/// <summary>
/// Odd Versor Product of a list of basis blades given by their IDs
/// </summary>
/// <param name="oddVersor"></param>
/// <param name="basisBladeIDs"></param>
/// <returns></returns>
public IEnumerable <GaNumMultivector> OddVersorProduct(GaNumMultivector oddVersor, IEnumerable <int> basisBladeIDs)
{
var oddVersorReverse = oddVersor.Reverse();
var oddVersorNorm2Inverse = 1.0d / Sp[oddVersor, oddVersorReverse][0];
var oddVersorInverse = oddVersorReverse * oddVersorNorm2Inverse;
return(basisBladeIDs.Select(id =>
{
var mv = GaNumMultivector.CreateTerm(
GaSpaceDimension,
id,
id.BasisBladeIdHasNegativeGradeInv() ? -1.0d : 1.0d
);
return
Gp[Gp[oddVersor, mv], oddVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
/// <summary>
/// Create a derived frame system where the derived frame is the reciprocal of the base frame
/// </summary>
/// <param name="baseFrame"></param>
/// <returns></returns>
public static GaNumMetricNonOrthogonal CreateReciprocalCbmFrameSystem(GaNumFrame baseFrame)
{
if (baseFrame.IsOrthogonal)
{
var cbmat = baseFrame.Ipm.Inverse();
var b2DOm = baseFrame.Ipm.ToOutermorphismTree();
var d2BOm = (cbmat as Matrix).ToOutermorphismTree();
var derivedFrame = CreateOrthogonal(cbmat.Diagonal());
return(new GaNumMetricNonOrthogonal(baseFrame, derivedFrame, d2BOm, b2DOm));
}
var cbmArray = new double[baseFrame.VSpaceDimension, baseFrame.VSpaceDimension];
var mv2 = baseFrame.CreateInverseUnitPseudoScalar();
for (var i = 0; i < baseFrame.VSpaceDimension; i++)
{
var id = (1 << i) ^ baseFrame.MaxBasisBladeId;
var mv1 = GaNumMultivector.CreateTerm(baseFrame.GaSpaceDimension, id, 1.0d);
var mv = baseFrame.Lcp[mv1, mv2];
foreach (var term in mv.NonZeroTerms)
{
var j = term.Key.BasisBladeIndex();
if ((i & 1) == 1)
{
cbmArray[i, j] = term.Value;
}
else
{
cbmArray[i, j] = -term.Value;
}
}
}
var cbm = DenseMatrix.OfArray(cbmArray);
return(CreateDerivedCbmFrameSystem(baseFrame, cbm));
}
public GaNumMultivector CreateInverseUnitPseudoScalar()
{
return(GaNumMultivector.CreateTerm(GaSpaceDimension, MaxBasisBladeId, UnitPseudoScalarCoef));
}