#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 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.
from ... import opcodes as OperandDef
from ...serialization.serializables import KeyField
from ..core import Tensor, TensorOrder
from ..operands import TensorOperand, TensorOperandMixin
from ..datasource import tensor as astensor
from ..array_utils import device, as_same_device, is_sparse_module
from .tensordot import tensordot
class TensorDot(TensorOperand, TensorOperandMixin):
_op_type_ = OperandDef.DOT
_a = KeyField("a")
_b = KeyField("b")
@property
def a(self):
return self._a
@property
def b(self):
return self._b
def _set_inputs(self, inputs):
super()._set_inputs(inputs)
self._a, self._b = self._inputs
@classmethod
def execute(cls, ctx, op):
chunk = op.outputs[0]
(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 dot
ctx[chunk.key] = xp.dot(a, b, sparse=False)
else:
ctx[chunk.key] = xp.dot(a, b)
[docs]def dot(a, b, out=None, sparse=None):
"""
Dot product of two arrays. Specifically,
- If both `a` and `b` are 1-D arrays, it is inner product of vectors
(without complex conjugation).
- If both `a` and `b` are 2-D arrays, it is matrix multiplication,
but using :func:`matmul` or ``a @ b`` is preferred.
- If either `a` or `b` is 0-D (scalar), it is equivalent to :func:`multiply`
and using ``numpy.multiply(a, b)`` or ``a * b`` is preferred.
- If `a` is an N-D array and `b` is a 1-D array, it is a sum product over
the last axis of `a` and `b`.
- If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a
sum product over the last axis of `a` and the second-to-last axis of `b`::
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
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, must be
C-contiguous, 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
scalars or both 1-D arrays then a scalar is returned; otherwise
a tensor 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`.
See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
einsum : Einstein summation convention.
matmul : '@' operator as method with out parameter.
Examples
--------
>>> import mars.tensor as mt
>>> mt.dot(3, 4).execute()
12
Neither argument is complex-conjugated:
>>> mt.dot([2j, 3j], [2j, 3j]).execute()
(-13+0j)
For 2-D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> mt.dot(a, b).execute()
array([[4, 1],
[2, 2]])
>>> a = mt.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = mt.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> mt.dot(a, b)[2,3,2,1,2,2].execute()
499128
>>> mt.sum(a[2,3,2,:] * b[1,2,:,2]).execute()
499128
"""
a, b = astensor(a), astensor(b)
if a.isscalar() and b.isscalar():
ret = a * b
else:
ret = tensordot(a, b, axes=((a.ndim - 1,), (b.ndim - 2,)), sparse=sparse)
if out is None:
return ret
# set to out
if not isinstance(out, Tensor):
raise TypeError(f"`out` must be a Tensor, got {type(out)} instead")
if out.shape != ret.shape:
raise ValueError("output tensor has wrong dimensions")
if not (
out.dtype == ret.dtype
and out.ndim == ret.ndim
and out.order == TensorOrder.C_ORDER
):
raise ValueError(
"output tensor is not acceptable "
"(must have the right datatype, number of dimensions and be a C-Tensor"
)
out.data = ret.astype(out.dtype, order=out.order.value, copy=False).data
return out