/// <summary>
/// Maps the non-negative abscissas/weights from the interval [-1, 1] to the interval [intervalBegin, intervalEnd].
/// </summary>
/// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
/// <param name="gaussPoint">Object containing the non-negative abscissas/weights, order, and intervalBegin/intervalEnd. The non-negative abscissas/weights are generated over the interval [-1,1] for the given order.</param>
/// <returns>Object containing the abscissas/weights, order, and intervalBegin/intervalEnd.</returns>
private static GaussPoint <T> Map <T>(
T intervalBegin,
T intervalEnd,
GaussPoint gaussPoint) where T : unmanaged
{
//TODO: not sure wat this work for Complex
var la = LinearAlgebraFactory.GetLinearAlgebra <T>();
var abscissas = new T[gaussPoint.Order];
var weights = new T[gaussPoint.Order];
var num1 = la.Mult(la.Cast(0.5), la.Sub(intervalEnd, intervalBegin));
var num2 = la.Mult(la.Cast(0.5), la.Sum(intervalEnd, intervalBegin));
var num3 = gaussPoint.Order + 1 >> 1;
for (var index1 = 1; index1 <= num3; ++index1)
{
var index2 = gaussPoint.Order - index1;
var index3 = index1 - 1;
var index4 = num3 - index1;
abscissas[index2] = la.Sum(la.Mult(la.Cast(gaussPoint.Abscissas[index4]), num1), num2);
abscissas[index3] = la.Sum(la.Mult(la.Cast(gaussPoint.Abscissas[index4]), la.Mult(num1, la.Cast(-1))), num2);
weights[index2] = weights[index3] = la.Mult(la.Cast(gaussPoint.Weights[index4]), num1);
}
return(new GaussPoint <T>(gaussPoint.Order, abscissas, weights, intervalBegin, intervalEnd));
}
/// <summary>Getter for the GaussPoint.</summary>
/// <param name="order">Defines an Nth order Gauss-Legendre rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.</param>
/// <returns>Object containing the non-negative abscissas/weights, order, and intervalBegin/intervalEnd. The non-negative abscissas/weights are generated over the interval [-1,1] for the given order.</returns>
public static GaussPoint GetGaussPoint(int order)
{
if ((_gaussLegendrePoint == null ? 0 : _gaussLegendrePoint.Order == order ? 1 : 0) != 0)
{
return(_gaussLegendrePoint);
}
if (!GaussLegendrePoints.PreComputed.TryGetValue(order, out _gaussLegendrePoint))
{
_gaussLegendrePoint = GaussLegendrePoints.Generate(order, 1E-10);
}
return(_gaussLegendrePoint);
}