# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import itertools
import numpy as np
from ... import opcodes as OperandDef
from ...serialization.serializables import KeyField, StringField
from ...utils import has_unknown_shape
from ..arithmetic.utils import chunk_tree_add
from ..array_utils import as_same_device, device, is_sparse_module
from ..core import Tensor, TensorOrder
from ..datasource import tensor as astensor
from ..operands import TensorOperand, TensorOperandMixin
from ..utils import broadcast_shape, check_order, check_out_param, unify_chunks
class TensorMatmul(TensorOperand, TensorOperandMixin):
_op_type_ = OperandDef.MATMUL
_a = KeyField("a")
_b = KeyField("b")
_casting = StringField("casting")
_order = StringField("order")
def __init__(self, casting=None, order=None, **kw):
super().__init__(_casting=casting, _order=order, **kw)
if self._casting is None:
self._casting = "same_kind"
if self._order is None:
self._order = "K"
check_order(self._order)
@property
def a(self):
return self._a
@property
def b(self):
return self._b
@property
def casting(self):
return self._casting
@property
def order(self):
return self._order
def _set_inputs(self, inputs):
super()._set_inputs(inputs)
self._a = self._inputs[0]
self._b = self._inputs[1]
def _calc_order(self, a, b, out):
if out is not None:
return out.order
if self._order in "A":
if a.order == TensorOrder.C_ORDER or b.order == TensorOrder.C_ORDER:
return TensorOrder.C_ORDER
else:
return TensorOrder.F_ORDER
elif self._order in "CK":
return TensorOrder.C_ORDER
else:
return TensorOrder.F_ORDER
def __call__(self, a, b, out=None):
from ..base import broadcast_to
if a.ndim == 0 or b.ndim == 0:
raise ValueError("Scalar operands are not allowed, use '*' instead")
if out is not None and not isinstance(out, Tensor):
raise TypeError(f"out must be a Tensor, got {type(out)} instead")
a_is_1d = False
if a.ndim == 1:
a_is_1d = True
a = a[np.newaxis, :]
b_is_1d = False
if b.ndim == 1:
b_is_1d = True
b = b[:, np.newaxis]
if a.ndim < b.ndim:
a = a[(b.ndim - a.ndim) * (np.newaxis,)]
elif a.ndim > b.ndim:
b = b[(a.ndim - b.ndim) * (np.newaxis,)]
if a.shape[-1] != b.shape[-2]:
raise ValueError(
f"shape {a.shape} and {b.shape} not aligned: "
f"{a.shape[-1]} (dim {a.ndim - 1}) != {b.shape[-2]} (dim {b.ndim - 2})"
)
shape = broadcast_shape(a.shape[:-2], b.shape[:-2]) + (a.shape[-2], b.shape[-1])
order = self._calc_order(a, b, out)
t = self.new_tensor([a, b], shape, order=order)
if a_is_1d:
t = t[..., 0, :]
if b_is_1d:
t = t[..., 0]
if out is not None:
check_out_param(out, t, self._casting)
t = broadcast_to(t, out.shape)
out.data = t.data
return out
return t
@classmethod
def tile(cls, op):
a, b = op.inputs
tensor = op.outputs[0]
# the axes to align on
a_axes = list(range(a.ndim - 2))[::-1] + [tensor.ndim - 2, tensor.ndim - 1]
b_axes = list(range(b.ndim - 2))[::-1] + [tensor.ndim - 1, tensor.ndim]
if has_unknown_shape(a, b):
yield
a, b = yield from unify_chunks((a, a_axes), (b, b_axes))
get_nsplit = lambda i: a.nsplits[i] if a.nsplits[i] != (1,) else b.nsplits[i]
get_idx = lambda ch, idx: tuple(
0 if ch.nsplits[j] == (1,) else ix for j, ix in enumerate(idx)
)
prefix_idxes = [range(len(get_nsplit(i))) for i in range(a.ndim - 2)]
out_idxes = prefix_idxes + [
range(len(a.nsplits[-2])),
range(len(b.nsplits[-1])),
]
out_chunks = []
for out_idx in itertools.product(*out_idxes):
chunks = []
get_s = lambda x, idx: x[idx] if x != (1,) else x[0]
shape = tuple(
max(get_s(a_s, j), get_s(b_s, j))
for a_s, b_s, j in zip(a.nsplits[:-2], b.nsplits[:-2], out_idx[:-2])
) + (get_s(a.nsplits[-2], out_idx[-2]), get_s(b.nsplits[-1], out_idx[-1]))
for contract_idx in range(len(a.nsplits[-1])):
a_idx = get_idx(a, out_idx[: a.ndim - 1] + (contract_idx,))
a_chunk = a.cix[a_idx]
b_idx = get_idx(
b, out_idx[: b.ndim - 2] + (contract_idx,) + out_idx[-1:]
)
b_chunk = b.cix[b_idx]
chunk_op = op.copy().reset_key()
c = chunk_op.new_chunk(
[a_chunk, b_chunk], shape=shape, order=tensor.order
)
chunks.append(c)
if len(chunks) == 1:
c = chunks[0]
out_chunk_op = c.op.copy()
out_chunk = out_chunk_op.new_chunk(
out_chunk_op.inputs,
shape=c.shape,
index=out_idx,
order=tensor.order,
)
else:
out_chunk = chunk_tree_add(
tensor.op.dtype, chunks, out_idx, shape, sparse=tensor.op.sparse
)
out_chunks.append(out_chunk)
nsplits = tuple(get_nsplit(i) for i in range(a.ndim - 2)) + (
a.nsplits[-2],
b.nsplits[-1],
)
new_op = op.copy()
return new_op.new_tensors(
[a, b], tensor.shape, order=tensor.order, chunks=out_chunks, nsplits=nsplits
)
@classmethod
def execute(cls, ctx, op):
(a, b), device_id, xp = as_same_device(
[ctx[c.key] for c in op.inputs], device=op.device, ret_extra=True
)
with device(device_id):
if not op.sparse and is_sparse_module(xp):
# tell sparse to do calculation on numpy or cupy matmul
ctx[op.outputs[0].key] = xp.matmul(a, b, sparse=False)
else:
try:
# `np.matmul` support `order` argument in version 1.16
ctx[op.outputs[0].key] = xp.matmul(
a, b, casting=op.casting, order=op.order
)
except TypeError: # pragma: no cover
ctx[op.outputs[0].key] = xp.matmul(a, b).astype(
dtype=op.dtype, casting=op.casting, order=op.order
)
[docs]def matmul(a, b, sparse=None, out=None, **kw):
"""
Matrix product of two tensors.
The behavior depends on the arguments in the following way.
- If both arguments are 2-D they are multiplied like conventional
matrices.
- If either argument is N-D, N > 2, it is treated as a stack of
matrices residing in the last two indexes and broadcast accordingly.
- If the first argument is 1-D, it is promoted to a matrix by
prepending a 1 to its dimensions. After matrix multiplication
the prepended 1 is removed.
- If the second argument is 1-D, it is promoted to a matrix by
appending a 1 to its dimensions. After matrix multiplication
the appended 1 is removed.
Multiplication by a scalar is not allowed, use ``*`` instead. Note that
multiplying a stack of matrices with a vector will result in a stack of
vectors, but matmul will not recognize it as such.
``matmul`` differs from ``dot`` in two important ways.
- Multiplication by scalars is not allowed.
- Stacks of matrices are broadcast together as if the matrices
were elements.
Parameters
----------
a : array_like
First argument.
b : array_like
Second argument.
out : Tensor, optional
Output argument. This must have the exact kind that would be returned
if it was not used. In particular, it must have the right type,
and its dtype must be the dtype that would be returned
for `dot(a,b)`. This is a performance feature. Therefore, if these
conditions are not met, an exception is raised, instead of attempting
to be flexible.
Returns
-------
output : Tensor
Returns the dot product of `a` and `b`. If `a` and `b` are both
1-D arrays then a scalar is returned; otherwise an array is
returned. If `out` is given, then it is returned.
Raises
------
ValueError
If the last dimension of `a` is not the same size as
the second-to-last dimension of `b`.
If scalar value is passed.
See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
dot : alternative matrix product with different broadcasting rules.
Notes
-----
The matmul function implements the semantics of the `@` operator introduced
in Python 3.5 following PEP465.
Examples
--------
For 2-D arrays it is the matrix product:
>>> import mars.tensor as mt
>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> mt.matmul(a, b).execute()
array([[4, 1],
[2, 2]])
For 2-D mixed with 1-D, the result is the usual.
>>> a = [[1, 0], [0, 1]]
>>> b = [1, 2]
>>> mt.matmul(a, b).execute()
array([1, 2])
>>> mt.matmul(b, a).execute()
array([1, 2])
Broadcasting is conventional for stacks of arrays
>>> a = mt.arange(2*2*4).reshape((2,2,4))
>>> b = mt.arange(2*2*4).reshape((2,4,2))
>>> mt.matmul(a,b).shape
(2, 2, 2)
>>> mt.matmul(a,b)[0,1,1].execute()
98
>>> mt.sum(a[0,1,:] * b[0,:,1]).execute()
98
Vector, vector returns the scalar inner product, but neither argument
is complex-conjugated:
>>> mt.matmul([2j, 3j], [2j, 3j]).execute()
(-13+0j)
Scalar multiplication raises an error.
>>> mt.matmul([1,2], 3)
Traceback (most recent call last):
...
ValueError: Scalar operands are not allowed, use '*' instead
"""
a = astensor(a)
b = astensor(b)
sparse = sparse if sparse is not None else a.issparse() and b.issparse()
op = TensorMatmul(dtype=np.promote_types(a.dtype, b.dtype), sparse=sparse, **kw)
return op(a, b, out=out)