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blas.py
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blas.py
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"""Ops and optimizations for using BLAS calls
BLAS = Basic Linear Algebra Subroutines
Learn more about BLAS here:
http://www.netlib.org/blas/blast-forum/
The standard BLAS libraries implement what is called "legacy BLAS" in that
document.
This documentation describes Aesara's BLAS optimization pipeline.
Where there is a discrepancy between how things do work and how they *should*
work, both aspects should be documented.
There are four kinds of BLAS Ops in Aesara:
- Python implementations (this file)
- SciPy-based (blas_scipy)
- C-based (blas_c)
- GPU-based (aesara.gpuarray)
Notes
-----
Unfortunately (because it's confusing) this file currently contains Ops
that contain both Python and C versions. I think it would be better to
move the C implementations to blas_c so that this file is pure Python.
-JB
Ops
===
GEMM: Dot22, Dot22Scalar, GemmRelated, Gemm
-------------------------------------------
The BLAS GEMM operation implements Z <- a X Y + b Z,
where Z, X and Y are matrices, and a and b are scalars.
Dot22 is a GEMM where a=1, b=0, and Z is allocated every time.
Dot22Scalar is a GEMM where b=0 and Z is allocated every time.
Gemm is a GEMM in all its generality.
In the future we can refactor the GemmRelated, Gemm, Dot22 and
Dot22Scalar Ops into a single Op. That new Op (Gemm2) is basically a
normal Gemm, but with an additional configuration variable that says
to ignore the input Z. Setting that configuration variable to True
would make Gemm2 equivalent to the current Dot22 and Dot22Scalar.
This would make the file a lot easier to read, and save a few hundred
lines of library, to say nothing of testing and documentation.
GEMV: Gemv
----------
The BLAS GEMV operation implements Z <- a X Y + b Z,
where X is a matrix, Y, and Z are vectors, and a and b are scalars.
GER: Ger
--------
The BLAS GER operation implements Z <- a X' Y + Z,
where X and Y are vectors, and matrix Z gets a rank-1 update.
Other Notable BLAS-related Ops
------------------------------
SYRK is another useful special case of GEMM. Particularly SYRK preserves
symmetry in the matrix that it updates. See how the linear-algebra module uses
symmetry hints before implementing this Op, so that this Op is compatible with
that system.
Optimizations
=============
The optimization pipeline works something like this:
1. identify dot22 from dot
2. identify gemm from dot22
3. identify dot22scalar from dot22 that are not gemm
4. specialize gemm to gemv where applicable
5. specialize gemm to ger where applicable
6. specialize dot22 -> gemv or ger where applicable
:note: GEMM is the most canonical BLAS signature that we deal with so far, it
would be good to turn most things into GEMM (dot, inner, outer, dot22,
dot22scalar), and then to specialize from gemm to the various other L2 and
L3 operations.
Identify Dot22
--------------
Numpy's dot supports arguments that are of any rank, and we should support that
too (just for compatibility). The BLAS optimizations work with Dot Ops whose
inputs are each either vector or matrix. So the first part of the optimization
pipeline is to transform qualifying Dot Ops to Dot22 Ops. Dot22 Ops may be
transformed further, but they will get implemented by a BLAS call.
More precisely, Dot nodes whose inputs are all vectors or matrices and whose
inputs both have the same dtype, and whose dtype is float or complex, become
Dot22. This is implemented in `local_dot_to_dot22`.
Identify Gemm from Dot22
------------------------
This is complicated, done in GemmOptimizer.
Identify Dot22Scalar from Dot22
-------------------------------
Dot22 Ops that remain after the GemmOptimizer is done have not
qualified as GEMM Ops. Still they might be scaled by a factor, in
which case we use Dot22Scalar which is like Gemm, but without the b
and the Z. In the future it would be good to merge this into the
GemmOptimizer.
Specialize Gemm to Gemv
-----------------------
If arguments to GEMM are dimshuffled vectors, then we can use GEMV
instead. This optimization is `local_gemm_to_gemv`.
"""
import copy
import logging
import os
import time
import numpy as np
import numpy.distutils
try:
import numpy.distutils.__config__ # noqa
except ImportError:
pass
from functools import reduce
from typing import Tuple, Union
import aesara.scalar
from aesara.compile.mode import optdb
from aesara.configdefaults import config
from aesara.graph.basic import Apply, view_roots
from aesara.graph.features import ReplacementDidNotRemoveError, ReplaceValidate
from aesara.graph.fg import InconsistencyError
from aesara.graph.op import COp, Op
from aesara.graph.opt import (
EquilibriumOptimizer,
GlobalOptimizer,
in2out,
inherit_stack_trace,
local_optimizer,
)
from aesara.graph.optdb import SequenceDB
from aesara.graph.params_type import ParamsType
from aesara.graph.utils import MethodNotDefined, TestValueError
from aesara.printing import FunctionPrinter, debugprint, pprint
from aesara.scalar import bool as bool_t
from aesara.tensor import basic as aet
from aesara.tensor.basic_opt import local_dimshuffle_lift
from aesara.tensor.blas_headers import blas_header_text, blas_header_version
from aesara.tensor.elemwise import DimShuffle, Elemwise
from aesara.tensor.exceptions import NotScalarConstantError
from aesara.tensor.math import Dot, add, mul, neg, sub
from aesara.tensor.type import integer_dtypes, tensor, values_eq_approx_remove_inf_nan
from aesara.utils import memoize
_logger = logging.getLogger("aesara.tensor.blas")
try:
import scipy.linalg.blas
have_fblas = True
try:
fblas = scipy.linalg.blas.fblas
except AttributeError:
# A change merged in Scipy development version on 2012-12-02 replaced
# `scipy.linalg.blas.fblas` with `scipy.linalg.blas`.
# See http://github.com/scipy/scipy/pull/358
fblas = scipy.linalg.blas
_blas_gemv_fns = {
np.dtype("float32"): fblas.sgemv,
np.dtype("float64"): fblas.dgemv,
np.dtype("complex64"): fblas.cgemv,
np.dtype("complex128"): fblas.zgemv,
}
except ImportError as e:
have_fblas = False
# This is used in Gemv and ScipyGer. We use CGemv and CGer
# when config.blas__ldflags is defined. So we don't need a
# warning in that case.
if not config.blas__ldflags:
_logger.warning(
"Failed to import scipy.linalg.blas, and "
"Aesara flag blas__ldflags is empty. "
"Falling back on slower implementations for "
"dot(matrix, vector), dot(vector, matrix) and "
f"dot(vector, vector) ({str(e)})"
)
# If check_init_y() == True we need to initialize y when beta == 0.
def check_init_y():
if check_init_y._result is None:
if not have_fblas:
check_init_y._result = False
y = float("NaN") * np.ones((2,))
x = np.ones((2,))
A = np.ones((2, 2))
gemv = _blas_gemv_fns[y.dtype]
gemv(1.0, A.T, x, 0.0, y, overwrite_y=True, trans=True)
check_init_y._result = np.isnan(y).any()
return check_init_y._result
check_init_y._result = None
class Gemv(Op):
"""
expression is beta * y + alpha * A x
A is matrix
x, y are vectors
alpha, beta are scalars
output is a vector that can be inplace on y
"""
__props__ = ("inplace",)
def __init__(self, inplace):
self.inplace = inplace
if inplace:
self.destroy_map = {0: [0]}
def __str__(self):
if self.inplace:
return "%s{inplace}" % self.__class__.__name__
else:
return "%s{no_inplace}" % self.__class__.__name__
def make_node(self, y, alpha, A, x, beta):
y = aet.as_tensor_variable(y)
x = aet.as_tensor_variable(x)
A = aet.as_tensor_variable(A)
alpha = aet.as_tensor_variable(alpha)
beta = aet.as_tensor_variable(beta)
if y.dtype != A.dtype or y.dtype != x.dtype:
raise TypeError(
"Gemv requires matching dtypes", (y.dtype, A.dtype, x.dtype)
)
if A.ndim != 2:
raise TypeError("gemv requires matrix for A", A.type)
if x.ndim != 1:
raise TypeError("gemv requires vector for x", x.type)
if y.ndim != 1:
raise TypeError("gemv requires vector for y", y.type)
return Apply(self, [y, alpha, A, x, beta], [y.type()])
def perform(self, node, inputs, out_storage, params=None):
y, alpha, A, x, beta = inputs
if (
have_fblas
and y.shape[0] != 0
and x.shape[0] != 0
and y.dtype in _blas_gemv_fns
):
gemv = _blas_gemv_fns[y.dtype]
if A.shape[0] != y.shape[0] or A.shape[1] != x.shape[0]:
raise ValueError(
"Incompatible shapes for gemv "
f"(beta * y + alpha * dot(A, x)). y: {y.shape}, A: {A.shape}, x: {x.shape}"
)
if beta == 0 and check_init_y():
y.fill(0)
# Here I suppose that A is in c order. If we don't make it
# explicitly as fortran order, scipy 0.7.2 seam to create
# a copy in fortran order instead of just reshaping it
# and using the trans flag.
# If A is already in fortran order, make it in c order and using the
# trans flag don't seam to cause slowdown.
# out_storage[0][0] = gemv(alpha, A, x, beta, y,
# overwrite_y=self.inplace)
out_storage[0][0] = gemv(
alpha, A.T, x, beta, y, overwrite_y=self.inplace, trans=True
)
else:
out = np.dot(A, x)
if alpha != 1:
out *= alpha
if beta != 0:
if beta != 1:
out += beta * y
else:
out += y
out_storage[0][0] = np.asarray(out, dtype=y.dtype)
def infer_shape(self, fgraph, node, input_shapes):
return [input_shapes[0]]
gemv_no_inplace = Gemv(inplace=False)
gemv_inplace = Gemv(inplace=True)
# For the user interface. Opt will make them inplace later
gemv = gemv_no_inplace
class Ger(Op):
"""
BLAS defines general rank-1 update GER as A <- A + alpha x y'
for matrix A, scalar alpha, vectors x and y.
This interface to GER allows non-destructive operation on A via the
`destructive` argument to the constructor.
"""
__props__ = ("destructive",)
def __init__(self, destructive):
self.destructive = destructive
if destructive:
self.destroy_map = {0: [0]}
def __str__(self):
if self.destructive:
return "%s{destructive}" % self.__class__.__name__
else:
return "%s{non-destructive}" % self.__class__.__name__
def make_node(self, A, alpha, x, y):
A = aet.as_tensor_variable(A)
y = aet.as_tensor_variable(y)
x = aet.as_tensor_variable(x)
alpha = aet.as_tensor_variable(alpha)
if not (A.dtype == x.dtype == y.dtype == alpha.dtype):
raise TypeError(
"ger requires matching dtypes", (A.dtype, alpha.dtype, x.dtype, y.dtype)
)
if alpha.ndim != 0:
raise TypeError("ger requires scalar alpha", alpha.type)
if A.ndim != 2:
raise TypeError("ger requires matrix for A", A.type)
if x.ndim != 1:
raise TypeError("ger requires vector for x", x.type)
if y.ndim != 1:
raise TypeError("ger requires vector for y", y.type)
if x.dtype not in ("float32", "float64", "complex64", "complex128"):
raise TypeError("only float and complex types supported", x.dtype)
return Apply(self, [A, alpha, x, y], [A.type()])
def perform(self, node, inp, out, params=None):
cA, calpha, cx, cy = inp
(cZ,) = out
if self.destructive:
A = cA
else:
A = cA.copy()
if calpha != 1:
A += calpha * np.outer(cx, cy)
else:
A += np.outer(cx, cy)
cZ[0] = A
def infer_shape(self, fgraph, node, input_shapes):
return [input_shapes[0]]
ger = Ger(destructive=False)
ger_destructive = Ger(destructive=True)
def ldflags(libs=True, flags=False, libs_dir=False, include_dir=False):
"""Extract a list of compilation flags from config.blas__ldflags.
Depending on the options, different type of flags will be kept.
It returns a list of libraries against which an Op's object file
should be linked to benefit from a BLAS implementation.
Parameters
----------
libs : bool, optional
Extract flags starting with "-l" (the default is True).
libs_dir : bool, optional
Extract flags starting with "-L" (the default is False).
include_dir : bool, optional
Extract flags starting with "-I" (the default is False).
flags: bool, optional
Extract all the other flags (the default is False).
Returns
-------
list of strings
Extracted flags.
"""
ldflags_str = config.blas__ldflags
return _ldflags(
ldflags_str=ldflags_str,
libs=libs,
flags=flags,
libs_dir=libs_dir,
include_dir=include_dir,
)
@memoize
def _ldflags(ldflags_str, libs, flags, libs_dir, include_dir):
"""Extract list of compilation flags from a string.
Depending on the options, different type of flags will be kept.
Parameters
----------
ldflags_str : string
The string to process. Typically, this will be the content of
`config.blas__ldflags`.
libs : bool
Extract flags starting with "-l".
flags: bool
Extract all the other flags.
libs_dir: bool
Extract flags starting with "-L".
include_dir: bool
Extract flags starting with "-I".
Returns
-------
list of strings
Extracted flags.
"""
rval = []
if libs_dir:
found_dyn = False
dirs = [x[2:] for x in ldflags_str.split() if x.startswith("-L")]
l = _ldflags(
ldflags_str=ldflags_str,
libs=True,
flags=False,
libs_dir=False,
include_dir=False,
)
for d in dirs:
for f in os.listdir(d.strip('"')):
if f.endswith(".so") or f.endswith(".dylib") or f.endswith(".dll"):
if any([f.find(ll) >= 0 for ll in l]):
found_dyn = True
if not found_dyn and dirs:
_logger.warning(
"We did not find a dynamic library in the "
"library_dir of the library we use for blas. If you use "
"ATLAS, make sure to compile it with dynamics library."
)
for t in ldflags_str.split():
# Remove extra quote.
if (t.startswith("'") and t.endswith("'")) or (
t.startswith('"') and t.endswith('"')
):
t = t[1:-1]
try:
t0, t1, t2 = t[0:3]
assert t0 == "-"
except Exception:
raise ValueError(f'invalid token "{t}" in ldflags_str: "{ldflags_str}"')
if libs_dir and t1 == "L":
rval.append(t[2:])
elif include_dir and t1 == "I":
raise ValueError(
"Include dirs are not used for blas. We disable"
" this as this can hide other headers and this"
" is not wanted.",
t,
)
rval.append(t[2:])
elif libs and t1 == "l": # example -lmkl
rval.append(t[2:])
elif flags and t1 not in ["L", "I", "l"]: # example -openmp
rval.append(t)
elif flags and t1 == "L":
# to find it when we load the compiled op if the env of the
# used is not well configured.
rval.append("-Wl,-rpath," + t[2:])
return rval
class GemmRelated(COp):
"""Base class for Gemm and Dot22.
This class provides a kind of templated gemm Op.
"""
__props__: Union[Tuple, Tuple[str]] = ()
def c_support_code(self, **kwargs):
# return cblas_header_text()
mod_str = """
#ifndef MOD
#define MOD %
#endif
static double time_time() // a time function like time.time()
{
struct timeval tv;
gettimeofday(&tv, 0);
return (double) tv.tv_sec + (double) tv.tv_usec / 1000000.0;
}
"""
return blas_header_text() + mod_str
def c_headers(self, **kwargs):
# std.cout doesn't require the '%' symbol to print stuff...
# so it works much better with python's string-substitution stuff.
return ["<iostream>", "<time.h>", "<sys/time.h>"]
def c_libraries(self, **kwargs):
return ldflags()
# code_cache_version is built by subclasses from
# build_gemm_version
def c_compile_args(self, **kwargs):
return ldflags(libs=False, flags=True)
def c_lib_dirs(self, **kwargs):
return ldflags(libs=False, libs_dir=True)
def c_header_dirs(self, **kwargs):
return ldflags(libs=False, include_dir=True)
declare_NS = """
int unit = 0;
int type_num = PyArray_DESCR(%(_x)s)->type_num;
int type_size = PyArray_DESCR(%(_x)s)->elsize; // in bytes
npy_intp* Nx = PyArray_DIMS(%(_x)s);
npy_intp* Ny = PyArray_DIMS(%(_y)s);
npy_intp* Nz = 0; //PyArray_DIMS(%(_zout)s);
npy_intp* Sx = PyArray_STRIDES(%(_x)s);
npy_intp* Sy = PyArray_STRIDES(%(_y)s);
npy_intp* Sz = 0; //PyArray_STRIDES(%(_zout)s);
//strides for x, y, z in dimensions 0, 1
int sx_0, sx_1, sy_0, sy_1, sz_0, sz_1;
"""
# implement if you don't have an inplace props
# setup_z_Nz_Sz = None
# otherwise implement
# setup_z_Nz_Sz_inplace = None
# setup_z_Nz_Sz_outplace = None
check_xyz_rank2 = """
if (PyArray_NDIM(%(_x)s) != 2) {
PyErr_Format(PyExc_NotImplementedError,
"rank(x) != 2. rank(x) is %%d.",
PyArray_NDIM(%(_x)s));
%(fail)s;
}
if (PyArray_NDIM(%(_y)s) != 2) {
PyErr_Format(PyExc_NotImplementedError,
"rank(y) != 2. rank(y) is %%d.", PyArray_NDIM(%(_y)s));
%(fail)s;
}
if (%(_zout)s && PyArray_NDIM(%(_zout)s) != 2) {
PyErr_Format(PyExc_NotImplementedError,
"rank(z) != 2. rank(z) is %%d.", PyArray_NDIM(%(_zout)s));
%(fail)s;
}
"""
check_xyz_double_or_float = """
if ((PyArray_DESCR(%(_x)s)->type_num != NPY_DOUBLE)
&& (PyArray_DESCR(%(_x)s)->type_num != NPY_FLOAT))
{PyErr_SetString(PyExc_NotImplementedError, "type(x) is not double or float"); %(fail)s;}
if ((PyArray_DESCR(%(_y)s)->type_num != NPY_DOUBLE)
&& (PyArray_DESCR(%(_y)s)->type_num != NPY_FLOAT))
{PyErr_SetString(PyExc_NotImplementedError, "type(y) is not double or float"); %(fail)s;}
if ((PyArray_DESCR(%(_zout)s)->type_num != NPY_DOUBLE)
&& (PyArray_DESCR(%(_zout)s)->type_num != NPY_FLOAT))
{PyErr_SetString(PyExc_NotImplementedError, "type(z) is not double or float"); %(fail)s;}
if ((PyArray_DESCR(%(_x)s)->type_num != PyArray_DESCR(%(_y)s)->type_num)
||(PyArray_DESCR(%(_x)s)->type_num != PyArray_DESCR(%(_zout)s)->type_num))
{ PyErr_SetString(PyExc_NotImplementedError, "type(x), type(y), type(z) are not all the same"); %(fail)s; }
"""
# it is not necessary that a or b have the same type as x,y,z
check_ab_double_or_float = """
if ((PyArray_DESCR(%(_a)s)->type_num != NPY_DOUBLE)
&& (PyArray_DESCR(%(_a)s)->type_num != NPY_FLOAT))
{PyErr_SetString(PyExc_NotImplementedError, "type(a) is not double or float"); %(fail)s;}
if ((PyArray_DESCR(%(_b)s)->type_num != NPY_DOUBLE)
&& (PyArray_DESCR(%(_b)s)->type_num != NPY_FLOAT))
{PyErr_SetString(PyExc_NotImplementedError, "type(b) is not double or float"); %(fail)s;}
"""
check_dims = """
if (Nx[0] != Nz[0])
{
PyErr_Format(PyExc_ValueError,
"Shape mismatch: x has %%ld rows but z has %%ld rows",
(long int)Nx[0], (long int)Nz[0]);
%(fail)s;
}
if (Nx[1] != Ny[0])
{
PyErr_Format(PyExc_ValueError,
"Shape mismatch: x has %%ld cols (and %%ld rows) but y has %%ld rows (and %%ld cols)",
(long int)Nx[1], (long int)Nx[0], (long int)Ny[0], (long int)Ny[1]);
%(fail)s;
}
if (Ny[1] != Nz[1])
{
PyErr_Format(PyExc_ValueError,
"Shape mismatch: y has %%ld cols but z has %%ld cols",
(long int)Ny[1], (long int)Nz[1]);
%(fail)s;
}
// We must not raise an error when Nx[1] == 0. This would disable cases
// that numpy.dot accept.
"""
check_strides = """
/*
If some matrices are not contiguous on either dimensions,
or have invalid strides, copy their content into a contiguous one
*/
if ((Sx[0] < 1) || (Sx[1] < 1) || (Sx[0] MOD type_size) || (Sx[1] MOD type_size)
|| ((Sx[0] != type_size) && (Sx[1] != type_size)))
{
PyArrayObject * _x_copy = (PyArrayObject *) PyArray_Copy(%(_x)s);
if (!_x_copy)
%(fail)s
Py_XDECREF(%(_x)s);
%(_x)s = _x_copy;
Sx = PyArray_STRIDES(%(_x)s);
}
if ((Sy[0] < 1) || (Sy[1] < 1) || (Sy[0] MOD type_size) || (Sy[1] MOD type_size)
|| ((Sy[0] != type_size) && (Sy[1] != type_size)))
{
PyArrayObject * _y_copy = (PyArrayObject *) PyArray_Copy(%(_y)s);
if (!_y_copy)
%(fail)s
Py_XDECREF(%(_y)s);
%(_y)s = _y_copy;
Sy = PyArray_STRIDES(%(_y)s);
}
if ((Sz[0] < 1) || (Sz[1] < 1) || (Sz[0] MOD type_size) || (Sz[1] MOD type_size)
|| ((Sz[0] != type_size) && (Sz[1] != type_size)))
{
PyArrayObject * _z_copy = (PyArrayObject *) PyArray_Copy(%(_zout)s);
if (!_z_copy)
%(fail)s
Py_XDECREF(%(_zout)s);
%(_zout)s = _z_copy;
Sz = PyArray_STRIDES(%(_zout)s);
}
"""
encode_strides_in_unit = """
/*
encode the stride structure of _x,_y,_zout into a single integer
*/
unit |= ((Sx[1] == type_size || Nx[1]==1) ? 0x0 : (Sx[0] == type_size || Nx[0]==1) ? 0x1 : 0x2) << 8;
unit |= ((Sy[1] == type_size || Ny[1]==1) ? 0x0 : (Sy[0] == type_size || Ny[0]==1) ? 0x1 : 0x2) << 4;
unit |= ((Sz[1] == type_size || Nz[1]==1) ? 0x0 : (Sz[0] == type_size || Nz[0]==1) ? 0x1 : 0x2) << 0;
"""
compute_strides = """
/* create appropriate strides for malformed matrices that are row or column
* vectors, or empty matrices.
* In that case, the value of the stride does not really matter, but
* some versions of BLAS insist that:
* - they are not smaller than the number of elements in the array,
* - they are not 0.
*/
sx_0 = (Nx[0] > 1) ? Sx[0]/type_size : (Nx[1] + 1);
sx_1 = (Nx[1] > 1) ? Sx[1]/type_size : (Nx[0] + 1);
sy_0 = (Ny[0] > 1) ? Sy[0]/type_size : (Ny[1] + 1);
sy_1 = (Ny[1] > 1) ? Sy[1]/type_size : (Ny[0] + 1);
sz_0 = (Nz[0] > 1) ? Sz[0]/type_size : (Nz[1] + 1);
sz_1 = (Nz[1] > 1) ? Sz[1]/type_size : (Nz[0] + 1);
"""
begin_switch_typenum = """
switch (type_num)
{
"""
case_float = """
case NPY_FLOAT:
{
"""
# case_float_ab_constants = None
case_float_gemm = """
float* x = (float*)PyArray_DATA(%(_x)s);
float* y = (float*)PyArray_DATA(%(_y)s);
float* z = (float*)PyArray_DATA(%(_zout)s);
char N = 'N';
char T = 'T';
int Nz0 = Nz[0], Nz1 = Nz[1], Nx1 = Nx[1];
//std::cerr << (unit/256) MOD 16 << (unit / 16) MOD 16 << unit MOD 16<< '\\n';
//double t0 = time_time();
switch(unit)
{
case 0x000: sgemm_(&N, &N, &Nz1, &Nz0, &Nx1, &a, y, &sy_0, x, &sx_0, &b, z, &sz_0); break;
case 0x100: sgemm_(&N, &T, &Nz1, &Nz0, &Nx1, &a, y, &sy_0, x, &sx_1, &b, z, &sz_0); break;
case 0x010: sgemm_(&T, &N, &Nz1, &Nz0, &Nx1, &a, y, &sy_1, x, &sx_0, &b, z, &sz_0); break;
case 0x110: sgemm_(&T, &T, &Nz1, &Nz0, &Nx1, &a, y, &sy_1, x, &sx_1, &b, z, &sz_0); break;
case 0x001: sgemm_(&T, &T, &Nz0, &Nz1, &Nx1, &a, x, &sx_0, y, &sy_0, &b, z, &sz_1); break;
case 0x101: sgemm_(&N, &T, &Nz0, &Nz1, &Nx1, &a, x, &sx_1, y, &sy_0, &b, z, &sz_1); break;
case 0x011: sgemm_(&T, &N, &Nz0, &Nz1, &Nx1, &a, x, &sx_0, y, &sy_1, &b, z, &sz_1); break;
case 0x111: sgemm_(&N, &N, &Nz0, &Nz1, &Nx1, &a, x, &sx_1, y, &sy_1, &b, z, &sz_1); break;
default: PyErr_SetString(PyExc_ValueError, "some matrix has no unit stride"); %(fail)s;
};
//fprintf(stderr, "Calling sgemm %%i %%i %%i %%i took %%f\\n", unit, Nz1, Nz0, Nx1, time_time() - t0);
"""
case_double = """
}
break;
case NPY_DOUBLE:
{
"""
# case_double_ab_constants = None
case_double_gemm = """
double* x = (double*)PyArray_DATA(%(_x)s);
double* y = (double*)PyArray_DATA(%(_y)s);
double* z = (double*)PyArray_DATA(%(_zout)s);
char N = 'N';
char T = 'T';
int Nz0 = Nz[0], Nz1 = Nz[1], Nx1 = Nx[1];
//std::cerr << (unit/256) MOD 16 << (unit / 16) MOD 16 << unit MOD 16<< '\\n';
//double t0 = time_time();
//fprintf(stderr, "unit=%%x N= %%i %%i %%i S = %%i %%i %%i %%i %%i %%i\\n", unit,
//Nz1, Nz0, Nx1,
//sy_0, sy_1,
//sx_0, sx_1,
//sz_0, sz_1
//);
switch(unit)
{
case 0x000: dgemm_(&N, &N, &Nz1, &Nz0, &Nx1, &a, y,
&sy_0, x, &sx_0, &b, z, &sz_0); break;
case 0x100: dgemm_(&N, &T, &Nz1, &Nz0, &Nx1, &a, y,
&sy_0, x, &sx_1, &b, z, &sz_0); break;
case 0x010: dgemm_(&T, &N, &Nz1, &Nz0, &Nx1, &a, y,
&sy_1, x, &sx_0, &b, z, &sz_0); break;
case 0x110: dgemm_(&T, &T, &Nz1, &Nz0, &Nx1, &a, y,
&sy_1, x, &sx_1, &b, z, &sz_0); break;
case 0x001: dgemm_(&T, &T, &Nz0, &Nz1, &Nx1, &a, x,
&sx_0, y, &sy_0, &b, z, &sz_1); break;
case 0x101: dgemm_(&N, &T, &Nz0, &Nz1, &Nx1, &a, x,
&sx_1, y, &sy_0, &b, z, &sz_1); break;
case 0x011: dgemm_(&T, &N, &Nz0, &Nz1, &Nx1, &a, x,
&sx_0, y, &sy_1, &b, z, &sz_1); break;
case 0x111: dgemm_(&N, &N, &Nz0, &Nz1, &Nx1, &a, x,
&sx_1, y, &sy_1, &b, z, &sz_1); break;
default: PyErr_SetString(PyExc_ValueError,
"some matrix has no unit stride");
%(fail)s;
};
//fprintf(stderr, "Calling dgemm %%i %%i %%i %%i took %%f\\n",
// unit, Nz1, Nz0, Nx1, time_time()- t0);
"""
end_switch_typenum = """
}
break;
}
"""
def build_gemm_call(self):
if hasattr(self, "inplace"):
setup_z_Nz_Sz = "if(%(params)s->inplace){{{}}}else{{{}}}".format(
self.setup_z_Nz_Sz_inplace,
self.setup_z_Nz_Sz_outplace,
)
else:
setup_z_Nz_Sz = self.setup_z_Nz_Sz
return reduce(
str.__add__,
(
self.declare_NS,
self.check_xyz_rank2,
setup_z_Nz_Sz,
self.check_xyz_double_or_float,
self.check_ab_double_or_float,
self.check_dims,
self.check_strides,
self.encode_strides_in_unit,
self.compute_strides,
self.begin_switch_typenum,
self.case_float,
self.case_float_ab_constants,
self.case_float_gemm,
self.case_double,
self.case_double_ab_constants,
self.case_double_gemm,
self.end_switch_typenum,
),
"",
)
def build_gemm_version(self):
return (13, blas_header_version())
class Gemm(GemmRelated):
"""In-place version of matrix-matrix multiplication (with accumulation).
When a and b are scalars and x, y, and z are matrices, then
gemm(z,a,x,y,b)
is similar to
b*z + a*dot(x,y)
The difference between the two is that the top form is destructive
on z, whereas the bottom form is not. Gemm works in-place on the
storage associated with z, and the L{Variable} returned by Gemm
has a storage that will be aliased to the storage of the z
argument. Because of this in-place computation, an L{Apply} of
this op will destroy the L{Variable} z on which it operates. (See
L{DestructiveOps} for an explanation of what destroying means in
the context of aesara graphs. See L{BlasLapackSupport} for more
optimized linear algebra operations.)
"""
E_rank = "gemm only works for rank 2"
E_scalar = "gemm requires scalar argument"
E_z_uniq = "argument z aliased to x or y" # TODO: justify / delete this
E_mixed = "gemm requires matching dtypes"
E_float = "gemm requires floating-point dtypes"
__props__ = ("inplace",)
params_type = ParamsType(
inplace=bool_t,
)
check_input = False
def __init__(self, inplace):
self.inplace = inplace
if self.inplace:
self.destroy_map = {0: [0]}
def __str__(self):
if self.inplace:
inplace_str = "inplace"
else:
inplace_str = "no_inplace"
return f"{self.__class__.__name__}{{{inplace_str}}}"
def __setstate__(self, dct):
self.__dict__.update(dct)
# Correctly reload older pickles where destroy_map were not
# saved
if "destroy_map" not in self.__dict__ and self.inplace:
self.destroy_map = {0: [0]}
def __getstate__(self):
rval = self.__dict__.copy()
# Do not serialize the setup code, it will be restored in __setstate__
# depending on the value of 'inplace'
rval.pop("setup_z_Nz_Sz", None)
return rval
def make_node(self, *inputs):
inputs = list(map(aet.as_tensor_variable, inputs))
if len(inputs) != 5:
raise TypeError(
f"Wrong number of inputs for {self} (expected 5, got {len(inputs)})"
)
z, a, x, y, b = inputs
zr, xr, yr = [set(view_roots(i)) for i in (z, x, y)]
# We want the gemm to be inplace. When this op is inplace, it
# declare to be inplace only on z. So to make it safe, we
# raise an error if z can be a view on x or y.
# I don't know if Aesara currently can support that case. As
# this case don't happen in our code, I won't spent time
# investigating this. So the assert is for safety. I also
# think there is another mechanism that would prevent this,
# but I don't what to modify old code and have chance to break
# something.
if self.inplace:
if zr.intersection(xr):
raise InconsistencyError(Gemm.E_z_uniq, (z, x))
if zr.intersection(yr):
raise InconsistencyError(Gemm.E_z_uniq, (z, y))
if z.ndim != 2:
raise TypeError(Gemm.E_rank, z)
if a.ndim != 0:
raise TypeError(Gemm.E_scalar, a)
if x.ndim != 2:
raise TypeError(Gemm.E_rank, x)
if y.ndim != 2:
raise TypeError(Gemm.E_rank, y)
if b.ndim != 0:
raise TypeError(Gemm.E_scalar, b)
if not (z.dtype == a.dtype == x.dtype == y.dtype == b.dtype):
raise TypeError(Gemm.E_mixed, (z.dtype, a.dtype, x.dtype, y.dtype, b.dtype))
if not z.dtype.startswith("float") and not z.dtype.startswith("complex"):
raise TypeError(Gemm.E_float, (z.dtype))
output = z.type()
return Apply(self, inputs, [output])
def perform(self, node, inp, out, params):
z, a, x, y, b = inp
(zout,) = out
assert a.shape == ()
assert b.shape == ()
if not params.inplace:
z = z.copy() # the original z will not be changed
if z.shape == ():
z.itemset(z * a + b * np.dot(x, y))
zout[0] = z
else:
if b == 0.0:
if a == 1.0:
z[:] = np.dot(x, y)
elif a == -1.0:
z[:] = -np.dot(x, y)
else:
z[:] = a * np.dot(x, y)
elif b == 1.0:
if a == 1.0:
z += np.dot(x, y)
elif a == -1.0:
z -= np.dot(x, y)
else:
z += a * np.dot(x, y)
else:
z *= b
z += a * np.dot(x, y)
zout[0] = z
def infer_shape(self, fgraph, node, input_shapes):
return [input_shapes[0]]
setup_z_Nz_Sz_inplace = """
if (%(_zout)s != %(_z)s)
{
if (%(_zout)s)
{
Py_DECREF(%(_zout)s);
}
%(_zout)s = %(_z)s;
Py_INCREF(%(_zout)s);
}
Nz = PyArray_DIMS(%(_z)s);
Sz = PyArray_STRIDES(%(_z)s);
"""
setup_z_Nz_Sz_outplace = """
if ((NULL == %(_zout)s)
|| (PyArray_DIMS(%(_zout)s)[0] != PyArray_DIMS(%(_z)s)[0])
|| (PyArray_DIMS(%(_zout)s)[1] != PyArray_DIMS(%(_z)s)[1])
|| (PyArray_STRIDES(%(_zout)s)[0] <= 0)
|| (PyArray_STRIDES(%(_zout)s)[1] <= 0)
|| (PyArray_STRIDES(%(_zout)s)[0] MOD type_size)
|| (PyArray_STRIDES(%(_zout)s)[1] MOD type_size)