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
}
}