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提交 20ff202e authored 作者: Ricardo Vieira's avatar Ricardo Vieira 提交者： Ricardo Vieira
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Define all batched dot operations as matmul

New rewrite is added to convert unpaired batched row/column matvec or vec products as equivalent matmul products.
上级 e265debc
隐藏空白字符变更
内嵌 并排
正在显示 包含 282 行增加 和 105 行删除
pytensor/tensor/math.py
浏览文件 @ 20ff202e
......@@ -3921,23 +3921,7 @@ def logsumexp(x, axis=None, keepdims=False):
return log(sum(exp(x), axis=axis, keepdims=keepdims))
# Predefine all batched variations of Dot
_inner_prod = Blockwise(
_dot,
signature="(n),(n)->()",
)
_matrix_vec_prod = Blockwise(
_dot,
signature="(m,k),(k)->(m)",
)
_vec_matrix_prod = Blockwise(
_dot,
signature="(k),(k,n)->(n)",
)
_matrix_matrix_matmul = Blockwise(
_matmul = Blockwise(
_dot,
signature="(m,k),(k,n)->(m,n)",
gufunc_spec=("numpy.matmul", 2, 1),
......@@ -3993,11 +3977,11 @@ def matmul(x1: "ArrayLike", x2: "ArrayLike", dtype: Optional["DTypeLike"] = None
if x1.type.ndim == 1 and x2.type.ndim == 1:
out = _dot(x1, x2)
elif x1.type.ndim == 1:
out = _matrix_matrix_matmul(x1[None], x2).squeeze(-2)
out = vecmat(x1, x2)
elif x2.type.ndim == 1:
out = _matrix_matrix_matmul(x1, x2[:, None]).squeeze(-1)
out = matvec(x1, x2)
else:
out = _matrix_matrix_matmul(x1, x2)
out = _matmul(x1, x2)
if dtype is not None:
out = out.astype(dtype)
......@@ -4047,7 +4031,7 @@ def vecdot(
>>> z_batch = pt.vecdot(x_batch, y_batch) # shape (3,)
>>> # Equivalent to numpy.vecdot(x_batch, y_batch)
"""
out = _inner_prod(x1, x2)
out = matmul(x1[..., None, :], x2[..., :, None]).squeeze((-2, -1))
if dtype is not None:
out = out.astype(dtype)
......@@ -4096,7 +4080,7 @@ def matvec(
>>> result = pt.matvec(batched_A, batched_v) # shape (2, 3)
>>> # Equivalent to numpy.matvec(batched_A, batched_v)
"""
out = _matrix_vec_prod(x1, x2)
out = matmul(x1, x2[..., None]).squeeze(-1)
if dtype is not None:
out = out.astype(dtype)
......@@ -4134,18 +4118,18 @@ def vecmat(
--------
>>> import pytensor.tensor as pt
>>> # Vector-matrix product
>>> v = pt.vector("v", shape=(3,)) # shape (3,)
>>> A = pt.matrix("A", shape=(3, 4)) # shape (3, 4)
>>> v = pt.vector("v", shape=(3,))
>>> A = pt.matrix("A", shape=(3, 4))
>>> result = pt.vecmat(v, A) # shape (4,)
>>> # Equivalent to numpy.vecmat(v, A)
>>>
>>> # Batched vector-matrix product
>>> batched_v = pt.matrix("v", shape=(2, 3)) # shape (2, 3)
>>> batched_A = pt.tensor3("A", shape=(2, 3, 4)) # shape (2, 3, 4)
>>> batched_v = pt.matrix("v", shape=(2, 3))
>>> batched_A = pt.tensor3("A", shape=(2, 3, 4))
>>> result = pt.vecmat(batched_v, batched_A) # shape (2, 4)
>>> # Equivalent to numpy.vecmat(batched_v, batched_A)
"""
out = _vec_matrix_prod(x1, x2)
out = matmul(x2.mT, x1[..., None]).squeeze(-1)
if dtype is not None:
out = out.astype(dtype)
......@@ -4160,18 +4144,18 @@ def vectorize_node_dot(op, node, batched_x, batched_y):
old_y_ndim = old_y.type.ndim
match (old_x_ndim, old_y_ndim):
case (1, 1):
batch_op = _inner_prod
batch_fn = vecdot
case (2, 1):
batch_op = _matrix_vec_prod
batch_fn = matvec
case (1, 2):
batch_op = _vec_matrix_prod
batch_fn = vecmat
case (2, 2):
batch_op = _matrix_matrix_matmul
batch_fn = matmul
case _:
raise ValueError(
f"Core dot Op should have 1D or 2D inputs, got {old_x_ndim}D and {old_y_ndim}D."
)
return batch_op(batched_x, batched_y).owner
return batch_fn(batched_x, batched_y).owner
def nan_to_num(x, nan=0.0, posinf=None, neginf=None):
......
pytensor/tensor/rewriting/blas.py
浏览文件 @ 20ff202e
......@@ -98,7 +98,7 @@ from pytensor.tensor.elemwise import DimShuffle, Elemwise
from pytensor.tensor.exceptions import NotScalarConstantError
from pytensor.tensor.math import (
Dot,
_matrix_matrix_matmul,
_matmul,
add,
mul,
neg,
......@@ -908,7 +908,7 @@ blas_optdb.register(
@register_specialize
@node_rewriter([_matrix_matrix_matmul])
@node_rewriter([_matmul])
def specialize_matmul_to_batched_dot(fgraph, node):
"""Rewrite Matmul (Blockwise matrix-matrix) without implicit broadcasted batched dimension as BatchedDot.
......
pytensor/tensor/rewriting/elemwise.py
浏览文件 @ 20ff202e
......@@ -39,6 +39,7 @@ from pytensor.tensor.rewriting.basic import (
broadcasted_by,
register_canonicalize,
register_specialize,
register_stabilize,
)
from pytensor.tensor.variable import TensorConstant, TensorVariable
......@@ -341,6 +342,7 @@ def is_dimshuffle_useless(new_order, input):
@register_canonicalize
@register_stabilize
@register_specialize
@node_rewriter([DimShuffle])
def local_dimshuffle_lift(fgraph, node):
......
pytensor/tensor/rewriting/linalg.py
浏览文件 @ 20ff202e
......@@ -26,7 +26,7 @@ from pytensor.tensor.basic import (
from pytensor.tensor.blas import Dot22
from pytensor.tensor.blockwise import Blockwise
from pytensor.tensor.elemwise import DimShuffle, Elemwise
from pytensor.tensor.math import Dot, Prod, _matrix_matrix_matmul, log, outer, prod
from pytensor.tensor.math import Dot, Prod, _matmul, log, outer, prod
from pytensor.tensor.nlinalg import (
SVD,
KroneckerProduct,
......@@ -284,7 +284,7 @@ def cholesky_ldotlt(fgraph, node):
# This rewrite only applies to matrix Dot
and A.owner.inputs[0].type.ndim == 2
)
or (A.owner.op == _matrix_matrix_matmul)
or (A.owner.op == _matmul)
)
):
return
......
pytensor/tensor/rewriting/math.py
浏览文件 @ 20ff202e
......@@ -28,6 +28,7 @@ from pytensor.tensor.basic import (
as_tensor_variable,
cast,
constant,
expand_dims,
get_underlying_scalar_constant_value,
moveaxis,
ones_like,
......@@ -35,7 +36,6 @@ from pytensor.tensor.basic import (
switch,
zeros_like,
)
from pytensor.tensor.blockwise import Blockwise
from pytensor.tensor.elemwise import CAReduce, DimShuffle, Elemwise
from pytensor.tensor.exceptions import NotScalarConstantError
from pytensor.tensor.extra_ops import broadcast_arrays
......@@ -45,10 +45,7 @@ from pytensor.tensor.math import (
Sum,
_conj,
_dot,
_inner_prod,
_matrix_matrix_matmul,
_matrix_vec_prod,
_vec_matrix_prod,
_matmul,
add,
digamma,
dot,
......@@ -182,7 +179,7 @@ def local_lift_transpose_through_dot(fgraph, node):
if not (
is_matrix_transpose(node.outputs[0])
and node.inputs[0].owner
and ((dot_op := node.inputs[0].owner.op) in (_dot, _matrix_matrix_matmul))
and ((dot_op := node.inputs[0].owner.op) in (_dot, _matmul))
):
return False
......@@ -197,60 +194,157 @@ def local_lift_transpose_through_dot(fgraph, node):
return ret
@register_stabilize
@register_specialize
@node_rewriter(tracks=[Blockwise])
def local_batched_matmul_to_core_matmul(fgraph, node):
"""Rewrite matmul where only one of the inputs has batch dimensions to a reshaped core matmul.
def _batched_matmul_to_core_matmul(fgraph, node, allow_reshape: bool):
"""Move batch dimensions of matmul operands to core matmul
Example, if x has batch dimensions, but y not:
Example, if x has batch dimensions that don't overlap with batch dimensions of y
x @ y -> (x.reshape(-1, x.shape[-1]) @ y).reshape(*x.shape[:-1], y.shape[-1])
It also works when y has batch dimensions, but x not.
"""
It also works for batch dimensions of y that don't overlap with batch dimensions of x
# Check whether we have a matmul operation in this node
if not (
isinstance(node.op.core_op, Dot)
and len(node.op.inputs_sig[0]) == 2
and len(node.op.inputs_sig[1]) == 2
):
return None
The rewrite only uses reshape when mixing dimensions, and it can refuse to apply if `allow_reshape=False`
"""
x, y = node.inputs
batch_ndim = node.op.batch_ndim(node)
# Check if x has batch dimensions, but y not (or only broadcastable dimensions)
if any(not b_dim for b_dim in x.type.broadcastable[:-2]) and all(
y.type.broadcastable[:-2]
):
x_stacked = x.reshape((-1, x.shape[-1]))
out_stacked = x_stacked @ y.squeeze(tuple(range(batch_ndim)))
out = out_stacked.reshape((*x.shape[:-1], y.shape[-1]))
return [out]
# Otherwise, check if y has batch dimension, but x not
elif any(not b_dim for b_dim in y.type.broadcastable[:-2]) and all(
x.type.broadcastable[:-2]
):
# For the y batch case we need to first move the batch axes and then reshape
# y.shape == (*b, k, n)
y_tr = moveaxis(y, -2, 0) # (k, *b, n)
y_stacked = y_tr.reshape((y.shape[-2], -1)) # (k, *b * n)
out_stacked = x.squeeze(tuple(range(batch_ndim))) @ y_stacked # (m, *b * n)
out_stacked_tr = out_stacked.reshape(
(x.shape[-2], *y.shape[:-2], y.shape[-1])
) # (m, *b, n)
out = moveaxis(out_stacked_tr, 0, -2) # (*b, m, n)
return [out]
# Both x and y have batch dimensions, nothing to do here
return None
x_axis_to_merge = [
i
for i, (bcast_x, bcast_y) in enumerate(
zip(x.type.broadcastable[:-2], y.type.broadcastable[:-2])
)
if bcast_y and not bcast_x
]
y_axis_to_merge = [
i
for i, (bcast_x, bcast_y) in enumerate(
zip(x.type.broadcastable[:-2], y.type.broadcastable[:-2])
)
if bcast_x and not bcast_y
]
if not (x_axis_to_merge or y_axis_to_merge):
return None
x_shape = tuple(x.shape)
y_shape = tuple(y.shape)
x_is_row = x.type.broadcastable[-2]
y_is_col = y.type.broadcastable[-1]
n_x_axis_to_merge = len(x_axis_to_merge)
n_y_axis_to_merge = len(y_axis_to_merge)
n_axis_to_merge = n_x_axis_to_merge + n_y_axis_to_merge
x_stacked, y_stacked = x, y
dims_were_merged = False
if n_x_axis_to_merge:
# ravel batch dimensions of x on the core (m) axis
x_axis_destination = tuple(range(-n_x_axis_to_merge - 2, -2))
x_stacked = moveaxis(x, x_axis_to_merge, x_axis_destination)
if x_is_row:
# x was a row matrix, squeeze it to clean up the graph
x_stacked = x_stacked.squeeze(-2)
if n_x_axis_to_merge > 1 or not x_is_row:
if not allow_reshape:
# TODO: We could allow the y rewrite to go on
# Or just move one axis (the largest) if x is row
return None
# Ravel moved batch dims together with (m) if needed
x_stacked_shape = tuple(x_stacked.shape)
x_stacked = x_stacked.reshape(
(*x_stacked_shape[: batch_ndim - n_x_axis_to_merge], -1, x_shape[-1])
)
dims_were_merged = True
if n_y_axis_to_merge:
# ravel batch dimensions of y on the core (n) axis
y_axis_destination = tuple(range(-n_y_axis_to_merge - 1, -1))
y_stacked = moveaxis(y, y_axis_to_merge, y_axis_destination)
if y_is_col:
# y was a column matrix, squeeze it to clean up the graph
y_stacked = y_stacked.squeeze(-1)
if n_y_axis_to_merge > 1 or not y_is_col:
if not allow_reshape:
# TODO: We could allow the x rewrite to go on
# Or just move one axis (the largest) if y is col
return None
# Ravel moved batch dims together with (n) if needed
y_stacked_shape = tuple(y_stacked.shape)
y_stacked = y_stacked.reshape(
(*y_stacked_shape[: batch_ndim - n_y_axis_to_merge], y_shape[-2], -1)
)
dims_were_merged = True
# Squeeze x_dims corresponding to merged dimensions of y
x_axis_to_squeeze = np.array(y_axis_to_merge)
for i in reversed(x_axis_to_merge):
# The corresponding dimensions of y may have shifted when we merged dimensions of x
x_axis_to_squeeze[x_axis_to_squeeze > i] -= 1
x_stacked = x_stacked.squeeze(tuple(x_axis_to_squeeze))
# Same for y
y_axis_to_squeeze = np.array(x_axis_to_merge)
for i in reversed(y_axis_to_merge):
y_axis_to_squeeze[y_axis_to_squeeze > i] -= 1
y_stacked = y_stacked.squeeze(tuple(y_axis_to_squeeze))
out_stacked = x_stacked @ y_stacked
# Split back any merged dimensions
if dims_were_merged:
x_merged_shapes = [x_shape[i] for i in x_axis_to_merge]
if not x_is_row:
# Otherwise we handle that later with expand_dims, which is cleaner
x_merged_shapes.append(x_shape[-2])
y_merged_shapes = [y_shape[i] for i in y_axis_to_merge]
if not y_is_col:
# Otherwise we handle that later with expand_dims, which is cleaner
y_merged_shapes.append(y_shape[-1])
out_stacked_shape = tuple(out_stacked.shape)
out_unstacked = out_stacked.reshape(
(
*out_stacked_shape[: batch_ndim - n_axis_to_merge],
*x_merged_shapes,
*y_merged_shapes,
)
)
else:
out_unstacked = out_stacked
# Add back dummy row, col axis
# We do this separately to avoid the reshape as much as we can
if y_is_col and (n_y_axis_to_merge or dims_were_merged):
out_unstacked = expand_dims(out_unstacked, -1)
if x_is_row and (n_x_axis_to_merge or dims_were_merged):
out_unstacked = expand_dims(out_unstacked, -n_y_axis_to_merge - 2)
# Move batch axis back to their original location
source = range(-n_axis_to_merge - 2, 0)
destination = (*x_axis_to_merge, -2, *y_axis_to_merge, -1)
out = moveaxis(out_unstacked, source, destination)
return [out]
@register_canonicalize
@node_rewriter(tracks=[_matmul])
def local_batched_matmul_to_core_matmul(fgraph, node):
# Allow passing batch dimensions of matmul to core vector / column matrices
return _batched_matmul_to_core_matmul(fgraph, node, allow_reshape=False)
@register_specialize
@node_rewriter(tracks=[_matmul])
def local_batched_matmul_to_core_matmul_with_reshape(fgraph, node):
# Allow stacking batch dimensions of matmul with core dimensions, with a reshape operation
# We only apply this in specialize, because grahs with reshape are hard to work with
return _batched_matmul_to_core_matmul(fgraph, node, allow_reshape=True)
@register_canonicalize
@register_specialize
@node_rewriter([_inner_prod, _matrix_vec_prod, _vec_matrix_prod, _matrix_matrix_matmul])
@node_rewriter([_matmul])
def local_blockwise_dot_to_mul(fgraph, node):
"""Rewrite blockwise dots that correspond to multiplication without summation.
......
tests/tensor/rewriting/test_blas.py
浏览文件 @ 20ff202e
import numpy as np
import pytest
from pytensor import function
from pytensor import config, function
from pytensor import tensor as pt
from pytensor.compile import get_default_mode
from pytensor.graph import FunctionGraph
from pytensor.graph import FunctionGraph, ancestors
from pytensor.tensor import (
col,
dscalar,
......@@ -21,7 +21,6 @@ from pytensor.tensor import (
vectorize,
)
from pytensor.tensor.blas import BatchedDot
from pytensor.tensor.blockwise import Blockwise
from pytensor.tensor.elemwise import DimShuffle
from pytensor.tensor.rewriting.blas import (
_as_scalar,
......@@ -37,8 +36,11 @@ def XYZab():
return matrix(), matrix(), matrix(), scalar(), scalar()
@pytest.mark.parametrize("valid_case", (True, False))
def test_specialize_matmul_to_batched_dot(valid_case):
@pytest.mark.skipif(
config.mode == "FAST_COMPILE", reason="Test requires specialization rewrites"
)
@pytest.mark.parametrize("aligned", (True, False))
def test_specialize_matmul_to_batched_dot(aligned):
signature = BatchedDot.gufunc_signature
rewrite = specialize_matmul_to_batched_dot.__name__
......@@ -49,23 +51,36 @@ def test_specialize_matmul_to_batched_dot(valid_case):
return np.matmul(x, y)
x = tensor(shape=(7, 5, 3, 3))
if valid_case:
if aligned:
y = tensor(shape=(7, 5, 3, 3))
else:
y = tensor(shape=(5, 3, 3))
out = vectorize(core_pt, signature=signature)(x, y)
assert (
sum(
isinstance(var.owner.op, BatchedDot)
for var in ancestors([out])
if var.owner
)
== 0
)
vectorize_pt = function(
[x, y],
vectorize(core_pt, signature=signature)(x, y),
out,
mode=get_default_mode().including(rewrite),
)
blocwkise_node = any(
isinstance(node.op, Blockwise) for node in vectorize_pt.maker.fgraph.apply_nodes
assert (
sum(
isinstance(var.owner.op, BatchedDot)
for var in ancestors(vectorize_pt.maker.fgraph.outputs)
if var.owner
)
== 1
)
if valid_case:
assert not blocwkise_node
else:
assert blocwkise_node
x_test = np.random.normal(size=x.type.shape).astype(x.type.dtype)
y_test = np.random.normal(size=y.type.shape).astype(y.type.dtype)
......
tests/tensor/rewriting/test_math.py
浏览文件 @ 20ff202e
......@@ -42,6 +42,7 @@ from pytensor.tensor.math import (
Prod,
Sum,
_conj,
_matmul,
add,
arccosh,
arcsinh,
......@@ -4566,6 +4567,88 @@ def test_local_batched_matmul_to_core_matmul():
np.testing.assert_allclose(fn(x_test, y_test), x_test @ y_test)
@pytest.mark.parametrize(
"mat_shape, vec_shape",
[
[(1, 2, 2), (5, 2)],
[(5, 2, 2), (1, 2)],
[(1, 1, 2, 2), (7, 5, 2)],
[(7, 5, 2, 2), (1, 1, 5, 2)],
[(1, 5, 1, 2, 2), (7, 5, 7, 2)],
[(7, 5, 7, 2, 2), (1, 5, 1, 2)],
[(5, 1, 3, 1, 2, 2), (1, 7, 3, 7, 2)],
[(1, 7, 3, 7, 2, 2), (5, 1, 3, 1, 2)],
],
ids=str,
)
@pytest.mark.parametrize("func", ("matvec", "vecmat", "vecdot"))
def test_batch_matvec_to_matmul(func, mat_shape, vec_shape):
def count_matvec_nodes(graph):
# Counts how many matmul nodes actually correspond to matvec or vecmat
return len(
[
var
for var in ancestors([graph])
if (
var.owner is not None
and var.owner.op == _matmul
and (
(var.owner.inputs[0].type.shape[-2] == 1)
or (var.owner.inputs[1].type.shape[-1] == 1)
)
)
]
)
mat = pt.tensor("mat", shape=mat_shape, dtype="float64")
vec = pt.tensor("vec", shape=vec_shape, dtype="float64")
if func == "matvec":
out = pt.matvec(mat, vec)
elif func == "vecmat":
out = pt.vecmat(vec, mat)
elif func == "vecdot":
out = pt.vecdot(mat[..., 0], vec)
else:
raise NotImplementedError(func)
assert count_matvec_nodes(out) == 1
rewritten_out = rewrite_graph(
out,
include=(
"canonicalize",
"specialize",
),
exclude=(
"local_eager_useless_unbatched_blockwise",
"specialize_matmul_to_batched_dot",
),
)
# No `matvec` in the rewritten out if one of the vector can be treated as a matrix
expected = not any(
mat_dim == 1 and vec_dim != 1
for vec_dim, mat_dim in zip(vec_shape[:-1], mat_shape[:-2])
)
if not expected and func == "vecdot":
# In this case there are two vectors, so we may still end up with a `matvec` unless the second vec can also be treated as matrix
expected = not any(
mat_dim != 1 and vec_dim == 1
for vec_dim, mat_dim in zip(vec_shape[:-1], mat_shape[:-2])
)
assert count_matvec_nodes(rewritten_out) == expected
rng = np.random.default_rng(mat_shape + vec_shape)
eval_dict = {mat: rng.random(mat.type.shape), vec: rng.random(vec.type.shape)}
# Evaluate results are correct without further rewrites
no_optimization = Mode(linker="py", optimizer=None)
np.testing.assert_allclose(
rewritten_out.eval(eval_dict, mode=no_optimization),
out.eval(eval_dict, mode=no_optimization),
)
def test_log_kv_stabilization():
x = pt.scalar("x")
out = log(kv(4.5, x))
......@@ -4616,8 +4699,8 @@ def test_local_dot_to_mul(batched, a_shape, b_shape):
out = dot(a, b)
if batched:
batch_a = tensor("batch_a", shape=(1, 5, *a_shape))
batch_b = tensor("batch_b", shape=(7, 1, *b_shape))
batch_a = tensor("batch_a", shape=(2, 1, 5, *a_shape))
batch_b = tensor("batch_b", shape=(2, 7, 1, *b_shape))
out = vectorize_graph(out, {a: batch_a, b: batch_b})
a = batch_a
b = batch_b
......
tests/tensor/test_math.py
浏览文件 @ 20ff202e
......@@ -2092,9 +2092,9 @@ class TestDot:
def test_matrix_vector_ops():
"""Test vecdot, matvec, and vecmat helper functions."""
rng = np.random.default_rng(seed=utt.fetch_seed())
rng = np.random.default_rng(2089)
# Create test data with batch dimension (2)
atol = 1e-7 if config.floatX == "float32" else 1e-15
batch_size = 2
dim_k = 4 # Common dimension
dim_m = 3 # Matrix rows
......@@ -2109,7 +2109,6 @@ def test_matrix_vector_ops():
mat_kn_val = random(batch_size, dim_k, dim_n, rng=rng).astype(config.floatX)
vec_k_val = random(batch_size, dim_k, rng=rng).astype(config.floatX)
# Create tensor variables with matching dtype
mat_mk = tensor(
name="mat_mk", shape=(batch_size, dim_m, dim_k), dtype=config.floatX
)
......@@ -2130,7 +2129,7 @@ def test_matrix_vector_ops():
expected_vecdot = np.zeros((batch_size,), dtype=np.int32)
for i in range(batch_size):
expected_vecdot[i] = np.sum(vec_k_val[i] * vec_k_val[i])
np.testing.assert_allclose(result, expected_vecdot)
np.testing.assert_allclose(result, expected_vecdot, atol=atol)
# Test 2: matvec - matrix-vector product
matvec_out = matvec(mat_mk, vec_k)
......@@ -2141,7 +2140,7 @@ def test_matrix_vector_ops():
expected_matvec = np.zeros((batch_size, dim_m), dtype=config.floatX)
for i in range(batch_size):
expected_matvec[i] = np.dot(mat_mk_val[i], vec_k_val[i])
np.testing.assert_allclose(result_matvec, expected_matvec)
np.testing.assert_allclose(result_matvec, expected_matvec, atol=atol)
# Test 3: vecmat - vector-matrix product
vecmat_out = vecmat(vec_k, mat_kn)
......@@ -2152,7 +2151,7 @@ def test_matrix_vector_ops():
expected_vecmat = np.zeros((batch_size, dim_n), dtype=config.floatX)
for i in range(batch_size):
expected_vecmat[i] = np.dot(vec_k_val[i], mat_kn_val[i])
np.testing.assert_allclose(result_vecmat, expected_vecmat)
np.testing.assert_allclose(result_vecmat, expected_vecmat, atol=atol)
class TestTensordot:
......
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