/// <summary>
/// Create a derived frame system using a change of basis matrix for the basis vectors
/// </summary>
/// <param name="baseFrame">The base frame. It may be any kind of frame</param>
/// <param name="cbm">The 'Change Of Basis Vectors' matrix. It must be invertable</param>
/// <returns></returns>
public static GaNumMetricNonOrthogonal CreateDerivedCbmFrameSystem(GaNumFrame baseFrame, Matrix cbm)
{
var baseIpm = baseFrame.Ipm;
var cbmTrans = (Matrix)cbm.Transpose();
var cbmInverseTrans = (Matrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedCba = cbmInverseTrans.ToOutermorphismTree();
var derivedToBaseCba = cbmTrans.ToOutermorphismTree();
if ((ipm as Matrix).IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.Diagonal());
return(new GaNumMetricNonOrthogonal(baseFrame, derivedFrame, derivedToBaseCba, baseToDerivedCba));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaNumFrameNonOrthogonal(baseFrame, ipm as Matrix, derivedToBaseCba, baseToDerivedCba);
return(derivedFrame.NonOrthogonalMetric);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm as Matrix);
return(gaFrame.NonOrthogonalMetric);
//return new DerivedFrameSystem(baseFrame, gaFrame, derivedToBaseOm, baseToDerivedOm);
}
/// <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));
}
internal GaNumFrameNonOrthogonal(GaNumFrame baseOrthoFrame, Matrix ipm, GaNumOutermorphism derivedToBaseOm, GaNumOutermorphism baseToDerivedOm)
{
if (baseOrthoFrame.IsOrthogonal == false)
{
throw new GMacNumericException("Base frame must be orthogonal");
}
if (ipm.IsDiagonal())
{
throw new GMacNumericException("Inner product matrix must be non-diagonal");
}
InnerProductMatrix = ipm;
NonOrthogonalMetric =
new GaNumMetricNonOrthogonal(
baseOrthoFrame,
this,
derivedToBaseOm,
baseToDerivedOm
);
Op = ComputedOp = new GaNumOp(VSpaceDimension);
Gp = ComputedGp = GaNumBilinearProductCba.CreateGp(NonOrthogonalMetric);
Sp = ComputedSp = GaNumBilinearProductCba.CreateSp(NonOrthogonalMetric);
Lcp = ComputedLcp = GaNumBilinearProductCba.CreateLcp(NonOrthogonalMetric);
Rcp = ComputedRcp = GaNumBilinearProductCba.CreateRcp(NonOrthogonalMetric);
Fdp = ComputedFdp = GaNumBilinearProductCba.CreateFdp(NonOrthogonalMetric);
Hip = ComputedHip = GaNumBilinearProductCba.CreateHip(NonOrthogonalMetric);
Acp = ComputedAcp = GaNumBilinearProductCba.CreateAcp(NonOrthogonalMetric);
Cp = ComputedCp = GaNumBilinearProductCba.CreateCp(NonOrthogonalMetric);
UnitPseudoScalarCoef =
(MaxBasisBladeId.BasisBladeIdHasNegativeReverse() ? -1.0d : 1.0d) /
BasisBladeSignature(MaxBasisBladeId)[0];
}