torch_lstsq {torch}

Lstsq

Description

Lstsq

Arguments

self

(Tensor) the matrix B

A

(Tensor) the m by n matrix A

lstsq(input, A, out=NULL) -> Tensor

Computes the solution to the least squares and least norm problems for a full rank matrix A of size (m \times n) and a matrix B of size (m \times k).

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

\begin{array}{ll} \min_X & \|AX-B\|_2. \end{array}

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

\begin{array}{llll} \min_X & \|X\|_2 & \mbox{subject to} & AX = B. \end{array}

Returned tensor X has shape (\mbox{max}(m, n) \times k). The first n rows of X contains the solution. If m \geq n, the residual sum of squares for the solution in each column is given by the sum of squares of elements in the remaining m - n rows of that column.

Note

The case when \eqn{m < n} is not supported on the GPU.