/// <summary>Shortcut to InnerProduct() </summary>
public static ArrayList ip(BasisBlade A, BasisBlade B, Metric M, InnerProductType type)
{
return InnerProduct(A, B, M, type);
}
/// <summary>Shortcut to InnerProduct() </summary>
public static BasisBlade ip(BasisBlade A, BasisBlade B, double[] m, InnerProductType type)
{
return InnerProduct(A, B, m, type);
}
/// <summary>
/// Computes the inner product of two basis blades in Euclidean metric.
/// </summary>
/// <param name="A">input blade</param>
/// <param name="B">input blade</param>
/// <param name="M">The Metric to be used.</param>
/// <param name="type">inner product type to be used. Use one of the InnerProductType constants:
/// LEFT_CONTRACTION, RIGHT_CONTRACTION, HESTENES_INNER_PRODUCT, MODIFIED_HESTENES_INNER_PRODUCT or SCALAR_PRODUCT.</param>
/// <returns>Inner product of <paramref name="A"/> and <paramref name="B"/>.</returns>
public static ArrayList InnerProduct(BasisBlade A, BasisBlade B, Metric M, InnerProductType type)
{
return InnerProductFilter(A.Grade(), B.Grade(), GeometricProduct(A, B, M), type);
}
/// <summary>
/// Computes the inner product of two basis blades in Euclidean metric.
/// </summary>
/// <param name="A">input blade</param>
/// <param name="B">input blade</param>
/// <param name="m">an array of doubles giving the metric for each basis vector.</param>
/// <param name="type">inner product type to be used. Use one of the InnerProductType constants:
/// LEFT_CONTRACTION, RIGHT_CONTRACTION, HESTENES_INNER_PRODUCT, MODIFIED_HESTENES_INNER_PRODUCT or SCALAR_PRODUCT.</param>
/// <returns>Inner product of <paramref name="A"/> and <paramref name="B"/>.</returns>
public static BasisBlade InnerProduct(BasisBlade A, BasisBlade B, double[] m, InnerProductType type)
{
return InnerProductFilter(A.Grade(), B.Grade(), GeometricProduct(A, B, m), type);
}
/// <summary>
/// Applies the inner product 'filter' to a BasisBlade in order to turn a geometric product into an inner product
/// </summary>
/// <param name="ga">Grade of argument 'a'</param>
/// <param name="gb">Grade of argument 'b'</param>
/// <param name="r">the basis blade to be filtered</param>
/// <param name="type">type the type of inner product required</param>
/// <returns>Either <paramref name="r"/> or ZERO, or null when <paramref name="type"/> is invalid</returns>
private static BasisBlade InnerProductFilter(int ga, int gb, BasisBlade r, InnerProductType type)
{
switch (type)
{
case InnerProductType.LEFT_CONTRACTION:
if ((ga > gb) || (r.Grade() != (gb - ga)))
return ZERO; // return zero
else return r; // return input blade
case InnerProductType.RIGHT_CONTRACTION:
if ((ga < gb) || (r.Grade() != (ga - gb)))
return ZERO; // return zero
else return r; // return input blade
case InnerProductType.HESTENES_INNER_PRODUCT:
if ((ga == 0) || (gb == 0)) return new BasisBlade();
if (Math.Abs(ga - gb) == r.Grade()) return r; // return input blade
else return ZERO; // return zero
case InnerProductType.MODIFIED_HESTENES_INNER_PRODUCT:
if (Math.Abs(ga - gb) == r.Grade()) return r; // return input blade
else return ZERO; // return zero
case InnerProductType.SCALAR_PRODUCT:
if (r.Grade() == 0) return r;
else return ZERO; // return zero
default:
return null;
}
}
/// <param name="ga">grade of left hand side argument of inner product.</param>
/// <param name="gb">grade of right hand side argument of inner product.</param>
/// <param name="R">Array of Basis Blades to which the filter should be applied.</param>
/// <param name="type">InnerProductType (one of LEFT_CONTRACTION, RIGHT_CONTRACTION, HESTENES_INNER_PRODUCT, MODIFIED_HESTENES_INNER_PRODUCT or SCALAR_PRODUCT)</param>
/// <summary>
/// Applies the inner product 'filter' to an array of BasisBlades in order turn
/// a geometric product into an inner product.
/// </summary>
private static ArrayList InnerProductFilter(int ga, int gb, ArrayList R, InnerProductType type)
{
ArrayList result = new ArrayList();
foreach (BasisBlade r in R) {
BasisBlade B = InnerProductFilter(ga, gb, r, type);
if (B.scale != 0.0)
result.Add(B);
}
return result;
}
