/// <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>
static GaussPoint Map(double intervalBegin, double intervalEnd, GaussPoint gaussPoint)
{
double[] abscissas = new double[gaussPoint.Order];
double[] weights = new double[gaussPoint.Order];
double a = 0.5 * (intervalEnd - intervalBegin);
double b = 0.5 * (intervalEnd + intervalBegin);
int m = (gaussPoint.Order + 1) >> 1;
var gaussPointAbscissas = gaussPoint.Abscissas;
var gaussPointWeights = gaussPoint.Weights;
for (int i = 1; i <= m; i++)
{
int index1 = gaussPoint.Order - i;
int index2 = i - 1;
int index3 = m - i;
abscissas[index1] = gaussPointAbscissas[index3] * a + b;
abscissas[index2] = -gaussPointAbscissas[index3] * a + b;
weights[index1] = gaussPointWeights[index3] * a;
weights[index2] = gaussPointWeights[index3] * a;
}
return(new GaussPoint(intervalBegin, intervalEnd, gaussPoint.Order, abscissas, weights));
}
/// <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 calulcated 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)
{
// Try to get the GaussPoint from the cached static field.
bool gaussLegendrePointIsCached = _gaussLegendrePoint != null && _gaussLegendrePoint.Order == order;
if (!gaussLegendrePointIsCached)
{
// Try to find the GaussPoint in the precomputed dictionary.
if (!GaussLegendrePoint.PreComputed.TryGetValue(order, out _gaussLegendrePoint))
{
_gaussLegendrePoint = GaussLegendrePoint.Generate(order, 1e-10); // Generate the GaussPoint on the fly.
}
}
return _gaussLegendrePoint;
}
/// <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)
{
// Try to get the GaussPoint from the cached static field.
bool gaussLegendrePointIsCached = _gaussLegendrePoint != null && _gaussLegendrePoint.Order == order;
if (!gaussLegendrePointIsCached)
{
// Try to find the GaussPoint in the precomputed dictionary.
if (!GaussLegendrePoint.PreComputed.TryGetValue(order, out _gaussLegendrePoint))
{
_gaussLegendrePoint = GaussLegendrePoint.Generate(order, 1e-10); // Generate the GaussPoint on the fly.
}
}
return(_gaussLegendrePoint);
}
/// <summary>
/// Initializes a new instance of the <see cref="GaussLegendreRule"/> class.
/// </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="order">Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calulcated on the fly.</param>
public GaussLegendreRule(double intervalBegin, double intervalEnd, int order)
{
_gaussLegendrePoint = GaussLegendrePointFactory.GetGaussPoint(intervalBegin, intervalEnd, order);
}
/// <summary>
/// Maps the non-negative abscissas/weights from the interval [-1, 1] to the interval [intervalBegin, intervalEnd].
/// </summary>
/// <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>
/// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
/// <returns>Object containing the abscissas/weights, order, and intervalBegin/intervalEnd.</returns>
private static GaussPoint Map(GaussPoint gaussPoint, double intervalBegin, double intervalEnd)
{
double[] abscissas = new double[gaussPoint.Order];
double[] weights = new double[gaussPoint.Order];
double a = 0.5*(intervalEnd - intervalBegin);
double b = 0.5*(intervalEnd + intervalBegin);
int m = (gaussPoint.Order + 1) >> 1;
for (int i = 1; i <= m; i++)
{
int index1 = gaussPoint.Order - i;
int index2 = i - 1;
int index3 = m - i;
abscissas[index1] = gaussPoint.Abscissas[index3]*a + b;
abscissas[index2] = -gaussPoint.Abscissas[index3]*a + b;
weights[index1] = gaussPoint.Weights[index3]*a;
weights[index2] = gaussPoint.Weights[index3]*a;
}
return new GaussPoint(intervalBegin, intervalEnd, gaussPoint.Order, abscissas, weights);
}