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Solve Linear System

Source: R/api.R, R/api-generics.R
nv_solve.Rd

Solves the linear system a %*% x = b for x. Uses LU decomposition with partial pivoting internally, so a need only be square and non-singular.

Usage

nv_solve(a, b)

# S3 method for class 'AnvlArray'
solve(a, b, ...)

Arguments

a

(arrayish)
Coefficient matrix.

b

(arrayish)
Right-hand side. If missing, returns nv_inv() of a.

...

No additional arguments.

Value

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

Details

$$A x = b$$ $$P A = L U$$ $$L U x = P b$$ $$L y = P b$$ $$U x = y$$

Shapes

  • a: (n, n)

  • b: (n,) or (n, k)

  • output: same shape as b

See also

nv_chol(), nv_triangular_solve(), prim_lu()

Examples

a <- nv_matrix(c(4, 3, 6, 3), nrow = 2, dtype = "f64")
b <- nv_matrix(c(1, 2), nrow = 2, dtype = "f64")
nv_solve(a, b)
#> AnvlArray
#>   1.5000
#>  -0.8333
#> [ CPUf64{2,1} ]