mindspore.scipy.linalg.lstsq

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

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 \((*, M, N)\), where \(*\) is zero or more batch dimensions.

  • B (Tensor) – RHS input tensor of shape \((*, M, K)\), where \(*\) 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 \((*, N, K)\), where \(*\) is same as broadcast batch dimensions.

  • residual (Tensor), Square of the 2-norm for each column in \(AX - B\), It has shape \((*, K)\), where \(*\) 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 \((*)\), where \(*\) 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 \((*, min(M, N))\), where \(*\) 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.]