mindspore.scipy.linalg.lu

mindspore.scipy.linalg.lu(a, permute_l=False, overwrite_a=False, check_finite=True)[source]

Compute pivoted LU decomposition of a general matrix.

The decomposition is:

\[A = P L U\]

where \(P\) is a permutation matrix, \(L\) lower triangular with unit diagonal elements, and \(U\) upper triangular.

Parameters

  • a (Tensor) – a \((M, N)\) matrix to decompose. Note that if the input tensor is not a float, then it will be casted to :class:’mstype.float32’.

  • permute_l (bool, optional) – Perform the multiplication \(P L\) (Default: do not permute). Default: False.

  • overwrite_a (bool, optional) – Whether to overwrite data in \(A\) (may improve performance). Default: False.

  • check_finite (bool, optional) – Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. Default: True.

Returns

If permute_l == False

  • Tensor, \((M, M)\) permutation matrix.

  • Tensor, \((M, K)\) lower triangular or trapezoidal matrix with unit diagonal. \(K = min(M, N)\).

  • Tensor, \((K, N)\) upper triangular or trapezoidal matrix.

If permute_l == True

  • Tensor, \((M, K)\) permuted L matrix. \(K = min(M, N)\).

  • Tensor, \((K, N)\) upper triangular or trapezoidal matrix.

Supported Platforms:

CPU GPU

Examples

>>> import numpy as onp
>>> from mindspore.common import Tensor
>>> from mindspore.scipy.linalg import lu
>>> A = Tensor(onp.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]).astype(onp.float64))
>>> p, l, u = lu(A)
>>> p
Tensor(shape=[4, 4], dtype=Int32, value=
[[0, 1, 0, 0],
 [0, 0, 0, 1],
 [1, 0, 0, 0],
 [0, 0, 1, 0]])
>>> l
Tensor(shape=[4, 4], dtype=Float64, value=
[[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
 [ 2.85714298e-01,  1.00000000e+00,  0.00000000e+00,  0.00000000e+00],
 [ 7.14285731e-01,  1.19999997e-01,  1.00000000e+00,  0.00000000e+00],
 [ 7.14285731e-01, -4.39999998e-01, -4.61538464e-01,  1.00000000e+00]])
>>> u
Tensor(shape=[4, 4], dtype=Float64, value=
[[ 7.00000000e+00,  5.00000000e+00,  6.00000000e+00,  6.00000000e+00],
 [ 0.00000000e+00,  3.57142854e+00,  6.28571415e+00,  5.28571415e+00],
 [ 0.00000000e+00,  0.00000000e+00, -1.03999996e+00,  3.07999992e+00],
 [ 0.00000000e+00, -0.00000000e+00, -0.00000000e+00,  7.46153831e+00]])