public GaSymMapBilinearCombined AddMapping(MathematicaScalar coef, IGaSymMapBilinear linearMap)
{
if (
linearMap.DomainVSpaceDimension != DomainVSpaceDimension ||
linearMap.TargetVSpaceDimension != TargetVSpaceDimension
)
{
throw new InvalidOperationException("Linear map dimensions mismatch");
}
_termsList.Add(new GaSymMapBilinearCombinedTerm(coef, linearMap));
return(this);
}
internal GaSymFrameEuclidean(int vSpaceDim)
{
EuclideanMetric = GaSymMetricEuclidean.Create(vSpaceDim);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymEuclideanGp(VSpaceDimension);
Sp = ComputedSp = new GaSymEuclideanSp(VSpaceDimension);
Lcp = ComputedLcp = new GaSymEuclideanLcp(VSpaceDimension);
Rcp = ComputedRcp = new GaSymEuclideanRcp(VSpaceDimension);
Fdp = ComputedFdp = new GaSymEuclideanFdp(VSpaceDimension);
Hip = ComputedHip = new GaSymEuclideanHip(VSpaceDimension);
Acp = ComputedAcp = new GaSymEuclideanAcp(VSpaceDimension);
Cp = ComputedCp = new GaSymEuclideanCp(VSpaceDimension);
UnitPseudoScalarCoef = CasConstants.One;
}
public static GaSymMapBilinearTree ToTreeMap(this IGaSymMapBilinear bilinearMap)
{
var resultMap = GaSymMapBilinearTree.Create(
bilinearMap.DomainVSpaceDimension,
bilinearMap.TargetVSpaceDimension
);
foreach (var basisBladeMapping in bilinearMap.BasisBladesMaps())
{
var id1 = basisBladeMapping.Item1;
var id2 = basisBladeMapping.Item2;
var mv = basisBladeMapping.Item3;
resultMap.SetBasisBladesMap(id1, id2, mv);
}
return(resultMap);
}
public static GaSymMapBilinearCoefSums ToCoefSumsMap(this IGaSymMapBilinear bilinearMap)
{
var resultMap = GaSymMapBilinearCoefSums.Create(
bilinearMap.DomainVSpaceDimension,
bilinearMap.TargetVSpaceDimension
);
foreach (var basisBladeMapping in bilinearMap.BasisBladesMaps())
{
var id1 = basisBladeMapping.Item1;
var id2 = basisBladeMapping.Item2;
var mv = basisBladeMapping.Item3;
foreach (var term in mv.NonZeroExprTerms)
{
resultMap.SetFactor(term.Key, id1, id2, term.Value);
}
}
return(resultMap);
}
internal GaSymFrameOrthogonal(IEnumerable <MathematicaScalar> basisVectorsSignaturesList)
{
BasisVectorsSignatures = basisVectorsSignaturesList.ToArray();
OrthogonalMetric = GaSymMetricOrthogonal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymOrthogonalGp(OrthogonalMetric);
Sp = ComputedSp = new GaSymOrthogonalSp(OrthogonalMetric);
Lcp = ComputedLcp = new GaSymOrthogonalLcp(OrthogonalMetric);
Rcp = ComputedRcp = new GaSymOrthogonalRcp(OrthogonalMetric);
Fdp = ComputedFdp = new GaSymOrthogonalFdp(OrthogonalMetric);
Hip = ComputedHip = new GaSymOrthogonalHip(OrthogonalMetric);
Acp = ComputedAcp = new GaSymOrthogonalAcp(OrthogonalMetric);
Cp = ComputedCp = new GaSymOrthogonalCp(OrthogonalMetric);
UnitPseudoScalarCoef = (
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? CasConstants.MinusOne
: CasConstants.One
) / OrthogonalMetric.GetSignature(MaxBasisBladeId);
}
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();
}
/// <summary>
/// frameSigList must have all items equal to 1 (false) or -1 (true) with at least one negative item
/// </summary>
/// <param name="frameSigList"></param>
internal GaSymFrameOrthonormal(IEnumerable <bool> frameSigList)
{
BasisVectorsSignatures = frameSigList.Select(b => b ? -1 : 1).ToArray();
OrthonormalMetric = GaSymMetricOrthonormal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymOrthonormalGp(OrthonormalMetric);
Sp = ComputedSp = new GaSymOrthonormalSp(OrthonormalMetric);
Lcp = ComputedLcp = new GaSymOrthonormalLcp(OrthonormalMetric);
Rcp = ComputedRcp = new GaSymOrthonormalRcp(OrthonormalMetric);
Fdp = ComputedFdp = new GaSymOrthonormalFdp(OrthonormalMetric);
Hip = ComputedHip = new GaSymOrthonormalHip(OrthonormalMetric);
Acp = ComputedAcp = new GaSymOrthonormalAcp(OrthonormalMetric);
Cp = ComputedCp = new GaSymOrthonormalCp(OrthonormalMetric);
UnitPseudoScalarCoef =
MathematicaScalar.Create(
SymbolicUtils.Cas,
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? -1.0d / OrthonormalMetric[MaxBasisBladeId]
: 1.0d / OrthonormalMetric[MaxBasisBladeId]
);
}
private GaSymBilinearProductCba(GaSymMetricNonOrthogonal metric, IGaSymMapBilinear baseProductMap)
{
NonOrthogonalMetric = metric;
BaseProductMap = baseProductMap;
}
internal GaSymMapBilinearCombinedTerm(MathematicaScalar coef, IGaSymMapBilinear linearMap)
{
Coef = coef;
LinearMap = linearMap;
}
