mindspore.scipy.linalg.lstsq

mindspore.scipy.linalg.lstsq(A, B, rcond=None, driver=None)

Computes a solution to the least squares problem of a system of linear equations $AX=B$.

Note

• lstsq is currently only used in mindscience scientific computing scenarios and dose not support other usage scenarios.

• lstsq is not supported on Windows platform yet.

Parameters

• A (Tensor) – LHS input tensor of shape $(\ast ,M,N)$, where $\ast$ is zero or more batch dimensions.

• B (Tensor) – RHS input tensor of shape $(\ast ,M,K)$, where $\ast$ is zero or more batch dimensions.

• rcond (number.Number, optional) – Not implemented now, Default is None.

• driver (string, optional) – Which LAPACK driver is used to solve the least-squares problem. Options are "gels", "gelsy", "gelss", "gelsd". Default is None ("gelsy"). if A is well-conditioned, "gels" is a good choice for full-rank matrix, and "gelsy" for a general matrix. if A is not well-conditioned, "gelsd" works good, "gelss" was used historically. It is generally slow but uses less memory.

Returns

• solution (Tensor), Least-squares solution. It has shape $(\ast ,N,K)$, where $\ast$ is same as broadcast batch dimensions.

• residual (Tensor), Square of the 2-norm for each column in $AX-B$, It has shape $(\ast ,K)$, where $\ast$ is same as broadcast batch dimensions. It is computed when driver is one of ("gels", "gelss", "gelsd") and $M>N$ , otherwise, it is an empty tensor.

• rank (Tensor), Effective rank of A. It has shape $(\ast )$, where $\ast$ is same as batch dimensions of A. It is computed when driver is one of ("gelsy", "gelss", "gelsd"), otherwise it is an empty tensor.

• singular_value (Tensor), Singular values of A. It has shape $(\ast ,min(M,N))$, where $\ast$ is same as batch dimensions of A. It is computed when driver is one of ("gelss", "gelsd"), otherwise it is an empty tensor.

Raises

• TypeError – If dtype of A and B are not the same.

• ValueError – If A is less than 2 dimension.

• ValueError – If the shape of A and B are not matched.

• ValueError – If driver is not in set {None, "gels", "gelsy", "gelss", "gelsd"}.

Supported Platforms:

Ascend CPU

Examples

>>> import numpy as onp
>>> import mindspore
>>> from mindspore import Tensor
>>> from mindspore.scipy.linalg import lstsq
>>> a = Tensor(onp.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]], onp.float32))
>>> b = Tensor(onp.array([3, 1, 3, 4], onp.float32))
>>> solution, residual, rank, singular_value = lstsq(a, b)
>>> print(solution)
[ 1. -1.  2.  2.]
>>> print(a @ solution)  # Check the result
[3. 1. 3. 4.]