# Copyright 2022-2023 Huawei Technologies Co., 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
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# ============================================================================
"""Operators for linalg."""
from __future__ import absolute_import
from mindspore import _checkparam as Validator
from mindspore.ops.primitive import Primitive
from mindspore.ops.primitive import prim_attr_register
[docs]class Geqrf(Primitive):
r"""
Decomposes a matrix into the product of an orthogonal matrix `Q` and an upper triangular matrix `R`.
The process is called QR decomposition: :math:`A = QR`.
Both `Q` and `R` matrices are stored in the same output tensor `y`.
The elements of `R` are stored on and above the diagonal, whereas elementary reflectors
(or Householder vectors) implicitly defining matrix `Q` are stored below the diagonal.
This function returns two tensors (`y`, `tau`).
.. warning::
This is an experimental API that is subject to change or deletion.
Inputs:
- **x** (Tensor) - Tensor of shape :math:`(*, m, n)`, input must be a matrix greater than or equal to 2D,
with dtype of float32, float64, complex64, complex128.
Outputs:
- **y** (Tensor) - Tensor of shape :math:`(*, m, n)`, has the same dtype as the `x`.
- **tau** (Tensor) - Tensor of shape :math:`(*, p)` and :math:`p = min(m, n)`, has the same dtype as the `x`.
Raises:
TypeError: If `x` is not a Tensor.
TypeError: If the dtype of `x` is neither float32, float64, complex64, complex128.
ValueError: If `x` dimension is less than 2
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> input_x = Tensor(np.array([[-2.0, -1.0], [1.0, 2.0]]).astype(np.float32))
>>> geqrf = ops.Geqrf()
>>> y, tau = geqrf(input_x)
>>> print(y)
[[ 2.236068 1.7888544]
[-0.236068 1.3416407]]
>>> print(tau)
[1.8944271 0. ]
"""
@prim_attr_register
def __init__(self):
"""Initialize Geqrf"""
self.init_prim_io_names(inputs=['x'], outputs=['y', 'tau'])
[docs]class Svd(Primitive):
"""
Computes the singular value decompositions of one or more matrices.
Refer to :func:`mindspore.ops.svd` for more details.
Args:
full_matrices (bool, optional): If true, compute full-sized :math:`U` and :math:`V`. If false, compute
only the leading P singular vectors, with P is the minimum of M and N.
Default: False.
compute_uv (bool, optional): If true, compute the left and right singular vectors.
If false, compute only the singular values. Default: True.
Inputs:
- **input** (Tensor) - Tensor of the matrices to be decomposed. The shape should be :math:`(*, M, N)`,
the supported dtype are float32 and float64.
Outputs:
- **s** (Tensor) - Singular values. The shape is :math:`(*, P)`.
- **u** (Tensor) - Left singular vectors. If `compute_uv` is False, u will be zero value.
The shape is :math:`(*, M, P)`. If `full_matrices` is True, the shape will be :math:`(*, M, M)`.
- **v** (Tensor) - Right singular vectors. If `compute_uv` is False, v will be zero value.
The shape is :math:`(*, N, P)`. If `full_matrices` is True, the shape will be :math:`(*, N, N)`.
Supported Platforms:
``GPU`` ``CPU``
Examples:
>>> import numpy as np
>>> from mindspore import Tensor, set_context
>>> from mindspore import ops
>>> set_context(device_target="CPU")
>>> svd = ops.Svd(full_matrices=True, compute_uv=True)
>>> a = Tensor(np.array([[1, 2], [-4, -5], [2, 1]]).astype(np.float32))
>>> s, u, v = svd(a)
>>> print(s)
[7.0652843 1.040081 ]
>>> print(u)
[[ 0.30821905 -0.48819482 0.81649697]
[-0.90613353 0.11070572 0.40824813]
[ 0.2896955 0.8656849 0.4082479 ]]
>>> print(v)
[[ 0.63863593 0.769509 ]
[ 0.769509 -0.63863593]]
"""
@prim_attr_register
def __init__(self, full_matrices=False, compute_uv=True):
super().__init__(name="Svd")
self.init_prim_io_names(inputs=['a'], outputs=['s', 'u', 'v'])
self.full_matrices = Validator.check_value_type("full_matrices", full_matrices, [bool], self.name)
self.compute_uv = Validator.check_value_type("compute_uv", compute_uv, [bool], self.name)
self.add_prim_attr('full_matrices', self.full_matrices)
self.add_prim_attr('compute_uv', self.compute_uv)
class Eigh(Primitive):
"""
Eigh decomposition(Symmetric matrix)
Ax = lambda * x
"""
@prim_attr_register
def __init__(self, compute_eigenvectors=True, lower=True):
super().__init__(name="Eigh")
self.init_prim_io_names(inputs=['A'], outputs=['output_w', 'output_v'])
self.compute_eigenvectors = Validator.check_value_type(
"compute_eigenvectors", compute_eigenvectors, [bool], self.name)
self.lower = Validator.check_value_type("lower", lower, [bool], self.lower)
self.add_prim_attr('lower', self.lower)
self.add_prim_attr('compute_eigenvectors', self.compute_eigenvectors)