Solve Linear System

Solves the linear system a %*% x = b for x, where a is a symmetric positive-definite matrix. Uses Cholesky decomposition internally. Supports batched inputs: a and b must have the same batch dimensions (all dimensions before the last two).

Usage

nv_solve(a, b)

Arguments

a

(tensorish)
Symmetric positive-definite matrix.

b

(tensorish)
Right-hand side matrix or vector. Must have the same data type and batch dimensions as a.

Value

tensorish
The solution x such that a %*% x = b.

Shapes

• a: (..., n, n)

• b: (..., n, k)

• output: same shape as b

where ... are zero or more batch dimensions that must match between a and b.

See also

nv_cholesky(), nvl_cholesky(), nvl_triangular_solve()

Examples

jit_eval({
  a <- nv_tensor(matrix(c(4, 2, 2, 3), nrow = 2), dtype = "f32")
  b <- nv_tensor(matrix(c(1, 2), nrow = 2), dtype = "f32")
  nv_solve(a, b)
})
#> AnvilTensor
#>  -0.1250
#>   0.7500
#> [ CPUf32{2,1} ]