import collections
import numpy
import six
import cupy
from cupy import core
from cupy import internal
matmul = core.matmul
[docs]def dot(a, b, out=None):
"""Returns a dot product of two arrays.
For arrays with more than one axis, it computes the dot product along the
last axis of ``a`` and the second-to-last axis of ``b``. This is just a
matrix product if the both arrays are 2-D. For 1-D arrays, it uses their
unique axis as an axis to take dot product over.
Args:
a (cupy.ndarray): The left argument.
b (cupy.ndarray): The right argument.
out (cupy.ndarray): Output array.
Returns:
cupy.ndarray: The dot product of ``a`` and ``b``.
.. seealso:: :func:`numpy.dot`
"""
# TODO(okuta): check type
return a.dot(b, out)
[docs]def vdot(a, b):
"""Returns the dot product of two vectors.
The input arrays are flattened into 1-D vectors and then it performs inner
product of these vectors.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: Zero-dimensional array of the dot product result.
.. seealso:: :func:`numpy.vdot`
"""
if a.size != b.size:
raise ValueError('Axis dimension mismatch')
return core.tensordot_core(a, b, None, 1, 1, a.size, ())
[docs]def inner(a, b):
"""Returns the inner product of two arrays.
It uses the last axis of each argument to take sum product.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: The inner product of ``a`` and ``b``.
.. seealso:: :func:`numpy.inner`
"""
a_ndim = a.ndim
b_ndim = b.ndim
if a_ndim == 0 or b_ndim == 0:
return cupy.multiply(a, b)
a_axis = a_ndim - 1
b_axis = b_ndim - 1
if a.shape[-1] != b.shape[-1]:
raise ValueError('Axis dimension mismatch')
if a_axis:
a = cupy.rollaxis(a, a_axis, 0)
if b_axis:
b = cupy.rollaxis(b, b_axis, 0)
ret_shape = a.shape[1:] + b.shape[1:]
k = a.shape[0]
n = a.size // k
m = b.size // k
return core.tensordot_core(a, b, None, n, m, k, ret_shape)
[docs]def outer(a, b, out=None):
"""Returns the outer product of two vectors.
The input arrays are flattened into 1-D vectors and then it performs outer
product of these vectors.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
out (cupy.ndarray): Output array.
Returns:
cupy.ndarray: 2-D array of the outer product of ``a`` and ``b``.
.. seealso:: :func:`numpy.outer`
"""
n = a.size
m = b.size
ret_shape = (n, m)
if out is None:
return core.tensordot_core(a, b, None, n, m, 1, ret_shape)
if out.size != n * m:
raise ValueError('Output array has an invalid size')
if out.flags.c_contiguous:
return core.tensordot_core(a, b, out, n, m, 1, ret_shape)
else:
out[:] = core.tensordot_core(a, b, None, n, m, 1, ret_shape)
return out
[docs]def tensordot(a, b, axes=2):
"""Returns the tensor dot product of two arrays along specified axes.
This is equivalent to compute dot product along the specified axes which
are treated as one axis by reshaping.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
axes:
- If it is an integer, then ``axes`` axes at the last of ``a`` and
the first of ``b`` are used.
- If it is a pair of sequences of integers, then these two
sequences specify the list of axes for ``a`` and ``b``. The
corresponding axes are paired for sum-product.
out (cupy.ndarray): Output array.
Returns:
cupy.ndarray: The tensor dot product of ``a`` and ``b`` along the
axes specified by ``axes``.
.. seealso:: :func:`numpy.tensordot`
"""
a_ndim = a.ndim
b_ndim = b.ndim
if a_ndim == 0 or b_ndim == 0:
if axes != 0 and axes != ((), ()):
raise ValueError('An input is zero-dim while axes has dimensions')
return cupy.multiply(a, b)
if isinstance(axes, collections.Sequence):
if len(axes) != 2:
raise ValueError('Axes must consist of two arrays.')
a_axes, b_axes = axes
if numpy.isscalar(a_axes):
a_axes = a_axes,
if numpy.isscalar(b_axes):
b_axes = b_axes,
else:
a_axes = tuple(six.moves.range(a_ndim - axes, a_ndim))
b_axes = tuple(six.moves.range(axes))
sum_ndim = len(a_axes)
if sum_ndim != len(b_axes):
raise ValueError('Axes length mismatch')
for a_axis, b_axis in zip(a_axes, b_axes):
if a.shape[a_axis] != b.shape[b_axis]:
raise ValueError('Axis dimension mismatch')
# Make the axes non-negative
a = _move_axes_to_head(a, [axis % a_ndim for axis in a_axes])
b = _move_axes_to_head(b, [axis % b_ndim for axis in b_axes])
ret_shape = a.shape[sum_ndim:] + b.shape[sum_ndim:]
k = internal.prod(a.shape[:sum_ndim])
n = a.size // k
m = b.size // k
return core.tensordot_core(a, b, None, n, m, k, ret_shape)
# TODO(okuta): Implement einsum
# TODO(okuta): Implement matrix_power
# TODO(okuta): Implement kron
def _move_axes_to_head(a, axes):
# This function moves the axes of ``s`` to the head of the shape.
for idx, axis in enumerate(axes):
if idx != axis:
break
else:
return a
return a.transpose(
axes + [i for i in six.moves.range(a.ndim) if i not in axes])