/// <summary>
/// Returns lowest grade basis blade in this MV.
/// </summary>
/// <returns>lowest grade basis blade in this MV.</returns>
public int LowestGrade()
{
int lg = int.MaxValue;
for (int g = 0; g < m_basisBlades.Length; g++)
{
for (int e = 0; e < m_basisBlades[g].Length; e++)
{
RefGA.BasisBlade srcB = m_basisBlades[g][e];
if (srcB.Grade() < lg)
{
lg = srcB.Grade();
}
}
}
return(lg);
}
/// <summary>
/// Returns highest grade basis blade in this MV.
/// </summary>
/// <returns>highest grade basis blade in this MV.</returns>
public int HighestGrade()
{
int hg = -1;
for (int g = 0; g < m_basisBlades.Length; g++)
{
for (int e = 0; e < m_basisBlades[g].Length; e++)
{
RefGA.BasisBlade srcB = m_basisBlades[g][e];
if (srcB.Grade() > hg)
{
hg = srcB.Grade();
}
}
}
return(hg);
}
/// <summary>
/// Computes the inner product of two basis blades in arbitary non-Euclidean metric.
/// </summary>
/// <param name="A">input blade</param>
/// <param name="B">input blade</param>
/// <param name="M">The Metric to be used</param>
/// <returns>Scalar product of <paramref name="A"/> and <paramref name="B"/>.</returns>
public static ArrayList ScalarProduct(BasisBlade A, BasisBlade B, Metric M)
{
InnerProductType type = InnerProductType.SCALAR_PRODUCT;
return InnerProductFilter(A.Grade(), B.Grade(), GeometricProduct(A, B, M), type);
}
/// <summary>
/// Computes the inner product of two basis blades in diagonal non-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>
/// <returns>Scalar product of <paramref name="A"/> and <paramref name="B"/>.</returns>
public static BasisBlade ScalarProduct(BasisBlade A, BasisBlade B, double[] m)
{
InnerProductType type = InnerProductType.SCALAR_PRODUCT;
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">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;
}
}