LU
LU
LU factorization of a matrix as the product of a lower triangular matrix and an upper triangular matrix.
bool matrix::LU(
matrix& L, // lower triangular matrix
matrix& U // upper triangular matrix
);Parameters
- L key
[out] Lower triangular matrix.
- U
[out] Upper triangular matrix.
Return Value
Returns true on success, false otherwise.
Example
matrix matrix_a={{1,2,3,4},
{5,2,6,7},
{8,9,3,10},
{11,12,14,4}};
matrix matrix_l,matrix_u;
//--- LU decomposition
matrix_a.LU(matrix_l,matrix_u);
Print("matrix_l\n",matrix_l);
Print("matrix_u\n",matrix_u);
//--- check if A = L * U
Print("check\n",matrix_l.MatMul(matrix_u));
/*
matrix_l
[[1,0,0,0]
[5,1,0,0]
[8,0.875,1,0]
[11,1.25,0.5904761904761905,1]]
matrix_u
[[1,2,3,4]
[0,-8,-9,-13]
[0,0,-13.125,-10.625]
[0,0,0,-17.47619047619047]]
check
[[1,2,3,4]
[5,2,6,7]
[8,9,3,10]
[11,12,14,4]]
*/Last updated on