public static void Main(string[] argv)
{
MagicSquareExample.print("\n Test of Matrix Class, using magic squares.\n");
MagicSquareExample.print(" See MagicSquareExample.main() for an explanation.\n");
MagicSquareExample.print("\n n trace max_eig rank cond lu_res qr_res\n\n");
DateTime now = DateTime.Now;
double num = Math.Pow(2.0, -52.0);
for (int i = 3; i <= 32; i++)
{
MagicSquareExample.print(MagicSquareExample.fixedWidthIntegertoString(i, 7));
JamaMatrix jamaMatrix = MagicSquareExample.magic(i);
int n = (int)jamaMatrix.trace();
MagicSquareExample.print(MagicSquareExample.fixedWidthIntegertoString(n, 10));
EigenvalueDecomposition eigenvalueDecomposition = new EigenvalueDecomposition(jamaMatrix.plus(jamaMatrix.transpose()).times(0.5));
double[] realEigenvalues = eigenvalueDecomposition.RealEigenvalues;
MagicSquareExample.print(MagicSquareExample.fixedWidthDoubletoString(realEigenvalues[i - 1], 14, 3));
int n2 = jamaMatrix.rank();
MagicSquareExample.print(MagicSquareExample.fixedWidthIntegertoString(n2, 7));
double num2 = jamaMatrix.cond();
MagicSquareExample.print((num2 < 1.0 / num) ? MagicSquareExample.fixedWidthDoubletoString(num2, 12, 3) : " Inf");
LUDecomposition lUDecomposition = new LUDecomposition(jamaMatrix);
JamaMatrix l = lUDecomposition.L;
JamaMatrix u = lUDecomposition.U;
int[] pivot = lUDecomposition.Pivot;
JamaMatrix jamaMatrix2 = l.times(u).minus(jamaMatrix.getMatrix(pivot, 0, i - 1));
double x = jamaMatrix2.norm1() / ((double)i * num);
MagicSquareExample.print(MagicSquareExample.fixedWidthDoubletoString(x, 12, 3));
QRDecomposition qRDecomposition = new QRDecomposition(jamaMatrix);
JamaMatrix q = qRDecomposition.Q;
jamaMatrix2 = qRDecomposition.R;
jamaMatrix2 = q.times(jamaMatrix2).minus(jamaMatrix);
x = jamaMatrix2.norm1() / ((double)i * num);
MagicSquareExample.print(MagicSquareExample.fixedWidthDoubletoString(x, 12, 3));
MagicSquareExample.print("\n");
}
double x2 = (double)(DateTime.Now.Ticks - now.Ticks) / 1000.0;
MagicSquareExample.print("\nElapsed Time = " + MagicSquareExample.fixedWidthDoubletoString(x2, 12, 3) + " seconds\n");
MagicSquareExample.print("Adios\n");
}
public static JamaMatrix magic(int n)
{
double[][] array = new double[n][];
for (int i = 0; i < n; i++)
{
array[i] = new double[n];
}
if (n % 2 == 1)
{
int num = (n + 1) / 2;
int num2 = n + 1;
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
array[i][j] = (double)(n * ((i + j + num) % n) + (i + 2 * j + num2) % n + 1);
}
}
}
else
{
if (n % 4 == 0)
{
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
if ((i + 1) / 2 % 2 == (j + 1) / 2 % 2)
{
array[i][j] = (double)(n * n - n * i - j);
}
else
{
array[i][j] = (double)(n * i + j + 1);
}
}
}
}
else
{
int num3 = n / 2;
int num4 = (n - 2) / 4;
JamaMatrix jamaMatrix = MagicSquareExample.magic(num3);
for (int j = 0; j < num3; j++)
{
for (int i = 0; i < num3; i++)
{
double num5 = jamaMatrix.get_Renamed(i, j);
array[i][j] = num5;
array[i][j + num3] = num5 + (double)(2 * num3 * num3);
array[i + num3][j] = num5 + (double)(3 * num3 * num3);
array[i + num3][j + num3] = num5 + (double)(num3 * num3);
}
}
for (int i = 0; i < num3; i++)
{
for (int j = 0; j < num4; j++)
{
double num6 = array[i][j];
array[i][j] = array[i + num3][j];
array[i + num3][j] = num6;
}
for (int j = n - num4 + 1; j < n; j++)
{
double num6 = array[i][j];
array[i][j] = array[i + num3][j];
array[i + num3][j] = num6;
}
}
double num7 = array[num4][0];
array[num4][0] = array[num4 + num3][0];
array[num4 + num3][0] = num7;
num7 = array[num4][num4];
array[num4][num4] = array[num4 + num3][num4];
array[num4 + num3][num4] = num7;
}
}
return(new JamaMatrix(array));
}