public static SquareMatrix Inverse(SquareMatrix A)
{
int N = A.x.GetLength(0);
SquareMatrix Acp = new SquareMatrix(A);
SquareMatrix Ainv = Identity(N);
double tmp;
int c;
for (int i = 0; i < N; i++)
{
c = i;
for (int k = i + 1; k < N; k++)
{
if (Math.Abs(Acp.x[c, i]) < Math.Abs(Acp.x[k, i])) c = k;
}
if (c != i)
{
for (int j = 0; j < N; j++)
{
tmp = Acp.x[c, j];
Acp.x[c, j] = Acp.x[i, j];
Acp.x[i, j] = tmp;
tmp = Ainv.x[c, j];
Ainv.x[c, j] = Ainv.x[i, j];
Ainv.x[i, j] = tmp;
}
}
tmp = Acp.x[i, i];
for (int j = 0; j < N; j++)
{
Acp.x[i, j] /= tmp;
Ainv.x[i, j] /= tmp;
}
for (int k = 0; k < N; k++)
{
if (k == i) continue;
tmp = Acp.x[k, i];
for (int j = 0; j < N; j++)
{
Acp.x[k, j] -= tmp * Acp.x[i, j];
Ainv.x[k, j] -= tmp * Ainv.x[i, j];
}
}
}
return Ainv;
}
public static double Det(SquareMatrix A)
{
int N = A.x.GetLength(0);
SquareMatrix Acp = new SquareMatrix(A);
double det = 1.0;
double tmp;
int c;
for (int i = 0; i < N; i++)
{
c = i;
for (int k = i + 1; k < N; k++)
{
if (Math.Abs(Acp.x[c, i]) < Math.Abs(Acp.x[k, i])) c = k;
}
if (c != i)
{
for (int j = 0; j < N; j++)
{
tmp = Acp.x[c, j];
Acp.x[c, j] = Acp.x[i, j];
Acp.x[i, j] = tmp;
}
det = -det;
}
tmp = Acp.x[i, i];
for (int j = i; j < N; j++)
{
Acp.x[i, j] /= tmp;
}
det *= tmp;
for (int k = i + 1; k < N; k++)
{
tmp = Acp.x[k, i];
for (int j = i; j < N; j++)
{
Acp.x[k, j] -= tmp * Acp.x[i, j];
}
}
}
return det;
}
public SquareMatrix(SquareMatrix A)
{
this.x = (double[,])A.x.Clone();
}
public static double Tr(SquareMatrix A)
{
int N = A.x.GetLength(0);
double tr = 0.0;
for (int k = 0; k < N; k++)
{
tr += A.x[k, k];
}
return tr;
}
public static SquareMatrix Pow(SquareMatrix A, int n)
{
SquareMatrix pow = Identity(n);
for (int k = 1; k <= Math.Abs(n); k++)
{
pow *= A;
}
if (n < 0) pow = Inverse(pow);
return pow;
}
static void Main(string[] args)
{
Complex I = Complex.I;
Complex z1 = 1+I;
Complex z2 = -1+2*I;
Complex z3 = z1/z2;
Complex z4 = Complex.Exp(I*Math.PI/2);
Console.WriteLine("Complex");
Console.WriteLine((-z1).ToString());
Console.WriteLine(Complex.Arg(-I));
double[,] x = {
{2, 2, 1},
{3, 0, 2},
{4, 3, 2}
};
Console.WriteLine("\n@A");
SquareMatrix A = new SquareMatrix(x);
Console.WriteLine(A.ToString());
SquareMatrix Ainv = SquareMatrix.Inverse(A);
Console.WriteLine(SquareMatrix.Det(A));
Console.WriteLine(Ainv.ToString());
double[,] y = {
{1, 2, 1},
{2, 1, 0},
{1, 1, 2}
};
Console.WriteLine("\n@B");
SquareMatrix B = new SquareMatrix(y);
Console.WriteLine(B.ToString());
SquareMatrix Binv = SquareMatrix.Inverse(B);
Console.WriteLine(SquareMatrix.Det(B));
Console.WriteLine(Binv.ToString("f1"));
double[] a = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
double[] b = { 2.0, 3.5, 5.0, 4.0, 5.5, 7.0};
Console.WriteLine("\nStatistics");
Console.WriteLine(Statistics.Average(a) + ", " + Statistics.Average(b));
Console.WriteLine(Statistics.Variance(a) + ", " + Statistics.Variance(b));
Console.WriteLine(Statistics.UnbiasedVariance(a) + ", " + Statistics.UnbiasedVariance(b));
Console.WriteLine(Statistics.Covariance(a, b));
Console.WriteLine(Statistics.Corr(a, b));
Console.WriteLine(Statistics.Erf(1.0));
/*
Console.WriteLine("\nAnalysis");
const int N = 256;
double[] f1 = new double[N];
for (int n = 0; n < N; n++)
{
f1[n] = n <= N / 2 ? -1.0 + 4.0 * n / N : 3.0 - 4.0 * n / N;
}
Complex[] c1 = Analysis.DFT(f1);
Complex[] c2 = Analysis.FFT(f1);
for (int n = 0; n < N; n++)
{
Console.WriteLine(Complex.Re(c1[n]).ToString("f4") + ", " + Complex.Re(c2[n]).ToString("f4"));
}
*/
Console.WriteLine("\nSequences");
Console.WriteLine(Sequences.Fac(6));
Console.WriteLine(Sequences.Fac(4));
Console.WriteLine(Sequences.Fac(7));
Console.WriteLine(Sequences.DFac(3));
Console.WriteLine(Sequences.DFac(8));
Console.WriteLine(Sequences.DFac(5));
Console.WriteLine(Sequences.Fibonacci(8));
Console.WriteLine(Sequences.Fibonacci(4));
Console.WriteLine(Sequences.Fibonacci(10));
Console.WriteLine(Sequences.C(1, 0));
Console.WriteLine(Sequences.C(2, 0));
Console.WriteLine(Sequences.C(2, 1));
Console.WriteLine(Sequences.C(3, 3));
Console.WriteLine(Sequences.C(4, 2));
Console.WriteLine(Sequences.Catalan(1));
Console.WriteLine(Sequences.Catalan(4));
Console.WriteLine(Sequences.Catalan(7));
GraphForm gph = new GraphForm();
double[] x1 = new double[501];
double[] y1 = new double[501];
double t;
for (int n = 0; n <= 500; n++)
{
t = Math.PI * n / 125.0;
x1[n] = 6.0*Math.Cos(3*t);
y1[n] = 6.0*Math.Sin(4*t);
}
gph.DrawCurve2D(x1, y1);
// Application.Run(gph);
Console.ReadKey();
}