common_methods_invocations.py

from functools import reduce, wraps
from operator import mul, itemgetter
import collections

import torch
import numpy as np
from torch._six import inf, istuple
from torch.autograd import Variable

from typing import List, Tuple, Dict, Any

from torch.testing import \
    (make_non_contiguous, _dispatch_dtypes, floating_types, floating_types_and,
     floating_and_complex_types, floating_and_complex_types_and,
     all_types_and_complex_and, all_types_and)
from torch.testing._internal.common_device_type import \
    (skipCUDAIfNoMagma, skipCPUIfNoLapack, skipCPUIfNoMkl, skipCUDAIfRocm,
     expectedAlertNondeterministic, precisionOverride)
from torch.testing._internal.common_utils import \
    (prod_single_zero, random_square_matrix_of_rank,
     random_symmetric_matrix, random_symmetric_psd_matrix,
     random_symmetric_pd_matrix, make_nonzero_det,
     random_fullrank_matrix_distinct_singular_value, set_rng_seed,
     TEST_WITH_ROCM, IS_WINDOWS, IS_MACOS, make_tensor, TEST_SCIPY,
     torch_to_numpy_dtype_dict, TEST_WITH_SLOW)

if TEST_SCIPY:
    import scipy.special

class SkipInfo(object):
    """Describes which test, or type of tests, should be skipped when testing
       an operator. Any test that matches all provided arguments will be skipped.
       The skip will only be checked if the active_if argument is True."""

    __slots__ = ['cls_name', 'test_name', 'device_type', 'dtypes', 'active_if']

    def __init__(self, cls_name=None, test_name=None, *,
                 device_type=None, dtypes=None, active_if=True):
        self.cls_name = cls_name
        self.test_name = test_name
        self.device_type = device_type
        self.dtypes = dtypes
        self.active_if = active_if

class SampleInput(object):
    """Represents sample inputs to a function."""

    __slots__ = ['input', 'args', 'kwargs']

    def __init__(self, input, *, args=tuple(), kwargs=None):
        # test_ops.py expects input to be a tuple
        self.input = input if isinstance(input, tuple) else (input,)
        self.args = args
        self.kwargs = kwargs if kwargs is not None else {}


_NOTHING = object()  # Unique value to distinguish default from anything else


# Extension of getattr to support qualified names
# e.g. _getattr_qual(torch, 'linalg.norm') -> torch.linalg.norm
def _getattr_qual(obj, name, default=_NOTHING):
    try:
        for path in name.split('.'):
            obj = getattr(obj, path)
        return obj
    except AttributeError:
        if default is not _NOTHING:
            return default
        else:
            raise


# Classes and methods for the operator database
class OpInfo(object):
    """Operator information and helper functions for acquiring it."""

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 op=None,  # the function variant of the operation, populated as torch.<name> if None
                 dtypes=floating_types(),  # dtypes this function is expected to work with
                 dtypesIfCPU=None,  # dtypes this function is expected to work with on CPU
                 dtypesIfCUDA=None,  # dtypes this function is expected to work with on CUDA
                 dtypesIfROCM=None,  # dtypes this function is expected to work with on ROCM
                 default_test_dtypes=None,  # dtypes to test with by default. Gets intersected
                                            # with the dtypes support on the tested device
                 test_inplace_grad=True,  # whether to gradcheck and gradgradcheck the inplace variant
                 test_complex_grad=True,  # whether to gradcheck and gradgradcheck for complex dtypes
                 skip_bfloat16_grad=False,  # whether to skip grad and gradgradcheck for bfloat16 dtype
                 assert_autodiffed=False,  # if a op's aten::node is expected to be symbolically autodiffed
                 autodiff_nonfusible_nodes=None,  # a list of strings with node names that are expected to be in a
                                                  # DifferentiableGraph when autodiffed. Ex: ['aten::add', 'aten::mm'],
                                                  # default is populated to be ['aten::(name of Python operator)']
                 autodiff_fusible_nodes=None,  # a list of strings with node names that are expected to be in FusionGroups
                                               # inside of DifferentiableGraphs when this operation is autodiffed.
                                               # Ex: ['aten::add', 'aten::mm'], defaults to an empty list
                                               # Note: currently no ops use fusible nodes
                 output_func=lambda x: x,  # fn mapping output to part that should be gradcheck'ed
                 supports_tensor_out=True,  # whether the op supports the out kwarg, returning a Tensor
                 skips=tuple(),  # information about which tests to skip
                 decorators=None,  # decorators to apply to generated tests
                 promotes_integers_to_float=False,  # whether op promotes unary output to float or not
                 sample_inputs_func=None,  # function to generate sample inputs
                 aten_name=None,  # name of the corresponding aten:: operator
                 ):

        # Validates the dtypes are generated from the dispatch-related functions
        for dtype_list in (dtypes, dtypesIfCPU, dtypesIfCUDA, dtypesIfROCM):
            assert isinstance(dtype_list, (_dispatch_dtypes, type(None)))

        self.name = name
        self.aten_name = aten_name if aten_name is not None else name

        self.dtypes = set(dtypes)
        self.dtypesIfCPU = set(dtypesIfCPU) if dtypesIfCPU is not None else self.dtypes
        self.dtypesIfCUDA = set(dtypesIfCUDA) if dtypesIfCUDA is not None else self.dtypes
        self.dtypesIfROCM = set(dtypesIfROCM) if dtypesIfROCM is not None else self.dtypes
        self._default_test_dtypes = set(default_test_dtypes) if default_test_dtypes is not None else None

        # NOTE: if the op is unspecified it is assumed to be under the torch namespace
        self.op = op if op else _getattr_qual(torch, self.name)
        self.method_variant = getattr(torch.Tensor, name, None)
        inplace_name = name + "_"
        self.inplace_variant = getattr(torch.Tensor, inplace_name, None)
        self.skip_bfloat16_grad = skip_bfloat16_grad

        self.test_inplace_grad = test_inplace_grad
        self.test_complex_grad = test_complex_grad
        self.supports_tensor_out = supports_tensor_out
        self.promotes_integers_to_float = promotes_integers_to_float

        self.skips = skips
        self.decorators = decorators
        self.output_func = output_func
        self.sample_inputs_func = sample_inputs_func

        self.assert_autodiffed = assert_autodiffed
        self.autodiff_fusible_nodes = autodiff_fusible_nodes if autodiff_fusible_nodes else []
        if autodiff_nonfusible_nodes is None:
            self.autodiff_nonfusible_nodes = ['aten::' + self.name]
        else:
            self.autodiff_nonfusible_nodes = autodiff_nonfusible_nodes



    def __call__(self, *args, **kwargs):
        """Calls the function variant of the operator."""
        return self.op(*args, **kwargs)

    def get_op(self):
        """Returns the function variant of the operator, torch.<op_name>."""
        return self.op

    def get_method(self):
        """Returns the method variant of the operator, torch.Tensor.<op_name>.
        Returns None if the operator has no method variant.
        """
        return self.method_variant

    def get_inplace(self):
        """Returns the inplace variant of the operator, torch.Tensor.<op_name>_.
        Returns None if the operator has no inplace variant.
        """
        return self.inplace_variant

    def sample_inputs(self, device, dtype, requires_grad=False):
        """Returns an iterable of SampleInputs."""
        return self.sample_inputs_func(self, device, dtype, requires_grad)

    # Returns True if the test should be skipped and False otherwise
    def should_skip(self, cls_name, test_name, device_type, dtype):
        for si in self.skips:
            if not si.active_if:
                continue

            cls_name_match = si.cls_name is None or cls_name == si.cls_name
            name_match = si.test_name is None or test_name == si.test_name
            device_type_match = si.device_type is None or device_type == si.device_type
            dtype_match = si.dtypes is None or dtype in si.dtypes
            if cls_name_match and name_match and device_type_match and dtype_match:
                return True

        return False

    def supported_dtypes(self, device_type):
        if device_type == 'cpu':
            return self.dtypesIfCPU
        if device_type == 'cuda':
            return self.dtypesIfROCM if TEST_WITH_ROCM else self.dtypesIfCUDA
        else:
            return self.dtypes


    def supports_dtype(self, dtype, device_type):
        return dtype in self.supported_dtypes(device_type)

    def default_test_dtypes(self, device_type):
        """Returns the default dtypes used to test this operator on the device.

        Equal to the operator's default_test_dtypes filtered to remove dtypes
        not supported by the device.
        """
        supported = self.supported_dtypes(device_type)
        return (supported if self._default_test_dtypes is None
                else supported.intersection(self._default_test_dtypes))


L = 20
M = 10
S = 5


def sample_inputs_unary(op_info, device, dtype, requires_grad):
    low, high = op_info.domain
    low = low if low is None else low + op_info._domain_eps
    high = high if high is None else high - op_info._domain_eps

    return (SampleInput(make_tensor((L,), device, dtype,
                                    low=low, high=high,
                                    requires_grad=requires_grad)),
            SampleInput(make_tensor((), device, dtype,
                                    low=low, high=high,
                                    requires_grad=requires_grad)))

# Metadata class for unary "universal functions (ufuncs)" that accept a single
# tensor and have common properties like:
class UnaryUfuncInfo(OpInfo):
    """Operator information for 'universal unary functions (unary ufuncs).'
    These are functions of a single tensor with common properties like:
      - they are elementwise functions
      - the input shape is the output shape
      - they typically have method and inplace variants
      - they typically support the out kwarg
      - they typically have NumPy or SciPy references
    See NumPy's universal function documentation
    (https://numpy.org/doc/1.18/reference/ufuncs.html) for more details
    about the concept of ufuncs.
    """

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 ref,  # a reference function
                 dtypes=floating_types(),
                 dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
                 dtypesIfCUDA=floating_and_complex_types_and(torch.half),
                 dtypesIfROCM=floating_types_and(torch.half),
                 domain=(None, None),  # the [low, high) domain of the function
                 handles_large_floats=True,  # whether the op correctly handles large float values (like 1e20)
                 handles_extremals=True,  # whether the op correctly handles extremal values (like inf)
                 handles_complex_extremals=True,  # whether the op correct handles complex extremals (like inf -infj)
                 sample_inputs_func=sample_inputs_unary,
                 **kwargs):
        super(UnaryUfuncInfo, self).__init__(name,
                                             dtypes=dtypes,
                                             dtypesIfCPU=dtypesIfCPU,
                                             dtypesIfCUDA=dtypesIfCUDA,
                                             dtypesIfROCM=dtypesIfROCM,
                                             sample_inputs_func=sample_inputs_func,
                                             **kwargs)
        self.ref = ref
        self.domain = domain
        self.handles_large_floats = handles_large_floats
        self.handles_extremals = handles_extremals
        self.handles_complex_extremals = handles_complex_extremals

        # Epsilon to ensure grad and gradgrad checks don't test values
        #   outside a function's domain.
        self._domain_eps = 1e-5


def sample_inputs_addmm(op_info, device, dtype, requires_grad):
    return (SampleInput((make_tensor((S, S), device, dtype,
                                     low=None, high=None,
                                     requires_grad=requires_grad),
                        make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=requires_grad),
                        make_tensor((S, S), device, dtype,
                                    low=None, high=None,
                                    requires_grad=False))),)

def np_unary_ufunc_integer_promotion_wrapper(fn):
    # Wrapper that passes PyTorch's default scalar
    #   type as an argument to the wrapped NumPy
    #   unary ufunc when given an integer input.
    #   This mimicks PyTorch's integer->floating point
    #   type promotion.
    #
    # This is necessary when NumPy promotes
    #   integer types to double, since PyTorch promotes
    #   integer types to the default scalar type.

    # Helper to determine if promotion is needed
    def is_integral(dtype):
        return dtype in [np.bool, np.uint8, np.int8, np.int16, np.int32, np.int64]

    # NOTE: Promotion in PyTorch is from integer types to the default dtype
    np_dtype = torch_to_numpy_dtype_dict[torch.get_default_dtype()]

    @wraps(fn)
    def wrapped_fn(x):
        if is_integral(x.dtype):
            return fn(x, dtype=np_dtype)
        return fn(x)

    return wrapped_fn


# Metadata class for Fast Fourier Transforms in torch.fft.
class SpectralFuncInfo(OpInfo):
    """Operator information for torch.fft transforms. """

    def __init__(self,
                 name,  # the string name of the function
                 *,
                 ref=None,  # Reference implementation (probably in np.fft namespace)
                 dtypes=floating_and_complex_types(),
                 dtypesIfCPU=None,
                 dtypesIfCUDA=None,
                 dtypesIfROCM=None,
                 ndimensional: bool,  # Whether dim argument can be a tuple
                 skips=None,
                 decorators=None,
                 **kwargs):
        dtypesIfCPU = dtypesIfCPU if dtypesIfCPU is not None else dtypes
        dtypesIfCUDA = dtypesIfCUDA if dtypesIfCUDA is not None else dtypes
        dtypesIfROCM = dtypesIfROCM if dtypesIfROCM is not None else dtypes

        # gradgrad is quite slow
        if not TEST_WITH_SLOW:
            skips = skips if skips is not None else []
            skips.append(SkipInfo('TestGradients', 'test_fn_gradgrad'))

        decorators = decorators if decorators is not None else []
        decorators += [skipCPUIfNoMkl, skipCUDAIfRocm]

        super().__init__(name=name,
                         dtypes=dtypes,
                         dtypesIfCPU=dtypesIfCPU,
                         dtypesIfCUDA=dtypesIfCUDA,
                         dtypesIfROCM=dtypesIfROCM,
                         skips=skips,
                         decorators=decorators,
                         **kwargs)
        self.ref = ref if ref is not None else _getattr_qual(np, name)
        self.ndimensional = ndimensional


    def sample_inputs(self, device, dtype, requires_grad=False):
        tensor = make_tensor((L, M), device, dtype,
                             low=None, high=None,
                             requires_grad=requires_grad)
        if self.ndimensional:
            return [
                SampleInput(tensor),
                SampleInput(tensor, kwargs=dict(dim=(-2,))),
                SampleInput(tensor, kwargs=dict(norm='ortho')),
                SampleInput(tensor, kwargs=dict(s=(10, 15))),
                SampleInput(tensor, kwargs=dict(s=10, dim=1, norm='ortho')),
            ]
        else:
            return [
                SampleInput(tensor),
                SampleInput(tensor, kwargs=dict(dim=-2)),
                SampleInput(tensor, kwargs=dict(norm='ortho')),
                SampleInput(tensor, kwargs=dict(n=15)),
                SampleInput(tensor, kwargs=dict(n=10, dim=1, norm='ortho')),
            ]


# Operator database (sorted alphabetically)
op_db: List[OpInfo] = [
    # NOTE: CPU complex acos produces incorrect outputs (https://github.com/pytorch/pytorch/issues/42952)
    UnaryUfuncInfo('acos',
                   ref=np.arccos,
                   domain=(-1, 1),
                   handles_complex_extremals=False,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   default_test_dtypes=[torch.long, torch.half, torch.bfloat16, torch.float32, torch.cfloat],
                   skip_bfloat16_grad=True,
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.float16: 1e-2,
                                                  torch.bfloat16: 1e-1,
                                                  torch.complex64: 1e-2}),),
                   promotes_integers_to_float=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.float16],
                                active_if=TEST_WITH_ROCM),
                       SkipInfo('TestGradients', 'test_fn_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestGradients', 'test_method_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestGradients', 'test_inplace_grad',
                                dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                   )),
    # NOTE: the derivative for inplace acosh is not implemented
    UnaryUfuncInfo('acosh',
                   ref=np.arccosh,
                   domain=(1, float('inf')),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   test_inplace_grad=False,
                   skips=(
                       # RuntimeError: "rsqrt_cuda" not implemented for 'BFloat16'
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                device_type='cuda', dtypes=[torch.bfloat16]),
                   )),
    OpInfo('addmm',
           dtypes=floating_types(),
           dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
           dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128),
           dtypesIfROCM=floating_types_and(torch.half),
           assert_autodiffed=True,
           autodiff_nonfusible_nodes=['aten::add', 'aten::mm'],
           skips=(
               SkipInfo('TestCommon', 'test_variant_consistency_eager',
                        dtypes=[torch.cfloat, torch.cdouble]),
               SkipInfo('TestCommon', 'test_variant_consistency_jit',
                        dtypes=[torch.cfloat, torch.cdouble, torch.bfloat16, torch.float16]),
               SkipInfo('TestGradients', 'test_method_gradgrad',
                        dtypes=[torch.cdouble]),
               SkipInfo('TestGradients', 'test_method_grad',
                        dtypes=[torch.cdouble]),
               SkipInfo('TestGradients', 'test_fn_gradgrad',
                        dtypes=[torch.cdouble]),
               SkipInfo('TestGradients', 'test_fn_grad',
                        dtypes=[torch.cdouble]),),
           sample_inputs_func=sample_inputs_addmm),
    UnaryUfuncInfo('asin',
                   ref=np.arcsin,
                   domain=(-1, 1),
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   promotes_integers_to_float=True,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    # NOTE: derivative for inplace asinh is not implemented
    UnaryUfuncInfo('asinh',
                   ref=np.arcsinh,
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   test_inplace_grad=False,
                   skips=(
                       # RuntimeError: "rsqrt_cuda" not implemented for 'BFloat16'
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                device_type='cuda', dtypes=[torch.bfloat16]),
                   )),
    UnaryUfuncInfo('atan',
                   ref=np.arctan,
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   promotes_integers_to_float=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('atanh',
                   ref=np.arctanh,
                   domain=(-1, 1),
                   dtypes=all_types_and(torch.bool),
                   dtypesIfCPU=all_types_and(torch.bool),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   test_inplace_grad=False,
                   skips=(
                       # RuntimeError: "isfinite" not implemented for 'BFloat16'
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                device_type='cuda', dtypes=[torch.bfloat16]),
                   )),
    UnaryUfuncInfo('cos',
                   ref=np.cos,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   handles_large_floats=False,
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics', device_type='cpu',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.float], active_if=TEST_WITH_ROCM),
                   )),
    UnaryUfuncInfo('cosh',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.cosh),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   promotes_integers_to_float=True,
                   assert_autodiffed=True,
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/48641
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.int8]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics', device_type='cpu',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                device_type='cuda', dtypes=[torch.float16]),
                   )),
    SpectralFuncInfo('fft.fft',
                     aten_name='fft_fft',
                     ref=np.fft.fft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.fftn',
                     aten_name='fft_fftn',
                     ref=np.fft.fftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,
                     decorators=[precisionOverride(
                         {torch.float: 1e-4, torch.cfloat: 1e-4})],),
    SpectralFuncInfo('fft.hfft',
                     aten_name='fft_hfft',
                     ref=np.fft.hfft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.rfft',
                     aten_name='fft_rfft',
                     ref=np.fft.rfft,
                     ndimensional=False,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.rfftn',
                     aten_name='fft_rfftn',
                     ref=np.fft.rfftn,
                     ndimensional=True,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,
                     decorators=[precisionOverride({torch.float: 1e-4})],),
    SpectralFuncInfo('fft.ifft',
                     aten_name='fft_ifft',
                     ref=np.fft.ifft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.ifftn',
                     aten_name='fft_ifftn',
                     ref=np.fft.ifftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.ihfft',
                     aten_name='fft_ihfft',
                     ref=np.fft.ihfft,
                     ndimensional=False,
                     dtypes=all_types_and(torch.bool),
                     default_test_dtypes=floating_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.irfft',
                     aten_name='fft_irfft',
                     ref=np.fft.irfft,
                     ndimensional=False,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    SpectralFuncInfo('fft.irfftn',
                     aten_name='fft_irfftn',
                     ref=np.fft.irfftn,
                     ndimensional=True,
                     dtypes=all_types_and_complex_and(torch.bool),
                     default_test_dtypes=floating_and_complex_types(),
                     supports_tensor_out=False,
                     test_inplace_grad=False,),
    UnaryUfuncInfo('log',
                   ref=np.log,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('log10',
                   ref=np.log10,
                   domain=(0, float('inf')),
                   decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   promotes_integers_to_float=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                   )),
    UnaryUfuncInfo('log1p',
                   ref=np.log1p,
                   domain=(-1, float('inf')),
                   dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                   decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                   promotes_integers_to_float=True,
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True),
    UnaryUfuncInfo('log2',
                   ref=np.log2,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.cfloat, torch.cdouble]),
                   )),
    UnaryUfuncInfo('neg',
                   ref=np.negative,
                   skip_bfloat16_grad=True,
                   dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.half, torch.bfloat16),
                   assert_autodiffed=True,),
    UnaryUfuncInfo('sin',
                   ref=np.sin,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   handles_large_floats=False,
                   handles_complex_extremals=False,
                   promotes_integers_to_float=True,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.float], active_if=TEST_WITH_ROCM),
                   )),
    UnaryUfuncInfo('sinh',
                   ref=np_unary_ufunc_integer_promotion_wrapper(np.sinh),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   promotes_integers_to_float=True,
                   assert_autodiffed=True,
                   decorators=(precisionOverride({torch.float16: 1e-2}),),
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_WINDOWS),
                       # Reference: https://github.com/pytorch/pytorch/issues/48641
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.int8]),
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                device_type='cuda', dtypes=[torch.float16]),
                   )),
    UnaryUfuncInfo('tan',
                   ref=np.tan,
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   promotes_integers_to_float=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.bfloat16]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.float64],
                                active_if=TEST_WITH_ROCM),
                   )),
    UnaryUfuncInfo('tanh',
                   ref=np.tanh,
                   decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                   dtypes=all_types_and_complex_and(torch.bool),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   promotes_integers_to_float=True,
                   skips=(
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=(IS_MACOS or IS_WINDOWS)),
                   )),
    UnaryUfuncInfo('exp2',
                   ref=np.exp2,
                   dtypes=floating_types_and(torch.half),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None),
    UnaryUfuncInfo('nan_to_num',
                   ref=np.nan_to_num,
                   dtypes=all_types_and(torch.half, torch.bool),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None),
    UnaryUfuncInfo('sqrt',
                   ref=np.sqrt,
                   domain=(0, float('inf')),
                   dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                   dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                   assert_autodiffed=True,
                   skip_bfloat16_grad=True,
                   decorators=(precisionOverride({torch.bfloat16: 7e-2}),),
                   skips=(
                       # Reference: https://github.com/pytorch/pytorch/issues/47358
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                active_if=IS_MACOS),
                       # Reference: https://github.com/pytorch/pytorch/pull/47293#issuecomment-721774436
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                dtypes=[torch.bfloat16]),
                       # RuntimeError: sqrt does not support automatic differentiation for outputs with complex dtype.
                       SkipInfo('TestGradients', 'test_fn_grad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestGradients', 'test_fn_gradgrad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestGradients', 'test_method_grad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestGradients', 'test_method_gradgrad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestGradients', 'test_inplace_grad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestGradients', 'test_inplace_gradgrad',
                                dtypes=[torch.cdouble]),
                       SkipInfo('TestCommon', 'test_variant_consistency_eager',
                                dtypes=[torch.cfloat, torch.cdouble]),
                       SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                dtypes=[torch.cfloat, torch.cdouble])),
                   promotes_integers_to_float=True,
                   handles_complex_extremals=False),
]

if TEST_SCIPY:
    def reference_sigmoid(x):
        # 'scipy.special.expit' not supported for the input types
        if x.dtype in [np.complex64, np.complex128]:
            return (1 / (1 + np.exp(-x)))
        return scipy.special.expit(x)

    op_db_scipy_reference: List[OpInfo] = [
        UnaryUfuncInfo('sigmoid',
                       ref=reference_sigmoid,
                       decorators=(precisionOverride({torch.float16: 1e-2,
                                                      torch.bfloat16: 1e-2}),),
                       skips=(
                           SkipInfo('TestUnaryUfuncs', 'test_reference_numerics',
                                    device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                           # RuntimeError: sigmoid does not support automatic differentiation for outputs with complex dtype.
                           SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                    dtypes=[torch.complex64, torch.complex128]),
                           SkipInfo('TestCommon', 'test_variant_consistency_eager',
                                    dtypes=[torch.complex64, torch.complex128]),),
                       dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                       dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16),
                       dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                       promotes_integers_to_float=True,
                       skip_bfloat16_grad=True,
                       assert_autodiffed=True,
                       test_complex_grad=False),  # Reference: https://github.com/pytorch/pytorch/issues/48552
        UnaryUfuncInfo('erf',
                       ref=scipy.special.erf,
                       decorators=(precisionOverride({torch.float16: 1e-2,
                                                      torch.bfloat16: 1e-2}),),
                       dtypes=all_types_and(torch.bool),
                       dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                       dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                       skips=(
                           # RuntimeError: "pow" not implemented for 'BFloat16'
                           SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                    dtypes=[torch.bfloat16]),),
                       assert_autodiffed=True,
                       promotes_integers_to_float=True),
        UnaryUfuncInfo('erfc',
                       ref=scipy.special.erfc,
                       decorators=(precisionOverride({torch.float16: 1e-2,
                                                      torch.bfloat16: 1e-2}),),
                       dtypes=all_types_and(torch.bool),
                       dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                       dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                       skips=(
                           # RuntimeError: "pow" not implemented for 'BFloat16'
                           SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                    dtypes=[torch.bfloat16]),),
                       assert_autodiffed=True,
                       promotes_integers_to_float=True),
    ]
    op_db = op_db + op_db_scipy_reference

# Common operator groupings
unary_ufuncs = [op for op in op_db if isinstance(op, UnaryUfuncInfo)]
spectral_funcs = [op for op in op_db if isinstance(op, SpectralFuncInfo)]

def index_variable(shape, max_indices):
    if not isinstance(shape, tuple):
        shape = (shape,)
    index = torch.rand(*shape).mul_(max_indices).floor_().long()
    return index


def index_perm_variable(shape, max_indices):
    if not isinstance(shape, tuple):
        shape = (shape,)

    index = torch.randperm(max_indices).narrow(0, 0, reduce(mul, shape)).view(shape)
    return index


def gather_variable(shape, index_dim, max_indices, duplicate=False):
    assert len(shape) == 2
    assert index_dim < 2
    batch_dim = 1 - index_dim
    index = torch.LongTensor(*shape)
    for i in range(shape[index_dim]):
        index.select(index_dim, i).copy_(
            torch.randperm(max_indices)[:shape[batch_dim]])
    if duplicate:
        index.select(batch_dim, 0).copy_(index.select(batch_dim, 1))
    return index


def bernoulli_scalar():
    return torch.tensor(0, dtype=torch.bool).bernoulli_()


def mask_not_all_zeros(shape):
    assert len(shape) > 0
    while True:
        result = torch.randn(shape).gt(0)
        if result.sum() > 0:
            return result


def uniform_scalar(offset=0, requires_grad=False):
    v = torch.rand(()) + offset
    v.requires_grad = requires_grad
    return v


def normal_scalar_clamp(amin, amax, requires_grad=False):
    v = torch.randn(()).clamp(amin, amax)
    v.requires_grad = requires_grad
    return v


def prod_zeros(dim_size, dim_select):
    assert len(dim_select) == 2
    result = torch.randn(dim_size, dim_size, dim_size)
    result.narrow(dim_select[0], 0, 1).narrow(dim_select[1], 1, 1).zero_()
    result.narrow(dim_select[0], 2, 1).narrow(dim_select[1], 3, 1).zero_()
    result.narrow(dim_select[0], 4, 1).narrow(dim_select[1], 3, 1).zero_()
    return result


non_differentiable = collections.namedtuple('non_differentiable', ['tensor'])


class dont_convert(tuple):
    pass


class NoArgsClass(object):
    def __iter__(self):
        return self

    def __next__(self):
        raise StopIteration()
    next = __next__  # Python 2 compatibility

    def __len__(self):
        return 0

NO_ARGS = NoArgsClass()

def ident(x):
    return x

# (
#   method name,
#   input size/constructing fn,
#   args (tuple represents shape of a tensor arg),
#   test variant name (will be used at test name suffix),    // optional
#   (should_check_autodiff[bool], nonfusible_nodes, fusible_nodes) for autodiff, // optional
#   indices for possible dim arg,                            // optional
#   fn mapping output to part that should be gradcheck'ed,   // optional
#   kwargs                                                   // optional
# )
# Note: some functions have separate schema for (Tensor other) and (Scalar other),
#       and it's possible that we only support AD for Scalar version but not Tensor
#       version, and vice versa.
#       When writing tests, only scalar(float/int) input triggers the Scalar schema.
#       uniform_scalar produces a scalar **Tensor** which won't match Scalar input.
def method_tests():
    set_rng_seed(0)
    return [
        ('add', (S, S, S), ((S, S, S),), '', (True,)),
        ('add', (S, S, S), ((S, S),), 'broadcast_rhs', (True,)),
        ('add', (S, S), ((S, S, S),), 'broadcast_lhs', (True,)),
        ('add', (S, 1, S), ((M, S),), 'broadcast_all', (True,)),
        ('add', (), ((),), 'scalar', (True,)),
        ('add', (S, S, S), ((),), 'scalar_broadcast_rhs', (True,)),
        ('add', (), ((S, S, S),), 'scalar_broadcast_lhs', (True,)),
        ('add', (S, S, S), (3.14,), 'constant', (True,)),
        ('add', (), (3.14,), 'scalar_constant', (True,)),
        ('add', (S, S, S), (3.14j,), 'complex_scalar_constant', (True,)),
        ('__radd__', (S, S, S), (3.14,), 'constant', (True, 'aten::add')),
        ('__radd__', (), (3.14,), 'scalar_constant', (True, 'aten::add')),
        ('sub', (S, S, S), ((S, S, S),), '', (True,)),
        ('sub', (S, S, S), ((S, S),), 'broadcast_rhs', (True,)),
        ('sub', (S, S), ((S, S, S),), 'broadcast_lhs', (True,)),
        ('sub', (S, 1, S), ((M, S),), 'broadcast_all', (True,)),
        ('sub', (S, S, S), ((),), 'scalar_broadcast_rhs', (True,)),
        ('sub', (), ((S, S, S),), 'scalar_broadcast_lhs', (True,)),
        ('sub', (S, S, S), (3.14,), 'constant', (True,)),
        ('sub', (), (3.14,), 'scalar_constant', (True,)),
        ('sub', (S, S, S), (3.14j,), 'complex_scalar_constant', (True,)),
        ('__rsub__', (S, S, S), (3.14,), 'constant', (True, 'aten::rsub')),
        ('__rsub__', (), (3.14,), 'scalar_constant', (True, 'aten::rsub')),
        ('mul', (S, S, S), ((S, S, S),), '', (True,)),
        ('mul', (), ((),), 'scalar', (True,)),
        ('mul', (S, S, S), ((S, S),), 'broadcast_rhs', (True,)),
        ('mul', (S, S), ((S, S, S),), 'broadcast_lhs', (True,)),
        ('mul', (S, 1, S), ((M, S),), 'broadcast_all', (True,)),
        ('mul', (S, S, S), ((),), 'scalar_broadcast_rhs', (True,)),
        ('mul', (), ((S, S, S),), 'scalar_broadcast_lhs', (True,)),
        ('mul', (S, S, S), (3.14,), 'constant', (True,)),
        ('mul', (), (3.14,), 'scalar_constant', (True,)),
        # TODO(@anjali411): enable these tests
        # ('mul', (S, S, S), (3.14j,), 'imaginary_constant', (True,)),
        # ('mul', (), (3.14j,), 'imaginary_scalar_constant', (True,)),
        ('__rmul__', (S, S, S), (3.14,), 'constant', (True, 'aten::mul')),
        ('__rmul__', (), (3.14,), 'scalar_constant', (True, 'aten::mul')),
        ('div', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
        ('div', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
        ('div', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
        ('div', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
        ('div', (), (uniform_scalar(0.1),), 'scalar', (True,)),
        ('div', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
        ('div', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
        ('div', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
        ('div', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
        ('true_divide', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
        ('true_divide', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
        ('true_divide', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
        ('true_divide', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
        ('true_divide', (), (uniform_scalar(0.1),), 'scalar', (True,)),
        ('true_divide', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
        ('true_divide', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
        ('true_divide', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
        ('true_divide', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
        ('__rdiv__', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-1, (3.14j,), 'complex_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('__rdiv__', uniform_scalar(1e-1 * (1 + 1j), requires_grad=True), (3.14j,), 'complex_scalar_constant',
            (True, [], ['aten::mul', 'aten::reciprocal'])),
        ('div', (S, S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex', (True,)),
        ('div', (S, S, S), (torch.rand(S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_rhs', (True,)),
        ('div', (S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_lhs', (True,)),
        ('div', (S, 1, S), (torch.rand(M, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_all', (True,)),
        ('div', (), (uniform_scalar(0.1j),), 'complex_scalar', (True,)),
        ('div', (S, S, S), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_rhs', (True,)),
        ('div', (), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_lhs', (True,)),
        ('div', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-1, (3.14j,), 'complex_constant', (True,)),
        ('div', uniform_scalar(1e-1j, requires_grad=True), (3.14j,), 'complex_scalar_constant', (True,)),
        ('pow', torch.rand(S, S, S) + 1e-3, (torch.rand(S, S, S) + 0.1,), '', (True,)),
        ('pow', torch.rand(S, S, S) + 1e-3, (torch.rand(1,) + 0.1,), 'broadcast_rhs', (True,)),
        ('pow', torch.rand(1,) + 1e-3, (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
        ('pow', torch.rand(S, 1, S) + 1e-3, (torch.rand(1, S, 1) + 0.1,), 'broadcast_all', (True,)),
        ('pow', uniform_scalar(1e-3, requires_grad=True), (uniform_scalar(0.1),), 'scalar', (True,)),
        ('pow', torch.rand(S, S, S) + 1e-3, (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
        ('pow', uniform_scalar(1e-3, requires_grad=True), (torch.rand(S, S, S) + 0.1,), 'scalar_broadcast_lhs', (True,)),
        ('pow', torch.rand(S, S, S) + 1e-3, (3.14,), 'constant', (True,)),
        ('pow', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-3 * (1 + 1j), (3.14,), 'complex_constant', (True,)),
        ('__rpow__', torch.rand(S, S, S) + 1e-3, (3.14,), 'constant', (True, 'aten::pow')),
        ('pow', uniform_scalar(1e-3, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
        ('pow', uniform_scalar(1e-3 * (1 + 1j), requires_grad=True), (3.14,), 'complex_scalar_constant', (True,)),
        ('pow', uniform_scalar(1e-3 * (1 + 1j), requires_grad=True), (3.14j,), 'complex_imaginary_exponent', (True,)),
        ('__rpow__', uniform_scalar(1e-3, requires_grad=True), (3.14,), 'scalar_constant', (True, 'aten::pow')),
        ('float_power', torch.rand(S, S, S) + 1e-3, (torch.rand(S, S, S) + 0.1,), ''),
        ('float_power', torch.rand(S, S, S) + 1e-3, (torch.rand(1,) + 0.1,), 'broadcast_rhs'),
        ('float_power', torch.rand(1,) + 1e-3, (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs'),
        ('float_power', torch.rand(S, 1, S) + 1e-3, (torch.rand(1, S, 1) + 0.1,), 'broadcast_all'),
        ('float_power', uniform_scalar(1e-3, requires_grad=True), (uniform_scalar(0.1),), 'scalar'),
        ('float_power', torch.rand(S, S, S) + 1e-3, (uniform_scalar(0.1),), 'scalar_broadcast_rhs'),
        ('float_power', uniform_scalar(1e-3, requires_grad=True), (torch.rand(S, S, S) + 0.1,), 'scalar_broadcast_lhs'),
        ('float_power', torch.rand(S, S, S) + 1e-3, (3.14,), 'constant'),
        ('transpose', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('transpose', (), (0, 0), 'scalar', (False,)),
        ('transpose', (1,), (0, 0), '1d', (False,)),
        ('transpose', (L, L), (0, 1), '2d', (False,)),
        ('transpose', (S, S, S), (2, 0), '3d', (False,)),
        ('swapdims', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('swapdims', (), (0, 0), 'scalar', (False,)),
        ('swapdims', (1,), (0, 0), '1d', (False,)),
        ('swapdims', (L, L), (0, 1), '2d', (False,)),
        ('swapdims', (S, S, S), (2, 0), '3d', (False,)),
        ('swapaxes', (1, 2, 3), (1, 2), 'dim', (False,), [0, 1]),
        ('swapaxes', (), (0, 0), 'scalar', (False,)),
        ('swapaxes', (1,), (0, 0), '1d', (False,)),
        ('swapaxes', (L, L), (0, 1), '2d', (False,)),
        ('swapaxes', (S, S, S), (2, 0), '3d', (False,)),
        ('t', (1, 2), NO_ARGS, '', (False,)),
        ('view', (S, S, S), (S * S, S), '', (False,)),
        ('view', (torch.Size([S * S, S]),), (S, S, S), 'size', (False,)),
        ('view', (S,), (S,), '1d', (False,)),
        ('view', (), (dont_convert(()),), 'scalar_to_scalar', (False,)),
        ('view', (), (1,), 'scalar_to_1d', (False,)),
        ('ravel', (S, S, S), NO_ARGS, '', (False,)),
        ('reshape', (S, S, S), (S * S, S), '', (False,)),
        ('reshape', (torch.Size([S * S, S]),), (S, S, S), 'size', (False,)),
        ('reshape', (S,), (S,), '1d', (False,)),
        ('reshape', (), (dont_convert(()),), 'scalar_to_scalar', (False,)),
        ('reshape', (), (1,), 'scalar_to_1d', (False,)),
        ('reshape_as', (S, S, S), (non_differentiable(torch.rand(S * S, S)),)),
        ('reshape_as', (), (non_differentiable(torch.tensor(42.)),), 'scalar'),
        ('reshape_as', (), (non_differentiable(torch.rand(1, 1)),), 'scalar_to_dims'),
        ('flip', (S, S, S), ([0],), 'd0'),
        ('flip', (S, S, S), ([0, 1, 2],), 'd012'),
        ('flip', (S, S, S), ([0, 2],), 'd02'),
        ('flip', (S, S, S), ([2, 0],), 'd20'),
        ('flip', (S, S, S), ([-1],), 'neg_d'),
        ('fliplr', (S, S, S), ()),
        ('flipud', (S, S, S), ()),
        ('roll', (S, S, S), (0, 0), 'd0'),
        ('roll', (S, S, S), (1, 2), 'd12'),
        ('roll', (S, S, S), (0, 2,), 'd02'),
        ('roll', (S, S, S), (2, 0,), 'd20'),
        ('roll', (S, S, S), (-1, 0), 'neg_shift'),
        ('roll', (S, S, S), (10000, 1), 'loop_shift'),
        ('roll', (S, S, S), (2,), 'flattened'),
        ('roll', (S, S, S), ([1, 2, -1], [0, 1, 2]), 'three_dims'),
        ('rot90', (S, S, S), (1, [0, 1],), 'k1_d01'),
        ('rot90', (S, S, S), (1, [1, 2],), 'k1_d12'),
        ('rot90', (S, S, S), (1, [1, -1],), 'k1_neg_d'),
        ('rot90', (S, S, S), (), 'default'),
        ('view_as', (S, S, S), (non_differentiable(torch.rand(S * S, S)),)),
        ('view_as', (), (non_differentiable(torch.tensor(5.5)),), 'scalar'),
        ('view_as', (), (non_differentiable(torch.rand(1, 1)),), 'scalar_to_dims'),
        ('expand', (S, 1, 1), (S, S, S), '', (False,)),
        ('expand', (torch.Size([S, 1, S]),), (S, S, S), 'size', (False,)),
        ('expand', (S, 1), (S, S, S), 'new_dim', (False,)),
        ('expand', (1,), (S, S, S), '1_element', (False,)),
        ('expand', (1, S), (1, 1, S), 'new_dim_front_old_front_1', (False,)),
        ('expand', (), (dont_convert(()),), 'scalar_to_scalar'),
        ('expand', (), (1, 3, 2), 'scalar_to_dims', (False,)),
        ('expand_as', (S, 1, 1), (torch.rand(S, S, S),), '', (False,)),
        ('exp', (S, S, S), NO_ARGS, '', (True,)),
        ('exp', (), NO_ARGS, 'scalar', (True,)),
        ('expm1', (S, S, S), NO_ARGS, '', (True,)),
        ('expm1', (), NO_ARGS, 'scalar', (True,)),
        ('erfinv', torch.rand(S, S, S).clamp(-0.9, 0.9), NO_ARGS),
        ('erfinv', normal_scalar_clamp(-0.9, 0.9, requires_grad=True), NO_ARGS, 'scalar'),
        ('logit', torch.randn(S, S, S).clamp(0.1, 0.9).requires_grad_(True), NO_ARGS, ''),
        ('logit', torch.randn(S, S, S).clamp(0.1, 0.9).requires_grad_(True), (0.2,), 'eps'),
        ('logit', uniform_scalar().clamp(0.1, 0.9).requires_grad_(True), NO_ARGS, 'scalar'),
        ('logit', uniform_scalar().clamp(0.1, 0.9).requires_grad_(True), (0.2,), 'scalar_eps'),
        ('conj', (S, S, S), NO_ARGS),
        ('copysign', (S, S, S), ((S, S, S),), '', (False,)),
        ('copysign', (S, S, S), ((S, S),), 'broadcast_rhs', (False,)),
        ('copysign', (S, S), ((S, S, S),), 'broadcast_lhs', (False,)),
        ('copysign', (S, 1, S), ((M, S),), 'broadcast_all', (False,)),
        ('copysign', (S, S), (3.14,), 'scalar', (False,)),
        ('copysign', (S, S), (0.0,), 'scalar_pos_zero', (False,)),
        # TorchScript does not recognize -0.0: Issue #46848
        # https://github.com/pytorch/pytorch/issues/46848
        # ('copysign', (S, S), (-0.0,), 'scalar_neg_zero', (False,)),
        ('real', (S, S, S), NO_ARGS, 'complex'),
        ('imag', (S, S, S), NO_ARGS, 'complex'),
        ('view_as_real', (S, S, S), NO_ARGS, 'complex'),
        ('view_as_complex', (S, S, 2), NO_ARGS),
        ('complex', (S, S, S), ((S, S, S),), ''),
        ('abs', (S, S, S), NO_ARGS, '', (True,)),
        ('abs', (), NO_ARGS, 'scalar', (True,)),
        ('angle', (S, S, S), NO_ARGS, '', (True,)),
        ('angle', (), NO_ARGS, 'scalar', (True,)),
        ('clamp', (S, S, S), (0, 1), '', (True,)),
        ('clamp', (S, S, S), (None, 0.5), 'min', (True,)),
        ('clamp', (S, S, S), (0.5, None), 'max', (True,)),
        ('clamp', (), (0, 1), 'scalar', (True,)),
        ('clamp', (), (None, 0.5), 'min_scalar', (True,)),
        ('clamp', (), (0.5, None), 'max_scalar', (True,)),
        ('clamp', (S, S), (), 'max_scalar_kwarg', (True,), (), (), ident, {'max': 1}),
        ('atan2', (S, S, S), ((S, S, S),)),
        ('atan2', (), ((),), 'scalar'),
        ('atan2', (S, S, S), ((S,),), 'broadcast_rhs'),
        ('atan2', (S,), ((S, S, S),), 'broadcast_lhs'),
        ('atan2', (S, 1, S), ((S, S),), 'broadcast_all'),
        ('reciprocal', torch.rand(S, S, S) + 0.1, NO_ARGS, '', (True,)),
        ('reciprocal', uniform_scalar(0.1, requires_grad=True), NO_ARGS, 'scalar', (True,)),
        ('reciprocal', torch.randn(S, S, S, dtype=torch.cdouble) + 0.1, NO_ARGS, 'complex', (True,)),
        ('reciprocal', uniform_scalar(0.1j), NO_ARGS, 'complex_scalar', (True,)),
        ('round', (S, S, S), NO_ARGS, '', (True,)),
        ('round', (), NO_ARGS, 'scalar', (True,)),
        ('sign', (S, S, S), NO_ARGS),
        ('sign', (), NO_ARGS, 'scalar'),
        ('sgn', (S, S, S), NO_ARGS),
        ('sgn', (), NO_ARGS, 'scalar'),
        ('trunc', (S, S, S), NO_ARGS, '', (True,)),
        ('trunc', (), NO_ARGS, 'scalar', (True,)),
        ('floor', (S, S, S), NO_ARGS, '', (True,)),
        ('floor', (), NO_ARGS, 'scalar', (True,)),
        ('ceil', (S, S, S), NO_ARGS, '', (True,)),
        ('ceil', (), NO_ARGS, 'scalar', (True,)),
        ('rad2deg', (S, S, S), NO_ARGS),
        ('deg2rad', (S, S, S), NO_ARGS),
        ('rsqrt', torch.rand(S, S, S) + 1e-2, NO_ARGS, '', (True,)),
        ('rsqrt', uniform_scalar(1e-2, requires_grad=True), NO_ARGS, 'scalar', (True,)),
        ('rsqrt', torch.rand(S, S, S, dtype=torch.cfloat) + 1e-2, NO_ARGS, 'complex', (True,)),
        ('rsqrt', uniform_scalar(1e-2 * (1 + 1j), requires_grad=True), NO_ARGS, 'complex_scalar', (True,)),
        ('frac', (S, S, S), NO_ARGS, '', (True,)),
        ('frac', (), NO_ARGS, 'scalar', (True,)),
        ('fmod', (S, S, S), (1.5,), '', (True,)),
        ('fmod', (), (1.5,), 'scalar', (True,)),
        ('fmod', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
        ('fmod', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
        ('fmod', (S, S, S), (non_differentiable(torch.rand(S) + 1.5),), 'tensor_broadcast_rhs'),
        ('fmod', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
        ('fmod', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
        ('fmod', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
        ('fmod', (S, S, S), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor_broadcast_rhs'),
        ('hypot', (S, S), ((S, S),)),
        ('remainder', (S, S, S), (1.5,), '', (True,)),
        ('remainder', (), (1.5,), 'scalar', (True,)),
        ('remainder', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
        ('remainder', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
        ('remainder', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
        ('remainder', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
        ('remainder', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
        ('lerp', (S, S, S), ((S, S, S), 0.4), 'scalar_no_broadcast', (True,)),
        ('lerp', (S, S, S), ((S,), 0.4), 'broadcast_rhs', (True,)),
        ('lerp', (S,), ((S, S, S), 0.4), 'broadcast_lhs', (True,)),
        ('lerp', (S, 1, S), ((S, S), 0.4), 'broadcast_all', (True,)),
        ('lerp', (), ((), 0.4), 'scalar', (True,)),
        ('lerp', (S, S, S), ((), 0.4), 'scalar_broadcast_rhs', (True,)),
        ('lerp', (), ((S, S, S), 0.4), 'scalar_broadcast_lhs', (True,)),
        ('max', (S, S, S), NO_ARGS),
        ('max', (S, S, S), (1,), 'dim', (), [0]),
        ('max', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('max', (), NO_ARGS, 'scalar'),
        ('max', (), (0,), 'scalar_dim', (), [0]),
        ('max', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('max', (S, S, S), ((S, S, S),), 'elementwise', (True,)),
        ('max', (S, S, S), ((S,),), 'elementwise_broadcast_rhs', (True,)),
        ('max', (S,), ((S, S, S),), 'elementwise_broadcast_lhs', (True,)),
        ('max', (S, 1, S), ((S, S),), 'elementwise_broadcast_all', (True,)),
        ('max', (), ((),), 'scalar_elementwise', (True,)),
        ('max', (S, S, S), ((),), 'scalar_elementwise_broadcast_rhs', (True,)),
        ('max', (), ((S, S, S),), 'scalar_elementwise_broadcast_lhs', (True,)),
        ('min', (S, S, S), NO_ARGS, ),
        ('min', (S, S, S), (1,), 'dim', (), [0]),
        ('min', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('min', (), NO_ARGS, 'scalar'),
        ('min', (), (0,), 'scalar_dim', (), [0]),
        ('min', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('min', (S, S, S), ((S, S, S),), 'elementwise', (True,)),
        ('min', (S, S, S), ((S,),), 'elementwise_broadcast_rhs', (True,)),
        ('min', (S,), ((S, S, S),), 'elementwise_broadcast_lhs', (True,)),
        ('min', (S, 1, S), ((S, S),), 'elementwise_broadcast_all', (True,)),
        ('min', (), ((),), 'scalar_elementwise', (True,)),
        ('min', (S, S, S), ((),), 'scalar_elementwise_broadcast_rhs', (True,)),
        ('min', (), ((S, S, S),), 'scalar_elementwise_broadcast_lhs', (True,)),
        ('amax', (S, S, S), NO_ARGS),
        ('amax', (S, S, S), (1,), 'dim'),
        ('amax', (S, S, S), ([1, 2],), 'multiple_dim'),
        ('amax', (S, S, S), (1, True,), 'keepdim_dim'),
        ('amax', (), NO_ARGS, 'scalar'),
        ('amax', (), (0,), 'scalar_dim'),
        ('amax', (), (0, True,), 'scalar_keepdim_dim'),
        ('amin', (S, S, S), NO_ARGS, ),
        ('amin', (S, S, S), (1,), 'dim',),
        ('amin', (S, S, S), ([1, 2],), 'multiple_dim'),
        ('amin', (S, S, S), (1, True,), 'keepdim_dim'),
        ('amin', (), NO_ARGS, 'scalar'),
        ('amin', (), (0,), 'scalar_dim'),
        ('amin', (), (0, True,), 'scalar_keepdim_dim'),
        ('mean', (S, S, S), NO_ARGS, '', (True,)),
        ('mean', (S, S, S), (1,), 'dim', (True,), [0]),
        ('mean', (S, S, S), (1, True,), 'keepdim_dim', (True,), [0]),
        ('mean', (), NO_ARGS, 'scalar', (True,)),
        ('mean', (), (0,), 'scalar_dim', (True,), [0]),
        ('mean', (), (0, True,), 'scalar_keepdim_dim', (True,), [0]),
        ('mean', (S, S, S), (), 'dtype', (True,), (), (), ident, {'dtype': torch.float64}),
        ('kthvalue', (S, S, S), (2,)),
        ('kthvalue', (S, S, S), (2, 1,), 'dim', (), [1]),
        ('kthvalue', (S, S, S), (2, 1,), 'dim_alert_nondeterministic', (), [1],
            [expectedAlertNondeterministic('kthvalue CUDA', 'cuda')]),
        ('kthvalue', (S, S, S), (2, 1, True,), 'keepdim_dim', (), [1]),
        ('kthvalue', (S,), (2, 0,), 'dim_1d', (), [1]),
        ('kthvalue', (S,), (2, 0, True,), 'keepdim_dim_1d', (), [1]),
        ('kthvalue', (), (1,), 'scalar', (), ()),
        ('kthvalue', (), (1, 0,), 'scalar_dim', (), [1]),
        ('kthvalue', (), (1, 0, True), 'scalar_keepdim_dim', (), [1]),
        ('quantile', (S, S, S), (0.5,)),
        ('quantile', (S, S, S), (0.5, 0), 'dim', (), [1]),
        ('quantile', (S, S, S), (0.5, None, True), 'keepdim'),
        ('quantile', (S, S, S), (0.5, 0, True), 'keepdim_dim', (), [1]),
        ('quantile', (), (0.5,), 'scalar'),
        ('nanquantile', (S, S, S), (0.5,)),
        ('nanquantile', (S, S, S), (0.5, 0), 'dim', (), [1]),
        ('nanquantile', (S, S, S), (0.5, None, True), 'keepdim'),
        ('nanquantile', (S, S, S), (0.5, 0, True), 'keepdim_dim', (), [1]),
        ('nanquantile', (), (0.5,), 'scalar'),
        ('median', (S, S, S), NO_ARGS),
        ('median', (S, S, S), (1,), 'dim', (), [0]),
        ('median', (S, S, S), (1,), 'dim_alert_nondeterministic', (), [0],
            [expectedAlertNondeterministic('median CUDA with indices output', 'cuda')]),
        ('median', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('median', (), NO_ARGS, 'scalar'),
        ('median', (), (0,), 'scalar_dim', (), [0]),
        ('median', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('nanmedian', (S, S, S), NO_ARGS),
        ('nanmedian', (S, S, S), (1,), 'dim', (), [0]),
        ('nanmedian', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('nanmedian', (), NO_ARGS, 'scalar'),
        ('nanmedian', (), (0,), 'scalar_dim', (), [0]),
        ('nanmedian', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('mode', (S, S, S), NO_ARGS),
        ('mode', (S, S, S), (1,), 'dim', (), [0]),
        ('mode', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('mode', (), NO_ARGS, 'scalar'),
        ('mode', (), (0,), 'scalar_dim', (), [0]),
        ('mode', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('sum', (S, S, S), NO_ARGS),
        ('sum', (S, S, S), (1,), 'dim', (), [0]),
        ('sum', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('sum', (), NO_ARGS, 'scalar'),
        ('sum', (), (0,), 'scalar_dim', (), [0]),
        ('sum', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('sum', (S, S, S), ([1, 2],), 'multi_dim'),
        ('sum', (S, S, S), ([1, 2], True,), 'multi_dim_keepdim'),
        ('nansum', (S, S, S), NO_ARGS),
        ('nansum', (S, S, S), (1,), 'dim', (), [0]),
        ('nansum', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('nansum', (), NO_ARGS, 'scalar'),
        ('nansum', (), (0,), 'scalar_dim', (), [0]),
        ('nansum', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('nansum', (S, S, S), ([1, 2],), 'multi_dim'),
        ('nansum', (S, S, S), ([1, 2], True,), 'multi_dim_keepdim'),
        ('prod', (S, S, S), NO_ARGS),
        ('prod', (S, S, S), (1,), 'dim', (), [0]),
        ('prod', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
        ('prod', (), NO_ARGS, 'scalar'),
        ('prod', (), (0,), 'scalar_dim', (), [0]),
        ('prod', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
        ('prod', prod_zeros(S, [0, 1]), NO_ARGS, 'zerodims2'),
        ('prod', prod_zeros(S, [0, 2]), NO_ARGS, 'zerodims1'),
        ('prod', prod_zeros(S, [1, 2]), NO_ARGS, 'zerodims0'),
        ('prod', prod_zeros(S, [0, 1]), (1,), 'zeros_dims2', (), [0]),
        ('prod', prod_zeros(S, [0, 2]), (1,), 'zeros_dims1', (), [0]),
        ('prod', prod_zeros(S, [1, 2]), (1,), 'zeros_dims0', (), [0]),
        ('prod', prod_zeros(S, [0, 1]), (1, True), 'keepdim_zeros_dims2', (), [0]),
        ('prod', prod_zeros(S, [0, 2]), (1, True), 'keepdim_zeros_dims1', (), [0]),
        ('prod', prod_zeros(S, [1, 2]), (1, True), 'keepdim_zeros_dims0', (), [0]),
        ('prod', prod_single_zero(S), NO_ARGS, 'single_zero'),
        ('prod', (torch.tensor(0., requires_grad=True)), NO_ARGS, 'scalar_zero'),
        ('prod', (torch.tensor(0., requires_grad=True)), (0,), 'scalar_dim_zero', (), [0]),
        ('prod', (torch.tensor(0., requires_grad=True)), (0, True,), 'scalar_keepdim_dim_zero', (), [0]),
        ('var', (S, S, S), NO_ARGS, '', (True,)),
        ('var', (S, S, S), (1,), 'dim', (True,), [0]),
        ('var', (S, S, S), (1, True, True), 'keepdim_dim', (True,), [0]),
        ('var', (S,), (0,), 'dim_1d', (True,), [0]),
        ('var', (S,), (0, True, True), 'keepdim_dim_1d', (True,), [0]),
        ('std', (S, S, S), NO_ARGS, '', (True,)),
        ('std', (S, S, S), (1,), 'dim', (True,), [0]),
        ('std', (S, S, S), (1, True, True), 'keepdim_dim', (True,), [0]),
        ('std', (S,), (0,), 'dim_1d', (True,), [0]),
        ('std', (S,), (0, True, True), 'keepdim_dim_1d', (True,), [0]),
        ('var_mean', (S, S, S), NO_ARGS, ''),
        ('var_mean', (S, S, S), (1,), 'dim', [0]),
        ('var_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
        ('var_mean', (S,), (0,), 'dim_1d', [0]),
        ('var_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
        ('std_mean', (S, S, S), NO_ARGS, ''),
        ('std_mean', (S, S, S), (1,), 'dim', [0]),
        ('std_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
        ('std_mean', (S,), (0,), 'dim_1d', [0]),
        ('std_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
        ('renorm', (S, S, S), (2, 1, 0.5), 'dim', (), [1]),
        ('renorm', (S, S, S), (1, 2, 3), 'norm_1'),
        ('renorm', (S, S, S), (inf, 2, 0.5), 'norm_inf'),
        ('repeat', (S,), (2,), 'single_number'),
        ('repeat', (), (2, 3), 'scalar'),
        ('repeat', (2, 2), (3, 2)),
        ('repeat', (2, 2), (1, 3, 1, 2), 'unsqueeze'),
        ('repeat', (S, S), (1, 1), 'keepdim0'),
        ('repeat', (S, S), (3, 1, 1), 'keepdim1'),
        ('repeat', (S,), (0, ), 'zero_dim'),
        ('repeat', (S,), (0, 2), 'zero_dim_multi'),
        ('logcumsumexp', (S, S, S), (0,), 'dim0', (), [0]),
        ('logcumsumexp', (S, S, S), (1,), 'dim1', (), [0]),
        ('logcumsumexp', (), (0,), 'dim0_scalar', (), [0]),
        ('cummax', (S, S, S), (0,), 'dim0', (), [0]),
        ('cummax', (S, S, S), (1,), 'dim1', (), [0]),
        ('cummax', (), (0,), 'dim0_scalar', (), [0]),
        ('cummin', (S, S, S), (0,), 'dim0', (), [0]),
        ('cummin', (S, S, S), (1,), 'dim1', (), [0]),
        ('cummin', (), (0,), 'dim0_scalar', (), [0]),
        ('cumsum', (S, S, S), (0,), 'dim0', (), [0]),
        ('cumsum', (S, S, S), (1,), 'dim1', (), [0]),
        ('cumsum', (S, S, S), (1,), 'dim1_cast', (), [0], (), ident, {'dtype': torch.float64}),
        ('cumsum', (), (0,), 'dim0_scalar', (), [0]),
        ('cumprod', (S, S, S), (0,)),
        ('cumprod', (S, S, S), (1,), 'dim1', (), [0]),
        ('cumprod', (), (0,), 'scalar'),
        ('cumprod', (torch.tensor(0., requires_grad=True)), (0,), 'scalar_zeros'),
        ('cumprod', prod_zeros(S, [0, 1]), (1,), 'zeros_dim2', (), [0]),
        ('cumprod', prod_zeros(S, [0, 2]), (1,), 'zeros_dim1', (), [0]),
        ('cumprod', prod_zeros(S, [1, 2]), (1,), 'zeros_dim0', (), [0]),
        ('cumprod', prod_zeros(S, [1, 2]), (1,), 'zeros_dim0_cast', (), [0], (), ident, {'dtype': torch.float64}),
        ('log_softmax', (S, S, S), (1, torch.float64,), 'kwarg_dtype_would_break_jit_loader', (True,)),
        ('unfold', (), (0, 1, 1), 'scalar', (), [0]),
        ('unfold', (S, S, S, S), (0, 3, 1), '4d_dim0_step1', (), [0]),
        ('unfold', (S, S, S, S), (1, 3, 1), '4d_dim1_step1', (), [0]),
        ('unfold', (S, S, S, S), (2, 3, 1), '4d_dim2_step1', (), [0]),
        ('unfold', (S, S, S, S), (3, 3, 1), '4d_dim3_step1', (), [0]),
        ('unfold', (S, S, S, S), (0, 3, 2), '4d_dim0_step2', (), [0]),
        ('unfold', (S, S, S, S), (1, 3, 2), '4d_dim1_step2', (), [0]),
        ('unfold', (S, S, S, S), (2, 3, 2), '4d_dim2_step2', (), [0]),
        ('unfold', (S, S, S, S), (3, 3, 2), '4d_dim3_step2', (), [0]),
        ('unfold', (S, S, S, S), (0, 4, 1), '4d_dim0_size4', (), [0]),
        ('unfold', (S, S, S, S), (1, 4, 1), '4d_dim1_size4', (), [0]),
        ('unfold', (S, S, S, S), (2, 4, 1), '4d_dim2_size4', (), [0]),
        ('unfold', (S, S, S, S), (3, 4, 1), '4d_dim3_size4', (), [0]),
        ('unfold', (M,), (0, 3, 1), '1d_step1', (), [0]),
        ('unfold', (M,), (0, 3, 2), '1d_step2', (), [0]),
        ('unfold', (M,), (0, 3, 3), '1d_step3', (), [0]),
        ('unfold', (1000,), (0, 3, 11), '1d_step_gt_size', (), [0]),
        ('unfold', (1000,), (0, 2, 27), '1d_step_gt_size2', (), [0]),
        ('unfold', (10, 10), (0, 1, 2), '2d_step_gt_size', (), [0]),
        ('unfold', (10, 10), (1, 2, 3), '2d_step_gt_size2', (), [0]),
        ('unfold', (10, 10), (1, 2, 2), '2d_step_ge_size2', (), [0]),
        ('unfold', (S, S, S), (2, 3, 2), 'lastdim', (), [0]),
        ('addmm', (S, M), ((S, S), (S, M)), '', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (1,), ((S, S), (S, M)), 'broadcast_lhs', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (S, M), ((S, S), (S, M)), 'coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmm', (1,), ((S, S), (S, M)), 'broadcast_lhs_coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmm', (), ((S, S), (S, M)), 'scalar_broadcast_lhs', (True, ['aten::add', 'aten::mm'])),
        ('addmm', (), ((S, S), (S, M)), 'scalar_broadcast_lhs_coef', (True,), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addbmm', (S, M), ((S, S, S), (S, S, M)),),
        ('addbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs'),
        ('addbmm', (S, M), ((S, S, S), (S, S, M)), 'coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs_coef', (),
         (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs'),
        ('addbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs_coef', (), (), (), ident,
         {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (S, S, M), ((S, S, S), (S, S, M)),),
        ('baddbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs'),
        ('baddbmm', (S, S, M), ((S, S, S), (S, S, M)), 'coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (1,), ((S, S, S), (S, S, M)), 'broadcast_lhs_coef', (),
         (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('baddbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs'),
        ('baddbmm', (), ((S, S, S), (S, S, M)), 'scalar_broadcast_lhs_coef', (), (), (), ident,
         {'beta': 0.2, 'alpha': 0.6}),
        ('addmv', (S,), ((S, M), (M,)),),
        ('addmv', (1,), ((S, M), (M,)), 'broadcast_lhs'),
        ('addmv', (S,), ((S, M), (M,)), 'coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmv', (1,), ((S, M), (M,)), 'broadcast_lhs_coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addmv', (), ((S, M), (M,)), 'scalar_broadcast_lhs'),
        ('addmv', (), ((S, M), (M,)), 'scalar_broadcast_lhs_coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addr', (S, M), ((S,), (M,)),),
        ('addr', (), ((S,), (M,)), 'broadcast_lhs'),
        ('addr', (S, M), ((S,), (M,)), 'coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('addr', (), ((S,), (M,)), 'broadcast_lhs_coef', (), (), (), ident, {'beta': 0.2, 'alpha': 0.6}),
        ('dot', (L,), ((L,),), '', (True,)),
        ('vdot', (L,), ((L,),),),
        ('mm', (S, M), ((M, S),), '', (True,)),
        ('bmm', (M, S, M), ((M, M, S),), '', (True,)),
        ('mv', (S, M), ((M,),), '', (True,)),
        ('ger', (S,), ((M,),)),
        ('inner', (S,), ((S,),), "1d_1d", (False,)),
        ('inner', (), ((S, S),), "scalar_2d", (False,)),
        ('matmul', (L,), ((L,),), '', (True,)),
        ('matmul', (S, M), ((M,),), "2d_1d", (True,)),
        ('matmul', (M,), ((M, S),), "1d_2d", (True,)),
        ('matmul', (S, M), ((M, S),), "2d_2d", (True,)),
        ('matmul', (S, S, M), ((M,),), "3d_1d", (True,)),
        ('matmul', (S, S, M), ((M, S),), "3d_2d", (True,)),
        ('matmul', (M,), ((S, M, S),), "1d_3d", (True,)),
        ('matmul', (S, M), ((S, M, S),), "2d_3d", (True,)),
        ('matmul', (S, S, M, M), ((S, S, M, S),), "4d_4d", (True,)),
        ('matmul', (S, S, M, M), ((M,),), "4d_1d", (True,)),
        ('matmul', (M,), ((S, S, M, S),), "1d_4d", (True,)),
        ('matrix_power', (S, S), [2], "n=2"),
        ('matrix_power', (S, S, S), [3], "n=3"),
        ('matrix_power', (S, S, S), [1], "n=1"),
        ('matrix_power', (S, S, S), [0], "n=0"),
        ('matrix_power', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S), [-1], "n=-1", (),
         NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('matrix_power', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S), [-3], "n=-3", (),
         NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('matrix_power', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, S), [-2], "n=-2", (),
         NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('matrix_exp', (S, S), NO_ARGS, "single_matrix"),
        ('matrix_exp', (S, S, S), NO_ARGS, "batch_of_matrices"),
        ('mvlgamma', torch.empty(S,).uniform_(0.5, 1), [1], "p=1"),
        ('mvlgamma', torch.empty(S,).uniform_(1, 2), [2], "p=2"),
        ('mvlgamma', torch.empty(S, S).uniform_(1.5, 3), [3], "p=3"),
        ('mvlgamma', torch.empty(S, S).uniform_(2.5, 5), [5], "p=5"),
        ('addcmul', (S, S), ((S, S), (S, S)), '', (True,)),
        ('addcmul', (S, S), ((S, 1), (1, S)), 'broadcast_rhs', (True,)),
        ('addcmul', (1,), ((S, S, 1), (1, S)), 'broadcast_all', (True,)),
        ('addcmul', (S, S), ((S, S), (S, S)), 'scale', (True,), (), (), ident, {'value': 0.5}),
        ('addcmul', (S, S), ((S, 1), (1, S)), 'scale_broadcast_rhs', (True,), (), (), ident, {'value': 0.5}),
        ('addcmul', (1,), ((S, S, 1), (1, S)), 'scale_broadcast_all', (True,), (), (), ident, {'value': 0.5}),
        ('addcmul', (), ((), ()), 'scalar', (True,)),
        ('addcmul', (S, S), ((), ()), 'scalar_broadcast_rhs', (True,)),
        ('addcmul', (), ((S, S, 1), (1, S)), 'scalar_broadcast_lhs', (True,)),
        ('addcmul', (), ((), ()), 'scalar_scale', (True,), (), (), ident, {'value': 0.5}),
        ('addcmul', (S, S), ((), ()), 'scalar_scale_broadcast_rhs', (True,), (), (), ident, {'value': 0.5}),
        ('addcmul', (), ((S, S, 1), (1, S)), 'scalar_scale_broadcast_lhs', (True,), (), (), ident, {'value': 0.5}),
        ('addcdiv', (S, S), ((S, S), (S, S))),
        ('addcdiv', (S, S), ((S, 1), (1, S)), 'broadcast_rhs'),
        ('addcdiv', (1,), ((S, S, 1), (1, S)), 'broadcast_all'),
        ('addcdiv', (S, S), ((S, S), (S, S)), 'scale', (), (), (), ident, {'value': 0.5}),
        ('addcdiv', (S, S), ((S, 1), (1, S)), 'scale_broadcast_rhs', (), (), (), ident, {'value': 0.5}),
        ('addcdiv', (1,), ((S, S, 1), (1, S)), 'scale_broadcast_all', (), (), (), ident, {'value': 0.5}),
        ('addcdiv', (), ((), ()), 'scalar'),
        ('addcdiv', (S, S), ((), ()), 'scalar_broadcast_rhs'),
        ('addcdiv', (), ((S, S, 1), (1, S)), 'scalar_broadcast_lhs'),
        ('addcdiv', (), ((), ()), 'scalar_scale', (), (), (), ident, {'value': 0.5}),
        ('addcdiv', (S, S), ((), ()), 'scalar_scale_broadcast_rhs', (), (), (), ident, {'value': 0.5}),
        ('addcdiv', (), ((S, S, 1), (1, S)), 'scalar_scale_broadcast_lhs', (), (), (), ident, {'value': 0.5}),
        ('zero_', (S, S, S), NO_ARGS),
        ('zero_', (), NO_ARGS, 'scalar'),
        ('logaddexp', (S, S), ((S, S),)),
        ('logaddexp2', (S, S), ((S, S),)),
        ('logsumexp', (S, S), (1,), '', (True,)),
        ('logsumexp', (), (0,), 'scalar', (True,)),
        ('norm', (S, S), (), 'default'),
        ('norm', (S, S), (2,), '2'),
        ('norm', (S, S), (0,), '0'),
        ('norm', (S, S), (0.5,), '0_5'),
        ('norm', (S, S), (1,), '1'),
        ('norm', (S, S), (3,), '3'),
        ('norm', (S, S), (inf,), 'inf'),
        ('norm', (S, S), (-inf,), '-inf'),
        ('norm', (S, S), ('fro',), 'fro_default'),
        ('norm', (S, S), ('fro', [0, 1],), 'fro'),
        ('norm', (S, S), ('nuc',), 'nuc', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('norm', (S, S, S), ('nuc', [1, 2]), 'nuc_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('norm', (S, S), (-1,), 'neg_1'),
        ('norm', (S, S), (-2,), 'neg_2'),
        ('norm', (S, S), (-0.5,), 'neg_0_5'),
        ('norm', (S, S), (-1.5,), 'neg_1_5'),
        ('norm', (S, S), (-2, 1,), 'neg_2_2_dim', (), [1]),
        ('norm', (S, S), (-1, 1,), 'neg_1_2_dim', (), [1]),
        ('norm', (S, S), (0, 1,), '0_2_dim', (), [1]),
        ('norm', (S, S), (1, 1,), '1_2_dim', (), [1]),
        ('norm', (S, S), (2, 1,), '2_2_dim', (), [1]),
        ('norm', (S, S), (3, 1,), '3_2_dim', (), [1]),
        ('norm', (S, S), (inf, 1,), 'inf_2_dim'),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5,), '1_5_default'),
        ('norm', (S, S, S), (2, 1), '2_dim', (), [1]),
        ('norm', (S, S, S), (3, 1), '3_dim', (), [1]),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1), '1_5_dim', (), [1]),
        ('norm', (S, S, S), (2, 1, True), 'keepdim_2_dim', (), [1]),
        ('norm', (S, S, S), (3, 1, True), 'keepdim_3_dim', (), [1]),
        ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1, True), 'keepdim_1_5_dim', (), [1]),
        ('norm', (), (2, 0), '2_dim_scalar', (), [1]),
        ('norm', (), (3, 0), '3_dim_scalar', (), [1]),
        ('norm', (), (2, 0, True), 'keepdim_2_dim_scalar', (), [1]),
        ('norm', (), (3, 0, True), 'keepdim_3_dim_scalar', (), [1]),
        ('clone', (S, M, S), NO_ARGS),
        ('clone', (), NO_ARGS, 'scalar'),
        ('contiguous', (S, S), NO_ARGS, '', (True,)),
        ('contiguous', torch.randn(S, S).transpose(0, 1), NO_ARGS, 'not_contiguous', (True,)),
        ('dist', (S, S, S), ((S, S, S),)),
        ('dist', (S, S, S), ((S,),), 'broadcast_rhs'),
        ('dist', (S,), ((S, S, S),), 'broadcast_lhs'),
        ('dist', (S, 1, S), ((S, S),), 'broadcast_all'),
        ('dist', (), ((),), 'scalar'),
        ('dist', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('dist', (), ((S, S, S),), 'scalar_broadcast_lhs'),
        ('dist', (S, S, S), ((S, S, S), 4), '4'),
        ('dist', (S, S, S), ((S,), 4), '4_broadcast_rhs'),
        ('dist', (S,), ((S, S, S), 4), '4_broadcast_lhs'),
        ('dist', (S, 1, S), ((S, S), 4), '4_broadcast_all'),
        ('dist', (), ((), 4), 'scalar_4'),
        ('dist', (S, S, S), ((), 4), 'scalar_4_broadcast_rhs'),
        ('dist', (), ((S, S, S), 4), 'scalar_4_broadcast_lhs'),
        ('diag', (M, M), NO_ARGS, '2d'),
        ('diag', (3, 5), NO_ARGS, '2d_wide'),
        ('diag', (3, 5), (2,), '2d_wide_pos'),
        ('diag', (3, 5), (-2,), '2d_wide_neg'),
        ('diag', (5, 3), NO_ARGS, '2d_tall'),
        ('diag', (5, 3), (2,), '2d_tall_pos'),
        ('diag', (5, 3), (-2,), '2d_tall_neg'),
        ('diag', (M,), NO_ARGS, '1d'),
        ('diag', (M, M), (1,), '2d_1'),
        ('diag', (M, M), (2,), '2d_2'),
        ('diag_embed', (S, S), NO_ARGS),
        ('diagonal', (M, M), NO_ARGS, '2d'),
        ('diagonal', (3, 5), NO_ARGS, '2d_wide'),
        ('diagonal', (3, 5), (2,), '2d_wide_pos'),
        ('diagonal', (3, 5), (-2,), '2d_wide_neg'),
        ('diagonal', (5, 3), NO_ARGS, '2d_tall'),
        ('diagonal', (5, 3), (2,), '2d_tall_pos'),
        ('diagonal', (5, 3), (-2,), '2d_tall_neg'),
        ('diagonal', (M, M), (1,), '2d_1'),
        ('diagonal', (M, M), (2,), '2d_2'),
        ('diagonal', (M, M, M), (1, 1, 2), '3d_1'),
        ('diagonal', (M, M, M), (2, 0, 1), '3d_2'),
        ('diagonal', (M, M, M), (-2, 0, 1), '3d_3'),
        ('tile', (S, S, S), ([S, S, S, S],), 'more_reps_dims', (False,)),
        ('tile', (S, S, S), ([S, S, S],), 'same_reps_dims', (False,)),
        ('tile', (S, S, S), ([S, M],), 'less_reps_dims', (False,)),
        ('tile', (S, S, S), ([S, S, 0],), 'zero_rep_dim', (False,)),
        ('tile', (), ([S, S, S],), 'empty_tensor', (False,)),
        ('tril', (M, M), NO_ARGS),
        ('tril', (M, M), (2,), 'idx'),
        ('tril', (S, M, M), NO_ARGS, 'batched'),
        ('tril', (S, M, M), (2,), 'batched_idx'),
        ('tril', (3, 3, S, S), NO_ARGS, 'more_batched'),
        ('triu', (M, M), NO_ARGS),
        ('triu', (M, M), (2,), 'idx'),
        ('triu', (S, M, M), NO_ARGS, 'batched'),
        ('triu', (S, M, M), (2,), 'batched_idx'),
        ('triu', (3, 3, S, S), NO_ARGS, 'more_batched'),
        ('trace', (M, M), NO_ARGS),
        ('cross', (S, 3), ((S, 3),)),
        ('cross', (S, 3, S), ((S, 3, S), 1), 'dim'),
        ('index_select', (S, S, S), (0, index_variable(2, S)), 'dim', (), [0]),
        ('index_select', (), (0, torch.tensor([0], dtype=torch.int64)), 'scalar_mixed_dim', (), [0]),
        ('index_select', (), (0, torch.tensor(0, dtype=torch.int64)), 'scalar_dim', (), [0]),
        ('index_add', (S, S), (0, index_variable(2, S), (2, S)), 'dim', (), [0]),
        ('index_add', (), (0, torch.tensor([0], dtype=torch.int64), (1,)), 'scalar_input_dim', (), [0]),
        ('index_add', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalar_all_dim', (), [0]),
        ('index_add', (S, S), (0, index_variable(2, S), (2, S)), 'alert_nondeterministic', (), [0],
            [expectedAlertNondeterministic('index_add_cuda_', 'cuda')]),
        ('index_copy', (S, S), (0, index_perm_variable(2, S), (2, S)), 'dim', (), [0]),
        ('index_copy', (S, S), (0, index_perm_variable(2, S), (2, S)), 'dim_alert_nondeterministic', (), [0],
            [expectedAlertNondeterministic('index_copy')]),
        ('index_copy', (), (0, torch.tensor([0], dtype=torch.int64), (1,)), 'scalar_input_dim', (), [0]),
        ('index_copy', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalar_all_dim', (), [0]),
        ('index_fill', (S, S), (0, index_variable(2, S), 2), 'dim', (), [0]),
        ('index_fill', (S, S), (0, index_variable(2, S), ()), 'variable_dim', (), [0]),
        ('index_fill', (S, S), (0, torch.tensor(0, dtype=torch.int64), 2), 'scalar_index_dim', (), [0]),
        ('index_fill', (), (0, torch.tensor([0], dtype=torch.int64), 2), 'scalar_input_dim', (), [0]),
        ('index_fill', (), (0, torch.tensor(0, dtype=torch.int64), 2), 'scalar_both_dim', (), [0]),
        ('inverse', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
            NO_ARGS, '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('inverse', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 2, 3, dtype=dtype).to(device),
         NO_ARGS, 'batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', (S, S), NO_ARGS, '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', (1, 1), NO_ARGS, '1x1', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_matrix(S), NO_ARGS, 'symmetric', (),
            NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_psd_matrix(S),
            NO_ARGS, 'symmetric_psd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_pd_matrix(S),
            NO_ARGS, 'symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_square_matrix_of_rank(S, S - 2),
            NO_ARGS, 'dim2_null', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_square_matrix_of_rank(S, 1), NO_ARGS, 'rank1', (),
            NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_square_matrix_of_rank(S, 2), NO_ARGS, 'rank2', (),
            NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S), NO_ARGS,
         'distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', (3, 3, S, S), NO_ARGS, 'batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', (3, 3, 1, 1), NO_ARGS, 'batched_1x1', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_matrix(S, 3),
            NO_ARGS, 'batched_symmetric', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_psd_matrix(S, 3),
            NO_ARGS, 'batched_symmetric_psd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_symmetric_pd_matrix(S, 3),
            NO_ARGS, 'batched_symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('det', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3, 3), NO_ARGS,
         'batched_distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        # For `logdet` and `slogdet`, the function at det=0 is not smooth.
        # We need to exclude tests with det=0 (e.g. dim2_null, rank1, rank2) and use
        # `make_nonzero_det` to make the random matrices have nonzero det. For
        # `logdet`, we also set `make_nonzero_det(matrix, sign=1)` to make the
        # matrix have positive det.
        ('logdet', lambda dtype, device: make_nonzero_det(torch.randn(S, S), 1),
            NO_ARGS, '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(torch.randn(1, 1), 1),
            NO_ARGS, '1x1', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_symmetric_matrix(S), 1), NO_ARGS,
         'symmetric', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_symmetric_pd_matrix(S), 1), NO_ARGS,
         'symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_fullrank_matrix_distinct_singular_value(S), 1, 0), NO_ARGS,
         'distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(torch.randn(3, 3, S, S), 1),
            NO_ARGS, 'batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(torch.randn(3, 3, 1, 1), 1),
            NO_ARGS, 'batched_1x1', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_symmetric_matrix(S, 3), 1), NO_ARGS,
         'batched_symmetric', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_symmetric_pd_matrix(S, 3), 1), NO_ARGS,
         'batched_symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('logdet', lambda dtype, device: make_nonzero_det(random_fullrank_matrix_distinct_singular_value(S, 3), 1, 0), NO_ARGS,
         'batched_distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(1, 1), 1), NO_ARGS,
         '1x1_pos_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(1, 1), -1), NO_ARGS,
         '1x1_neg_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(S, S), 1), NO_ARGS,
         'pos_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(S, S), -1), NO_ARGS,
         'neg_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(random_symmetric_matrix(S)), NO_ARGS,
         'symmetric', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: random_symmetric_pd_matrix(S), NO_ARGS,
         'symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S), NO_ARGS,
         'distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(3, 3, 1, 1), -1), NO_ARGS,
         'batched_1x1_neg_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(torch.randn(3, 3, S, S), 1), NO_ARGS,
         'batched_pos_det', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: make_nonzero_det(random_symmetric_matrix(S, 3)), NO_ARGS,
         'batched_symmetric', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: random_symmetric_pd_matrix(S, 3), NO_ARGS,
         'batched_symmetric_pd', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('slogdet', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3), NO_ARGS,
         'batched_distinct_singular_values', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], itemgetter(1)),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S),
            NO_ARGS, '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S)[:(S - 2)], NO_ARGS,
         'wide', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S)[:, :(S - 2)], NO_ARGS,
         'tall', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S)[:(S - 2)], (False,),
         'wide_all', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], lambda usv: (usv[0], usv[1], usv[2][:, :(S - 2)])),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S)[:, :(S - 2)], (False,),
         'tall_all', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma], lambda usv: (usv[0][:, :(S - 2)], usv[1], usv[2])),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(M), NO_ARGS,
         'large', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3), NO_ARGS,
         'batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3)[..., :(S - 2), :], NO_ARGS,
         'wide_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3)[..., :, :(S - 2)], NO_ARGS,
         'tall_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3, 3)[..., :(S - 2), :], (False,),
         'wide_all_batched', (), NO_ARGS,
         [skipCPUIfNoLapack, skipCUDAIfNoMagma], lambda usv: (usv[0], usv[1], usv[2][..., :, :(S - 2)])),
        ('svd', lambda dtype, device: random_fullrank_matrix_distinct_singular_value(S, 3, 3)[..., :, :(S - 2)], (False,),
         'tall_all_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma],
         lambda usv: (usv[0][..., :, :(S - 2)], usv[1], usv[2])),
        ('qr', (S, S), (False,), 'square_single', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (S, S - 2), (True,), 'tall_single' , (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (S - 2, S), (False,), 'wide_single' , (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, S, S), (False,), 'square_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, S, S - 2), (True,), 'tall_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, S - 2, S), (True,), 'wide_batched' , (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, 2, S, S), (False,), 'square_many_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, 2, S, S - 2), (True,), 'tall_many_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('qr', (3, 2, S - 2, S), (True,), 'wide_many_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (S, S), (True, False), 'square_single_no_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (S, S), (True, True), 'square_single_with_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (3, S, S), (True, False), 'square_batch_no_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (3, S, S), (True, True), 'square_batch_with_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (3, 3, S, S), (True, False), 'square_many_batches_no_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('lu', (3, 3, S, S), (True, True), 'square_many_batches_with_info', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('solve', (S, S), (lambda dtype, device: random_fullrank_matrix_distinct_singular_value(
            S, silent=True, dtype=dtype, device=device),), '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('solve', (S, S, S),
            (lambda dtype, device:
                random_fullrank_matrix_distinct_singular_value(S, S, silent=True, dtype=dtype, device=device),),
         'batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('solve', (2, 3, S, S),
            (lambda dtype, device:
                random_fullrank_matrix_distinct_singular_value(S, 2, 3, silent=True, dtype=dtype, device=device),),
         'batched_dims', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('solve', (2, 2, S, S),
            (lambda dtype, device:
                random_fullrank_matrix_distinct_singular_value(S, 1, silent=True, dtype=dtype, device=device),),
         'batched_broadcast_A', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('solve', (1, S, S),
            (lambda dtype, device:
                random_fullrank_matrix_distinct_singular_value(S, 2, 2, silent=True, dtype=dtype, device=device),),
         'batched_broadcast_b', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('fill_', (S, S, S), (1,), 'number'),
        ('fill_', (), (1,), 'number_scalar'),
        ('fill_', (S, S, S), ((),), 'variable'),
        ('eq_', (S, S, S), ((S, S, S),)),
        ('eq_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('eq_', (), ((),), 'scalar'),
        ('eq_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('ne_', (S, S, S), ((S, S, S),)),
        ('ne_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('ne_', (), ((),), 'scalar'),
        ('ne_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('gt_', (S, S, S), ((S, S, S),)),
        ('gt_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('gt_', (), ((),), 'scalar'),
        ('gt_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('ge_', (S, S, S), ((S, S, S),)),
        ('ge_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('ge_', (), ((),), 'scalar'),
        ('ge_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('lt_', (S, S, S), ((S, S, S),)),
        ('lt_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('lt_', (), ((),), 'scalar'),
        ('lt_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('le_', (S, S, S), ((S, S, S),)),
        ('le_', (S, S, S), ((1,),), 'broadcast_rhs'),
        ('le_', (), ((),), 'scalar'),
        ('le_', (S, S, S), ((),), 'scalar_broadcast_rhs'),
        ('eq_', (S, S, S), (0,), 'pyscalar'),
        ('ne_', (S, S, S), (0,), 'pyscalar'),
        ('gt_', (S, S, S), (0,), 'pyscalar'),
        ('ge_', (S, S, S), (0,), 'pyscalar'),
        ('le_', (S, S, S), (0,), 'pyscalar'),
        ('lt_', (), (0,), 'pyscalar'),
        ('eq_', (), (0,), 'pyscalar_scalar'),
        ('ne_', (), (0,), 'pyscalar_scalar'),
        ('gt_', (), (0,), 'pyscalar_scalar'),
        ('ge_', (), (0,), 'pyscalar_scalar'),
        ('lt_', (), (0,), 'pyscalar_scalar'),
        ('le_', (), (0,), 'pyscalar_scalar'),
        ('permute', (1, 2, 3, 4), (0, 2, 3, 1), '', (True,)),
        ('permute', (1, 2, 3, 4), (0, -2, -1, 1), 'neg_dim', (True,)),
        ('permute', (), (dont_convert(()),), 'scalar', (True,)),
        ('select', (S, S, S), (1, 2), 'dim', (), [0]),
        ('select', (S, S, S), (1, -1), 'wrap_dim', (), [0]),
        ('select', (S,), (0, 2), '1d'),
        ('narrow', (S, S, S), (1, 2, 2), 'dim', (), [0]),
        ('narrow', (S, S, S), (1, 0, 0), 'empty_dim', (), [0]),
        ('squeeze', (S, 1, S, 1), NO_ARGS, '', (True,)),
        ('squeeze', (1, 1, 1, 1), NO_ARGS, 'input_sizes_are_ones', (True,)),
        ('squeeze', (S, 1, S, 1), (1,), '1_dim', (True,), [0]),
        ('squeeze', (S, 1, S, 1), (2,), 'not_1_dim', (True,), [0]),
        ('squeeze', (), (0,), 'scalar', (True,), [0]),
        ('unsqueeze', (S, S, S), (0,), 'first', (True,), [0]),
        ('unsqueeze', (S, S, S), (1,), 'middle', (True,), [0]),
        ('unsqueeze', (S, S, S), (3,), 'last', (True,), [0]),
        ('unsqueeze', (), (0,), 'scalar', (True,), [0]),
        ('chunk', (S, S, S), (2,), '', (True, 'prim::ConstantChunk')),
        ('chunk', (S, S, S), (S, 1), 'dim', (True, 'prim::ConstantChunk'), [1]),
        ('split', (S, S, S), (2,), '', (True,)),
        ('split', (S, S, S), (S, 1), 'dim', (True,), [1]),
        ('split', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'size_list',
            (True, 'aten::split_with_sizes')),
        ('split', (S, S, S), ([int(S / 2), S - int(S / 2) * 2, int(S / 2)], 2), 'size_list_dim',
            (True, 'aten::split_with_sizes'), [1]),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), '', (True,)),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3), 0],), 'size_0', (True, )),
        ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'dim', (True, ), [1]),
        ('tensor_split', (S, S, S), (3,), 'sections', (False,)),
        ('tensor_split', (S, S, S), (3, 1), 'sections_dim', (False,), [1]),
        ('tensor_split', (S, S, S), ([2, 4],), 'indices', (False,)),
        ('tensor_split', (S, S, S), ([2, 4], 1), 'indices_dim', (False,), [1]),
        ('gather', (M, S), (0, gather_variable((S, S), 1, M, True)), 'dim0', (), [0]),
        ('gather', (M, S), (1, gather_variable((M, S // 2), 0, S, True)), 'dim1', (), [0]),
        ('gather', (), (0, torch.tensor([0], dtype=torch.int64)), 'scalar_input', (), [0]),
        ('gather', (S,), (0, torch.tensor(0, dtype=torch.int64)), 'scalar_index', (), [0]),
        ('gather', (), (0, torch.tensor(0, dtype=torch.int64)), 'scalar_both', (), [0]),
        ('scatter', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'dim0', (), [0]),
        ('scatter', (M, S), (1, gather_variable((M, S // 2), 0, S), (M, S // 2)), 'dim1', (), [0]),
        ('scatter', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalartensor_all_dim0', (), [0]),
        ('scatter', (), (0, torch.tensor(0, dtype=torch.int64), 2.5), 'scalar_all_dim0', (), [0]),
        ('scatter_add', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'dim0', (), [0]),
        ('scatter_add', (M, S), (1, gather_variable((M, S // 2), 0, S), (M, S // 2)), 'dim1', (), [0]),
        ('scatter_add', (), (0, torch.tensor(0, dtype=torch.int64), ()), 'scalar_all_dim0', (), [0]),
        ('scatter_add', (M, S), (0, gather_variable((S, S), 1, M), (S, S)), 'alert_nondeterministic', (), [0],
            [expectedAlertNondeterministic('scatter_add_cuda_kernel', 'cuda')]),
        ('masked_select', (M, M), (mask_not_all_zeros((M, M)),)),
        ('masked_select', (M, M), (mask_not_all_zeros((M,)),), 'broadcast_rhs'),
        ('masked_select', (M,), (mask_not_all_zeros((M, M)),), 'broadcast_lhs'),
        ('masked_select', (M, 1, M), (mask_not_all_zeros((M, M)),),
         'broadcast_all'),
        ('masked_select', (), (torch.tensor(1, dtype=torch.bool),), 'scalar'),
        ('masked_select', (M, M), (torch.tensor(1, dtype=torch.bool),), 'scalar_broadcast_rhs'),
        ('masked_select', (), (mask_not_all_zeros((M, M)),), 'scalar_broadcast_lhs'),
        ('masked_fill', (M, M), (torch.BoolTensor(M, M).bernoulli_(), 10)),
        ('masked_fill', (M, M), (torch.BoolTensor(M, M).bernoulli_(), ()), 'tensor'),
        ('masked_fill', (M,), (torch.BoolTensor(M, M).bernoulli_(), 10), 'broadcast_lhs'),
        ('masked_fill', (M, M), (torch.BoolTensor(M,).bernoulli_(), 10), 'broadcast_rhs'),
        ('masked_fill', (), (torch.tensor(0, dtype=torch.bool).bernoulli_(), 10), 'scalar'),
        ('masked_fill', (), (torch.tensor(0, dtype=torch.bool).bernoulli_(), ()),
         'scalar_variable'),
        ('masked_fill', (M, M), (torch.tensor(0, dtype=torch.bool).bernoulli_(), 10),
         'scalar_broadcast_rhs'),
        ('masked_scatter', (M, M), (torch.BoolTensor(M, M).bernoulli_(), (M, M))),
        ('masked_scatter', (M,), (torch.BoolTensor(M, M).bernoulli_(), (M, M)),
         'broadcast_lhs'),
        ('masked_scatter', (M, M), (torch.BoolTensor(M,).bernoulli_(), (M, M)),
         'broadcast_rhs'),
        ('masked_scatter', (M, M), (bernoulli_scalar(), (M, M)), 'scalar'),
        ('masked_scatter', (M, M), (bernoulli_scalar(), (M, M)),
         'scalar_broadcast_rhs'),
        ('maximum', (S, S), ((S, S),)),
        ('minimum', (S, S), ((S, S),)),
        ('resize_', (S, S, S), (torch.Size([S * S, S])), 'fewer_dims'),
        ('resize_', (), (dont_convert(()),), 'scalar'),
        ('resize_', (), (torch.Size([1, 1, 1])), 'scalar_to_dims'),
        ('resize_as_', (), (non_differentiable(torch.tensor(5.)),), 'scalar'),
        ('resize_as_', (), (non_differentiable(torch.randn((1, 1, 1))),), 'scalar_to_dims'),
        ('resize_as_', (S, S, S), (non_differentiable(torch.randn(S * S, S)),)),
        ('sort', (S, M, S), NO_ARGS),
        ('sort', (S, M, S), (1,), 'dim'),
        ('sort', (S, M, S), (1, True), 'dim_desc'),
        ('sort', (), NO_ARGS, 'scalar'),
        ('sort', (), (0,), 'dim_scalar'),
        ('sort', (), (0, True), 'dim_desc_scalar'),
        ('msort', (S, M, S), NO_ARGS),
        ('topk', (S, M, S), (3,)),
        ('topk', (S, M, S), (3, 1), 'dim', (), [1]),
        ('topk', (S, M, S), (3, 1, True), 'dim_desc', (), [1]),
        ('topk', (S, M, S), (3, 1, True, True), 'dim_desc_sort', (), [1]),
        ('topk', (), (1,), 'scalar'),
        ('topk', (), (1, 0), 'dim_scalar', (), [1]),
        ('topk', (), (1, 0, True), 'dim_desc_scalar', (), [1]),
        ('topk', (), (1, 0, True, True), 'dim_desc_sort_scalar', (), [1]),
        ('take', (S, S, S), (torch.LongTensor([[-3, 2], [20, 2]]),)),
        ('take', (S, S, S), (torch.tensor(0, dtype=torch.int64),), 'scalar_index'),
        ('take', (), (torch.LongTensor([0]),), 'scalar_data'),
        ('take', (), (torch.tensor(0, dtype=torch.int64),), 'scalar_both'),
        ('where', (M, M), (mask_not_all_zeros((M, M)), (M, M)), '', (True,)),
        ('where', (M, 1, M), (mask_not_all_zeros((M, M)), (M, M, 1)), 'broadcast_all', (True,)),
        ('where', (), (bernoulli_scalar(), ()), 'scalar', (True,)),
        ('where', (M, 1, M), (bernoulli_scalar(), (M, M, 1)), 'scalar_broadcast_mask', (True,)),
        ('where', (), (mask_not_all_zeros((M, M)), ()), 'scalar_broadcast_non_mask', (True,)),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([1, 2]),)),
        ('__getitem__', torch.randn(S, S, S), (slice(0, 3),), 'slice'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([slice(0, 3), 1]),), 'slice_index'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 2, 3], [1, 3, 3], [0, 0, 2]]),), 'adv_index'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 0, 3], [1, 1, 3], [0, 0, 2]]),), 'adv_index_dup'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([slice(None), slice(None), [0, 3]]),), 'adv_index_end'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([slice(None), [0, 3], slice(None)]),), 'adv_index_mid'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 3], slice(None), slice(None)]),), 'adv_index_beg'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 3], [1, 2], slice(None)]),), 'adv_index_comb'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 3], ]),), 'adv_index_sub'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 3], slice(None)]),), 'adv_index_sub_2'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 3], Ellipsis]),), 'adv_index_sub_3'),
        ('__getitem__', torch.randn(S, S, S), (dont_convert([[0, 2, 3], [1, 3, 3],
                                                             torch.LongTensor([0, 0, 2])]),), 'adv_index_var'),
        ('to_sparse', (S, S), (), '', (), (), [], lambda x: x.to_dense()),
        ('triangular_solve', (S, M), ((S, S), ), '', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
        ('kron', (S, S), ((M, L),))
    ]

def create_input(call_args, requires_grad=True, non_contiguous=False, call_kwargs=None, dtype=torch.double, device=None):
    if not isinstance(call_args, tuple):
        call_args = (call_args,)

    def map_arg(arg):
        def maybe_non_contig(tensor):
            return tensor if not non_contiguous else make_non_contiguous(tensor)

        if isinstance(arg, torch.Size) or isinstance(arg, dont_convert):
            return arg
        elif isinstance(arg, tuple) and len(arg) == 0:
            var = torch.randn((), dtype=dtype, device=device)
            var.requires_grad = requires_grad
            return var
        elif isinstance(arg, tuple) and not isinstance(arg[0], torch.Tensor):
            return Variable(maybe_non_contig(torch.randn(*arg, dtype=dtype, device=device)), requires_grad=requires_grad)
        # double check casting
        elif isinstance(arg, non_differentiable):
            if isinstance(arg.tensor, torch.Tensor):
                return maybe_non_contig(arg.tensor.to(device=device))
            return maybe_non_contig(arg.tensor.to(device=device))
        elif isinstance(arg, torch.Tensor):
            if arg.dtype == torch.float:
                arg = arg.double()
            if arg.dtype == torch.cfloat:
                arg = arg.to(torch.cdouble)
            if arg.is_complex() != dtype.is_complex:
                raise RuntimeError("User provided tensor is real for a test that runs with complex dtype, ",
                                   "which is not supported for now")
            # NOTE: We do clone() after detach() here because we need to be able to change size/storage of v afterwards
            v = maybe_non_contig(arg).detach().to(device=device).clone()
            v.requires_grad = requires_grad and (v.is_floating_point() or v.is_complex())
            return v
        elif callable(arg):
            return map_arg(arg(dtype=dtype, device=device))
        else:
            return arg
    args_out = tuple(map_arg(arg) for arg in call_args)
    kwargs_out = {k: map_arg(v) for k, v in call_kwargs.items()} if call_kwargs else {}
    return args_out, kwargs_out


def _compare_trilu_indices(
        self, row, col, offset=0, dtype=torch.long, device='cpu'):
    if row == 0 or col == 0:
        # have to handle this separately as tril and triu does not take
        # empty matrix as input
        self.assertEqual(
            torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))

        self.assertEqual(
            torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
            torch.triu_indices(row, col, offset, dtype=dtype, device=device))

    else:
        # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
        self.assertEqualIgnoreType(
            torch.ones(row, col, device='cpu')
                 .tril(offset).nonzero().to(dtype).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))

        # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
        self.assertEqualIgnoreType(
            torch.ones(row, col, device='cpu')
                 .tril(offset).nonzero().to(dtype).transpose(0, 1),
            torch.tril_indices(row, col, offset, dtype=dtype, device=device))


def _compare_large_trilu_indices(
        self, row, col, offset=0, dtype=torch.long, device='cpu'):
    l = torch.ones(row, col, dtype=dtype, device='cpu').tril(offset) \
             .nonzero()[-100:-1, :].transpose(0, 1).to(device)
    torch.cuda.empty_cache()

    r = torch.tril_indices(
        row, col, offset, dtype=dtype, device=device)[:, -100:-1]
    self.assertEqual(l, r)
    torch.cuda.empty_cache()

    l = torch.ones(row, col, dtype=dtype, device='cpu').triu(offset) \
             .nonzero()[-100:-1, :].transpose(0, 1).to(device)
    torch.cuda.empty_cache()

    r = torch.triu_indices(
        row, col, offset, dtype=dtype, device=device)[:, -100:-1]
    self.assertEqual(l, r)
    torch.cuda.empty_cache()

# (
#   row
#   col
#   offset (optional)
#   dtype (optional)
# )
tri_tests_args = [
    (1, 1),
    (3, 3),
    (3, 3, 1),
    (3, 3, 2),
    (3, 3, 200),
    (3, 3, -1),
    (3, 3, -2),
    (3, 3, -200),
    (0, 3, 0),
    (0, 3, 1),
    (0, 3, -1),
    (3, 0, 0),
    (3, 0, 1),
    (3, 0, -1),
    (0, 0, 0),
    (0, 0, 1),
    (0, 0, -1),
    (3, 6, 0),
    (3, 6, 1),
    (3, 6, 3),
    (3, 6, 9),
    (3, 6, -1),
    (3, 6, -3),
    (3, 6, -9),
    (6, 3, 0),
    (6, 3, 1),
    (6, 3, 3),
    (6, 3, 9),
    (6, 3, -1),
    (6, 3, -3),
    (6, 3, -9),
    (258, 253, 1, torch.float32),
    (257, 258, 1, torch.float64),
    (258, 258, 1, torch.short),
    (3, 513, 1, torch.long),
    (513, 3, 1, torch.int),
    (513, 0, 1, torch.double),
    (1024, 1024),
    (1024, 1024, 500, torch.float32),
    (1024, 1024, 1023),
    (1024, 1024, -500),
    (1023, 1025),
    (1025, 1023, 1022),
    (1024, 1024, -500),
    (3, 2028),
    (3, 2028, 1),
    (3, 2028, -1),
    (2028, 3),
    (2028, 1),
    (2028, 1, -1)
]

tri_large_tests_args: List[Tuple[int, ...]] = [
    # Large test cases below are deliberately commented out to speed up CI
    # tests and to avoid OOM error. When modifying implementations of
    # tril_indices and triu_indices, please enable these tests and make sure
    # they pass.
    #
    # (1, 268435455),
    # (5000, 5000),
    # (10000, 10000),
    # (268435455, 1),
    # (134217727, 2, 1),
    # (2, 134217727, 1),
    # (536870901, 1),
    # (1, 536870901),
    # (268435455, 2, 1),
    # (2, 268435455, 1)
]


def run_additional_tri_tests(self, device):
    x = torch.ones(
        3, 3, dtype=torch.long, device=device, layout=torch.strided)
    l = x.tril(0).nonzero().transpose(0, 1)
    u = x.triu(0).nonzero().transpose(0, 1)
    self.assertEqual(l, torch.tril_indices(3, 3, device=device))
    self.assertEqual(
        l, torch.tril_indices(3, 3, device=device, layout=torch.strided))

    self.assertEqual(u, torch.triu_indices(3, 3, device=device))
    self.assertEqual(
        u, torch.triu_indices(3, 3, device=device, layout=torch.strided))

    self.assertRaises(
        RuntimeError,
        lambda: torch.triu_indices(
            1, 1, device=device, layout=torch.sparse_coo))

    self.assertRaises(
        RuntimeError,
        lambda: torch.tril_indices(
            1, 1, device=device, layout=torch.sparse_coo))


def unpack_variables(args):
    if istuple(args):
        return tuple(unpack_variables(elem) for elem in args)
    else:
        return args


EXCLUDE_FUNCTIONAL = {
    'addmm',
    'addmm_',
    'addbmm',
    'baddbmm',
    'addmv',
    'addmv_',
    'addr',
    'addr_',
    'reshape',
    'where'  # argument order
}
EXCLUDE_GRADCHECK: Dict[str, Any] = {
}
EXCLUDE_GRADGRADCHECK: Dict[str, Any] = {
}
EXCLUDE_GRADGRADCHECK_BY_TEST_NAME = {
    # *det methods uses svd in backward when matrix is not invertible. However,
    # svd backward is unstable unless the matrix has positive distinct singular
    # values. Generated random matrices satisfy this with high probability, but
    # we can't rely on it. So only test gradgrad on invertible test cases and
    # _distinct_singular_values.
    'test_det',
    'test_det_1x1',
    'test_det_symmetric',
    'test_det_symmetric_psd',
    'test_det_dim2_null',
    'test_det_rank1',
    'test_det_rank2',
    'test_det_batched',
    'test_det_batched_1x1',
    'test_det_batched_symmetric',
    'test_det_batched_symmetric_psd',
    # `other` expand_as(self, other) is not used in autograd.
    'test_expand_as',
    'test_logdet',
    'test_logdet_1x1',
    'test_logdet_symmetric',
    'test_logdet_batched',
    'test_logdet_batched_1x1',
    'test_logdet_batched_symmetric',
    'test_slogdet_1x1_neg_det',
    'test_slogdet_neg_det',
    'test_slogdet_symmetric',
    'test_slogdet_batched_1x1_neg_det',
    'test_slogdet_batched_symmetric',
    'test_cdist',
}


def exclude_tensor_method(name, test_name):
    # there are no tensor equivalents for these (inplace or out)
    exclude_all_tensor_method_by_test_name = {
        'test_slice',
        'test_where',
        'test_where_broadcast_all',
        'test_where_scalar',
        'test_where_scalar_broadcast_mask',
        'test_where_scalar_broadcast_non_mask',
        'test_var_mean_keepdim_dim_1d',
        'test_var_mean_keepdim_dim',
        'test_var_mean_dim_1d',
        'test_var_mean_dim',
        'test_var_mean',
        'test_std_mean_keepdim_dim_1d',
        'test_std_mean_keepdim_dim',
        'test_std_mean_dim_1d',
        'test_std_mean_dim',
        'test_std_mean',
        'test_view_as_complex',
        'test_view_as_real_complex',
        'test_real_complex',
        'test_imag_complex',
        'test_complex'
    }
    # there are no out-of-place tensor equivalents for these
    exclude_outplace_tensor_method = {
        'index_add',
        'index_copy',
        'index_fill',
        'masked_fill',
        'masked_scatter',
        'scatter',
        'scatter_add',
        'det',
    }
    if test_name in exclude_all_tensor_method_by_test_name:
        return True
    is_magic_method = name[:2] == '__' and name[-2:] == '__'
    is_inplace = name[-1] == "_" and not is_magic_method
    if not is_inplace and name in exclude_outplace_tensor_method:
        return True
    if 'fft.' in name:
        return True
    return False