Skip to contents

LU Decomposition

Source: R/api.R
nv_lu.Rd

Computes the partial-pivoted LU decomposition of a matrix operand: $$P A = L U,$$ where \(P\) is a permutation matrix, \(L\) is unit lower triangular, and \(U\) is upper triangular.

This function returns L and U as separate matrices. Use prim_lu() to get them in packed LU form.

Usage

nv_lu(operand)

Arguments

operand

(arrayish)
Matrix of data type floating-point with exactly 2 dimensions.

Value

Named list:

  • L – unit lower-triangular factor of shape (m, k), where (m, n) = shape(operand) and k = min(m, n).

  • U – upper-triangular factor of shape (k, n).

  • pivots – length k, dtype i32. LAPACK-style sequential 1-based row swaps as returned by getrf.

  • permutation – length m, dtype i32. A 1-based permutation vector representing \(P\).

See also

prim_lu()

Examples

x <- nv_matrix(c(4, 3, 6, 3), nrow = 2, dtype = "f64")
nv_lu(x)
#> $L
#> AnvlArray
#>  1.0000 0.0000
#>  0.7500 1.0000
#> [ CPUf64{2,2} ] 
#> 
#> $U
#> AnvlArray
#>   4.0000  6.0000
#>   0.0000 -1.5000
#> [ CPUf64{2,2} ] 
#> 
#> $pivots
#> AnvlArray
#>  1
#>  2
#> [ CPUi32{2} ] 
#> 
#> $permutation
#> AnvlArray
#>  1
#>  2
#> [ CPUi32{2} ] 
#>