/// <summary>
/// LU decomposition and LU inverse example
/// </summary>
public static void LUExample()
{
double[,] m = {{2, 3, 3, 5},
{6, 6, 8, 9},
{10, 11, 12, 13},
{14, 15, 17, 17}};
PZMath_matrix matrix = new PZMath_matrix(m);
matrix.ScreenWriteLine();
// LU decomposition
// correct answer:
// L =
// 1.0000 0 0 0
// 0.1429 1.0000 0 0
// 0.4286 -0.5000 1.0000 0
// 0.7143 0.3333 -0.3333 1.0000
// U =
// 14.0000 15.0000 17.0000 17.0000
// 0 0.8571 0.5714 2.5714
// 0 0 1.0000 3.0000
// 0 0 0 1.0000
// P =
// 0 0 0 1
// 1 0 0 0
// 0 1 0 0
// 0 0 1 0
PZMath_permutation p = new PZMath_permutation(matrix.RowCount);
PZMath_matrix LU = matrix.LUDecomp(p);
LU.ScreenWriteLine();
// LU Invert
// correct answer:
// inv(m) =
// -2.0833 0.6667 3.5000 -2.4167
// 1.0000 -1.0000 -1.0000 1.0000
// 1.0000 0 -3.0000 2.0000
// -0.1667 0.3333 1.0000 -0.8333
PZMath_matrix inverse = matrix.LUInvert();
inverse.ScreenWriteLine();
}