Solve

torch_solve(self, A)

Arguments

self

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

A

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

Note

Irrespective of the original strides, the returned matrices
`solution` and `LU` will be transposed, i.e. with strides like
`B$contiguous()$transpose(-1, -2)$stride()` and
`A$contiguous()$transpose(-1, -2)$stride()` respectively.

solve(input, A) -> (Tensor, Tensor)

This function returns the solution to the system of linear equations represented by \(AX = B\) and the LU factorization of A, in order as a namedtuple solution, LU.

LU contains L and U factors for LU factorization of A.

torch_solve(B, A) can take in 2D inputs B, A or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs solution, LU.

Examples

if (torch_is_installed()) { A = torch_tensor(rbind(c(6.80, -2.11, 5.66, 5.97, 8.23), c(-6.05, -3.30, 5.36, -4.44, 1.08), c(-0.45, 2.58, -2.70, 0.27, 9.04), c(8.32, 2.71, 4.35, -7.17, 2.14), c(-9.67, -5.14, -7.26, 6.08, -6.87)))$t() B = torch_tensor(rbind(c(4.02, 6.19, -8.22, -7.57, -3.03), c(-1.56, 4.00, -8.67, 1.75, 2.86), c(9.81, -4.09, -4.57, -8.61, 8.99)))$t() out = torch_solve(B, A) X = out[[1]] LU = out[[2]] torch_dist(B, torch_mm(A, X)) # Batched solver example A = torch_randn(c(2, 3, 1, 4, 4)) B = torch_randn(c(2, 3, 1, 4, 6)) out = torch_solve(B, A) X = out[[1]] LU = out[[2]] torch_dist(B, A$matmul(X)) }
#> torch_tensor #> 1.72252e-05 #> [ CPUFloatType{} ]