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mindspore.scipy.linalg.lu

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

Compute pivoted LU decomposition of a general matrix.

The decomposition is:

$$a=plu$$

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

Note

• lu is not supported on Windows platform yet.

• Only float32, float64, int32, int64 are supported Tensor dtypes. If Tensor with dtype int32 or int64 is passed, it will be cast to mstype.float64.

Parameters

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

• permute_l (bool, optional) – Perform the multiplication $PL$ (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:

GPU CPU

Examples

>>> import numpy as onp
>>> from mindspore 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)
>>> print(p)
[[0 1 0 0]
 [0 0 0 1]
 [1 0 0 0]
 [0 0 1 0]]
>>> print(l)
[[ 1.          0.          0.          0.        ]
 [ 0.2857143   1.          0.          0.        ]
 [ 0.71428573  0.12        1.          0.        ]
 [ 0.71428573 -0.44       -0.46153846  1.        ]]
>>> print(u)
[[ 7.          5.          6.          6.        ]
 [ 0.          3.57142854  6.28571415  5.28571415]
 [ 0.          0.         -1.03999996  3.07999992]
 [ 0.         -0.         -0.          7.46153831]]