Cholesky_solve

Usage

torch_cholesky_solve(self, input2, upper = FALSE)

Arguments

self

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

input2

(Tensor) input matrix $u$ of size $(\ast ,m,m)$, where $\ast$ 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
#> -7.6257e-05  7.2004e-02
#>  2.6285e+01  5.7017e+01
#> -2.4348e+01 -5.3802e+01
#> [ CPUFloatType{3,2} ]