// H^j(x) part of the formula
// which is H^j(x) = (x-xj)*l2j(x)
// the jIndex is the j of the formula (surprise!!!)
// and x is the argument of the function
private double HchapeaujX(int jIndex, double x)
{
// the (x-xj) part
double leftPart = (x - interpolationSamples[samplesXIndex, jIndex]);
// the l2j(x) part
double rightPart = Math.Pow(LagrangeMethod.langrangeForX(jIndex, x, interpolationSamples), 2);
return(leftPart * rightPart);
}
// Hj(x) part of the formula
// which is Hj(x) = [1-2(x-xj)*l'j(xj)]*l2j(x)
// the jIndex is the j of the formula (surprise!!!)
// and x is the argument of the function
private double HjX(int jIndex, double x)
{
// the [1-2(x-xj)*l'j(xj)] part
double leftPart = 0;
// the l'j(xj) part
double lagDerivative = LagrangeDiffrentiationMethod.lagrangeDerivative(jIndex, interpolationSamples[samplesXIndex, jIndex], interpolationSamples);
leftPart = (1 - (2 * (x - interpolationSamples[samplesXIndex, jIndex]) * lagDerivative));
// the l2j(x) part
double rightPart = Math.Pow(LagrangeMethod.langrangeForX(jIndex, x, interpolationSamples), 2);
return(leftPart * rightPart);
}
private string HjStringForX(int jIndex)
{
double currentXi = interpolationSamples[samplesXIndex, jIndex];
// the [1-2(x-xj)*l'j(xj)] part
// build Hj(x) string
// first the [1-2(x-xj)*l'j(xj)]
// note that the Hj(x) formula can be changed from
// [1-2(x-xj)*l'j(xj)]*l2j(x) to [a*x - b]* l2j(x)
// where a = 2 * l'j(xj) and b = a * xj + 1
double a = 2 * LagrangeDiffrentiationMethod.lagrangeDerivative(jIndex, interpolationSamples[samplesXIndex, jIndex], interpolationSamples);
double b = a * currentXi + 1;
char bInversedSign = b >= 0 ? '-' : '+';
StringBuilder builder = new StringBuilder("[" + UIDoubleAbs(a) + "x " + bInversedSign + " " + UIDoubleAbs(b) + "]");
// the l2j(x) part
builder.Append("(" + LagrangeMethod.langrangeString(jIndex, interpolationSamples) + ")^2");
return(builder.ToString());
}
// H^j(x) part of the formula
// which is H^j(x) = (x-xj)*l2j(x)
// the jIndex is the j of the formula (surprise!!!)
// and x is the argument of the function
private string HchapeaujStringForX(int jIndex)
{
double currentXi = interpolationSamples[samplesXIndex, jIndex];
char currentXiReversedSign = currentXi >= 0 ? '-' : '+';
// the (x-xj) part
StringBuilder builder = new StringBuilder();
if (UIDoubleAbs(currentXi) == 0)
{
builder.Append("(x)");
}
else
{
builder.Append("(x " + currentXiReversedSign + " " + UIDoubleAbs(currentXi) + ")");
}
// the l2j(x) part
builder.Append("[" + LagrangeMethod.langrangeString(jIndex, interpolationSamples) + "]^2");
return(builder.ToString());
}