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] ); }