torch (version 0.8.1)

torch_cholesky_solve: Cholesky_solve

Description

Cholesky_solve

Usage

torch_cholesky_solve(self, input2, upper = FALSE)

Arguments

self

(Tensor) input matrix \(b\) of size \((*, m, k)\), where \(*\) is zero or more batch dimensions

input2

(Tensor) input matrix \(u\) of size \((*, m, m)\), where \(*\) is zero of more batch dimensions composed of upper or lower triangular Cholesky factor

upper

(bool, optional) whether to consider the Cholesky factor as a lower or upper triangular matrix. Default: FALSE.

cholesky_solve(input, input2, upper=False, out=NULL) -> Tensor

Solves a linear system of equations with a positive semidefinite matrix to be inverted given its Cholesky factor matrix \(u\).

If upper is FALSE, \(u\) is and lower triangular and c is returned such that:

$$ c = (u u^T)^{{-1}} b $$ If upper is TRUE or not provided, \(u\) is upper triangular and c is returned such that:

$$ c = (u^T u)^{{-1}} b $$ torch_cholesky_solve(b, u) can take in 2D inputs b, u or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs c

Examples

if (torch_is_installed()) {

a = torch_randn(c(3, 3))
a = torch_mm(a, a$t()) # make symmetric positive definite
u = torch_cholesky(a)
a
b = torch_randn(c(3, 2))
b
torch_cholesky_solve(b, u)
torch_mm(a$inverse(), b)
}