public double DfDx(MatrixFunctionWithMatrixArgument Func, Matrix x, int FuncIndex1, int FuncIndex2, int xIndex1, int xIndex2, double h)
{
int n1 = x.Values.GetLength(0);
int n2 = x.Values.GetLength(1);
Matrix XPrev = new Matrix(n1, n2);
Matrix XNext = new Matrix(n1, n2);
double Prev, Next;
for (int i = 0; i < n1; i++)
{
for (int j = 0; j < n2; j++)
{
XPrev.Values[i, j] = x.Values[i, j];
XNext.Values[i, j] = x.Values[i, j];
if (i == xIndex1)
{
if (j == xIndex2)
{
XPrev.Values[i, j] -= h;
XNext.Values[i, j] += h;
}
}
}
}
Prev = Func(XPrev).Values[FuncIndex1, FuncIndex2];
Next = Func(XNext).Values[FuncIndex1, FuncIndex2];
return((Next - Prev) / (2.0D * h));
}
public double[, , ,] DfDx(MatrixFunctionWithMatrixArgument Func, Matrix x)
{
///<sumary>
/// retruns an array with all derivatives of the function
/// </summary>
int n1 = x.Values.GetLength(0);
int n2 = x.Values.GetLength(1);
int m1 = Func(x).Values.GetLength(0);
int m2 = Func(x).Values.GetLength(1);
double[, , ,] D = new double[m1, m2, n1, n2];
for (int i = 0; i < m1; i++)
{
for (int j = 0; j < m2; j++)
{
for (int k = 0; k < n1; k++)
{
for (int l = 0; l < n2; l++)
{
D[i, j, k, l] = DfDx(Func, x, i, j, k, l);
}
}
}
}
return(D);
}
public double DfDx(MatrixFunctionWithMatrixArgument Func, Matrix x, int FuncIndex1, int FuncIndex2, int xIndex1, int xIndex2, double InitialStepSize, double Precision)
{
double precision = Precision; // precision to evaluate derivative
double h = InitialStepSize; // initial step size
double c = 10.0D; // factor do divide h (i.e., h_new =h_old/c)
double eps = 1.0E-100D; // small number
int maxSteps = 100; // maximum times to divid h
double devOld, devNew; // old derivative
double calcPrecision; // new derivative
// calculate initial derivative
devOld = this.DfDx(Func, x, FuncIndex1, FuncIndex2, xIndex1, xIndex2, h);
devNew = devOld;
for (int i = 0; i < maxSteps; i++)
{
// reduce h
h /= c;
// calculate new derivative
devNew = this.DfDx(Func, x, FuncIndex1, FuncIndex2, xIndex1, xIndex2, h);
//calculate precision
if (Math.Abs(devNew) > eps)
{
calcPrecision = Math.Abs((devNew - devOld) / devNew);
}
else
{
// don't divide by devNew if devNew is small
calcPrecision = Math.Abs(devNew - devOld);
}
// stop if precision is met
if (calcPrecision < precision)
{
//Console.Write("number of steps = "+i.ToString()+"\n");
//Console.Write("Calculated precision = "+calcPrecision.ToString()+"\n");
return(devNew);
}
devOld = devNew;
}
return(devNew);
}
public double DfDx(MatrixFunctionWithMatrixArgument Func, Matrix x, int FuncIndex1, int FuncIndex2, int xIndex1, int xIndex2)
{
return(DfDx(Func, x, FuncIndex1, FuncIndex2, xIndex1, xIndex2, 1.0E-2D, 1.0E-14D));
}