lu

Syntax

lu(obj, [permute=false])

Arguments

obj is a matrix with no NULL values.

permute is a Boolean value. The default value is false.

Details

Compute pivoted LU decomposition of a matrix.

If permute is false, return 3 matrices (L, U and P) with obj = P'LU. P is a permutation matrix, L is a lower triangular matrix with unit diagonal elements, and U is an upper triangular matrix.

If permute is true, return 2 matrices (L and U) with obj = L*U.

Examples

A = matrix([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]);

P, L, U = lu(A);
P;
#0 #1 #2 #3
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0 
L;
#0 #1 #2 #3
1 0 0 0
0.875 1 0 0
0.25 0.72 1 0
0.625 0.12 0.233871 1 
U;
#0 #1 #2 #3
8 2 6 4
0 6.25 0.75 4.5
0 0 4.96 0.76
0 0 0 0.782258 
L, U = lu(A, true);
L;
#0 #1 #2 #3
0.25 0.72 1 0
0.625 0.12 0.233871 1
1 0 0 0
0.875 1 0 0 
U;
#0 #1 #2 #3
8 2 6 4
0 6.25 0.75 4.5
0 0 4.96 0.76
0 0 0 0.782258