mindspore.ops.Lstsq

class mindspore.ops.Lstsq(fast=True, l2_regularizer=0.0)[source]

Computes the solutions of the least squares and minimum norm problems of full-rank matrix x of size \((m \times n)\) and matrix a of size \((m \times k)\).

If \(m \geq n\), Lstsq solves the least-squares problem:

\[\begin{array}{ll} \min_y & \|xy-a\|_2. \end{array}\]

If \(m < n\), Lstsq solves the least-norm problem:

\[\begin{array}{llll} \min_y & \|y\|_2 & \text{subject to} & xy = a. \end{array}\]
Parameters

  • fast (bool, optional) –

    Solving algorithm. Default: True.

    • If fast is True, then the solution is computed by solving the normal equations using Cholesky decomposition.

    • If fast is False, an algorithm based on numerically robust completee orthogonal decomposition is used.

  • l2_regularizer (float, optional) – L2 regularization coefficient. Default: 0.0.

Inputs:

  • x (Tensor) - The m by n matrix x. The input tensor whose data type is float16, float32 or float64.

  • a (Tensor) - The m by k matrix a. The input tensor whose data type is float16, float32 or float64.

Outputs:

Tensor, the least squares or minimum norm problems solution, which has shape \((n \times k)\). The data type is the same with x.

Raises

  • TypeError – If the input x or a is not a Tensor.

  • TypeError – If dtype of x or a is not one of: float16, float32, float64.

  • TypeError – If the dtypes of x and a are not the same.

  • ValueError – If the dimension of x is not equal to 2.

  • ValueError – If the dimension of a is not equal to 2 or 1.

  • ValueError – If the length of x_dims[0] is not equal to the length of a_dims[0].

Supported Platforms:

CPU

Examples

>>> x = Tensor(np.array([[2,1,5],[3,5,1],[1,1,1]]),mindspore.float32)
>>> a = Tensor(np.array([[10,5],[15,8],[7,4]]),mindspore.float32)
>>> op = ops.Lstsq()
>>> output = op(x, a)
>>> print(output)
[[17.000002  11.000002 ]
 [-6.5000005 -4.500001 ]
 [-3.500002  -2.5000017]]