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)
}
#> torch_tensor
#> -153.3679  -95.1678
#>  615.5350  381.9453
#>  581.8021  363.1131
#> [ CPUFloatType{3,2} ]