LUP
具有部分轴的 LUP 因数分解，仅指具有行排列的 LU 分解：PA=LU。
bool LUP(
matrix& L, // 下三角矩阵
matrix& U, // 上三角矩阵
matrix& P // 排列矩阵
);参数
L 键
[输出] 下三角矩阵。
U
[输出] 上三角矩阵。
P
[out] Permutations matrix
返回值
成功时返回 true，否则返回 false。
举例
matrix matrix_a={{1,2,3,4},
{5,2,6,7},
{8,9,3,10},
{11,12,14,4}};
matrix matrix_l,matrix_u,matrix_p;
//--- LUP 分解
matrix_a.LUP(matrix_l,matrix_u,matrix_p);
Print("matrix_l\n",matrix_l);
Print("matrix_u\n",matrix_u);
Print("matrix_p\n",matrix_p);
//--- 验算是否 P * A = L * U
Print("P * A\n",matrix_p.MatMul(matrix_a));
Print("L * U\n",matrix_l.MatMul(matrix_u));
/*
matrix_l
[[1,0,0,0]
[0.4545454545454545,1,0,0]
[0.7272727272727273,-0.07894736842105282,1,0]
[0.09090909090909091,-0.2631578947368421,-0.2262773722627738,1]]
matrix_u
[[11,12,14,4]
[0,-3.454545454545454,-0.3636363636363633,5.181818181818182]
[0,0,-7.210526315789473,7.500000000000001]
[0,0,0,6.697080291970803]]
matrix_p
[[0,0,0,1]
[0,1,0,0]
[0,0,1,0]
[1,0,0,0]]
P * A
[[11,12,14,4]
[5,2,6,7]
[8,9,3,10]
[1,2,3,4]]
L * U
[[11,12,14,4]
[5,2,6,7]
[8,9,3.000000000000001,10]
[1,2,3,4]]
*/