public static Matrix ConditionalGradientByF(Matrix f_old, Matrix KSI, double alpha, double R, double h, double tau)
{
int N = f_old.Length.n;
int M = f_old.Length.m;
double NORM = 0;
Matrix KSI2 = new Matrix(N, M);
Matrix f_new = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
KSI2[i, j] = Math.Pow(Math.Abs(KSI[i, j]), 2);
}
}
NORM = Math.Sqrt(MyMath.IntegrateSurface(KSI2, tau, h));
double f_prime = 0;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
//R = 10;
f_prime = -R * KSI[i, j] / NORM;
f_new[i, j] = (1d - alpha) * f_old[i, j] + alpha * f_prime;
}
}
return(f_new);
}
public Matrix Pu(Matrix f, double R, double h, double tau)
{
int N = f.Length.n;
int M = f.Length.m;
double NORM = 0;
Matrix f2 = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
f2[i, j] = Math.Pow(Math.Abs(f[i, j]), 2);
}
}
NORM = Math.Sqrt(MyMath.IntegrateSurface(f2, tau, h));
if (NORM < R)
{
return(f);
}
else
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
f2[i, j] = R * f[i, j] / NORM;
}
}
return(f2);
}
}
public static double dJ_f(Matrix KSI, Matrix f, double h, double tau)
{
int N = f.Length.n;
int M = f.Length.m;
double I = 0;
Matrix KSI2 = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
KSI2[i, j] = KSI[i, j] * f[i, j];
}
}
I = MyMath.IntegrateSurface(KSI2, tau, h);
return(Math.Abs(I));
}
double Calculate_L2NORM(Matrix f, double h, double tau)
{
int N = f.Length.n;
int M = f.Length.m;
double NORM = 0;
Matrix f2 = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
f2[i, j] = Math.Pow(Math.Abs(f[i, j]), 2);
}
}
NORM = Math.Sqrt(MyMath.IntegrateSurface(f2, tau, h));
return(NORM);
}
public static Matrix GrdientProjectionByF(Matrix f_old, Matrix KSI, double alpha, double R, double h, double tau)
{
int N = f_old.Length.n;
int M = f_old.Length.m;
double I = 0;
Matrix T = new Matrix(N, M);
Matrix f_new = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
T[i, j] = Math.Pow(Math.Abs(f_old[i, j] - alpha * KSI[i, j]), 2);
}
}
I = MyMath.IntegrateSurface(T, tau, h);
if (I <= R * R)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
f_new[i, j] = f_old[i, j] - alpha * KSI[i, j];
}
}
}
else
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
f_new[i, j] = R * (f_old[i, j] - alpha * KSI[i, j]) / Math.Sqrt(I);
}
}
}
return(f_new);
}
public double ChooseAplpha_LipMethodForConditionalGradient(Matrix KSI, Matrix f, double alpha, double tau, double h)
{
double rho = ChooseAlpha_LipMethod();
int N = f.Length.n;
int M = f.Length.m;
double NORM = 0;
Matrix KSI2 = new Matrix(N, M);
Matrix f2 = new Matrix(N, M);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
KSI2[i, j] = Math.Pow(Math.Abs(KSI[i, j]), 2);
}
}
NORM = Math.Sqrt(MyMath.IntegrateSurface(KSI2, tau, h));
double f_prime = 0, temp = 0;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
//R = 10;
f_prime = -R * KSI[i, j] / NORM;
temp = f_prime - f[i, j];
f2[i, j] = temp * temp;
}
}
NORM = MyMath.IntegrateSurface(f2, tau, h);
double dJ = DifferentialEquation.dJ_f(KSI, f, h, tau);
//MessageBox.Show("dJ = " + dJ + " NORM = " + NORM);
return(min(1d, rho * dJ / (NORM)));
}