cuda:0'))
            if TEST_NUMPY:
                assertEqual('cuda:0', lambda: torch.tensor(np.random.randn(2, 3), device='cuda:0'))

            if torch.cuda.device_count() > 1:
                assertEqual('cuda:1', lambda: torch.tensor(5).cuda(1))
                assertEqual('cuda:1', lambda: torch.tensor(5).cuda('cuda:1'))
                assertEqual('cuda:1', lambda: torch.tensor(5, dtype=torch.int64, device=1))
                assertEqual('cuda:1', lambda: torch.tensor(5, dtype=torch.int64, device='cuda:1'))
                assertEqual('cuda:1', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cuda:1'))
                if TEST_NUMPY:
                    assertEqual('cuda:1', lambda: torch.tensor(np.random.randn(2, 3), device='cuda:1'))

    def test_to(self):
        def test_copy_behavior(t, non_blocking=False):
            self.assertIs(t, t.to(t, non_blocking=non_blocking))
            self.assertIs(t, t.to(t.dtype, non_blocking=non_blocking))
            self.assertIs(t, t.to(torch.empty_like(t), non_blocking=non_blocking))
            self.assertIsNot(t, t.to(t, non_blocking=non_blocking, copy=True))
            self.assertIsNot(t, t.to(t.dtype, non_blocking=non_blocking, copy=True))
            self.assertIsNot(t, t.to(torch.empty_like(t), non_blocking=non_blocking, copy=True))

            devices = [t.device]
            if t.device.type == 'cuda':
                if t.device.index == -1:
                    devices.append('cuda:{}'.format(torch.cuda.current_device()))
                elif t.device.index == torch.cuda.current_device():
                    devices.append('cuda')
            for device in devices:
                self.assertIs(t, t.to(device, non_blocking=non_blocking))
                self.assertIs(t, t.to(device, t.dtype, non_blocking=non_blocking))
                self.assertIsNot(t, t.to(device, non_blocking=non_blocking, copy=True))
                self.assertIsNot(t, t.to(device, t.dtype, non_blocking=non_blocking, copy=True))

        a = torch.tensor(5)
        test_copy_behavior(a)
        self.assertEqual(a.device, a.to('cpu').device)
        self.assertEqual(a.device, a.to('cpu', dtype=torch.float32).device)
        self.assertIs(torch.float32, a.to('cpu', dtype=torch.float32).dtype)
        self.assertEqual(a.device, a.to(torch.float32).device)
        self.assertIs(torch.float32, a.to(dtype=torch.float32).dtype)
        self.assertEqual(a.data_ptr(), a.to('cpu').data_ptr())
        self.assertEqual(a.data_ptr(), a.to(dtype=a.dtype, device=a.device, copy=False).data_ptr())
        self.assertEqual(a.data_ptr(), a.to('cpu', copy=False).data_ptr())
        self.assertNotEqual(a.data_ptr(), a.to('cpu', copy=True).data_ptr())

        if torch.cuda.is_available():
            for non_blocking in [True, False]:
                for cuda in ['cuda', 'cuda:0' if torch.cuda.device_count() == 1 else 'cuda:1']:
                    b = torch.tensor(5., device=cuda)
                    test_copy_behavior(b, non_blocking)
                    self.assertEqual(b.device, b.to(cuda, non_blocking=non_blocking).device)
                    self.assertEqual(a.device, b.to('cpu', non_blocking=non_blocking).device)
                    self.assertEqual(b.device, a.to(cuda, non_blocking=non_blocking).device)
                    self.assertIs(torch.int32, b.to('cpu', dtype=torch.int32, non_blocking=non_blocking).dtype)
                    self.assertEqual(a.device, b.to('cpu', dtype=torch.int32, non_blocking=non_blocking).device)
                    self.assertIs(torch.int32, b.to(dtype=torch.int32).dtype)
                    self.assertEqual(b.device, b.to(dtype=torch.int32).device)

    def test_to_with_tensor(self):
        a = torch.tensor(5)
        self.assertEqual(a.device, a.to(a).device)

        if torch.cuda.is_available():
            for non_blocking in [True, False]:
                for cuda in ['cuda', 'cuda:0' if torch.cuda.device_count() == 1 else 'cuda:1']:
                    b = torch.tensor(5., device=cuda)
                    self.assertEqual(b.device, b.to(b, non_blocking=non_blocking).device)
                    self.assertEqual(a.device, b.to(a, non_blocking=non_blocking).device)
                    self.assertEqual(b.device, a.to(b, non_blocking=non_blocking).device)

    def test_empty_full(self):
        do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, torch.device('cpu'))
        if torch.cuda.device_count() > 0:
            do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, None)
            do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, torch.device('cuda:0'))

    def test_dtype_out_match(self):
        d = torch.autograd.Variable(torch.DoubleTensor(2, 3))
        self.assertRaises(RuntimeError, lambda: torch.zeros((2, 3), out=d, dtype=torch.float32))

    def test_constructor_dtypes(self):
        default_type = torch.Tensor().type()
        self.assertIs(torch.Tensor().dtype, torch.get_default_dtype())

        self.assertIs(torch.uint8, torch.ByteTensor.dtype)
        self.assertIs(torch.float32, torch.FloatTensor.dtype)
        self.assertIs(torch.float64, torch.DoubleTensor.dtype)

        torch.set_default_tensor_type('torch.FloatTensor')
        self.assertIs(torch.float32, torch.get_default_dtype())
        self.assertIs(torch.FloatStorage, torch.Storage)

        torch.set_default_dtype(torch.float64)
        self.assertIs(torch.float64, torch.get_default_dtype())
        self.assertIs(torch.DoubleStorage, torch.Storage)

        torch.set_default_tensor_type(torch.FloatTensor)
        self.assertIs(torch.float32, torch.get_default_dtype())
        self.assertIs(torch.FloatStorage, torch.Storage)

        if torch.cuda.is_available():
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertIs(torch.float32, torch.get_default_dtype())
            self.assertIs(torch.float32, torch.cuda.FloatTensor.dtype)
            self.assertIs(torch.cuda.FloatStorage, torch.Storage)

            torch.set_default_dtype(torch.float64)
            self.assertIs(torch.float64, torch.get_default_dtype())
            self.assertIs(torch.cuda.DoubleStorage, torch.Storage)

        # don't support integral or sparse default types.
        self.assertRaises(TypeError, lambda: torch.set_default_tensor_type('torch.IntTensor'))
        self.assertRaises(TypeError, lambda: torch.set_default_dtype(torch.int64))

        # don't allow passing dtype to set_default_tensor_type
        self.assertRaises(TypeError, lambda: torch.set_default_tensor_type(torch.float32))

        torch.set_default_tensor_type(default_type)

    def test_constructor_device_legacy(self):
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor(device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor((2.0, 3.0), device='cuda'))

        self.assertRaises(RuntimeError, lambda: torch.Tensor(device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.Tensor(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.Tensor((2.0, 3.0), device='cuda'))

        x = torch.randn((3,), device='cpu')
        self.assertRaises(RuntimeError, lambda: x.new(device='cuda'))
        self.assertRaises(RuntimeError, lambda: x.new(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: x.new((2.0, 3.0), device='cuda'))

        if torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor(device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor((2.0, 3.0), device='cpu'))

            default_type = torch.Tensor().type()
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertRaises(RuntimeError, lambda: torch.Tensor(device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.Tensor(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.Tensor((2.0, 3.0), device='cpu'))
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            torch.set_default_tensor_type(default_type)

            x = torch.randn((3,), device='cuda')
            self.assertRaises(RuntimeError, lambda: x.new(device='cpu'))
            self.assertRaises(RuntimeError, lambda: x.new(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: x.new((2.0, 3.0), device='cpu'))

    def test_type(self):
        x = torch.randn(3, 3).double()
        self.assertEqual(x.type('torch.FloatTensor').dtype, torch.float32)
        self.assertEqual(x.type(torch.FloatTensor).dtype, torch.float32)
        self.assertEqual(x.int().type(torch.Tensor).dtype, torch.get_default_dtype())
        self.assertEqual(x.type(torch.int32).dtype, torch.int32)

    def test_tensor_factory(self):
        expected = torch.Tensor([1, 1])
        # test data
        res1 = torch.tensor([1, 1])
        self.assertEqual(res1, expected)

        res1 = torch.tensor([1, 1], dtype=torch.int)
        self.assertEqual(res1, expected)
        self.assertIs(torch.int, res1.dtype)

        # test copy
        res2 = torch.tensor(expected)
        self.assertEqual(res2, expected)
        res2[1] = 2
        self.assertEqual(expected, torch.ones_like(expected))

        res2 = torch.tensor(expected, dtype=torch.int)
        self.assertEqual(res1, expected)
        self.assertIs(torch.int, res1.dtype)

        # test copy with numpy
        if TEST_NUMPY:
            for dtype in [np.float64, np.int64, np.int8, np.uint8]:
                a = np.array([5.]).astype(dtype)
                res1 = torch.tensor(a)
                self.assertEqual(5., res1[0].item())
                a[0] = 7.
                self.assertEqual(5., res1[0].item())

        # test boolean tensor
        a = torch.tensor([True, True, False, True, True], dtype=torch.bool)
        b = torch.tensor([-1, -1.1, 0, 1, 1.1], dtype=torch.bool)
        self.assertEqual(a, b)

    def test_tensor_factory_copy_var(self):

        def check_copy(copy, is_leaf, requires_grad, data_ptr=None):
            if data_ptr is None:
                data_ptr = copy.data_ptr
            self.assertEqual(copy.data, source.data)
            self.assertTrue(copy.is_leaf == is_leaf)
            self.assertTrue(copy.requires_grad == requires_grad)
            self.assertTrue(copy.data_ptr == data_ptr)

        source = torch.randn(5, 5, dtype=torch.double, requires_grad=True)
        # test torch.tensor()
        check_copy(torch.tensor(source), True, False)
        check_copy(torch.tensor(source, requires_grad=False), True, False)
        check_copy(torch.tensor(source, requires_grad=True), True, True)

        # test tensor.new_tensor()
        copy = torch.randn(1)
        check_copy(copy.new_tensor(source), True, False)
        check_copy(copy.new_tensor(source, requires_grad=False), True, False)
        check_copy(copy.new_tensor(source, requires_grad=True), True, True)

        # test torch.as_tensor()
        check_copy(torch.as_tensor(source), source.is_leaf, source.requires_grad, source.data_ptr)  # not copy
        check_copy(torch.as_tensor(source, dtype=torch.float), False, True)  # copy and keep the graph

    def test_tensor_factory_type_inference(self):
        def test_inference(default_dtype):
            saved_dtype = torch.get_default_dtype()
            torch.set_default_dtype(default_dtype)
            self.assertIs(default_dtype, torch.tensor(()).dtype)
            self.assertIs(default_dtype, torch.tensor(5.).dtype)
            self.assertIs(torch.int64, torch.tensor(5).dtype)
            self.assertIs(torch.bool, torch.tensor(True).dtype)
            self.assertIs(torch.int32, torch.tensor(5, dtype=torch.int32).dtype)
            self.assertIs(default_dtype, torch.tensor(((7, 5), (9, 5.))).dtype)
            self.assertIs(default_dtype, torch.tensor(((5., 5), (3, 5))).dtype)
            self.assertIs(torch.int64, torch.tensor(((5, 3), (3, 5))).dtype)

            if TEST_NUMPY:
                self.assertIs(torch.float64, torch.tensor(np.array(())).dtype)
                self.assertIs(torch.float64, torch.tensor(np.array(5.)).dtype)
                if np.array(5).dtype == np.int64:  # np long, which can be 4 bytes (e.g. on windows)
                    self.assertIs(torch.int64, torch.tensor(np.array(5)).dtype)
                else:
                    self.assertIs(torch.int32, torch.tensor(np.array(5)).dtype)
                self.assertIs(torch.uint8, torch.tensor(np.array(3, dtype=np.uint8)).dtype)
                self.assertIs(default_dtype, torch.tensor(((7, np.array(5)), (np.array(9), 5.))).dtype)
                self.assertIs(torch.float64, torch.tensor(((7, 5), (9, np.array(5.)))).dtype)
                self.assertIs(torch.int64, torch.tensor(((5, np.array(3)), (np.array(3), 5))).dtype)
            torch.set_default_dtype(saved_dtype)

        test_inference(torch.float64)
        test_inference(torch.float32)

    def test_qengine(self):
        qengines = torch.backends.quantized.supported_engines
        original_qe = torch.backends.quantized.engine
        for qe in qengines:
            torch.backends.quantized.engine = qe
            assert torch.backends.quantized.engine == qe, 'qengine not set successfully'
        torch.backends.quantized.engine = original_qe

    def test_new_tensor(self):
        expected = torch.autograd.Variable(torch.ByteTensor([1, 1]))
        # test data
        res1 = expected.new_tensor([1, 1])
        self.assertEqual(res1, expected)
        res1 = expected.new_tensor([1, 1], dtype=torch.int)
        self.assertEqual(res1, expected)
        self.assertIs(torch.int, res1.dtype)

        # test copy
        res2 = expected.new_tensor(expected)
        self.assertEqual(res2, expected)
        res2[1] = 2
        self.assertEqual(expected, torch.ones_like(expected))
        res2 = expected.new_tensor(expected, dtype=torch.int)
        self.assertEqual(res2, expected)
        self.assertIs(torch.int, res2.dtype)

        # test copy with numpy
        if TEST_NUMPY:
            a = np.array([5.])
            res1 = torch.tensor(a)
            res1 = res1.new_tensor(a)
            self.assertEqual(5., res1[0].item())
            a[0] = 7.
            self.assertEqual(5., res1[0].item())

        if torch.cuda.device_count() >= 2:
            expected = expected.cuda(1)
            res1 = expected.new_tensor([1, 1])
            self.assertEqual(res1.get_device(), expected.get_device())
            res1 = expected.new_tensor([1, 1], dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res1.get_device(), expected.get_device())

            res2 = expected.new_tensor(expected)
            self.assertEqual(res2.get_device(), expected.get_device())
            res2 = expected.new_tensor(expected, dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res2.get_device(), expected.get_device())
            res2 = expected.new_tensor(expected, dtype=torch.int, device=0)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res2.get_device(), 0)

            res1 = expected.new_tensor(1)
            self.assertEqual(res1.get_device(), expected.get_device())
            res1 = expected.new_tensor(1, dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res1.get_device(), expected.get_device())

    def test_as_tensor(self):
        # from python data
        x = [[0, 1], [2, 3]]
        self.assertEqual(torch.tensor(x), torch.as_tensor(x))
        self.assertEqual(torch.tensor(x, dtype=torch.float32), torch.as_tensor(x, dtype=torch.float32))

        # python data with heterogeneous types
        z = [0, 'torch']
        with self.assertRaisesRegex(TypeError, "invalid data type"):
            torch.tensor(z)
            torch.as_tensor(z)

        # python data with self-referential lists
        z = [0]
        z += [z]
        with self.assertRaisesRegex(TypeError, "self-referential lists are incompatible"):
            torch.tensor(z)
            torch.as_tensor(z)

        z = [[1, 2], z]
        with self.assertRaisesRegex(TypeError, "self-referential lists are incompatible"):
            torch.tensor(z)
            torch.as_tensor(z)

        # from tensor (doesn't copy unless type is different)
        y = torch.tensor(x)
        self.assertIs(y, torch.as_tensor(y))
        self.assertIsNot(y, torch.as_tensor(y, dtype=torch.float32))
        if torch.cuda.is_available():
            self.assertIsNot(y, torch.as_tensor(y, device='cuda'))
            y_cuda = y.to('cuda')
            self.assertIs(y_cuda, torch.as_tensor(y_cuda))
            self.assertIs(y_cuda, torch.as_tensor(y_cuda, device='cuda'))

        if TEST_NUMPY:
            # doesn't copy
            for dtype in [np.float64, np.int64, np.int8, np.uint8]:
                n = np.random.rand(5, 6).astype(dtype)
                n_astensor = torch.as_tensor(n)
                self.assertEqual(torch.tensor(n), n_astensor)
                n_astensor[0][0] = 25.7
                self.assertEqual(torch.tensor(n), n_astensor)

            # changing dtype causes copy
            n = np.random.rand(5, 6).astype(np.float32)
            n_astensor = torch.as_tensor(n, dtype=torch.float64)
            self.assertEqual(torch.tensor(n, dtype=torch.float64), n_astensor)
            n_astensor[0][1] = 250.8
            self.assertNotEqual(torch.tensor(n, dtype=torch.float64), n_astensor)

            # changing device causes copy
            if torch.cuda.is_available():
                n = np.random.randn(5, 6)
                n_astensor = torch.as_tensor(n, device='cuda')
                self.assertEqual(torch.tensor(n, device='cuda'), n_astensor)
                n_astensor[0][2] = 250.9
                self.assertNotEqual(torch.tensor(n, device='cuda'), n_astensor)

    def test_diag(self):
        x = torch.rand(100, 100)
        res1 = torch.diag(x)
        res2 = torch.Tensor()
        torch.diag(x, out=res2)
        self.assertEqual(res1, res2)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_diagonal_multidim(self):
        x = torch.randn(10, 11, 12, 13)
        xn = x.numpy()
        for args in [(2, 2, 3),
                     (2,),
                     (-2, 1, 2),
                     (0, -2, -1)]:
            result = torch.diagonal(x, *args)
            expected = xn.diagonal(*args)
            self.assertEqual(expected.shape, result.shape)
            self.assertTrue(np.allclose(expected, result.numpy()))
        # test non-continguous
        xp = x.permute(1, 2, 3, 0)
        result = torch.diagonal(xp, 0, -2, -1)
        expected = xp.numpy().diagonal(0, -2, -1)
        self.assertEqual(expected.shape, result.shape)
        self.assertTrue(np.allclose(expected, result.numpy()))

    @staticmethod
    def _test_diag_embed(self, dtype, device):
        x = torch.arange(3 * 4, dtype=dtype, device=device).view(3, 4)
        result = torch.diag_embed(x)
        expected = torch.stack([torch.diag(r) for r in x], 0)
        self.assertEqual(result, expected)

        result = torch.diag_embed(x, offset=1, dim1=0, dim2=2)
        expected = torch.stack([torch.diag(r, 1) for r in x], 1)
        self.assertEqual(result, expected)

    def test_diag_embed(self):
        self._test_diag_embed(self, dtype=torch.float32, device='cpu')

    def test_renorm(self):
        m1 = torch.randn(10, 5)
        res1 = torch.Tensor()

        def renorm(matrix, value, dim, max_norm):
            m1 = matrix.transpose(dim, 0).contiguous()
            # collapse non-dim dimensions.
            m2 = m1.clone().resize_(m1.size(0), int(math.floor(m1.nelement() / m1.size(0))))
            norms = m2.norm(value, 1, True)
            # clip
            new_norms = norms.clone()
            new_norms[torch.gt(norms, max_norm)] = max_norm
            new_norms.div_(norms.add_(1e-7))
            # renormalize
            m1.mul_(new_norms.expand_as(m1))
            return m1.transpose(dim, 0)

        # note that the axis fed to torch.renorm is different (2~=1)
        maxnorm = m1.norm(2, 1).mean()
        m2 = renorm(m1, 2, 1, maxnorm)
        m1.renorm_(2, 1, maxnorm)
        self.assertEqual(m1, m2, 1e-5)
        self.assertEqual(m1.norm(2, 0), m2.norm(2, 0), 1e-5)

        m1 = torch.randn(3, 4, 5)
        m2 = m1.transpose(1, 2).contiguous().clone().resize_(15, 4)
        maxnorm = m2.norm(2, 0).mean()
        m2 = renorm(m2, 2, 1, maxnorm)
        m1.renorm_(2, 1, maxnorm)
        m3 = m1.transpose(1, 2).contiguous().clone().resize_(15, 4)
        self.assertEqual(m3, m2)
        self.assertEqual(m3.norm(2, 0), m2.norm(2, 0))

    @staticmethod
    def _test_multinomial(self, type):
        def make_prob_dist(shape, is_contiguous):
            if is_contiguous:
                return type(*shape).uniform_()
            elif len(shape) == 1:
                return type(*(shape + [5])).uniform_()[:, 2]
            else:
                # num dim = 2
                new_shape = [2, shape[1], 7, 1, shape[0], 1, 10]
                prob_dist = type(*new_shape).uniform_()
                prob_dist = prob_dist.transpose(1, 4)
                prob_dist = prob_dist[1, :, 5, 0, :, 0, 4]
                assert not prob_dist.is_contiguous()  # sanity check
                return prob_dist

        for is_contiguous in (True, False):
            # with replacement
            n_row = 3
            for n_col in range(4, 5 + 1):
                prob_dist = make_prob_dist([n_row, n_col], is_contiguous)
                # indices that shouldn't be sampled (<0 means none)
                zero_prob_indices = torch.LongTensor(n_row).random_(-2, n_col).tolist()
                for i, j in enumerate(zero_prob_indices):
                    if j >= 0:
                        prob_dist[i, j] = 0
                n_sample = n_col * 3
                sample_indices = torch.multinomial(prob_dist, n_sample, True)
                self.assertEqual(prob_dist.dim(), 2)
                self.assertEqual(sample_indices.size(1), n_sample)
                for i in range(n_row):
                    zero_prob_idx = zero_prob_indices[i]
                    if zero_prob_idx < 0:
                        continue
                    for j in range(n_sample):
                        self.assertNotEqual(sample_indices[i, j], zero_prob_idx,
                                            "sampled an index with zero probability")

            # without replacement
            n_row = 3
            for n_col in range(2, 10 + 1, 2):
                prob_dist = make_prob_dist([n_row, n_col], is_contiguous)
                # indices that shouldn't be sampled (<0 means none)
                zero_prob_indices = torch.LongTensor(n_row).random_(-1, n_col).tolist()
                for i, j in enumerate(zero_prob_indices):
                    if j >= 0:
                        prob_dist[i, j] = 0
                n_sample = max(1, n_col - 2)
                sample_indices = torch.multinomial(prob_dist, n_sample, False)
                self.assertEqual(prob_dist.dim(), 2)
                self.assertEqual(sample_indices.size(1), n_sample)
                for i in range(n_row):
                    row_samples = {}
                    zero_prob_idx = zero_prob_indices[i]
                    for j in range(n_sample):
                        sample_idx = sample_indices[i, j]
                        if zero_prob_idx >= 0:
                            self.assertNotEqual(sample_idx, zero_prob_idx,
                                                "sampled an index with zero probability")
                        self.assertNotIn(sample_idx, row_samples, "sampled an index twice")
                        row_samples[sample_idx] = True

            # vector
            n_col = 4
            prob_dist = make_prob_dist([n_col], is_contiguous).fill_(1)
            zero_prob_idx = 1  # index that shouldn't be sampled
            prob_dist[zero_prob_idx] = 0
            n_sample = 20
            sample_indices = torch.multinomial(prob_dist, n_sample, True)
            for sample_index in sample_indices:
                self.assertNotEqual(sample_index, zero_prob_idx, "sampled an index with zero probability")
            s_dim = sample_indices.dim()
            self.assertEqual(sample_indices.dim(), 1, "wrong number of dimensions")
            self.assertEqual(prob_dist.dim(), 1, "wrong number of prob_dist dimensions")
            self.assertEqual(sample_indices.size(0), n_sample, "wrong number of samples")

    def test_multinomial(self):
        self._test_multinomial(self, torch.FloatTensor)

    def _spawn_method(self, method, arg):
        try:
            mp.set_start_method('spawn')
        except RuntimeError:
            pass
        with mp.Pool(1) as pool:
            self.assertTrue(pool.map(method, [arg]))

    @staticmethod
    def _test_multinomial_invalid_probs(probs):
        try:
            # n_sample = 1 is a special case, test n_sample=2 which is more general
            torch.multinomial(probs.to('cpu'), 2)
            return False  # Should not be reached
        except RuntimeError as e:
            return 'invalid multinomial distribution' in str(e)

    @unittest.skipIf(NO_MULTIPROCESSING_SPAWN, "Disabled for environments that \
                     don't support multiprocessing with spawn start method")
    @unittest.skipIf(IS_WINDOWS, 'FIXME: CUDA OOM error on Windows')
    @unittest.skipIf(not PY3,
                     "spawn start method is not supported in Python 2, \
                     but we need it for for testing failure case for CPU RNG on Windows")
    def test_multinomial_invalid_probs(self):
        test_method = _TestTorchMixin._test_multinomial_invalid_probs
        self._spawn_method(test_method, torch.Tensor([1, -1, 1]))
        self._spawn_method(test_method, torch.Tensor([1, inf, 1]))
        self._spawn_method(test_method, torch.Tensor([1, -inf, 1]))
        self._spawn_method(test_method, torch.Tensor([1, 1, nan]))
        self._spawn_method(test_method, torch.Tensor([0, 1, 0]))

    @suppress_warnings
    def test_range(self):
        res1 = torch.range(0, 1)
        res2 = torch.Tensor()
        torch.range(0, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Check range for non-contiguous tensors.
        x = torch.zeros(2, 3)
        torch.range(0, 3, out=x.narrow(1, 1, 2))
        res2 = torch.Tensor(((0, 0, 1), (0, 2, 3)))
        self.assertEqual(x, res2, 1e-16)

        # Check negative
        res1 = torch.Tensor((1, 0))
        res2 = torch.Tensor()
        torch.range(1, 0, -1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Equal bounds
        res1 = torch.ones(1)
        res2 = torch.Tensor()
        torch.range(1, 1, -1, out=res2)
        self.assertEqual(res1, res2, 0)
        torch.range(1, 1, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # FloatTensor
        res1 = torch.range(0.6, 0.9, 0.1, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 4)
        res1 = torch.range(1, 10, 0.3, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 31)

        # DoubleTensor
        res1 = torch.range(0.6, 0.9, 0.1, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 4)
        res1 = torch.range(1, 10, 0.3, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 31)

    def test_range_warning(self):
        with warnings.catch_warnings(record=True) as w:
            torch.range(0, 10)
            self.assertEqual(len(w), 1)

    def test_arange(self):
        res1 = torch.arange(0, 1)
        res2 = torch.Tensor()
        torch.arange(0, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Check arange with only one argument
        res1 = torch.arange(10)
        res2 = torch.arange(0, 10)
        self.assertEqual(res1, res2, 0)

        # Check arange for non-contiguous tensors.
        x = torch.zeros(2, 3)
        torch.arange(0, 4, out=x.narrow(1, 1, 2))
        res2 = torch.Tensor(((0, 0, 1), (0, 2, 3)))
        self.assertEqual(x, res2, 1e-16)

        # Check negative
        res1 = torch.Tensor((1, 0))
        res2 = torch.Tensor()
        torch.arange(1, -1, -1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Equal bounds
        res1 = torch.ones(1)
        res2 = torch.Tensor()
        torch.arange(1, 0, -1, out=res2)
        self.assertEqual(res1, res2, 0)
        torch.arange(1, 2, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # FloatTensor
        res1 = torch.arange(0.6, 0.89, 0.1, out=torch.FloatTensor())
        self.assertEqual(res1, [0.6, 0.7, 0.8])
        res1 = torch.arange(1, 10, 0.3, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 30)
        self.assertEqual(res1[0], 1)
        self.assertEqual(res1[29], 9.7)

        # DoubleTensor
        res1 = torch.arange(0.6, 0.89, 0.1, out=torch.DoubleTensor())
        self.assertEqual(res1, [0.6, 0.7, 0.8])
        res1 = torch.arange(1, 10, 0.3, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 30)
        self.assertEqual(res1[0], 1)
        self.assertEqual(res1[29], 9.7)

        # Check that it's exclusive
        r = torch.arange(0, 5)
        self.assertEqual(r.min(), 0)
        self.assertEqual(r.max(), 4)
        self.assertEqual(r.numel(), 5)

        r = torch.arange(0, 5, 2)
        self.assertEqual(r.min(), 0)
        self.assertEqual(r.max(), 4)
        self.assertEqual(r.numel(), 3)

        r1 = torch.arange(0, 5 + 1e-6)
        r2 = torch.arange(0, 5)
        r3 = torch.arange(0, 5 - 1e-6)
        self.assertEqual(r1[:-1], r2, 0)
        self.assertEqual(r2, r3, 0)

        r1 = torch.arange(10, -1 + 1e-6, -1)
        r2 = torch.arange(10, -1, -1)
        r3 = torch.arange(10, -1 - 1e-6, -1)
        self.assertEqual(r1, r2, 0)
        self.assertEqual(r2, r3[:-1], 0)

        x = torch.empty(1).expand(10)
        self.assertRaises(RuntimeError, lambda: torch.arange(10, out=x))
        msg = "unsupported range"
        self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('inf')))
        self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('inf')))

        for device in torch.testing.get_all_device_types():
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(-5, float('nan'), device=device))
            # check with step size
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('-inf'), -1, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('inf'), device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('-inf'), 10, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('nan'), 10, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('inf'), device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('nan'), device=device))

            self.assertRaisesRegex(
                RuntimeError, "overflow",
                lambda: torch.arange(1.175494351e-38, 3.402823466e+38, device=device))

            # check that it holds a consistent output shape on precision-cornered step sizes
            d = torch.arange(-4.0, 4.0, 0.01, dtype=torch.float32, device=device)
            self.assertEqual(d.shape[0], 800)

    def test_arange_inference(self):
        saved_dtype = torch.get_default_dtype()
        torch.set_default_dtype(torch.float32)
        # end only
        self.assertIs(torch.float32, torch.arange(1.).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1.)).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1., dtype=torch.float64)).dtype)

        self.assertIs(torch.int64, torch.arange(1).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1)).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1, dtype=torch.int16)).dtype)

        # start, end, [step]
        self.assertIs(torch.float32, torch.arange(1., 3).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1., dtype=torch.float64), 3).dtype)
        self.assertIs(torch.float32, torch.arange(1, 3.).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1, dtype=torch.int16), torch.tensor(3.)).dtype)
        self.assertIs(torch.float32, torch.arange(1, 3, 1.).dtype)
        self.assertIs(torch.float32,
                      torch.arange(torch.tensor(1),
                                   torch.tensor(3, dtype=torch.int16),
                                   torch.tensor(1., dtype=torch.float64)).dtype)

        self.assertIs(torch.int64, torch.arange(1, 3).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1), 3).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1), torch.tensor(3, dtype=torch.int16)).dtype)
        self.assertIs(torch.int64, torch.arange(1, 3, 1).dtype)
        self.assertIs(torch.int64,
                      torch.arange(torch.tensor(1),
                                   torch.tensor(3),
                                   torch.tensor(1, dtype=torch.int16)).dtype)
        torch.set_default_dtype(saved_dtype)

    def test_randint_inference(self):
        size = (2, 1)
        for args in [(3,), (1, 3)]:  # (low,) and (low, high)
            self.assertIs(torch.int64, torch.randint(*args, size=size).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, layout=torch.strided).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, generator=torch.default_generator).dtype)
            self.assertIs(torch.float32, torch.randint(*args, size=size, dtype=torch.float32).dtype)
            out = torch.empty(size, dtype=torch.float32)
            self.assertIs(torch.float32, torch.randint(*args, size=size, out=out).dtype)
            self.assertIs(torch.float32, torch.randint(*args, size=size, out=out, dtype=torch.float32).dtype)
            out = torch.empty(size, dtype=torch.int64)
            self.assertIs(torch.int64, torch.randint(*args, size=size, out=out).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, out=out, dtype=torch.int64).dtype)

    def test_broadcast_empty(self):
        # empty + empty
        self.assertRaises(RuntimeError, lambda: torch.randn(5, 0) + torch.randn(0, 5))
        self.assertEqual(torch.randn(5, 0), torch.randn(0) + torch.randn(5, 0))
        self.assertEqual(torch.randn(5, 0, 0), torch.randn(0) + torch.randn(5, 0, 1))

        # scalar + empty
        self.assertEqual(torch.randn(5, 0, 6), torch.randn(()) + torch.randn(5, 0, 6))

        # non-empty, empty
        self.assertEqual(torch.randn(0), torch.randn(0) + torch.randn(1))
        self.assertEqual(torch.randn(0, 7, 0, 6, 5, 0, 7),
                         torch.randn(0, 7, 0, 6, 5, 0, 1) + torch.randn(1, 1, 5, 1, 7))
        self.assertRaises(RuntimeError, lambda: torch.randn(7, 0) + torch.randn(2, 1))

    def test_broadcast_tensors(self):
        x0 = torch.randn(2, 1, 3)
        x1 = torch.randn(3)
        x2 = torch.randn(3, 1)
        expected_size = (2, 3, 3)

        y0, y1, y2 = torch.broadcast_tensors(x0, x1, x2)
        self.assertTrue(y0.size() == expected_size)
        self.assertTrue(y1.size() == expected_size)
        self.assertTrue(y2.size() == expected_size)

    def test_scalars_as_floats(self):
        "zero-dim variables that don't require grad should bind to scalar arguments"
        x = torch.tensor(2.)
        y = torch.tensor(3.)
        # 3 + (3 * 3) * 2
        self.assertEqual(y.addcmul(y, y, value=x), 21)

        x = torch.tensor(2., requires_grad=True)
        self.assertRaises(Exception, lambda: y.addcmul(y, y, value=x))

    def test_copy_broadcast(self):
        torch.zeros(5, 6).copy_(torch.zeros(6))
        self.assertRaises(RuntimeError, lambda: torch.zeros(5, 6).copy_(torch.zeros(30)))

    def test_copy_many_to_one(self):
        # Testing in-place copy where it attempt to write from many memory
        # storage to a single storage would cause RuntimeError to be thrown
        self.assertRaises(RuntimeError, lambda: torch.zeros(1, 6).expand(5, 6).copy_(torch.zeros(5, 6)))

    def test_random(self):
        # This test is flaky with p<=(2/(ub-lb))^200=6e-36
        t = torch.FloatTensor(200)
        lb = 1
        ub = 4

        t.fill_(-1)
        t.random_(lb, ub)
        self.assertEqual(t.min(), lb)
        self.assertEqual(t.max(), ub - 1)

        t.fill_(-1)
        t.random_(ub)
        self.assertEqual(t.min(), 0)
        self.assertEqual(t.max(), ub - 1)

    def test_not_equal(self):
        ones = torch.ones(10, dtype=torch.int)
        self.assertRaisesRegex(AssertionError, "0 not greater than or equal to",
                               lambda: self.assertNotEqual(ones, ones))

    def assertIsOrdered(self, order, x, mxx, ixx, task):
        SIZE = 4
        if order == 'descending':
            def check_order(a, b):
                # `a != a` because we put NaNs
                # at the end of ascending sorted lists,
                # and the beginning of descending ones.
                return a != a or a >= b
        elif order == 'ascending':
            def check_order(a, b):
                # see above
                return b != b or a <= b
        else:
            error('unknown order "{}", must be "ascending" or "descending"'.format(order))

        are_ordered = True
        for j, k in product(range(SIZE), range(1, SIZE)):
            self.assertTrue(check_order(mxx[j][k - 1], mxx[j][k]),
                            'torch.sort ({}) values unordered for {}'.format(order, task))

        seen = set()
        indicesCorrect = True
        size = x.size(x.dim() - 1)
        for k in range(size):
            seen.clear()
            for j in range(size):
                self.assertEqual(x[k][ixx[k][j]], mxx[k][j],
                                 'torch.sort ({}) indices wrong for {}'.format(order, task))
                seen.add(ixx[k][j])
            self.assertEqual(len(seen), size)

    def test_sort(self):
        SIZE = 4
        x = torch.rand(SIZE, SIZE)
        res1val, res1ind = torch.sort(x)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.sort(x, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)
        self.assertEqual(torch.argsort(x), res1ind)
        self.assertEqual(x.argsort(), res1ind)

        # Test sorting of random numbers
        self.assertIsOrdered('ascending', x, res2val, res2ind, 'random')

        # Test simple sort
        self.assertEqual(
            torch.sort(torch.Tensor((50, 40, 30, 20, 10)))[0],
            torch.Tensor((10, 20, 30, 40, 50)),
            0
        )

        # Test that we still have proper sorting with duplicate keys
        x = torch.floor(torch.rand(SIZE, SIZE) * 10)
        torch.sort(x, out=(res2val, res2ind))
        self.assertIsOrdered('ascending', x, res2val, res2ind, 'random with duplicate keys')

        # DESCENDING SORT
        x = torch.rand(SIZE, SIZE)
        res1val, res1ind = torch.sort(x, x.dim() - 1, True)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.sort(x, x.dim() - 1, True, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)
        self.assertEqual(torch.argsort(x, x.dim() - 1, True), res1ind)
        self.assertEqual(x.argsort(x.dim() - 1, True), res1ind)

        # Test sorting of random numbers
        self.assertIsOrdered('descending', x, res2val, res2ind, 'random')

        # Test simple sort task
        self.assertEqual(
            torch.sort(torch.Tensor((10, 20, 30, 40, 50)), 0, True)[0],
            torch.Tensor((50, 40, 30, 20, 10)),
            0
        )

        # Test that we still have proper sorting with duplicate keys
        self.assertIsOrdered('descending', x, res2val, res2ind, 'random with duplicate keys')

        # Test sorting with NaNs
        x = torch.rand(SIZE, SIZE)
        x[1][2] = float('NaN')
        x[3][0] = float('NaN')
        torch.sort(x, out=(res2val, res2ind))
        self.assertIsOrdered('ascending', x, res2val, res2ind,
                             'random with NaNs')
        torch.sort(x, out=(res2val, res2ind), descending=True)
        self.assertIsOrdered('descending', x, res2val, res2ind,
                             'random with NaNs')

    def test_topk(self):
        def topKViaSort(t, k, dim, dir):
            sorted, indices = t.sort(dim, dir)
            return sorted.narrow(dim, 0, k), indices.narrow(dim, 0, k)

        def compareTensors(t, res1, ind1, res2, ind2, dim):
            # Values should be exactly equivalent
            self.assertEqual(res1, res2, 0)

            # Indices might differ based on the implementation, since there is
            # no guarantee of the relative order of selection
            if not ind1.eq(ind2).all():
                # To verify that the indices represent equivalent elements,
                # gather from the input using the topk indices and compare against
                # the sort indices
                vals = t.gather(dim, ind2)
                self.assertEqual(res1, vals, 0)

        def compare(t, k, dim, dir):
            topKVal, topKInd = t.topk(k, dim, dir, True)
            sortKVal, sortKInd = topKViaSort(t, k, dim, dir)
            compareTensors(t, sortKVal, sortKInd, topKVal, topKInd, dim)

        t = torch.rand(random.randint(1, SIZE),
                       random.randint(1, SIZE),
                       random.randint(1, SIZE))

        for _kTries in range(3):
            for _dimTries in range(3):
                for transpose in (True, False):
                    for dir in (True, False):
                        testTensor = t
                        if transpose:
                            dim1 = random.randrange(t.ndimension())
                            dim2 = dim1
                            while dim1 == dim2:
                                dim2 = random.randrange(t.ndimension())

                            testTensor = t.transpose(dim1, dim2)

                        dim = random.randrange(testTensor.ndimension())
                        k = random.randint(1, testTensor.size(dim))
                        compare(testTensor, k, dim, dir)

    def test_topk_arguments(self):
        q = torch.randn(10, 2, 10)
        # Make sure True isn't mistakenly taken as the 2nd dimension (interpreted as 1)
        self.assertRaises(TypeError, lambda: q.topk(4, True))

    def test_median(self):
        for size in (155, 156):
            x = torch.rand(size, size)
            x0 = x.clone()

            nelem = x.nelement()
            res1val = torch.median(x)
            res2val, _ = torch.sort(x.view(nelem))
            ind = int(math.floor((nelem + 1) / 2) - 1)

            self.assertEqual(res2val[ind], res1val, 0)

            res1val, res1ind = torch.median(x, dim=1, keepdim=False)
            res2val, res2ind = torch.sort(x)
            ind = int(math.floor((size + 1) / 2) - 1)

            self.assertEqual(res2val.select(1, ind), res1val, 0)
            self.assertEqual(res2val.select(1, ind), res1val, 0)

            # Test use of result tensor
            res2val = torch.Tensor()
            res2ind = torch.LongTensor()
            torch.median(x, dim=-1, keepdim=False, out=(res2val, res2ind))
            self.assertEqual(res2val, res1val, 0)
            self.assertEqual(res2ind, res1ind, 0)

            # Test non-default dim
            res1val, res1ind = torch.median(x, 0, keepdim=False)
            res2val, res2ind = torch.sort(x, 0)
            self.assertEqual(res1val, res2val[ind], 0)
            self.assertEqual(res1ind, res2ind[ind], 0)

            # input unchanged
            self.assertEqual(x, x0, 0)

    def test_mode(self):
        x = torch.arange(1., SIZE * SIZE + 1).clone().resize_(SIZE, SIZE)
        x[:2] = 1
        x[:, :2] = 1
        x0 = x.clone()

        # Pre-calculated results.
        res1val = torch.Tensor(SIZE).fill_(1)
        # The indices are the position of the last appearance of the mode element.
        res1ind = torch.LongTensor(SIZE).fill_(1)
        res1ind[0] = SIZE - 1
        res1ind[1] = SIZE - 1

        res2val, res2ind = torch.mode(x, keepdim=False)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.mode(x, keepdim=False, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # Test non-default dim
        res2val, res2ind = torch.mode(x, 0, False)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # input unchanged
        self.assertEqual(x, x0, 0)

    def test_trilu_indices(self):
        for test_args in tri_tests_args:
            _compare_trilu_indices(self, *test_args)
        run_additional_tri_tests(self, 'cpu')

        # test default options
        x = torch.ones(
            3, 3, dtype=torch.long, device='cpu', layout=torch.strided)
        self.assertEqual(
            x.tril(0).nonzero().transpose(0, 1), torch.tril_indices(3, 3))
        self.assertEqual(
            x.triu(0).nonzero().transpose(0, 1), torch.triu_indices(3, 3))

        # test stride 0 cases
        x = torch.ones(
            3, 1, 3, 3, dtype=torch.long, device='cpu', layout=torch.strided)
        output = x.triu(2).expand(3, 3, 3, 3)
        b = x.clone().expand(3, 3, 3, 3)
        self.assertEqual(b.triu(2), output)
        self.assertRaises(RuntimeError, lambda: b.triu_(2))

    def test_cat(self):
        SIZE = 10
        for dtype in (torch.half, torch.double, torch.int):
            for dim in range(-3, 3):
                pos_dim = dim if dim >= 0 else 3 + dim
                x = torch.randint(low=-100, high=100, size=(13, SIZE, SIZE)).to(dtype).transpose(0, pos_dim)
                y = torch.randint(low=-100, high=100, size=(17, SIZE, SIZE)).to(dtype).transpose(0, pos_dim)
                z = torch.randint(low=-100, high=100, size=(19, SIZE, SIZE)).to(dtype).transpose(0, pos_dim)

                res1 = torch.cat((x, y, z), dim)
                self.assertEqual(res1.narrow(pos_dim, 0, 13), x, 0)
                self.assertEqual(res1.narrow(pos_dim, 13, 17), y, 0)
                self.assertEqual(res1.narrow(pos_dim, 30, 19), z, 0)

            x = torch.randint(low=-100, high=100, size=(20, SIZE, SIZE)).to(dtype)
            self.assertEqual(torch.cat(torch.split(x, 7)), x)
            self.assertEqual(torch.cat(torch.chunk(x, 7)), x)

            y = torch.randint(low=-100, high=100, size=(1, SIZE, SIZE)).to(dtype)
            z = torch.cat([x, y])
            self.assertEqual(z.size(), (21, SIZE, SIZE))

            self.assertRaises(RuntimeError, lambda: torch.cat([]))
            self.assertRaisesRegex(TypeError, 'got None', lambda: torch.cat([x, None]))

    def test_cat_bad_input_sizes(self):
        x = torch.randn(2, 1)
        y = torch.randn(2, 1, 1)
        z = torch.randn(2, 1, 1)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, y, z]))

        x = torch.randn(2, 1, 2)
        y = torch.randn(2, 1, 1)
        z = torch.randn(2, 2, 1)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, y, z], dim=1))

    def test_cat_scalars(self):
        x = torch.tensor(0)
        y = torch.tensor(1)
        with self.assertRaisesRegex(RuntimeError, 'zero-dimensional.*cannot be concatenated'):
            torch.cat([x, y])

    @slowTest
    def test_cat_big(self):
        SIZE1 = 6500
        SIZE2 = 4500
        concat_list = []
        concat_list.append(torch.ones((SIZE1, 1024 * 512), dtype=torch.uint8))
        concat_list.append(torch.ones((SIZE2, 1024 * 512), dtype=torch.uint8))
        result = torch.cat(concat_list)
        self.assertEqual(result.size(0), SIZE1 + SIZE2)

    def test_narrow(self):
        x = torch.Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
        self.assertEqual(x.narrow(0, 0, 1), torch.Tensor([[0, 1, 2]]))
        self.assertEqual(x.narrow(0, 0, 2), torch.Tensor([[0, 1, 2], [3, 4, 5]]))
        self.assertEqual(x.narrow(0, 1, 1), torch.Tensor([[3, 4, 5]]))
        self.assertEqual(x.narrow(0, -1, 1), torch.Tensor([[6, 7, 8]]))
        self.assertEqual(x.narrow(0, -2, 2), torch.Tensor([[3, 4, 5], [6, 7, 8]]))
        self.assertEqual(x.narrow(0, -3, 3), torch.Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]]))
        self.assertEqual(x.narrow(-1, -1, 1), torch.Tensor([[2], [5], [8]]))
        self.assertEqual(x.narrow(-2, -1, 1), torch.Tensor([[6, 7, 8]]))

    def test_stack(self):
        for dtype in (torch.half, torch.double, torch.int):
            x = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            y = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            z = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            for dim in range(4):
                res = torch.stack((x, y, z), dim)
                res_neg = torch.stack((x, y, z), dim - 4)
                expected_size = x.size()[:dim] + (3,) + x.size()[dim:]
                self.assertEqual(res, res_neg)
                self.assertEqual(res.size(), expected_size)
                self.assertEqual(res.select(dim, 0), x, 0)
                self.assertEqual(res.select(dim, 1), y, 0)
                self.assertEqual(res.select(dim, 2), z, 0)

    def test_stack_out(self):
        for dtype in (torch.half, torch.double, torch.int):
            x = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            y = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            z = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            for dim in range(4):
                expected_size = x.size()[:dim] + (3,) + x.size()[dim:]
                res_out = x.new(expected_size)
                res_neg_out = x.new(expected_size)
                res_out_dp = res_out.data_ptr()
                res_out_neg_dp = res_neg_out.data_ptr()
                torch.stack((x, y, z), dim, out=res_out)
                torch.stack((x, y, z), dim - 4, out=res_neg_out)
                self.assertEqual(res_out, res_neg_out)
                self.assertEqual(res_out.size(), expected_size)
                self.assertEqual(res_out_dp, res_out.data_ptr())
                self.assertEqual(res_out_neg_dp, res_neg_out.data_ptr())
                self.assertEqual(res_out.select(dim, 0), x, 0)
                self.assertEqual(res_out.select(dim, 1), y, 0)
                self.assertEqual(res_out.select(dim, 2), z, 0)

    def test_unbind(self):
        x = torch.rand(2, 3, 4, 5)
        for dim in range(4):
            res = torch.unbind(x, dim)
            res2 = x.unbind(dim)
            self.assertEqual(x.size(dim), len(res))
            self.assertEqual(x.size(dim), len(res2))
            for i in range(dim):
                self.assertEqual(x.select(dim, i), res[i])
                self.assertEqual(x.select(dim, i), res2[i])

    def test_logspace(self):
        _from = random.random()
        to = _from + random.random()
        res1 = torch.logspace(_from, to, 137)
        res2 = torch.Tensor()
        torch.logspace(_from, to, 137, out=res2)
        self.assertEqual(res1, res2, 0)
        self.assertRaises(RuntimeError, lambda: torch.logspace(0, 1, -1))
        self.assertEqual(torch.logspace(0, 1, 1), torch.ones(1), 0)

        # Check non-default base=2
        self.assertEqual(torch.logspace(1, 1, 1, 2), torch.ones(1) * 2)
        self.assertEqual(torch.logspace(0, 2, 3, 2), torch.Tensor((1, 2, 4)))

        # Check logspace_ for generating with start > end.
        self.assertEqual(torch.logspace(1, 0, 2), torch.Tensor((10, 1)), 0)

        # Check logspace_ for non-contiguous tensors.
        x = torch.zeros(2, 3)
        y = torch.logspace(0, 3, 4, out=x.narrow(1, 1, 2))
        self.assertEqual(x, torch.Tensor(((0, 1, 10), (0, 100, 1000))), 0)

    def test_rand(self):
        torch.manual_seed(123456)
        res1 = torch.rand(SIZE, SIZE)
        res2 = torch.Tensor()
        torch.manual_seed(123456)
        torch.rand(SIZE, SIZE, out=res2)
        self.assertEqual(res1, res2)

    def test_randint(self):
        torch.manual_seed(123456)
        res1 = torch.randint(0, 6, (SIZE, SIZE))
        res2 = torch.Tensor()
        torch.manual_seed(123456)
        torch.randint(0, 6, (SIZE, SIZE), out=res2)
        torch.manual_seed(123456)
        res3 = torch.randint(6, (SIZE, SIZE))
        res4 = torch.Tensor()
        torch.manual_seed(123456)
        torch.randint(6, (SIZE, SIZE), out=res4)
        self.assertEqual(res1, res2)
        self.assertEqual(res1, res3)
        self.assertEqual(res1, res4)
        self.assertEqual(res2, res3)
        self.assertEqual(res2, res4)
        self.assertEqual(res3, res4)
        res1 = res1.view(-1)
        high = (res1 < 6).type(torch.LongTensor)
        low = (res1 >= 0).type(torch.LongTensor)
        tensorSize = res1.size()[0]
        assert(tensorSize == high.sum())
        assert(tensorSize == low.sum())

    def test_randn(self):
        torch.manual_seed(123456)
        res1 = torch.randn(SIZE, SIZE)
        res2 = torch.Tensor()
        torch.manual_seed(123456)
        torch.randn(SIZE, SIZE, out=res2)
        self.assertEqual(res1, res2)

    def test_slice(self):
        empty = torch.empty(0, 4)
        x = torch.arange(0., 16).view(4, 4)
        self.assertEqual(x[:], x)
        self.assertEqual(x[:4], x)
        # start and stop are clamped to the size of dim
        self.assertEqual(x[:5], x)
        # if start >= stop then the result is empty
        self.assertEqual(x[2:1], empty)
        self.assertEqual(x[2:2], empty)
        # out of bounds is also empty
        self.assertEqual(x[10:12], empty)
        # additional correctness checks
        self.assertEqual(x[:1].data.tolist(), [[0, 1, 2, 3]])
        self.assertEqual(x[:-3].data.tolist(), [[0, 1, 2, 3]])
        self.assertEqual(x[:, -2:3].data.tolist(), [[2], [6], [10], [14]])
        self.assertEqual(x[0:-1:2].data.tolist(), [[0, 1, 2, 3], [8, 9, 10, 11]])

    @skipIfNoLapack
    def test_ormqr(self):
        mat1 = torch.randn(7, 7)
        mat2 = torch.randn(7, 7)
        q, r = torch.qr(mat1)
        m, tau = torch.geqrf(mat1)
        out_holder = torch.empty_like(mat1)

        res1 = torch.mm(q, mat2)
        res2 = torch.ormqr(m, tau, mat2, left=True, transpose=False)
        torch.ormqr(m, tau, mat2, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(mat2, q)
        res2 = torch.ormqr(m, tau, mat2, left=False, transpose=False)
        torch.ormqr(m, tau, mat2, left=False, transpose=False, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(q.t(), mat2)
        res2 = torch.ormqr(m, tau, mat2, left=True, transpose=True)
        torch.ormqr(m, tau, mat2, left=True, transpose=True, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(mat2, q.t())
        res2 = torch.ormqr(m, tau, mat2, left=False, transpose=True)
        torch.ormqr(m, tau, mat2, left=False, transpose=True, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

    @staticmethod
    def _test_triangular_solve_batched(self, cast):
        from common_utils import triangular_solve_test_helper

        def triangular_solve_batch_helper(A_dims, b_dims, cast, upper, unitriangular, transpose):
            b, A = triangular_solve_test_helper(A_dims, b_dims, cast, upper, unitriangular)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.triangular_solve(b[i], A[i], upper=upper,
                                                         unitriangular=unitriangular, transpose=transpose)[0])
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.triangular_solve(b, A, upper=upper,
                                           unitriangular=unitriangular, transpose=transpose)[0]  # Actual output
            self.assertEqual(x_act, x_exp)  # Equality check
            if transpose:
                self.assertLessEqual(b.dist(torch.matmul(A.transpose(-2, -1), x_act)), 3e-12)  # Correctness check
            else:
                self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 3e-12)  # Correctness check

        for (upper, unitriangular, transpose), batchsize in product(product([True, False], repeat=3), [1, 3, 4]):
            triangular_solve_batch_helper((batchsize, 5, 5), (batchsize, 5, 10), cast,
                                          upper, unitriangular, transpose)

    @skipIfNoLapack
    def test_triangular_solve_batched(self):
        self._test_triangular_solve_batched(self, lambda t: t)

    @skipIfNoLapack
    def test_eig(self):
        a = torch.Tensor(((1.96, 0.00, 0.00, 0.00, 0.00),
                          (-6.49, 3.80, 0.00, 0.00, 0.00),
                          (-0.47, -6.39, 4.17, 0.00, 0.00),
                          (-7.20, 1.50, -1.51, 5.70, 0.00),
                          (-0.65, -6.34, 2.67, 1.80, -7.10))).t().contiguous()
        e = torch.eig(a)[0]
        ee, vv = torch.eig(a, True)
        te = torch.Tensor()
        tv = torch.Tensor()
        eee, vvv = torch.eig(a, True, out=(te, tv))
        self.assertEqual(e, ee, 1e-12)
        self.assertEqual(ee, eee, 1e-12)
        self.assertEqual(ee, te, 1e-12)
        self.assertEqual(vv, vvv, 1e-12)
        self.assertEqual(vv, tv, 1e-12)

        # test reuse
        X = torch.randn(4, 4)
        X = torch.mm(X.t(), X)
        e, v = torch.zeros(4, 2), torch.zeros(4, 4)
        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(torch.mm(v, torch.diag(e.select(1, 0))), v.t())
        self.assertEqual(X, Xhat, 1e-8, 'VeV\' wrong')
        self.assertFalse(v.is_contiguous(), 'V is contiguous')

        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(v, torch.mm(e.select(1, 0).diag(), v.t()))
        self.assertEqual(X, Xhat, 1e-8, 'VeV\' wrong')
        self.assertFalse(v.is_contiguous(), 'V is contiguous')

        # test non-contiguous
        X = torch.randn(4, 4)
        X = torch.mm(X.t(), X)
        e = torch.zeros(4, 2, 2)[:, 1]
        v = torch.zeros(4, 2, 4)[:, 1]
        self.assertFalse(v.is_contiguous(), 'V is contiguous')
        self.assertFalse(e.is_contiguous(), 'E is contiguous')
        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(torch.mm(v, torch.diag(e.select(1, 0))), v.t())
        self.assertEqual(X, Xhat, 1e-8, 'VeV\' wrong')

    @staticmethod
    def _test_fft_ifft_rfft_irfft(self, device='cpu'):
        def _test_complex(sizes, signal_ndim, prepro_fn=lambda x: x):
            x = prepro_fn(torch.randn(*sizes, device=device))
            for normalized in (True, False):
                res = x.fft(signal_ndim, normalized=normalized)
                rec = res.ifft(signal_ndim, normalized=normalized)
                self.assertEqual(x, rec, 1e-8, 'fft and ifft')
                res = x.ifft(signal_ndim, normalized=normalized)
                rec = res.fft(signal_ndim, normalized=normalized)
                self.assertEqual(x, rec, 1e-8, 'ifft and fft')

        def _test_real(sizes, signal_ndim, prepro_fn=lambda x: x):
            x = prepro_fn(torch.randn(*sizes, device=device))
            signal_numel = 1
            signal_sizes = x.size()[-signal_ndim:]
            for normalized, onesided in product((True, False), repeat=2):
                res = x.rfft(signal_ndim, normalized=normalized, onesided=onesided)
                if not onesided:  # check Hermitian symmetry
                    def test_one_sample(res, test_num=10):
                        idxs_per_dim = [torch.LongTensor(test_num).random_(s).tolist() for s in signal_sizes]
                        for idx in zip(*idxs_per_dim):
                            reflected_idx = tuple((s - i) % s for i, s in zip(idx, res.size()))
                            idx_val = res.__getitem__(idx)
                            reflected_val = res.__getitem__(reflected_idx)
                            self.assertEqual(idx_val[0], reflected_val[0], 'rfft hermitian symmetry on real part')
                            self.assertEqual(idx_val[1], -reflected_val[1], 'rfft hermitian symmetry on imaginary part')
                    if len(sizes) == signal_ndim:
                        test_one_sample(res)
                    else:
                        output_non_batch_shape = res.size()[-(signal_ndim + 1):]
                        flatten_batch_res = res.view(-1, *output_non_batch_shape)
                        nb = flatten_batch_res.size(0)
                        test_idxs = torch.LongTensor(min(nb, 4)).random_(nb)
                        for test_idx in test_idxs.tolist():
                            test_one_sample(flatten_batch_res[test_idx])
                    # compare with C2C
                    xc = torch.stack([x, torch.zeros_like(x)], -1)
                    xc_res = xc.fft(signal_ndim, normalized=normalized)
                    self.assertEqual(res, xc_res)
                test_input_signal_sizes = [signal_sizes]
                rec = res.irfft(signal_ndim, normalized=normalized,
                                onesided=onesided, signal_sizes=signal_sizes)
                self.assertEqual(x, rec, 1e-8, 'rfft and irfft')
                if not onesided:  # check that we can use C2C ifft
                    rec = res.ifft(signal_ndim, normalized=normalized)
                    self.assertEqual(x, rec.select(-1, 0), 1e-8, 'twosided rfft and ifft real')
                    self.assertEqual(rec.select(-1, 1).data.abs().mean(), 0, 1e-8, 'twosided rfft and ifft imaginary')

        # contiguous case
        _test_real((100,), 1)
        _test_real((10, 1, 10, 100), 1)
        _test_real((100, 100), 2)
        _test_real((2, 2, 5, 80, 60), 2)
        _test_real((50, 40, 70), 3)
        _test_real((30, 1, 50, 25, 20), 3)

        _test_complex((100, 2), 1)
        _test_complex((100, 100, 2), 1)
        _test_complex((100, 100, 2), 2)
        _test_complex((1, 20, 80, 60, 2), 2)
        _test_complex((50, 40, 70, 2), 3)
        _test_complex((6, 5, 50, 25, 20, 2), 3)

        # non-contiguous case
        _test_real((165,), 1, lambda x: x.narrow(0, 25, 100))  # input is not aligned to complex type
        _test_real((100, 100, 3), 1, lambda x: x[:, :, 0])
        _test_real((100, 100), 2, lambda x: x.t())
        _test_real((20, 100, 10, 10), 2, lambda x: x.view(20, 100, 100)[:, :60])
        _test_real((65, 80, 115), 3, lambda x: x[10:60, 13:53, 10:80])
        _test_real((30, 20, 50, 25), 3, lambda x: x.transpose(1, 2).transpose(2, 3))

        _test_complex((2, 100), 1, lambda x: x.t())
        _test_complex((100, 2), 1, lambda x: x.expand(100, 100, 2))
        _test_complex((300, 200, 3), 2, lambda x: x[:100, :100, 1:])  # input is not aligned to complex type
        _test_complex((20, 90, 110, 2), 2, lambda x: x[:, 5:85].narrow(2, 5, 100))
        _test_complex((40, 60, 3, 80, 2), 3, lambda x: x.transpose(2, 0).select(0, 2)[5:55, :, 10:])
        _test_complex((30, 55, 50, 22, 2), 3, lambda x: x[:, 3:53, 15:40, 1:21])

        # non-contiguous with strides not representable as aligned with complex type
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [3, 2, 1]))
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [4, 2, 2]))
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [4, 3, 1]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [3, 3, 1]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [4, 2, 2]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [4, 3, 1]))

    @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
    def test_fft_ifft_rfft_irfft(self):
        self._test_fft_ifft_rfft_irfft(self)

    @unittest.skip("Not implemented yet")
    def test_conv2(self):
        x = torch.rand(math.floor(torch.uniform(50, 100)), math.floor(torch.uniform(50, 100)))
        k = torch.rand(math.floor(torch.uniform(10, 20)), math.floor(torch.uniform(10, 20)))
        imvc = torch.conv2(x, k)
        imvc2 = torch.conv2(x, k, 'V')
        imfc = torch.conv2(x, k, 'F')

        ki = k.clone()
        ks = k.storage()
        kis = ki.storage()
        for i in range(ks.size() - 1, 0, -1):
            kis[ks.size() - i + 1] = ks[i]
        # for i=ks.size(), 1, -1 do kis[ks.size()-i+1]=ks[i] end
        imvx = torch.xcorr2(x, ki)
        imvx2 = torch.xcorr2(x, ki, 'V')
        imfx = torch.xcorr2(x, ki, 'F')

        self.assertEqual(imvc, imvc2, 0, 'torch.conv2')
        self.assertEqual(imvc, imvx, 0, 'torch.conv2')
        self.assertEqual(imvc, imvx2, 0, 'torch.conv2')
        self.assertEqual(imfc, imfx, 0, 'torch.conv2')
        self.assertLessEqual(math.abs(x.dot(x) - torch.xcorr2(x, x)[0][0]), 1e-10, 'torch.conv2')

        xx = torch.Tensor(2, x.size(1), x.size(2))
        xx[1].copy_(x)
        xx[2].copy_(x)
        kk = torch.Tensor(2, k.size(1), k.size(2))
        kk[1].copy_(k)
        kk[2].copy_(k)

        immvc = torch.conv2(xx, kk)
        immvc2 = torch.conv2(xx, kk, 'V')
        immfc = torch.conv2(xx, kk, 'F')

        self.assertEqual(immvc[0], immvc[1], 0, 'torch.conv2')
        self.assertEqual(immvc[0], imvc, 0, 'torch.conv2')
        self.assertEqual(immvc2[0], imvc2, 0, 'torch.conv2')
        self.assertEqual(immfc[0], immfc[1], 0, 'torch.conv2')
        self.assertEqual(immfc[0], imfc, 0, 'torch.conv2')

    @unittest.skip("Not implemented yet")
    def test_conv3(self):
        x = torch.rand(math.floor(torch.uniform(20, 40)),
                       math.floor(torch.uniform(20, 40)),
                       math.floor(torch.uniform(20, 40)))
        k = torch.rand(math.floor(torch.uniform(5, 10)),
                       math.floor(torch.uniform(5, 10)),
                       math.floor(torch.uniform(5, 10)))
        imvc = torch.conv3(x, k)
        imvc2 = torch.conv3(x, k, 'V')
        imfc = torch.conv3(x, k, 'F')

        ki = k.clone()
        ks = k.storage()
        kis = ki.storage()
        for i in range(ks.size() - 1, 0, -1):
            kis[ks.size() - i + 1] = ks[i]
        imvx = torch.xcorr3(x, ki)
        imvx2 = torch.xcorr3(x, ki, 'V')
        imfx = torch.xcorr3(x, ki, 'F')

        self.assertEqual(imvc, imvc2, 0, 'torch.conv3')
        self.assertEqual(imvc, imvx, 0, 'torch.conv3')
        self.assertEqual(imvc, imvx2, 0, 'torch.conv3')
        self.assertEqual(imfc, imfx, 0, 'torch.conv3')
        self.assertLessEqual(math.abs(x.dot(x) - torch.xcorr3(x, x)[0][0][0]), 4e-10, 'torch.conv3')

        xx = torch.Tensor(2, x.size(1), x.size(2), x.size(3))
        xx[1].copy_(x)
        xx[2].copy_(x)
        kk = torch.Tensor(2, k.size(1), k.size(2), k.size(3))
        kk[1].copy_(k)
        kk[2].copy_(k)

        immvc = torch.conv3(xx, kk)
        immvc2 = torch.conv3(xx, kk, 'V')
        immfc = torch.conv3(xx, kk, 'F')

        self.assertEqual(immvc[0], immvc[1], 0, 'torch.conv3')
        self.assertEqual(immvc[0], imvc, 0, 'torch.conv3')
        self.assertEqual(immvc2[0], imvc2, 0, 'torch.conv3')
        self.assertEqual(immfc[0], immfc[1], 0, 'torch.conv3')
        self.assertEqual(immfc[0], imfc, 0, 'torch.conv3')

    @unittest.skip("Not implemented yet")
    def _test_conv_corr_eq(self, fn, fn_2_to_3):
        ix = math.floor(random.randint(20, 40))
        iy = math.floor(random.randint(20, 40))
        iz = math.floor(random.randint(20, 40))
        kx = math.floor(random.randint(5, 10))
        ky = math.floor(random.randint(5, 10))
        kz = math.floor(random.randint(5, 10))

        x = torch.rand(ix, iy, iz)
        k = torch.rand(kx, ky, kz)

        o3 = fn(x, k)
        o32 = torch.zeros(o3.size())
        fn_2_to_3(x, k, o3, o32)
        self.assertEqual(o3, o32)

    @unittest.skip("Not implemented yet")
    def test_xcorr3_xcorr2_eq(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.xcorr2(x[i + j - 1], k[j]))
        self._test_conv_corr_eq(torch.xcorr3, reference)

    @unittest.skip("Not implemented yet")
    def test_xcorr3_xcorr2_eq_full(self):
        def reference(x, k, o3, o32):
            for i in range(x.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.xcorr2(x[i], k[k.size(1) - j + 1], 'F'))
        self._test_conv_corr_eq(lambda x, k: torch.xcorr3(x, k, 'F'), reference)

    @unittest.skip("Not implemented yet")
    def test_conv3_conv2_eq_valid(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.conv2(x[i + j - 1], k[k.size(1) - j + 1]))
        self._test_conv_corr_eq(torch.conv3, reference)

    @unittest.skip("Not implemented yet")
    def test_fconv3_fconv2_eq(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i + j - 1].add(torch.conv2(x[i], k[j], 'F'))
        self._test_conv_corr_eq(lambda x, k: torch.conv3(x, k, 'F'), reference)

    def test_isfinite(self):
        x = torch.Tensor([1, inf, 2, -inf, nan, -10])
        self.assertEqual(torch.isfinite(x), torch.BoolTensor([True, False, True, False, False, True]))

    def test_isfinite_int(self):
        x = torch.tensor([1, 2, 3])
        self.assertEqual(torch.isfinite(x), torch.BoolTensor([True, True, True]))

    def test_isfinite_type(self):
        with self.assertRaises(TypeError):
            torch.isfinite(1)  # Parameter must be a tensor

    def test_isinf_type(self):
        with self.assertRaises(TypeError):
            torch.isinf(1)  # Parameter must be a tensor

    def test_isnan(self):
        x = torch.Tensor([1, nan, 2])
        self.assertEqual(torch.isnan(x), torch.ByteTensor([0, 1, 0]))

    def test_RNGState(self):
        state = torch.get_rng_state()
        stateCloned = state.clone()
        before = torch.rand(1000)

        self.assertEqual(state.ne(stateCloned).long().sum(), 0, 0)

        torch.set_rng_state(state)
        after = torch.rand(1000)
        self.assertEqual(before, after, 0)

    def test_RNGStateAliasing(self):
        # Fork the random number stream at this point
        gen = torch.Generator()
        gen.set_state(torch.get_rng_state())
        self.assertEqual(gen.get_state(), torch.get_rng_state())

        target_value = torch.rand(1000)
        # Dramatically alter the internal state of the main generator
        _ = torch.rand(100000)
        forked_value = torch.rand(1000, generator=gen)
        self.assertEqual(target_value, forked_value, 0, "RNG has not forked correctly.")

    def test_RNG_after_pickle(self):
        torch.random.manual_seed(100)
        before = torch.rand(10)

        torch.random.manual_seed(100)
        buf = io.BytesIO()
        tensor = torch.Tensor([1, 2, 3])
        ForkingPickler(buf, pickle.HIGHEST_PROTOCOL).dump(tensor)
        after = torch.rand(10)

        self.assertEqual(before, after, 0)

    def test_boxMullerState(self):
        torch.manual_seed(123)
        odd_number = 101
        seeded = torch.randn(odd_number)
        state = torch.get_rng_state()
        midstream = torch.randn(odd_number)
        torch.set_rng_state(state)
        repeat_midstream = torch.randn(odd_number)
        torch.manual_seed(123)
        reseeded = torch.randn(odd_number)
        self.assertEqual(midstream, repeat_midstream, 0,
                         'get_rng_state/set_rng_state not generating same sequence of normally distributed numbers')
        self.assertEqual(seeded, reseeded, 0,
                         'repeated calls to manual_seed not generating same sequence of normally distributed numbers')

    def test_manual_seed(self):
        rng_state = torch.get_rng_state()
        torch.manual_seed(2)
        x = torch.randn(100)
        self.assertEqual(torch.initial_seed(), 2)
        torch.manual_seed(2)
        y = torch.randn(100)
        self.assertEqual(x, y)
        torch.set_rng_state(rng_state)

    def test_numel(self):
        b = torch.ByteTensor(3, 100, 100)
        self.assertEqual(b.nelement(), 3 * 100 * 100)
        self.assertEqual(b.numel(), 3 * 100 * 100)

    def _consecutive(self, size, start=1):
        sequence = torch.ones(int(torch.Tensor(size).prod(0))).cumsum(0)
        sequence.add_(start - 1)
        return sequence.resize_(*size)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_empty_storage_view(self):
        # we should be able to "modify" slices of a 0-element
        # array without an error being raised due to
        # trying to resize its storage
        t = torch.from_numpy(np.empty((0, 4)))
        t[:, 1::2] *= 1

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_newaxis_numpy_comparison(self):
        def run_test(tensor, *idx):
            npt = tensor.numpy()
            self.assertEqual(tensor[idx], npt[idx])

        # 1D Tensor Tests
        x = torch.arange(0, 10)
        cases = [
            [None],
            [None, None],
            [Ellipsis, None],
            [None, Ellipsis],
            [2, None],
            [None, 2],
            [Ellipsis, None, 2],
            [Ellipsis, 2, None],
            [2, Ellipsis, None],
            [2, None, Ellipsis],
            [None, 2, Ellipsis],
            [None, Ellipsis, 2],
        ]

        for case in cases:
            run_test(x, *case)

        # 2D Tensor Tests
        x = torch.arange(0, 12).view(3, 4)
        cases = [
            [None],
            [None, None],
            [None, None, None],
            [Ellipsis, None],
            [Ellipsis, None, None],
            [None, Ellipsis],
            [None, Ellipsis, None],
            [None, None, Ellipsis],
            [2, None],
            [2, None, Ellipsis],
            [2, Ellipsis, None],
            [None, 2, Ellipsis],
            [Ellipsis, 2, None],
            [Ellipsis, None, 2],
            [None, Ellipsis, 2],
            [1, 2, None],
            [1, 2, Ellipsis, None],
            [1, Ellipsis, 2, None],
            [Ellipsis, 1, None, 2],
            [Ellipsis, 1, 2, None],
            [1, None, 2, Ellipsis],
            [None, 1, Ellipsis, 2],
            [None, 1, 2, Ellipsis],
        ]

        for case in cases:
            run_test(x, *case)

    def test_newindex(self):
        reference = self._consecutive((3, 3, 3))
        # This relies on __index__() being correct - but we have separate tests for that

        def checkPartialAssign(index):
            reference = torch.zeros(3, 3, 3)
            reference[index] = self._consecutive((3, 3, 3))[index]
            self.assertEqual(reference[index], self._consecutive((3, 3, 3))[index], 0)
            reference[index] = 0
            self.assertEqual(reference, torch.zeros(3, 3, 3), 0)

        checkPartialAssign(0)
        checkPartialAssign(1)
        checkPartialAssign(2)
        checkPartialAssign((0, 1))
        checkPartialAssign((1, 2))
        checkPartialAssign((0, 2))
        checkPartialAssign(torch.LongTensor((0, 2)))

        with self.assertRaises(IndexError):
            reference[1, 1, 1, 1] = 1
        with self.assertRaises(IndexError):
            reference[1, 1, 1, (1, 1)] = 1
        with self.assertRaises(IndexError):
            reference[3, 3, 3, 3, 3, 3, 3, 3] = 1
        with self.assertRaises(IndexError):
            reference[0.0] = 1
        with self.assertRaises(TypeError):
            reference[0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, :, 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, ..., 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, :, 0.0] = 1

    def test_index_add(self):
        num_copy, num_dest = 3, 3
        dest = torch.randn(num_dest, 4, 5)
        src = torch.randn(num_copy, 4, 5)
        idx = torch.randperm(num_dest).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_add_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] += src[i]
        self.assertEqual(dest, dest2)

        dest = torch.randn(num_dest)
        src = torch.randn(num_copy)
        idx = torch.randperm(num_dest).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_add_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] = dest2[idx[i]] + src[i]
        self.assertEqual(dest, dest2)

    def test_t(self):
        # Test 0D tensors
        x = torch.randn(())
        self.assertEqual(x, x.t())
        x = x.to_sparse()
        self.assertEqual(x, x.t())

        # Test 1D tensors
        x = torch.arange(4)
        self.assertEqual(x, x.t())
        x = x.to_sparse()
        self.assertEqual(x, x.t())

        # Test 2D tensors
        x = torch.rand((2, 2))
        self.assertEqual(x.t(), x.transpose(0, 1))
        x = x.to_sparse()
        self.assertEqual(x.t(), x.transpose(0, 1))

        # Test 3D tensor
        x = torch.rand((2, 2, 2))
        with self.assertRaisesRegex(RuntimeError, 'expects a tensor with <= 2 dimensions, but self is 3D'):
            x.t()
        x = x.to_sparse()
        with self.assertRaisesRegex(RuntimeError, 'expects a tensor with <= 2 sparse and 0 dense dimensions'):
            x.t()

    def test_take(self):
        def check(src, idx):
            expected = src.contiguous().view(-1).index_select(
                0, idx.contiguous().view(-1)).view_as(idx)
            actual = src.take(idx)
            self.assertEqual(actual.size(), idx.size())
            self.assertEqual(expected, actual)

        src = torch.randn(2, 3, 5)
        idx = torch.LongTensor([[0, 2], [3, 4]])
        check(src, idx)
        check(src.transpose(1, 2), idx)
        check(src.bool(), idx)

    def test_put_(self):
        def check(dst, idx, value):
            expected = dst.clone().view(-1).index_copy_(
                0, idx.contiguous().view(-1), value.contiguous().view(-1))
            expected = expected.view_as(dst)
            dst.put_(idx, value)
            self.assertEqual(expected, dst)

        dst = torch.randn(2, 3, 5)
        idx = torch.LongTensor([[0, 2], [3, 4]])
        values = torch.randn(2, 2)
        check(dst, idx, values)
        check(dst.transpose(1, 2), idx, values)

        values = torch.tensor([[False, False], [False, False]])
        check(dst.bool(), idx, values)

    def test_put_accumulate(self):
        dst = torch.ones(2, 2)
        idx = torch.LongTensor([[0, 1], [0, 1]])
        src = torch.Tensor([1, 2, 3, 4])
        dst.put_(idx, src, accumulate=True)
        self.assertEqual(dst.tolist(), [[5, 7], [1, 1]])

    # Fill idx with valid indices.
    @staticmethod
    def _fill_indices(self, idx, dim, dim_size, elems_per_row, m, n, o):
        for i in range(1 if dim == 0 else m):
            for j in range(1 if dim == 1 else n):
                for k in range(1 if dim == 2 else o):
                    ii = [i, j, k]
                    ii[dim] = slice(0, idx.size(dim) + 1)
                    idx[tuple(ii)] = torch.randperm(dim_size)[0:elems_per_row]

    def test_flatten(self):
        # Test that flatten returns 1-dim tensor when given a 0-dim tensor
        zero_dim_tensor = torch.tensor(123)
        flat0 = zero_dim_tensor.flatten()
        one_dim_tensor = torch.tensor([123])
        flat1 = zero_dim_tensor.flatten()

        self.assertEqual(zero_dim_tensor.shape, torch.Size([]))
        self.assertEqual(flat0.shape, torch.Size([1]))
        self.assertEqual(one_dim_tensor.shape, torch.Size([1]))
        self.assertEqual(flat1.shape, torch.Size([1]))
        self.assertEqual(flat0, one_dim_tensor)
        self.assertEqual(flat0, flat1)
        self.assertEqual(flat0.shape, flat1.shape)

        # Test both float tensor and quantized tensor
        tensors = [torch.randn(5, 5, 5, 5),
                   torch._empty_affine_quantized([5, 5, 5, 5],
                                                 scale=2,
                                                 zero_point=3,
                                                 dtype=torch.quint8)]
        for src in tensors:
            flat = src.flatten(0, -1)
            self.assertEqual(flat.shape, torch.Size([625]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(0, 2)
            self.assertEqual(flat.shape, torch.Size([125, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(0, 1)
            self.assertEqual(flat.shape, torch.Size([25, 5, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(1, 2)
            self.assertEqual(flat.shape, torch.Size([5, 25, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(2, 3)
            self.assertEqual(flat.shape, torch.Size([5, 5, 25]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(-2, -1)
            self.assertEqual(flat.shape, torch.Size([5, 5, 25]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(2, 2)
            self.assertEqual(flat, src)

            # out of bounds index
            with self.assertRaisesRegex(IndexError, 'Dimension out of range'):
                src.flatten(5, 10)

            # invalid start and end
            with self.assertRaisesRegex(RuntimeError, 'start_dim cannot come after end_dim'):
                src.flatten(2, 0)

    @staticmethod
    def _test_gather(self, cast, test_bounds=True):
        m, n, o = random.randint(10, 20), random.randint(10, 20), random.randint(10, 20)
        elems_per_row = random.randint(1, 10)
        dim = random.randrange(3)

        src = torch.randn(m, n, o)
        idx_size = [m, n, o]
        idx_size[dim] = elems_per_row
        idx = torch.LongTensor().resize_(*idx_size)
        _TestTorchMixin._fill_indices(self, idx, dim, src.size(dim), elems_per_row, m, n, o)

        src = cast(src)
        idx = cast(idx)

        actual = torch.gather(src, dim, idx)
        expected = cast(torch.Tensor().resize_(*idx_size))
        for i in range(idx_size[0]):
            for j in range(idx_size[1]):
                for k in range(idx_size[2]):
                    ii = [i, j, k]
                    ii[dim] = idx[i, j, k]
                    expected[i, j, k] = src[tuple(ii)]
        self.assertEqual(actual, expected, 0)

        if test_bounds:
            idx[0][0][0] = 23
            self.assertRaises(RuntimeError, lambda: torch.gather(src, dim, idx))

        src = cast(torch.randn(3, 4, 5))
        expected, idx = src.max(2, True)
        expected = cast(expected)
        idx = cast(idx)
        actual = torch.gather(src, 2, idx)
        self.assertEqual(actual, expected, 0)

        # Bool test case
        t = torch.tensor([[False, True], [True, True]])
        self.assertEqual(torch.gather(t, 1, torch.tensor([[0, 0], [1, 0]])), torch.tensor([[False, False], [True, True]]))

    def test_gather(self):
        self._test_gather(self, lambda t: t)

    @staticmethod
    def _test_scatter_base(self, cast, method, is_scalar=False, test_bounds=True):
        m, n, o = random.randint(10, 20), random.randint(10, 20), random.randint(10, 20)
        elems_per_row = random.randint(1, 10)
        dim = random.randrange(3)

        idx_size = [m, n, o]
        idx_size[dim] = elems_per_row
        idx = cast(torch.LongTensor().resize_(*idx_size))
        _TestTorchMixin._fill_indices(self, idx, dim, ([m, n, o])[dim], elems_per_row, m, n, o)

        if is_scalar:
            src = random.random()
        else:
            src = cast(torch.Tensor(*idx_size).normal_())

        base = cast(torch.randn(m, n, o))
        actual = getattr(base.clone(), method)(dim, idx, src)
        expected = base.clone()
        for i in range(idx_size[0]):
            for j in range(idx_size[1]):
                for k in range(idx_size[2]):
                    ii = [i, j, k]
                    ii[dim] = idx[i, j, k]
                    if method == 'scatter_' and not is_scalar:
                        expected[tuple(ii)] = src[i, j, k]
                    elif method == 'scatter_add_':
                        expected[tuple(ii)] += src[i, j, k]
                    else:
                        expected[tuple(ii)] = src
        self.assertEqual(actual, expected, 0)

        if test_bounds:
            idx[0][0][0] = 34
            with self.assertRaises(RuntimeError):
                getattr(base.clone(), method)(dim, idx, src)

        # test for empty index, should be a no-op
        idx = cast(torch.LongTensor())
        actual = getattr(base.clone(), method)(dim, idx, src)
        self.assertEqual(actual, base, 0)

    def test_scatter(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_')

    def test_scatterAdd(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_add_')

    def test_scatterFill(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_', True)

    def test_masked_scatter(self):
        with warnings.catch_warnings(record=True) as w:
            for maskType in [torch.uint8, torch.bool]:
                for dt in torch.testing.get_all_dtypes():
                    num_copy, num_dest = 3, 10
                    dest = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype=dt)
                    dest2 = dest.clone()
                    src = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dt)
                    mask = torch.tensor((0, 0, 0, 0, 1, 0, 1, 0, 1, 0), dtype=maskType)

                    if dt == torch.bool:
                        # torch.bool is a special case and is being tested
                        # in a separate test
                        continue

                    if dt == torch.half:
                        self.assertRaises(RuntimeError, lambda: dest.masked_scatter_(mask, src))
                        continue

                    dest.masked_scatter_(mask, src)
                    j = 0
                    for i in range(num_dest):
                        if mask[i]:
                            dest2[i] = src[j]
                            j += 1
                    self.assertEqual(dest, dest2, 0)

                    # make source bigger than number of 1s in mask
                    src = torch.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=dt)
                    dest.masked_scatter_(mask, src)

                    # make src smaller. this should fail
                    src = torch.randn(num_copy - 1)
                    with self.assertRaises(RuntimeError):
                        dest.masked_scatter_(mask, src)
        self.assertEqual(len(w), 25)

        warn = 'masked_scatter_ received a mask with dtype torch.uint8,'
        for wi in w:
            self.assertEqual(str(wi.message)[0:55], str(warn))

    def test_masked_fill(self):
        with warnings.catch_warnings(record=True) as w:
            for dt in torch.testing.get_all_dtypes():
                for dtype in [torch.uint8, torch.bool]:
                    num_dest = 10
                    dst = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dt)
                    mask = torch.rand(num_dest).mul(2).floor().to(dtype)
                    val = random.random()
                    dst2 = dst.clone()

                    if dt == torch.half:
                        self.assertRaises(RuntimeError, lambda: dst.masked_fill_(mask, val))
                        continue

                    dst.masked_fill_(mask, val)
                    for i in range(num_dest):
                        if mask[i]:
                            dst2[i] = val
                    self.assertEqual(dst, dst2, 0)

                    # test non-contiguous case
                    dst = torch.randn(num_dest, num_dest, num_dest).permute((2, 0, 1))
                    dst2 = dst.clone()
                    dst.masked_fill_((dst > 0).to(dtype), val)
                    dst2.masked_fill_((dst2 > 0).to(dtype), val)
                    self.assertEqual(dst, dst2, 0)
            self.assertEqual(len(w), 28)

            warn = 'masked_fill_ received a mask with dtype torch.uint8,'
            for wi in w:
                self.assertEqual(str(wi.message)[0:52], str(warn))

    def test_abs(self):
        def _test_abs(tensors_dict):
            for _category, tensors in tensors_dict.items():
                for data in tensors:
                    _test_abs_single(data)

        def _test_abs_single(data):
            switch = torch.rand(data.size()).mul(2).floor().mul(2).add(-1).type(data.dtype)
            res = torch.mul(data, switch)
            self.assertTensorsSlowEqual(res.abs(), data, 1e-16)

        shapes = [(3, 4), (3, 5, 7), (2, 2, 5, 8, 2, 3), (1000,), (10, 10, 10)]

        for shape in shapes:
            # Test all except char/byte
            _test_abs(self._make_tensors(shape, val_range=(0, 1000)))

            # Test char
            _test_abs_single(torch.CharTensor(*shape).random_(0, 100))

            # Test byte
            byte_tensor = torch.ByteTensor(*shape).random_(0, 100)
            self.assertTensorsSlowEqual(byte_tensor, byte_tensor.abs(), 1e-16)

        # Checking that the right abs function is called for LongTensor
        bignumber = 2 ** 31 + 1
        res = torch.LongTensor((-bignumber,))
        self.assertGreater(res.abs()[0], 0)

        # One of
        rec = torch.randn(2, 2, 3, 7, 6, 2).type(torch.float64).clamp(0, 1)
        val1 = rec.select(-1, -1).data[0][0][0].sum()
        val2 = rec.select(-1, -1).data.abs()[0][0][0].sum()
        self.assertEqual(val1, val2, 1e-8, 'absolute value')

        # Both abs(0.0) and abs(-0.0) should result in 0.0
        for dtype in (torch.float, torch.double):
            for abs_zeros in (torch.tensor([0.0, -0.0], dtype=dtype).abs().tolist(),
                              # test a large tensor so that the vectorized version is tested
                              torch.abs(-torch.zeros(10000, dtype=dtype)).tolist()):
                for num in abs_zeros:
                    self.assertGreater(math.copysign(1.0, num), 0.0)

    def test_hardshrink(self):
        data_original = torch.tensor([1, 0.5, 0.3, 0.6]).view(2, 2)
        float_types = [
            'torch.DoubleTensor',
            'torch.FloatTensor'
        ]
        for t in float_types:
            data = data_original.type(t)
            self.assertEqual(torch.tensor([1, 0.5, 0, 0.6]).view(2, 2), data.hardshrink(0.3))
            self.assertEqual(torch.tensor([1, 0, 0, 0.6]).view(2, 2), data.hardshrink(0.5))

            # test default lambd=0.5
            self.assertEqual(data.hardshrink(), data.hardshrink(0.5))

            # test non-contiguous case
            self.assertEqual(torch.tensor([1, 0, 0.5, 0.6]).view(2, 2), data.t().hardshrink(0.3))

    def test_hardshrink_edge_cases(self):
        def h(t, values, l_expected):
            for l, expected in l_expected.items():
                values_tensor = torch.tensor([float(v) for v in values]).type(t)
                expected_tensor = torch.tensor([float(v) for v in expected]).type(t)
                self.assertEqual(expected_tensor == values_tensor.hardshrink(l),
                                 torch.ones_like(values_tensor))

        def test_helper(t, min, max):
            h(t, [0.0, min, -min, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
              {0.0: [0.0, min, -min, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
               min: [0.0, 0.0, 0.0, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
               0.1: [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, max, -max, inf, -inf],
               1.0: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, max, -max, inf, -inf],
               max: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, inf, -inf],
               inf: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]})

        test_helper(torch.DoubleTensor,
                    torch.finfo(torch.double).tiny, torch.finfo(torch.double).max)
        test_helper(torch.FloatTensor,
                    torch.finfo(torch.float).tiny, torch.finfo(torch.float).max)

    def test_unbiased(self):
        tensor = torch.randn(100)
        self.assertEqual(tensor.var(0), tensor.var(0, unbiased=True))
        self.assertEqual(tensor.var(), tensor.var(unbiased=True))
        self.assertEqual(tensor.var(unbiased=False), tensor.var(0, unbiased=False))

        tensor = torch.FloatTensor([1.0, 2.0])
        self.assertEqual(tensor.var(unbiased=True), 0.5)
        self.assertEqual(tensor.var(unbiased=False), 0.25)

        tensor = torch.FloatTensor([1.0, 2.0, 3.0])
        self.assertEqual(tensor.var(unbiased=True), 1.0)
        self.assertEqual(tensor.var(unbiased=False), 2.0 / 3.0)

        tensor = torch.randn(100)
        self.assertEqual(tensor.std(0), tensor.std(0, unbiased=True))
        self.assertEqual(tensor.std(), tensor.std(unbiased=True))
        self.assertEqual(tensor.std(unbiased=False), tensor.std(0, unbiased=False))

    def test_structseq_repr(self):
        a = torch.arange(250).reshape(5, 5, 10)
        expected = """
        torch.return_types.max(
        values=tensor([[ 40,  41,  42,  43,  44,  45,  46,  47,  48,  49],
                [ 90,  91,  92,  93,  94,  95,  96,  97,  98,  99],
                [140, 141, 142, 143, 144, 145, 146, 147, 148, 149],
                [190, 191, 192, 193, 194, 195, 196, 197, 198, 199],
                [240, 241, 242, 243, 244, 245, 246, 247, 248, 249]]),
        indices=tensor([[4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]))"""
        self.assertEqual(repr(a.max(1)), textwrap.dedent(expected).strip())

    def test_var_stability(self):
        tensor = torch.FloatTensor([2281.5, 2281.25])
        self.assertEqual(tensor.var(dim=0), 0.03125)
        self.assertEqual(tensor.var(), 0.03125)

    def test_view_empty(self):
        x = torch.randn(0, 6)
        self.assertEqual((1, 0, 6, 1, 1), x.view(1, 0, 6, 1, 1).shape)

    def test_reshape(self):
        x = torch.randn(3, 3)
        self.assertEqual(x.data_ptr(), x.reshape(-1).data_ptr())
        self.assertEqual(x.data_ptr(), x.reshape(1, 9, 1).data_ptr())
        self.assertEqual(torch.reshape(x, (9,)), x.reshape(9))
        self.assertRaises(RuntimeError, lambda: x.reshape(-1, -1))

        y = torch.randn(4, 4, 4)[:, 0, :]
        self.assertNotEqual(y.data_ptr(), y.reshape(-1).data_ptr())
        self.assertEqual(y.contiguous().view(-1), y.reshape(-1))
        self.assertEqual(y.reshape(2, 2, 4).data_ptr(), y.data_ptr())

        s = torch.randn(())
        self.assertEqual(s.data_ptr(), s.reshape(()).data_ptr())
        self.assertEqual(s.reshape(-1).shape, (1,))
        self.assertRaises(RuntimeError, lambda: s.reshape(2))

        empty = torch.tensor([])
        self.assertEqual(empty, empty.reshape(-1))
        self.assertEqual(empty, empty.reshape([0]))
        # TODO: fix these once we have multi-dimensional empty tensors
        self.assertEqual(empty.reshape([0, 1]).shape, (0, 1))
        self.assertEqual(empty.reshape([1, -1]).shape, (1, 0))
        self.assertRaises(RuntimeError, lambda: empty.reshape(1))

        x = torch.randn(3, 3)
        self.assertEqual(x.data_ptr(), x.reshape_as(torch.rand(9)).data_ptr())
        self.assertEqual(x.data_ptr(), x.reshape_as(torch.rand(1, 9, 1)).data_ptr())
        self.assertRaises(RuntimeError, lambda: x.reshape_as(torch.rand(10)))

    def test_empty_reshape(self):
        x = torch.randn(0, 6)
        self.assertEqual((1, 0, 6, 1, 1), x.reshape(1, 0, 6, 1, 1).shape)
        # should be viewable -- i.e. data_ptr is the same.
        self.assertEqual(x.data_ptr(), x.reshape(1, 0, 6, 1, 1).data_ptr())

        # match NumPy semantics -- don't infer the size of dimension with a degree of freedom
        self.assertRaises(RuntimeError, lambda: x.reshape(0, -1))

    def check_single_matmul(self, x, y, shape):
        a = np.array(x, copy=False)
        b = np.array(y, copy=False)
        expected = np.matmul(a, b)

        ans = torch.matmul(x, y)
        self.assertTrue(ans.is_contiguous())
        self.assertTrue(np.array_equal(ans, expected))

        out = torch.zeros(*shape, dtype=torch.int64)
        ans = torch.matmul(x, y, out=out)
        self.assertIs(ans, out)
        self.assertTrue(ans.is_contiguous())
        self.assertTrue(np.array_equal(ans, expected))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_matmul_small_brute_force_1d_Nd(self):
        # Issue #20452: range(0, 10) does not work.
        n = 1
        for m in range(1, 8):
            for p in range(1, 8):
                for o in range(1, 5):
                    # 1d, 3d, inner dimensions C
                    x = torch.arange(m)
                    y = torch.arange(o * m * p).reshape(o, m, p)
                    self.check_single_matmul(x, y, (o, n, p))

                    # 1d, 3d, inner dimensions Fortran
                    x = torch.arange(m)
                    y = torch.arange(o * p * m).reshape(o, p, m).transpose(-1, -2)
                    self.check_single_matmul(x, y, (o, n, p))

                    # 1d, 3d, inner dimensions non-contiguous
                    x = torch.arange(2 * m)[::2]
                    y = torch.arange(o * m * 2 * p).reshape(o, m, 2 * p)[:, :, ::2]
                    self.check_single_matmul(x, y, (o, n, p))

                    for r in range(1, 5):
                        # 1d, 4d, inner dimensions C
                        x = torch.arange(m)
                        y = torch.arange(r * o * m * p).reshape(r, o, m, p)
                        self.check_single_matmul(x, y, (r, o, n, p))

                        # 1d, 4d, inner dimensions Fortran
                        x = torch.arange(m)
                        y = torch.arange(r * o * p * m).reshape(r, o, p, m).transpose(-1, -2)
                        self.check_single_matmul(x, y, (r, o, n, p))

                        # 1d, 4d, inner dimensions non-contiguous
                        x = torch.arange(2 * m)[::2]
                        y = torch.arange(r * o * m * 2 * p).reshape(r, o, m, 2 * p)[:, :, :, ::2]
                        self.check_single_matmul(x, y, (r, o, n, p))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_matmul_small_brute_force_2d_Nd(self):
        # Issue #20452: range(0, 10) does not work.
        for n in range(1, 5):
            for m in range(1, 5):
                for p in range(1, 5):
                    for o in range(1, 3):
                        # 2d, 3d, inner dimensions C
                        x = torch.arange(n * m).reshape(n, m)
                        y = torch.arange(o * m * p).reshape(o, m, p)
                        self.check_single_matmul(x, y, (o, n, p))

                        # 2d, 3d, inner dimensions Fortran
                        x = torch.arange(m * n).reshape(m, n).transpose(-1, -2)
                        y = torch.arange(o * p * m).reshape(o, p, m).transpose(-1, -2)
                        self.check_single_matmul(x, y, (o, n, p))

                        # 2d, 3d, inner dimensions non-contiguous
                        x = torch.arange(n * 2 * m).reshape(n, 2 * m)[:, ::2]
                        y = torch.arange(o * m * 2 * p).reshape(o, m, 2 * p)[:, :, ::2]
                        self.check_single_matmul(x, y, (o, n, p))

                        for r in range(1, 2):
                            # 2d, 4d, inner dimensions C
                            x = torch.arange(n * m).reshape(n, m)
                            y = torch.arange(r * o * m * p).reshape(r, o, m, p)
                            self.check_single_matmul(x, y, (r, o, n, p))

                            # 2d, 4d, inner dimensions Fortran
                            x = torch.arange(m * n).reshape(m, n).transpose(-1, -2)
                            y = torch.arange(r * o * p * m).reshape(r, o, p, m).transpose(-1, -2)
                            self.check_single_matmul(x, y, (r, o, n, p))

                            # 2d, 4d, inner dimensions non-contiguous
                            x = torch.arange(n * 2 * m).reshape(n, 2 * m)[:, ::2]
                            y = torch.arange(r * o * m * 2 * p).reshape(r, o, m, 2 * p)[:, :, :, ::2]
                            self.check_single_matmul(x, y, (r, o, n, p))

    def test_expand(self):
        tensor = torch.rand(1, 8, 1)
        tensor2 = torch.rand(5)
        template = torch.rand(4, 8, 5)
        target = template.size()
        self.assertEqual(tensor.expand_as(template).size(), target)
        self.assertEqual(tensor.expand(4, 8, 5).size(), target)
        self.assertEqual(tensor.expand(target).size(), target)
        self.assertEqual(tensor2.expand_as(template).size(), target)
        self.assertEqual(tensor2.expand(4, 8, 5).size(), target)
        self.assertEqual(tensor2.expand(target).size(), target)

        # test double expand
        self.assertEqual(tensor2.expand(1, 5).expand(2, 2, 5), tensor2.repeat(2, 2, 1))

        # test non-contiguous
        noncontig = torch.randn(5, 2, 1, 3)[:, 0]
        self.assertFalse(noncontig.is_contiguous())
        self.assertEqual(noncontig.expand(2, 5, 4, 3), noncontig.contiguous().repeat(2, 1, 4, 1))

        # make sure it's compatible with unsqueeze
        expanded = tensor2.expand(1, 1, 5)
        unsqueezed = tensor2.unsqueeze(0).unsqueeze(1)
        self.assertEqual(expanded, unsqueezed)
        self.assertEqual(expanded.stride(), unsqueezed.stride())

        # test -1 as target size
        self.assertEqual(tensor.expand(4, -1, 5), tensor.expand(4, 8, 5))
        self.assertRaises(RuntimeError, lambda: tensor2.expand(-1, -1))

        # test expanding empty to empty
        self.assertEqual(torch.zeros(0).expand((0,)), torch.zeros(0))

    def test_repeat(self):
        initial_shape = (8, 4)
        tensor = torch.rand(*initial_shape)

        size = (3, 1, 1)
        torchSize = torch.Size(size)
        target = [3, 8, 4]
        self.assertEqual(tensor.repeat(*size).size(), target, 'Error in repeat')
        self.assertEqual(tensor.repeat(torchSize).size(), target,
                         'Error in repeat using LongStorage')
        result = tensor.repeat(*size)
        self.assertEqual(result.size(), target, 'Error in repeat using result')
        result = tensor.repeat(torchSize)
        self.assertEqual(result.size(), target, 'Error in repeat using result and LongStorage')
        self.assertEqual(result.mean(0).view(8, 4), tensor, 'Error in repeat (not equal)')

        zeroDimTarget = torch.Size([24, 0])
        self.assertEqual(tensor.repeat((3, 0)).size(), zeroDimTarget, "Error when calling with 0 repeats")

    def test_repeat_interleave(self):
        x = torch.tensor([0, 1, 2, 3])
        expected = torch.tensor([1, 2, 2, 3, 3, 3])
        self.assertEqual(torch.repeat_interleave(x), expected)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.arange(4).reshape(2, 2))

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.arange(4.0))

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.tensor([1, 2, -1, 3, 4]))

        y = torch.tensor([[1, 2], [3, 4]])

        y1_v1 = torch.repeat_interleave(y, 2)
        y1_v2 = torch.repeat_interleave(y, torch.tensor(2))
        y1_v3 = torch.repeat_interleave(y, torch.tensor([2]))
        y1_expect = torch.tensor([1, 1, 2, 2, 3, 3, 4, 4])
        self.assertEqual(y1_v1, y1_expect)
        self.assertEqual(y1_v2, y1_expect)
        self.assertEqual(y1_v3, y1_expect)

        y2 = torch.repeat_interleave(y, 3, dim=1)
        y2_expect = torch.tensor([[1, 1, 1, 2, 2, 2],
                                  [3, 3, 3, 4, 4, 4]])
        self.assertEqual(y2, y2_expect)

        y3 = torch.repeat_interleave(y, torch.tensor([1, 2]), dim=0)
        y3_expect = torch.tensor([[1, 2],
                                  [3, 4],
                                  [3, 4]])
        self.assertEqual(y3, y3_expect)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(y, torch.tensor([1, 2, 3]), dim=0)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(y, torch.arange(9).reshape(3, 3), dim=0)

        # test zero sized dimension
        x = torch.zeros((5, 0))
        y = torch.repeat_interleave(x, repeats=3, dim=1)
        self.assertEqual(y, x.new_zeros(5, 0))

        x = torch.tensor([], dtype=torch.int64)
        y = torch.repeat_interleave(x, x)
        self.assertEqual(y, x)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_repeat_tile(self):

        initial_shape = (8, 4)

        repeats = ((3, 1, 1),
                   (3, 3, 3),
                   (1, 2, 1),
                   (2, 2, 2, 2))

        def _generate_noncontiguous_input():

            out = np.broadcast_to(np.random.random((1, 4)),
                                  initial_shape)

            assert not (out.flags.c_contiguous or out.flags.f_contiguous)

            return out

        for repeat in repeats:
            for tensor in (torch.from_numpy(np.random.random(initial_shape)),
                           torch.from_numpy(_generate_noncontiguous_input()),):

                self.assertEqual(tensor.repeat(*repeat).numpy(),
                                 np.tile(tensor.numpy(), repeat))

    def test_is_same_size(self):
        t1 = torch.Tensor(3, 4, 9, 10)
        t2 = torch.Tensor(3, 4)
        t3 = torch.Tensor(1, 9, 3, 3)
        t4 = torch.Tensor(3, 4, 9, 10)

        self.assertFalse(t1.is_same_size(t2))
        self.assertFalse(t1.is_same_size(t3))
        self.assertTrue(t1.is_same_size(t4))

    def test_is_set_to(self):
        t1 = torch.Tensor(3, 4, 9, 10)
        t2 = torch.Tensor(3, 4, 9, 10)
        t3 = torch.Tensor().set_(t1)
        t4 = t3.clone().resize_(12, 90)
        self.assertFalse(t1.is_set_to(t2))
        self.assertTrue(t1.is_set_to(t3))
        self.assertTrue(t3.is_set_to(t1), "is_set_to should be symmetric")
        self.assertFalse(t1.is_set_to(t4))
        self.assertFalse(torch.Tensor().is_set_to(torch.Tensor()),
                         "Tensors with no storages should not appear to be set "
                         "to each other")

        t1 = torch.tensor([True, True], dtype=torch.bool)
        t2 = torch.tensor([0], dtype=torch.bool).set_(t1)
        self.assertTrue(t1.is_set_to(t2))

    def test_tensor_set(self):
        t1 = torch.Tensor()
        t2 = torch.Tensor(3, 4, 9, 10).uniform_()
        t1.set_(t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        size = torch.Size([9, 3, 4, 10])
        t1.set_(t2.storage(), 0, size)
        self.assertEqual(t1.size(), size)
        t1.set_(t2.storage(), 0, tuple(size))
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), (120, 40, 10, 1))
        stride = (10, 360, 90, 1)
        t1.set_(t2.storage(), 0, size, stride)
        self.assertEqual(t1.stride(), stride)
        t1.set_(t2.storage(), 0, size=size, stride=stride)
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), stride)

        # test argument names
        t1 = torch.Tensor()
        # 1. case when source is tensor
        t1.set_(source=t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        # 2. case when source is storage
        t1.set_(source=t2.storage())
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        # 3. case when source is storage, and other args also specified
        t1.set_(source=t2.storage(), storage_offset=0, size=size, stride=stride)
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), stride)

        t1 = torch.tensor([True, True], dtype=torch.bool)
        t2 = torch.tensor([False, False], dtype=torch.bool)
        t1.set_(t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)

    def test_tensor_set_errors(self):
        f_cpu = torch.randn((2, 3), dtype=torch.float32)
        d_cpu = torch.randn((2, 3), dtype=torch.float64)

        # change dtype
        self.assertRaises(RuntimeError, lambda: f_cpu.set_(d_cpu.storage()))
        self.assertRaises(RuntimeError,
                          lambda: f_cpu.set_(d_cpu.storage(), 0, d_cpu.size(), d_cpu.stride()))
        self.assertRaises(RuntimeError, lambda: f_cpu.set_(d_cpu))

        # change device
        if torch.cuda.is_available():
            f_cuda = torch.randn((2, 3), dtype=torch.float32, device='cuda')

            # cpu -> cuda
            self.assertRaises(RuntimeError, lambda: f_cpu.set_(f_cuda.storage()))
            self.assertRaises(RuntimeError,
                              lambda: f_cpu.set_(f_cuda.storage(), 0, f_cuda.size(), f_cuda.stride()))
            self.assertRaises(RuntimeError, lambda: f_cpu.set_(f_cuda))

            # cuda -> cpu
            self.assertRaises(RuntimeError, lambda: f_cuda.set_(f_cpu.storage()))
            self.assertRaises(RuntimeError,
                              lambda: f_cuda.set_(f_cpu.storage(), 0, f_cpu.size(), f_cpu.stride()))
            self.assertRaises(RuntimeError, lambda: f_cuda.set_(f_cpu))

    def test_equal(self):
        # Contiguous, 1D
        t1 = torch.Tensor((3, 4, 9, 10))
        t2 = t1.contiguous()
        t3 = torch.Tensor((1, 9, 3, 10))
        t4 = torch.Tensor((3, 4, 9))
        t5 = torch.Tensor()
        self.assertTrue(t1.equal(t2))
        self.assertFalse(t1.equal(t3))
        self.assertFalse(t1.equal(t4))
        self.assertFalse(t1.equal(t5))
        self.assertTrue(torch.equal(t1, t2))
        self.assertFalse(torch.equal(t1, t3))
        self.assertFalse(torch.equal(t1, t4))
        self.assertFalse(torch.equal(t1, t5))

        # Non contiguous, 2D
        s = torch.Tensor(((1, 2, 3, 4), (5, 6, 7, 8)))
        s1 = s[:, 1:3]
        s2 = s1.clone()
        s3 = torch.Tensor(((2, 3), (6, 7)))
        s4 = torch.Tensor(((0, 0), (0, 0)))

        self.assertFalse(s1.is_contiguous())
        self.assertTrue(s1.equal(s2))
        self.assertTrue(s1.equal(s3))
        self.assertFalse(s1.equal(s4))
        self.assertTrue(torch.equal(s1, s2))
        self.assertTrue(torch.equal(s1, s3))
        self.assertFalse(torch.equal(s1, s4))

    def test_element_size(self):
        byte = torch.ByteStorage().element_size()
        char = torch.CharStorage().element_size()
        short = torch.ShortStorage().element_size()
        int = torch.IntStorage().element_size()
        long = torch.LongStorage().element_size()
        float = torch.FloatStorage().element_size()
        double = torch.DoubleStorage().element_size()
        bool = torch.BoolStorage().element_size()
        bfloat16 = torch.BFloat16Storage().element_size()

        self.assertEqual(byte, torch.ByteTensor().element_size())
        self.assertEqual(char, torch.CharTensor().element_size())
        self.assertEqual(short, torch.ShortTensor().element_size())
        self.assertEqual(int, torch.IntTensor().element_size())
        self.assertEqual(long, torch.LongTensor().element_size())
        self.assertEqual(float, torch.FloatTensor().element_size())
        self.assertEqual(double, torch.DoubleTensor().element_size())
        self.assertEqual(bool, torch.BoolTensor().element_size())

        self.assertGreater(byte, 0)
        self.assertGreater(char, 0)
        self.assertGreater(short, 0)
        self.assertGreater(int, 0)
        self.assertGreater(long, 0)
        self.assertGreater(float, 0)
        self.assertGreater(double, 0)
        self.assertGreater(bool, 0)
        self.assertGreater(bfloat16, 0)

        # These tests are portable, not necessarily strict for your system.
        self.assertEqual(byte, 1)
        self.assertEqual(char, 1)
        self.assertEqual(bool, 1)
        self.assertGreaterEqual(short, 2)
        self.assertGreaterEqual(int, 2)
        self.assertGreaterEqual(int, short)
        self.assertGreaterEqual(long, 4)
        self.assertGreaterEqual(long, int)
        self.assertGreaterEqual(double, float)

    def test_split(self):
        tensor = torch.rand(7, 4)
        split_size = 3
        dim = 0
        target_sizes = ([3, 4], [3, 4], [1, 4])
        splits = tensor.split(split_size, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        # Variable sections split
        tensor = torch.randn(20, 10)
        dim = 0
        split_sizes = [5, 5, 10]
        target_sizes = ([[5, 10], [5, 10], [10, 10]])
        splits = tensor.split(split_sizes, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        split_sizes = [2, 2, 6]
        target_sizes = ([20, 2], [20, 2], [20, 6])
        dim = 1
        splits = tensor.split(split_sizes, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

    def test_chunk(self):
        tensor = torch.rand(4, 7)
        num_chunks = 3
        dim = 1
        target_sizes = ([4, 3], [4, 3], [4, 1])
        splits = tensor.chunk(num_chunks, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        # Invalid chunk sizes
        error_regex = 'chunk expects.*greater than 0'
        with self.assertRaisesRegex(RuntimeError, error_regex):
            tensor.chunk(0)
        with self.assertRaisesRegex(RuntimeError, error_regex):
            tensor.chunk(-2)

    def test_tolist(self):
        list0D = []
        tensor0D = torch.Tensor(list0D)
        self.assertEqual(tensor0D.tolist(), list0D)

        table1D = [1, 2, 3]
        tensor1D = torch.Tensor(table1D)
        storage = torch.Storage(table1D)
        self.assertEqual(tensor1D.tolist(), table1D)
        self.assertEqual(storage.tolist(), table1D)
        self.assertEqual(tensor1D.tolist(), table1D)
        self.assertEqual(storage.tolist(), table1D)

        table2D = [[1, 2], [3, 4]]
        tensor2D = torch.Tensor(table2D)
        self.assertEqual(tensor2D.tolist(), table2D)

        tensor3D = torch.Tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
        tensorNonContig = tensor3D.select(1, 1)
        self.assertFalse(tensorNonContig.is_contiguous())
        self.assertEqual(tensorNonContig.tolist(), [[3, 4], [7, 8]])

    def test_permute(self):
        orig = [1, 2, 3, 4, 5, 6, 7]
        perm = torch.randperm(7).tolist()
        x = torch.Tensor(*orig).fill_(0)
        new = list(map(lambda x: x - 1, x.permute(*perm).size()))
        self.assertEqual(perm, new)
        self.assertEqual(x.size(), orig)

    def test_reversed(self):
        val = torch.arange(0, 10)
        self.assertEqual(reversed(val), torch.arange(9, -1, -1))

        val = torch.arange(1, 10).view(3, 3)
        self.assertEqual(reversed(val), torch.tensor([[7, 8, 9], [4, 5, 6], [1, 2, 3]]))

        val = torch.tensor(42)
        self.assertEqual(reversed(val), torch.tensor(42))

    def test_contains(self):
        x = torch.arange(0, 10)
        self.assertEqual(4 in x, True)
        self.assertEqual(12 in x, False)

        x = torch.arange(1, 10).view(3, 3)
        val = torch.arange(1, 4)
        self.assertEqual(val in x, True)
        val += 10
        self.assertEqual(val in x, False)

        self.assertRaisesRegex(
            RuntimeError,
            "Tensor.__contains__ only supports Tensor or scalar, but you passed in a {}.".format(type("foo")),
            lambda: "foo" in x)
        self.assertRaisesRegex(
            RuntimeError,
            "Tensor.__contains__ only supports Tensor or scalar, but you passed in a {}.".format(type([1, 2])),
            lambda: [1, 2] in x)

    def test_storage(self):
        v = torch.randn(3, 5)
        self.assertEqual(v.storage()[0], v.data[0][0])
        self.assertEqual(v.storage()[14], v.data[2][4])

    def test_deepcopy(self):
        from copy import deepcopy
        a = torch.randn(5, 5)
        b = torch.randn(5, 5)
        c = a.view(25)
        q = [a, [a.storage(), b.storage()], b, c]
        w = deepcopy(q)
        self.assertEqual(w[0], q[0], 0)
        self.assertEqual(w[1][0], q[1][0], 0)
        self.assertEqual(w[1][1], q[1][1], 0)
        self.assertEqual(w[1], q[1], 0)
        self.assertEqual(w[2], q[2], 0)

        # Check that deepcopy preserves sharing
        w[0].add_(1)
        for i in range(a.numel()):
            self.assertEqual(w[1][0][i], q[1][0][i] + 1)
        self.assertEqual(w[3], c + 1)
        w[2].sub_(1)
        for i in range(a.numel()):
            self.assertEqual(w[1][1][i], q[1][1][i] - 1)

    def test_deepcopy_scalar(self):
        from copy import deepcopy
        a = torch.tensor(5)
        self.assertEqual(a.size(), deepcopy(a).size())
        self.assertEqual(a, deepcopy(a))

    def test_deepcopy_parameter(self):
        from copy import deepcopy
        l = torch.nn.Linear(10, 1)
        s = l.state_dict(keep_vars=True)
        self.assertEqual(torch.nn.Parameter, type(s['weight']))
        self.assertEqual(torch.nn.Parameter, type(s['bias']))

        s2 = deepcopy(s)
        self.assertEqual(torch.nn.Parameter, type(s2['weight']))
        self.assertEqual(torch.nn.Parameter, type(s2['bias']))

    def test_pickle(self):
        if sys.version_info[0] == 2:
            import cPickle as pickle
        else:
            import pickle
        a = torch.randn(5, 5)
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertEqual(a, b)

    def test_pickle_parameter(self):
        if sys.version_info[0] == 2:
            import cPickle as pickle
        else:
            import pickle
        a = torch.nn.Parameter(torch.randn(5, 5))
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.nn.Parameter))
        self.assertEqual(a.requires_grad, b.requires_grad)
        self.assertEqual(a, b)

    def test_pickle_parameter_no_requires_grad(self):
        if sys.version_info[0] == 2:
            import cPickle as pickle
        else:
            import pickle
        a = torch.nn.Parameter(torch.randn(5, 5), requires_grad=False)
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.nn.Parameter))
        self.assertEqual(a.requires_grad, b.requires_grad)
        self.assertEqual(a, b)

    def test_pickle_dtype(self):
        t = torch.float32
        serialized = pickle.dumps(t)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.dtype))
        self.assertEqual(id(b), id(t))

    def test_pickle_size(self):
        a = torch.rand(10).size()
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.Size))
        self.assertEqual(a, b)

    def test_norm_fastpaths(self):
        x = torch.randn(3, 5)

        # slow path
        result = torch.norm(x, 4.5, 1)
        expected = torch.pow(x.abs().pow(4.5).sum(1), 1.0 / 4.5)
        self.assertEqual(result, expected)

        # fast 0-norm
        result = torch.norm(x, 0, 1)
        expected = (x != 0).type_as(x).sum(1)
        self.assertEqual(result, expected)

        # fast 1-norm
        result = torch.norm(x, 1, 1)
        expected = x.abs().sum(1)
        self.assertEqual(result, expected)

        # fast 2-norm
        result = torch.norm(x, 2, 1)
        expected = torch.sqrt(x.pow(2).sum(1))
        self.assertEqual(result, expected)

        # fast 3-norm
        result = torch.norm(x, 3, 1)
        expected = torch.pow(x.pow(3).abs().sum(1), 1.0 / 3.0)
        self.assertEqual(result, expected)

    @staticmethod
    def _test_bernoulli(self, t_dtype, p_dtype, device):
        for trivial_p in ([0, 1], [1, 0, 1, 1, 0, 1]):
            x = torch.tensor(trivial_p, dtype=p_dtype, device=device)
            self.assertEqual(x.bernoulli().tolist(), trivial_p)

        def isBinary(t):
            return torch.ne(t, 0).mul_(torch.ne(t, 1)).sum().item() == 0

        p = torch.rand(5, 5, dtype=p_dtype, device=device)
        self.assertTrue(isBinary(p.bernoulli()))

        p = torch.rand(5, dtype=p_dtype, device=device).expand(5, 5)
        self.assertTrue(isBinary(p.bernoulli()))

        p = torch.rand(5, 5, dtype=p_dtype, device=device)
        torch.bernoulli(torch.rand_like(p), out=p)
        self.assertTrue(isBinary(p))

        p = torch.rand(5, dtype=p_dtype, device=device).expand(5, 5)
        torch.bernoulli(torch.rand_like(p), out=p)
        self.assertTrue(isBinary(p))

        t = torch.empty(10, 10, dtype=t_dtype, device=device)

        t.fill_(2)
        t.bernoulli_(0.5)
        self.assertTrue(isBinary(t))

        p = torch.rand(10, dtype=p_dtype, device=device).expand(10, 10)
        t.fill_(2)
        t.bernoulli_(p)
        self.assertTrue(isBinary(t))

        t.fill_(2)
        torch.bernoulli(torch.rand_like(t, dtype=p_dtype), out=t)
        self.assertTrue(isBinary(t))

        t.fill_(2)
        t.bernoulli_(torch.rand_like(t, dtype=p_dtype))
        self.assertTrue(isBinary(t))

    def test_bernoulli(self):
        self._test_bernoulli(self, torch.float32, torch.float64, 'cpu')
        # test that it works with integral tensors
        self._test_bernoulli(self, torch.uint8, torch.float64, 'cpu')
        # test that it works with bool tensors
        self._test_bernoulli(self, torch.bool, torch.float32, 'cpu')

    def test_bernoulli_edge_cases(self):
        # Need to draw a lot of samples to cover every random floating point number.
        a = torch.zeros(10000, 10000, dtype=torch.float32)  # probability of drawing "1" is 0
        num_ones = (torch.bernoulli(a) == 1).sum()
        self.assertEqual(num_ones, 0)

        b = torch.ones(10000, 10000, dtype=torch.float32)  # probability of drawing "1" is 1
        num_zeros = (torch.bernoulli(b) == 0).sum()
        self.assertEqual(num_zeros, 0)

    def test_generator_cpu(self):
        # test default generators are equal
        self.assertEqual(torch.default_generator, torch.default_generator)

        # tests Generator API
        # manual_seed, seed, initial_seed, get_state, set_state
        g1 = torch.Generator()
        g2 = torch.Generator()
        g1.manual_seed(12345)
        g2.manual_seed(12345)
        self.assertEqual(g1.initial_seed(), g2.initial_seed())

        g1.seed()
        g2.seed()
        self.assertNotEqual(g1.initial_seed(), g2.initial_seed())

        g1 = torch.Generator()
        g2_state = g2.get_state()
        g2_randn = torch.randn(1, generator=g2)
        g1.set_state(g2_state)
        g1_randn = torch.randn(1, generator=g1)
        self.assertEqual(g1_randn, g2_randn)

        default_state = torch.default_generator.get_state()
        q = torch.Tensor(100)
        g1_normal = q.normal_()
        g2 = torch.Generator()
        g2.set_state(default_state)
        g2_normal = q.normal_(generator=g2)
        self.assertEqual(g1_normal, g2_normal)

    def test_sobolengine_unscrambled_lowdim(self):
        engine_1d = torch.quasirandom.SobolEngine(1)
        expected_1d = torch.tensor([0.5, 0.75, 0.25, 0.375, 0.875, 0.625, 0.125, 0.1875, 0.6875, 0.9375])
        actual_1d = engine_1d.draw(10)
        self.assertEqual(actual_1d.view(-1), expected_1d)
        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))

        # Test out kwarg
        engine_1d.reset()
        actual_1d_out = torch.Tensor().float()
        engine_1d.draw(10, out=actual_1d_out)
        self.assertEqual(actual_1d.view(-1), expected_1d)

        engine_3d = torch.quasirandom.SobolEngine(3)
        expected_3d = torch.tensor([0.5, 0.75, 0.25, 0.625, 0.125, 0.375, 0.875, 0.3125, 0.8125, 0.5625])
        actual_3d = engine_3d.draw(10)
        self.assertEqual(actual_3d[:, 2], expected_3d)
        self.assertEqual(actual_3d[:, 0], expected_1d)
        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))

        engine_3d = torch.quasirandom.SobolEngine(3)
        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
        self.assertEqual(draws, actual_3d)

        engine_3d = torch.quasirandom.SobolEngine(3).fast_forward(5)
        draws = engine_3d.draw(5)
        self.assertEqual(draws, actual_3d[5:])
        engine_3d.reset()
        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
        engine_3d.fast_forward(2)
        self.assertEqual(engine_3d.draw(5), actual_3d[5:])

    def test_sobolengine_unscrambled_highdim(self):
        from collections import Counter
        engine = torch.quasirandom.SobolEngine(1111)
        count1 = dict(Counter(engine.draw().view(-1).tolist()))
        count2 = dict(Counter(engine.draw().view(-1).tolist()))
        count3 = dict(Counter(engine.draw().view(-1).tolist()))
        self.assertTrue(count1 == {0.5: 1111})
        self.assertTrue(count2 == {0.25: 580, 0.75: 531})
        self.assertTrue(count3 == {0.25: 531, 0.75: 580})

        engine = torch.quasirandom.SobolEngine(1111)
        draws = engine.draw(1000)
        self.assertTrue(torch.all(draws <= 1))
        self.assertTrue(torch.all(draws >= 0))

    def test_sobolengine_scrambled_lowdim(self):
        engine_1d = torch.quasirandom.SobolEngine(1, scramble=True, seed=1729)
        expected_1d = [0.16478512, 0.43221009, 0.84261382, 0.99750268, 0.27460563,
                       0.01084163, 0.73373985, 0.65039611, 0.12329865, 0.35587373]
        actual_1d = engine_1d.draw(10)
        self.assertEqual(actual_1d.flatten(), torch.tensor(expected_1d))
        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))
        # make sure random seed if chosen if none is provided
        engine_1d_a = torch.quasirandom.SobolEngine(1, scramble=True)
        engine_1d_b = torch.quasirandom.SobolEngine(1, scramble=True)
        self.assertNotEqual(engine_1d_a.draw(2), engine_1d_b.draw(2))

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        expected_3d = [0.32642800, 0.17881306, 0.68837059, 0.46492538, 0.91789097,
                       0.58075899, 0.03642474, 0.68229187, 0.20051685, 0.30083340]
        actual_3d = engine_3d.draw(10)
        self.assertEqual(actual_3d[:, 2], torch.tensor(expected_3d))
        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
        self.assertEqual(draws, actual_3d)

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        engine_3d.fast_forward(5)
        draws = engine_3d.draw(5)
        self.assertEqual(draws, actual_3d[5:])
        engine_3d.reset()
        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
        engine_3d.fast_forward(2)
        self.assertEqual(engine_3d.draw(5), actual_3d[5:])

    def test_sobolengine_scrambled_highdim(self):
        engine = torch.quasirandom.SobolEngine(1111, scramble=True)
        draws = engine.draw(1000)
        self.assertTrue(torch.all(draws <= 1))
        self.assertTrue(torch.all(draws >= 0))

    def test_parsing_int64(self):
        # accepts integer arguments
        x = torch.cumsum(torch.ones(5, 5), 0)
        self.assertEqual(x, torch.cumsum(torch.ones(5, 5), torch.tensor(0)))
        # doesn't accept floating point variables
        self.assertRaises(TypeError, lambda: torch.cumsum(torch.ones(5, 5), torch.tensor(0.)))

    def test_parsing_double(self):
        # accepts floating point and integer arguments
        x = torch.randn(2, 3)
        torch.isclose(x, x, 1, 1)
        self.assertTrue(torch.isclose(x, x, 1, 1).all())
        self.assertTrue(torch.isclose(x, x, 1.5, 1.).all())
        # accepts floating point and integer tensors
        self.assertTrue(torch.isclose(x, x, torch.tensor(1), torch.tensor(1)).all())
        self.assertTrue(torch.isclose(x, x, torch.tensor(1.5), torch.tensor(1.)).all())
        # doesn't accept variables with requires_grad
        self.assertRaises(TypeError,
                          lambda: torch.isclose(x, x, torch.tensor(1.5), torch.tensor(1., requires_grad=True)).all())

    def test_parsing_intlist(self):
        #  parse with integer variables
        self.assertEqual(torch.Size([3, 4]), torch.ones((torch.tensor(3), torch.tensor(4))).shape)
        self.assertEqual(torch.Size([3, 4]), torch.ones(torch.tensor(3), torch.tensor(4)).shape)
        # parse with numpy integers
        if TEST_NUMPY:
            self.assertEqual(torch.Size([3, 4]), torch.ones((np.array(3), np.int64(4))).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones(np.array(3), np.int64(4)).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones((np.int64(3), np.array(4))).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones(np.int64(3), np.array(4)).shape)

        # fail parse with float variables
        self.assertRaises(TypeError, lambda: torch.ones((torch.tensor(3.), torch.tensor(4))))
        # fail parse with numpy floats
        if TEST_NUMPY:
            self.assertRaises(TypeError, lambda: torch.ones((np.float(3.), torch.tensor(4))))
            self.assertRaises(TypeError, lambda: torch.ones((np.array(3.), torch.tensor(4))))

        # fail parse with > 1 element variables
        self.assertRaises(TypeError, lambda: torch.ones(torch.tensor(3, 3)))
        self.assertRaises(TypeError, lambda: torch.ones((torch.tensor(3, 3))))
        if TEST_NUMPY:
            self.assertRaises(TypeError, lambda: torch.ones(np.array(3, 3)))
            self.assertRaises(TypeError, lambda: torch.ones((np.array(3, 3))))

        # fail parse with additional positional args after intlist arg
        self.assertRaisesRegex(TypeError,
                               "received an invalid combination of arguments",
                               lambda: torch.LongTensor((6, 0), 1, 1, 0))
        self.assertRaisesRegex(TypeError,
                               "missing 1 required positional arguments",
                               lambda: torch.tensor().new_zeros((5, 5), 0))

    def _test_serialization_data(self):
        a = [torch.randn(5, 5).float() for i in range(2)]
        b = [a[i % 2] for i in range(4)]  # 0-3
        b += [a[0].storage()]  # 4
        b += [a[0].reshape(-1)[1:4].storage()]  # 5
        b += [torch.arange(1, 11).int()]  # 6
        t1 = torch.FloatTensor().set_(a[0].reshape(-1)[1:4].clone().storage(), 0, (3,), (1,))
        t2 = torch.FloatTensor().set_(a[0].reshape(-1)[1:4].clone().storage(), 0, (3,), (1,))
        b += [(t1.storage(), t1.storage(), t2.storage())]  # 7
        b += [a[0].reshape(-1)[0:2].storage()]  # 8
        return b

    def _test_serialization_assert(self, b, c):
        self.assertEqual(b, c, 0)
        self.assertTrue(isinstance(c[0], torch.FloatTensor))
        self.assertTrue(isinstance(c[1], torch.FloatTensor))
        self.assertTrue(isinstance(c[2], torch.FloatTensor))
        self.assertTrue(isinstance(c[3], torch.FloatTensor))
        self.assertTrue(isinstance(c[4], torch.FloatStorage))
        c[0].fill_(10)
        self.assertEqual(c[0], c[2], 0)
        self.assertEqual(c[4], torch.FloatStorage(25).fill_(10), 0)
        c[1].fill_(20)
        self.assertEqual(c[1], c[3], 0)
        # I have to do it in this roundabout fashion, because there's no
        # way to slice storages
        for i in range(4):
            self.assertEqual(c[4][i + 1], c[5][i])

        # check that serializing the same storage view object unpickles
        # it as one object not two (and vice versa)
        views = c[7]
        self.assertEqual(views[0]._cdata, views[1]._cdata)
        self.assertEqual(views[0], views[2])
        self.assertNotEqual(views[0]._cdata, views[2]._cdata)

        rootview = c[8]
        self.assertEqual(rootview.data_ptr(), c[0].data_ptr())

    def test_serialization(self):
        # Test serialization with a real file
        b = self._test_serialization_data()
        for use_name in (False, True):
            # Passing filename to torch.save(...) will cause the file to be opened twice,
            # which is not supported on Windows
            if sys.platform == "win32" and use_name:
                continue
            with tempfile.NamedTemporaryFile() as f:
                handle = f if not use_name else f.name
                torch.save(b, handle)
                f.seek(0)
                c = torch.load(handle)
            self._test_serialization_assert(b, c)
        # test non-ascii encoding of bytes arrays/strings
        # The following bytes are produced by serializing
        #   [b'\xc5\xbc\xc4\x85\xc4\x85\xc3\xb3\xc5\xbc\xc4\x85\xc5\xbc', torch.zeros(1, dtype=torch.float), 2]
        # in Python 2.7.12 and PyTorch 0.4.1, where the first element contains
        # bytes of some utf-8 characters (i.e., `utf8_str.encode('utf-8')`).
        serialized = (
            b'\x80\x02\x8a\nl\xfc\x9cF\xf9 j\xa8P\x19.\x80\x02M\xe9\x03.'
            b'\x80\x02}q\x01(U\x10protocol_versionq\x02M\xe9\x03U\n'
            b'type_sizesq\x03}q\x04(U\x03intq\x05K\x04U\x05shortq\x06K\x02U'
            b'\x04longq\x07K\x04uU\rlittle_endianq\x08\x88u.\x80\x02]q'
            b'\x01(U\x0e\xc5\xbc\xc4\x85\xc4\x85\xc3\xb3\xc5\xbc\xc4\x85'
            b'\xc5\xbcq\x02ctorch._utils\n_rebuild_tensor_v2\nq\x03((U'
            b'\x07storageq\x04ctorch\nFloatStorage\nq\x05U\x0845640624q'
            b'\x06U\x03cpuq\x07\x8a\x01\x01NtQK\x00K\x01\x85K\x01\x85'
            b'\x89NtRq\x08K\x02e.\x80\x02]q\x01U\x0845640624q\x02a.\x01\x00'
            b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00'
        )
        buf = io.BytesIO(serialized)
        utf8_bytes = b'\xc5\xbc\xc4\x85\xc4\x85\xc3\xb3\xc5\xbc\xc4\x85\xc5\xbc'
        utf8_str = utf8_bytes.decode('utf-8')
        if PY3:
            loaded_utf8 = torch.load(buf, encoding='utf-8')
            self.assertEqual(loaded_utf8, [utf8_str, torch.zeros(1, dtype=torch.float), 2])
            buf.seek(0)
            loaded_bytes = torch.load(buf, encoding='bytes')
        else:
            loaded_bytes = torch.load(buf)
        self.assertEqual(loaded_bytes, [utf8_bytes, torch.zeros(1, dtype=torch.float), 2])

    def test_serialization_filelike(self):
        # Test serialization (load and save) with a filelike object
        b = self._test_serialization_data()
        with BytesIOContext() as f:
            torch.save(b, f)
            f.seek(0)
            c = torch.load(f)
        self._test_serialization_assert(b, c)

    @unittest.skipIf(IS_WINDOWS, "TODO: need to fix this test case for Windows")
    def test_serialization_fake_zip(self):
        data = [
            ord('P'),
            ord('K'),
            5,
            6
        ]
        for i in range(0, 100):
            data.append(0)
        t = torch.tensor(data, dtype=torch.uint8)

        with tempfile.NamedTemporaryFile() as f:
            torch.save(t, f.name)

            # If this check is False for all Python versions (i.e. the fix
            # has been backported), this test and torch.serialization._is_zipfile
            # can be deleted
            self.assertTrue(zipfile.is_zipfile(f))
            self.assertFalse(torch.serialization._is_zipfile(f))
            self.assertEqual(torch.load(f.name), t)

    def test_serialization_gzip(self):
        # Test serialization with gzip file
        b = self._test_serialization_data()
        f1 = tempfile.NamedTemporaryFile(delete=False)
        f2 = tempfile.NamedTemporaryFile(delete=False)
        torch.save(b, f1)
        with open(f1.name, 'rb') as f_in, gzip.open(f2.name, 'wb') as f_out:
            shutil.copyfileobj(f_in, f_out)

        with gzip.open(f2.name, 'rb') as f:
            c = torch.load(f)
        self._test_serialization_assert(b, c)

    def test_serialization_offset(self):
        a = torch.randn(5, 5)
        b = torch.randn(1024, 1024, 512, dtype=torch.float32)
        m = torch.nn.Conv2d(1, 1, (1, 3))
        i, j = 41, 43
        with tempfile.NamedTemporaryFile() as f:
            pickle.dump(i, f)
            torch.save(a, f)
            pickle.dump(j, f)
            torch.save(b, f)
            torch.save(m, f)
            self.assertTrue(f.tell() > 2 * 1024 * 1024 * 1024)
            f.seek(0)
            i_loaded = pickle.load(f)
            a_loaded = torch.load(f)
            j_loaded = pickle.load(f)
            b_loaded = torch.load(f)
            m_loaded = torch.load(f)
        self.assertTrue(torch.equal(a, a_loaded))
        self.assertTrue(torch.equal(b, b_loaded))
        self.assertTrue(m.kernel_size == m_loaded.kernel_size)
        self.assertEqual(i, i_loaded)
        self.assertEqual(j, j_loaded)

    def test_serialization_offset_filelike(self):
        a = torch.randn(5, 5)
        b = torch.randn(1024, 1024, 512, dtype=torch.float32)
        i, j = 41, 43
        with BytesIOContext() as f:
            pickle.dump(i, f)
            torch.save(a, f)
            pickle.dump(j, f)
            torch.save(b, f)
            self.assertTrue(f.tell() > 2 * 1024 * 1024 * 1024)
            f.seek(0)
            i_loaded = pickle.load(f)
            a_loaded = torch.load(f)
            j_loaded = pickle.load(f)
            b_loaded = torch.load(f)
        self.assertTrue(torch.equal(a, a_loaded))
        self.assertTrue(torch.equal(b, b_loaded))
        self.assertEqual(i, i_loaded)
        self.assertEqual(j, j_loaded)

    def test_serialization_offset_gzip(self):
        a = torch.randn(5, 5)
        i = 41
        f1 = tempfile.NamedTemporaryFile(delete=False)
        f2 = tempfile.NamedTemporaryFile(delete=False)
        with open(f1.name, 'wb') as f:
            pickle.dump(i, f)
            torch.save(a, f)
        with open(f1.name, 'rb') as f_in, gzip.open(f2.name, 'wb') as f_out:
            shutil.copyfileobj(f_in, f_out)

        with gzip.open(f2.name, 'rb') as f:
            j = pickle.load(f)
            b = torch.load(f)
        self.assertTrue(torch.equal(a, b))
        self.assertEqual(i, j)

    def test_half_tensor(self):
        x = torch.randn(5, 5).float()
        y = torch.randn(5, 5).float()
        xh, yh = x.half(), y.half()

        self.assertEqual(x.half().float(), x, 1e-3)

        z = torch.Tensor(5, 5)
        self.assertEqual(z.copy_(xh), x, 1e-3)

        with tempfile.NamedTemporaryFile() as f:
            torch.save(xh, f)
            f.seek(0)
            xh2 = torch.load(f)
            self.assertEqual(xh.float(), xh2.float())

    def test_serialize_device(self):
        device_str = ['cpu', 'cpu:0', 'cuda', 'cuda:0']
        device_obj = [torch.device(d) for d in device_str]
        for device in device_obj:
            device_copied = copy.deepcopy(device)
            self.assertEqual(device, device_copied)

    def test_serialization_backwards_compat(self):
        a = [torch.arange(1 + i, 26 + i).view(5, 5).float() for i in range(2)]
        b = [a[i % 2] for i in range(4)]
        b += [a[0].storage()]
        b += [a[0].reshape(-1)[1:4].clone().storage()]
        path = download_file('https://download.pytorch.org/test_data/legacy_serialized.pt')
        c = torch.load(path)
        self.assertEqual(b, c, 0)
        self.assertTrue(isinstance(c[0], torch.FloatTensor))
        self.assertTrue(isinstance(c[1], torch.FloatTensor))
        self.assertTrue(isinstance(c[2], torch.FloatTensor))
        self.assertTrue(isinstance(c[3], torch.FloatTensor))
        self.assertTrue(isinstance(c[4], torch.FloatStorage))
        c[0].fill_(10)
        self.assertEqual(c[0], c[2], 0)
        self.assertEqual(c[4], torch.FloatStorage(25).fill_(10), 0)
        c[1].fill_(20)
        self.assertEqual(c[1], c[3], 0)

        # test some old tensor serialization mechanism
        class OldTensorBase(object):
            def __init__(self, new_tensor):
                self.new_tensor = new_tensor

            def __getstate__(self):
                return (self.new_tensor.storage(),
                        self.new_tensor.storage_offset(),
                        tuple(self.new_tensor.size()),
                        self.new_tensor.stride())

        class OldTensorV1(OldTensorBase):
            def __reduce__(self):
                return (torch.Tensor, (), self.__getstate__())

        class OldTensorV2(OldTensorBase):
            def __reduce__(self):
                return (_rebuild_tensor, self.__getstate__())

        x = torch.randn(30).as_strided([2, 3], [9, 3], 2)
        for old_cls in [OldTensorV1, OldTensorV2]:
            with tempfile.NamedTemporaryFile() as f:
                old_x = old_cls(x)
                torch.save(old_x, f)
                f.seek(0)
                load_x = torch.load(f)
                self.assertEqual(x.storage(), load_x.storage())
                self.assertEqual(x.storage_offset(), load_x.storage_offset())
                self.assertEqual(x.size(), load_x.size())
                self.assertEqual(x.stride(), load_x.stride())

    # unique_key is necessary because on Python 2.7, if a warning passed to
    # the warning module is the same, it is not raised again.
    def _test_serialization_container(self, unique_key, filecontext_lambda):
        tmpmodule_name = 'tmpmodule{}'.format(unique_key)

        def import_module(name, filename):
            if sys.version_info >= (3, 5):
                import importlib.util
                spec = importlib.util.spec_from_file_location(name, filename)
                module = importlib.util.module_from_spec(spec)
                spec.loader.exec_module(module)
            else:
                import imp
                module = imp.load_source(name, filename)
            sys.modules[module.__name__] = module
            return module

        with filecontext_lambda() as checkpoint:
            fname = get_file_path_2(os.path.dirname(__file__), 'data', 'network1.py')
            module = import_module(tmpmodule_name, fname)
            torch.save(module.Net(), checkpoint)

            # First check that the checkpoint can be loaded without warnings
            checkpoint.seek(0)
            with warnings.catch_warnings(record=True) as w:
                loaded = torch.load(checkpoint)
                self.assertTrue(isinstance(loaded, module.Net))
                if can_retrieve_source:
                    self.assertEquals(len(w), 0)

            # Replace the module with different source
            fname = get_file_path_2(os.path.dirname(__file__), 'data', 'network2.py')
            module = import_module(tmpmodule_name, fname)
            checkpoint.seek(0)
            with warnings.catch_warnings(record=True) as w:
                loaded = torch.load(checkpoint)
                self.assertTrue(isinstance(loaded, module.Net))
                if can_retrieve_source:
                    self.assertEquals(len(w), 1)
                    self.assertTrue(w[0].category, 'SourceChangeWarning')

    def test_serialization_container(self):
        self._test_serialization_container('file', tempfile.NamedTemporaryFile)

    def test_serialization_container_filelike(self):
        self._test_serialization_container('filelike', BytesIOContext)

    def test_serialization_map_location(self):
        test_file_path = download_file('https://download.pytorch.org/test_data/gpu_tensors.pt')

        def map_location(storage, loc):
            return storage

        def load_bytes():
            with open(test_file_path, 'rb') as f:
                return io.BytesIO(f.read())

        fileobject_lambdas = [lambda: test_file_path, load_bytes]
        cpu_map_locations = [
            map_location,
            {'cuda:0': 'cpu'},
            'cpu',
            torch.device('cpu'),
        ]
        gpu_0_map_locations = [
            {'cuda:0': 'cuda:0'},
            'cuda',
            'cuda:0',
            torch.device('cuda'),
            torch.device('cuda', 0)
        ]
        gpu_last_map_locations = [
            'cuda:{}'.format(torch.cuda.device_count() - 1),
        ]

        def check_map_locations(map_locations, tensor_class, intended_device):
            for fileobject_lambda in fileobject_lambdas:
                for map_location in map_locations:
                    tensor = torch.load(fileobject_lambda(), map_location=map_location)

                    self.assertEqual(tensor.device, intended_device)
                    self.assertIsInstance(tensor, tensor_class)
                    self.assertEqual(tensor, tensor_class([[1.0, 2.0], [3.0, 4.0]]))

        check_map_locations(cpu_map_locations, torch.FloatTensor, torch.device('cpu'))
        if torch.cuda.is_available():
            check_map_locations(gpu_0_map_locations, torch.cuda.FloatTensor, torch.device('cuda', 0))
            check_map_locations(
                gpu_last_map_locations,
                torch.cuda.FloatTensor,
                torch.device('cuda', torch.cuda.device_count() - 1)
            )

    @unittest.skipIf(torch.cuda.is_available(), "Testing torch.load on CPU-only machine")
    @unittest.skipIf(not PY3, "Test tensors were serialized using python 3")
    def test_load_nonexistent_device(self):
        # Setup: create a serialized file object with a 'cuda:0' restore location
        # The following was generated by saving a torch.randn(2, device='cuda') tensor.
        serialized = (b'\x80\x02\x8a\nl\xfc\x9cF\xf9 j\xa8P\x19.\x80\x02M\xe9'
                      b'\x03.\x80\x02}q\x00(X\x10\x00\x00\x00protocol_versionq'
                      b'\x01M\xe9\x03X\r\x00\x00\x00little_endianq\x02\x88X\n'
                      b'\x00\x00\x00type_sizesq\x03}q\x04(X\x05\x00\x00\x00shortq'
                      b'\x05K\x02X\x03\x00\x00\x00intq\x06K\x04X\x04\x00\x00\x00'
                      b'longq\x07K\x04uu.\x80\x02ctorch._utils\n_rebuild_tensor_v2'
                      b'\nq\x00((X\x07\x00\x00\x00storageq\x01ctorch\nFloatStorage'
                      b'\nq\x02X\x0e\x00\x00\x0094919395964320q\x03X\x06\x00\x00'
                      b'\x00cuda:0q\x04K\x02Ntq\x05QK\x00K\x02\x85q\x06K\x01\x85q'
                      b'\x07\x89Ntq\x08Rq\t.\x80\x02]q\x00X\x0e\x00\x00\x00'
                      b'94919395964320q\x01a.\x02\x00\x00\x00\x00\x00\x00\x00\xbb'
                      b'\x1f\x82\xbe\xea\x81\xd1>')

        buf = io.BytesIO(serialized)

        error_msg = r'Attempting to deserialize object on a CUDA device'
        with self.assertRaisesRegex(RuntimeError, error_msg):
            _ = torch.load(buf)

    def test_serialization_filelike_api_requirements(self):
        filemock = FilelikeMock(b'', has_readinto=False)
        tensor = torch.randn(3, 5)
        torch.save(tensor, filemock)
        expected_superset = {'write', 'flush'}
        self.assertTrue(expected_superset.issuperset(filemock.calls))

        # Reset between save and load
        filemock.seek(0)
        filemock.calls.clear()

        _ = torch.load(filemock)
        expected_superset = {'read', 'readline', 'seek', 'tell'}
        self.assertTrue(expected_superset.issuperset(filemock.calls))

    def _test_serialization_filelike(self, tensor, mock, desc):
        f = mock(b'')
        torch.save(tensor, f)
        f.seek(0)
        data = mock(f.read())

        msg = 'filelike serialization with {}'

        b = torch.load(data)
        self.assertTrue(torch.equal(tensor, b), msg.format(desc))

    def test_serialization_filelike_missing_attrs(self):
        # Test edge cases where filelike objects are missing attributes.
        # The Python io docs suggests that these attributes should really exist
        # and throw io.UnsupportedOperation, but that isn't always the case.
        mocks = [
            ('no readinto', lambda x: FilelikeMock(x)),
            ('has readinto', lambda x: FilelikeMock(x, has_readinto=True)),
            ('no fileno', lambda x: FilelikeMock(x, has_fileno=False)),
        ]

        to_serialize = torch.randn(3, 10)
        for desc, mock in mocks:
            self._test_serialization_filelike(to_serialize, mock, desc)

    def test_serialization_filelike_stress(self):
        a = torch.randn(11 * (2 ** 9) + 1, 5 * (2 ** 9))

        # This one should call python read multiple times
        self._test_serialization_filelike(a, lambda x: FilelikeMock(x, has_readinto=False),
                                          'read() stress test')
        self._test_serialization_filelike(a, lambda x: FilelikeMock(x, has_readinto=True),
                                          'readinto() stress test')

    def test_serialization_filelike_uses_readinto(self):
        # For maximum effiency, when reading a file-like object,
        # ensure the C API calls readinto instead of read.
        a = torch.randn(5, 4)

        f = io.BytesIO()
        torch.save(a, f)
        f.seek(0)
        data = FilelikeMock(f.read(), has_readinto=True)

        b = torch.load(data)
        self.assertTrue(data.was_called('readinto'))

    def test_serialization_storage_slice(self):
        # Generated using:
        #
        # t = torch.zeros(2);
        # s1 = t.storage()[:1]
        # s2 = t.storage()[1:]
        # torch.save((s1, s2), 'foo.ser')
        #
        # with PyTorch 0.3.1
        serialized = (b'\x80\x02\x8a\nl\xfc\x9cF\xf9 j\xa8P\x19.\x80\x02M\xe9\x03'
                      b'.\x80\x02}q\x00(X\n\x00\x00\x00type_sizesq\x01}q\x02(X\x03'
                      b'\x00\x00\x00intq\x03K\x04X\x05\x00\x00\x00shortq\x04K\x02X'
                      b'\x04\x00\x00\x00longq\x05K\x04uX\x10\x00\x00\x00protocol_versionq'
                      b'\x06M\xe9\x03X\r\x00\x00\x00little_endianq\x07\x88u.\x80\x02'
                      b'(X\x07\x00\x00\x00storageq\x00ctorch\nFloatStorage\nq\x01X\x0e'
                      b'\x00\x00\x0094279043900432q\x02X\x03\x00\x00\x00cpuq\x03K\x02'
                      b'X\x0e\x00\x00\x0094279029750368q\x04K\x00K\x01\x87q\x05tq\x06'
                      b'Q(h\x00h\x01X\x0e\x00\x00\x0094279043900432q\x07h\x03K\x02X'
                      b'\x0e\x00\x00\x0094279029750432q\x08K\x01K\x01\x87q\ttq\nQ'
                      b'\x86q\x0b.\x80\x02]q\x00X\x0e\x00\x00\x0094279043900432q'
                      b'\x01a.\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00'
                      b'\x00\x00\x00\x00')

        buf = io.BytesIO(serialized)
        (s1, s2) = torch.load(buf)
        self.assertEqual(s1[0], 0)
        self.assertEqual(s2[0], 0)
        self.assertEqual(s1.data_ptr() + 4, s2.data_ptr())

    def test_load_unicode_error_msg(self):
        # This Pickle contains a Python 2 module with Unicode data and the
        # loading should fail if the user explicitly specifies ascii encoding!
        path = download_file('https://download.pytorch.org/test_data/legacy_conv2d.pt')
        if sys.version_info >= (3, 0):
            self.assertRaises(UnicodeDecodeError, lambda: torch.load(path, encoding='ascii'))
        else:
            # Just checks the module loaded
            self.assertIsNotNone(torch.load(path))

    def test_load_python2_unicode_module(self):
        # This Pickle contains some Unicode data!
        path = download_file('https://download.pytorch.org/test_data/legacy_conv2d.pt')
        self.assertIsNotNone(torch.load(path))

    def test_load_error_msg(self):
        expected_err_msg = (".*You can only torch.load from a file that is seekable. " +
                            "Please pre-load the data into a buffer like io.BytesIO and " +
                            "try to load from it instead.")

        resource = FilelikeMock(data=b"data")
        delattr(resource, "tell")
        delattr(resource, "seek")
        self.assertRaisesRegex(AttributeError, expected_err_msg, lambda: torch.load(resource))

    def test_from_buffer(self):
        a = bytearray([1, 2, 3, 4])
        self.assertEqual(torch.ByteStorage.from_buffer(a).tolist(), [1, 2, 3, 4])
        shorts = torch.ShortStorage.from_buffer(a, 'big')
        self.assertEqual(shorts.size(), 2)
        self.assertEqual(shorts.tolist(), [258, 772])
        ints = torch.IntStorage.from_buffer(a, 'little')
        self.assertEqual(ints.size(), 1)
        self.assertEqual(ints[0], 67305985)
        f = bytearray([0x40, 0x10, 0x00, 0x00])
        floats = torch.FloatStorage.from_buffer(f, 'big')
        self.assertEqual(floats.size(), 1)
        self.assertEqual(floats[0], 2.25)

        f = bytearray([0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x10, 0x40])
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 8)
        self.assertEqual(bools.tolist(), [False, True, True, True, True, True, True, True])
        self.assertEqual(bools.type(), 'torch.BoolStorage')

        f = bytearray(b'\x80\x02\x8a\nl\xfc\x9cF\xf9 j\xa8P\x19.\x80\x02M\xe9')
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 19)

        f = bytearray(b'\0x4A')
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 4)
        self.assertEqual(bools.tolist(), [False, True, True, True])

    def test_storage_casts(self):
        storage = torch.IntStorage([-1, 0, 1, 2, 3, 4])
        self.assertEqual(storage.size(), 6)
        self.assertEqual(storage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(storage.type(), 'torch.IntStorage')
        self.assertIs(storage.dtype, torch.int32)

        floatStorage = storage.float()
        self.assertEqual(floatStorage.size(), 6)
        self.assertEqual(floatStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(floatStorage.type(), 'torch.FloatStorage')
        self.assertEqual(floatStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(floatStorage.dtype, torch.float32)

        halfStorage = storage.half()
        self.assertEqual(halfStorage.size(), 6)
        self.assertEqual(halfStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(halfStorage.type(), 'torch.HalfStorage')
        self.assertEqual(halfStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(halfStorage.dtype, torch.float16)

        bfloat16Storage = storage.bfloat16()
        self.assertEqual(bfloat16Storage.size(), 6)
        self.assertEqual(bfloat16Storage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(bfloat16Storage.type(), 'torch.BFloat16Storage')
        self.assertEqual(bfloat16Storage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(bfloat16Storage.dtype, torch.bfloat16)

        longStorage = storage.long()
        self.assertEqual(longStorage.size(), 6)
        self.assertEqual(longStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(longStorage.type(), 'torch.LongStorage')
        self.assertEqual(longStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(longStorage.dtype, torch.int64)

        shortStorage = storage.short()
        self.assertEqual(shortStorage.size(), 6)
        self.assertEqual(shortStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(shortStorage.type(), 'torch.ShortStorage')
        self.assertEqual(shortStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(shortStorage.dtype, torch.int16)

        doubleStorage = storage.double()
        self.assertEqual(doubleStorage.size(), 6)
        self.assertEqual(doubleStorage.tolist(), [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
        self.assertEqual(doubleStorage.type(), 'torch.DoubleStorage')
        self.assertEqual(doubleStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(doubleStorage.dtype, torch.float64)

        charStorage = storage.char()
        self.assertEqual(charStorage.size(), 6)
        self.assertEqual(charStorage.tolist(), [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
        self.assertEqual(charStorage.type(), 'torch.CharStorage')
        self.assertEqual(charStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(charStorage.dtype, torch.int8)

        byteStorage = storage.byte()
        self.assertEqual(byteStorage.size(), 6)
        self.assertEqual(byteStorage.tolist(), [255, 0, 1, 2, 3, 4])
        self.assertEqual(byteStorage.type(), 'torch.ByteStorage')
        self.assertEqual(byteStorage.int().tolist(), [255, 0, 1, 2, 3, 4])
        self.assertIs(byteStorage.dtype, torch.uint8)

        boolStorage = storage.bool()
        self.assertEqual(boolStorage.size(), 6)
        self.assertEqual(boolStorage.tolist(), [True, False, True, True, True, True])
        self.assertEqual(boolStorage.type(), 'torch.BoolStorage')
        self.assertEqual(boolStorage.int().tolist(), [1, 0, 1, 1, 1, 1])
        self.assertIs(boolStorage.dtype, torch.bool)

    @unittest.skipIf(IS_WINDOWS, "TODO: need to fix this test case for Windows")
    def test_from_file(self):
        size = 10000
        with tempfile.NamedTemporaryFile() as f:
            s1 = torch.FloatStorage.from_file(f.name, True, size)
            t1 = torch.FloatTensor(s1).copy_(torch.randn(size))

            # check mapping
            s2 = torch.FloatStorage.from_file(f.name, True, size)
            t2 = torch.FloatTensor(s2)
            self.assertEqual(t1, t2, 0)

            # check changes to t1 from t2
            rnum = random.uniform(-1, 1)
            t1.fill_(rnum)
            self.assertEqual(t1, t2, 0)

            # check changes to t2 from t1
            rnum = random.uniform(-1, 1)
            t2.fill_(rnum)
            self.assertEqual(t1, t2, 0)

    @unittest.skipIf(IS_WINDOWS, "TODO: need to fix this test case for Windows")
    def test_torch_from_file(self):
        size = 10000
        with tempfile.NamedTemporaryFile() as f:
            s1 = torch.from_file(f.name, True, size, dtype=torch.float)
            t1 = torch.FloatTensor(s1).copy_(torch.randn(size))

            # check mapping
            s2 = torch.from_file(f.name, True, size, dtype=torch.float)
            t2 = torch.FloatTensor(s2)
            self.assertEqual(t1, t2, 0)

            # check changes to t1 from t2
            rnum = random.uniform(-1, 1)
            t1.fill_(rnum)
            self.assertEqual(t1, t2, 0)

            # check changes to t2 from t1
            rnum = random.uniform(-1, 1)
            t2.fill_(rnum)
            self.assertEqual(t1, t2, 0)

    def test_print(self):
        default_type = torch.Tensor().type()
        for t in torch._tensor_classes:
            if t == torch.HalfTensor:
                continue  # HalfTensor does not support fill
            if t.is_sparse:
                continue
            if t.is_cuda and not torch.cuda.is_available():
                continue
            if t == torch.cuda.BFloat16Tensor:
                self.assertRaises(RuntimeError, lambda: t(100, 100).fill_(1))
                continue
            obj = t(100, 100).fill_(1)
            obj.__repr__()
            str(obj)
        # test half tensor
        obj = torch.rand(100, 100, device='cpu').half()
        obj.__repr__()
        str(obj)
        for t in torch._storage_classes:
            if t == torch.BFloat16Storage:
                continue  # Fix once fill is enabled for bfloat16
            if t.is_cuda and not torch.cuda.is_available():
                continue
            if t == torch.BoolStorage or t == torch.cuda.BoolStorage:
                obj = t(100).fill_(True)
            else:
                obj = t(100).fill_(1)
            obj.__repr__()
            str(obj)

        # test big integer
        x = torch.tensor(2341234123412341)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(2341234123412341)''')

        # test scientific notation
        x = torch.tensor([1e28, 1e-28])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+28, 1.0000e-28])''')

        # test scientific notation using set_printoptions
        x = torch.tensor([1e2, 1e-2])
        torch.set_printoptions(sci_mode=True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+02, 1.0000e-02])''')
        torch.set_printoptions(sci_mode=False)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([  100.0000,     0.0100])''')
        torch.set_printoptions(sci_mode=None)  # reset to the default value

        # test no leading space if all elements positive
        x = torch.tensor([1, 2])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1, 2])''')

        # test for leading space if there are negative elements
        x = torch.tensor([1, -2])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([ 1, -2])''')

        # test inf and nan
        x = torch.tensor([4, inf, 1.5, -inf, 0, nan, 1])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([4.0000,    inf, 1.5000,   -inf, 0.0000,    nan, 1.0000])''')

        # test dtype
        torch.set_default_dtype(torch.float)
        x = torch.tensor([1e-324, 1e-323, 1e-322, 1e307, 1e308, 1e309], dtype=torch.float64)
        self.assertEqual(x.__repr__(), str(x))
        expected_str = '''\
tensor([ 0.0000e+00, 9.8813e-324, 9.8813e-323, 1.0000e+307, 1.0000e+308,
                inf], dtype=torch.float64)'''
        self.assertExpectedInline(str(x), expected_str)

        # test changing default dtype
        torch.set_default_dtype(torch.float64)
        self.assertEqual(x.__repr__(), str(x))
        expected_str = '''\
tensor([ 0.0000e+00, 9.8813e-324, 9.8813e-323, 1.0000e+307, 1.0000e+308,
                inf])'''
        self.assertExpectedInline(str(x), expected_str)

        # test summary
        x = torch.zeros(10000)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([0., 0., 0.,  ..., 0., 0., 0.])''')

        # test internal summary function
        x = torch.rand(1, 20, 5, 30)
        summary = torch._tensor_str.get_summarized_data(x)
        self.assertEqual(summary.shape, (1, 6, 5, 6))
        first_and_last = [0, 1, 2, -3, -2, -1]
        self.assertEqual(summary, x[:, first_and_last][..., first_and_last])

        # test device
        if torch.cuda.is_available():
            x = torch.tensor([123], device='cuda:0')
            self.assertEqual(x.__repr__(), str(x))
            self.assertExpectedInline(str(x), '''tensor([123], device='cuda:0')''')

            # test changing default to cuda
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertEqual(x.__repr__(), str(x))
            self.assertExpectedInline(str(x), '''tensor([123])''')

            # test printing a tensor on a different gpu than current one.
            if torch.cuda.device_count() >= 2:
                with torch.cuda.device(1):
                    self.assertEqual(x.__repr__(), str(x))
                    self.assertExpectedInline(str(x), '''tensor([123], device='cuda:0')''')

            # test printing cpu tensor when default device is cuda
            y = torch.tensor([123], device='cpu')
            self.assertEqual(y.__repr__(), str(y))
            self.assertExpectedInline(str(y), '''tensor([123], device='cpu')''')
        torch.set_default_tensor_type(default_type)

        # test integral floats and requires_grad
        x = torch.tensor([123.], requires_grad=True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([123.], requires_grad=True)''')

        # test non-contiguous print
        # sliced tensor should have > PRINT_OPTS.threshold elements
        x = torch.ones(100, 2, 2, 10)
        y = x.as_strided(size=(100, 2, 10), stride=(2 * 2 * 10, 2 * 10, 1))
        self.assertEqual(str(y), y.__repr__())
        expected_str = '''\
tensor([[[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        ...,

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]]])\
'''

        self.assertExpectedInline(str(y), expected_str)

        # test print 0-dim tensor: there's no 0-dim in Numpy, we match arrayprint style
        x = torch.tensor(0.00002)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(2.0000e-05)''')

        # test print boolean tensor
        x = torch.tensor([True])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([True])''')

        x = torch.tensor(True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(True)''')

        # [Numpy] test print float in sci_mode when min < 0.0001.
        x = torch.tensor([0.00002])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([2.0000e-05])''')

        # [Numpy] test print float in sci_mode when max > 1e8.
        # TODO: Pytorch uses fixed precision to print, while Numpy uses dragon4_scientific
        # to do automatic trimming and padding.
        x = torch.tensor([123456789.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.2346e+08])''')

        # [Numpy] test print float in sci_mode when max / min > 1000.
        x = torch.tensor([0.01, 11])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e-02, 1.1000e+01])''')

        # [Numpy] test print int max / min > 1000, no sci_mode
        x = torch.tensor([1, 1010])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([   1, 1010])''')

        # [Numpy] test print int > 1e8, no sci_mode
        x = torch.tensor([1000000000])  # 1e9
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1000000000])''')

        # [Numpy] test printing float in int_mode
        x = torch.tensor([1., 1000.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([   1., 1000.])''')

        # [Numpy] test printing float in int_mode in sci format when max / min > 1000.
        x = torch.tensor([1., 1010.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+00, 1.0100e+03])''')

    def test_sizeof(self):
        sizeof_empty = torch.randn(0).storage().__sizeof__()
        sizeof_10 = torch.randn(10).storage().__sizeof__()
        sizeof_100 = torch.randn(100).storage().__sizeof__()
        self.assertEqual((sizeof_100 - sizeof_empty) // (sizeof_10 - sizeof_empty), 10)
        self.assertEqual((sizeof_100 - sizeof_empty) % (sizeof_10 - sizeof_empty), 0)

        sizeof_empty = torch.randn(0).type(torch.ByteTensor).storage().__sizeof__()
        sizeof_10 = torch.randn(10).type(torch.ByteTensor).storage().__sizeof__()
        sizeof_100 = torch.randn(100).type(torch.ByteTensor).storage().__sizeof__()
        self.assertEqual((sizeof_100 - sizeof_empty) // (sizeof_10 - sizeof_empty), 10)
        self.assertEqual((sizeof_100 - sizeof_empty) % (sizeof_10 - sizeof_empty), 0)

    def test_unsqueeze(self):
        x = torch.randn(2, 3, 4)
        y = x.unsqueeze(1)
        self.assertEqual(y, x.view(2, 1, 3, 4))
        y = x.clone().unsqueeze_(2)
        self.assertEqual(y, x.view(2, 3, 1, 4))

        x = x[:, 1]
        self.assertFalse(x.is_contiguous())
        y = x.unsqueeze(1)
        self.assertEqual(y, x.contiguous().view(2, 1, 4))
        y = x.clone().unsqueeze_(2)
        self.assertEqual(y, x.contiguous().view(2, 4, 1))

    def test_iter(self):
        x = torch.randn(5, 5)
        for i, sub in enumerate(x):
            self.assertEqual(sub, x[i])

        x = torch.Tensor()
        self.assertEqual(list(x), [])

    def test_accreal_type(self):
        x = torch.ones(2, 3, 4)
        self.assertIsInstance(x.double().sum().item(), float)
        self.assertIsInstance(x.float().sum().item(), float)
        self.assertIsInstance(x.long().sum().item(), int)
        self.assertIsInstance(x.int().sum().item(), int)
        self.assertIsInstance(x.short().sum().item(), int)
        self.assertIsInstance(x.char().sum().item(), int)
        self.assertIsInstance(x.byte().sum().item(), int)

    def test_assertEqual(self):
        x = torch.FloatTensor([0])
        self.assertEqual(x, 0)
        xv = torch.autograd.Variable(x)
        self.assertEqual(xv, 0)
        self.assertEqual(x, xv)
        self.assertEqual(xv, x)

    def test_new(self):
        x = torch.autograd.Variable(torch.Tensor())
        y = torch.autograd.Variable(torch.randn(4, 4))
        z = torch.autograd.Variable(torch.IntTensor([1, 2, 3]))
        self.assertEqual(x.new().shape, [0])
        self.assertEqual(x.new(), x)
        self.assertEqual(x.new(1, 2).shape, [1, 2])
        self.assertEqual(x.new(torch.Size([3, 4])).shape, [3, 4])
        self.assertEqual(x.new([3, 4]).shape, [2])
        self.assertEqual(x.new([3, 4]).tolist(), [3, 4])
        self.assertEqual(x.new((3, 4)).tolist(), [3, 4])
        if TEST_NUMPY:
            self.assertEqual(x.new([np.int32(3), np.float64(4)]).tolist(), [3, 4])
            self.assertEqual(x.new(np.array((3, 4))).tolist(), [3, 4])
        self.assertEqual(x.new([z[2], z[0] + 3]).tolist(), [3, 4])
        self.assertEqual(x.new(size=(3, 4)).shape, [3, 4])
        self.assertEqual(x.new(()).shape, [0])
        self.assertEqual(x.new(y.storage()).data_ptr(), y.data_ptr())
        self.assertEqual(x.new(y).data_ptr(), y.data_ptr())
        self.assertIsNot(x.new(y), y)

        self.assertRaises(TypeError, lambda: x.new(z))
        # TypeError would be better
        self.assertRaises(RuntimeError, lambda: x.new(z.storage()))

    def test_empty_like(self):
        x = torch.autograd.Variable(torch.Tensor())
        y = torch.autograd.Variable(torch.randn(4, 4))
        z = torch.autograd.Variable(torch.IntTensor([1, 2, 3]))
        for a in (x, y, z):
            self.assertEqual(torch.empty_like(a).shape, a.shape)
            self.assertEqual(torch.empty_like(a).type(), a.type())

    def test_pin_memory(self):
        x = torch.randn(3, 5)
        self.assertFalse(x.is_pinned())
        if not torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: x.pin_memory())
        else:
            pinned = x.pin_memory()
            self.assertTrue(pinned.is_pinned())
            self.assertEqual(pinned, x)
            self.assertNotEqual(pinned.data_ptr(), x.data_ptr())
            # test that pin_memory on already pinned tensor has no effect
            self.assertIs(pinned, pinned.pin_memory())
            self.assertEqual(pinned.data_ptr(), pinned.pin_memory().data_ptr())

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_unresizable(self):
        x = np.zeros((2, 2))
        y = torch.from_numpy(x)
        with self.assertRaises(ValueError):
            x.resize((5, 5))

        z = torch.randn(5, 5)
        w = z.numpy()
        with self.assertRaises(RuntimeError):
            z.resize_(10, 10)
        with self.assertRaises(ValueError):
            w.resize((10, 10))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_to_numpy(self):
        def get_castable_tensor(shape, tp):
            dtype = tp.dtype
            if dtype.is_floating_point:
                dtype_info = torch.finfo(dtype)
                # can't directly use min and max, because for double, max - min
                # is greater than double range and sampling always gives inf.
                low = max(dtype_info.min, -1e10)
                high = min(dtype_info.max, 1e10)
                t = torch.empty(shape, dtype=torch.float64).uniform_(low, high)
            else:
                # can't directly use min and max, because for int64_t, max - min
                # is greater than int64_t range and triggers UB.
                dtype_info = torch.iinfo(dtype)
                low = max(dtype_info.min, int(-1e10))
                high = min(dtype_info.max, int(1e10))
                dtype_info = torch.iinfo(dtype)
                t = torch.empty(shape, dtype=torch.int64).random_(low, high)
            return t.to(dtype)

        types = [
            torch.ByteTensor,
            torch.CharTensor,
            torch.ShortTensor,
            torch.IntTensor,
            torch.HalfTensor,
            torch.FloatTensor,
            torch.DoubleTensor,
            torch.LongTensor,
        ]
        for tp in types:
            # 1D
            sz = 10
            x = get_castable_tensor(sz, tp)
            y = x.numpy()
            for i in range(sz):
                self.assertEqual(x[i], y[i])

            # 1D > 0 storage offset
            xm = get_castable_tensor(sz * 2, tp)
            x = xm.narrow(0, sz - 1, sz)
            self.assertTrue(x.storage_offset() > 0)
            y = x.numpy()
            for i in range(sz):
                self.assertEqual(x[i], y[i])

            def check2d(x, y):
                for i in range(sz1):
                    for j in range(sz2):
                        self.assertEqual(x[i][j], y[i][j])

            # empty
            x = torch.Tensor().type(tp)
            y = x.numpy()
            self.assertEqual(y.size, 0)

            # contiguous 2D
            sz1 = 3
            sz2 = 5
            x = get_castable_tensor((sz1, sz2), tp)
            y = x.numpy()
            check2d(x, y)
            self.assertTrue(y.flags['C_CONTIGUOUS'])

            # with storage offset
            xm = get_castable_tensor((sz1 * 2, sz2), tp)
            x = xm.narrow(0, sz1 - 1, sz1)
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)
            self.assertTrue(y.flags['C_CONTIGUOUS'])

            # non-contiguous 2D
            x = get_castable_tensor((sz2, sz1), tp).t()
            y = x.numpy()
            check2d(x, y)
            self.assertFalse(y.flags['C_CONTIGUOUS'])

            # with storage offset
            xm = get_castable_tensor((sz2 * 2, sz1), tp)
            x = xm.narrow(0, sz2 - 1, sz2).t()
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)

            # non-contiguous 2D with holes
            xm = get_castable_tensor((sz2 * 2, sz1 * 2), tp)
            x = xm.narrow(0, sz2 - 1, sz2).narrow(1, sz1 - 1, sz1).t()
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)

            if tp != torch.HalfTensor:
                # check writeable
                x = get_castable_tensor((3, 4), tp)
                y = x.numpy()
                self.assertTrue(y.flags.writeable)
                y[0][1] = 3
                self.assertTrue(x[0][1] == 3)
                y = x.t().numpy()
                self.assertTrue(y.flags.writeable)
                y[0][1] = 3
                self.assertTrue(x[0][1] == 3)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_to_numpy_bool(self):
        x = torch.tensor([True, False], dtype=torch.bool)
        self.assertEqual(x.dtype, torch.bool)

        y = x.numpy()
        self.assertEqual(y.dtype, np.bool)
        for i in range(len(x)):
            self.assertEqual(x[i], y[i])

        x = torch.tensor([True], dtype=torch.bool)
        self.assertEqual(x.dtype, torch.bool)

        y = x.numpy()
        self.assertEqual(y.dtype, np.bool)
        self.assertEqual(x[0], y[0])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_from_numpy(self):
        dtypes = [
            np.double,
            np.float,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.int8,
            np.uint8,
            np.longlong,
            np.bool,
        ]
        for dtype in dtypes:
            array = np.array([1, 2, 3, 4], dtype=dtype)
            tensor_from_array = torch.from_numpy(array)
            # TODO: change to tensor equality check once HalfTensor
            # implements `==`
            for i in range(len(array)):
                self.assertEqual(tensor_from_array[i], array[i])
            # This is a special test case for Windows
            # https://github.com/pytorch/pytorch/issues/22615
            array2 = array % 2
            tensor_from_array2 = torch.from_numpy(array2)
            for i in range(len(array2)):
                self.assertEqual(tensor_from_array2[i], array2[i])

        # Test unsupported type
        array = np.array([1, 2, 3, 4], dtype=np.complex)
        with self.assertRaises(TypeError):
            tensor_from_array = torch.from_numpy(array)

        # check storage offset
        x = np.linspace(1, 125, 125)
        x.shape = (5, 5, 5)
        x = x[1]
        expected = torch.arange(1, 126).view(5, 5, 5)[1]
        self.assertEqual(torch.from_numpy(x), expected)

        # check noncontiguous
        x = np.linspace(1, 25, 25)
        x.shape = (5, 5)
        expected = torch.arange(1, 26).view(5, 5).t()
        self.assertEqual(torch.from_numpy(x.T), expected)

        # check noncontiguous with holes
        x = np.linspace(1, 125, 125)
        x.shape = (5, 5, 5)
        x = x[:, 1]
        expected = torch.arange(1, 126).view(5, 5, 5)[:, 1]
        self.assertEqual(torch.from_numpy(x), expected)

        # check zero dimensional
        x = np.zeros((0, 2))
        self.assertEqual(torch.from_numpy(x).shape, (0, 2))
        x = np.zeros((2, 0))
        self.assertEqual(torch.from_numpy(x).shape, (2, 0))

        # check ill-sized strides raise exception
        x = np.array([3., 5., 8.])
        x.strides = (3,)
        self.assertRaises(ValueError, lambda: torch.from_numpy(x))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_ctor_with_numpy_scalar_ctor(self):
        dtypes = [
            np.double,
            np.float,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.uint8,
            np.bool,
        ]
        for dtype in dtypes:
            self.assertEqual(dtype(42), torch.tensor(dtype(42)).item())

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_index(self):
        i = np.int32([0, 1, 2])
        x = torch.randn(5, 5)
        for idx in i:
            self.assertFalse(isinstance(idx, int))
            self.assertEqual(x[idx], x[int(idx)])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_array_interface(self):
        types = [
            torch.DoubleTensor,
            torch.FloatTensor,
            torch.HalfTensor,
            torch.LongTensor,
            torch.IntTensor,
            torch.ShortTensor,
            torch.ByteTensor,
        ]
        dtypes = [
            np.float64,
            np.float32,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.uint8,
        ]
        for tp, dtype in zip(types, dtypes):
            if np.dtype(dtype).kind == 'u':
                x = torch.Tensor([1, 2, 3, 4]).type(tp)
                array = np.array([1, 2, 3, 4], dtype=dtype)
            else:
                x = torch.Tensor([1, -2, 3, -4]).type(tp)
                array = np.array([1, -2, 3, -4], dtype=dtype)

            # Test __array__ w/o dtype argument
            asarray = np.asarray(x)
            self.assertIsInstance(asarray, np.ndarray)
            self.assertEqual(asarray.dtype, dtype)
            for i in range(len(x)):
                self.assertEqual(asarray[i], x[i])

            # Test __array_wrap__, same dtype
            abs_x = np.abs(x)
            abs_array = np.abs(array)
            self.assertIsInstance(abs_x, tp)
            for i in range(len(x)):
                self.assertEqual(abs_x[i], abs_array[i])

        # Test __array__ with dtype argument
        for dtype in dtypes:
            x = torch.IntTensor([1, -2, 3, -4])
            asarray = np.asarray(x, dtype=dtype)
            self.assertEqual(asarray.dtype, dtype)
            if np.dtype(dtype).kind == 'u':
                wrapped_x = np.array([1, -2, 3, -4], dtype=dtype)
                for i in range(len(x)):
                    self.assertEqual(asarray[i], wrapped_x[i])
            else:
                for i in range(len(x)):
                    self.assertEqual(asarray[i], x[i])

        # Test some math functions with float types
        float_types = [torch.DoubleTensor, torch.FloatTensor]
        float_dtypes = [np.float64, np.float32]
        for tp, dtype in zip(float_types, float_dtypes):
            x = torch.Tensor([1, 2, 3, 4]).type(tp)
            array = np.array([1, 2, 3, 4], dtype=dtype)
            for func in ['sin', 'sqrt', 'ceil']:
                ufunc = getattr(np, func)
                res_x = ufunc(x)
                res_array = ufunc(array)
                self.assertIsInstance(res_x, tp)
                for i in range(len(x)):
                    self.assertEqual(res_x[i], res_array[i])

        # Test functions with boolean return value
        for tp, dtype in zip(types, dtypes):
            x = torch.Tensor([1, 2, 3, 4]).type(tp)
            array = np.array([1, 2, 3, 4], dtype=dtype)
            geq2_x = np.greater_equal(x, 2)
            geq2_array = np.greater_equal(array, 2).astype('uint8')
            self.assertIsInstance(geq2_x, torch.ByteTensor)
            for i in range(len(x)):
                self.assertEqual(geq2_x[i], geq2_array[i])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_multiplication_numpy_scalar(self):
        for np_dtype in [np.float32, np.float64, np.int32, np.int64, np.int16, np.uint8]:
            for t_dtype in [torch.float, torch.double]:
                np_sc = np_dtype(2.0)
                t = torch.ones(2, requires_grad=True, dtype=t_dtype)
                r1 = t * np_sc
                self.assertIsInstance(r1, torch.Tensor)
                self.assertTrue(r1.dtype == t_dtype)
                self.assertTrue(r1.requires_grad)
                r2 = np_sc * t
                self.assertIsInstance(r2, torch.Tensor)
                self.assertTrue(r2.dtype == t_dtype)
                self.assertTrue(r2.requires_grad)

    def test_error_msg_type_translation(self):
        with self.assertRaisesRegex(
                RuntimeError,
                # message includes both Double and Long
                '(?=.*Double)(?=.*Long)'):

            # Calls model with a DoubleTensor input but LongTensor weights
            input = torch.autograd.Variable(torch.randn(1, 1, 1, 6).double())
            weight = torch.zeros(1, 1, 1, 3).long()
            model = torch.nn.Conv2d(1, 1, (1, 3), stride=1, padding=0, bias=False)
            model.weight.data = weight
            out = model(input)

    def test_tensor_from_sequence(self):
        class MockSequence(object):
            def __init__(self, lst):
                self.lst = lst

            def __len__(self):
                return len(self.lst)

            def __getitem__(self, item):
                raise TypeError

        class GoodMockSequence(MockSequence):
            def __getitem__(self, item):
                return self.lst[item]

        bad_mock_seq = MockSequence([1.0, 2.0, 3.0])
        good_mock_seq = GoodMockSequence([1.0, 2.0, 3.0])
        with self.assertRaisesRegex(ValueError, 'could not determine the shape'):
            torch.Tensor(bad_mock_seq)
        self.assertEqual(torch.Tensor([1.0, 2.0, 3.0]), torch.Tensor(good_mock_seq))

    def test_comparison_ops(self):
        x = torch.randn(5, 5)
        y = torch.randn(5, 5)

        eq = x == y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] == y[idx], eq[idx] == 1)

        ne = x != y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] != y[idx], ne[idx] == 1)

        lt = x < y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] < y[idx], lt[idx] == 1)

        le = x <= y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] <= y[idx], le[idx] == 1)

        gt = x > y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] > y[idx], gt[idx] == 1)

        ge = x >= y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] >= y[idx], ge[idx] == 1)

    def test_comparison_ops_must_take_bool_output(self):
        with self.assertRaisesRegex(RuntimeError, 'The output tensor of lt must be a bool'):
            for op in [torch.lt, torch.le, torch.gt, torch.ge, torch.eq, torch.ne]:
                op(torch.tensor([True]), torch.tensor([False]), out=torch.empty(1, dtype=torch.uint8))

    def test_inplace_comparison_ops_require_inputs_have_same_dtype(self):
        with self.assertRaisesRegex(RuntimeError, 'Expected object of scalar type'):
            for op in ['lt_', 'le_', 'gt_', 'ge_', 'eq_', 'ne_']:
                x = torch.tensor([1], dtype=torch.int)
                y = torch.tensor([2], dtype=torch.long)
                in_place_method = getattr(x, op)
                in_place_method(y)

    def test_comparison_ops_check_for_scalar_overflow(self):
        with self.assertRaisesRegex(RuntimeError, 'value cannot be converted to type'):
            torch.tensor([1 << 5], dtype=torch.uint8) < (1 << 20)
            (1 << 20) < torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) <= (1 << 20)
            (1 << 20) <= torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) > (1 << 20)
            (1 << 20) > torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) >= (1 << 20)
            (1 << 20) >= torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) == (1 << 20)
            (1 << 20) == torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) != (1 << 20)
            (1 << 20) != torch.tensor([1 << 5], dtype=torch.uint8)

    def test_comparison_ops_check_for_zerodim_tensor_overflow(self):
        with self.assertRaisesRegex(RuntimeError, 'value cannot be converted to type'):
            torch.tensor([1 << 5], dtype=torch.uint8) < torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) < torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) <= torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) <= torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) > torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) > torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) >= torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) >= torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) == torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) == torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) != torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) != torch.tensor([1 << 30], dtype=torch.int32)

    def test_bitwise_ops(self):
        x = torch.randn(5, 5).gt(0)
        y = torch.randn(5, 5).gt(0)

        and_result = x & y
        for idx in iter_indices(x):
            if and_result[idx]:
                self.assertTrue(x[idx] and y[idx])
            else:
                self.assertFalse(x[idx] and y[idx])

        or_result = x | y
        for idx in iter_indices(x):
            if or_result[idx]:
                self.assertTrue(x[idx] or y[idx])
            else:
                self.assertFalse(x[idx] or y[idx])

        xor_result = x ^ y
        for idx in iter_indices(x):
            if xor_result[idx]:
                self.assertTrue(x[idx] ^ y[idx])
            else:
                self.assertFalse(x[idx] ^ y[idx])

        x_clone = x.clone()
        x_clone &= y
        self.assertEqual(x_clone, and_result)

        x_clone = x.clone()
        x_clone |= y
        self.assertEqual(x_clone, or_result)

        x_clone = x.clone()
        x_clone ^= y
        self.assertEqual(x_clone, xor_result)

    def test_op_invert(self):
        res = 0xffff - torch.arange(127, dtype=torch.int8)
        for dtype in (torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            a = torch.arange(127, dtype=dtype)
            self.assertEqual(res.to(dtype), ~a)

        self.assertEqual(torch.tensor([True, False]),
                         ~torch.tensor([False, True]))

        # test exceptions
        for dtype in(torch.half, torch.float, torch.double):
            a = torch.zeros(10, dtype=dtype)
            with self.assertRaises(TypeError):
                b = ~a

    def test_apply(self):
        x = torch.arange(1, 6)
        res = x.clone().apply_(lambda k: k + k)
        self.assertEqual(res, x * 2)
        self.assertRaises(TypeError, lambda: x.apply_(lambda k: "str"))

    def test_map(self):
        x = torch.autograd.Variable(torch.randn(3, 3))
        y = torch.autograd.Variable(torch.randn(3))
        res = x.clone()
        res.map_(y, lambda a, b: a + b)
        self.assertEqual(res, x + y)
        self.assertRaisesRegex(TypeError, "not callable", lambda: res.map_(y, "str"))

    def test_map2(self):
        x = torch.autograd.Variable(torch.randn(3, 3))
        y = torch.autograd.Variable(torch.randn(3))
        z = torch.autograd.Variable(torch.randn(1, 3))
        res = x.clone()
        res.map2_(y, z, lambda a, b, c: a + b * c)
        self.assertEqual(res, x + y * z)
        z.requires_grad = True
        self.assertRaisesRegex(
            RuntimeError, "requires grad",
            lambda: res.map2_(y, z, lambda a, b, c: a + b * c))

    def test_Size(self):
        x = torch.Size([1, 2, 3])
        self.assertIsInstance(x, tuple)
        self.assertEqual(x[0], 1)
        self.assertEqual(x[1], 2)
        self.assertEqual(x[2], 3)
        self.assertEqual(len(x), 3)
        self.assertRaises(TypeError, lambda: torch.Size(torch.ones(3)))

        self.assertIsInstance(x * 2, torch.Size)
        self.assertIsInstance(x[:-1], torch.Size)
        self.assertIsInstance(x + x, torch.Size)

    def test_Size_scalar(self):
        three = torch.tensor(3)
        two = torch.tensor(2)
        x = torch.Size([0, 1, two, three, 4])
        for i in range(1, 5):
            self.assertEqual(x[i], i)

    def test_Size_iter(self):
        for sizes in [iter([1, 2, 3, 4, 5]), range(1, 6)]:
            x = torch.Size(sizes)
            for i in range(0, 5):
                self.assertEqual(x[i], i + 1)

    def test_t_not_2d_error(self):
        self.assertRaises(RuntimeError, lambda: torch.randn(2, 3, 4).t())
        self.assertRaises(RuntimeError, lambda: torch.randn(2, 3, 4).t_())

    # unit test for special case transposed copy (see ATen/native/Copy.cpp for details)
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_big_transpose(self):
        t = torch.rand(456, 789)
        t1 = t.t().contiguous()
        t2 = torch.from_numpy(t.numpy().transpose())
        self.assertEqual(t1, t2)

    def test_inplace_division(self):
        t = torch.rand(5, 5)
        id_before = id(t)
        t /= 2
        id_after = id(t)
        self.assertEqual(id_before, id_after)

    def test_simple_scalar_cast(self):
        ok = [torch.Tensor([1.5]), torch.zeros(1, 1, 1, 1)]
        ok_values = [1.5, 0]

        not_ok = map(torch.Tensor, [[], [1, 2], [[1, 2], [3, 4]]])

        for tensor, value in zip(ok, ok_values):
            self.assertEqual(int(tensor), int(value))
            self.assertEqual(float(tensor), float(value))
            if sys.version_info[0] < 3:
                self.assertEqual(long(tensor), long(value))

        for tensor in not_ok:
            self.assertRaises(ValueError, lambda: int(tensor))
            self.assertRaises(ValueError, lambda: float(tensor))
            if sys.version_info[0] < 3:
                self.assertRaises(ValueError, lambda: long(tensor))

    def test_offset_scalar_cast(self):
        x = torch.Tensor([1, 2, 3])
        y = x[2:]
        self.assertEqual(int(y), 3)

    # skip this test for now as it affects all tests
    @unittest.skipIf(True, "flush_denormal not supported")
    def test_set_flush_denormal(self):
        tiny_float = 1e-42
        tiny_double = 1e-320
        float_tensor = torch.FloatTensor([1.0, tiny_float])
        double_tensor = torch.DoubleTensor([1.0, tiny_float, tiny_double])

        self.assertEqual(float_tensor[0], 1.0, prec=0.0)
        self.assertEqual(float_tensor[1], tiny_float, prec=tiny_float / 16)
        self.assertEqual(double_tensor[0], 1.0, prec=0.0)
        self.assertEqual(double_tensor[1], tiny_float, prec=0.0)
        self.assertEqual(double_tensor[2], tiny_double, prec=0.0)

        torch.set_flush_denormal(True)
        self.assertEqual(float_tensor[0], 1.0, prec=0.0)
        self.assertEqual(float_tensor[1], 0.0, prec=0.0)  # tiny_float to zero
        self.assertEqual(double_tensor[0], 1.0, prec=0.0)
        # tiny_float is not converted to zero in double type
        self.assertEqual(double_tensor[1], tiny_float, prec=0.0)
        self.assertEqual(double_tensor[2], 0.0, prec=0.0)  # tiny_double to zero
        torch.set_flush_denormal(False)

    def test_show_config(self):
        # We can't usefully test the output; just make sure this doesn't crash
        torch.__config__.show()

    def test_parallel_info(self):
        torch.__config__.parallel_info()

    @staticmethod
    def _test_bincount(self, device):
        # negative input throws
        with self.assertRaisesRegex(RuntimeError, '1-d non-negative integral'):
            torch.bincount(torch.tensor([1, -1], device=device))
        # n-d input, with n > 1 throws
        with self.assertRaisesRegex(RuntimeError, '1-d non-negative integral'):
            torch.bincount(torch.tensor([[1, 2], [3, 4]], device=device))
        # floating input type throws
        with self.assertRaisesRegex(RuntimeError, 'not implemented'):
            torch.bincount(torch.tensor([1., 0.3], device=device))
        # minlength < 0 throws
        with self.assertRaisesRegex(RuntimeError, 'minlength should be >= 0'):
            torch.bincount(torch.tensor([1, 3], device=device),
                           torch.tensor([.2, .2], device=device),
                           minlength=-1)
        # input and weights dim mismatch
        with self.assertRaisesRegex(RuntimeError, 'same length'):
            torch.bincount(torch.tensor([1, 0], device=device),
                           torch.tensor([1., 0.3, 0.5], device=device))
        # 1-d input with no elements and default minlength
        self.assertEqual(torch.bincount(torch.tensor([], device=device, dtype=torch.long)),
                         torch.zeros(0, dtype=torch.long, device=device))
        # 1-d input with no elements and specified minlength
        self.assertEqual(torch.bincount(torch.tensor([], device=device, dtype=torch.long), minlength=10),
                         torch.zeros(10, dtype=torch.long, device=device))

        # test tensor method without weights
        long_counts = torch.tensor(
            [0, 3, 2, 1, 3], dtype=torch.uint8, device=device).bincount()
        self.assertEqual(
            torch.tensor([1, 1, 1, 2], dtype=torch.int64, device=device),
            long_counts)
        # test minlength functionality
        int_counts = torch.bincount(
            torch.tensor([1, 1, 1, 1], device=device), minlength=5)
        self.assertEqual(
            torch.tensor([0, 4, 0, 0, 0], dtype=torch.int64, device=device),
            int_counts)
        # test weights
        byte_counts = torch.bincount(
            torch.tensor([0, 1, 1, 1, 4], device=device),
            torch.tensor([.1, .2, .3, .4, .5], device=device))
        self.assertEqual(
            torch.tensor([0.1, 0.9, 0, 0, 0.5], device=device), byte_counts)
        byte_counts = torch.bincount(
            torch.tensor([0, 1, 1, 1, 4], device=device),
            torch.tensor([1, 2, 3, 4, 5], dtype=torch.int8, device=device))
        self.assertEqual(
            torch.tensor([1, 9, 0, 0, 5], device=device), byte_counts)
        # test non-contiguous inputs and weights
        inputs = torch.tensor([[0, 0], [3, 1], [2, 1], [1, 1], [3, 4]], device=device)
        weights = torch.tensor([[.1, 1], [.2, 2], [.3, 3], [.4, 4], [.5, 5]], device=device)
        for i in [0, 1]:
            assert not inputs[:, i].is_contiguous(), "Inputs are supposed to be non-contiguous"
            assert not weights[:, i].is_contiguous(), "Weights are supposed to be non-contiguous"
        # inputs are non-contiguous but weights are contiguous
        self.assertEqual(inputs[:, 0].bincount(), torch.tensor([1, 1, 1, 2]))
        # inputs and weights are non-contiguous
        self.assertEqual(inputs[:, 1].bincount(weights[:, 1]), torch.tensor([1, 9, 0, 0, 5]))
        # weights are non-contiguous but inputs are contiguous
        self.assertEqual(inputs[:, 1].contiguous().bincount(weights[:, 1]),
                         torch.tensor([1, 9, 0, 0, 5]))

        # test bincount on non-contiguous slices
        all0s = torch.zeros((32, 2), dtype=torch.int64, device=device)
        self.assertEqual(all0s[:, 0].bincount(), torch.tensor([32]))

        all1s = torch.ones((32, 2), dtype=torch.int64, device=device)
        self.assertEqual(all1s[:, 0].bincount(), torch.tensor([0, 32]))

        # test large number of bins - global memory use
        big_exp = torch.zeros(10000000, device=device)
        big_exp[-1] = 50.0
        big_w = torch.tensor([.5] * 100, device=device)
        big_out = torch.tensor([9999999] * 100, device=device).bincount(big_w)
        self.assertEqual(big_exp, big_out)
        # test large input size
        big_exp = torch.zeros(2, device=device)
        big_exp[1] = 1000000
        big_out = torch.ones(1000000, dtype=torch.int8, device=device).bincount()
        self.assertEqual(big_exp, big_out)

    @slowTest
    def test_slow_test(self):
        # Just a smoketest to make sure our slowTest decorator works.
        pass

    def test_bincount_cpu(self):
        self._test_bincount(self, device='cpu')

    def test_is_nonzero(self):
        self.assertExpectedRaises(RuntimeError, lambda: torch.tensor([]).is_nonzero(), subname="empty")
        self.assertExpectedRaises(RuntimeError, lambda: torch.tensor([0, 0]).is_nonzero(), subname="multiple")
        self.assertFalse(torch.tensor(0).is_nonzero())
        self.assertTrue(torch.tensor(1).is_nonzero())
        self.assertFalse(torch.tensor([0]).is_nonzero())
        self.assertTrue(torch.tensor([1]).is_nonzero())
        self.assertFalse(torch.tensor([[0]]).is_nonzero())
        self.assertTrue(torch.tensor([[1]]).is_nonzero())

    def test_meshgrid(self):
        a = torch.tensor(1)
        b = torch.tensor([1, 2, 3])
        c = torch.tensor([1, 2])
        grid_a, grid_b, grid_c = torch.meshgrid([a, b, c])
        self.assertEqual(grid_a.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_b.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_c.shape, torch.Size([1, 3, 2]))
        grid_a2, grid_b2, grid_c2 = torch.meshgrid(a, b, c)
        self.assertEqual(grid_a2.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_b2.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_c2.shape, torch.Size([1, 3, 2]))
        expected_grid_a = torch.ones(1, 3, 2, dtype=torch.int64)
        expected_grid_b = torch.tensor([[[1, 1],
                                         [2, 2],
                                         [3, 3]]])
        expected_grid_c = torch.tensor([[[1, 2],
                                         [1, 2],
                                         [1, 2]]])
        self.assertTrue(grid_a.equal(expected_grid_a))
        self.assertTrue(grid_b.equal(expected_grid_b))
        self.assertTrue(grid_c.equal(expected_grid_c))
        self.assertTrue(grid_a2.equal(expected_grid_a))
        self.assertTrue(grid_b2.equal(expected_grid_b))
        self.assertTrue(grid_c2.equal(expected_grid_c))

    # NB: we must not be built with CUDA; if we are built with CUDA but no CUDA
    # is available, we get a different error.
    @unittest.skipIf(torch.backends.cuda.is_built() or IS_SANDCASTLE, "CUDA is built, can't test CUDA not built error")
    def test_cuda_not_built(self):
        msg = "Torch not compiled with CUDA enabled"
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.cuda.current_device())
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1], device="cuda"))
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1]).cuda())
        self.assertRaisesRegex(TypeError, msg, lambda: torch.cuda.FloatTensor())
        self.assertRaisesRegex(TypeError, msg, lambda: torch.set_default_tensor_type(torch.cuda.FloatTensor))
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1]).to(device="cuda"))

    def test_cast_binary_op(self):
        # Scalar
        a = torch.tensor(2)
        b = torch.tensor(3)
        a_copy = a.clone()
        b_copy = b.clone()

        self.assertEqual(torch.tensor(6), a.float() * b)

        self.assertEqual(a.type(), a_copy.type())
        self.assertEqual(a.data.type(), a_copy.data.type())
        self.assertEqual(b.type(), b_copy.type())
        self.assertEqual(b.data.type(), b_copy.type())

    def test_cartesian_prod(self):
        a = torch.tensor([1])
        b = torch.tensor([1, 2, 3])
        c = torch.tensor([1, 2])
        prod = torch.cartesian_prod(a, b, c)
        expected = torch.tensor(list(product([a], b, c)))
        self.assertEqual(expected, prod)

        # test 0 size input
        d = torch.empty(0, dtype=b.dtype)
        prod = torch.cartesian_prod(a, b, c, d)
        expected = torch.empty(0, 4, dtype=b.dtype)
        self.assertEqual(expected, prod)

        # test single input
        prod = torch.cartesian_prod(b)
        self.assertEqual(b, prod)

    def test_combinations(self):
        a = torch.tensor([1, 2, 3])

        c = torch.combinations(a, r=1)
        expected = torch.tensor(list(combinations(a, r=1)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=1, with_replacement=True)
        expected = torch.tensor(list(combinations_with_replacement(a, r=1)))
        self.assertEqual(c, expected)

        c = torch.combinations(a)
        expected = torch.tensor(list(combinations(a, r=2)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, with_replacement=True)
        expected = torch.tensor(list(combinations_with_replacement(a, r=2)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=3)
        expected = torch.tensor(list(combinations(a, r=3)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=4)
        expected = torch.empty(0, 4, dtype=a.dtype)
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=5)
        expected = torch.empty(0, 5, dtype=a.dtype)
        self.assertEqual(c, expected)

        # test empty imput
        a = torch.empty(0)
        c1 = torch.combinations(a)
        c2 = torch.combinations(a, with_replacement=True)
        expected = torch.empty(0, 2, dtype=a.dtype)
        self.assertEqual(c1, expected)
        self.assertEqual(c2, expected)

    def test_has_internal_overlap(self):
        OVERLAP_NO = 0
        OVERLAP_YES = 1
        OVERLAP_TOO_HARD = 2

        # Check for contiguous tensors
        a = torch.randn(3, 3)
        self.assertEqual(torch._debug_has_internal_overlap(a), OVERLAP_NO)

        # Checks for zero strides
        b = torch.randn(1, 3)
        b_expanded = b.expand(4, 3)
        self.assertEqual(torch._debug_has_internal_overlap(b_expanded), OVERLAP_YES)

    def test_allow_tensor_metadata_change(self):
        def do_test(t):
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_sizes_contiguous is not allowed on a Tensor created from .data or .detach()"):
                t.resize_((2, 1))
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_storage is not allowed on a Tensor created from .data or .detach()"):
                t.set_()
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_storage_offset is not allowed on a Tensor created from .data or .detach()"):
                t.set_(t.storage(), 0, t.size(), list(t.stride()))

        do_test(torch.tensor([[1, 2]]).data)
        do_test(torch.tensor([[1, 2]]).detach())

    def test_c10_layer_norm(self):
        # test that we can call c10 ops and they return a reasonable result
        X = torch.rand(5, 5, dtype=torch.float)
        weight = torch.rand(*X.size()[1:], dtype=torch.float)
        bias = torch.rand(*X.size()[1:], dtype=torch.float)
        epsilon = 1e-4

        expected_norm = torch.nn.functional.layer_norm(
            X, X.size()[1:], weight=weight, bias=bias, eps=epsilon)
        actual_norm, actual_mean, actual_stdev = \
            torch.ops._caffe2.LayerNorm(torch.tensor(X), torch.tensor(
                weight), torch.tensor(bias), 1, epsilon, True)
        torch.testing.assert_allclose(expected_norm, actual_norm)

    def test_memory_format(self):
        x = torch.randn(10, 3, 32, 32)
        nhwc = x.contiguous(memory_format=torch.channels_last)
        self.assertFalse(nhwc.is_contiguous())
        self.assertTrue(nhwc.is_contiguous(memory_format=torch.channels_last))
        self.assertEqual(nhwc, x)

    def test_memory_format_contiguous_returns_same_tensor_if_already_satisfies(self):
        x = torch.randn(10, 32, 32, 3).permute(0, 3, 1, 2)
        alias = x.contiguous(memory_format=torch.channels_last)
        alias.fill_(7)
        self.assertEqual(x, alias)

    def test_memory_format_empty(self):
        with self.assertRaises(RuntimeError):
            x = torch.empty((3, 3), memory_format=torch.channels_last)
        x = torch.empty((3, 3, 3, 3), memory_format=torch.channels_last)
        self.assertTrue(x.is_contiguous(memory_format=torch.channels_last))

    def test_subclass_tensors(self):
        # raise an error when trying to subclass FloatTensor
        with self.assertRaisesRegex(TypeError, "type 'torch.FloatTensor' is not an acceptable base type"):
            class Foo1(torch.FloatTensor):
                pass

        # but allow subclassing Tensor:
        class Foo2(torch.Tensor):
            def foo(self):
                return 5
        f = Foo2()
        self.assertEqual(f.foo(), 5)

    def test_ndim(self):
        a = torch.randn(1, 2, 3)
        self.assertEqual(3, a.ndim)
        b = torch.randn(())
        self.assertEqual(0, b.ndim)
        c = torch.randn(1, 0)
        self.assertEqual(2, c.ndim)

    def test_T(self):
        a = torch.randn(2, 3, 4)
        t1 = a.T
        t2 = a.permute(2, 1, 0)
        self.assertEqual(t2, t1)
        b = torch.randn(10)
        self.assertEqual(b, b.T)
        scalar = torch.tensor(5)
        self.assertEqual(scalar, scalar.T)

    def test_python_types(self):
        a1 = torch.randn((1, 2), dtype=torch.float64)
        a2 = torch.randn((1, 2), dtype=float)
        self.assertEqual(a1.dtype, a2.dtype)

        b1 = torch.arange(10, 20, dtype=torch.int64)
        b2 = torch.arange(10, 20, dtype=int)
        self.assertEqual(b1.dtype, b2.dtype)

        c1 = torch.tensor([True, False], dtype=torch.bool)
        c2 = torch.tensor([True, False], dtype=bool)
        self.assertEqual(c1.dtype, c2.dtype)

    def test_fill_diagonal(self):
        a1 = torch.randn(7, 3)
        a2 = a1.clone()
        v = 1
        for i in range(3):
            a2[i][i] = v
        a1.fill_diagonal_(v)
        self.assertEqual(a1, a2)

        b1 = torch.randn(7, 3)
        b2 = b1.clone()
        for i in range(3):
            b2[i][i] = v
            b2[i + 4][i] = v
        b1.fill_diagonal_(v, wrap=True)
        self.assertEqual(b1, b2)

        c1 = torch.rand(3, 3, 3)
        c2 = c1.clone()
        for i in range(3):
            c2[i][i][i] = v
        c1.fill_diagonal_(v)
        self.assertEqual(c1, c2)

        # non-contiguous tensor
        d1 = torch.rand(3, 3, 3)[:, 1, ...]
        d2 = d1.clone()
        for i in range(3):
            d2[i][i] = v
        d1.fill_diagonal_(v)
        self.assertEqual(d1, d2)

        e1 = torch.rand(7, 3, 3)[:, 1, ...]
        e2 = e1.clone()
        for i in range(3):
            e2[i][i] = v
            e2[i + 4][i] = v
        e1.fill_diagonal_(v, wrap=True)
        self.assertEqual(e1, e2)

# Functions to test negative dimension wrapping
METHOD = 1
INPLACE_METHOD = 2
FUNCTIONAL = 4
DIM_ARG = None

def make_neg_dim_test(name, tensor_arg, arg_constr, types, extra_dim=0):
    def neg_dim_test(self):
        if isinstance(tensor_arg, list):
            assert METHOD not in types and INPLACE_METHOD not in types
            x = [torch.randn(arg) for arg in tensor_arg]
            ndim = len(tensor_arg[-1])
        else:
            x = torch.randn(*tensor_arg)
            ndim = len(tensor_arg)
        ndim += extra_dim

        n_dim_to_test = sum(map(lambda e: e is DIM_ARG, arg_constr()))

        for dims_val in combinations(range(ndim), n_dim_to_test):
            arg = arg_constr()
            arg_neg = copy.deepcopy(arg)
            idx = 0
            for i, v in enumerate(arg):
                if v is DIM_ARG:
                    arg[i] = dims_val[idx]
                    arg_neg[i] = dims_val[idx] - ndim
                    idx += 1

            if METHOD in types:
                a = getattr(x, name)(*arg)
                b = getattr(x, name)(*arg_neg)
                self.assertEqual(a, b)

            if INPLACE_METHOD in types:
                a = x.clone()
                getattr(a, name + '_')(*arg)
                b = x.clone()
                getattr(b, name + '_')(*arg_neg)
                self.assertEqual(a, b)

            if FUNCTIONAL in types:
                a = getattr(torch, name)(x, *arg)
                b = getattr(torch, name)(x, *arg_neg)
                self.assertEqual(a, b)

    return neg_dim_test


def idx_tensor(size, max_val):
    return torch.LongTensor(*size).random_(0, max_val - 1)


def add_neg_dim_tests():
    neg_dim_tests = [
        ('narrow', (10, 20, 30), lambda: [DIM_ARG, 0, 5], [METHOD]),
        ('transpose', (10, 20, 30), lambda: [DIM_ARG, DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('size', (10, 20, 30), lambda: [DIM_ARG], [METHOD]),
        ('cat', [(2, 3, 4), (2, 3, 4)], lambda: [DIM_ARG], [FUNCTIONAL]),
        ('chunk', (10, 20, 30), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('gather', (10, 20), lambda: [DIM_ARG, idx_tensor((10, 20), 10)], [METHOD, FUNCTIONAL]),
        ('index_select', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10)], [METHOD, FUNCTIONAL]),
        ('split', (10, 20), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('squeeze', (10, 1, 20, 1), lambda: [DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('unbind', (2, 3, 4), lambda: [DIM_ARG], [FUNCTIONAL]),
        ('unsqueeze', (10, 20), lambda: [DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL], 1),
        ('cumprod', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('cumsum', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('mean', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('median', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('mode', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('norm', (10, 20), lambda: [2, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('prod', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('std', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('sum', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('var', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('kthvalue', (10, 20), lambda: [3, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('max', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('min', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('sort', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('topk', (10, 20), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('renorm', (10, 20), lambda: [2, DIM_ARG, 1], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('index_add', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('index_copy', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('index_fill', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), 12], [INPLACE_METHOD]),
        ('scatter', (10, 10), lambda: [DIM_ARG, idx_tensor((10, 10), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('select', (10, 20), lambda: [DIM_ARG, 3], [METHOD]),
        ('unfold', (10, 20), lambda: [DIM_ARG, 5, 2], [METHOD]),
    ]

    for decl in neg_dim_tests:
        if len(decl) == 4:
            name, tensor_arg, arg_constr, types = decl
            extra_dim = 0
        elif len(decl) == 5:
            name, tensor_arg, arg_constr, types, extra_dim = decl

        test_name = 'test_' + name + '_neg_dim'

        assert not hasattr(_TestTorchMixin, test_name), "Duplicated test name: " + test_name
        setattr(_TestTorchMixin, test_name, make_neg_dim_test(name, tensor_arg, arg_constr, types, extra_dim))


# Device-generic tests. Instantiated below and not run directly.
class TestTorchDeviceType(TestCase):
    def check_internal_mem_overlap(self, inplace_op, num_inputs, device,
                                   expected_failure=False):
        if isinstance(inplace_op, str):
            inplace_op = getattr(torch.Tensor, inplace_op)
        input = torch.randn(1, device=device).expand(3, 3)
        inputs = [input] + [torch.randn_like(input)
                            for i in range(num_inputs - 1)]
        if not expected_failure:
            with self.assertRaisesRegex(RuntimeError, 'single memory location'):
                inplace_op(*inputs)
        else:
            with self.assertRaises(AssertionError):
                with self.assertRaisesRegex(RuntimeError, 'single memory location'):
                    inplace_op(*inputs)

    def unary_check_input_output_mem_overlap(self, data, sz, op,
                                             expected_failure=False):

        def _test(op, output, input):
            output_exp = torch.empty_like(output)
            op(input, out=output_exp)
            self.assertEqual(op(input, out=output), output_exp, op.__name__)

        # output is identical to input:
        _test(op, output=data[0:sz], input=data[0:sz])
        # output and input are independent:
        _test(op, output=data[0:sz], input=data[sz:2 * sz])
        # output partially overlaps with input:
        if not expected_failure:
            with self.assertRaisesRegex(RuntimeError, 'unsupported operation'):
                _test(op, data[0:sz], data[1:sz + 1])
        else:
            with self.assertRaises(AssertionError):
                with self.assertRaisesRegex(RuntimeError, 'unsupported operation'):
                    _test(op, data[0:sz], data[1:sz + 1])

    def binary_check_input_output_mem_overlap(self, op, device,
                                              expected_failure=False):
        sz = 3
        data = torch.randn(2 * sz, device=device)
        other = torch.randn(sz, device=device)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other, input, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(input, other, out=out),
            expected_failure=expected_failure)

    def ternary_check_input_output_mem_overlap(self, op, device,
                                               expected_failure=False):
        sz = 3
        data = torch.randn(2 * sz, device=device)
        other1 = torch.randn(sz, device=device)
        other2 = torch.randn(sz, device=device)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(input, other1, other2, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other1, input, other2, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other1, other2, input, out=out),
            expected_failure=expected_failure)

    def _test_pow(self, base, exponent, np_exponent=None):
        if np_exponent is None:
            np_exponent = exponent

        def to_np(value):
            if isinstance(value, torch.Tensor):
                return value.cpu().numpy()
            return value

        try:
            expected = torch.from_numpy(
                np.power(to_np(base), to_np(np_exponent)))
        except ValueError as e:
            err_msg = "Integers to negative integer powers are not allowed."
            self.assertEqual(str(e), err_msg)
            out = torch.empty_like(base)
            test_cases = [
                lambda: base.pow(exponent),
                lambda: base.pow_(exponent),
                lambda: torch.pow(base, exponent),
                lambda: torch.pow(base, exponent, out=out)
            ]
            for test_case in test_cases:
                self.assertRaisesRegex(RuntimeError, err_msg, test_case)
        else:
            if isinstance(base, torch.Tensor):
                actual = base.pow(exponent)
                self.assertEqual(actual, expected, allow_inf=True)

                actual = base.clone()
                actual2 = actual.pow_(exponent)
                self.assertEqual(actual, expected, allow_inf=True)
                self.assertEqual(actual2, expected, allow_inf=True)

            actual = torch.pow(base, exponent)
            self.assertEqual(actual, expected, allow_inf=True)

            actual2 = torch.pow(base, exponent, out=actual)
            self.assertEqual(actual, expected, allow_inf=True)
            self.assertEqual(actual2, expected, allow_inf=True)

    def _select_broadcastable_dims(self, dims_full=None):
        # select full dimensionality
        if dims_full is None:
            dims_full = []
            ndims = random.randint(1, 4)
            dims_full = [random.randint(1, 8) for _ in range(ndims)]
        else:
            ndims = len(dims_full)

        # select actual dimensions for ops:
        # larger: full ndims, individual sizes may be reduced
        # smaller: possibly reduced ndims, sizes may be reduced
        smaller_ndims = random.randint(1, ndims)
        dims_small = []
        dims_large = []
        for i in range(ndims - 1, -1, -1):
            j = random.randint(1, 3)
            if j == 1:  # no reduced singleton dimension
                ds = dims_full[i]
                dl = dims_full[i]
            elif j == 2:  # larger may have reduced singleton dimension
                ds = dims_full[i]
                dl = 1 if len(dims_small) < smaller_ndims else dims_full[i]
            elif j == 3:  # smaller may have reduced singleton dimension
                ds = 1
                dl = dims_full[i]
            dims_large = [dl] + dims_large
            if len(dims_small) < smaller_ndims:
                dims_small = [ds] + dims_small
        return (dims_small, dims_large, dims_full)

    def test_diagonal(self, device):
        x = torch.randn((100, 100), device=device)
        result = torch.diagonal(x)
        expected = torch.diag(x)
        self.assertEqual(result, expected)

        x = torch.randn((100, 100), device=device)
        result = torch.diagonal(x, 17)
        expected = torch.diag(x, 17)
        self.assertEqual(result, expected)

    def test_pow(self, device):
        # [res] torch.pow([res,] x)

        # pow has dedicated implementation for different exponents
        for dtype in torch.testing.get_all_math_dtypes(device):

            # This test won't work on torch.half because math.pow will generate a much more accurate result. We skip it
            # for now.
            if dtype == torch.half:
                continue

            m1 = torch.empty(0, dtype=dtype, device=device)
            if m1.is_floating_point():
                m1 = torch.rand(100, 100, dtype=dtype, device=device) + 0.5
            else:
                # math.pow will overflow and throw exceptions for large integers
                range_high = 4 if dtype in (torch.int8, torch.uint8) else 10
                m1 = torch.randint(1, range_high, (100, 100), dtype=dtype, device=device)

            for num in [-2.8, -2, -1, -0.5, 0, 0.5, 1, 2, 3, 4, 3.3]:
                if isinstance(num, int) and num < 0 and not m1.is_floating_point():
                    with self.assertRaisesRegex(RuntimeError,
                                                r'Integers to negative integer powers are not allowed\.'):
                        torch.pow(m1[4], num)
                else:
                    # base - tensor, exponent - number
                    # contiguous
                    res1 = torch.pow(m1[4], num)
                    res2 = res1.clone().zero_()
                    for i in range(res2.size(0)):
                        res2[i] = math.pow(m1[4][i], num)
                    self.assertEqual(res1, res2)

                    # non-contiguous
                    res1 = torch.pow(m1[:, 4], num)
                    res2 = res1.clone().zero_()
                    for i in range(res2.size(0)):
                        res2[i] = math.pow(m1[i, 4], num)
                    self.assertEqual(res1, res2)

            # base - number, exponent - tensor
            # contiguous
            res1 = torch.pow(3, m1[4])
            res2 = res1.clone().zero_()
            for i in range(res2.size(0)):
                res2[i] = math.pow(3, m1[4, i])
            self.assertEqual(res1, res2)

            # non-contiguous
            res1 = torch.pow(3, m1[:, 4])
            res2 = res1.clone().zero_()
            for i in range(res2.size(0)):
                res2[i] = math.pow(3, m1[i][4])
            self.assertEqual(res1, res2)

            # resize behavior for exp == 1
            out = torch.zeros(1, dtype=dtype, device=device)
            torch.pow(m1, 1, out=out)
            self.assertEqual(out, m1)

    def test_neg(self, device):
        int_types = [torch.int, torch.short, torch.int8, torch.uint8]
        float_types = [torch.float, torch.double, torch.long]

        # Tests bool tensor negation raises the correct error
        self.assertRaisesRegex(
            RuntimeError,
            r"Negation, the `\-` operator, on a bool tensor is not supported. "
            r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
            lambda: - torch.tensor([False, True], device=device))

        for dtype in float_types + int_types:
            if dtype in float_types:
                a = torch.randn(100, 90).type(dtype).to(device)
            else:
                a = torch.randint(-128, 128, (100, 90), dtype=dtype, device=device)
            zeros = torch.Tensor().type(dtype).resize_as_(a).zero_().to(device)

            if dtype == torch.uint8:
                res_add = torch.add(zeros, a, alpha=255)
            else:
                res_add = torch.add(zeros, a, alpha=-1)

            res_neg = a.clone()
            res_neg.neg_()
            self.assertEqual(res_neg, res_add)

            # test out of place as well
            res_neg_out_place = a.clone().neg()
            self.assertEqual(res_neg_out_place, res_add)

            # test via __neg__ operator
            res_neg_op = -a.clone()
            self.assertEqual(res_neg_op, res_add)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_inverse(self, device):
        from common_utils import random_fullrank_matrix_distinct_singular_value

        # no batches: 2-D tensors
        matrix = random_fullrank_matrix_distinct_singular_value(5).to(device)
        matrix_inverse = torch.inverse(matrix)
        identity = torch.eye(5).to(device)
        self.assertEqual(identity, torch.mm(matrix, matrix_inverse), 1e-8, 'inverse value')
        self.assertEqual(identity, torch.mm(matrix_inverse, matrix), 1e-8, 'inverse value')

        matrix_inverse_out = torch.empty(5, 5).to(device)
        torch.inverse(matrix, out=matrix_inverse_out)
        self.assertEqual(matrix_inverse_out, matrix_inverse, 0, 'inverse value in-place')
        # second call, now that matrix_inverse_out is transposed
        torch.inverse(matrix, out=matrix_inverse_out)
        self.assertEqual(matrix_inverse_out, matrix_inverse, 0, 'inverse value in-place')

        # one batch
        matrix = random_fullrank_matrix_distinct_singular_value(5, 1).to(device)
        matrix_inverse = torch.inverse(matrix)
        expected_inv = matrix.squeeze(0).inverse()
        self.assertEqual(matrix_inverse, expected_inv.unsqueeze(0))

        # four batches
        matrices = random_fullrank_matrix_distinct_singular_value(5, 4).to(device)
        expected_inv_list = []
        for i in range(0, 4):
            expected_inv_list.append(torch.inverse(matrices[i]))
        expected_inv = torch.stack(expected_inv_list)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(matrices_inverse, expected_inv)

        # six batches (2 x 3)
        matrices = random_fullrank_matrix_distinct_singular_value(5, 2, 3).to(device)
        expected_inv_list = []
        for mat in matrices.view(-1, 5, 5):
            expected_inv_list.append(torch.inverse(mat))
        expected_inv = torch.stack(expected_inv_list).view(2, 3, 5, 5)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(matrices_inverse, expected_inv)

        # incorrect input test
        with self.assertRaisesRegex(RuntimeError, "must be batches of square matrices"):
            torch.inverse(torch.randn(2, 3, 4, 3))

        # correctness test
        matrices = random_fullrank_matrix_distinct_singular_value(5, 3).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices, matrices_inverse), identity.expand_as(matrices))
        self.assertEqual(torch.matmul(matrices_inverse, matrices), identity.expand_as(matrices))

        # torch.inverse with out and batches
        matrices = random_fullrank_matrix_distinct_singular_value(5, 3).to(device)
        matrices_inverse = torch.empty(3, 5, 5).to(device)
        torch.inverse(matrices, out=matrices_inverse)
        self.assertEqual(torch.inverse(matrices), matrices_inverse)

        # non-contiguous inputs
        if not TEST_NUMPY:
            return

        from numpy.linalg import inv
        matrices = random_fullrank_matrix_distinct_singular_value(3, 2).to(device).permute(0, 2, 1)
        assert not matrices.is_contiguous()
        matrices_inverse = torch.inverse(matrices)
        expected_inv = torch.as_tensor(inv(matrices.cpu().numpy()))
        self.assertEqual(matrices_inverse, expected_inv.to(device))

    def test_bitwise_not(self, device):
        res = 0xffff - torch.arange(127, dtype=torch.int8, device=device)
        for dtype in (torch.bool, torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            if dtype == torch.bool:
                a = torch.tensor([True, False], device=device)
                expected_res = torch.tensor([False, True], device=device)
            else:
                a = torch.arange(127, dtype=dtype, device=device)
                expected_res = res.type(dtype)
            # new tensor
            self.assertEqual(expected_res, a.bitwise_not())
            # out
            b = torch.empty(0, dtype=dtype, device=device)
            torch.bitwise_not(a, out=b)
            self.assertEqual(expected_res, b)
            # in-place
            a.bitwise_not_()
            self.assertEqual(expected_res, a)

        # test exceptions
        for dtype in(torch.half, torch.float, torch.double):
            a = torch.zeros(10, dtype=dtype, device=device)
            # new tensor
            with self.assertRaises(RuntimeError):
                a.bitwise_not()
            # out
            b = torch.empty(0, dtype=dtype, device=device)
            with self.assertRaises(RuntimeError):
                torch.bitwise_not(a, out=b)
            # in-place
            with self.assertRaises(RuntimeError):
                a.bitwise_not_()

    def test_logical_not(self, device):
        for dtype in torch.testing.get_all_dtypes():
            a = torch.tensor([10, 1, 0], dtype=dtype, device=device)
            if dtype == torch.bfloat16:
                self.assertRaises(RuntimeError, lambda: a.logical_not())
                continue
            expected_res = torch.tensor([0, 0, 1], dtype=dtype, device=device)
            # new tensor
            self.assertEqual(expected_res.bool(), a.logical_not())
            # out
            for out_dtype in torch.testing.get_all_dtypes():
                b = torch.empty(0, dtype=out_dtype, device=device)
                if out_dtype == torch.bfloat16:
                    self.assertRaises(RuntimeError, lambda: torch.logical_not(a, out=b))
                    continue
                torch.logical_not(a, out=b)
                self.assertEqual(expected_res.bool(), b.bool())
            # in-place
            a.logical_not_()
            self.assertEqual(expected_res, a)

    def test_logical_xor(self, device):
        for dtype in (torch.bool,):  # Will add more dtypes in the future
            expected_res = torch.tensor([0, 0, 1, 1], dtype=dtype, device=device)
            a = torch.tensor([10, 0, 1, 0], dtype=dtype, device=device)
            b = torch.tensor([1, 0, 0, 10], dtype=dtype, device=device)
            # new tensor
            self.assertEqual(expected_res, a.logical_xor(b))
            # out
            c = torch.empty(0, dtype=dtype, device=device)
            torch.logical_xor(a, b, out=c)
            self.assertEqual(expected_res, c)
            # out is not bool
            c = torch.empty(0, dtype=torch.uint8, device=device)
            with self.assertRaisesRegex(RuntimeError,
                                        r"The output tensor of logical_xor must be a bool tensor\."):
                torch.logical_xor(a, b, out=c)
            # in-place
            a.logical_xor_(b)
            self.assertEqual(expected_res, a)

    def test_isinf(self, device):
        t1 = torch.Tensor([1, inf, 2, -inf, nan]).to(device)
        t2 = torch.ByteTensor([1, 2, 3]).to(device)
        t3 = torch.CharTensor([1, 2, 3]).to(device)
        t4 = torch.ShortTensor([1, 2, 3]).to(device)
        t5 = torch.IntTensor([1, 2, 3]).to(device)
        t6 = torch.LongTensor([1, 2, 3]).to(device)
        self.assertEqual(torch.isinf(t1), torch.ByteTensor([0, 1, 0, 1, 0]).to(device))
        self.assertEqual(torch.isinf(t2), torch.ByteTensor([0, 0, 0]).to(device))
        self.assertEqual(torch.isinf(t3), torch.ByteTensor([0, 0, 0]).to(device))
        self.assertEqual(torch.isinf(t4), torch.ByteTensor([0, 0, 0]).to(device))
        self.assertEqual(torch.isinf(t5), torch.ByteTensor([0, 0, 0]).to(device))
        self.assertEqual(torch.isinf(t6), torch.ByteTensor([0, 0, 0]).to(device))

    def test_clamp(self, device):
        m1 = torch.rand(100, device=device).mul(5).add(-2.5)  # uniform in [-2.5, 2.5]
        # just in case we're extremely lucky.
        min_val = -1
        max_val = 1
        m1[1] = min_val
        m1[2] = max_val

        res1 = m1.clone()
        res1.clamp_(min_val, max_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = max(min_val, min(max_val, res2[i]))
        self.assertEqual(res1, res2)

        out = m1.clone()
        torch.clamp(m1, min=min_val, max=max_val, out=out)
        self.assertEqual(out, res1)

        res1 = torch.clamp(m1, min=min_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = max(min_val, res2[i])
        self.assertEqual(res1, res2)

        torch.clamp(m1, min=min_val, out=out)
        self.assertEqual(out, res1)

        res1 = torch.clamp(m1, max=max_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = min(max_val, res2[i])
        self.assertEqual(res1, res2)

        torch.clamp(m1, max=max_val, out=out)
        self.assertEqual(out, res1)

        # if the tensor contains nan case
        test_tens = torch.tensor([nan], device=device)

        res1 = test_tens.clone()
        res1.clamp_(min_val, max_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = max(min(res2[i], max_val), min_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        out = test_tens.clone()
        torch.clamp(test_tens, min=min_val, max=max_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        res1 = torch.clamp(test_tens, min=min_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = max(res2[i], min_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        torch.clamp(test_tens, min=min_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        res1 = torch.clamp(test_tens, max=max_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = min(res2[i], max_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        torch.clamp(test_tens, max=max_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        error_msg = 'At least one of \'min\' or \'max\' must not be None'
        with self.assertRaisesRegex(RuntimeError, error_msg):
            m1.clamp()
        with self.assertRaisesRegex(RuntimeError, error_msg):
            m1.clamp_()

    def test_cat_empty_legacy(self, device):
        # FIXME: this is legacy behavior and should be removed
        # when we support empty tensors with arbitrary sizes
        dtype = torch.float32

        x = torch.randn((4, 3, 32, 32), dtype=dtype, device=device)
        empty = torch.randn((0,), dtype=dtype, device=device)

        res1 = torch.cat([x, empty], dim=1)
        res2 = torch.cat([empty, x], dim=1)
        self.assertEqual(res1, res2)

        conv = torch.nn.Conv2d(3, 3, kernel_size=1).float().to(device)
        res1 = torch.cat([conv(x), empty], dim=1)
        res2 = torch.cat([empty, conv(x)], dim=1)
        self.assertEqual(res1, res2)

        res1 = torch.cat([empty, empty], dim=1)
        self.assertEqual(res1, empty)

        with self.assertRaisesRegex(RuntimeError,
                                    'non-empty list of Tensors'):
            torch.cat([], dim=1)

    def test_cat_empty(self, device):
        dtype = torch.float32

        x = torch.randn((4, 3, 32, 32), dtype=dtype, device=device)
        empty = torch.randn((4, 0, 32, 32), dtype=dtype, device=device)

        res1 = torch.cat([x, empty], dim=1)
        res2 = torch.cat([empty, x], dim=1)
        self.assertEqual(res1, res2)

        conv = torch.nn.Conv2d(3, 3, kernel_size=1).float().to(device)
        res1 = torch.cat([conv(x), empty], dim=1)
        res2 = torch.cat([empty, conv(x)], dim=1)
        self.assertEqual(res1, res2)

        res1 = torch.cat([empty, empty], dim=1)
        self.assertEqual(res1, empty)

        # check non-legacy-behavior (sizes don't match)
        empty = torch.randn((4, 0, 31, 32), dtype=dtype, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, empty], dim=1))
        self.assertRaises(RuntimeError, lambda: torch.cat([empty, x], dim=1))

        # check non-legacy-behavior (dimensions don't match)
        empty = torch.randn((4, 0), dtype=dtype, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, empty], dim=1))
        self.assertRaises(RuntimeError, lambda: torch.cat([empty, x], dim=1))

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_inverse_many_batches(self, device):
        from common_utils import random_fullrank_matrix_distinct_singular_value

        matrices = random_fullrank_matrix_distinct_singular_value(5, 256, 256).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices_inverse, matrices),
                         torch.eye(5).to(device).expand_as(matrices))

        matrices = random_fullrank_matrix_distinct_singular_value(3, 512, 512).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices, matrices_inverse),
                         torch.eye(3).to(device).expand_as(matrices))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_pinverse(self, device):
        from common_utils import random_fullrank_matrix_distinct_singular_value as fullrank

        def run_test(M):
            # Testing against definition for pseudo-inverses
            MPI = torch.pinverse(M)
            if M.numel() > 0:
                self.assertEqual(M, M.matmul(MPI).matmul(M), 1e-8, 'pseudo-inverse condition 1')
                self.assertEqual(MPI, MPI.matmul(M).matmul(MPI), 1e-8, 'pseudo-inverse condition 2')
                self.assertEqual(M.matmul(MPI), (M.matmul(MPI)).transpose(-2, -1), 1e-8, 'pseudo-inverse condition 3')
                self.assertEqual(MPI.matmul(M), (MPI.matmul(M)).transpose(-2, -1), 1e-8, 'pseudo-inverse condition 4')
            else:
                self.assertEqual(M.shape, MPI.shape[:-2] + (MPI.shape[-1], MPI.shape[-2]))
        for sizes in [(5, 5), (3, 5, 5), (3, 7, 5, 5),  # square matrices
                      (3, 2), (5, 3, 2), (7, 5, 3, 2),  # fat matrices
                      (2, 3), (5, 2, 3), (7, 5, 2, 3),  # thin matrices
                      (0, 0), (0, 2), (2, 0), (3, 0, 0), (0, 3, 0), (0, 0, 3)]:  # zero numel matrices
            M = torch.randn(*sizes, device=device)
            run_test(M)

        # Test inverse and pseudo-inverse for invertible matrix
        for sizes in [(5, 5), (3, 5, 5), (3, 7, 5, 5)]:
            matsize = sizes[-1]
            batchdims = sizes[:-2]
            M = fullrank(matsize, *batchdims).to(device=device)
            self.assertEqual(torch.eye(matsize, device=device).expand(sizes), M.pinverse().matmul(M),
                             1e-7, 'pseudo-inverse for invertible matrix')

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_matrix_rank(self, device):
        a = torch.eye(10, device=device)
        self.assertEqual(torch.matrix_rank(a).item(), 10)
        self.assertEqual(torch.matrix_rank(a, True).item(), 10)

        a[5, 5] = 0
        self.assertEqual(torch.matrix_rank(a).item(), 9)
        self.assertEqual(torch.matrix_rank(a, True).item(), 9)

        a = torch.randn(24, 42, device=device)
        self.assertEqual(torch.matrix_rank(a), torch.matrix_rank(a.t()))
        aaT = torch.mm(a, a.t())
        self.assertEqual(torch.matrix_rank(aaT), torch.matrix_rank(aaT, True))
        aTa = torch.mm(a.t(), a)
        self.assertEqual(torch.matrix_rank(aTa), torch.matrix_rank(aTa, True))

        if TEST_NUMPY:
            from numpy.linalg import matrix_rank
            a = torch.randn(35, 75, device=device)
            self.assertEqual(torch.matrix_rank(a).item(), matrix_rank(a.cpu().numpy()))
            self.assertEqual(torch.matrix_rank(a, 0.01).item(), matrix_rank(a.cpu().numpy(), 0.01))

            aaT = torch.mm(a, a.t())
            self.assertEqual(torch.matrix_rank(aaT).item(), matrix_rank(aaT.cpu().numpy()))
            self.assertEqual(torch.matrix_rank(aaT, 0.01).item(), matrix_rank(aaT.cpu().numpy(), 0.01))

            if np.lib.NumpyVersion(np.__version__) >= '1.14.0':
                self.assertEqual(torch.matrix_rank(aaT, True).item(), matrix_rank(aaT.cpu().numpy(), True))
                self.assertEqual(torch.matrix_rank(aaT, 0.01, True).item(),
                                 matrix_rank(aaT.cpu().numpy(), 0.01, True))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_matrix_power(self, device):
        def run_test(M, sign=1):
            if sign == -1:
                M = M.inverse()
            MP2 = torch.matrix_power(M, 2)
            self.assertEqual(MP2, torch.matmul(M, M))

            MP3 = torch.matrix_power(M, 3)
            self.assertEqual(MP3, torch.matmul(MP2, M))

            MP4 = torch.matrix_power(M, 4)
            self.assertEqual(MP4, torch.matmul(MP2, MP2))

            MP6 = torch.matrix_power(M, 6)
            self.assertEqual(MP6, torch.matmul(MP3, MP3))

            MP0 = torch.matrix_power(M, 0)
            self.assertEqual(MP0, torch.eye(M.size(-2)).expand_as(M))

        # Single matrix
        M = torch.randn(5, 5, device=device)
        run_test(M)

        # Batch matrices
        M = torch.randn(3, 3, 3, device=device)
        run_test(M)

        # Many batch matrices
        M = torch.randn(2, 3, 3, 3, device=device)
        run_test(M)

        # This is for negative powers
        from common_utils import random_fullrank_matrix_distinct_singular_value
        M = random_fullrank_matrix_distinct_singular_value(5).to(device)
        run_test(M, sign=-1)

        M = random_fullrank_matrix_distinct_singular_value(3, 3).to(device)
        run_test(M, sign=-1)

        M = random_fullrank_matrix_distinct_singular_value(3, 2, 3).to(device)
        run_test(M, sign=-1)

    def test_chain_matmul(self, device):
        def product(matrices):
            for mat in matrices[1:]:
                matrices[0] = matrices[0].mm(mat)
            return matrices[0]

        def run_test(p, device):
            matrices = []
            for (pi, pi_1) in zip(p[:-1], p[1:]):
                matrices.append(torch.randn(pi, pi_1, device=device))
            self.assertEqual(torch.chain_matmul(*matrices), product(matrices))

        run_test([10, 20, 30, 5], device)
        run_test([15, 5, 10, 20, 25], device)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_det_logdet_slogdet(self, device):
        def reference_slogdet(M):
            if TEST_NUMPY:
                sdet, logabsdet = np.linalg.slogdet(M.detach().cpu().numpy())
                return M.new_tensor(sdet), M.new_tensor(logabsdet)
            else:
                # naive row reduction
                M = M.clone()
                l = M.size(0)
                multiplier = 1
                for i in range(l):
                    if M[i, 0].item() != 0:
                        if i != 0:
                            M[0], M[i] = M[i], M[0]
                            multiplier = -1
                        break
                else:
                    return 0
                for i in range(1, l):
                    row = M[i]
                    for j in range(i):
                        row -= row[j] / M[j, j] * M[j]
                    M[i] = row
            sdet = M.diag().sign().prod()
            logabsdet = M.diag().abs_().log_().sum().add_(math.log(multiplier))
            return sdet, logabsdet

        def test_single_det(M, target, desc):
            target_sdet, target_logabsdet = target

            det = M.det()
            logdet = M.logdet()
            sdet, logabsdet = M.slogdet()

            # Test det
            self.assertEqual(det, target_sdet * target_logabsdet.exp(), 1e-7, '{} (det)'.format(desc))

            # Test slogdet
            # Compare the overall value rather than individual parts because of
            # precision issues when det is near zero.
            self.assertEqual(sdet * logabsdet.exp(), target_sdet * target_logabsdet.exp(), 1e-7, '{} (slogdet)'.format(desc))

            # Test logdet
            # Compare logdet against our own pytorch slogdet because they should
            # be consistent, while it may behave slightly differently with other
            # slogdet implementations when det is near zero due to precision
            # issues.
            if sdet.item() < 0:
                self.assertTrue(logdet.item() != logdet.item(), '{} (logdet negative case)'.format(desc))
            else:
                self.assertEqual(logdet.exp(), target_logabsdet.exp(), 1e-7, '{} (logdet non-negative case)'.format(desc))

        eye = torch.eye(5, device=device)
        test_single_det(eye, (torch.ones((), device=device), torch.zeros((), device=device)), 'identity')

        def test(M):
            assert M.size(0) >= 5, 'this helper fn assumes M to be at least 5x5'
            M = M.to(device)

            ref_M_sdet, ref_M_logabsdet = reference_slogdet(M)

            test_single_det(M, (ref_M_sdet, ref_M_logabsdet), 'basic')
            if ref_M_logabsdet.exp().item() >= 1e-6:  # skip singular
                M_inv = M.inverse()
                test_single_det(M_inv, reference_slogdet(M_inv), 'inverse')

            test_single_det(M, (ref_M_sdet, ref_M_logabsdet), 'transpose')

            for x in [0, 2, 4]:
                for scale in [-2, -0.1, 0, 10]:
                    if scale > 0:
                        target = ref_M_sdet, ref_M_logabsdet + math.log(scale)
                    elif scale == 0:
                        target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                    else:
                        target = ref_M_sdet.neg(), ref_M_logabsdet + math.log(-scale)

                    # dim 0
                    M_clone = M.clone()
                    M_clone[:, x] *= scale
                    test_single_det(M_clone, target, 'scale a row')
                    # dim 1
                    M_clone = M.clone()
                    M_clone[x, :] *= scale
                    test_single_det(M_clone, target, 'scale a column')

            for x1, x2 in [(0, 3), (4, 1), (3, 2)]:
                assert x1 != x2, 'x1 and x2 needs to be different for this test'
                target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                # dim 0
                M_clone = M.clone()
                M_clone[:, x2] = M_clone[:, x1]
                test_single_det(M_clone, target, 'two rows are same')
                # dim 1
                M_clone = M.clone()
                M_clone[x2, :] = M_clone[x1, :]
                test_single_det(M_clone, target, 'two columns are same')

                for scale1, scale2 in [(0.3, -1), (0, 2), (10, 0.1)]:
                    det_scale = scale1 * scale2 * -1
                    if det_scale > 0:
                        target = ref_M_sdet, ref_M_logabsdet + math.log(det_scale)
                    elif det_scale == 0:
                        target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                    else:
                        target = ref_M_sdet.neg(), ref_M_logabsdet + math.log(-det_scale)

                    # dim 0
                    M_clone = M.clone()
                    t = M_clone[:, x1] * scale1
                    M_clone[:, x1] += M_clone[:, x2] * scale2
                    M_clone[:, x2] = t
                    test_single_det(M_clone, target, 'exchanging rows')
                    # dim 1
                    M_clone = M.clone()
                    t = M_clone[x1, :] * scale1
                    M_clone[x1, :] += M_clone[x2, :] * scale2
                    M_clone[x2, :] = t
                    test_single_det(M_clone, target, 'exchanging columns')

        def get_random_mat_scale(n):
            # For matrices with values i.i.d. with 0 mean, unit variance, and
            # subexponential tail, we have:
            #   E[log det(A^2)] \approx log((n-1)!)
            #
            # Notice:
            #   log Var[det(A)] = log E[det(A^2)] >= E[log det(A^2)]
            #
            # So:
            #   stddev[det(A)] >= sqrt( (n-1)! )
            #
            # We use this as an intuitive guideline to scale random generated
            # matrices so our closeness tests can work more robustly:
            #   scale by sqrt( (n-1)! )^(-1/n) = ( (n-1)! )^(-1/(2n))
            #
            # source: https://arxiv.org/pdf/1112.0752.pdf

            # TODO: technically we need subexponential distn for this to hold,
            #       but we mostly use gaussian entries below. Consider switching
            #       to Chi-sq if this turns out not stable enough, since Chi-sq
            #       is easy enough to sample from.
            return math.factorial(n - 1) ** (-1.0 / (2 * n))

        for n in [5, 10, 25]:
            scale = get_random_mat_scale(n)
            test(torch.randn(n, n, device=device) * scale)
            r = torch.randn(n, n, device=device) * scale
            # symmetric psd
            test(r.mm(r.t()))
            # symmetric pd
            r = torch.randn(n, n, device=device) * scale
            test(r.mm(r.t()) + torch.eye(n, device=device) * 1e-6)
            # symmetric
            r = torch.randn(n, n, device=device) * scale
            for i in range(n):
                for j in range(i):
                    r[i, j] = r[j, i]
            test(r)
            # non-contiguous
            test((torch.randn(n, n, n + 1, device=device) * scale)[:, 2, 1:])
            # det = 0
            r = torch.randn(n, n, device=device) * scale
            u, s, v = r.svd()
            if reference_slogdet(u)[0] < 0:
                u = -u
            if reference_slogdet(v)[0] < 0:
                v = -v
            s[0] *= -1
            s[-1] = 0
            test(u.mm(s.diag()).mm(v))

        # Small values to test numerical stability. Note that we don't scale
        # this matrix.
        r = torch.randn(512, 512, device=device)
        u, s, v = r.svd()
        s.fill_(1. / (100 * s.numel()))
        test(u.mm(s.diag()).mm(v))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_det_logdet_slogdet_batched(self, device):
        from common_utils import (random_symmetric_matrix, random_symmetric_psd_matrix,
                                  random_symmetric_pd_matrix, random_square_matrix_of_rank)

        # mat_chars denotes matrix characteristics
        # possible values are: sym, sym_psd, sym_pd, sing, non_sym
        def run_test(matsize, batchdims, mat_chars):
            num_matrices = reduce(lambda x, y: x * y, batchdims, 1)
            list_of_matrices = []

            for idx in range(num_matrices):
                mat_type = idx % len(mat_chars)
                if mat_chars[mat_type] == 'sym':
                    list_of_matrices.append(random_symmetric_matrix(matsize).to(device=device))
                elif mat_chars[mat_type] == 'sym_psd':
                    list_of_matrices.append(random_symmetric_psd_matrix(matsize).to(device=device))
                elif mat_chars[mat_type] == 'sym_pd':
                    list_of_matrices.append(random_symmetric_pd_matrix(matsize).to(device=device))
                elif mat_chars[mat_type] == 'sing':
                    list_of_matrices.append(torch.ones(matsize, matsize, device=device))
                elif mat_chars[mat_type] == 'non_sing':
                    list_of_matrices.append(random_square_matrix_of_rank(matsize, matsize).to(device=device))
            full_tensor = torch.stack(list_of_matrices, dim=0).reshape(batchdims + (matsize, matsize))
            # Scaling adapted from `get_random_mat_scale` in _test_det_logdet_slogdet
            full_tensor *= (math.factorial(matsize - 1) ** (-1.0 / (2 * matsize)))

            for fn in [torch.det, torch.logdet, torch.slogdet]:
                expected_value = []
                actual_value = fn(full_tensor)
                for full_idx in product(*map(lambda x: list(range(x)), batchdims)):
                    expected_value.append(fn(full_tensor[full_idx]))

                if fn == torch.slogdet:
                    sign_value = torch.stack([tup[0] for tup in expected_value], dim=0).reshape(batchdims)
                    expected_value = torch.stack([tup[1] for tup in expected_value], dim=0).reshape(batchdims)
                    self.assertEqual(sign_value, actual_value[0], allow_inf=True)
                    self.assertEqual(expected_value, actual_value[1], allow_inf=True)
                else:
                    expected_value = torch.stack(expected_value, dim=0).reshape(batchdims)
                    self.assertEqual(actual_value, expected_value, allow_inf=True)

        for matsize, batchdims in product([3, 5], [(3,), (5, 3)]):
            run_test(matsize, batchdims, mat_chars=['sym_pd'])
            run_test(matsize, batchdims, mat_chars=['sing'])
            run_test(matsize, batchdims, mat_chars=['non_sing'])
            run_test(matsize, batchdims, mat_chars=['sym', 'sym_pd', 'sym_psd'])
            run_test(matsize, batchdims, mat_chars=['sing', 'non_sing'])

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_solve(self, device):
        from common_utils import solve_test_helper
        for (k, n) in zip([2, 3, 5], [3, 5, 7]):
            b, A = solve_test_helper((n,), (n, k), lambda t: t.to(device))
            x = torch.solve(b, A)[0]
            self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_solve_batched(self, device):
        from common_utils import solve_test_helper

        def solve_batch_helper(A_dims, b_dims, device):
            b, A = solve_test_helper(A_dims, b_dims, lambda t: t.to(device))
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.solve(b[i], A[i])[0])
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.solve(b, A)[0]  # Actual output
            self.assertEqual(x_exp, x_act)  # Equality check
            self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 1e-12)  # Correctness check

        for batchsize in [1, 3, 4]:
            solve_batch_helper((5, batchsize), (batchsize, 5, 10), device)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_solve_batched_non_contiguous(self, device):
        from numpy.linalg import solve
        from common_utils import random_fullrank_matrix_distinct_singular_value
        A = random_fullrank_matrix_distinct_singular_value(2, 2).to(device).permute(1, 0, 2)
        b = torch.randn(2, 2, 2, device=device).permute(2, 1, 0)
        x, _ = torch.solve(b, A)
        x_exp = torch.Tensor(solve(A.cpu().numpy(), b.cpu().numpy())).to(device)
        self.assertEqual(x.data, x_exp)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_solve_batched_many_batches(self, device):
        from common_utils import solve_test_helper

        b, A = solve_test_helper((5, 256, 256), (5, 1), lambda t: t.to(device))
        x, _ = torch.solve(b, A)
        self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 1)))

        b, A = solve_test_helper((3,), (512, 512, 3, 1), lambda t: t.to(device))
        x, _ = torch.solve(b, A)
        self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_solve_batched_broadcasting(self, device):
        from numpy.linalg import solve
        from common_utils import solve_test_helper

        def cast(t):
            return t.to(device)

        def run_test(A_dims, b_dims, cast):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            b, A = solve_test_helper((A_matrix_size,) + A_batch_dims, b_dims, cast)
            x, _ = torch.solve(b, A)
            x_exp = torch.Tensor(solve(A.cpu().numpy(), b.cpu().numpy()))
            self.assertEqual(x, cast(x_exp))

        # test against numpy.linalg.solve
        for upper in [True, False]:
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), cast)  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6), cast)  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2), cast)  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), cast)  # broadcasting A & b

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_solve(self, device):
        from common_utils import cholesky_solve_test_helper
        for (k, n), upper in product(zip([2, 3, 5], [3, 5, 7]), [True, False]):
            b, A, L = cholesky_solve_test_helper((n,), (n, k), lambda t: t.to(device), upper)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_solve_batched(self, device):
        from common_utils import cholesky_solve_test_helper

        def cholesky_solve_batch_helper(A_dims, b_dims, cast, upper):
            b, A, L = cholesky_solve_test_helper(A_dims, b_dims, cast, upper)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.cholesky_solve(b[i], L[i], upper=upper))
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.cholesky_solve(b, L, upper=upper)  # Actual output
            self.assertEqual(x_act, x_exp)  # Equality check
            self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 2e-12)  # Correctness check

        for upper, batchsize in product([True, False], [1, 3, 4]):
            cholesky_solve_batch_helper((5, batchsize), (batchsize, 5, 10), lambda t: t.to(device), upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_cholesky_solve_batched_non_contiguous(self, device):
        from numpy.linalg import solve
        from common_utils import random_symmetric_pd_matrix

        for upper in [True, False]:
            A = random_symmetric_pd_matrix(2, 2)
            b = torch.randn(2, 2, 2)
            x_exp = torch.Tensor(solve(A.permute(0, 2, 1).numpy(), b.permute(2, 1, 0).numpy())).to(device)
            A = A.to(device).permute(0, 2, 1)
            b = b.to(device).permute(2, 1, 0)
            assert not A.is_contiguous() and not b.is_contiguous(), "contiguous inputs"
            L = torch.cholesky(A, upper)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertEqual(x, x_exp)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_solve_batched_many_batches(self, device):
        from common_utils import cholesky_solve_test_helper

        for upper in [True, False]:
            b, A, L = cholesky_solve_test_helper((5, 256, 256), (5, 10), lambda t: t.to(device), upper)
            x = torch.cholesky_solve(b, L, upper)
            self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 10)))

            b, A, L = cholesky_solve_test_helper((5,), (512, 512, 5, 10), lambda t: t.to(device), upper)
            x = torch.cholesky_solve(b, L, upper)
            self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_cholesky_solve_batched_broadcasting(self, device):
        from numpy.linalg import solve
        from common_utils import random_symmetric_pd_matrix

        def cast(t):
            return t.to(device)

        def run_test(A_dims, b_dims, cast, upper):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            A = random_symmetric_pd_matrix(A_matrix_size, *A_batch_dims)
            b = torch.randn(*b_dims)
            x_exp = torch.Tensor(solve(A.numpy(), b.numpy()))
            A, b = cast(A), cast(b)
            L = torch.cholesky(A, upper)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertEqual(x, cast(x_exp))

        # test against numpy.linalg.solve
        for upper in [True, False]:
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), cast, upper)  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6), cast, upper)  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2), cast, upper)  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), cast, upper)  # broadcasting A & b

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_inverse(self, device):
        from common_utils import random_symmetric_pd_matrix
        a = random_symmetric_pd_matrix(5).to(device)

        # compute inverse directly
        inv0 = torch.inverse(a)

        # default case
        chol = torch.cholesky(a)
        inv1 = torch.cholesky_inverse(chol, False)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

        # upper Triangular Test
        chol = torch.cholesky(a, True)
        inv1 = torch.cholesky_inverse(chol, True)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

        # lower Triangular Test
        chol = torch.cholesky(a, False)
        inv1 = torch.cholesky_inverse(chol, False)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_batched_many_batches(self, device):
        from common_utils import random_symmetric_pd_matrix

        def cholesky_test_helper(n, batchsize, device, upper):
            A = random_symmetric_pd_matrix(n, batchsize).to(device)
            chol_fact = torch.cholesky(A, upper=upper)
            if upper:
                # Correctness check
                self.assertEqual(A, chol_fact.transpose(-2, -1).matmul(chol_fact))
                # Upper triangular check
                self.assertEqual(chol_fact, chol_fact.triu())
            else:
                # Correctness check
                self.assertEqual(A, chol_fact.matmul(chol_fact.transpose(-2, -1)))
                # Lower triangular check
                self.assertEqual(chol_fact, chol_fact.tril())

        for upper, batchsize in product([True, False], [262144, 524288]):
            cholesky_test_helper(2, batchsize, device, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky_batched(self, device):
        from common_utils import random_symmetric_pd_matrix

        def cholesky_test_helper(n, batch_dims, device, upper):
            A = random_symmetric_pd_matrix(n, *batch_dims).to(device)
            cholesky_exp = torch.stack([m.cholesky(upper=upper) for m in A.reshape(-1, n, n)])
            cholesky_exp = cholesky_exp.reshape_as(A)
            self.assertEqual(cholesky_exp, torch.cholesky(A, upper=upper))

        for upper, batchsize in product([True, False], [(3,), (3, 4), (2, 3, 4)]):
            cholesky_test_helper(3, batchsize, device, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_cholesky(self, device):
        x = torch.rand(10, 10, device=device) + 1e-1
        A = torch.mm(x, x.t())

        # default Case
        C = torch.cholesky(A)
        B = torch.mm(C, C.t())
        self.assertEqual(A, B, 1e-14)

        # test Upper Triangular
        U = torch.cholesky(A, True)
        B = torch.mm(U.t(), U)
        self.assertEqual(A, B, 1e-14, 'cholesky (upper) did not allow rebuilding the original matrix')

        # test Lower Triangular
        L = torch.cholesky(A, False)
        B = torch.mm(L, L.t())
        self.assertEqual(A, B, 1e-14, 'cholesky (lower) did not allow rebuilding the original matrix')

    def test_view(self, device):
        tensor = torch.rand(15, device=device)
        template = torch.rand(3, 5, device=device)
        empty = torch.empty(0, device=device)
        target = template.size()
        self.assertEqual(tensor.view_as(template).size(), target)
        self.assertEqual(tensor.view(3, 5).size(), target)
        self.assertEqual(tensor.view(torch.Size([3, 5])).size(), target)
        self.assertEqual(tensor.view(-1, 5).size(), target)
        self.assertEqual(tensor.view(3, -1).size(), target)
        tensor_view = tensor.view(5, 3)
        tensor_view.fill_(random.uniform(0, 1))
        self.assertEqual(empty.view_as(empty), empty)
        self.assertEqual(empty.view(0), empty)
        self.assertEqual(empty.view(0, 3, 0, 1).size(), torch.Size([0, 3, 0, 1]))
        self.assertEqual(empty.view(0, 3, 0, 1).view(0), empty)

        # test size inference with empty tensors
        self.assertEqual(empty.view(-1).size(), torch.Size([0]))
        self.assertEqual(empty.view(10, 3, -1).size(), torch.Size([10, 3, 0]))

        with self.assertRaisesRegex(RuntimeError, r"because the unspecified dimension size -1 can be any value"):
            empty.view(-1, 0)

        with self.assertRaisesRegex(RuntimeError, r"because the unspecified dimension size -1 can be any value"):
            empty.view(3, 0, -1, 0)

        self.assertRaises(RuntimeError, lambda: tensor.view(15, 0))
        self.assertRaises(RuntimeError, lambda: tensor.view(7, -1))
        self.assertRaises(RuntimeError, lambda: tensor.view(15, -1, -1))

        # test view when tensor is not contiguous in every dimension, but only
        # contiguous dimensions are touched.
        tensor = torch.rand(4, 2, 5, 1, 6, 2, 9, 3, device=device).transpose(-1, 2).transpose(-2, 3)
        # size:                      [   4,    2,    3,    9,    6,    2,    1,    5]
        # stride:                    [3840, 1620,    1,    3,   54,   27,  324,  324]
        # contiguous dim chunks:     [__________, ____, ____, __________, ____, ____]
        # merging 1 to chunk after:  [__________, ____, ____, __________, __________]
        contig_tensor = tensor.clone()
        # [4, 2] => [8, 1]
        # [3] => [3]
        # [9] => [3, 3]
        # [6, 2] => [4, 1, 3]
        # [1, 5] => [5]
        view_size = [8, 1, 3, 3, 3, 4, 1, 3, 5]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))
        # [4, 2] => [2, 4]
        # [3] => [3]
        # [9] => [1, 9]
        # [6, 2] => [2, 2, 3]
        # [1, 5] => [5, 1]
        view_size = [2, 4, 3, 1, 9, 2, 2, 3, 5, 1]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))
        # adding size 1 dims
        view_size = [1, 1, 2, 1, 4, 3, 1, 1, 9, 1, 2, 1, 2, 3, 1, 5, 1, 1]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))

        # invalid views
        self.assertRaises(RuntimeError, lambda: tensor.view(-1))
        # crossing [4, 2], [3]
        self.assertRaises(RuntimeError, lambda: tensor.view(24, 9, 6, 2, 1, 5))
        # crossing [6, 2], [1, 5]
        self.assertRaises(RuntimeError, lambda: tensor.view(8, 3, 9, 6, 10))
        # crossing [9], [6, 2]
        self.assertRaises(RuntimeError, lambda: tensor.view(8, 3, 54, 2, 1, 5))

        # view with stride 0 dims
        tensor = torch.empty(1, 1, device=device).expand(3, 4)  # all dims are contiguous
        contig_tensor = tensor.clone()
        self.assertEqual(tensor.view(-1), contig_tensor.view(-1))
        self.assertEqual(tensor.view(1, -1, 1), contig_tensor.view(1, -1, 1))
        self.assertEqual(tensor.view(-1, 1), contig_tensor.view(-1, 1))
        self.assertEqual(tensor.view(6, 2, 1), contig_tensor.view(6, 2, 1))
        self.assertEqual(tensor.view(1, 6, 2, 1), contig_tensor.view(1, 6, 2, 1))

    def test_flip(self, device):
        data = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8], device=device).view(2, 2, 2)

        self.assertEqual(torch.tensor([5, 6, 7, 8, 1, 2, 3, 4]).view(2, 2, 2), data.flip(0))
        self.assertEqual(torch.tensor([3, 4, 1, 2, 7, 8, 5, 6]).view(2, 2, 2), data.flip(1))
        self.assertEqual(torch.tensor([2, 1, 4, 3, 6, 5, 8, 7]).view(2, 2, 2), data.flip(2))
        self.assertEqual(torch.tensor([7, 8, 5, 6, 3, 4, 1, 2]).view(2, 2, 2), data.flip(0, 1))
        self.assertEqual(torch.tensor([8, 7, 6, 5, 4, 3, 2, 1]).view(2, 2, 2), data.flip(0, 1, 2))

        # check for wrap dim
        self.assertEqual(torch.tensor([2, 1, 4, 3, 6, 5, 8, 7]).view(2, 2, 2), data.flip(-1))
        # check for permute
        self.assertEqual(torch.tensor([6, 5, 8, 7, 2, 1, 4, 3]).view(2, 2, 2), data.flip(0, 2))
        self.assertEqual(torch.tensor([6, 5, 8, 7, 2, 1, 4, 3]).view(2, 2, 2), data.flip(2, 0))

        # not allow flip on the same dim more than once
        self.assertRaises(RuntimeError, lambda: data.flip(0, 1, 1))
        # not allow empty list as input
        self.assertRaises(TypeError, lambda: data.flip())

        # not allow size of flip dim > total dims
        self.assertRaises(IndexError, lambda: data.flip(0, 1, 2, 3))
        # not allow dim > max dim
        self.assertRaises(IndexError, lambda: data.flip(3))

        # test for non-contiguous case
        expanded_data = torch.arange(1, 4, device=device).view(3, 1).expand(3, 2)
        transposed_data = torch.arange(1, 9, device=device).view(2, 2, 2).transpose(0, 1)
        self.assertEqual(torch.tensor([3, 3, 2, 2, 1, 1]).view(3, 2), expanded_data.flip(0))
        self.assertEqual(torch.tensor([8, 7, 4, 3, 6, 5, 2, 1]).view(2, 2, 2), transposed_data.flip(0, 1, 2))

        # test for shape
        data = torch.randn(2, 3, 4, device=device)
        size = [2, 3, 4]
        test_dims = []
        for i in range(1, 3):
            test_dims += combinations(range(len(size)), i)

        for ds in test_dims:
            self.assertEqual(size, list(data.flip(ds).size()))

        # test rectangular case
        data = torch.tensor([1, 2, 3, 4, 5, 6]).view(2, 3).to(device)
        flip0_result = torch.tensor([[4, 5, 6], [1, 2, 3]]).to(device)
        flip1_result = torch.tensor([[3, 2, 1], [6, 5, 4]]).to(device)

        self.assertEqual(flip0_result, data.flip(0))
        self.assertEqual(flip1_result, data.flip(1))

        # test empty tensor, should just return an empty tensor of the same shape
        data = torch.tensor([])
        self.assertEqual(data, data.flip(0))

    def test_rot90(self, device):
        data = torch.arange(1, 5, device=device).view(2, 2)
        self.assertEqual(torch.tensor([1, 2, 3, 4]).view(2, 2), data.rot90(0, [0, 1]))
        self.assertEqual(torch.tensor([2, 4, 1, 3]).view(2, 2), data.rot90(1, [0, 1]))
        self.assertEqual(torch.tensor([4, 3, 2, 1]).view(2, 2), data.rot90(2, [0, 1]))
        self.assertEqual(torch.tensor([3, 1, 4, 2]).view(2, 2), data.rot90(3, [0, 1]))

        # test for default args k=1, dims=[0, 1]
        self.assertEqual(data.rot90(), data.rot90(1, [0, 1]))

        # test for reversed order of dims
        self.assertEqual(data.rot90(3, [0, 1]), data.rot90(1, [1, 0]))

        # test for modulo of k
        self.assertEqual(data.rot90(5, [0, 1]), data.rot90(1, [0, 1]))
        self.assertEqual(data.rot90(3, [0, 1]), data.rot90(-1, [0, 1]))
        self.assertEqual(data.rot90(-5, [0, 1]), data.rot90(-1, [0, 1]))

        # test for dims out-of-range error
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, -3]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 2]))

        # test tensor with more than 2D
        data = torch.arange(1, 9, device=device).view(2, 2, 2)
        self.assertEqual(torch.tensor([2, 4, 1, 3, 6, 8, 5, 7]).view(2, 2, 2), data.rot90(1, [1, 2]))
        self.assertEqual(data.rot90(1, [1, -1]), data.rot90(1, [1, 2]))

        # test for errors
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 3]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [1, 1]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 1, 2]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0]))

    def test_signal_window_functions(self, device):
        if not TEST_SCIPY:
            raise unittest.SkipTest('Scipy not found')

        def test(name):
            torch_method = getattr(torch, name + '_window')
            for size in [1, 2, 5, 10, 50, 100, 1024, 2048]:
                for periodic in [True, False]:
                    res = torch_method(size, periodic=periodic, device=device)
                    ref = torch.from_numpy(signal.get_window(name, size, fftbins=periodic))
                    self.assertEqual(res, ref)
            with self.assertRaisesRegex(RuntimeError, r'not implemented for sparse types'):
                torch_method(3, layout=torch.sparse_coo)
            with self.assertRaisesRegex(RuntimeError, r'floating point'):
                torch_method(3, dtype=torch.long)
            self.assertTrue(torch_method(3, requires_grad=True).requires_grad)
            self.assertFalse(torch_method(3).requires_grad)

        for window in ['hann', 'hamming', 'bartlett', 'blackman']:
            test(window)

    def test_broadcast(self, device):

        # all functions
        fns = {
            "dist", "atan2", "pow", "lerp", "add",
            "sub", "mul", "div", "fmod", "remainder",
            "eq", "ge", "gt", "le", "lt", "max", "min", "ne",
            "addcdiv", "addcmul", "masked_scatter", "masked_select", "masked_fill",
            "map", "map2", "copy"
        }
        # functions with three tensor arguments
        fns_3_args = {"addcdiv", "addcmul", "map2"}

        for fn in fns:
            (dims_small, dims_large, dims_full) = self._select_broadcastable_dims()
            full1d = torch.randn(*dims_full, device=device).flatten().float()
            small = torch.randn(*dims_small, device=device).float()
            large = torch.randn(*dims_large, device=device).float()
            small_expanded = small.expand(*dims_full)
            large_expanded = large.expand(*dims_full)
            small2 = None
            small2_expanded = None
            if fn in fns_3_args:
                # create another smaller tensor
                (dims_small2, _, _) = self._select_broadcastable_dims(dims_full)
                small2 = torch.randn(*dims_small2, device=device).float()
                small2_expanded = small2.expand(*dims_full)

            if small.is_cuda and fn in ['map', 'map2']:
                # map and map2 are not implementd on CUDA tensors
                continue

            if hasattr(large_expanded, fn):
                # run through tensor versions of functions
                # and verify fully expanded inputs give same results
                expanded = {large: large_expanded, small: small_expanded, small2: small2_expanded}

                def tensorfn(myfn, t1, t2):
                    if fn == "lerp":
                        return myfn(t1, 0.5)
                    elif fn == "masked_select":
                        return myfn(t1 < 0)
                    elif fn == "masked_scatter":
                        return myfn(t1 < 0.5, full1d)
                    elif fn == "masked_fill":
                        return myfn(t1 < 0.5, 1.0)
                    elif fn in fns_3_args:
                        return myfn(1, t1, t2)
                    else:
                        return myfn(t1)

                # test various orders
                for first, second, third in [(large, small, small2), (small, large, small2),
                                             (small2, small, large), (small2, large, small)]:
                    if first is None:
                        break  # ignore last iter when small2 is None
                    method_expanded = getattr(expanded[first], fn)
                    method = getattr(first, fn)
                    r1 = tensorfn(method_expanded, expanded[second], expanded[third])
                    r2 = tensorfn(method, second, third)
                    self.assertEqual(r1, r2)

            # now for torch. versions of functions
            if hasattr(torch, fn):
                fntorch = getattr(torch, fn)
                expanded = {large: large_expanded, small: small_expanded, small2: small2_expanded}

                def torchfn(t1, t2, t3):
                    if fn == "lerp":
                        return fntorch(t1, t2, 0.5)
                    elif fn == "masked_select":
                        return fntorch(t1, t2 < 0)
                    elif fn == "masked_scatter":
                        return fntorch(t1, t2 < 0.5, full1d)
                    elif fn == "masked_fill":
                        return fntorch(t1, t2 < 0.5, 1.0)
                    elif fn in fns_3_args:
                        return fntorch(t1, 1.0, t2, t3)
                    else:
                        return fntorch(t1, t2)

                # test various orders
                for first, second, third in [(large, small, small2), (small, large, small2),
                                             (small2, small, large), (small2, large, small)]:
                    if first is None:
                        break  # ignore last iter when small2 is None
                    r1 = torchfn(expanded[first], expanded[second], expanded[third])
                    r2 = torchfn(first, second, third)
                    self.assertEqual(r1, r2)

            # now for in place functions
            # in-place tensor is not broadcastable; test only guaranteed
            # to work by broadcasting other argument(s)
            if not hasattr(large_expanded, fn + "_"):
                continue

            # need to clone largeExpanded so we can reuse, since functions are in-place
            large_expanded_clone = large_expanded.clone()

            def tensorfn_inplace(t0, t1, t2=None):
                t0_fn = getattr(t0, fn + "_")
                if fn == "lerp":
                    return t0_fn(t1, 0.5)
                elif fn == "masked_scatter":
                    return t0_fn(t1 < 0.5, full1d)
                elif fn == "masked_fill":
                    return t0_fn(t1 < 0.5, 1.0)
                elif fn == "map":
                    return t0_fn(t1, lambda x, y: x + y)
                elif fn == "map2":
                    return t0_fn(t1, t2, lambda x, y, z: x + y + z)
                elif fn in fns_3_args:
                    return t0_fn(1.0, t1, t2)
                else:
                    return t0_fn(t1)
            # in-place pointwise operations don't actually work if the in-place
            # tensor is 0-strided (numpy has the same issue)
            if (0 not in large_expanded.stride() and 0 not in large_expanded_clone.stride()):
                r1 = tensorfn_inplace(large_expanded, small_expanded, small2_expanded)
                r2 = tensorfn_inplace(large_expanded_clone, small, small2)
                self.assertEqual(r1, r2)

            def broadcastable(t0, t1, t2=None):
                try:
                    t1.expand_as(t0)
                    if t2 is not None:
                        t2.expand_as(t0)
                except RuntimeError:
                    return False
                return True

            def _test_in_place_broadcastable(t0, t1, t2=None):
                if not broadcastable(t0, t1, t2):
                    same_size = t0.numel() == t1.numel() and (t0.numel() == t2.numel() if t2 is not None else True)
                    if not same_size:
                        self.assertRaises(RuntimeError, lambda: tensorfn_inplace(t0, t1, t2))
                else:
                    tensorfn_inplace(t0, t1, t2)

            if fn not in fns_3_args:
                _test_in_place_broadcastable(small, large_expanded)
                _test_in_place_broadcastable(small, large)
            else:
                _test_in_place_broadcastable(small2, small_expanded, large_expanded)
                _test_in_place_broadcastable(small2, small, large)

    def test_broadcast_fused_matmul(self, device):
        fns = ["baddbmm", "addbmm", "addmm", "addmv", "addr"]

        for fn in fns:
            batch_dim = random.randint(1, 8)
            n_dim = random.randint(1, 8)
            m_dim = random.randint(1, 8)
            p_dim = random.randint(1, 8)

            def dims_full_for_fn():
                if fn == "baddbmm":
                    return ([batch_dim, n_dim, p_dim], [batch_dim, n_dim, m_dim], [batch_dim, m_dim, p_dim])
                elif fn == "addbmm":
                    return ([n_dim, p_dim], [batch_dim, n_dim, m_dim], [batch_dim, m_dim, p_dim])
                elif fn == "addmm":
                    return ([n_dim, p_dim], [n_dim, m_dim], [m_dim, p_dim])
                elif fn == "addmv":
                    return ([n_dim], [n_dim, m_dim], [m_dim])
                elif fn == "addr":
                    return ([n_dim, m_dim], [n_dim], [m_dim])
                else:
                    raise AssertionError("unknown function")

            (t0_dims_full, t1_dims, t2_dims) = dims_full_for_fn()
            (t0_dims_small, _, _) = self._select_broadcastable_dims(t0_dims_full)

            t0_small = torch.randn(*t0_dims_small, device=device).float()
            t1 = torch.randn(*t1_dims, device=device).float()
            t2 = torch.randn(*t2_dims, device=device).float()

            t0_full = t0_small.expand(*t0_dims_full).to(device)

            fntorch = getattr(torch, fn)
            r0 = fntorch(t0_small, t1, t2)
            r1 = fntorch(t0_full, t1, t2)
            self.assertEqual(r0, r1)

    def test_broadcast_batched_matmul(self, device):
        n_dim = random.randint(1, 8)
        m_dim = random.randint(1, 8)
        p_dim = random.randint(1, 8)
        full_batch_dims = [random.randint(1, 3) for i in range(random.randint(1, 3))]
        (batch_dims_small, _, _) = self._select_broadcastable_dims(full_batch_dims)

        def verify_batched_matmul(full_lhs, one_dimensional):
            if not one_dimensional:
                lhs_dims = [n_dim, m_dim]
                rhs_dims = [m_dim, p_dim]
                result_dims = [n_dim, p_dim]
            else:
                lhs_dims = [n_dim, m_dim] if full_lhs else [m_dim]
                rhs_dims = [m_dim, p_dim] if not full_lhs else [m_dim]
                result_dims = [n_dim] if full_lhs else [p_dim]

            lhs_mat_dims = lhs_dims if len(lhs_dims) != 1 else [1, m_dim]
            rhs_mat_dims = rhs_dims if len(rhs_dims) != 1 else [m_dim, 1]
            full_mat_dims = lhs_mat_dims if full_lhs else rhs_mat_dims
            dim0_dims = rhs_dims if full_lhs else lhs_dims
            small_dims = batch_dims_small + (rhs_mat_dims if full_lhs else lhs_mat_dims)

            small = torch.randn(*(small_dims), device=device).float()
            dim0 = torch.randn(*(dim0_dims), device=device).float()
            full = torch.randn(*(full_batch_dims + full_mat_dims), device=device).float()
            if not one_dimensional:
                (lhsTensors, rhsTensors) = ((full,), (small, dim0)) if full_lhs else ((small, dim0), (full,))
            else:
                (lhsTensors, rhsTensors) = ((full,), (dim0,)) if full_lhs else ((dim0,), (full,))

            def maybe_squeeze_result(l, r, result):
                if len(lhs_dims) == 1 and l.dim() != 1:
                    return result.squeeze(-2)
                elif len(rhs_dims) == 1 and r.dim() != 1:
                    return result.squeeze(-1)
                else:
                    return result

            for lhs in lhsTensors:
                lhs_expanded = lhs.expand(*(torch.Size(full_batch_dims) + torch.Size(lhs_mat_dims)))
                lhs_expanded_matmul_fn = lhs_expanded.matmul
                for rhs in rhsTensors:
                    rhs_expanded = ((rhs if len(rhs_dims) != 1 else rhs.unsqueeze(-1)).
                                    expand(*(torch.Size(full_batch_dims) + torch.Size(rhs_mat_dims))))
                    truth = maybe_squeeze_result(lhs_expanded, rhs_expanded, lhs_expanded_matmul_fn(rhs_expanded))
                    for l in (lhs, lhs_expanded):
                        for r in (rhs, rhs_expanded):
                            l_matmul_fn = l.matmul
                            result = maybe_squeeze_result(l, r, l_matmul_fn(r))
                            self.assertEqual(truth, result)
                            # test torch.matmul function as well
                            torch_result = maybe_squeeze_result(l, r, torch.matmul(l, r))
                            self.assertEqual(truth, torch_result)
                            # test torch.matmul with out
                            out = torch.zeros_like(torch_result)
                            torch.matmul(l, r, out=out)
                            self.assertEqual(truth, maybe_squeeze_result(l, r, out))

                # compare to bmm
                bmm_result = (torch.bmm(lhs_expanded.contiguous().view(-1, *lhs_mat_dims),
                                        rhs_expanded.contiguous().view(-1, *rhs_mat_dims)))
                self.assertEqual(truth.view(-1, *result_dims), bmm_result.view(-1, *result_dims))

        for indices in product((True, False), repeat=2):
            verify_batched_matmul(*indices)

    def test_contiguous(self, device):
        x = torch.randn(1, 16, 5, 5, device=device)
        self.assertTrue(x.is_contiguous())
        stride = list(x.stride())
        stride[0] = 20
        # change the stride in dimension 0. the tensor is still contiguous because size[0] is 1
        x.set_(x.storage(), 0, x.size(), stride)
        self.assertTrue(x.is_contiguous())

    def test_index(self, device):

        def consec(size, start=1):
            sequence = torch.ones(int(torch.Tensor(size).prod(0))).cumsum(0)
            sequence.add_(start - 1)
            return sequence.view(*size)

        reference = consec((3, 3, 3)).to(device)

        # empty tensor indexing
        self.assertEqual(reference[torch.LongTensor().to(device)], reference.new(0, 3, 3))

        self.assertEqual(reference[0], consec((3, 3)), 0)
        self.assertEqual(reference[1], consec((3, 3), 10), 0)
        self.assertEqual(reference[2], consec((3, 3), 19), 0)
        self.assertEqual(reference[0, 1], consec((3,), 4), 0)
        self.assertEqual(reference[0:2], consec((2, 3, 3)), 0)
        self.assertEqual(reference[2, 2, 2], 27, 0)
        self.assertEqual(reference[:], consec((3, 3, 3)), 0)

        # indexing with Ellipsis
        self.assertEqual(reference[..., 2], torch.Tensor([[3, 6, 9],
                                                          [12, 15, 18],
                                                          [21, 24, 27]]), 0)
        self.assertEqual(reference[0, ..., 2], torch.Tensor([3, 6, 9]), 0)
        self.assertEqual(reference[..., 2], reference[:, :, 2], 0)
        self.assertEqual(reference[0, ..., 2], reference[0, :, 2], 0)
        self.assertEqual(reference[0, 2, ...], reference[0, 2], 0)
        self.assertEqual(reference[..., 2, 2, 2], 27, 0)
        self.assertEqual(reference[2, ..., 2, 2], 27, 0)
        self.assertEqual(reference[2, 2, ..., 2], 27, 0)
        self.assertEqual(reference[2, 2, 2, ...], 27, 0)
        self.assertEqual(reference[...], reference, 0)

        reference_5d = consec((3, 3, 3, 3, 3)).to(device)
        self.assertEqual(reference_5d[..., 1, 0], reference_5d[:, :, :, 1, 0], 0)
        self.assertEqual(reference_5d[2, ..., 1, 0], reference_5d[2, :, :, 1, 0], 0)
        self.assertEqual(reference_5d[2, 1, 0, ..., 1], reference_5d[2, 1, 0, :, 1], 0)
        self.assertEqual(reference_5d[...], reference_5d, 0)

        # LongTensor indexing
        reference = consec((5, 5, 5)).to(device)
        idx = torch.LongTensor([2, 4]).to(device)
        self.assertEqual(reference[idx], torch.stack([reference[2], reference[4]]))
        # TODO: enable one indexing is implemented like in numpy
        # self.assertEqual(reference[2, idx], torch.stack([reference[2, 2], reference[2, 4]]))
        # self.assertEqual(reference[3, idx, 1], torch.stack([reference[3, 2], reference[3, 4]])[:, 1])

        # None indexing
        self.assertEqual(reference[2, None], reference[2].unsqueeze(0))
        self.assertEqual(reference[2, None, None], reference[2].unsqueeze(0).unsqueeze(0))
        self.assertEqual(reference[2:4, None], reference[2:4].unsqueeze(1))
        self.assertEqual(reference[None, 2, None, None], reference.unsqueeze(0)[:, 2].unsqueeze(0).unsqueeze(0))
        self.assertEqual(reference[None, 2:5, None, None], reference.unsqueeze(0)[:, 2:5].unsqueeze(2).unsqueeze(2))

        # indexing 0-length slice
        self.assertEqual(torch.empty(0, 5, 5), reference[slice(0)])
        self.assertEqual(torch.empty(0, 5), reference[slice(0), 2])
        self.assertEqual(torch.empty(0, 5), reference[2, slice(0)])
        self.assertEqual(torch.tensor([]), reference[2, 1:1, 2])

        # indexing with step
        reference = consec((10, 10, 10)).to(device)
        self.assertEqual(reference[1:5:2], torch.stack([reference[1], reference[3]], 0))
        self.assertEqual(reference[1:6:2], torch.stack([reference[1], reference[3], reference[5]], 0))
        self.assertEqual(reference[1:9:4], torch.stack([reference[1], reference[5]], 0))
        self.assertEqual(reference[2:4, 1:5:2], torch.stack([reference[2:4, 1], reference[2:4, 3]], 1))
        self.assertEqual(reference[3, 1:6:2], torch.stack([reference[3, 1], reference[3, 3], reference[3, 5]], 0))
        self.assertEqual(reference[None, 2, 1:9:4], torch.stack([reference[2, 1], reference[2, 5]], 0).unsqueeze(0))
        self.assertEqual(reference[:, 2, 1:6:2],
                         torch.stack([reference[:, 2, 1], reference[:, 2, 3], reference[:, 2, 5]], 1))

        lst = [list(range(i, i + 10)) for i in range(0, 100, 10)]
        tensor = torch.DoubleTensor(lst).to(device)
        for _i in range(100):
            idx1_start = random.randrange(10)
            idx1_end = idx1_start + random.randrange(1, 10 - idx1_start + 1)
            idx1_step = random.randrange(1, 8)
            idx1 = slice(idx1_start, idx1_end, idx1_step)
            if random.randrange(2) == 0:
                idx2_start = random.randrange(10)
                idx2_end = idx2_start + random.randrange(1, 10 - idx2_start + 1)
                idx2_step = random.randrange(1, 8)
                idx2 = slice(idx2_start, idx2_end, idx2_step)
                lst_indexed = list(map(lambda l: l[idx2], lst[idx1]))
                tensor_indexed = tensor[idx1, idx2]
            else:
                lst_indexed = lst[idx1]
                tensor_indexed = tensor[idx1]
            self.assertEqual(torch.DoubleTensor(lst_indexed), tensor_indexed)

        self.assertRaises(ValueError, lambda: reference[1:9:0])
        self.assertRaises(ValueError, lambda: reference[1:9:-1])

        self.assertRaises(IndexError, lambda: reference[1, 1, 1, 1])
        self.assertRaises(IndexError, lambda: reference[1, 1, 1, 1:1])
        self.assertRaises(IndexError, lambda: reference[3, 3, 3, 3, 3, 3, 3, 3])

        self.assertRaises(IndexError, lambda: reference[0.0])
        self.assertRaises(TypeError, lambda: reference[0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, :, 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, ..., 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, :, 0.0])

        def delitem():
            del reference[0]

        self.assertRaises(TypeError, delitem)

    @skipCUDANonDefaultStreamIf(True)
    def test_advancedindex(self, device):
        # Tests for Integer Array Indexing, Part I - Purely integer array
        # indexing

        def consec(size, start=1):
            numel = reduce(lambda x, y: x * y, size, 1)
            sequence = torch.ones(numel).cumsum(0)
            sequence.add_(start - 1)
            return sequence.view(*size)

        # pick a random valid indexer type
        def ri(indices):
            choice = random.randint(0, 2)
            if choice == 0:
                return torch.LongTensor(indices).to(device)
            elif choice == 1:
                return list(indices)
            else:
                return tuple(indices)

        def validate_indexing(x):
            self.assertEqual(x[[0]], consec((1,)))
            self.assertEqual(x[ri([0]), ], consec((1,)))
            self.assertEqual(x[ri([3]), ], consec((1,), 4))
            self.assertEqual(x[[2, 3, 4]], consec((3,), 3))
            self.assertEqual(x[ri([2, 3, 4]), ], consec((3,), 3))
            self.assertEqual(x[ri([0, 2, 4]), ], torch.Tensor([1, 3, 5]))

        def validate_setting(x):
            dtype = x.type()
            x[[0]] = -2
            self.assertEqual(x[[0]], torch.Tensor([-2]).type(dtype))
            x[[0]] = -1
            self.assertEqual(x[ri([0]), ], torch.Tensor([-1]).type(dtype))
            x[[2, 3, 4]] = 4
            self.assertEqual(x[[2, 3, 4]], torch.Tensor([4, 4, 4]).type(dtype))
            x[ri([2, 3, 4]), ] = 3
            self.assertEqual(x[ri([2, 3, 4]), ], torch.Tensor([3, 3, 3]).type(dtype))
            x[ri([0, 2, 4]), ] = torch.Tensor([5, 4, 3]).type(dtype).to(device)
            self.assertEqual(x[ri([0, 2, 4]), ], torch.Tensor([5, 4, 3]).type(dtype))

        # First, we will test indexing to generate return values

        # Case 1: Purely Integer Array Indexing
        reference = consec((10,)).to(device)
        validate_indexing(reference)
        validate_indexing(reference.type(torch.half))

        # setting values
        validate_setting(reference)
        validate_setting(reference.type(torch.half))

        # Tensor with stride != 1

        # strided is [1, 3, 5, 7]
        reference = consec((10,)).to(device)
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), storage_offset=0,
                     size=torch.Size([4]), stride=[2])

        self.assertEqual(strided[[0]], torch.Tensor([1]))
        self.assertEqual(strided[ri([0]), ], torch.Tensor([1]))
        self.assertEqual(strided[ri([3]), ], torch.Tensor([7]))
        self.assertEqual(strided[[1, 2]], torch.Tensor([3, 5]))
        self.assertEqual(strided[ri([1, 2]), ], torch.Tensor([3, 5]))
        self.assertEqual(strided[ri([[2, 1], [0, 3]]), ],
                         torch.Tensor([[5, 3], [1, 7]]))

        # stride is [4, 8]
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), storage_offset=4,
                     size=torch.Size([2]), stride=[4])
        self.assertEqual(strided[[0]], torch.Tensor([5]))
        self.assertEqual(strided[ri([0]), ], torch.Tensor([5]))
        self.assertEqual(strided[ri([1]), ], torch.Tensor([9]))
        self.assertEqual(strided[[0, 1]], torch.Tensor([5, 9]))
        self.assertEqual(strided[ri([0, 1]), ], torch.Tensor([5, 9]))
        self.assertEqual(strided[ri([[0, 1], [1, 0]]), ],
                         torch.Tensor([[5, 9], [9, 5]]))

        # reference is 1 2
        #              3 4
        #              5 6
        reference = consec((3, 2)).to(device)
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])], torch.Tensor([1, 3, 5]))
        self.assertEqual(reference[ri([0, 1, 2]), ri([1])], torch.Tensor([2, 4, 6]))
        self.assertEqual(reference[ri([0]), ri([0])], consec((1,)))
        self.assertEqual(reference[ri([2]), ri([1])], consec((1,), 6))
        self.assertEqual(reference[[ri([0, 0]), ri([0, 1])]], torch.Tensor([1, 2]))
        self.assertEqual(reference[[ri([0, 1, 1, 0, 2]), ri([1])]],
                         torch.Tensor([2, 4, 4, 2, 6]))
        self.assertEqual(reference[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.Tensor([1, 2, 3, 3]))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = [0],
        self.assertEqual(reference[rows, columns], torch.Tensor([[1, 1],
                                                                [3, 5]]))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([1, 0])
        self.assertEqual(reference[rows, columns], torch.Tensor([[2, 1],
                                                                [4, 5]]))
        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([[0, 1],
                      [1, 0]])
        self.assertEqual(reference[rows, columns], torch.Tensor([[1, 2],
                                                                [4, 5]]))

        # setting values
        reference[ri([0]), ri([1])] = -1
        self.assertEqual(reference[ri([0]), ri([1])], torch.Tensor([-1]))
        reference[ri([0, 1, 2]), ri([0])] = torch.Tensor([-1, 2, -4]).to(device)
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])], torch.Tensor([-1,
                         2, -4]))
        reference[rows, columns] = torch.Tensor([[4, 6], [2, 3]]).to(device)
        self.assertEqual(reference[rows, columns],
                         torch.Tensor([[4, 6], [2, 3]]))

        # Verify still works with Transposed (i.e. non-contiguous) Tensors

        reference = torch.Tensor([[0, 1, 2, 3],
                                  [4, 5, 6, 7],
                                  [8, 9, 10, 11]]).to(device).t_()

        # Transposed: [[0, 4, 8],
        #              [1, 5, 9],
        #              [2, 6, 10],
        #              [3, 7, 11]]

        self.assertEqual(reference[ri([0, 1, 2]), ri([0])], torch.Tensor([0, 1,
                         2]))
        self.assertEqual(reference[ri([0, 1, 2]), ri([1])], torch.Tensor([4, 5,
                         6]))
        self.assertEqual(reference[ri([0]), ri([0])], torch.Tensor([0]))
        self.assertEqual(reference[ri([2]), ri([1])], torch.Tensor([6]))
        self.assertEqual(reference[[ri([0, 0]), ri([0, 1])]], torch.Tensor([0, 4]))
        self.assertEqual(reference[[ri([0, 1, 1, 0, 3]), ri([1])]],
                         torch.Tensor([4, 5, 5, 4, 7]))
        self.assertEqual(reference[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.Tensor([0, 4, 1, 1]))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = [0],
        self.assertEqual(reference[rows, columns], torch.Tensor([[0, 0],
                                                                [1, 2]]))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([1, 0])
        self.assertEqual(reference[rows, columns], torch.Tensor([[4, 0],
                                                                [5, 2]]))
        rows = ri([[0, 0],
                   [1, 3]])
        columns = ri([[0, 1],
                      [1, 2]])
        self.assertEqual(reference[rows, columns], torch.Tensor([[0, 4],
                                                                [5, 11]]))

        # setting values
        reference[ri([0]), ri([1])] = -1
        self.assertEqual(reference[ri([0]), ri([1])], torch.Tensor([-1]))
        reference[ri([0, 1, 2]), ri([0])] = torch.Tensor([-1, 2, -4]).to(device)
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])], torch.Tensor([-1,
                         2, -4]))
        reference[rows, columns] = torch.Tensor([[4, 6], [2, 3]]).to(device)
        self.assertEqual(reference[rows, columns],
                         torch.Tensor([[4, 6], [2, 3]]))

        # stride != 1

        # strided is [[1 3 5 7],
        #             [9 11 13 15]]

        reference = torch.arange(0., 24).view(3, 8).to(device)
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), 1, size=torch.Size([2, 4]),
                     stride=[8, 2])

        self.assertEqual(strided[ri([0, 1]), ri([0])], torch.Tensor([1, 9]))
        self.assertEqual(strided[ri([0, 1]), ri([1])], torch.Tensor([3, 11]))
        self.assertEqual(strided[ri([0]), ri([0])], torch.Tensor([1]))
        self.assertEqual(strided[ri([1]), ri([3])], torch.Tensor([15]))
        self.assertEqual(strided[[ri([0, 0]), ri([0, 3])]], torch.Tensor([1, 7]))
        self.assertEqual(strided[[ri([1]), ri([0, 1, 1, 0, 3])]],
                         torch.Tensor([9, 11, 11, 9, 15]))
        self.assertEqual(strided[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.Tensor([1, 3, 9, 9]))

        rows = ri([[0, 0],
                   [1, 1]])
        columns = [0],
        self.assertEqual(strided[rows, columns], torch.Tensor([[1, 1],
                                                              [9, 9]]))

        rows = ri([[0, 1],
                   [1, 0]])
        columns = ri([1, 2])
        self.assertEqual(strided[rows, columns], torch.Tensor([[3, 13],
                                                              [11, 5]]))
        rows = ri([[0, 0],
                   [1, 1]])
        columns = ri([[0, 1],
                      [1, 2]])
        self.assertEqual(strided[rows, columns], torch.Tensor([[1, 3],
                                                              [11, 13]]))

        # setting values

        # strided is [[10, 11],
        #             [17, 18]]

        reference = torch.arange(0., 24).view(3, 8).to(device)
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])
        self.assertEqual(strided[ri([0]), ri([1])], torch.Tensor([11]))
        strided[ri([0]), ri([1])] = -1
        self.assertEqual(strided[ri([0]), ri([1])], torch.Tensor([-1]))

        reference = torch.arange(0., 24).view(3, 8).to(device)
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])
        self.assertEqual(strided[ri([0, 1]), ri([1, 0])], torch.Tensor([11,
                         17]))
        strided[ri([0, 1]), ri([1, 0])] = torch.Tensor([-1, 2]).to(device)
        self.assertEqual(strided[ri([0, 1]), ri([1, 0])], torch.Tensor([-1,
                         2]))

        reference = torch.arange(0., 24).view(3, 8).to(device)
        strided = torch.Tensor().to(device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])

        rows = ri([[0],
                   [1]])
        columns = ri([[0, 1],
                      [0, 1]])
        self.assertEqual(strided[rows, columns],
                         torch.Tensor([[10, 11], [17, 18]]))
        strided[rows, columns] = torch.Tensor([[4, 6], [2, 3]]).to(device)
        self.assertEqual(strided[rows, columns],
                         torch.Tensor([[4, 6], [2, 3]]))

        # Tests using less than the number of dims, and ellipsis

        # reference is 1 2
        #              3 4
        #              5 6
        reference = consec((3, 2)).to(device)
        self.assertEqual(reference[ri([0, 2]), ], torch.Tensor([[1, 2], [5, 6]]))
        self.assertEqual(reference[ri([1]), ...], torch.Tensor([[3, 4]]))
        self.assertEqual(reference[..., ri([1])], torch.Tensor([[2], [4], [6]]))

        # verify too many indices fails
        with self.assertRaises(IndexError):
            reference[ri([1]), ri([0, 2]), ri([3])]

        # test invalid index fails
        reference = torch.empty(10, device=device)
        # can't test cuda because it is a device assert
        if not reference.is_cuda:
            for err_idx in (10, -11):
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[err_idx]
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[torch.LongTensor([err_idx]).to(device)]
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[[err_idx]]

        if TEST_NUMPY:
            # we use numpy to compare against, to verify that our advanced
            # indexing semantics are the same, and also for ease of test
            # writing

            def tensor_indices_to_np(tensor, indices):
                # convert the Torch Tensor to a numpy array
                if (tensor.is_cuda):
                    tensor = tensor.cpu()
                npt = tensor.numpy()

                # convert indices
                idxs = tuple(i.tolist() if isinstance(i, torch.LongTensor) else
                             i for i in indices)

                return npt, idxs

            def get_numpy(tensor, indices):
                npt, idxs = tensor_indices_to_np(tensor, indices)

                # index and return as a Torch Tensor
                return torch.Tensor(npt[idxs])

            def set_numpy(tensor, indices, value):
                if not isinstance(value, int):
                    if value.is_cuda:
                        value = value.cpu()
                    value = value.numpy()

                npt, idxs = tensor_indices_to_np(tensor, indices)
                npt[idxs] = value
                return npt

            def assert_get_eq(tensor, indexer):
                self.assertEqual(tensor[indexer],
                                 get_numpy(tensor, indexer).to(device))

            def assert_set_eq(tensor, indexer, val):
                pyt = tensor.clone()
                numt = tensor.clone()
                pyt[indexer] = val
                numt = torch.Tensor(set_numpy(numt, indexer, val)).to(device)
                self.assertEqual(pyt, numt)

            def assert_backward_eq(tensor, indexer):
                cpu = tensor.float().clone().detach().requires_grad_(True)
                outcpu = cpu[indexer]
                gOcpu = torch.rand_like(outcpu)
                outcpu.backward(gOcpu)
                gpu = cpu.cuda().detach().requires_grad_(True)
                outgpu = gpu[indexer]
                outgpu.backward(gOcpu.cuda())
                self.assertEqual(cpu.grad, gpu.grad)

            def get_set_tensor(indexed, indexer):
                set_size = indexed[indexer].size()
                set_count = indexed[indexer].numel()
                set_tensor = torch.randperm(set_count).view(set_size).double().to(device)
                return set_tensor

            # Tensor is  0  1  2  3  4
            #            5  6  7  8  9
            #           10 11 12 13 14
            #           15 16 17 18 19
            reference = torch.arange(0., 20).view(4, 5).to(device)

            indices_to_test = [
                # grab the second, fourth columns
                [slice(None), [1, 3]],

                # first, third rows,
                [[0, 2], slice(None)],

                # weird shape
                [slice(None), [[0, 1],
                               [2, 3]]],
                # negatives
                [[-1], [0]],
                [[0, 2], [-1]],
                [slice(None), [-1]],
            ]

            # only test dupes on gets
            get_indices_to_test = indices_to_test + [[slice(None), [0, 1, 1, 2, 2]]]

            for indexer in get_indices_to_test:
                assert_get_eq(reference, indexer)
                if torch.cuda.is_available():
                    assert_backward_eq(reference, indexer)

            for indexer in indices_to_test:
                assert_set_eq(reference, indexer, 44)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))

            reference = torch.arange(0., 160).view(4, 8, 5).to(device)

            indices_to_test = [
                [slice(None), slice(None), [0, 3, 4]],
                [slice(None), [2, 4, 5, 7], slice(None)],
                [[2, 3], slice(None), slice(None)],
                [slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), [0], [1, 2, 4]],
                [slice(None), [0, 1, 3], [4]],
                [slice(None), [[0, 1], [1, 0]], [[2, 3]]],
                [slice(None), [[0, 1], [2, 3]], [[0]]],
                [slice(None), [[5, 6]], [[0, 3], [4, 4]]],
                [[0, 2, 3], [1, 3, 4], slice(None)],
                [[0], [1, 2, 4], slice(None)],
                [[0, 1, 3], [4], slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None)],
                [[[0, 1], [1, 0]], [[2, 3]], slice(None)],
                [[[0, 1], [2, 3]], [[0]], slice(None)],
                [[[2, 1]], [[0, 3], [4, 4]], slice(None)],
                [[[2]], [[0, 3], [4, 1]], slice(None)],
                # non-contiguous indexing subspace
                [[0, 2, 3], slice(None), [1, 3, 4]],

                # less dim, ellipsis
                [[0, 2], ],
                [[0, 2], slice(None)],
                [[0, 2], Ellipsis],
                [[0, 2], slice(None), Ellipsis],
                [[0, 2], Ellipsis, slice(None)],
                [[0, 2], [1, 3]],
                [[0, 2], [1, 3], Ellipsis],
                [Ellipsis, [1, 3], [2, 3]],
                [Ellipsis, [2, 3, 4]],
                [Ellipsis, slice(None), [2, 3, 4]],
                [slice(None), Ellipsis, [2, 3, 4]],

                # ellipsis counts for nothing
                [Ellipsis, slice(None), slice(None), [0, 3, 4]],
                [slice(None), Ellipsis, slice(None), [0, 3, 4]],
                [slice(None), slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), slice(None), [0, 3, 4], Ellipsis],
                [Ellipsis, [[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], Ellipsis, slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None), Ellipsis],
            ]

            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 212)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))
                if torch.cuda.is_available():
                    assert_backward_eq(reference, indexer)

            reference = torch.arange(0., 1296).view(3, 9, 8, 6).to(device)

            indices_to_test = [
                [slice(None), slice(None), slice(None), [0, 3, 4]],
                [slice(None), slice(None), [2, 4, 5, 7], slice(None)],
                [slice(None), [2, 3], slice(None), slice(None)],
                [[1, 2], slice(None), slice(None), slice(None)],
                [slice(None), slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), slice(None), [0], [1, 2, 4]],
                [slice(None), slice(None), [0, 1, 3], [4]],
                [slice(None), slice(None), [[0, 1], [1, 0]], [[2, 3]]],
                [slice(None), slice(None), [[0, 1], [2, 3]], [[0]]],
                [slice(None), slice(None), [[5, 6]], [[0, 3], [4, 4]]],
                [slice(None), [0, 2, 3], [1, 3, 4], slice(None)],
                [slice(None), [0], [1, 2, 4], slice(None)],
                [slice(None), [0, 1, 3], [4], slice(None)],
                [slice(None), [[0, 1], [3, 4]], [[2, 3], [0, 1]], slice(None)],
                [slice(None), [[0, 1], [3, 4]], [[2, 3]], slice(None)],
                [slice(None), [[0, 1], [3, 2]], [[0]], slice(None)],
                [slice(None), [[2, 1]], [[0, 3], [6, 4]], slice(None)],
                [slice(None), [[2]], [[0, 3], [4, 2]], slice(None)],
                [[0, 1, 2], [1, 3, 4], slice(None), slice(None)],
                [[0], [1, 2, 4], slice(None), slice(None)],
                [[0, 1, 2], [4], slice(None), slice(None)],
                [[[0, 1], [0, 2]], [[2, 4], [1, 5]], slice(None), slice(None)],
                [[[0, 1], [1, 2]], [[2, 0]], slice(None), slice(None)],
                [[[2, 2]], [[0, 3], [4, 5]], slice(None), slice(None)],
                [[[2]], [[0, 3], [4, 5]], slice(None), slice(None)],
                [slice(None), [3, 4, 6], [0, 2, 3], [1, 3, 4]],
                [slice(None), [2, 3, 4], [1, 3, 4], [4]],
                [slice(None), [0, 1, 3], [4], [1, 3, 4]],
                [slice(None), [6], [0, 2, 3], [1, 3, 4]],
                [slice(None), [2, 3, 5], [3], [4]],
                [slice(None), [0], [4], [1, 3, 4]],
                [slice(None), [6], [0, 2, 3], [1]],
                [slice(None), [[0, 3], [3, 6]], [[0, 1], [1, 3]], [[5, 3], [1, 2]]],
                [[2, 2, 1], [0, 2, 3], [1, 3, 4], slice(None)],
                [[2, 0, 1], [1, 2, 3], [4], slice(None)],
                [[0, 1, 2], [4], [1, 3, 4], slice(None)],
                [[0], [0, 2, 3], [1, 3, 4], slice(None)],
                [[0, 2, 1], [3], [4], slice(None)],
                [[0], [4], [1, 3, 4], slice(None)],
                [[1], [0, 2, 3], [1], slice(None)],
                [[[1, 2], [1, 2]], [[0, 1], [2, 3]], [[2, 3], [3, 5]], slice(None)],

                # less dim, ellipsis
                [Ellipsis, [0, 3, 4]],
                [Ellipsis, slice(None), [0, 3, 4]],
                [Ellipsis, slice(None), slice(None), [0, 3, 4]],
                [slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), [0, 2, 3], [1, 3, 4], Ellipsis],
                [Ellipsis, [0, 2, 3], [1, 3, 4], slice(None)],
                [[0], [1, 2, 4]],
                [[0], [1, 2, 4], slice(None)],
                [[0], [1, 2, 4], Ellipsis],
                [[0], [1, 2, 4], Ellipsis, slice(None)],
                [[1], ],
                [[0, 2, 1], [3], [4]],
                [[0, 2, 1], [3], [4], slice(None)],
                [[0, 2, 1], [3], [4], Ellipsis],
                [Ellipsis, [0, 2, 1], [3], [4]],
            ]

            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 1333)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))
            indices_to_test += [
                [slice(None), slice(None), [[0, 1], [1, 0]], [[2, 3], [3, 0]]],
                [slice(None), slice(None), [[2]], [[0, 3], [4, 4]]],
            ]
            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 1333)
                if torch.cuda.is_available():
                    assert_backward_eq(reference, indexer)

    def test_advancedindex_big(self, device):
        reference = torch.arange(0, 123344).int().to(device)

        self.assertEqual(reference[[0, 123, 44488, 68807, 123343], ],
                         torch.LongTensor([0, 123, 44488, 68807, 123343]))

    def test_kthvalue(self, device):
        SIZE = 50
        x = torch.rand(SIZE, SIZE, SIZE, device=device)
        x0 = x.clone()

        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(x, k, keepdim=False)
        res2val, res2ind = torch.sort(x)

        self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
        self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)
        # test use of result tensors
        k = random.randint(1, SIZE)
        res1val = torch.tensor([], device=device)
        res1ind = torch.tensor([], dtype=torch.long, device=device)
        torch.kthvalue(x, k, keepdim=False, out=(res1val, res1ind))
        res2val, res2ind = torch.sort(x)
        self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
        self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)

        # test non-default dim
        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(x, k, 0, keepdim=False)
        res2val, res2ind = torch.sort(x, 0)
        self.assertEqual(res1val, res2val[k - 1], 0)
        self.assertEqual(res1ind, res2ind[k - 1], 0)

        # non-contiguous
        y = x.narrow(1, 0, 1)
        y0 = y.contiguous()
        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(y, k)
        res2val, res2ind = torch.kthvalue(y0, k)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # check that the input wasn't modified
        self.assertEqual(x, x0, 0)

        # simple test case (with repetitions)
        y = torch.tensor((3., 5, 4, 1, 1, 5), device=device)
        self.assertEqual(torch.kthvalue(y, 3)[0], 3, 0)
        self.assertEqual(torch.kthvalue(y, 2)[0], 1, 0)

        # simple test case (with NaN)
        SIZE = 50
        x = torch.rand(SIZE, SIZE, SIZE, device=device)
        x[torch.arange(SIZE), :, torch.randint(50, (50,))] = nan
        ks = [random.randint(1, SIZE), 1, SIZE, SIZE - 1]
        res2val, res2ind = torch.sort(x)
        for k in ks:
            res1val, res1ind = torch.kthvalue(x, k, keepdim=False)
            self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
            self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_lu_solve_batched_non_contiguous(self, device):
        from numpy.linalg import solve
        from common_utils import random_fullrank_matrix_distinct_singular_value

        A = random_fullrank_matrix_distinct_singular_value(2, 2)
        b = torch.randn(2, 2, 2)
        x_exp = torch.as_tensor(solve(A.permute(0, 2, 1).numpy(), b.permute(2, 1, 0).numpy())).to(device)
        A = A.to(device).permute(0, 2, 1)
        b = b.to(device).permute(2, 1, 0)
        assert not A.is_contiguous() and not b.is_contiguous(), "contiguous inputs"
        LU_data, LU_pivots = torch.lu(A)
        x = torch.lu_solve(b, LU_data, LU_pivots)
        self.assertEqual(x, x_exp)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lu_solve_batched_many_batches(self, device):
        from common_utils import lu_solve_test_helper

        def cast(t):
            return t.to(device)

        def run_test(A_dims, b_dims, cast):
            b, A, LU_data, LU_pivots = lu_solve_test_helper(self, A_dims, b_dims, cast, True)
            x = torch.lu_solve(b, LU_data, LU_pivots)
            b_ = torch.matmul(A, x)
            self.assertEqual(b_, b.expand_as(b_))

        run_test((5, 65536), (65536, 5, 10), cast)
        run_test((5, 262144), (262144, 5, 10), cast)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    def test_lu_solve_batched_broadcasting(self, device):
        from numpy.linalg import solve
        from common_utils import random_fullrank_matrix_distinct_singular_value

        def run_test(A_dims, b_dims, device, pivot=True):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            A = random_fullrank_matrix_distinct_singular_value(A_matrix_size, *A_batch_dims)
            b = torch.randn(*b_dims)
            x_exp = torch.as_tensor(solve(A.numpy(), b.numpy())).to(device)
            A, b = A.to(device), b.to(device)
            LU_data, LU_pivots = torch.lu(A, pivot=pivot)
            x = torch.lu_solve(b, LU_data, LU_pivots)
            self.assertEqual(x, x_exp)

        # test against numpy.linalg.solve
        run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), device)  # no broadcasting
        run_test((2, 1, 3, 4, 4), (4, 6), device)  # broadcasting b
        run_test((4, 4), (2, 1, 3, 4, 2), device)  # broadcasting A
        run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), device)  # broadcasting A & b

    def test_dim_reduction(self, device):
        example = [[-1, 2, 1], [5, 3, 6]]

        types = [torch.double,
                 torch.float,
                 torch.int64,
                 torch.int32,
                 torch.int16]
        if self.device_type == 'cuda':  # 'cpu' and 'xla' do not support half
            types.append(torch.half)

        # This won't test for 256bit instructions, since we usually
        # only work on 1 cacheline (1024bit) at a time and these
        # examples aren't big enough to trigger that.
        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.sum().item(), 16)
            self.assertEqual(x.sum(0), torch.FloatTensor([4, 5, 7]))
            self.assertEqual(x.sum(1), torch.FloatTensor([2, 14]))
            y = torch.tensor(example, device=device, dtype=dtype)
            torch.sum(x, 0, out=y)
            self.assertEqual(x.sum(0), y)

        # Mean not supported for Int types
        for dtype in types[:2]:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.mean().item(), 16.0 / 6)
            self.assertEqual(x.mean(0), torch.FloatTensor([2.0, 2.5, 7.0 / 2]))
            self.assertEqual(x.mean(1), torch.FloatTensor([2.0 / 3, 14.0 / 3]))
            self.assertEqual(x.mean(), x.mean((0, 1)))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.prod().item(), -180)
            self.assertEqual(x.prod(0), torch.FloatTensor([-5, 6, 6]))
            self.assertEqual(x.prod(1), torch.FloatTensor([-2, 90]))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.max().item(), 6)
            self.assertEqual(x.max(0), (torch.FloatTensor([5, 3, 6]), torch.FloatTensor([1, 1, 1])))
            self.assertEqual(x.max(1), (torch.FloatTensor([2, 6]), torch.FloatTensor([1, 2])))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.min().item(), -1)
            self.assertEqual(x.min(0), (torch.FloatTensor([-1, 2, 1]), torch.FloatTensor([0, 0, 0])))
            self.assertEqual(x.min(1), (torch.FloatTensor([-1, 3]), torch.FloatTensor([0, 1])))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.argmax().item(), 5)
            self.assertEqual(x.argmax(dim=None).item(), 5)
            self.assertEqual(x.argmax(dim=0), torch.FloatTensor([1, 1, 1]))
            self.assertEqual(x.argmax(dim=1), torch.FloatTensor([1, 2]))
            self.assertEqual(x.argmax(dim=0, keepdim=True), torch.FloatTensor([[1, 1, 1]]))
            # test that non-contiguous tensors work
            self.assertEqual(x[:, :2].argmax().item(), 2)

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.argmin().item(), 0)
            self.assertEqual(x.argmin(dim=None).item(), 0)
            self.assertEqual(x.argmin(dim=0), torch.FloatTensor([0, 0, 0]))
            self.assertEqual(x.argmin(dim=1), torch.FloatTensor([0, 1]))
            self.assertEqual(x.argmin(dim=1, keepdim=True), torch.FloatTensor([[0], [1]]))
            # test that non-contiguous tensors work
            self.assertEqual(x[:, :2].argmin().item(), 0)

        dim_red_fns = [
            "mean", "median", "mode", "norm", "prod",
            "std", "sum", "var", "max", "min"]

        def normfn_attr(t, dim, keepdim=False, out=None):
            attr = torch.norm
            return attr(t, 2, dim, keepdim, out=out)

        for fn_name in dim_red_fns:
            fn_attr = getattr(torch, fn_name) if fn_name != "norm" else normfn_attr

            def fn(x, dim, keepdim=False, out=None):
                ans = fn_attr(x, dim, keepdim=keepdim, out=out)
                return ans if not istuple(ans) else ans[0]

            def fn_tuple(x, dim, keepdim=False, out=None):
                return fn_attr(x, dim, keepdim=keepdim, out=out)

            def test_multidim(x, dim):
                self.assertEqual(fn(x, dim).unsqueeze(dim), fn(x, dim, keepdim=True))
                self.assertEqual(x.ndimension() - 1, fn(x, dim).ndimension())
                self.assertEqual(x.ndimension(), fn(x, dim, keepdim=True).ndimension())

            # general case
            x = torch.randn(3, 4, 5, device=device)
            dim = random.randint(0, 2)
            test_multidim(x, dim)

            # check 1-d behavior
            x = torch.randn(1, device=device)
            dim = 0
            self.assertEqual(fn(x, dim).shape, ())
            self.assertEqual(fn(x, dim, keepdim=True).shape, (1,))

            # check reducing of a singleton dimension
            dims = [3, 4, 5]
            singleton_dim = random.randint(0, 2)
            dims[singleton_dim] = 1
            x = torch.randn(dims, device=device)
            test_multidim(x, singleton_dim)

            # check reducing with output kwargs
            if fn_name in ['median', 'mode', 'max', 'min']:
                y = torch.randn(5, 3, device=device)
                values = torch.randn(5, 3, device=device)
                indices = torch.zeros(5, 3, device=device).long() - 1
                fn_tuple(y, 1, keepdim=False, out=(values[:, 1], indices[:, 1]))
                values_expected, indices_expected = fn_tuple(y, 1, keepdim=False)
                self.assertEqual(values[:, 1], values_expected,
                                 '{} values with out= kwarg'.format(fn_name))
                self.assertEqual(indices[:, 1], indices_expected,
                                 '{} indices with out= kwarg'.format(fn_name))
                continue

            x = torch.randn(5, 3, device=device)
            y = torch.randn(5, 3, device=device)
            fn(y, 1, keepdim=False, out=x[:, 1])
            expected = fn(y, 1, keepdim=False)
            self.assertEqual(x[:, 1], expected, '{} with out= kwarg'.format(fn_name))

    def test_remainder_overflow(self, device):
        # Check Integer Overflows
        x = torch.tensor(23500, dtype=torch.int64, device=device)
        q = 392486996410368
        self.assertEqual(x % q, x)
        self.assertEqual(-x % q, q - x)
        self.assertEqual(x % -q, x - q)
        self.assertEqual(-x % -q, -x)

    def test_rpow(self, device):
        m = torch.randn(10, 10, device=device)
        self.assertEqual(torch.pow(2, m), 2**m)

        # test with scalar
        m = torch.randn(1, device=device).squeeze()
        assert m.dim() == 0, "m is intentionally a scalar"
        self.assertEqual(torch.pow(2, m), 2**m)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_symeig(self, device):
        from common_utils import random_symmetric_matrix

        def run_test(dims, eigenvectors, upper):
            x = random_symmetric_matrix(*dims).to(device)
            oute = torch.empty(dims[1:] + dims[:1], device=device)
            outv = torch.empty(dims[1:] + dims[:1] * 2, device=device)
            torch.symeig(x, eigenvectors=eigenvectors, upper=upper, out=(oute, outv))

            if eigenvectors:
                x_recon = torch.matmul(torch.matmul(outv, torch.diag_embed(oute)), outv.transpose(-2, -1))
                self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using V @ diag(e) @ V.T')
            else:
                eigvals, _ = torch.symeig(x, eigenvectors=True, upper=upper)
                self.assertEqual(eigvals, oute, 'Eigenvalues mismatch')
                self.assertEqual(torch.zeros_like(outv), outv, 'Eigenvector matrix not zero')

            rese, resv = x.symeig(eigenvectors=eigenvectors, upper=upper)
            self.assertEqual(rese, oute, "outputs of symeig and symeig with out don't match")
            self.assertEqual(resv, outv, "outputs of symeig and symeig with out don't match")

            # test non-contiguous
            x = random_symmetric_matrix(*dims).to(device)
            n_dim = len(dims) + 1
            # Reverse the batch dimensions and the matrix dimensions and then concat them
            x = x.permute(tuple(range(n_dim - 3, -1, -1)) + (n_dim - 1, n_dim - 2))
            assert not x.is_contiguous(), "x is intentionally non-contiguous"
            rese, resv = torch.symeig(x, eigenvectors=eigenvectors, upper=upper)
            if eigenvectors:
                x_recon = torch.matmul(torch.matmul(resv, torch.diag_embed(rese)), resv.transpose(-2, -1))
                self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using V @ diag(e) @ V.T')
            else:
                eigvals, _ = torch.symeig(x, eigenvectors=True, upper=upper)
                self.assertEqual(eigvals, rese, 'Eigenvalues mismatch')
                self.assertEqual(torch.zeros_like(resv), resv, 'Eigenvector matrix not zero')

        batch_dims_set = [(), (3,), (3, 5), (5, 3, 5)]
        for batch_dims, eigenvectors, upper in product(batch_dims_set, (True, False), (True, False)):
            run_test((5,) + batch_dims, eigenvectors, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_svd(self, device):
        def run_test(dims, some, compute_uv):
            x = torch.randn(*dims, device=device)
            outu, outs, outv = torch.Tensor().to(device), torch.Tensor().to(device), torch.Tensor().to(device)
            torch.svd(x, some=some, compute_uv=compute_uv, out=(outu, outs, outv))

            if compute_uv:
                if some:
                    x_recon = torch.matmul(outu, torch.matmul(outs.diag_embed(), outv.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using U @ diag(S) @ V.T')
                else:
                    narrow_u = outu[..., :min(*dims[-2:])]
                    narrow_v = outv[..., :min(*dims[-2:])]
                    x_recon = torch.matmul(narrow_u, torch.matmul(outs.diag_embed(), narrow_v.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using U @ diag(S) @ V.T')
            else:
                _, singvals, _ = torch.svd(x, compute_uv=True)
                self.assertEqual(singvals, outs, 'Singular values mismatch')
                self.assertEqual(outu, torch.zeros_like(outu), 'U not zero')
                self.assertEqual(outv, torch.zeros_like(outv), 'V not zero')

            resu, ress, resv = torch.svd(x, some=some, compute_uv=compute_uv)
            self.assertEqual(resu, outu, 'outputs of svd and svd with out differ')
            self.assertEqual(ress, outs, 'outputs of svd and svd with out differ')
            self.assertEqual(resv, outv, 'outputs of svd and svd with out differ')

            # test non-contiguous
            x = torch.randn(*dims, device=device)
            n_dim = len(dims)
            # Reverse the batch dimensions and the matrix dimensions and then concat them
            x = x.permute(tuple(range(n_dim - 3, -1, -1)) + (n_dim - 1, n_dim - 2))
            assert not x.is_contiguous(), "x is intentionally non-contiguous"
            resu, ress, resv = torch.svd(x, some=some, compute_uv=compute_uv)
            if compute_uv:
                if some:
                    x_recon = torch.matmul(resu, torch.matmul(ress.diag_embed(), resv.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using U @ diag(S) @ V.T')
                else:
                    narrow_u = resu[..., :min(*dims[-2:])]
                    narrow_v = resv[..., :min(*dims[-2:])]
                    x_recon = torch.matmul(narrow_u, torch.matmul(ress.diag_embed(), narrow_v.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, 1e-8, 'Incorrect reconstruction using U @ diag(S) @ V.T')
            else:
                _, singvals, _ = torch.svd(x, compute_uv=True)
                self.assertEqual(singvals, ress, 'Singular values mismatch')
                self.assertEqual(resu, torch.zeros_like(resu), 'U not zero')
                self.assertEqual(resv, torch.zeros_like(resv), 'V not zero')

        shapes = [(3, 3), (5, 3, 3), (7, 5, 3, 3),  # square matrices
                  (7, 3), (5, 7, 3), (7, 5, 7, 3),  # fat matrices
                  (3, 7), (5, 3, 7), (7, 5, 3, 7)]  # thin matrices
        for dims, some, compute_uv in product(shapes, [True, False], [True, False]):
            run_test(dims, some, compute_uv)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_svd_no_singularvectors(self, device):
        for size in [(5, 5), (5, 20), (20, 5)]:
            a = torch.randn(*size, device=device)
            u, s_expect, v = torch.svd(a)
            u, s_actual, v = torch.svd(a, compute_uv=False)
            self.assertEqual(s_expect, s_actual, "Singular values don't match")

    def test_lerp(self, device):
        start_end_shapes = [(), (5,), (5, 5), (5, 5, 5)]
        for shapes in product(start_end_shapes, start_end_shapes):
            start = torch.randn(shapes[0], device=device)
            end = torch.randn(shapes[1], device=device)

            # Tensor weights
            for weight in [torch.randn(shapes[0], device=device), random.random()]:
                actual = torch.lerp(start, end, weight)
                actual_method = start.lerp(end, weight)
                self.assertEqual(actual, actual_method)
                actual_out = torch.Tensor().to(device)
                torch.lerp(start, end, weight, out=actual_out)
                self.assertEqual(actual, actual_out)
                expected = start + weight * (end - start)
                self.assertEqual(expected, actual)

    def test_diagflat(self, device):
        dtype = torch.float32
        # Basic sanity test
        x = torch.randn((100,), dtype=dtype, device=device)
        result = torch.diagflat(x)
        expected = torch.diag(x)
        self.assertEqual(result, expected)

        # Test offset
        x = torch.randn((100,), dtype=dtype, device=device)
        result = torch.diagflat(x, 17)
        expected = torch.diag(x, 17)
        self.assertEqual(result, expected)

        # Test where input has more than one dimension
        x = torch.randn((2, 3, 4), dtype=dtype, device=device)
        result = torch.diagflat(x)
        expected = torch.diag(x.contiguous().view(-1))
        self.assertEqual(result, expected)

        # Noncontig input
        x = torch.randn((2, 3, 4), dtype=dtype, device=device).transpose(2, 0)
        self.assertFalse(x.is_contiguous())
        result = torch.diagflat(x)
        expected = torch.diag(x.contiguous().view(-1))
        self.assertEqual(result, expected)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_norm(self, device):
        # full reduction
        x = torch.randn(25, device=device)
        xn = x.cpu().numpy()
        for p in [0, 1, 2, 3, 4, inf, -inf]:
            res = x.norm(p).item()
            expected = np.linalg.norm(xn, p)
            self.assertEqual(res, expected, "full reduction failed for {}-norm".format(p))

        # one dimension
        x = torch.randn(25, 25, device=device)
        xn = x.cpu().numpy()
        for p in [0, 1, 2, 3, 4, inf, -inf]:
            res = x.norm(p, 1).cpu().numpy()
            expected = np.linalg.norm(xn, p, 1)
            self.assertEqual(res.shape, expected.shape)
            self.assertTrue(np.allclose(res, expected), "dim reduction failed for {}-norm".format(p))

        # matrix norm
        for p in ['fro', 'nuc']:
            res = x.norm(p).cpu().numpy()
            expected = np.linalg.norm(xn, p)
            self.assertEqual(res.shape, expected.shape)
            self.assertTrue(np.allclose(res, expected), "dim reduction failed for {}-norm".format(p))

        # larger tensor sanity check
        self.assertEqual(2 * torch.norm(torch.ones(10000)), torch.norm(torch.ones(40000)))

    @skipCUDAIfNoMagma
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_nuclear_norm_axes_small_brute_force(self, device):
        def check_single_nuclear_norm(x, axes):
            if x.is_cuda and randrange(100) < 95:
                return  # too many cpu <==> gpu copies

            a = np.array(x.cpu(), copy=False)
            expected = np.linalg.norm(a, "nuc", axis=axes)

            ans = torch.norm(x, "nuc", dim=axes)
            self.assertTrue(ans.is_contiguous())
            self.assertEqual(ans.shape, expected.shape)
            self.assertTrue(np.allclose(ans.cpu(), expected, rtol=1e-02, atol=1e-03, equal_nan=True))

            out = torch.zeros(expected.shape, dtype=x.dtype, device=x.device)
            ans = torch.norm(x, "nuc", dim=axes, out=out)
            self.assertIs(ans, out)
            self.assertTrue(ans.is_contiguous())
            self.assertEqual(ans.shape, expected.shape)
            self.assertTrue(np.allclose(ans.cpu(), expected, rtol=1e-02, atol=1e-03, equal_nan=True))

        for n in range(1, 3):
            for m in range(1, 3):
                for axes in permutations([0, 1], 2):
                    # 2d, inner dimensions C
                    x = torch.randn(n, m, device=device)
                    check_single_nuclear_norm(x, axes)

                    # 2d, inner dimensions Fortran
                    x = torch.randn(m, n, device=device).transpose(-1, -2)
                    check_single_nuclear_norm(x, axes)

                    # 2d, inner dimensions non-contiguous
                    x = torch.randn(n, 2 * m, device=device)[:, ::2]
                    check_single_nuclear_norm(x, axes)

                    # 2d, all dimensions non-contiguous
                    x = torch.randn(7 * n, 2 * m, device=device)[::7, ::2]
                    check_single_nuclear_norm(x, axes)

                for o in range(1, 3):
                    for axes in permutations([0, 1, 2], 2):
                        # 3d, inner dimensions C
                        x = torch.randn(o, n, m, device=device)
                        check_single_nuclear_norm(x, axes)

                        # 3d, inner dimensions Fortran
                        x = torch.randn(o, m, n, device=device).transpose(-1, -2)
                        check_single_nuclear_norm(x, axes)

                        # 3d, inner dimensions non-contiguous
                        x = torch.randn(o, n, 2 * m, device=device)[:, :, ::2]
                        check_single_nuclear_norm(x, axes)

                        # 3d, all dimensions non-contiguous
                        x = torch.randn(7 * o, 5 * n, 2 * m, device=device)[::7, ::5, ::2]
                        check_single_nuclear_norm(x, axes)

                    for r in range(1, 3):
                        for axes in permutations([0, 1, 2, 3], 2):
                            # 4d, inner dimensions C
                            x = torch.randn(r, o, n, m, device=device)
                            check_single_nuclear_norm(x, axes)

                            # 4d, inner dimensions Fortran
                            x = torch.randn(r, o, n, m, device=device).transpose(-1, -2)
                            check_single_nuclear_norm(x, axes)

                            # 4d, inner dimensions non-contiguous
                            x = torch.randn(r, o, n, 2 * m, device=device)[:, :, :, ::2]
                            check_single_nuclear_norm(x, axes)

                            # 4d, all dimensions non-contiguous
                            x = torch.randn(7 * r, 5 * o, 11 * n, 2 * m, device=device)[::7, ::5, ::11, ::2]
                            check_single_nuclear_norm(x, axes)

    @skipCUDAIfNoMagma
    def test_nuclear_norm_exceptions(self, device):
        for lst in [], [1], [1, 2]:
            for axes in (), (0,), (0, 1):
                x = torch.tensor(lst, dtype=torch.double, device=device)
                self.assertRaises(RuntimeError, torch.norm, x, "nuc", axes)

        x = torch.tensor([[0, 1, 2], [3, 4, 5]], dtype=torch.double, device=device)
        self.assertRaisesRegex(RuntimeError, "duplicate or invalid", torch.norm, x, "nuc", (0, 0))
        self.assertRaisesRegex(RuntimeError, "duplicate or invalid", torch.norm, x, "nuc", (0, 2))

    def test_dist(self, device):
        def run_test(x, y):
            for p in [0, 1, 2, 3, 4, inf, -inf]:
                dist_xy = torch.dist(x, y, p)
                dist_xy_norm = torch.norm(x - y, p)
                self.assertEqual(dist_xy, dist_xy_norm)

        run_test(torch.randn(5, device=device), torch.randn(5, device=device))

        x = torch.zeros(3, device=device)
        y = torch.zeros(3, device=device)
        y[1] = 1.
        run_test(x, y)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_geqrf(self, device):
        a = torch.randn(5, 5, device=device)
        b, c = torch.geqrf(a)
        b_placeholder, c_placeholder = torch.empty_like(b), torch.empty_like(c)
        torch.geqrf(a, out=(b_placeholder, c_placeholder))
        self.assertEqual(b, b_placeholder)
        self.assertEqual(c, c_placeholder)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_triangular_solve(self, device):
        from common_utils import triangular_solve_test_helper
        for (k, n), (upper, unitriangular, transpose) in product(zip([2, 3, 5], [3, 5, 7]),
                                                                 product([True, False], repeat=3)):
            b, A = triangular_solve_test_helper((n, n), (n, k), lambda t: t.to(device), upper, unitriangular)
            x = torch.triangular_solve(b, A, upper=upper, unitriangular=unitriangular, transpose=transpose)[0]
            if transpose:
                self.assertLessEqual(b.dist(A.t().mm(x)), 4e-12)
            else:
                self.assertLessEqual(b.dist(A.mm(x)), 4e-12)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_triangular_solve_batched_many_batches(self, device):
        from common_utils import triangular_solve_test_helper

        def cast(t):
            return t.to(device)

        for upper, transpose, unitriangular in product([True, False], repeat=3):
            b, A = triangular_solve_test_helper((256, 256, 5, 5), (5, 1), cast, upper, unitriangular)
            x, _ = torch.triangular_solve(b, A,
                                          upper=upper, transpose=transpose, unitriangular=unitriangular)
            if transpose:
                A = A.transpose(-2, -1)
            self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 1)))

            b, A = triangular_solve_test_helper((3, 3), (512, 512, 3, 1), cast, upper, unitriangular)
            x, _ = torch.triangular_solve(b, A,
                                          upper=upper, transpose=transpose, unitriangular=unitriangular)
            if transpose:
                A = A.transpose(-2, -1)
            self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_SCIPY, "SciPy not found")
    def test_triangular_solve_batched_broadcasting(self, device):
        from scipy.linalg import solve_triangular as tri_solve
        from common_utils import triangular_solve_test_helper

        def scipy_tri_solve_batched(A, B, upper, trans, diag):
            batch_dims_A, batch_dims_B = A.shape[:-2], B.shape[:-2]
            single_dim_A, single_dim_B = A.shape[-2:], B.shape[-2:]
            expand_dims = tuple(torch._C._infer_size(torch.Size(batch_dims_A),
                                                     torch.Size(batch_dims_B)))
            expand_A = np.broadcast_to(A, expand_dims + single_dim_A)
            expand_B = np.broadcast_to(B, expand_dims + single_dim_B)
            flat_A = expand_A.reshape((-1,) + single_dim_A)
            flat_B = expand_B.reshape((-1,) + single_dim_B)
            flat_X = np.vstack([tri_solve(a, b, lower=(not upper), trans=int(trans), unit_diagonal=diag)
                                for a, b in zip(flat_A, flat_B)])
            return flat_X.reshape(expand_B.shape)

        def run_test(A_dims, b_dims, device, upper, transpose, unitriangular):
            b, A = triangular_solve_test_helper(A_dims, b_dims, lambda t: t.to(device), upper, unitriangular)
            x_exp = torch.as_tensor(scipy_tri_solve_batched(A.cpu().numpy(), b.cpu().numpy(),
                                                            upper, transpose, unitriangular))
            x = torch.triangular_solve(b, A, upper=upper, transpose=transpose, unitriangular=unitriangular)[0]

            self.assertEqual(x, x_exp.to(device))

        for upper, transpose, unitriangular in product([True, False], repeat=3):
            # test against scipy.linalg.solve_triangular
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), device, upper, transpose, unitriangular)  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6), device, upper, transpose, unitriangular)  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2), device, upper, transpose, unitriangular)  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), device, upper, transpose, unitriangular)  # broadcasting A & b

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lstsq(self, device):
        def cast_fn(tensor):
            return tensor.to(device=device)

        def _test_underdetermined(a, b, expectedNorm):
            # underdetermined systems are not supported on the GPU
            if not torch.device(device).type == 'cpu':
                return

            m = a.size()[0]
            n = a.size()[1]
            assert(m <= n)

            a_copy = a.clone()
            b_copy = b.clone()
            res1 = torch.lstsq(b, a)[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            self.assertEqual((torch.mm(a, res1) - b).norm(), expectedNorm, 1e-8)

            ta = cast_fn(torch.Tensor())
            tb = cast_fn(torch.Tensor())
            res2 = torch.lstsq(b, a, out=(tb, ta))[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            self.assertEqual((torch.mm(a, res1) - b).norm(), expectedNorm, 1e-8)

            res3 = torch.lstsq(b, a, out=(b, a))[0]
            self.assertEqual((torch.mm(a_copy, b) - b_copy).norm(), expectedNorm, 1e-8)
            self.assertEqual(res1, tb, 0)
            self.assertEqual(res1, b, 0)
            self.assertEqual(res1, res2, 0)
            self.assertEqual(res1, res3, 0)

        def _test_overdetermined(a, b, expectedNorm):
            m = a.size()[0]
            n = a.size()[1]
            assert(m > n)

            def check_norm(a, b, expected_norm, gels_result):
                # Checks |ax - b| and the residual info from the result

                # The first n rows is the least square solution.
                # Rows n to m-1 contain residual information.
                x = gels_result[:n]
                resid_info = gels_result[n:]

                resid_norm = (torch.mm(a, x) - b).norm()
                self.assertEqual(resid_norm, expectedNorm, 1e-8)
                self.assertEqual(resid_info.norm(), resid_norm, 1e-8)

            a_copy = a.clone()
            b_copy = b.clone()
            res1 = torch.lstsq(b, a)[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            check_norm(a, b, expectedNorm, res1)

            ta = cast_fn(torch.Tensor())
            tb = cast_fn(torch.Tensor())
            res2 = torch.lstsq(b, a, out=(tb, ta))[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            check_norm(a, b, expectedNorm, res2)

            res3 = torch.lstsq(b, a, out=(b, a))[0]
            check_norm(a_copy, b_copy, expectedNorm, res3)

            self.assertEqual(res1, tb, 0)
            self.assertEqual(res1, b, 0)
            self.assertEqual(res1, res2, 0)
            self.assertEqual(res1, res3, 0)

        # basic test
        expectedNorm = 0
        a = cast_fn(torch.Tensor(((1.44, -9.96, -7.55, 8.34),
                                  (-7.84, -0.28, 3.24, 8.09),
                                  (-4.39, -3.24, 6.27, 5.28),
                                  (4.53, 3.83, -6.64, 2.06)))).t()
        b = cast_fn(torch.Tensor(((8.58, 8.26, 8.48, -5.28),
                                  (9.35, -4.43, -0.70, -0.26)))).t()
        _test_underdetermined(a, b, expectedNorm)

        # test overdetermined
        expectedNorm = 17.390200628863
        a = cast_fn(torch.Tensor(((1.44, -9.96, -7.55, 8.34, 7.08, -5.45),
                                  (-7.84, -0.28, 3.24, 8.09, 2.52, -5.70),
                                  (-4.39, -3.24, 6.27, 5.28, 0.74, -1.19),
                                  (4.53, 3.83, -6.64, 2.06, -2.47, 4.70)))).t()
        b = cast_fn(torch.Tensor(((8.58, 8.26, 8.48, -5.28, 5.72, 8.93),
                                  (9.35, -4.43, -0.70, -0.26, -7.36, -2.52)))).t()
        _test_overdetermined(a, b, expectedNorm)

        # test underdetermined
        expectedNorm = 0
        a = cast_fn(torch.Tensor(((1.44, -9.96, -7.55),
                                  (-7.84, -0.28, 3.24),
                                  (-4.39, -3.24, 6.27),
                                  (4.53, 3.83, -6.64)))).t()
        b = cast_fn(torch.Tensor(((8.58, 8.26, 8.48),
                                  (9.35, -4.43, -0.70)))).t()
        _test_underdetermined(a, b, expectedNorm)

        # test reuse
        expectedNorm = 0
        a = cast_fn(torch.Tensor(((1.44, -9.96, -7.55, 8.34),
                                  (-7.84, -0.28, 3.24, 8.09),
                                  (-4.39, -3.24, 6.27, 5.28),
                                  (4.53, 3.83, -6.64, 2.06)))).t()
        b = cast_fn(torch.Tensor(((8.58, 8.26, 8.48, -5.28),
                                  (9.35, -4.43, -0.70, -0.26)))).t()
        ta = cast_fn(torch.Tensor())
        tb = cast_fn(torch.Tensor())
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_qr(self, device):
        def run_test(tensor_dims, some):
            A = torch.randn(*tensor_dims, device=device)
            Q, R = torch.qr(A, some=some)

            # Check0: Q[-2:] = (m, n_columns), R[-2:] = (n_columns, n)
            m, n = tensor_dims[-2:]
            n_columns = m if (not some) and m > n else min(m, n)
            self.assertEqual(Q.size(-2), m)
            self.assertEqual(R.size(-1), n)
            self.assertEqual(Q.size(-1), n_columns)

            # Check1: A = QR
            self.assertEqual(A, torch.matmul(Q, R))

            # Check2: A = QR (with out)
            Q_out, R_out = torch.Tensor().to(device), torch.Tensor().to(device)
            torch.qr(A, some=some, out=(Q_out, R_out))
            self.assertEqual(A, torch.matmul(Q_out, R_out))

            # Check3: Q == Q_out, R == R_out
            self.assertEqual(Q, Q_out)
            self.assertEqual(R, R_out)

            # Check4: Q^{T}Q = I, triu(R) = R
            self.assertEqual(torch.matmul(Q.transpose(-2, -1), Q),
                             torch.eye(n_columns, device=device).expand(Q.shape[:-2] + (n_columns, n_columns)))
            self.assertEqual(R.triu(), R)

        tensor_dims_list = [(3, 5), (5, 5), (5, 3),  # Single matrix
                            (7, 3, 5), (7, 5, 5), (7, 5, 3),  # 3-dim Tensors
                            (7, 5, 3, 5), (7, 5, 5, 5), (7, 5, 5, 3)]  # 4-dim Tensors
        for tensor_dims, some in product(tensor_dims_list, [True, False]):
            run_test(tensor_dims, some)

    def test_randperm(self, device):
        if device == 'cpu':
            rng_device = None
        else:
            rng_device = [device]

        # Test core functionality. On CUDA, for small n, randperm is offloaded to CPU instead. For large n, randperm is
        # executed on GPU.
        for n in (100, 50000, 100000):
            # Ensure both integer and floating-point numbers are tested. Half follows an execution path that is
            # different from others on CUDA.
            for dtype in (torch.long, torch.half, torch.float):
                if n > 2049 and dtype == torch.half:  # Large n for torch.half will raise an exception, do not test here.
                    continue
                with torch.random.fork_rng(devices=rng_device):
                    res1 = torch.randperm(n, dtype=dtype, device=device)
                res2 = torch.empty(0, dtype=dtype, device=device)
                torch.randperm(n, out=res2, dtype=dtype, device=device)
                self.assertEqual(res1, res2, 0)

        # Default type is long
        for n in (100, 10000):
            self.assertEqual(torch.randperm(n, device=device).dtype, torch.long)

        # randperm of 0 elements is an empty tensor
        res1 = torch.randperm(0)
        res2 = torch.tensor(5, dtype=dtype, device=device)
        torch.randperm(0, out=res2)
        self.assertEqual(res1.numel(), 0)
        self.assertEqual(res2.numel(), 0)

        # Test exceptions when n is too large for a floating point type
        for dtype, small_n, large_n in ((torch.half, 2**11 + 1, 2**11 + 2),
                                        (torch.float, 2**24 + 1, 2**24 + 2),
                                        (torch.double, 2**25,  # 2**53 + 1 is too large to run
                                         2**53 + 2)):
            res = torch.empty(0, dtype=dtype, device=device)
            torch.randperm(small_n, out=res)  # No exception expected
            self.assertRaises(RuntimeError, lambda: torch.randperm(large_n, out=res, device=device))

        # Test non-contiguous tensors
        for n in (4, 5, 6, 10, 20):
            non_contiguous_tensor = torch.zeros((2, 3), dtype=torch.long, device=device).t()
            self.assertFalse(non_contiguous_tensor.is_contiguous())
            with torch.random.fork_rng(devices=rng_device):
                res = torch.randperm(n, dtype=torch.long, device=device)
            torch.randperm(n, out=non_contiguous_tensor)
            self.assertEqual(non_contiguous_tensor, res)

    def test_random_neg_values(self, device):
        signed_types = ['torch.DoubleTensor', 'torch.FloatTensor', 'torch.LongTensor',
                        'torch.IntTensor', 'torch.ShortTensor']
        for tname in signed_types:
            res = torch.rand(SIZE, SIZE).type(tname).to(device)
            res.random_(-10, -1)
            self.assertLessEqual(res.max().item(), 9)
            self.assertGreaterEqual(res.min().item(), -10)

    def test_triu_tril(self, device):
        def gen_mask(shape, diagonal, device, upper):
            mask = torch.zeros(*shape[-2:]).byte()
            for i in range(shape[-2]):
                for j in range(shape[-1]):
                    cond = j - i < diagonal if upper else j - i > diagonal
                    if cond:
                        mask[i, j] = 1
            return mask.expand(*shape).to(device)

        torch_functions = {True: torch.triu, False: torch.tril}
        if TEST_NUMPY:
            numpy_functions = {True: np.triu, False: np.tril}

        # TODO: remove this when bool and half are supported for torch.where
        def bool_half_compat_where(pred, true_tensor, false_tensor, dtype):
            if dtype == torch.bool or dtype == torch.half:
                return torch.where(pred.byte(), true_tensor.byte(), false_tensor.byte()).to(dtype=dtype)
            else:
                return torch.where(pred, true_tensor, false_tensor)

        def run_test(shape, device, diagonal, dtype):
            x = torch.empty(*shape, device=device, dtype=dtype).fill_(2)

            for upper in [True, False]:
                # normal test with mask
                torch_tri_func = torch_functions[upper]
                res1 = torch_tri_func(x, diagonal=diagonal)
                res2 = torch.empty(0, device=device, dtype=dtype)
                torch_tri_func(x, diagonal=diagonal, out=res2)
                exp_mask = gen_mask(shape, diagonal, device, upper)
                expected = bool_half_compat_where(exp_mask, torch.tensor(0).type_as(x), x, dtype)
                self.assertEqual(res1, res2, 0)
                self.assertEqual(expected, res1, 0)

                # non-contiguous and expanded tensors test
                if 0 not in shape:
                    for s in range(-len(shape), -1):
                        # non-contiguous tensors
                        x_nc = x.clone().transpose(s, s + 1)
                        exp_mask = gen_mask(x_nc.size(), diagonal, device, upper)
                        if 1 not in shape:
                            assert not x_nc.is_contiguous(), "x is intentionally non-contiguous"
                        exp_nc = bool_half_compat_where(exp_mask, torch.tensor(0).type_as(x), x_nc, dtype)
                        self.assertEqual(torch_tri_func(x_nc, diagonal), exp_nc, 0)
                        x_nc_is_contiguous = x_nc.is_contiguous()
                        if upper:
                            self.assertEqual(x_nc.triu_(diagonal), exp_nc, 0)
                        else:
                            self.assertEqual(x_nc.tril_(diagonal), exp_nc, 0)

                        self.assertTrue(x_nc.is_contiguous() == x_nc_is_contiguous,
                                        "contiguity of x_nc should not be changed")

                    # expanded tensors
                    expanded_size = (x.size(0),) + x.size()
                    x_expanded = x.clone().expand(*expanded_size)
                    if x.size(0) != 1:
                        assert 0 in x_expanded.stride(), "x intentionally has 0 in its stride"
                    output = torch_tri_func(x_expanded, diagonal)
                    self.assertEqual(output, expected.expand(expanded_size), 0)
                    if x.size(0) != 1:
                        self.assertTrue(0 in x_expanded.stride(),
                                        "geometry of x_expanded should be the same")
                    if upper:
                        self.assertEqual(output, x_expanded.triu_(diagonal), 0)
                    else:
                        self.assertEqual(output, x_expanded.tril_(diagonal), 0)

                if not TEST_NUMPY:
                    continue

                # numpy test
                numpy_tri_func = numpy_functions[upper]
                self.assertEqual(numpy_tri_func(x.to('cpu').numpy(), diagonal), res1.cpu().numpy())

        diagonals = [-2, -1, 0, 1, 2]
        shapes = [(3, 3), (5, 3, 3), (7, 5, 3, 3),  # square matrices
                  (7, 3), (5, 7, 3), (7, 5, 7, 3),  # fat matrices
                  (3, 7), (5, 3, 7), (7, 5, 3, 7),  # thin matrices
                  (3, 0), (0, 3, 3), (3, 3, 0, 0),  # no numel matrices
                  (3, 1), (5, 3, 1), (7, 5, 3, 1),  # very fat matrices
                  (1, 3), (5, 1, 3), (7, 5, 1, 3),  # very thin matrices
                  (1, 3, 3, 3), (3, 1, 3, 3, 3)]    # unsqueezed batch dimensions
        dtypes = [dtype for dtype in torch.testing.get_all_dtypes() if dtype != torch.bfloat16]
        for s, d, dtype in product(shapes, diagonals, dtypes):
            run_test(s, device, d, dtype)

    @skipCUDANonDefaultStreamIf(True)
    def test_multinomial_alias(self, device):
        # Get probs vector to use in setup
        def get_probs(length, is_contiguous):
            probs = torch.softmax(torch.randn(length), 0)
            if not is_contiguous:
                probs = torch.softmax(torch.randn(length, 2), 0)[:, 1]
            assert not (is_contiguous ^ probs.is_contiguous()), "contiguity requirement not met"
            return probs.to(device)

        for is_contiguous in [True, False]:
            probs = get_probs(4, is_contiguous)
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            for n_samples in [-1, 1, 10]:
                if n_samples > 0:
                    samples = torch._multinomial_alias_draw(prob_table, alias_table, n_samples)
                    self.assertEqual(prob_table.size(), torch.Size([4]), "size mismatch: probability table")
                    self.assertEqual(alias_table.size(), torch.Size([4]), "size mismatch: alias table")
                    self.assertEqual(samples.size(), torch.Size([n_samples]), "wrong number of samples")
                else:
                    with self.assertRaisesRegex(RuntimeError, "cannot sample <= 0 samples"):
                        torch._multinomial_alias_draw(prob_table, alias_table, n_samples)

            with self.assertRaisesRegex(RuntimeError, "expected 1-D"):
                probs = probs.view(2, 2)
                torch._multinomial_alias_setup(probs)

            with self.assertRaisesRegex(RuntimeError, "expected 1-D"):
                a_t, p_t = torch._multinomial_alias_setup(probs)
                torch._multinomial_alias_draw(p_t.view(2, 2), a_t.view(2, 2))

        MAX_SAMPLES = 200000
        for probs in [get_probs(4, True),
                      torch.tensor([0.8, 0.2], device=device),
                      torch.tensor([0.7, 0.2, 0.1], device=device)]:
            # Check how different the alias distribution and the original distribution are
            alias_dist = torch.zeros_like(probs)
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            alias_samples = torch._multinomial_alias_draw(prob_table, alias_table, MAX_SAMPLES)
            alias_dist = torch.unique(alias_samples, return_counts=True)[1].to(dtype=probs.dtype) / MAX_SAMPLES
            self.assertTrue(torch.allclose(alias_dist, probs, rtol=0.02, atol=0.0),
                            "Actual: {}\nExpected: {}".format(alias_dist, probs))

        for probs in [torch.tensor([0.2501, 0.25, 0.2499, 0.25], device=device),
                      torch.tensor([0.8, 0.199, 0.001], device=device),
                      torch.tensor([0.25001, 0.25, 0.24999, 0.25], device=device),
                      torch.tensor([0.33, 0.34, 0.33], device=device),
                      torch.tensor([0.8, 0.1999, 0.0001], device=device)]:
            # Check the difference between the original probabilities and the reconstructed
            # probabilities from the alias and probability tables output by _multinomial_alias_setup
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            actual = torch.zeros_like(probs)
            for i, vals in enumerate(zip(alias_table, prob_table)):
                idx, p = vals
                actual[i] += p
                actual[idx] += 1. - p
            actual = actual / len(probs)
            self.assertEqual(actual, probs, 1e-6)

        # Some special cases
        test_cases = [torch.tensor([1.0, 0.0, 0.0], device=device), torch.tensor([0.0, 1.0], device=device)]
        for probs in test_cases:
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            alias_samples = torch._multinomial_alias_draw(prob_table, alias_table, MAX_SAMPLES)
            self.assertEqual(alias_samples.unique(), probs.nonzero().squeeze(-1))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lapack_empty(self, device):
        # FIXME: these are just a selection of LAPACK functions -- we need a general strategy here.
        # The LAPACK functions themselves generally do NOT work with zero sized dimensions, although
        # numpy/sci often has a direct wrapper (e.g. lu_factor) and a wrapper that "does the right thing"
        # (e.g. lu).  We often name our functions identically to the lapack function, so it will take work
        # to name / migrate-to better wrappers.
        def fn(torchfn, *args):
            return torchfn(*tuple(torch.randn(shape, device=device) if isinstance(shape, tuple) else shape
                                  for shape in args))

        # inverse, pinverse
        self.assertEqual((0, 0), fn(torch.inverse, (0, 0)).shape)
        self.assertEqual((5, 0), fn(torch.pinverse, (0, 5)).shape)
        self.assertEqual((0, 5), fn(torch.pinverse, (5, 0)).shape)
        self.assertEqual((0, 0), fn(torch.pinverse, (0, 0)).shape)

        # det, logdet, slogdet
        self.assertEqual(torch.tensor(1., device=device), fn(torch.det, (0, 0)))
        self.assertEqual(torch.tensor(0., device=device), fn(torch.logdet, (0, 0)))
        self.assertEqual((torch.tensor(1., device=device), torch.tensor(0., device=device)),
                         fn(torch.slogdet, (0, 0)))

        # eig, symeig
        evalues, evectors = fn(torch.eig, (0, 0), True)
        self.assertEqual([(0, 2), (0, 0)], [evalues.shape, evectors.shape])
        evalues, evectors = fn(torch.symeig, (0, 0), True)
        self.assertEqual([(0,), (0, 0)], [evalues.shape, evectors.shape])

        # qr
        q, r = fn(torch.qr, (3, 0), True)
        self.assertEqual([(3, 0), (0, 0)], [q.shape, r.shape])
        q, r = fn(torch.qr, (0, 3), True)
        self.assertEqual([(0, 0), (0, 3)], [q.shape, r.shape])
        q, r = fn(torch.qr, (3, 0), False)
        self.assertEqual([(3, 3), (3, 0)], [q.shape, r.shape])

        # lstsq
        self.assertRaises(RuntimeError, lambda: torch.lstsq(torch.randn(0, 0), torch.randn(0, 0)))
        self.assertRaises(RuntimeError, lambda: torch.lstsq(torch.randn(0,), torch.randn(0, 0)))

    def test_roll(self, device):
        numbers = torch.arange(1, 9, device=device)

        single_roll = numbers.roll(1, 0)
        expected = torch.tensor([8, 1, 2, 3, 4, 5, 6, 7], device=device)
        self.assertEqual(single_roll, expected, "{} did not equal expected result".format(single_roll))

        roll_backwards = numbers.roll(-2, 0)
        expected = torch.tensor([3, 4, 5, 6, 7, 8, 1, 2], device=device)
        self.assertEqual(roll_backwards, expected, "{} did not equal expected result".format(roll_backwards))

        data = numbers.view(2, 2, 2)
        rolled = data.roll(1, 0)
        expected = torch.tensor([5, 6, 7, 8, 1, 2, 3, 4], device=device).view(2, 2, 2)
        self.assertEqual(expected, rolled, "{} did not equal expected result: {}".format(rolled, expected))

        data = data.view(2, 4)
        # roll a loop until back where started
        loop_rolled = data.roll(2, 0).roll(4, 1)
        self.assertEqual(data, loop_rolled, "{} did not equal the original: {}".format(loop_rolled, data))
        # multiple inverse loops
        self.assertEqual(data, data.roll(-20, 0).roll(-40, 1))
        self.assertEqual(torch.tensor([8, 1, 2, 3, 4, 5, 6, 7], device=device), numbers.roll(1, 0))

        # test non-contiguous
        # strided equivalent to numbers.as_strided(size=(4, 2), stride=(1, 4))
        strided = numbers.view(2, 4).transpose(0, 1)
        self.assertFalse(strided.is_contiguous(), "this test needs a non-contiguous tensor")
        expected = torch.tensor([4, 8, 1, 5, 2, 6, 3, 7]).view(4, 2)
        rolled = strided.roll(1, 0)
        self.assertEqual(expected, rolled,
                         "non contiguous tensor rolled to {} instead of {} ".format(rolled, expected))

        # test roll with no dimension specified
        expected = numbers.roll(1, 0).view(2, 4)
        self.assertEqual(expected, data.roll(1), "roll with no dims should flatten and roll.")
        self.assertEqual(expected, data.roll(1, dims=None), "roll with no dims should flatten and roll.")

        # test roll over multiple dimensions
        expected = torch.tensor([[7, 8, 5, 6], [3, 4, 1, 2]], device=device)
        double_rolled = data.roll(shifts=(2, -1), dims=(1, 0))
        self.assertEqual(double_rolled, expected,
                         "should be able to roll over two dimensions, got {}".format(double_rolled))

        self.assertRaisesRegex(RuntimeError, "required", lambda: data.roll(shifts=(), dims=()))
        self.assertRaisesRegex(RuntimeError, "required", lambda: data.roll(shifts=(), dims=1))
        # shifts/dims should align
        self.assertRaisesRegex(RuntimeError, "align", lambda: data.roll(shifts=(1, 2), dims=(1,)))
        self.assertRaisesRegex(RuntimeError, "align", lambda: data.roll(shifts=(1,), dims=(1, 2)))

    def test_nonzero_empty(self, device):
        def assert_tuple_empty(tup, dim):
            self.assertEqual(dim, len(tup))
            for t in tup:
                self.assertEqual(torch.Size([0]), t.shape)

        x = torch.randn(0, 2, 0, 5, 0, device=device)
        y = torch.nonzero(x)
        z = torch.nonzero(x, as_tuple=True)

        self.assertEqual(0, y.numel())
        self.assertEqual(torch.Size([0, 5]), y.shape)
        assert_tuple_empty(z, 5)

        x = torch.tensor(0.5, device=device)
        y = torch.nonzero(x)
        # nonzero with as_tuple returns a
        # tuple of len 1 for a zero-dim tensor.
        # This is done to match Numpy behavior.
        z = torch.nonzero(x, as_tuple=True)
        self.assertEqual(1, len(z))
        self.assertEqual(torch.zeros(1, dtype=torch.long), z[0])

        x = torch.zeros((), device=device)
        y = torch.nonzero(x)
        z = torch.nonzero(x, as_tuple=True)
        self.assertEqual(torch.Size([0, 0]), y.shape)
        self.assertEqual(1, len(z))
        self.assertEqual(torch.empty(0, dtype=torch.long), z[0])

    def test_normal(self, device):
        q = torch.empty(100, 100, device=device).normal_()
        self.assertEqual(q.mean(), 0, 0.2)
        self.assertEqual(q.std(), 1, 0.2)

        q.normal_(2, 3)
        self.assertEqual(q.mean(), 2, 0.3)
        self.assertEqual(q.std(), 3, 0.3)

        q = torch.empty(100, 100, device=device)
        q_row1 = q[0:1].clone()
        q[99:100].normal_()
        self.assertEqual(q[99:100].mean(), 0, 0.2)
        self.assertEqual(q[99:100].std(), 1, 0.2)
        self.assertEqual(q[0:1].clone(), q_row1)

        mean = torch.empty(100, 100, device=device)
        std = torch.empty(100, 100, device=device)
        mean[:50] = 0
        mean[50:] = 1
        std[:, :50] = 4
        std[:, 50:] = 1

        r = torch.normal(mean)
        self.assertEqual(r[:50].mean(), 0, 0.2)
        self.assertEqual(r[50:].mean(), 1, 0.2)
        self.assertEqual(r.std(), 1, 0.2)

        r = torch.normal(mean, 3)
        self.assertEqual(r[:50].mean(), 0, 0.2)
        self.assertEqual(r[50:].mean(), 1, 0.2)
        self.assertEqual(r.std(), 3, 0.2)

        r = torch.normal(2, std)
        self.assertEqual(r.mean(), 2, 0.2)
        self.assertEqual(r[:, :50].std(), 4, 0.3)
        self.assertEqual(r[:, 50:].std(), 1, 0.2)

        r = torch.normal(mean, std)
        self.assertEqual(r[:50].mean(), 0, 0.2)
        self.assertEqual(r[50:].mean(), 1, 0.2)
        self.assertEqual(r[:, :50].std(), 4, 0.3)
        self.assertEqual(r[:, 50:].std(), 1, 0.2)

        r = torch.normal(2, 3, (100, 100))
        self.assertEqual(r.mean(), 2, 0.2)
        self.assertEqual(r.std(), 3, 0.2)

    def test_empty_strided(self, device):
        for shape in [(2, 3, 4), (0, 2, 0)]:
            # some of these cases are pretty strange, just verifying that if as_strided
            # allows them then empty_strided can as well.
            for strides in [(12, 4, 1), (2, 4, 6), (0, 0, 0)]:
                empty_strided = torch.empty_strided(shape, strides, device=device)
                # as_strided checks the storage size is big enough to support such a strided tensor;
                # instead of repeating this calculation, we just use empty_strided which does the same
                # calculation when setting the storage size.
                as_strided = torch.empty(empty_strided.storage().size(),
                                         device=device).as_strided(shape, strides)
                self.assertEqual(empty_strided.shape, as_strided.shape)
                self.assertEqual(empty_strided.stride(), as_strided.stride())

    def test_sign(self, device):
        for dtype in torch.testing.get_all_math_dtypes(device):

            # Include NaN for floating point numbers
            if dtype.is_floating_point:
                dt_info = torch.finfo(dtype)

                # Create tensor (with NaN checking)
                a = torch.tensor([float('nan'), -12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                a_target = torch.tensor([0, -1, 0, 1, -1, 1], device=device, dtype=dtype)

            else:
                dt_info = torch.iinfo(dtype)

                # If unsigned type, everything should be >= 0
                if dt_info.min == 0:
                    a = torch.tensor([12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                    a_target = torch.tensor([1, 0, 1, 0, 1], device=device, dtype=dtype)
                else:
                    a = torch.tensor([-12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                    a_target = torch.tensor([-1, 0, 1, -1, 1], device=device, dtype=dtype)

            self.assertEqual(a.sign(), a_target, 'sign device={} dtype={}'.format(device, dtype))
            self.assertEqual(torch.sign(a), a_target, 'sign device={} dtype={}'.format(device, dtype))

            out = torch.empty_like(a)
            torch.sign(a, out=out)
            self.assertEqual(out, a_target, 'sign_out device={} dtype={}'.format(device, dtype))

            a.sign_()
            self.assertEqual(a, a_target, 'sign_ device={} dtype={}'.format(device, dtype))

        # Include test for bool dtype
        a_bool = torch.tensor([True, True, False, float('nan')], device=device).bool()
        a_bool_target = torch.tensor([True, True, False, True], device=device).bool()
        self.assertEqual(a_bool.sign(), a_bool_target, 'sign device={} dtype=bool'.format(device))
        self.assertEqual(torch.sign(a_bool), a_bool_target, 'sign device={} dtype=bool'.format(device))

        a_out = torch.empty_like(a_bool)
        torch.sign(a_bool, out=a_out)
        self.assertEqual(a_out, a_bool_target, 'sign_out device={} dtype=bool'.format(device))

        a_bool.sign_()
        self.assertEqual(a_bool, a_bool_target, 'sign_ device={} dtype=bool'.format(device))

    def test_logical_any(self, device):
        x = torch.zeros([2, 3, 400], dtype=torch.uint8, device=device)

        self.assertEqual(
            torch.tensor(0, dtype=torch.uint8, device=device),
            x.any())

        self.assertEqual(
            torch.zeros([1, 3, 400], dtype=torch.uint8, device=device),
            x.any(0, keepdim=True))

        self.assertEqual(
            torch.zeros([2, 1, 400], dtype=torch.uint8, device=device),
            x.any(1, keepdim=True))

        self.assertEqual(
            torch.zeros([2, 3, 1], dtype=torch.uint8, device=device),
            x.any(2, keepdim=True))

        # set the last element to 0
        x[-1][-1][-1] = 1

        self.assertEqual(
            torch.tensor(1, dtype=torch.uint8, device=device),
            x.any())

        y = torch.zeros([1, 3, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(0, keepdim=True))

        y = torch.zeros([2, 1, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(1, keepdim=True))

        y = torch.zeros([2, 3, 1], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(2, keepdim=True))

    def test_logical_all(self, device):
        x = torch.ones([2, 3, 400], dtype=torch.uint8, device=device)

        self.assertEqual(
            torch.tensor(1, dtype=torch.uint8, device=device),
            x.all())

        self.assertEqual(
            torch.ones([1, 3, 400], dtype=torch.uint8, device=device),
            x.all(0, keepdim=True))

        self.assertEqual(
            torch.ones([2, 1, 400], dtype=torch.uint8, device=device),
            x.all(1, keepdim=True))

        self.assertEqual(
            torch.ones([2, 3, 1], dtype=torch.uint8, device=device),
            x.all(2, keepdim=True))

        # set the last element to 0
        x[-1][-1][-1] = 0

        self.assertEqual(
            torch.tensor(0, dtype=torch.uint8, device=device),
            x.all())

        y = torch.ones([1, 3, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(0, keepdim=True))

        y = torch.ones([2, 1, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(1, keepdim=True))

        y = torch.ones([2, 3, 1], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(2, keepdim=True))

    def test_log_normal(self, device):
        a = torch.tensor([10], dtype=torch.float, device=device).log_normal_()
        self.assertEqual(a.dtype, torch.float)
        self.assertEqual(a.size(), torch.Size([1]))

    def test_geometric(self, device):
        a = torch.tensor([10], dtype=torch.float, device=device).geometric_(0.5)
        self.assertEqual(a.dtype, torch.float)
        self.assertEqual(a.size(), torch.Size([1]))

    def test_pairwise_distance_empty(self, device):
        shape = (2, 0)
        x = torch.randn(shape, device=device)
        y = torch.randn(shape, device=device)

        self.assertEqual(torch.zeros(2, device=device), torch.pairwise_distance(x, y))
        self.assertEqual(torch.zeros((2, 1), device=device), torch.pairwise_distance(x, y, keepdim=True))

        shape = (0, 2)
        x = torch.randn(shape, device=device)
        y = torch.randn(shape, device=device)
        self.assertEqual(torch.zeros(0, device=device), torch.pairwise_distance(x, y))
        self.assertEqual(torch.zeros((0, 1), device=device), torch.pairwise_distance(x, y, keepdim=True))

    def test_pdist_empty(self, device):
        shape = (0, 2)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.empty(0, device=device), torch.pdist(x))

        shape = (1, 2)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.empty(0, device=device), torch.pdist(x))

        shape = (3, 0)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.zeros(3, device=device), torch.pdist(x))

    def test_cdist_empty(self, device):
        x = torch.randn((0, 5), device=device)
        y = torch.randn((4, 5), device=device)
        self.assertEqual(torch.empty(0, 4, device=device), torch.cdist(x, y))

        x = torch.randn((2, 5), device=device)
        y = torch.randn((0, 5), device=device)
        self.assertEqual(torch.empty(2, 0, device=device), torch.cdist(x, y))

        x = torch.randn((2, 0), device=device)
        y = torch.randn((3, 0), device=device)
        self.assertEqual(torch.zeros(2, 3, device=device), torch.cdist(x, y))

        x = torch.randn((2, 0), device=device)
        y = torch.randn((0, 0), device=device)
        self.assertEqual(torch.empty(2, 0, device=device), torch.cdist(x, y))

    def test_cdist_norm(self, device):
        for r1 in [3, 4, 5, 6]:
            for m in [2, 3, 4, 10]:
                for r2 in [4, 6, 7, 8]:
                    for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                        x = torch.randn(r1, m, device=device)
                        y = torch.randn(r2, m, device=device)
                        actual = torch.cdist(x, y, p=p)
                        expected = brute_cdist(x, y, p=p)
                        self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_norm_batch(self, device):
        for r1 in [3, 4, 5, 6]:
            for m in [2, 3, 4, 10]:
                for r2 in [4, 6, 7, 8]:
                    for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                        x = torch.randn(2, 3, 6, r1, m, device=device)
                        y = torch.randn(2, 3, 6, r2, m, device=device)
                        actual = torch.cdist(x, y, p=p)
                        expected = brute_cdist(x, y, p=p)
                        self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_large(self, device):
        x = torch.randn(1000, 10, device=device)
        y = torch.randn(1000, 10, device=device)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_large_batch(self, device):
        x = torch.randn(4, 3, 1000, 10, device=device)
        y = torch.randn(4, 3, 1000, 10, device=device)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_non_contiguous(self, device):
        x = torch.randn(5, 7, device=device).transpose(-1, -2)
        y = torch.randn(5, 3, device=device).transpose(-1, -2)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertFalse(x.is_contiguous())
        self.assertFalse(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

        x = torch.randn(7, 5, device=device)
        y = torch.randn(5, 3, device=device).t()
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertTrue(x.is_contiguous())
        self.assertFalse(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

        x = torch.randn(5, 7, device=device).t()
        y = torch.randn(3, 5, device=device)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertFalse(x.is_contiguous())
        self.assertTrue(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_non_contiguous_batch(self, device):
        x = torch.randn(4, 3, 2, 5, 7, device=device).transpose(-1, -2)
        y = torch.randn(4, 3, 2, 5, 3, device=device).transpose(-1, -2)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertFalse(x.is_contiguous())
        self.assertFalse(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

        x = torch.randn(7, 2, 7, 5, device=device)
        y = torch.randn(7, 2, 5, 3, device=device).transpose(-1, -2)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertTrue(x.is_contiguous())
        self.assertFalse(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

        x = torch.randn(4, 5, 7, device=device).transpose(-1, -2)
        y = torch.randn(4, 3, 5, device=device)
        actual = torch.cdist(x, y, p=2)
        expected = brute_cdist(x, y, p=2)
        self.assertFalse(x.is_contiguous())
        self.assertTrue(y.is_contiguous())
        self.assertTrue(torch.allclose(expected, actual))

    def test_multinomial_constraints(self, device):
        x = torch.empty(1, 2, 3, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "prob_dist must be 1 or 2 dim",
            lambda: torch.multinomial(x, 2))
        x = torch.empty(1, 2, dtype=torch.long, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial only supports floating-point dtypes for input",
            lambda: torch.multinomial(x, 2))
        x = torch.empty(1, 2, dtype=torch.double, device=device)
        y = torch.empty(1, 2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial expects Long tensor out",
            lambda: torch.multinomial(x, 2, out=y))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample <= 0 samples",
            lambda: torch.multinomial(x, 0))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample <= 0 samples",
            lambda: torch.multinomial(x, -1))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample > prob_dist",
            lambda: torch.multinomial(x, 3, False))
        x = torch.empty(16777217, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "number of categories cannot exceed",
            lambda: torch.multinomial(x, 3))

    def test_add(self, device):
        # [res] torch.add([res,] tensor1, tensor2)
        m1 = torch.randn(100, 100, device=device)
        v1 = torch.randn(100, device=device)

        # contiguous
        res1 = torch.add(m1[4], v1)
        res2 = res1.clone().zero_()
        for i in range(m1.size(1)):
            res2[i] = m1[4, i] + v1[i]
        self.assertEqual(res1, res2)

        m1 = torch.randn(100, 100, device=device)
        v1 = torch.randn(100, device=device)

        # non-contiguous
        res1 = torch.add(m1[:, 4], v1)
        res2 = res1.clone().zero_()
        for i in range(m1.size(0)):
            res2[i] = m1[i, 4] + v1[i]
        self.assertEqual(res1, res2)

        # [res] torch.add([res,] tensor, value)
        m1 = torch.randn(10, 10, device=device)

        # contiguous
        res1 = m1.clone()
        res1[3].add_(2)
        res2 = m1.clone()
        for i in range(m1.size(1)):
            res2[3, i] = res2[3, i] + 2
        self.assertEqual(res1, res2)

        # non-contiguous
        m1 = torch.randn(10, 10, device=device)
        res1 = m1.clone()
        res1[:, 3].add_(2)
        res2 = m1.clone()
        for i in range(m1.size(0)):
            res2[i, 3] = res2[i, 3] + 2
        self.assertEqual(res1, res2)

        # inter-type
        m1 = torch.randn(10, 10, device=device)
        self.assertEqual(m1 + 3, m1 + torch.tensor(3))
        self.assertEqual(3 + m1, torch.tensor(3) + m1)
        one = torch.tensor(1, dtype=torch.uint8, device=device)
        self.assertEqual(torch.add(one, 1), 2)
        self.assertEqual(torch.add(one, 1).dtype, torch.uint8)

        # contiguous + non-contiguous
        m1 = torch.randn(10, 10, device=device)
        m2 = torch.randn(10, 10, device=device).t()
        res = m1 + m2
        self.assertTrue(res.is_contiguous())
        self.assertEqual(res, m1 + m2.contiguous())

        # 1d + empty
        m1 = torch.tensor([1.0], dtype=torch.float, device=device)
        m2 = torch.tensor([], dtype=torch.float, device=device)
        self.assertEqual(m1 + m2, [])

        # bool
        m1 = torch.tensor([True, False, False, True, False, False], dtype=torch.bool, device=device)
        m2 = torch.tensor([True, True, False, False, False, True], dtype=torch.bool, device=device)
        expected = torch.tensor([True, True, False, True, False, True], dtype=torch.bool, device=device)
        self.assertEqual(m1 + m2, expected)

        # fused multiply add
        a = torch.zeros(2, 3, dtype=torch.bool, device=device)
        res = torch.add(a, a, alpha=0)
        expected = torch.zeros(2, 3, device=device).bool()
        self.assertEqual(res, expected)

        # bfloat16
        m1 = torch.tensor([1., 2.], dtype=torch.bfloat16)
        m2 = torch.tensor([3., 4.], dtype=torch.bfloat16)
        self.assertEqual(m1 + m2, torch.tensor([4., 6.], dtype=torch.bfloat16))

    def test_bool_sub(self, device):
        m1 = torch.tensor([True, False, False, True, False, False], dtype=torch.bool, device=device)
        m2 = torch.tensor([True, True, False, False, False, True], dtype=torch.bool, device=device)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with two bool tensors is not supported. "
                               r"Use the `\^` or `logical_xor\(\)` operator instead.",
                               lambda: m1 - m2)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with a bool tensor is not supported. "
                               r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
                               lambda: 1 - m1)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with a bool tensor is not supported. "
                               r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
                               lambda: m2 - 1)

    def test_mul(self, device):
        m1 = torch.randn(10, 10, device=device)
        res1 = m1.clone()
        res1[:, 3].mul_(2)
        res2 = m1.clone()
        for i in range(res1.size(0)):
            res2[i, 3] = res2[i, 3] * 2
        self.assertEqual(res1, res2)

        a1 = torch.tensor([True, False, False, True], dtype=torch.bool, device=device)
        a2 = torch.tensor([True, False, True, False], dtype=torch.bool, device=device)
        self.assertEqual(a1 * a2, torch.tensor([True, False, False, False], dtype=torch.bool, device=device))

        if device == 'cpu':
            a1 = torch.tensor([0.1, 0.1], dtype=torch.bfloat16, device=device)
            a2 = torch.tensor([1.1, 0.1], dtype=torch.bfloat16, device=device)
            self.assertEqual(a1 * a2, torch.tensor([0.11, 0.01], dtype=torch.bfloat16, device=device), 0.01)
            self.assertEqual(a1.mul(a2), a1 * a2)

    def test_cumsum(self, device):
        x = torch.rand(100, 100, device=device)
        res1 = torch.cumsum(x, 1)
        res2 = torch.Tensor().to(device)
        torch.cumsum(x, 1, out=res2)
        self.assertEqual(res1, res2)

        a = torch.tensor([[True, False, True],
                          [False, False, False],
                          [True, True, True]], device=device)
        b = a.byte()
        aRes = torch.cumsum(a, 0)
        bRes = torch.cumsum(b, 0)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 1],
                                             [1, 0, 1],
                                             [2, 1, 2]]))

        aRes = torch.cumsum(a, 1)
        bRes = torch.cumsum(b, 1)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 1, 2],
                                             [0, 0, 0],
                                             [1, 2, 3]]))

    def test_cumprod(self, device):
        x = torch.rand(100, 100, device=device)
        res1 = torch.cumprod(x, 1)
        res2 = torch.Tensor().to(device)
        torch.cumprod(x, 1, out=res2)
        self.assertEqual(res1, res2)

        a = torch.tensor([[True, False, True],
                         [False, False, False],
                         [True, True, True]], dtype=torch.bool, device=device)
        b = a.byte()
        aRes = torch.cumprod(a, 0)
        bRes = torch.cumprod(b, 0)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 1],
                                             [0, 0, 0],
                                             [0, 0, 0]]))

        aRes = torch.cumprod(a, 1)
        bRes = torch.cumprod(b, 1)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 0],
                                             [0, 0, 0],
                                             [1, 1, 1]]))

    def test_std_mean(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for dim in range(x.dim()):
            for unbiased in [False, True]:
                for keepdim in [False, True]:
                    std1, mean1 = torch.std_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                    std2 = x.std(dim=dim, unbiased=unbiased, keepdim=keepdim)
                    mean2 = x.mean(dim=dim, keepdim=keepdim)
                    self.assertEqual(std1, std2)
                    self.assertEqual(mean1, mean2)

    def test_std_mean_all_dims(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for unbiased in [False, True]:
            std1, mean1 = torch.std_mean(x, unbiased=unbiased)
            std2 = x.std(unbiased=unbiased)
            mean2 = x.mean()
            self.assertEqual(std1, std2)
            self.assertEqual(mean1, mean2)

    def test_var_mean(self, device):
        x = torch.rand(100, 300, 50, device=device)
        for dim in range(x.dim()):
            for unbiased in [False, True]:
                for keepdim in [False, True]:
                    var1, mean1 = torch.var_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                    var2 = x.var(dim=dim, unbiased=unbiased, keepdim=keepdim)
                    mean2 = x.mean(dim=dim, keepdim=keepdim)
                    self.assertEqual(var1, var2)
                    self.assertEqual(mean1, mean2)

    def test_var_mean_all_dims(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for unbiased in [False, True]:
            var1, mean1 = torch.var_mean(x, unbiased=unbiased)
            var2 = x.var(unbiased=unbiased)
            mean2 = x.mean()
            self.assertEqual(var1, var2)
            self.assertEqual(mean1, mean2)

    def test_std_mean_some_dims(self, device):
        sizes = (4, 6, 7, 5, 3)
        dims = len(sizes)
        x = torch.rand(sizes, device=device)
        for num_of_dims in range(2, dims):
            dim_list = list(combinations(list(range(dims)), r=num_of_dims))
            for dim in dim_list:
                for unbiased in [False, True]:
                    for keepdim in [False, True]:
                        std1, mean1 = torch.std_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                        std2 = x.std(dim=dim, unbiased=unbiased, keepdim=keepdim)
                        mean2 = x.mean(dim=dim, keepdim=keepdim)
                        self.assertEqual(std1, std2)
                        self.assertEqual(mean1, mean2)

    def test_zeros_like(self, device):
        expected = torch.zeros((100, 100,), device=device)

        res1 = torch.zeros_like(expected)
        self.assertEqual(res1, expected)

    def test_histc(self, device):
        # negative nbins throws
        with self.assertRaisesRegex(RuntimeError, 'bins must be > 0'):
            torch.histc(torch.tensor([1], dtype=torch.float, device=device), bins=-1)

        # without nbins
        actual = torch.histc(
            torch.tensor([2, 5], dtype=torch.float, device=device))
        expected = torch.zeros(100, dtype=torch.float, device=device)
        expected.data[0] = 1
        expected.data[99] = 1
        self.assertEqual(expected, actual)
        # tensor with the same element
        actual = torch.histc(torch.ones(5, dtype=torch.float, device=device), bins=5)
        self.assertEqual(
            torch.tensor([0, 0, 5, 0, 0], dtype=torch.float, device=device),
            actual)
        # no element falls between [min, max]
        actual = torch.histc(
            torch.ones(5, dtype=torch.float, device=device), bins=5, min=2, max=3)
        self.assertEqual(
            torch.tensor([0, 0, 0, 0, 0], dtype=torch.float, device=device),
            actual)
        # element falls below min + integral bin size and
        actual = torch.histc(
            torch.tensor([2, 4, 2, 2, 5, 4], dtype=torch.float, device=device),
            bins=5, min=1, max=5)
        self.assertEqual(
            torch.tensor([0, 3, 0, 2, 1], dtype=torch.float, device=device),
            actual)
        # non-integral bin size
        actual = torch.histc(
            torch.tensor([1, 2, 1], dtype=torch.float, device=device),
            bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.float, device=device),
            actual)
        # double input
        actual = torch.histc(
            torch.tensor([1, 2, 1], dtype=torch.double, device=device), bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.double, device=device),
            actual)
        self.assertEqual(actual.dtype, torch.double)
        # mixed input
        actual = torch.histc(
            torch.tensor([1., 2, 1], dtype=torch.float, device=device),
            bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.float, device=device),
            actual)
        self.assertEqual(actual.dtype, torch.float)
        # scalar input and 1 bin -- should return a 1-dimensional tensor, not a scalar.
        actual = torch.histc(
            torch.tensor(0, dtype=torch.float, device=device),
            bins=1, min=0, max=3)
        self.assertEqual(
            torch.tensor([1], dtype=torch.float, device=device),
            actual)

        # test against numpy.histogram()
        def test_against_np(tensor, bins=100, min=0, max=0):
            if min == 0 and max == 0:
                min = tensor.min().item()
                max = tensor.max().item()
            nparr = tensor.cpu().numpy()
            actual = torch.histc(tensor, bins=bins, min=min, max=max)
            expected = torch.from_numpy(np.histogram(nparr, bins=bins, range=(min, max))[0])
            self.assertEqual(actual.cpu(), expected)

        if TEST_NUMPY:
            test_against_np(torch.tensor([1., 2, 1], device=device))
            test_against_np(torch.randn(5000, device=device))

            # Test bins arg
            test_against_np(torch.randn(301, device=device), bins=10)

            # Test truncated range
            test_against_np(torch.randn(201, device=device), min=0.1, max=1)

            noncontig = torch.randn(100, 3, device=device)[:, 2]
            test_against_np(noncontig)

            multidim = torch.randn(3, 5, 7, 2, device=device)
            test_against_np(multidim)

            expanded = torch.randn(1, 5, 1, 2, device=device).expand(3, 5, 7, 2)
            test_against_np(expanded)

    def test_bool_tensor_comparison_ops(self, device):
        a = torch.tensor([True, False, True, False, True, False], dtype=torch.bool, device=device)
        b = torch.tensor([True, False, True, True, True, True], dtype=torch.bool, device=device)
        self.assertEqual(a == b, torch.tensor([1, 1, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a != b, torch.tensor([0, 0, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertEqual(a < b, torch.tensor([0, 0, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertEqual(a > b, torch.tensor([0, 0, 0, 0, 0, 0], dtype=torch.bool, device=device))
        self.assertEqual(a >= b, torch.tensor([1, 1, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a <= b, torch.tensor([1, 1, 1, 1, 1, 1], dtype=torch.bool, device=device))
        self.assertEqual(a > False, torch.tensor([1, 0, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a == torch.tensor(True, dtype=torch.bool, device=device),
                         torch.tensor([1, 0, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a == torch.tensor(0, dtype=torch.bool, device=device),
                         torch.tensor([0, 1, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertFalse(a.equal(b))

    def test_bool_tensor_value_change(self, device):
        x = torch.tensor([True, False], dtype=torch.bool, device=device)
        x[0] = False
        x[1] = True
        self.assertEqual(x, torch.tensor([False, True], dtype=torch.bool, device=device))

    def test_unfold_all_devices_and_dtypes(self, device):
        for dt in torch.testing.get_all_dtypes():
            if dt == torch.bfloat16:
                self.assertRaises(RuntimeError, lambda: torch.randint(5, (0, 1, 3, 0), dtype=dt, device=device))
                continue

            if dt == torch.half and device == 'cpu':
                # fix once random is implemented for Half on CPU
                self.assertRaises(RuntimeError, lambda: torch.randint(5, (0, 1, 3, 0), dtype=dt, device=device))
            else:
                x = torch.randint(5, (0, 1, 3, 0), dtype=dt, device=device)
                self.assertEqual((0, 1, 1, 0, 3), x.unfold(2, 3, 2).shape)

    def test_copy_all_dtypes_and_devices(self, device):
        from copy import copy
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([1, 2, 3, 4], dtype=dt, device=device)
            x_clone = x.clone()
            if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                self.assertRaises(RuntimeError, lambda: copy(x))
                continue
            y = copy(x)
            y.fill_(1)
            # copy is a shallow copy, only copies the tensor view,
            # not the data
            self.assertEqual(x, y)

    def test_resize_all_dtypes_and_devices(self, device):
        shape = (2, 2)
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            x.resize_(shape)
            self.assertEqual(shape, x.shape)

    def test_resize_as_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            y = torch.tensor([[1, 2, 3], [4, 5, 6]], dtype=dt, device=device)
            x.resize_as_(y)
            self.assertEqual(y.shape, x.shape)

    def test_view_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                self.assertRaises(RuntimeError, lambda: x.view(6))
                continue
            self.assertEqual(x.view(6).shape, [6])

    def test_fill_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor((1, 1), dtype=dt, device=device)
            if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                self.assertRaises(RuntimeError, lambda: x.fill_(1))
                continue
            x.fill_(1)

            self.assertEqual(x, torch.tensor([1, 1], dtype=dt, device=device))
            self.assertEqual(dt, x.dtype)

    def test_clone_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor((1, 1), dtype=dt, device=device)
            y = x.clone()
            if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                # `x - y` is used inside of the assertEqual
                self.assertRaises(RuntimeError, lambda: x - y)
                continue
            self.assertEqual(x, y)

    def test_cat_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4]], dtype=dt, device=device)
            if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                self.assertRaises(RuntimeError, lambda: torch.cat((x, x), 0))
                continue

            expected1 = torch.tensor([[1, 2], [3, 4], [1, 2], [3, 4]], dtype=dt, device=device)
            self.assertEqual(torch.cat((x, x), 0), expected1)

            expected2 = torch.tensor([[1, 2, 1, 2], [3, 4, 3, 4]], dtype=dt, device=device)
            self.assertEqual(torch.cat((x, x), 1), expected2)

    def test_tensor_factories_empty(self, device):
        # ensure we can create empty tensors from each factory function
        shapes = [(5, 0, 1), (0,), (0, 0, 1, 0, 2, 0, 0)]

        for shape in shapes:
            for dt in torch.testing.get_all_dtypes():

                if (torch.device(device).type == 'cuda' and dt == torch.bfloat16):
                    self.assertRaises(RuntimeError, lambda: torch.zeros(shape, device=device, dtype=dt).shape)
                    self.assertRaises(RuntimeError, lambda: torch.zeros_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                    self.assertRaises(RuntimeError, lambda: torch.full(shape, 3, device=device, dtype=dt).shape)
                    self.assertRaises(RuntimeError, lambda: torch.full_like(torch.zeros(shape, device=device, dtype=dt), 3))
                    self.assertRaises(RuntimeError, lambda: torch.ones(shape, device=device, dtype=dt).shape)
                    self.assertRaises(RuntimeError, lambda: torch.ones_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                    self.assertRaises(RuntimeError, lambda: torch.empty_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                else:
                    self.assertEqual(shape, torch.zeros(shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.zeros_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                    self.assertEqual(shape, torch.full(shape, 3, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.full_like(torch.zeros(shape, device=device, dtype=dt), 3).shape)
                    self.assertEqual(shape, torch.ones(shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.ones_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                    self.assertEqual(shape, torch.empty(shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.empty_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                    self.assertEqual(shape, torch.empty_strided(shape, (0,) * len(shape), device=device, dtype=dt).shape)

                if dt == torch.half and device == "cpu":
                    # update once random is implemented for half on CPU
                    self.assertRaises(RuntimeError, lambda: torch.randint(6, shape, device=device, dtype=dt).shape)
                else:
                    if dt == torch.bfloat16:
                        self.assertRaises(RuntimeError, lambda: torch.randint(6, shape, device=device, dtype=dt))
                        continue  # Remove once random is supported for bfloat16 on cuda
                    self.assertEqual(shape, torch.randint(6, shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.randint_like(torch.zeros(shape, device=device, dtype=dt), 6).shape)

                if dt != torch.double and dt != torch.float and dt != torch.half:
                    self.assertRaises(RuntimeError, lambda: torch.rand(shape, device=device, dtype=dt).shape)

                if dt == torch.double or dt == torch.float:
                    self.assertEqual(shape, torch.randn(shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.randn_like(torch.zeros(shape, device=device, dtype=dt)).shape)

        self.assertEqual((0,), torch.arange(0, device=device).shape)
        self.assertEqual((0, 0), torch.eye(0, device=device).shape)
        self.assertEqual((0, 0), torch.eye(0, 0, device=device).shape)
        self.assertEqual((5, 0), torch.eye(5, 0, device=device).shape)
        self.assertEqual((0, 5), torch.eye(0, 5, device=device).shape)
        self.assertEqual((0,), torch.linspace(1, 1, 0, device=device).shape)
        self.assertEqual((0,), torch.logspace(1, 1, 0, device=device).shape)
        self.assertEqual((0,), torch.randperm(0, device=device).shape)
        self.assertEqual((0,), torch.bartlett_window(0, device=device).shape)
        self.assertEqual((0,), torch.bartlett_window(0, periodic=False, device=device).shape)
        self.assertEqual((0,), torch.hamming_window(0, device=device).shape)
        self.assertEqual((0,), torch.hann_window(0, device=device).shape)
        self.assertEqual((1, 1, 0), torch.tensor([[[]]], device=device).shape)
        self.assertEqual((1, 1, 0), torch.as_tensor([[[]]], device=device).shape)

    def test_eye(self, device):
        for dtype in torch.testing.get_all_dtypes():
            if dtype == torch.bfloat16:
                continue

            for n, m in product([3, 5, 7], repeat=2):
                # Construct identity using diagonal and fill
                res1 = torch.eye(n, m, device=device, dtype=dtype)
                naive_eye = torch.zeros(n, m, dtype=dtype, device=device)
                naive_eye.diagonal(dim1=-2, dim2=-1).fill_(1)
                self.assertEqual(naive_eye, res1)

                # Check eye_out outputs
                res2 = torch.empty(0, device=device, dtype=dtype)
                torch.eye(n, m, out=res2)
                self.assertEqual(res1, res2)

    def test_addcmul(self, device):
        def rand_tensor(size, dtype, device):
            if dtype.is_floating_point:
                return torch.rand(size=size, dtype=dtype, device=device)
            if dtype == torch.uint8:
                return torch.randint(1, 5, size=size, dtype=dtype, device=device)
            else:
                return torch.randint(-5, 5, size=size, dtype=dtype, device=device)

        for dtype in torch.testing.get_all_math_dtypes(device):
            a = rand_tensor((2, 2), dtype=dtype, device=device)
            b = rand_tensor((2, 2), dtype=dtype, device=device)
            c = rand_tensor((2, 2), dtype=dtype, device=device)
            if dtype.is_floating_point:
                alpha = 0.1
            else:
                alpha = 3
            actual = torch.addcmul(a, alpha, b, c)
            expected = a + alpha * b * c
            self.assertTrue(torch.allclose(expected, actual))

    def test_empty_tensor_props(self, device):
        sizes = [(0,), (0, 3), (5, 0), (5, 0, 3, 0, 2), (0, 3, 0, 2), (0, 5, 0, 2, 0)]
        for size in sizes:
            x = torch.empty(tuple(size), device=device)
            self.assertEqual(size, x.shape)
            self.assertTrue(x.is_contiguous())
            size_ones_instead_of_zeros = (x if x != 0 else 1 for x in size)
            y = torch.empty(tuple(size_ones_instead_of_zeros), device=device)
            self.assertEqual(x.stride(), y.stride())

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_tensordot(self, device):
        a = torch.arange(60., device=device).reshape(3, 4, 5)
        b = torch.arange(24., device=device).reshape(4, 3, 2)
        c = torch.tensordot(a, b, dims=([1, 0], [0, 1])).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy(),
                                           axes=([1, 0], [0, 1])))
        self.assertEqual(c, cn)
        a = torch.randn(2, 3, 4, 5, device=device)
        b = torch.randn(4, 5, 6, 7, device=device)
        c = torch.tensordot(a, b, dims=2).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy(),
                                           axes=2))
        self.assertEqual(c, cn)
        c = torch.tensordot(a, b).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy()))
        self.assertEqual(c, cn)

    def test_narrow_empty(self, device):
        x = torch.randn(2, 3, 4, device=device)
        for d in range(x.dim()):
            y = x.narrow(d, x.size(d), 0)
            sz = list(x.size())
            sz[d] = 0
            self.assertEqual(sz, y.size())

    def test_linspace(self, device):
        _from = random.random()
        to = _from + random.random()
        res1 = torch.linspace(_from, to, 137, device=device)
        res2 = torch.tensor((), device=device)
        torch.linspace(_from, to, 137, out=res2)
        self.assertEqual(res1, res2, 0)
        self.assertRaises(RuntimeError, lambda: torch.linspace(0, 1, -1, device=device))
        self.assertEqual(torch.linspace(0, 1, 1, device=device), torch.zeros(1, device=device), 0)

        # Check linspace for generating with start > end.
        self.assertEqual(torch.linspace(2, 0, 3, device=device), torch.tensor((2, 1, 0), device=device), 0)

        # Check linspace for non-contiguous tensors.
        x = torch.zeros(2, 3, device=device)
        y = torch.linspace(0, 3, 4, out=x.narrow(1, 1, 2))
        self.assertEqual(x, torch.tensor(((0, 0, 1), (0, 2, 3)), device=device), 0)

    def test_logical(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([1, 2, 3, 4], device=device, dtype=dt)
            b = torch.tensor([2], device=device, dtype=dt)

            if dt == torch.half and device == 'cpu':
                self.assertRaises(RuntimeError, lambda: x.lt(2))
                continue

            if dt == torch.bool:
                # torch.bool is a special case and is being tested later
                # in this test
                continue

            if torch.device(device).type == 'cuda' and dt == torch.bfloat16:
                self.assertRaises(RuntimeError, lambda: x > b)
                self.assertRaises(RuntimeError, lambda: x < b)
                self.assertRaises(RuntimeError, lambda: x == b)
                self.assertRaises(RuntimeError, lambda: x != b)
                self.assertRaises(RuntimeError, lambda: x >= b)
                self.assertRaises(RuntimeError, lambda: x <= b)
                continue

            self.assertEqual(x.lt(2), torch.tensor([True, False, False, False]))
            self.assertEqual(x.le(2), torch.tensor([True, True, False, False]))
            self.assertEqual(x.ge(2), torch.tensor([False, True, True, True]))
            self.assertEqual(x.gt(2), torch.tensor([False, False, True, True]))
            self.assertEqual(x.eq(2), torch.tensor([False, True, False, False]))
            self.assertEqual(x.ne(2), torch.tensor([True, False, True, True]))

            self.assertEqual(x.lt(b), torch.tensor([True, False, False, False]))
            self.assertEqual(x.le(b), torch.tensor([True, True, False, False]))
            self.assertEqual(x.ge(b), torch.tensor([False, True, True, True]))
            self.assertEqual(x.gt(b), torch.tensor([False, False, True, True]))
            self.assertEqual(x.eq(b), torch.tensor([False, True, False, False]))
            self.assertEqual(x.ne(b), torch.tensor([True, False, True, True]))

        # Bool Tensor
        x = torch.tensor([True, False, True, False], device=device)
        self.assertEqual(x.lt(True), torch.tensor([False, True, False, True]))
        self.assertEqual(x.le(True), torch.tensor([True, True, True, True]))
        self.assertEqual(x.ge(True), torch.tensor([True, False, True, False]))
        self.assertEqual(x.gt(True), torch.tensor([False, False, False, False]))
        self.assertEqual(x.eq(True), torch.tensor([True, False, True, False]))
        self.assertEqual(x.ne(True), torch.tensor([False, True, False, True]))

    def test_index_copy(self, device):
        num_copy, num_dest = 3, 20
        dest = torch.randn(num_dest, 4, 5, device=device)
        src = torch.randn(num_copy, 4, 5, device=device)
        idx = torch.randperm(num_dest, device=device).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_copy_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] = src[i]
        self.assertEqual(dest, dest2, 0)

        dest = torch.randn(num_dest, device=device)
        src = torch.randn(num_copy, device=device)
        idx = torch.randperm(num_dest, device=device).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_copy_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] = src[i]
        self.assertEqual(dest, dest2, 0)

        # Bool tensor
        dest = torch.zeros(2, 2, dtype=torch.bool, device=device)
        src = torch.tensor([[True, True], [True, True]], device=device)
        index = torch.tensor([0, 1], device=device)
        dest.index_copy_(0, index, src)
        self.assertEqual(dest, torch.tensor([[True, True], [True, True]], device=device))

        # Error cases
        a = torch.randn(3, 5)
        c = torch.zeros(3)
        self.assertRaises(IndexError, lambda: a.index_copy_(dim=1, index=torch.tensor([3]), source=c))

    def test_index_fill(self, device):
        for dt in torch.testing.get_all_dtypes():
            if dt == torch.half or dt == torch.bfloat16:
                continue

            x = torch.tensor([[1, 2], [4, 5]], dtype=dt, device=device)
            index = torch.tensor([0], device=device)
            x.index_fill_(1, index, 0)
            self.assertEqual(x, torch.tensor([[0, 2], [0, 5]], dtype=dt, device=device))

    def test_index_select(self, device):
        src = torch.randn(3, 4, 5, device=device)
        # Index can be duplicated.
        idx = torch.tensor([2, 1, 0, 1, 2], dtype=torch.long, device=device)
        dest = torch.index_select(src, 0, idx)
        self.assertEqual(dest.shape, (5, 4, 5))
        for i in range(idx.size(0)):
            self.assertEqual(dest[i], src[idx[i]])

        # Check that 'out' is used correctly.
        out = torch.randn(5 * 4 * 5, device=device)
        dest = torch.index_select(src, 0, idx, out=out.view(5, 4, 5))
        self.assertEqual(dest.shape, (5, 4, 5))
        for i in range(idx.size(0)):
            self.assertEqual(dest[i], src[idx[i]])
        out.fill_(0.123)
        self.assertEqual(out, dest.view(-1))  # Must point to the same storage.

        # Bool tensor
        src = torch.tensor([False, True, False, False], device=device, dtype=torch.bool)
        idx = torch.tensor([1], dtype=torch.long, device=device)
        dest = torch.index_select(src, 0, idx)
        self.assertEqual(torch.tensor([True]), dest)

    def test_take_empty(self, device):
        for input_shape in [(0,), (0, 1, 2, 0), (1, 2, 3)]:
            for indices_shape in [(0,), (0, 1, 2, 0)]:
                input = torch.empty(input_shape, device=device)
                indices = torch.empty(indices_shape, dtype=torch.int64, device=device)
                self.assertEqual(indices, torch.take(input, indices))

    def test_put_empty(self, device):
        for dst_shape in [(0,), (0, 1, 2, 0), (1, 2, 3)]:
            for indices_shape in [(0,), (0, 1, 2, 0)]:
                for accumulate in [False, True]:
                    dst = torch.randn(dst_shape, device=device)
                    indices = torch.empty(indices_shape, dtype=torch.int64, device=device)
                    src = torch.randn(indices_shape, device=device)
                    self.assertEqual(dst, dst.put_(indices, src, accumulate=accumulate))

    def test_scatter_to_large_input(self, device):
        input = torch.zeros(4, 4, device=device)
        src = torch.ones(2, 2, device=device)
        index = torch.tensor([[1], [2]], device=device, dtype=torch.long)
        input.scatter_(0, index, src)
        self.assertEqual(input, torch.tensor([[0, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [0, 0, 0, 0]], device=device))

    def test_scatter_add_to_large_input(self, device):
        input = torch.zeros(4, 4, device=device)
        src = torch.ones(2, 2, device=device)
        index = torch.tensor([[1], [2]], device=device, dtype=torch.long)
        input.scatter_add_(0, index, src)
        self.assertEqual(input, torch.tensor([[0, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [0, 0, 0, 0]], device=device))

    def test_scatter_bool(self, device):
        x = torch.tensor([[True, True, True], [True, True, True]], device=device)
        res = torch.zeros(3, 3, dtype=torch.bool, device=device)
        res = res.scatter_(0, torch.tensor([[0, 1, 2], [0, 1, 2]], device=device), x)
        self.assertEqual(res, torch.tensor([[True, False, False],
                                            [False, True, False],
                                            [False, False, True]], device=device))

    def test_scatter_add_bool(self, device):
        x = torch.tensor([[True, True, True, True, True], [True, True, True, True, True]], device=device)
        res = torch.zeros(3, 5, dtype=torch.bool, device=device)
        res = res.scatter_add_(0, torch.tensor([[0, 1, 2, 0, 0], [2, 0, 0, 1, 2]], device=device), x)
        self.assertEqual(res, torch.tensor([[True, True, True, True, True],
                                            [False, True, False, True, False],
                                            [True, False, True, False, True]], device=device))

    def test_masked_scatter_bool_tensor(self, device):
        src = torch.tensor([True, True, True], device=device)
        dst = torch.tensor([False, False, False], device=device)
        mask = torch.tensor([False, True, False], device=device)

        dst.masked_scatter_(mask, src)
        self.assertEqual(dst, torch.tensor([False, True, False], device=device))

        mask = torch.tensor([True, False, True], device=device)
        dst = dst.masked_scatter(mask, src)
        self.assertEqual(dst, torch.tensor([True, True, True], device=device))

    def test_masked_select(self, device):
        for dt in torch.testing.get_all_dtypes():
            with warnings.catch_warnings(record=True) as w:
                for maskType in [torch.uint8, torch.bool]:
                    num_src = 10
                    src = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dt, device=device)
                    mask = torch.rand(num_src, device=device).clamp(0, 1).mul(2).floor().to(maskType)

                    if dt == torch.bfloat16 and torch.device(device).type == 'cuda':
                        # remove once bfloat16 implemented on CUDA
                        self.assertRaises(RuntimeError, lambda: src.masked_select(mask))
                        continue

                    if dt == torch.half and torch.device(device).type == 'cpu':
                        self.assertRaises(RuntimeError, lambda: src.masked_select(mask))
                        continue

                    dst = src.masked_select(mask)
                    dst2 = []
                    for i in range(num_src):
                        if mask[i]:
                            dst2 += [src[i]]
                    self.assertEqual(dst, torch.tensor(dst2), 0)

                    dst3 = torch.empty_like(src, device=device)
                    torch.masked_select(src, mask, out=dst3)
                    self.assertEqual(dst3, torch.Tensor(dst2), 0)
        self.assertEqual(len(w), 1)

        warn = 'masked_select received a mask with dtype torch.uint8,'
        self.assertEqual(str(w[0].message)[0:53], str(warn))

    def test_masked_fill_bool_tensor(self, device):
        dst = torch.tensor([True, False, True], device=device)
        mask = torch.tensor([False, True, False], device=device)

        dst.masked_fill_(mask, True)
        self.assertEqual(dst, torch.tensor([True, True, True], device=device))

        dst = dst.masked_fill(mask, False)
        self.assertEqual(dst, torch.tensor([True, False, True], device=device))

    def test_tensor_shape_empty(self, device):
        x = torch.randn((0, 1, 3, 0), device=device)
        # flatten
        self.assertEqual((0,), torch.flatten(x, 0, 3).shape)
        self.assertEqual((0, 0), torch.flatten(x, 0, 2).shape)
        self.assertEqual((0, 3, 0), torch.flatten(x, 1, 2).shape)

        # squeeze, unsqueeze
        self.assertEqual((0, 1, 1, 3, 0), torch.unsqueeze(x, 1).shape)
        self.assertEqual((0, 3, 0), torch.squeeze(x, 1).shape)
        self.assertEqual((0, 3, 0), torch.squeeze(x).shape)

        # transpose, t
        self.assertEqual((0, 0, 3, 1), torch.transpose(x, 1, 3).shape)
        y = torch.randn((5, 0), device=device)
        self.assertEqual((0, 5), y.t().shape)

        # select
        self.assertEqual((0, 1, 0), torch.select(x, 2, 2).shape)

        # repeat, permute
        self.assertEqual((9, 0, 5, 6, 0), x.repeat(9, 7, 5, 2, 3).shape)
        self.assertEqual((3, 0, 0, 1), x.permute(2, 3, 0, 1).shape)

        # diagonal, diagflat
        self.assertEqual((0,), torch.diagonal(torch.randn((5, 0), device=device)).shape)
        self.assertEqual((0,), torch.diagonal(torch.randn((0, 5), device=device)).shape)
        # off the end offsets are valid
        self.assertEqual((0,), torch.diagonal(torch.randn((5, 0), device=device), offset=1).shape)
        self.assertEqual((0,), torch.diagonal(torch.randn((0, 5), device=device), offset=1).shape)
        # check non-zero sized offsets off the end
        self.assertEqual((5, 6, 0), torch.diagonal(torch.randn((3, 4, 5, 6), device=device), offset=45252).shape)
        self.assertEqual((5, 6, 0), torch.diagonal(torch.randn((3, 4, 5, 6), device=device), offset=-45252).shape)

        self.assertEqual((0, 0), torch.diagflat(torch.tensor([], device=device)).shape)
        self.assertEqual(torch.zeros(1, 1), torch.diagflat(torch.tensor([], device=device), offset=1))
        self.assertEqual((0, 0), torch.diagflat(torch.tensor([[]], device=device)).shape)
        self.assertEqual(torch.zeros(1, 1), torch.diagflat(torch.tensor([[]], device=device), offset=1))

        # stack, split, chunk
        self.assertEqual((4, 0, 1, 3, 0), torch.stack((x, x, x, x)).shape)
        self.assertEqual([(0, 1, 3, 0)],
                         [z.shape for z in torch.chunk(x, 1, dim=0)])

        self.assertEqual([(0, 1, 3, 0), ] * 3, [z.shape for z in torch.chunk(x, 3, dim=0)])
        self.assertEqual([(0, 1, 1, 0), ] * 3, [z.shape for z in torch.chunk(x, 3, dim=2)])

        # NOTE: split_with_sizes behaves differently than NumPy in that it
        # takes sizes rather than offsets
        self.assertEqual([(0, 1, 0, 0), (0, 1, 1, 0), (0, 1, 2, 0)],
                         [z.shape for z in torch.split(x, (0, 1, 2), dim=2)])

        self.assertRaises(RuntimeError, lambda: torch.split(x, 0, dim=1))
        # This is strange because the split size is larger than the dim size, but consistent with
        # how split handles that case generally (when no 0s are involved).
        self.assertEqual([(0, 1, 3, 0)], [z.shape for z in torch.split(x, 1, dim=0)])
        self.assertEqual([(0, 1, 3, 0)], [z.shape for z in torch.split(x, 0, dim=0)])

    # functions that operate over a dimension but don't reduce.
    def test_dim_function_empty(self, device):
        shape = (0, 1, 2, 0)
        x = torch.randn(shape, device=device)

        # size stride
        self.assertEqual(0, x.size(3))
        self.assertEqual(2, x.size(2))
        self.assertEqual(2, x.stride(0))
        self.assertEqual(1, x.stride(2))

        self.assertEqual(x, torch.nn.functional.glu(x, 0))
        self.assertEqual((0, 1, 1, 0), torch.nn.functional.glu(x, 2).shape)

        # softmax, logsoftmax
        self.assertEqual(x, torch.nn.functional.softmax(x, 0))
        self.assertEqual(x, torch.nn.functional.softmax(x, 2))
        self.assertEqual(x, torch.nn.functional.softmax(x, 3))

        self.assertEqual(x, torch.nn.functional.log_softmax(x, 0))
        self.assertEqual(x, torch.nn.functional.log_softmax(x, 2))
        self.assertEqual(x, torch.nn.functional.log_softmax(x, 3))

        # cumsum, cumprod
        self.assertEqual(shape, torch.cumsum(x, 0).shape)
        self.assertEqual(shape, torch.cumsum(x, 2).shape)
        self.assertEqual(shape, torch.cumprod(x, 0).shape)
        self.assertEqual(shape, torch.cumprod(x, 2).shape)

        # flip
        self.assertEqual(x, x.flip(0))
        self.assertEqual(x, x.flip(2))

        # roll
        self.assertEqual(x, x.roll(0, 1).roll(0, -1))
        self.assertEqual(x, x.roll(1, x.size(1)))
        self.assertEqual(x, x.roll(1))
        self.assertEqual(x, x.roll((1, 1), (3, 1)))

        # unbind
        self.assertEqual((), x.unbind(0))
        self.assertEqual((torch.empty((0, 1, 0), device=device), torch.empty((0, 1, 0), device=device)),
                         x.unbind(2))

        # cross
        y = torch.randn((0, 1, 3, 0), device=device)
        self.assertEqual(y.shape, torch.cross(y, y).shape)

        # renorm
        self.assertEqual(shape, torch.renorm(x, 1, 0, 5).shape)
        self.assertEqual(shape, torch.renorm(x, 1, 2, 5).shape)

        # sort
        self.assertEqual([shape, shape], [z.shape for z in torch.sort(x, dim=0)])
        self.assertEqual([shape, shape], [z.shape for z in torch.sort(x, dim=2)])

        # topk
        self.assertEqual([shape, shape], [z.shape for z in torch.topk(x, 0, dim=0)])
        self.assertEqual([(0, 1, 1, 0), (0, 1, 1, 0)], [z.shape for z in torch.topk(x, 1, dim=2)])

        y = torch.randn((2, 3, 4), device=device)
        self.assertEqual([(2, 3, 0), (2, 3, 0)], [z.shape for z in torch.topk(y, 0)])

        # gather
        self.assertEqual(shape, torch.gather(x, 0, torch.empty(shape, dtype=torch.int64, device=device)).shape)
        self.assertEqual(shape, torch.gather(x, 2, torch.empty(shape, dtype=torch.int64, device=device)).shape)
        larger_shape = torch.empty((0, 1, 3, 0), dtype=torch.int64, device=device)
        self.assertEqual(larger_shape.shape, torch.gather(x, 2, larger_shape).shape)
        smaller_shape = torch.empty((0, 1, 0, 0), dtype=torch.int64, device=device)
        self.assertEqual(smaller_shape.shape, torch.gather(x, 2, smaller_shape).shape)
        y = torch.randn((2, 3, 4), device=device)
        self.assertEqual((0, 3, 4),
                         torch.gather(y, 0, torch.empty((0, 3, 4), dtype=torch.int64, device=device)).shape)

        # scatter, scatter_add
        for dim in [0, 2]:
            y = torch.randn(shape, device=device)
            y_src = torch.randn(shape, device=device)
            ind = torch.empty(shape, dtype=torch.int64, device=device)
            self.assertEqual(shape, y.scatter_(dim, ind, y_src).shape)
            self.assertEqual(shape, y.scatter_add_(dim, ind, y_src).shape)

        z = torch.randn((2, 3, 4), device=device)
        z_src = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.scatter_(2, torch.empty((2, 3, 0), dtype=torch.int64, device=device), z_src))
        self.assertEqual(z, z.scatter_add_(2, torch.empty((2, 3, 0), dtype=torch.int64, device=device), z_src))

        # index_fill, index_copy, index_add
        c = x.clone()
        c_clone = c.clone()
        ind_empty = torch.tensor([], dtype=torch.int64, device=device)
        ind_01 = torch.tensor([0, 1], dtype=torch.int64, device=device)
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_fill_(2, ind_empty, -1))
        self.assertEqual(c_clone, c.index_fill_(2, torch.tensor([0, 1], dtype=torch.int64, device=device), -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_copy_(2, ind_empty, torch.empty((0, 1, 0, 0), device=device)))
        self.assertEqual(c_clone, c.index_copy_(2, ind_01, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(2, ind_empty, torch.empty((0, 1, 0, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(2, ind_01, torch.empty((0, 1, 2, 0), device=device)))

        c = torch.randn((0, 1, 2), device=device)
        c_clone = c.clone()
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2), device=device)))

        # index fill/copy/add non-empty
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_fill_(0, ind_empty, -1))
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_copy_(0, ind_empty, torch.empty((0, 3, 4), device=device)))
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_add_(0, ind_empty, torch.empty((0, 3, 4), device=device)))

        # index_select
        self.assertEqual(x, x.index_select(0, ind_empty))
        self.assertEqual((0, 1, 0, 0), x.index_select(2, ind_empty).shape)
        self.assertEqual(x, x.index_select(2, ind_01))
        z = torch.randn((2, 3, 4), device=device)  # non-empty
        self.assertEqual((0, 3, 4), z.index_select(0, ind_empty).shape)
        c = torch.randn((0, 1, 2), device=device)
        self.assertEqual(c, c.index_select(0, ind_empty))
        c = torch.randn((0, 1, 2), device=device)
        self.assertEqual(c, c.index_select(0, ind_empty))

    def test_nonzero(self, device):
        num_srcs = [
            12, 12, 12, 12, 12, 125,
        ]

        types = [
            'torch.ByteTensor',
            'torch.CharTensor',
            'torch.ShortTensor',
            'torch.IntTensor',
            'torch.FloatTensor',
            'torch.DoubleTensor',
            'torch.LongTensor',
        ]

        shapes = [
            torch.Size((12,)),
            torch.Size((12, 1)),
            torch.Size((1, 12)),
            torch.Size((6, 2)),
            torch.Size((3, 2, 2)),
            torch.Size((5, 5, 5)),
        ]

        def is_lexicographically_sorted(inds):
            """Check sorted ascending with
            i -> j -> k changing slowest to fastest"""
            assert inds.size(1) == 3
            if inds.size(0) > 1:
                i0, j0, k0 = inds[:-1].t()
                i1, j1, k1 = inds[+1:].t()
                i_ok = (i1 >= i0)
                j_ok = (j1 >= j0) | (i1 > i0)
                k_ok = (k1 >= k0) | (j1 > j0) | (i1 > i0)
                lex = torch.stack((i_ok, j_ok, k_ok), dim=1)
                return lex
            return torch.full_like(inds, 1)

        def gen_nontrivial_input(num_src, dtype, device):
            while True:
                tensor = torch.rand(num_src).mul(2).floor().type(dtype).to(device)
                if tensor.sum() > 0:
                    return tensor

        for dtype in types:
            for shape, num_src in zip(shapes, num_srcs):
                tensor = gen_nontrivial_input(num_src, dtype, device)
                tensor = tensor.clone().resize_(shape)
                dst1 = torch.nonzero(tensor)
                dst2 = tensor.nonzero()
                dst3 = torch.LongTensor().to(device)
                torch.nonzero(tensor, out=dst3)

                self.assertRaisesRegex(
                    TypeError,
                    "received an invalid combination of arguments",
                    lambda: torch.nonzero(tensor, as_tuple=True, out=dst3))
                if len(shape) == 1:
                    dst = []
                    for i in range(num_src):
                        if tensor[i] != 0:
                            dst += [i]
                    dst = torch.LongTensor(dst).to(device)
                    self.assertEqual(dst1.select(1, 0), dst, 0)
                    self.assertEqual(dst2.select(1, 0), dst, 0)
                    self.assertEqual(dst3.select(1, 0), dst, 0)
                elif len(shape) == 2:
                    # This test will allow through some False positives. It only checks
                    # that the elements flagged positive are indeed non-zero.
                    for i in range(dst1.size(0)):
                        self.assertNotEqual(tensor[dst1[i, 0], dst1[i, 1]].item(), 0)
                elif len(shape) == 3:
                    # This test will allow through some False positives. It only checks
                    # that the elements flagged positive are indeed non-zero.
                    for i in range(dst1.size(0)):
                        self.assertNotEqual(tensor[dst1[i, 0], dst1[i, 1], dst1[i, 2]].item(), 0)
                    lex = is_lexicographically_sorted(dst1)
                    self.assertEqual(torch.ones_like(lex), lex)
                if TEST_NUMPY:
                    tup1 = torch.nonzero(tensor, as_tuple=True)
                    tup2 = tensor.nonzero(as_tuple=True)
                    tup3 = torch.where(tensor)
                    np1 = tensor.cpu().numpy().nonzero()
                    for t in (tup1, tup2, tup3):
                        self.assertEqual(len(t), len(np1))
                        for i in range(len(t)):
                            self.assertEqual(t[i].cpu().numpy(), np1[i])

    def test_nonzero_non_diff(self, device):
        x = torch.randn(10, requires_grad=True)
        nz = x.nonzero()
        self.assertFalse(nz.requires_grad)

    def test_pdist_norm(self, device):
        def test_pdist_single(shape, device, p, dtype, trans):
            x = torch.randn(shape, dtype=dtype, device=device)
            if trans:
                x.transpose_(-2, -1)
            actual = torch.pdist(x, p=p)
            expected = brute_pdist(x, p=p)
            self.assertEqual(expected.shape, actual.shape)
            self.assertTrue(torch.allclose(expected, actual))

        for shape in [(4, 5), (3, 2), (2, 1)]:
            for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                for trans in [False, True]:
                    for dtype in [torch.float32, torch.float64]:
                        test_pdist_single(shape, device, p, dtype, trans)

        # do a simplified comparison with big inputs, see:
        # https://github.com/pytorch/pytorch/issues/15511
        for dtype in [torch.float32, torch.float64]:
            test_pdist_single((1000, 2), device, 2, dtype, False)

    def test_atan2(self, device):
        def _test_atan2_with_size(size, device):
            a = torch.rand(size=size, device=device, dtype=torch.double)
            b = torch.rand(size=size, device=device, dtype=torch.double)
            actual = a.atan2(b)
            x = a.view(-1)
            y = b.view(-1)
            expected = torch.tensor([math.atan2(x[i].item(), y[i].item()) for i in range(x.numel())],
                                    device=device, dtype=torch.double)
            self.assertTrue(torch.allclose(expected, actual.view(-1), rtol=0, atol=0.02))

        _test_atan2_with_size((2, 2), device)
        _test_atan2_with_size((3, 3), device)
        _test_atan2_with_size((5, 5), device)

    def test_atan2_edgecases(self, device):
        def _test_atan2(x, y, expected, device, dtype):
            expected_tensor = torch.tensor([expected], dtype=dtype, device=device)
            x_tensor = torch.tensor([x], dtype=dtype, device=device)
            y_tensor = torch.tensor([y], dtype=dtype, device=device)
            actual = torch.atan2(y_tensor, x_tensor)
            self.assertTrue(torch.allclose(expected_tensor, actual, rtol=0, atol=0.02))

        for dtype in [torch.float, torch.double]:
            _test_atan2(0, 0, 0, device, dtype)
            _test_atan2(0, 1, math.pi / 2, device, dtype)
            _test_atan2(0, -1, math.pi / -2, device, dtype)
            _test_atan2(-1, 0, math.pi, device, dtype)
            _test_atan2(1, 0, 0, device, dtype)
            _test_atan2(-1, -1, math.pi * -3 / 4 , device, dtype)
            _test_atan2(1, 1, math.pi / 4 , device, dtype)
            _test_atan2(1, -1, math.pi / -4 , device, dtype)
            _test_atan2(-1, 1, math.pi * 3 / 4 , device, dtype)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_trapz(self, device):
        def test_dx(sizes, dim, dx, device):
            t = torch.randn(sizes, device=device)
            actual = torch.trapz(t, dx=dx, dim=dim)
            expected = np.trapz(t.cpu().numpy(), dx=dx, axis=dim)
            self.assertEqual(expected.shape, actual.shape)
            self.assertTrue(np.allclose(expected, actual.cpu().numpy()))

        def test_x(sizes, dim, x, device):
            t = torch.randn(sizes, device=device)
            actual = torch.trapz(t, x=torch.tensor(x, device=device), dim=dim)
            expected = np.trapz(t.cpu().numpy(), x=x, axis=dim)
            self.assertEqual(expected.shape, actual.shape)
            self.assertTrue(np.allclose(expected, actual.cpu().numpy()))

        test_dx((2, 3, 4), 1, 1, device)
        test_dx((10, 2), 0, 0.1, device)
        test_dx((1, 10), 0, 2.3, device)
        test_dx((0, 2), 0, 1.0, device)
        test_dx((0, 2), 1, 1.0, device)
        test_x((2, 3, 4), 1, [1.0, 2.0, 3.0], device)
        test_x((10, 2), 0, [2.0, 3.0, 4.0, 7.0, 11.0, 14.0, 22.0, 26.0, 26.1, 30.3], device)
        test_x((1, 10), 0, [1.0], device)
        test_x((0, 2), 0, [], device)
        test_x((0, 2), 1, [1.0, 2.0], device)
        with self.assertRaisesRegex(
                IndexError,
                'Dimension out of range'):
            test_x((2, 3), 2, [], device)
            test_dx((2, 3), 2, 1.0, device)
        with self.assertRaisesRegex(
                RuntimeError,
                'There must be one `x` value for each sample point'):
            test_x((2, 3), 1, [1.0, 2.0], device)
            test_x((2, 3), 1, [1.0, 2.0, 3.0, 4.0], device)

    def test_reduction_empty(self, device):
        fns_to_test = [
            # name, function, identity
            ('max', torch.max, None),
            ('kthvalue', lambda *args, **kwargs: torch.kthvalue(*args, k=1, **kwargs), None),
            ('argmax', torch.argmax, None),
            ('min', torch.min, None),
            ('argmin', torch.argmin, None),
            ('mode', torch.mode, None),
            ('median', torch.median, None),

            ('prod', torch.prod, 1),
            ('sum', torch.sum, 0),
            ('norm', torch.norm, 0),
            ('mean', torch.mean, nan),
            ('var', torch.var, nan),
            ('std', torch.std, nan),
            ('logsumexp', torch.logsumexp, -inf),
        ]

        shape = (2, 0, 4)
        x = torch.randn(shape, device=device)

        for fn in [torch.max, torch.min]:
            ident_err = 'operation does not have an identity'
            self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x))

        for item in fns_to_test:
            name, fn, identity = item
            if identity is None:
                ident_err = 'does not have an identity'
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=2))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=2, keepdim=True))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=1))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=1, keepdim=True))
            else:
                self.assertEqual(torch.empty((2, 0), device=device), fn(x, dim=2))
                self.assertEqual(torch.empty((2, 0, 1), device=device), fn(x, dim=2, keepdim=True))
                # assertEqual doesn't work with inf, -inf, nan and two tensors.
                check = (torch.testing.assert_allclose if math.isnan(identity) or math.isinf(identity) else
                         self.assertEqual)
                check(torch.full((2, 4), identity, device=device), fn(x, dim=1))
                check(torch.full((2, 1, 4), identity, device=device), fn(x, dim=1, keepdim=True))
                try:
                    check(torch.full((), identity, device=device), fn(x))
                except TypeError as err:
                    # ignore if there is no allreduce.
                    self.assertTrue('dim' in str(err))

        # any
        xb = x.to(torch.uint8)
        yb = x.to(torch.uint8)
        self.assertEqual((2, 0), xb.any(2).shape)
        self.assertEqual((2, 0, 1), xb.any(2, keepdim=True).shape)
        self.assertEqual(torch.zeros((2, 4), device=device), xb.any(1))
        self.assertEqual(torch.zeros((2, 1, 4), device=device), xb.any(1, keepdim=True))
        self.assertEqual(torch.zeros((), device=device), xb.any())

        # all
        self.assertEqual((2, 0), xb.all(2).shape)
        self.assertEqual((2, 0, 1), xb.all(2, keepdim=True).shape)
        self.assertEqual(torch.ones((2, 4), device=device), xb.all(1))
        self.assertEqual(torch.ones((2, 1, 4), device=device), xb.all(1, keepdim=True))
        self.assertEqual(torch.ones((), device=device), xb.all())

    def test_addcdiv(self, device):
        def _test_addcdiv(a, alpha, b, c):
            actual = torch.addcdiv(a, alpha, b, c)
            # implementation of addcdiv downcasts alpha. arithmetic ops don't.
            if not actual.dtype.is_floating_point:
                alpha = int(alpha)
            expected = a + (alpha * b) / c
            self.assertTrue(torch.allclose(expected, actual, equal_nan=True))

        def non_zero_rand(size, dtype, device):
            if dtype.is_floating_point:
                a = torch.rand(size=size, dtype=dtype, device=device)
            elif dtype == torch.uint8:
                a = torch.randint(1, 5, size=size, dtype=dtype, device=device)
            else:
                a = torch.randint(-5, 5, size=size, dtype=dtype, device=device)
            return a + (a == 0).type(dtype)

        for dtype in torch.testing.get_all_math_dtypes(device):
            _test_addcdiv(
                non_zero_rand((2, 2), dtype=dtype, device=device),
                0.5,
                non_zero_rand((2, 2), dtype=dtype, device=device),
                non_zero_rand((2, 2), dtype=dtype, device=device))

    def test_unary_out_op_mem_overlap(self, device):
        sz = 3
        doubles = torch.randn(2 * sz, device=device)
        positives = torch.randint(1, 100, (2 * sz,), device=device).double()
        ints = torch.randint(-100, 100, (2 * sz,), device=device)
        unary_mem_overlap_cases = [
            ("abs", doubles, True, True, 'cpu'),
            ("abs", doubles, False, True, 'cuda'),
            ("acos", doubles, True, True, 'cpu'),
            ("acos", doubles, False, True, 'cuda'),
            ("asin", doubles, True, True, 'cpu'),
            ("asin", doubles, False, True, 'cuda'),
            ("atan", doubles, True, True, 'cpu'),
            ("atan", doubles, False, True, 'cuda'),
            ("bitwise_not", ints, True, True, 'cpu'),
            ("bitwise_not", ints, True, True, 'cuda'),
            ("ceil", doubles, True, True, 'cpu'),
            ("ceil", doubles, True, True, 'cuda'),
            ("cos", doubles, True, True, 'cpu'),
            ("cos", doubles, False, True, 'cuda'),
            ("cosh", doubles, True, True, 'cpu'),
            ("cosh", doubles, False, True, 'cuda'),
            ("digamma", doubles, True, True, 'cpu'),
            ("erf", doubles, True, True, 'cpu'),
            ("erf", doubles, False, True, 'cuda'),
            ("erfc", doubles, True, True, 'cpu'),
            ("erfc", doubles, False, True, 'cuda'),
            ("erfinv", doubles, True, True, 'cpu'),
            ("erfinv", doubles, True, True, 'cuda'),
            ("exp", doubles, True, True, 'cpu'),
            ("exp", doubles, False, True, 'cuda'),
            ("expm1", doubles, True, True, 'cpu'),
            ("expm1", doubles, True, True, 'cuda'),
            ("floor", doubles, True, True, 'cpu'),
            ("floor", doubles, True, True, 'cuda'),
            ("frac", doubles, True, True, 'cpu'),
            ("frac", doubles, False, True, 'cuda'),
            ("log", positives, True, True, 'cpu'),
            ("log", positives, True, True, 'cuda'),
            ("log10", positives, True, True, 'cpu'),
            ("log10", positives, False, True, 'cuda'),
            ("log1p", positives, True, True, 'cpu'),
            ("log1p", positives, False, True, 'cuda'),
            ("log2", positives, True, True, 'cpu'),
            ("log2", positives, False, True, 'cuda'),
            ("neg", doubles, True, True, 'cpu'),
            ("neg", doubles, True, True, 'cuda'),
            ("reciprocal", doubles, True, True, 'cpu'),
            ("reciprocal", doubles, False, True, 'cuda'),
            ("round", doubles, True, True, 'cpu'),
            ("round", doubles, True, True, 'cuda'),
            ("rsqrt", positives, True, True, 'cpu'),
            ("rsqrt", positives, True, True, 'cuda'),
            ("sin", doubles, True, True, 'cpu'),
            ("sin", doubles, False, True, 'cuda'),
            ("sinh", doubles, True, True, 'cpu'),
            ("sinh", doubles, False, True, 'cuda'),
            ("sigmoid", doubles, True, True, 'cpu'),
            ("sigmoid", doubles, False, False, 'cuda'),
            ("sqrt", doubles, True, True, 'cpu'),
            ("sqrt", doubles, False, True, 'cuda'),
            ("tan", doubles, True, True, 'cpu'),
            ("tan", doubles, False, True, 'cuda'),
            ("tanh", doubles, True, True, 'cpu'),
            ("tanh", doubles, False, True, 'cuda'),
            ("trunc", doubles, True, True, 'cpu'),
            ("trunc", doubles, True, True, 'cuda')
        ]

        for (fn, inputs, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in unary_mem_overlap_cases:
            if dev != device:
                continue
            out_fn = getattr(torch, fn)
            in_fn = getattr(torch.Tensor, fn + '_')

            self.unary_check_input_output_mem_overlap(inputs, sz, out_fn,
                                                      expected_failure=not has_input_output_mem_overlap_check)

            self.check_internal_mem_overlap(in_fn, num_inputs=1, device=dev,
                                            expected_failure=not has_internal_mem_overlap_check)

    def test_binary_op_mem_overlap(self, device):
        ops = [
            ("add", True, True, 'cpu'),
            ("add", True, True, 'cuda'),
            ("mul", True, True, 'cpu'),
            ("mul", True, True, 'cuda'),
            ("sub", True, True, 'cpu'),
            ("sub", True, True, 'cuda'),
            ("div", True, True, 'cpu'),
            ("div", True, True, 'cuda'),
            ("pow", True, True, 'cpu'),
            ("pow", True, True, 'cuda')
        ]

        for (fn, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in ops:
            if dev != device:
                continue
            out_op = getattr(torch, fn)
            inplace_op = getattr(torch.Tensor, fn + '_')
            self.check_internal_mem_overlap(
                inplace_op, num_inputs=2, device=device,
                expected_failure=not has_internal_mem_overlap_check)

            self.binary_check_input_output_mem_overlap(out_op, device,
                                                       expected_failure=not has_input_output_mem_overlap_check)

    def test_ternary_op_mem_overlap(self, device):
        ops = [
            ("addcmul", True, True, 'cpu'),
            ("addcmul", True, True, 'cuda'),
            ("addcdiv", True, True, 'cpu'),
            ("addcdiv", True, True, 'cuda'),
            ("lerp", True, True, 'cpu'),
            ("lerp", False, False, 'cuda')
        ]

        for (fn, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in ops:
            if dev != device:
                continue
            out_op = getattr(torch, fn)
            inplace_op = getattr(torch.Tensor, fn + '_')
            self.check_internal_mem_overlap(
                inplace_op, num_inputs=3, device=device,
                expected_failure=not has_internal_mem_overlap_check)
            self.ternary_check_input_output_mem_overlap(out_op, dev,
                                                        expected_failure=not has_input_output_mem_overlap_check)

    def test_copy_mem_overlap(self, device):
        self.check_internal_mem_overlap(
            torch.Tensor.copy_, num_inputs=2, device=device)
        sz = 3
        doubles = torch.randn(2 * sz, device=device)
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: out.copy_(input))

    def test_pow_scalar_overloads_mem_overlap(self, device):
        sz = 3
        doubles = torch.randn(2 * sz, device=device)
        self.check_internal_mem_overlap(
            lambda t: t.pow_(42), num_inputs=1, device=device)
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: torch.pow(input, 42, out=out))
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: torch.pow(42, input, out=out))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_int_pow(self, device):

        def _test_integral_pow(dt, range, dev):
            tensor = torch.tensor((3, 3), dtype=dt, device=dev).random_(*range)
            exps = [0, 1, 2, 4,
                    torch.tensor((3, 3), dtype=dt, device=dev).random_(0, 5)]
            for exp in exps:
                self._test_pow(tensor, exp)

        _test_integral_pow(torch.int8, (-3, 4), device)
        _test_integral_pow(torch.uint8, (0, 4), device)
        _test_integral_pow(torch.int16, (-5, 5), device)
        _test_integral_pow(torch.int64, (-10, 10), device)
        _test_integral_pow(torch.int32, (-10, 10), device)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_int_tensor_pow_neg_ints(self, device):
        ints = [torch.iinfo(torch.int32).min,
                -3, -2, -1, 0, 1, 2, 3,
                torch.iinfo(torch.int32).max]
        neg_ints = [torch.iinfo(torch.int32).min, -3, -2, -1]
        tensor = torch.tensor(ints, dtype=torch.int32, device=device)
        for pow in neg_ints:
            self._test_pow(tensor, pow)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_long_tensor_pow_floats(self, device):
        ints = [0, 1, 23, 4567]
        floats = [0.0, 1 / 3, 1 / 2, 1.0, 3 / 2, 2.0]
        tensor = torch.tensor(ints, dtype=torch.int64, device=device)
        for pow in floats:
            self._test_pow(tensor, pow)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_float_scalar_pow_float_tensor(self, device):
        floats = [2.0, -3 / 2, -1.0, -1 / 2, -1 / 3, 0.0,
                  1 / 3, 1 / 2, 1.0, 3 / 2, 2.0]
        tensor = torch.tensor(floats, dtype=torch.float32, device=device)
        for base in floats:
            self._test_pow(base, tensor)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_tensor_pow_tensor(self, dev):
        def rotate(l, n):
            return l[-n:] + l[:-n]

        def test_tensor_pow_tensor(values, torch_type, numpy_type):
            vals_tensor = torch.tensor(values, dtype=torch_type, device=dev)
            for i in range(len(values)):
                pows = rotate(values, i)
                pows_tensor = torch.tensor(pows, dtype=torch_type, device=dev)
                self._test_pow(vals_tensor, pows_tensor)

        ints = [0, 1, 2, 3]
        test_tensor_pow_tensor(ints, torch.int32, np.int32)
        test_tensor_pow_tensor(ints, torch.int64, np.int64)

        floats = [-3.0, -2.0, -1.0, -1 / 2, -1 / 3,
                  0.0,
                  1 / 3, 1 / 2, 1.0, 2.0, 3.0]
        test_tensor_pow_tensor(floats, torch.float32, np.float32)
        test_tensor_pow_tensor(floats, torch.float64, np.float64)

    def test_var_mean_some_dims(self, device):
        sizes = (4, 6, 7, 5, 3)
        dims = len(sizes)

        x = torch.rand(sizes, device=device)
        for num_of_dims in range(2, dims):
            dim_list = list(combinations(list(range(dims)), r=num_of_dims))
            for dim in dim_list:
                for unbiased in [False, True]:
                    for keepdim in [False, True]:
                        var1, mean1 = torch.var_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                        var2 = x.var(dim=dim, unbiased=unbiased, keepdim=keepdim)
                        mean2 = x.mean(dim=dim, keepdim=keepdim)
                        self.assertEqual(var1, var2)
                        self.assertEqual(mean1, mean2)

    # passes on ROCm w/ python 2.7, fails w/ python 3.6
    @skipCUDAIfRocm
    def test_stft(self, device):
        if not TEST_LIBROSA:
            raise unittest.SkipTest('librosa not found')

        def librosa_stft(x, n_fft, hop_length, win_length, window, center):
            if window is None:
                window = np.ones(n_fft if win_length is None else win_length)
            else:
                window = window.cpu().numpy()
            input_1d = x.dim() == 1
            if input_1d:
                x = x.view(1, -1)
            result = []
            for xi in x:
                ri = librosa.stft(xi.cpu().numpy(), n_fft, hop_length, win_length, window, center=center)
                result.append(torch.from_numpy(np.stack([ri.real, ri.imag], -1)))
            result = torch.stack(result, 0)
            if input_1d:
                result = result[0]
            return result

        def _test(sizes, n_fft, hop_length=None, win_length=None, win_sizes=None,
                  center=True, expected_error=None):
            x = torch.randn(*sizes, device=device)
            if win_sizes is not None:
                window = torch.randn(*win_sizes, device=device)
            else:
                window = None
            if expected_error is None:
                result = x.stft(n_fft, hop_length, win_length, window, center=center)
                ref_result = librosa_stft(x, n_fft, hop_length, win_length, window, center)
                self.assertEqual(result, ref_result, 7e-6, 'stft comparison against librosa')
            else:
                self.assertRaises(expected_error,
                                  lambda: x.stft(n_fft, hop_length, win_length, window, center=center))

        for center in [True, False]:
            _test((10,), 7, center=center)
            _test((10, 4000), 1024, center=center)

            _test((10,), 7, 2, center=center)
            _test((10, 4000), 1024, 512, center=center)

            _test((10,), 7, 2, win_sizes=(7,), center=center)
            _test((10, 4000), 1024, 512, win_sizes=(1024,), center=center)

            # spectral oversample
            _test((10,), 7, 2, win_length=5, center=center)
            _test((10, 4000), 1024, 512, win_length=100, center=center)

        _test((10, 4, 2), 1, 1, expected_error=RuntimeError)
        _test((10,), 11, 1, center=False, expected_error=RuntimeError)
        _test((10,), -1, 1, expected_error=RuntimeError)
        _test((10,), 3, win_length=5, expected_error=RuntimeError)
        _test((10,), 5, 4, win_sizes=(11,), expected_error=RuntimeError)
        _test((10,), 5, 4, win_sizes=(1, 1), expected_error=RuntimeError)

    @skipCUDAIfRocm
    def test_blas_empty(self, device):

        def fn(torchfn, *args):
            return torchfn(*tuple(torch.randn(shape, device=device) if isinstance(shape, tuple) else shape
                                  for shape in args))

        # mm, addmm
        self.assertEqual((0, 0), fn(torch.mm, (0, 0), (0, 0)).shape)
        self.assertEqual((0, 5), fn(torch.mm, (0, 0), (0, 5)).shape)
        self.assertEqual((5, 0), fn(torch.mm, (5, 0), (0, 0)).shape)
        self.assertEqual((3, 0), fn(torch.mm, (3, 2), (2, 0)).shape)
        self.assertEqual(torch.zeros((5, 6), device=device), fn(torch.mm, (5, 0), (0, 6)))

        self.assertEqual((0, 0), fn(torch.addmm, (0, 0), (0, 0), (0, 0)).shape)
        self.assertEqual((5, 6), fn(torch.addmm, (5, 6), (5, 0), (0, 6)).shape)

        # mv, addmv
        self.assertEqual((0,), fn(torch.mv, (0, 0), (0,)).shape)
        self.assertEqual((0,), fn(torch.mv, (0, 2), (2,)).shape)
        self.assertEqual(torch.zeros((3,), device=device), fn(torch.mv, (3, 0), (0,)))

        self.assertEqual((0,), fn(torch.addmv, (0,), (0, 0), (0,)).shape)
        self.assertEqual((3,), fn(torch.addmv, (3,), (3, 0), (0,)).shape)

        # ger, addr
        self.assertEqual((0, 0), fn(torch.ger, (0,), (0,)).shape)
        self.assertEqual((5, 0), fn(torch.ger, (5,), (0,)).shape)
        self.assertEqual((0, 4), fn(torch.ger, (0,), (4,)).shape)

        self.assertEqual((0, 0), fn(torch.addr, (0, 0), (0,), (0,)).shape)
        self.assertEqual((5, 0), fn(torch.addr, (5, 0), (5,), (0,)).shape)
        self.assertEqual((0, 4), fn(torch.addr, (0, 4), (0,), (4,)).shape)

        # bmm, baddbmm
        self.assertEqual((0, 0, 0), fn(torch.bmm, (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((3, 0, 5), fn(torch.bmm, (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((0, 5, 6), fn(torch.bmm, (0, 5, 0), (0, 0, 6)).shape)
        self.assertEqual(torch.zeros((3, 5, 6), device=device), fn(torch.bmm, (3, 5, 0), (3, 0, 6)))

        self.assertEqual((0, 0, 0), fn(torch.baddbmm, (0, 0, 0), (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((3, 0, 5), fn(torch.baddbmm, (3, 0, 5), (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((0, 5, 6), fn(torch.baddbmm, (0, 5, 6), (0, 5, 0), (0, 0, 6)).shape)
        self.assertEqual((3, 5, 6), fn(torch.baddbmm, (3, 5, 6), (3, 5, 0), (3, 0, 6)).shape)

        # addbmm
        self.assertEqual((0, 0), fn(torch.addbmm, (0, 0), (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((0, 5), fn(torch.addbmm, (0, 5), (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((5, 6), fn(torch.addbmm, (5, 6), (0, 5, 0), (0, 0, 6)).shape)

        # matmul
        self.assertEqual(torch.tensor(0., device=device), fn(torch.matmul, (0,), (0,)))
        self.assertEqual((0, 0), fn(torch.matmul, (0, 0), (0, 0)).shape)
        self.assertEqual((0, 0, 0), fn(torch.matmul, (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((5, 0, 0), fn(torch.matmul, (5, 0, 0), (5, 0, 0)).shape)
        self.assertEqual(torch.zeros((5, 3, 4), device=device), fn(torch.matmul, (5, 3, 0), (5, 0, 4)))

        # dot
        self.assertEqual(torch.tensor(0., device=device), fn(torch.dot, (0,), (0,)))

        if torch._C.has_lapack:
            # lu
            A_LU, pivots = fn(torch.lu, (0, 5, 5))
            self.assertEqual([(0, 5, 5), (0, 5)], [A_LU.shape, pivots.shape])
            A_LU, pivots = fn(torch.lu, (0, 0, 0))
            self.assertEqual([(0, 0, 0), (0, 0)], [A_LU.shape, pivots.shape])
            A_LU, pivots = fn(torch.lu, (2, 0, 0))
            self.assertEqual([(2, 0, 0), (2, 0)], [A_LU.shape, pivots.shape])

    @skipCUDAIfRocm
    def test_blas_alpha_beta_empty(self, device):
        # ensure beta is respected
        value = 11
        input = torch.full((2,), value, device=device)
        mat = torch.ones((2, 0), device=device)
        vec = torch.ones((0,), device=device)
        out = torch.randn((2,), device=device)
        alpha = 6
        beta = 3
        self.assertEqual(torch.full((2,), beta * value, device=device),
                         torch.addmv(input=input, mat=mat, vec=vec, alpha=alpha, beta=beta))
        self.assertEqual(torch.full((2,), beta * value, device=device),
                         torch.addmv(input=input, mat=mat, vec=vec, alpha=alpha, beta=beta, out=out))

        # torch.addmm
        input = torch.full((2, 3), value, device=device)
        mat2 = torch.ones((0, 3), device=device)
        out = torch.randn((2, 3), device=device)
        self.assertEqual(torch.full((2, 3), beta * value, device=device),
                         torch.addmm(input=input, mat1=mat, mat2=mat2, alpha=alpha, beta=beta))
        self.assertEqual(torch.full((2, 3), beta * value, device=device),
                         torch.addmm(input=input, mat1=mat, mat2=mat2, alpha=alpha, beta=beta, out=out))

    @skipCUDAIfRocm
    def test_unique_dim(self, device):
        self.assertFalse(hasattr(torch, 'unique_dim'))

        def run_test(device, dtype):
            x = torch.tensor([[[1., 1.],
                               [0., 1.],
                               [2., 1.],
                               [0., 1.]],
                              [[1., 1.],
                               [0., 1.],
                               [2., 1.],
                               [0., 1.]]],
                             dtype=dtype,
                             device=device)
            x_empty = torch.empty(5, 0, dtype=dtype, device=device)
            x_ill_formed_empty = torch.empty(5, 0, 0, dtype=dtype, device=device)
            x_ill_formed_empty_another = torch.empty(5, 0, 5, dtype=dtype, device=device)
            expected_unique_dim0 = torch.tensor([[[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_inverse_dim0 = torch.tensor([0, 0])
            expected_counts_dim0 = torch.tensor([2])
            expected_unique_dim1 = torch.tensor([[[0., 1.],
                                                  [1., 1.],
                                                  [2., 1.]],
                                                 [[0., 1.],
                                                  [1., 1.],
                                                  [2., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_inverse_dim1 = torch.tensor([1, 0, 2, 0])
            expected_counts_dim1 = torch.tensor([2, 1, 1])
            expected_unique_dim2 = torch.tensor([[[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]],
                                                 [[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_inverse_dim2 = torch.tensor([0, 1])
            expected_counts_dim2 = torch.tensor([1, 1])
            expected_unique_empty = torch.tensor([], dtype=dtype, device=device)
            expected_inverse_empty = torch.tensor([], dtype=torch.long, device=device)
            expected_counts_empty = torch.tensor([], dtype=torch.long, device=device)
            # dim0
            x_unique = torch.unique(x, dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_inverse_dim0, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_counts_dim0, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_inverse_dim0, x_inverse)
            self.assertEqual(expected_counts_dim0, x_counts)

            # dim1
            x_unique = torch.unique(x, dim=1)
            self.assertEqual(expected_unique_dim1, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=1)
            self.assertEqual(expected_unique_dim1, x_unique)
            self.assertEqual(expected_inverse_dim1, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=1)
            self.assertEqual(expected_unique_dim1, x_unique)
            self.assertEqual(expected_counts_dim1, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=1)
            self.assertEqual(expected_unique_dim1, x_unique)
            self.assertEqual(expected_inverse_dim1, x_inverse)
            self.assertEqual(expected_counts_dim1, x_counts)

            # dim2
            x_unique = torch.unique(x, dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_inverse_dim2, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_counts_dim2, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_inverse_dim2, x_inverse)
            self.assertEqual(expected_counts_dim2, x_counts)

            # test empty tensor
            x_unique, x_inverse, x_counts = torch.unique(
                x_empty,
                return_inverse=True,
                return_counts=True,
                dim=1)
            self.assertEqual(expected_unique_empty, x_unique)
            self.assertEqual(expected_inverse_empty, x_inverse)
            self.assertEqual(expected_counts_empty, x_counts)

            # test not a well formed tensor
            # Checking for runtime error, as this is the expected behaviour
            with self.assertRaises(RuntimeError):
                torch.unique(
                    x_ill_formed_empty,
                    return_inverse=True,
                    return_counts=True,
                    dim=1)

            # test along dim2
            with self.assertRaises(RuntimeError):
                torch.unique(
                    x_ill_formed_empty_another,
                    return_inverse=True,
                    return_counts=True,
                    dim=2)

            # test consecutive version
            y = torch.tensor(
                [[0, 1],
                 [0, 1],
                 [0, 1],
                 [1, 2],
                 [1, 2],
                 [3, 4],
                 [0, 1],
                 [0, 1],
                 [3, 4],
                 [1, 2]],
                dtype=dtype,
                device=device
            )
            expected_y_unique = torch.tensor(
                [[0, 1],
                 [1, 2],
                 [3, 4],
                 [0, 1],
                 [3, 4],
                 [1, 2]],
                dtype=dtype,
                device=device
            )
            expected_y_inverse = torch.tensor([0, 0, 0, 1, 1, 2, 3, 3, 4, 5], dtype=dtype, device=device)
            expected_y_counts = torch.tensor([3, 2, 1, 2, 1, 1], dtype=dtype, device=device)
            y_unique, y_inverse, y_counts = torch.unique_consecutive(y, return_inverse=True, return_counts=True, dim=0)
            self.assertEqual(expected_y_inverse, y_inverse)
            self.assertEqual(expected_y_counts, y_counts)

        run_test(device, torch.float)
        run_test(device, torch.double)
        run_test(device, torch.long)
        run_test(device, torch.uint8)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_reverse_binary_ops_multiple_device(self, devices):
        self.assertEqual(2 + torch.tensor(3), 2 + torch.tensor(3).to(devices[1]))    # __radd__
        self.assertEqual(2 - torch.tensor(3), 2 - torch.tensor(3).to(devices[1]))    # __rsub__
        self.assertEqual(2 * torch.tensor(3), 2 * torch.tensor(3).to(devices[1]))    # __rmul__
        self.assertEqual(2 / torch.tensor(3), 2 / torch.tensor(3).to(devices[1]))    # __rtruediv__
        self.assertEqual(2 // torch.tensor(3), 2 // torch.tensor(3).to(devices[1]))  # __rfloordiv__

        self.assertEqual(
            torch.tensor(2).to(devices[1]) + torch.tensor(3).to(devices[0]),
            torch.tensor(2) + torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) - torch.tensor(3).to(devices[0]),
            torch.tensor(2) - torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) * torch.tensor(3).to(devices[0]),
            torch.tensor(2) * torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) / torch.tensor(3).to(devices[0]),
            torch.tensor(2) / torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) // torch.tensor(3).to(devices[0]),
            torch.tensor(2) // torch.tensor(3))

    @onlyCUDA
    def test_ceil_out_mismatch(self, device):
        a = torch.randn(1)
        b = torch.randn(1, device=device)
        self.assertRaises(RuntimeError, lambda: torch.ceil(a, out=b))


    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_has_storage_numpy(self, device):
        for dtype in [np.float32, np.float64, np.int64,
                      np.int32, np.int16, np.uint8]:
            arr = np.array([1], dtype=dtype)
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.float32).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.double).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.int).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.long).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.uint8).storage())

    def test_all_any_empty(self, device):
        x = torch.ByteTensor().to(device)
        self.assertTrue(x.all())
        self.assertFalse(x.any())

        x = torch.BoolTensor().to(device)
        self.assertTrue(x.all())
        self.assertFalse(x.any())

    @onlyCUDA
    def test_multinomial_device_constrain(self, device):
        x = torch.empty(0, device="cpu")
        y = torch.empty(0, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial arguments must have the same device",
            lambda: torch.multinomial(x, 2, out=y))

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_multinomial_gpu_device_constrain(self, devices):
        x = torch.empty(0, device=devices[0])
        y = torch.empty(0, device=devices[1])
        self.assertRaisesRegex(
            RuntimeError, "multinomial arguments must have the same device",
            lambda: torch.multinomial(x, 2, out=y))

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_zeros_like_multiple_device(self, devices):
        expected = torch.zeros(100, 100, device=devices[0])
        x = torch.randn(100, 100, device=devices[1], dtype=torch.float32)
        output = torch.zeros_like(x)
        self.assertEqual(output, expected)

    @onlyCUDA
    def test_ones_like(self, device):
        expected = torch.ones(100, 100, device=device)

        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_ones_like_multiple_device(self, devices):
        expected = torch.ones(100, 100, device=devices[0])
        x = torch.randn(100, 100, device=devices[1], dtype=torch.float32)
        output = torch.ones_like(x)
        self.assertEqual(output, expected)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_device_guard(self, devices):
        # verify that all operators with `device_guard: False` behave properly with multiple devices.
        # TODO: if we had operator introspection we could figure out this set of operators automatically...
        x = torch.randn((1, 2, 3), device=devices[1])
        y = torch.zeros((1, 3, 2), device=devices[1])
        scalar = torch.tensor(5, device=devices[1])

        # property ops
        torch.cudnn_is_acceptable(x)
        x.is_distributed()
        x.is_floating_point()
        x.is_complex()
        x.is_same_size(y)
        x.is_signed()
        x.size(0)
        x.stride(0)
        x.numel()
        x.is_set_to(y)
        x.data_ptr()
        scalar.is_nonzero()

        # sparse property ops
        y[0][1] = 5
        y_sparse = y.to_sparse()
        y_sparse.sparse_dim()
        y_sparse._dimI()
        y_sparse.dense_dim()
        y_sparse._dimV()
        y_sparse._nnz()
        y_sparse.is_coalesced()
        y_sparse._indices()
        y_sparse._values()
        y_sparse.indices()
        y_sparse.values()

        # in-place ops
        def inplace():
            return torch.randn((1, 2, 3), device=devices[1])
        inplace().as_strided_(y.size(), y.stride())
        inplace().resize_(y.size())
        inplace().squeeze_()
        inplace().squeeze_(0)
        inplace().unsqueeze_(2)
        inplace().transpose_(1, 2)
        inplace().squeeze_().t_()
        inplace().set_(x.storage())
        inplace().set_(x.storage(), x.storage_offset(), x.size(), x.stride())
        inplace().set_(x)
        inplace().set_()
        y_sparse._coalesced_(True)

        # shape modification
        x.as_strided(y.size(), y.stride())
        x.expand((5, 2, 3))
        x.expand_as(x)
        x.sum_to_size((1,))
        torch.broadcast_tensors(x , x)
        x.reshape((1, 3, 2))
        x.reshape_as(y)
        x.squeeze()
        x.squeeze(0)
        x.squeeze().t()
        x.transpose(1, 2)
        x.unsqueeze(2)
        x.view((1, 3, 2))
        x.view_as(y)

        # chunk, split, etc.
        x.chunk(2, dim=1)
        x.split(1, dim=2)
        x.split_with_sizes([1, 2], dim=2)
        x.unfold(dimension=2, size=1, step=1)

        x.narrow(1, 1, 1)
        x.select(1, 1)
        torch.isnan(x)

        torch.empty((1, 3, 2), out=y)
        torch.empty_like(x)
        torch.empty_like(x, dtype=torch.int64)

        # to
        x.to(x)
        x.to(y)
        x.to(x, copy=True)

    @onlyCUDA
    def test_tensor_factory_gpu_type_inference(self, device):
        saved_type = torch.Tensor().type()
        torch.set_default_tensor_type(torch.cuda.DoubleTensor)
        torch.set_default_dtype(torch.float32)
        self.assertIs(torch.float32, torch.tensor(0.).dtype)
        self.assertEqual(torch.device(device), torch.tensor(0.).device)
        torch.set_default_dtype(torch.float64)
        self.assertIs(torch.float64, torch.tensor(0.).dtype)
        self.assertEqual(torch.device(device), torch.tensor(0.).device)
        torch.set_default_tensor_type(saved_type)

    @onlyCUDA
    def test_tensor_factory_gpu_type(self, device):
        saved_type = torch.Tensor().type()
        torch.set_default_tensor_type(torch.cuda.FloatTensor)
        x = torch.zeros((5, 5))
        self.assertIs(torch.float32, x.dtype)
        self.assertTrue(x.is_cuda)
        torch.set_default_tensor_type(torch.cuda.DoubleTensor)
        x = torch.zeros((5, 5))
        self.assertIs(torch.float64, x.dtype)
        self.assertTrue(x.is_cuda)
        torch.set_default_tensor_type(saved_type)

    @onlyCPU
    def test_renorm_ps(self, device):
        # full reduction
        x = torch.randn(5, 5)
        xn = x.numpy()
        for p in [1, 2, 3, 4, inf]:
            res = x.renorm(p, 1, 1)
            expected = x / x.norm(p, 0, keepdim=True).clamp(min=1)
            self.assertEqual(res.numpy(), expected.numpy(), "renorm failed for {}-norm".format(p))

    @onlyCUDA
    def test_topk_noncontiguous_gpu(self, device):
        t = torch.randn(20, device=device)[::2]
        top1, idx1 = t.topk(5)
        top2, idx2 = t.contiguous().topk(5)
        self.assertEqual(top1, top2)
        self.assertEqual(idx1, idx2)

    def test_is_signed(self, device):
        self.assertEqual(torch.IntTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.ByteTensor(5).to(device).is_signed(), False)
        self.assertEqual(torch.CharTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.FloatTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.HalfTensor(10).to(device).is_signed(), True)

    @onlyCUDA
    def test_solve_methods_arg_device(self, device):
        for b_device, A_device in product(['cpu', 'cuda'], repeat=2):
            if b_device == A_device:
                continue

            b = torch.randn(3, 1, device=b_device)
            A = torch.randn(3, 3, device=A_device)
            err_str = "Expected b and A to be on the same device"
            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.solve(b, A)

            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.cholesky_solve(b, A)

            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.triangular_solve(b, A)

            # b and A have to be modified to match accepted inputs sizes for lu_solve
            b = b.unsqueeze(0)
            A = A.unsqueeze(0)
            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.lu_solve(b, A, torch.rand(A.shape[:-1], device=A_device).int())

            # This checks if a suitable error message is thrown
            # when LU output and pivots are on the same device
            with self.assertRaisesRegex(RuntimeError,
                                        "Expected LU_pivots and LU_data to be on the same device"):
                torch.lu_solve(b, A, torch.rand(A.shape[:-1], device=b_device).int())

    # Note - reports a leak of 512 bytes on CUDA device 1
    @deviceCountAtLeast(2)
    @skipCUDAMemoryLeakCheckIf(True)
    @onlyCUDA
    def test_tensor_set_errors_multigpu(self, devices):
        f_cuda0 = torch.randn((2, 3), dtype=torch.float32, device=devices[0])
        f_cuda1 = torch.randn((2, 3), dtype=torch.float32, device=devices[1])

        self.assertRaises(RuntimeError, lambda: f_cuda0.set_(f_cuda1.storage()))
        self.assertRaises(RuntimeError,
                          lambda: f_cuda0.set_(f_cuda1.storage(), 0, f_cuda1.size(), f_cuda1.stride()))
        self.assertRaises(RuntimeError, lambda: f_cuda0.set_(f_cuda1))

    @onlyCUDA
    def test_half_tensor(self, device):
        x = torch.randn(5, 5).half()
        self.assertEqual(x.to(device), x)

        xc = x.to(device)
        with tempfile.NamedTemporaryFile() as f:
            torch.save(xc, f)
            f.seek(0)
            xc2 = torch.load(f)
            self.assertIsInstance(xc2, type(xc))
            self.assertEqual(xc.float(), xc2.float())

    @onlyCUDA
    @deviceCountAtLeast(1)  # Note: Tests works with one but prefers more devices
    def test_serialization(self, devices):
        def _test_serialization(filecontext_lambda):
            t0 = torch.cuda.FloatTensor(5).fill_(1)
            with torch.cuda.device(devices[-1]):
                tn = torch.cuda.FloatTensor(3).fill_(2)
            torch.cuda.set_device(devices[0])
            b = (t0, tn)
            with filecontext_lambda() as f:
                torch.save(b, f)
                f.seek(0)
                c = torch.load(f)
                self.assertEqual(b, c, 0)
                u0, un = c
                self.assertEqual(str(u0.device), devices[0])
                self.assertEqual(str(un.device), devices[-1])

        _test_serialization(tempfile.NamedTemporaryFile)
        _test_serialization(BytesIOContext)

    def test_memory_format_preserved_after_permute(self, device):
        x = torch.randn(10, 3, 32, 32, device=device)
        nhwc = x.contiguous(memory_format=torch.channels_last)
        y = nhwc.permute(0, 1, 3, 2).permute(0, 1, 3, 2)
        self.assertTrue(y.is_contiguous(memory_format=torch.channels_last))

    def test_memory_format_empty_like(self, device):
        x = torch.randn(10, 3, 32, 32, device=device)
        nhwc = x.contiguous(memory_format=torch.channels_last)

        like = torch.empty_like(nhwc, memory_format=torch.preserve_format)
        self.assertFalse(like.is_contiguous())
        self.assertTrue(like.is_contiguous(memory_format=torch.channels_last))

        like_x = torch.empty_like(x, memory_format=torch.preserve_format)
        self.assertTrue(like_x.is_contiguous())
        self.assertFalse(like_x.is_contiguous(memory_format=torch.channels_last))

        like = torch.empty_like(x, memory_format=torch.channels_last)
        self.assertFalse(like.is_contiguous())
        self.assertTrue(like.is_contiguous(memory_format=torch.channels_last))

        like = torch.empty_like(nhwc, memory_format=torch.contiguous_format)
        self.assertTrue(like.is_contiguous())
        self.assertFalse(like.is_contiguous(memory_format=torch.channels_last))

        like = torch.empty_like(nhwc)
        self.assertTrue(like.is_contiguous())
        self.assertFalse(like.is_contiguous(memory_format=torch.channels_last))

        sparse = x.to_sparse()
        with self.assertRaises(RuntimeError):
            z = torch.empty_like(sparse, memory_format=torch.preserve_format)

    def test_unique(self, device):
        x = torch.tensor([1, 2, 3, 2, 8, 5, 2, 3], device=device)
        expected_unique = torch.tensor([1, 2, 3, 5, 8], device=device)
        expected_inverse = torch.tensor([0, 1, 2, 1, 4, 3, 1, 2], device=device)
        expected_counts = torch.tensor([1, 3, 2, 1, 1], device=device)

        x_unique = torch.unique(x)
        self.assertEqual(
            expected_unique.tolist(), sorted(x_unique.tolist()))

        x_unique, x_inverse = x.unique(return_inverse=True)
        self.assertEqual(
            expected_unique.tolist(), sorted(x_unique.tolist()))
        self.assertEqual(expected_inverse.numel(), x_inverse.numel())

        x_unique = x.unique(sorted=True)
        self.assertEqual(expected_unique, x_unique)

        x_unique, x_counts = torch.unique(x, sorted=True, return_counts=True)
        self.assertEqual(expected_counts, x_counts)

        x_unique, x_inverse = torch.unique(
            x, sorted=True, return_inverse=True)
        self.assertEqual(expected_unique, x_unique)
        self.assertEqual(expected_inverse, x_inverse)

        x_unique, x_inverse, x_counts = torch.unique(
            x, sorted=True, return_inverse=True, return_counts=True)
        self.assertEqual(expected_unique, x_unique)
        self.assertEqual(expected_inverse, x_inverse)
        self.assertEqual(expected_counts, x_counts)

        # Tests per-element unique on a higher rank tensor.
        y = x.view(2, 2, 2)
        y_unique, y_inverse = y.unique(sorted=True, return_inverse=True)
        self.assertEqual(expected_unique, y_unique)
        self.assertEqual(expected_inverse.view(y.size()), y_inverse)

        y_unique, y_inverse, y_counts = torch.unique(
            y, sorted=True, return_inverse=True, return_counts=True)
        self.assertEqual(expected_unique, y_unique)
        self.assertEqual(expected_inverse.view(y.size()), y_inverse)
        self.assertEqual(expected_counts, y_counts)

        # Tests unique on other types.
        int_unique, int_inverse, int_counts = torch.unique(
            torch.tensor([2, 1, 2], dtype=torch.int, device=device),
            sorted=True,
            return_inverse=True,
            return_counts=True
        )
        self.assertEqual(torch.tensor([1, 2], dtype=torch.int, device=device), int_unique)
        self.assertEqual(torch.tensor([1, 0, 1], dtype=torch.long, device=device), int_inverse)
        self.assertEqual(torch.tensor([1, 2], dtype=torch.long, device=device), int_counts)

        double_unique, double_inverse, double_counts = torch.unique(
            torch.tensor([2., 1.5, 2.1, 2.], dtype=torch.double, device=device),
            sorted=True,
            return_inverse=True,
            return_counts=True
        )
        self.assertEqual(torch.tensor([1.5, 2., 2.1], dtype=torch.double, device=device), double_unique)
        self.assertEqual(torch.tensor([1, 0, 2, 1], dtype=torch.long, device=device), double_inverse)
        self.assertEqual(torch.tensor([1, 2, 1], dtype=torch.long, device=device), double_counts)

        byte_unique, byte_inverse, byte_counts = torch.unique(
            torch.tensor([133, 7, 7, 7, 42, 128], dtype=torch.uint8, device=device),
            sorted=True,
            return_inverse=True,
            return_counts=True
        )
        self.assertEqual(torch.tensor([7, 42, 128, 133], dtype=torch.uint8, device=device), byte_unique)
        self.assertEqual(torch.tensor([3, 0, 0, 0, 1, 2], dtype=torch.long, device=device), byte_inverse)
        self.assertEqual(torch.tensor([3, 1, 1, 1], dtype=torch.long, device=device), byte_counts)

        # test consecutive version
        z = torch.tensor([1, 2, 2, 2, 5, 5, 2, 2, 3], device=device)
        expected_z_unique = torch.tensor([1, 2, 5, 2, 3], device=device)
        expected_z_inverse = torch.tensor([0, 1, 1, 1, 2, 2, 3, 3, 4], device=device)
        expected_z_counts = torch.tensor([1, 3, 2, 2, 1], device=device)

        z_unique = torch.unique_consecutive(z)
        self.assertEqual(z_unique, expected_z_unique)

        z_unique, z_inverse = torch.unique_consecutive(z, return_inverse=True)
        self.assertEqual(z_unique, expected_z_unique)
        self.assertEqual(z_inverse, expected_z_inverse)

        z_unique, z_counts = torch.unique_consecutive(z, return_counts=True)
        self.assertEqual(z_unique, expected_z_unique)
        self.assertEqual(z_counts, expected_z_counts)

        z_unique, z_inverse, z_counts = torch.unique_consecutive(z, return_inverse=True, return_counts=True)
        self.assertEqual(z_unique, expected_z_unique)
        self.assertEqual(z_inverse, expected_z_inverse)
        self.assertEqual(z_counts, expected_z_counts)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_erfinv(self, device, dtype):
        # general testing. Narrow the range to avoid accuracy issues
        input_values = torch.randn(4, 4, dtype=dtype, device=device).clamp(-0.3, 0.3)
        self.assertEqual(input_values.erf().erfinv(), input_values)
        # test inf
        self.assertTrue(torch.equal(torch.tensor([-1, 1], dtype=dtype, device=device).erfinv(),
                        torch.tensor([-inf, inf], dtype=dtype, device=device)))
        # test nan
        self.assertEqual(torch.tensor([-2, 2], dtype=dtype, device=device).erfinv(),
                         torch.tensor([nan, nan], dtype=dtype, device=device))

        if dtype == torch.double:
            # double precision
            a = torch.tensor([0.5, 0.8], dtype=torch.double, device=device).erfinv()
            self.assertAlmostEqual(a[0].item(), 0.47693627620447, places=13)
            self.assertAlmostEqual(a[1].item(), 0.90619380243682, places=13)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_ctor_with_numpy_array(self, device):
        correct_dtypes = [
            np.double,
            np.float,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.int8,
            np.uint8,
            np.bool,
        ]

        incorrect_byteorder = '>' if sys.byteorder == 'little' else '<'
        incorrect_dtypes = map(lambda t: incorrect_byteorder + t, ['d', 'f'])

        for dtype in correct_dtypes:
            array = np.array([1, 2, 3, 4], dtype=dtype)

            # Upcast
            tensor = torch.DoubleTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

            # Downcast (sometimes)
            tensor = torch.FloatTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

            tensor = torch.HalfTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

    def test_dlpack_conversion(self, device):
        x = torch.randn(1, 2, 3, 4, device=device, dtype=torch.float)
        z = from_dlpack(to_dlpack(x))
        self.assertEqual(z, x)

    @onlyCUDA
    def test_pin_memory_from_constructor(self, device):
        def _get_like(t, **kwargs):
            return [
                torch.rand_like(t, **kwargs),
                torch.randn_like(t, **kwargs),
                torch.empty_like(t, **kwargs),
                torch.full_like(t, 4, **kwargs),
                torch.zeros_like(t, **kwargs),
                torch.ones_like(t, **kwargs),
            ]

        def _get_tensors(**kwargs):
            return [
                torch.tensor([10, 11], **kwargs),
                torch.randn(3, 5, **kwargs),
                torch.rand(3, **kwargs),
                # torch.randint(3, 5, **kwargs), // unsupported
                torch.zeros(3, **kwargs),
                torch.randperm(3, **kwargs),
                torch.empty(6, **kwargs),
                torch.ones(6, **kwargs),
                torch.eye(6, **kwargs),
                torch.arange(3, 5, **kwargs)]

        pinned_tensors = _get_tensors(pin_memory=True) + _get_like(torch.empty(5, dtype=torch.float64), pin_memory=True)
        for x in pinned_tensors:
            self.assertTrue(x.is_pinned())

        tensors = _get_tensors() + _get_like(torch.empty(5, dtype=torch.float64, pin_memory=True))
        for x in tensors:
            self.assertFalse(x.is_pinned())

    def test_storage_device(self, device):
        x = torch.tensor([], device=device)
        self.assertEqual(x.dtype, x.storage().dtype)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_storage_multigpu(self, devices):
        for device in devices:
            x = torch.tensor([], device=device)
            self.assertEqual(x.dtype, x.storage().dtype)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lu(self, device):
        from common_utils import random_fullrank_matrix_distinct_singular_value as fullrank

        def run_test(device, pivot):
            def run_subtest(matrix_size, batches, device, pivot):
                a = fullrank(matrix_size, *batches).to(device)
                a_LU_info, pivots_info, info_ = a.lu(pivot=pivot, get_infos=True)
                self.assertEqual(a_LU_info.size(), torch.Size(batches + (matrix_size, matrix_size)))
                self.assertEqual(pivots_info.size(), torch.Size(batches + (matrix_size,)))
                self.assertEqual(info_.size(), torch.Size(batches))
                self.assertEqual(info_.abs().sum(), 0)
                a_LU, pivots = a.lu(pivot=pivot)
                self.assertEqual(a_LU, a_LU_info)
                self.assertEqual(pivots_info, pivots)
                if a.is_cuda:
                    a_LU_info_nopiv, nopiv, info_nopiv = a.lu(pivot=False, get_infos=True)
                    self.assertEqual(nopiv, torch.arange(1, 1 + a.size(-1), device=device, dtype=torch.int32).expand(a.shape[:-1]))
                    self.assertEqual(info_, info_nopiv)
                P, L, U = torch.lu_unpack(a_LU, pivots)
                self.assertEqual(P.matmul(L.matmul(U)), a)

            for ms, batch in product([3, 5, 7], [(), (2,), (3,), (3, 5)]):
                run_subtest(ms, batch, device, pivot)

            # Info should be positive for rank deficient matrices
            a = torch.ones(5, 3, 3, device=device)
            self.assertGreater(a.lu(pivot=pivot, get_infos=True)[2][0], 0)

        run_test(device, True)

        if device == 'cpu':
            # Error checking, no pivoting variant on CPU
            with self.assertRaisesRegex(RuntimeError, 'lu without pivoting is not implemented on the CPU'):
                torch.lu(torch.empty(1, 2, 2), pivot=False)
        else:
            run_test(device, False)


add_neg_dim_tests()
instantiate_device_type_tests(TestTorchDeviceType, globals())

class TestTorch(TestCase, _TestTorchMixin):
    pass

if __name__ == '__main__':
    run_tests()