/// <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 GaSymMetricNonOrthogonal CreateDerivedCbmFrameSystem(GaSymFrame baseFrame, MathematicaMatrix cbm)
{
var baseIpm = baseFrame.Ipm.ToMathematicaMatrix();
var cbmTrans = (MathematicaMatrix)cbm.Transpose();
var cbmInverseTrans = (MathematicaMatrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedCba = cbmInverseTrans.ToOutermorphismTree();
var derivedToBaseCba = cbmTrans.ToOutermorphismTree();
if (ipm.IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.GetDiagonal());
return(new GaSymMetricNonOrthogonal(baseFrame, derivedFrame, derivedToBaseCba, baseToDerivedCba));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaSymFrameNonOrthogonal(baseFrame, ipm, derivedToBaseCba, baseToDerivedCba);
return(derivedFrame.NonOrthogonalMetric);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm.ToMathematicaMatrix());
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 GaSymMetricNonOrthogonal CreateReciprocalCbmFrameSystem(GaSymFrame baseFrame)
{
if (baseFrame.IsOrthogonal)
{
var cbmat = baseFrame.Ipm.Inverse();
var b2DOm = baseFrame.Ipm.ToOutermorphismTree();
var d2BOm = cbmat.ToOutermorphismTree();
var derivedFrame = CreateOrthogonal(cbmat.GetDiagonal());
return(new GaSymMetricNonOrthogonal(baseFrame, derivedFrame, d2BOm, b2DOm));
}
var cbmArray = new MathematicaScalar[baseFrame.VSpaceDimension, baseFrame.VSpaceDimension];
var mv2 = baseFrame.CreateInverseUnitPseudoScalar();
for (var i = 0; i < baseFrame.VSpaceDimension; i++)
{
var id = (1 << i) ^ baseFrame.MaxBasisBladeId;
var mv1 = GaSymMultivector.CreateTerm(baseFrame.GaSpaceDimension, id, SymbolicUtils.Constants.One);
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 = MathematicaMatrix.CreateFullMatrix(SymbolicUtils.Cas, cbmArray);
return(CreateDerivedCbmFrameSystem(baseFrame, cbm));
}
internal GaSymFrameNonOrthogonal(GaSymFrame baseOrthoFrame, ISymbolicMatrix ipm, GaSymOutermorphism derivedToBaseOm, GaSymOutermorphism baseToDerivedOm)
{
if (baseOrthoFrame.IsOrthogonal == false)
{
throw new GMacSymbolicException("Base frame must be orthogonal");
}
if (ipm.IsSymmetric() == false || ipm.IsDiagonal())
{
throw new GMacSymbolicException("Inner product matrix must be symmetric and non-diagonal");
}
InnerProductMatrix = ipm.ToMathematicaMatrix();
NonOrthogonalMetric =
new GaSymMetricNonOrthogonal(
baseOrthoFrame,
this,
derivedToBaseOm,
baseToDerivedOm
);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = GaSymBilinearProductCba.CreateGp(NonOrthogonalMetric);
Sp = ComputedSp = GaSymBilinearProductCba.CreateSp(NonOrthogonalMetric);
Lcp = ComputedLcp = GaSymBilinearProductCba.CreateLcp(NonOrthogonalMetric);
Rcp = ComputedRcp = GaSymBilinearProductCba.CreateRcp(NonOrthogonalMetric);
Fdp = ComputedFdp = GaSymBilinearProductCba.CreateFdp(NonOrthogonalMetric);
Hip = ComputedHip = GaSymBilinearProductCba.CreateHip(NonOrthogonalMetric);
Acp = ComputedAcp = GaSymBilinearProductCba.CreateAcp(NonOrthogonalMetric);
Cp = ComputedCp = GaSymBilinearProductCba.CreateCp(NonOrthogonalMetric);
UnitPseudoScalarCoef =
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? CasConstants.MinusOne / BasisBladeSignature(MaxBasisBladeId)[0].ToMathematicaScalar()
: CasConstants.One / BasisBladeSignature(MaxBasisBladeId)[0].ToMathematicaScalar();
}
