/// <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();
}
// fit data from y = exp(x), x :[0 : 2]
public static void TestLinearLeastSquareFit()
{
int i, n;
n = 19;
// -- prepare model parameters
double xi, yi, chisq;
PZMath_matrix X, cov;
PZMath_vector y, w, c;
X = new PZMath_matrix(n, 3);
y = new PZMath_vector(n);
w = new PZMath_vector(n);
c = new PZMath_vector(3);
cov = new PZMath_matrix(3, 3);
// -- data to be fitted
//PZMath_random_ParkMiller_Normal r = new PZMath_random_ParkMiller_Normal();
for (i = 0; i < n; i++)
{
xi = 0.1 + 0.1 * i;
yi = System.Math.Exp(xi); // f(x)
System.Console.WriteLine(xi + " " + yi);
X[i, 0] = 1.0;
X[i, 1] = xi;
X[i, 2] = xi * xi;
y[i] = yi;
w[i] = 1.0;
}
PZMath_multifit_linear l = new PZMath_multifit_linear();
l.Alloc(n, 3);
l.Wlinear(X, w, y, c, cov, out chisq);
System.Console.WriteLine("# best fit: Y = " + c[0] + " + " + c[1] + " X + " + c[2] + " X ^ 2");
System.Console.WriteLine("# covariance matrix:");
cov.ScreenWriteLine();
System.Console.WriteLine("# chisq = " + chisq);
}
public static void IOExample()
{
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.WriteFile("matrix.txt");
PZMath_matrix readMatrix = new PZMath_matrix();
readMatrix.ReadFile("matrix.txt");
readMatrix.ScreenWriteLine();
}