torch (version 0.8.1)

torch_cholesky: Cholesky

Description

Cholesky

Usage

torch_cholesky(self, upper = FALSE)

Arguments

self

(Tensor) the input tensor \(A\) of size \((*, n, n)\) where * is zero or more batch dimensions consisting of symmetric positive-definite matrices.

upper

(bool, optional) flag that indicates whether to return a upper or lower triangular matrix. Default: FALSE

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

Computes the Cholesky decomposition of a symmetric positive-definite matrix \(A\) or for batches of symmetric positive-definite matrices.

If upper is TRUE, the returned matrix U is upper-triangular, and the decomposition has the form:

$$ A = U^TU $$ If upper is FALSE, the returned matrix L is lower-triangular, and the decomposition has the form:

$$ A = LL^T $$ If upper is TRUE, and \(A\) is a batch of symmetric positive-definite matrices, then the returned tensor will be composed of upper-triangular Cholesky factors of each of the individual matrices. Similarly, when upper is FALSE, the returned tensor will be composed of lower-triangular Cholesky factors of each of the individual matrices.

Examples

if (torch_is_installed()) {

a = torch_randn(c(3, 3))
a = torch_mm(a, a$t()) # make symmetric positive-definite
l = torch_cholesky(a)
a
l
torch_mm(l, l$t())
a = torch_randn(c(3, 2, 2))
if (FALSE) {
a = torch_matmul(a, a$transpose(-1, -2)) + 1e-03 # make symmetric positive-definite
l = torch_cholesky(a)
z = torch_matmul(l, l$transpose(-1, -2))
torch_max(torch_abs(z - a)) # Max non-zero
}
}