Lstsq

Arguments

self

(Tensor) the matrix $B$

A

(Tensor) the $m$ by $n$ matrix $A$

Note

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

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 $m\ge n$, torch_lstsq() solves the least-squares problem:

$$\begin{array}{ll}\underset{X}{min}& \Vert AX-B{\Vert }_2.\end{array}$$ If $m<n$, torch_lstsq() solves the least-norm problem:

$$\begin{array}{llll}\underset{X}{min}& \Vert X{\Vert }_2& \text{subject to}& AX=B.\end{array}$$ Returned tensor $X$ has shape $(\text{max}(m,n)\times k)$. The first $n$ rows of $X$ contains the solution. If $m\ge n$, 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.