private void ValidateComputingMainProductsSymbolic(int grade1, int grade2)
{
ReportComposer.AppendLineAtNewLine();
ReportComposer.AppendHeader("Grades: <" + grade1 + ", " + grade2 + ">", 2);
//Initialize blades with random integer coefficients
var mv1 = RandomGenerator.GetSymBlade(SymbolicFrame.GaSpaceDimension, grade1);
var mv2 = RandomGenerator.GetSymBlade(SymbolicFrame.GaSpaceDimension, grade2);
//Compute their geometric product
var mvGp = SymbolicFrame.Gp[mv1, mv2];
//Compute their Outer Product and test its relation to the geometric product
var mvOp1 = SymbolicFrame.Op[mv1, mv2];
var mvOp2 = mvGp.GetKVectorPart(grade1 + grade2);
ValidateEqual("Outer Product: ", mvOp1, mvOp2);
//Compute their Scalar Product and test its relation to the geometric product
var mvSp1 = SymbolicFrame.Sp[mv1, mv2];
var mvSp2 = mvGp.GetKVectorPart(0);
ValidateEqual("Scalar Product: ", mvSp1, mvSp2);
//Compute their Left Contraction Product and test its relation to the geometric product
var mvLcp1 = SymbolicFrame.Lcp[mv1, mv2];
var mvLcp2 = mvGp.GetKVectorPart(grade2 - grade1);
ValidateEqual("Left Contraction Product: ", mvLcp1, mvLcp2);
//Compute their Right Contraction Product and test its relation to the geometric product
var mvRcp1 = SymbolicFrame.Rcp[mv1, mv2];
var mvRcp2 = mvGp.GetKVectorPart(grade1 - grade2);
ValidateEqual("Right Contraction Product: ", mvRcp1, mvRcp2);
//Compute their Fat-Dot Product and test its relation to the geometric product
var mvFdp1 = SymbolicFrame.Fdp[mv1, mv2];
var mvFdpGrade = grade1 == grade2 ? 0 : Math.Abs(grade1 - grade2);
var mvFdp2 = mvGp.GetKVectorPart(mvFdpGrade);
ValidateEqual("Fat-Dot Product: ", mvFdp1, mvFdp2);
//Compute their Anti-Commutator Product and test its relation to the geometric product
var mvAcp1 = SymbolicFrame.Acp[mv1, mv2];
var mvAcp2 = (SymbolicFrame.Gp[mv1, mv2] + SymbolicFrame.Gp[mv2, mv1]) / 2;
ValidateEqual("Anti-Commutator Product: ", mvAcp1, mvAcp2);
//Compute their Commutator Product and test its relation to the geometric product
var mvCp1 = SymbolicFrame.Cp[mv1, mv2];
var mvCp2 = (SymbolicFrame.Gp[mv1, mv2] - SymbolicFrame.Gp[mv2, mv1]) / 2;
ValidateEqual("Commutator Product: ", mvCp1, mvCp2);
ReportComposer.AppendLineAtNewLine();
}
public override string Validate()
{
ReportComposer.AppendHeader("Blade Operations Validations");
for (var grade1 = 0; grade1 < SymbolicFrame.VSpaceDimension; grade1++)
{
for (var grade2 = 0; grade2 < SymbolicFrame.VSpaceDimension; grade2++)
{
ValidateComputingMainProductsSymbolic(grade1, grade2);
}
}
return(ReportComposer.ToString());
}
private void ValidateNumericFrame()
{
ReportComposer.AppendHeader("Numeric Bilinear Products Validations");
//Initialize multivectors with random coefficients
var mv1 = RandomGenerator.GetNumMultivectorFull(SymbolicFrame.GaSpaceDimension);
var mv2 = RandomGenerator.GetNumMultivectorFull(SymbolicFrame.GaSpaceDimension);
var mvComputedGp = NumericFrame.ComputedGp[mv1, mv2];
var mvComputedOp = NumericFrame.ComputedOp[mv1, mv2];
var mvComputedSp = NumericFrame.ComputedSp[mv1, mv2];
var mvComputedLcp = NumericFrame.ComputedLcp[mv1, mv2];
var mvComputedRcp = NumericFrame.ComputedRcp[mv1, mv2];
var mvComputedFdp = NumericFrame.ComputedFdp[mv1, mv2];
var mvComputedHip = NumericFrame.ComputedHip[mv1, mv2];
var mvComputedAcp = NumericFrame.ComputedAcp[mv1, mv2];
var mvComputedCp = NumericFrame.ComputedCp[mv1, mv2];
//Compute their products using several methods
for (var i = 0; i < _methods.Length; i++)
{
var method = _methods[i];
var methodName = _methodNames[i];
if (NumericFrame.IsNonOrthogonal)
{
NumericFrame.BaseOrthogonalFrame.SetProductsImplementation(method);
}
NumericFrame.SetProductsImplementation(method);
ReportComposer.AppendLineAtNewLine();
ReportComposer.AppendHeader(methodName, 2);
ValidateEqual("Geometric Product: ", mvComputedGp, NumericFrame.Gp[mv1, mv2]);
ValidateEqual("Outer Product: ", mvComputedOp, NumericFrame.Op[mv1, mv2]);
ValidateEqual("Scalar Product: ", mvComputedSp, NumericFrame.Sp[mv1, mv2]);
ValidateEqual("Left Contraction Product: ", mvComputedLcp, NumericFrame.Lcp[mv1, mv2]);
ValidateEqual("Right Contraction Product: ", mvComputedRcp, NumericFrame.Rcp[mv1, mv2]);
ValidateEqual("Fat-Dot Product: ", mvComputedFdp, NumericFrame.Fdp[mv1, mv2]);
ValidateEqual("Hestenes Inner Product: ", mvComputedHip, NumericFrame.Hip[mv1, mv2]);
ValidateEqual("Anti-Commutator Product: ", mvComputedAcp, NumericFrame.Acp[mv1, mv2]);
ValidateEqual("Commutator Product: ", mvComputedCp, NumericFrame.Cp[mv1, mv2]);
ReportComposer.AppendLineAtNewLine();
}
ReportComposer.AppendLineAtNewLine();
}
private void ValidateBothFrame()
{
ReportComposer.AppendHeader("Numeric Bilinear Products Validations using Symbolic Computations");
SymbolicFrame.SetProductsImplementation(GaBilinearProductImplementation.Computed);
NumericFrame.SetProductsImplementation(GaBilinearProductImplementation.Computed);
//Initialize multivectors with random coefficients
var numMv1 = RandomGenerator.GetNumMultivectorFull(SymbolicFrame.GaSpaceDimension);
var numMv2 = RandomGenerator.GetNumMultivectorFull(SymbolicFrame.GaSpaceDimension);
var symMv1 = numMv1.ToSymbolic();
var symMv2 = numMv2.ToSymbolic();
ValidateEqual(
"Geometric Product: ",
SymbolicFrame.Gp[symMv1, symMv2],
NumericFrame.Gp[numMv1, numMv2]
);
ValidateEqual(
"Outer Product: ",
SymbolicFrame.Op[symMv1, symMv2],
NumericFrame.Op[numMv1, numMv2]
);
ValidateEqual(
"Scalar Product: ",
SymbolicFrame.Sp[symMv1, symMv2],
NumericFrame.Sp[numMv1, numMv2]
);
ValidateEqual(
"Left Contraction Product: ",
SymbolicFrame.Lcp[symMv1, symMv2],
NumericFrame.Lcp[numMv1, numMv2]
);
ValidateEqual(
"Right Contraction Product: ",
SymbolicFrame.Rcp[symMv1, symMv2],
NumericFrame.Rcp[numMv1, numMv2]
);
ValidateEqual(
"Fat-Dot Product: ",
SymbolicFrame.Fdp[symMv1, symMv2],
NumericFrame.Fdp[numMv1, numMv2]
);
ValidateEqual(
"Hestenes Inner Product: ",
SymbolicFrame.Hip[symMv1, symMv2],
NumericFrame.Hip[numMv1, numMv2]
);
ValidateEqual(
"Anti-Commutator Product: ",
SymbolicFrame.Acp[symMv1, symMv2],
NumericFrame.Acp[numMv1, numMv2]
);
ValidateEqual(
"Commutator Product: ",
SymbolicFrame.Cp[symMv1, symMv2],
NumericFrame.Cp[numMv1, numMv2]
);
}