public GaSymMultivector AddFactor(int grade, int index, Expr coef)
{
return(AddFactor(
GMacMathUtils.BasisBladeId(grade, index),
coef
));
}
public GMacMultivectorBinding BindCoefToConstant(int grade, int index, Expr valueExpr)
{
return(BindCoefToPattern(
GMacMathUtils.BasisBladeId(grade, index),
GMacScalarBinding.CreateConstant(BaseFrameMultivector.Root, valueExpr)
));
}
public GaSymMultivector SetTermCoef(int grade, int index, MathematicaScalar coef)
{
return(SetTermCoef(
GMacMathUtils.BasisBladeId(grade, index),
coef.Expression
));
}
public double this[int grade, int index]
{
get
{
return(this[GMacMathUtils.BasisBladeId(grade, index)]);
}
}
public GaSymMultivector SetTermCoef(int grade, int index, Expr coef)
{
return(SetTermCoef(
GMacMathUtils.BasisBladeId(grade, index),
coef
));
}
public GMacMultivectorBinding BindCoefToVariable(int grade, int index)
{
return(BindCoefToPattern(
GMacMathUtils.BasisBladeId(grade, index),
GMacScalarBinding.CreateVariable(BaseFrameMultivector.Root)
));
}
public GMacMultivectorBinding UnBindCoefs(int grade, IEnumerable <int> indexes)
{
foreach (var index in indexes)
{
_patternDictionary.Remove(GMacMathUtils.BasisBladeId(grade, index));
}
return(this);
}
public Expr this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
return((id == TermId) ? TermCoef : Expr.INT_ZERO);
}
}
public double this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
return((id == TermId) ? TermCoef : 0.0d);
}
}
private void GenerateOutermorphismToLinearTransformMacro(AstFrame frameInfo)
{
var commandsList = GMacDslSyntaxFactory.SyntaxElementsList(
GMacDslSyntaxFactory.DeclareLocalVariable(DefaultStructure.LinearTransform, "newTr"),
GMacDslSyntaxFactory.EmptyLine(),
GMacDslSyntaxFactory.FixedCode("let newTr.ImageE0 = Multivector(#E0# = '1')"),
GMacDslSyntaxFactory.EmptyLine()
);
for (var index = 1; index <= frameInfo.VSpaceDimension; index++)
{
var id = GMacMathUtils.BasisVectorId(index - 1);
commandsList.Add(
GMacDslSyntaxFactory.AssignToLocalVariable(
"newTr.ImageE" + id,
"om.ImageV" + index + ".@G1@"
)
);
}
commandsList.AddEmptyLine();
for (var grade = 2; grade <= frameInfo.VSpaceDimension; grade++)
{
var kvSpaceDim = frameInfo.KvSpaceDimension(grade);
for (var index = 0; index < kvSpaceDim; index++)
{
int id = GMacMathUtils.BasisBladeId(grade, index);
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
commandsList.Add(
GMacDslSyntaxFactory.AssignToLocalVariable(
"newTr.ImageE" + id,
" newTr.ImageE" + id1 + " op newTr.ImageE" + id2
)
);
}
commandsList.AddEmptyLine();
}
var commandsText = GMacLanguage.CodeGenerator.GenerateCode(commandsList);
GenerateMacro(
frameInfo,
DefaultMacro.Outermorphism.ToLinearTransform,
ComposeMacroInputs("om", DefaultStructure.Outermorphism),
DefaultStructure.LinearTransform,
commandsText,
"newTr"
);
}
public GaNumMultivector GetNumTerm(int gaSpaceDim, int grade, int index)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
var basisBladeId = GMacMathUtils.BasisBladeId(grade, index);
mv.SetTermCoef(basisBladeId, GetScalar());
return(mv);
}
public GaSymMultivector GetSymTerm(int gaSpaceDim, int grade, int index, double minValue, double maxValue)
{
var mv = GaSymMultivector.CreateZero(gaSpaceDim);
var basisBladeId = GMacMathUtils.BasisBladeId(grade, index);
mv.SetTermCoef(basisBladeId, GetSymbolicScalar(minValue, maxValue));
return(mv);
}
public Expr this[int grade, int index]
{
get
{
return(this[GMacMathUtils.BasisBladeId(grade, index)]);
}
set
{
this[GMacMathUtils.BasisBladeId(grade, index)] = value;
}
}
public double this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
double coef;
_termsDictionary.TryGetValue(id, out coef);
return(coef);
}
}
public virtual IEnumerable <Tuple <int, IGaSymMultivector> > BasisVectorMaps()
{
for (var index = 0; index < DomainVSpaceDimension; index++)
{
var mv = this[GMacMathUtils.BasisBladeId(1, index)];
if (!mv.IsNullOrZero())
{
yield return(new Tuple <int, IGaSymMultivector>(index, mv));
}
}
}
public Expr this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
List <Expr> coef;
_termsDictionary.TryGetValue(id, out coef);
return(ReferenceEquals(coef, null)
? Expr.INT_ZERO
: coef.Simplify());
}
}
/// <summary>
/// Create a default subspaces of k-vectors with a given grade and name
/// </summary>
private void DefineDefaultSubspaces_KVectors(GMacFrame frame, int grade, string subspaceName)
{
var basisCount = GMacMathUtils.KvSpaceDimension(frame.VSpaceDimension, grade);
var idsList = new List <int>(basisCount);
for (var index = 0; index < basisCount; index++)
{
idsList.Add(GMacMathUtils.BasisBladeId(grade, index));
}
var subspaceSignature = BooleanPattern.CreateFromTrueIndexes(frame.GaSpaceDimension, idsList);
var subspace = frame.DefineSubspace(subspaceName, subspaceSignature);
subspace.AddCodeLocation(Context.GetCodeLocation(frame.ParseNode));
}
public override IEnumerable <Tuple <int, int, IGaNumMultivector> > BasisVectorsMaps()
{
for (var index1 = 0; index1 < DomainVSpaceDimension; index1++)
{
for (var index2 = 0; index2 < DomainVSpaceDimension2; index2++)
{
var id1 = GMacMathUtils.BasisBladeId(1, index1);
var id2 = GMacMathUtils.BasisBladeId(1, index2);
var mv = MapToTerm(id1, id2);
if (!mv.IsZero())
{
yield return(new Tuple <int, int, IGaNumMultivector>(index1, index2, mv));
}
}
}
}
public virtual IEnumerable <Tuple <int, int, IGaSymMultivector> > BasisVectorsMaps()
{
for (var index1 = 0; index1 < DomainVSpaceDimension; index1++)
{
for (var index2 = 0; index2 < DomainVSpaceDimension; index2++)
{
var id1 = GMacMathUtils.BasisBladeId(1, index1);
var id2 = GMacMathUtils.BasisBladeId(1, index2);
var mv = this[id1, id2];
if (!mv.IsNullOrZero())
{
yield return(new Tuple <int, int, IGaSymMultivector>(index1, index2, mv));
}
}
}
}
private void GenerateTransposeOutermorphismMacro(AstFrame frameInfo)
{
var inputsText = ComposeMacroInputs(
"om", DefaultStructure.Outermorphism
);
var commandsList = GMacDslSyntaxFactory.SyntaxElementsList(
GMacDslSyntaxFactory.DeclareLocalVariable(DefaultStructure.Outermorphism, "newOm"),
GMacDslSyntaxFactory.EmptyLine()
);
var componentsText = new ListComposer("," + Environment.NewLine);
for (var index1 = 1; index1 <= frameInfo.VSpaceDimension; index1++)
{
componentsText.Clear();
var id1 = GMacMathUtils.BasisBladeId(1, index1 - 1);
commandsList.AddFixedCode("let newOm.ImageV" + index1 + " = Multivector(");
for (var index2 = 1; index2 <= frameInfo.VSpaceDimension; index2++)
{
var id2 = GMacMathUtils.BasisBladeId(1, index2 - 1);
componentsText.Add(" #E" + id2 + "# = om.ImageV" + index2 + ".#E" + id1 + "#");
}
commandsList.AddFixedCode(componentsText.ToString());
commandsList.AddFixedCode(")");
commandsList.AddEmptyLine();
}
var commandsText = GMacLanguage.CodeGenerator.GenerateCode(commandsList);
GenerateMacro(
frameInfo,
DefaultMacro.Outermorphism.Transpose,
inputsText,
DefaultStructure.Outermorphism,
commandsText,
"newOm"
);
}
public GaNumMultivector SetTermCoef(int grade, int index, bool isNegative, double coef)
{
var id = GMacMathUtils.BasisBladeId(grade, index);
var value = isNegative ? -coef : coef;
var node = TermsTree;
for (var i = VSpaceDimension - 1; i > 0; i--)
{
var bitPattern = (1 << i) & id;
node = node.GetOrAddInternalChildNode(bitPattern != 0);
}
if ((1 & id) != 0)
{
if (node.HasChildNode1)
{
node.LeafChildNode1.Value = value;
}
else
{
node.ResetLeafChildNode1(value);
}
return(this);
}
if (node.HasChildNode0)
{
node.LeafChildNode0.Value = value;
}
else
{
node.ResetLeafChildNode0(value);
}
return(this);
}
public GaNumMultivector AddFactor(int grade, int index, double coef)
{
AddFactorsCallCount++;
var id = GMacMathUtils.BasisBladeId(grade, index);
var node = TermsTree;
for (var i = VSpaceDimension - 1; i > 0; i--)
{
var bitPattern = (1 << i) & id;
node = node.GetOrAddInternalChildNode(bitPattern != 0);
}
if ((1 & id) != 0)
{
if (node.HasChildNode1)
{
node.LeafChildNode1.Value += coef;
}
else
{
node.ResetLeafChildNode1(coef);
}
return(this);
}
if (node.HasChildNode0)
{
node.LeafChildNode0.Value += coef;
}
else
{
node.ResetLeafChildNode0(coef);
}
return(this);
}
/// <summary>
/// Create the default subspace of odd multivectors named @odd@
/// </summary>
/// <returns></returns>
private GMacFrameSubspace DefineDefaultSubspaces_Odd(GMacFrame frame)
{
var idsList = new List <int>(frame.GaSpaceDimension);
for (var grade = 1; grade <= frame.VSpaceDimension; grade = grade + 2)
{
var basisCount = GMacMathUtils.KvSpaceDimension(frame.VSpaceDimension, grade);
for (var index = 0; index < basisCount; index++)
{
idsList.Add(GMacMathUtils.BasisBladeId(grade, index));
}
}
const string subspaceName = "Odd";
var subspaceSignature = BooleanPattern.CreateFromTrueIndexes(frame.GaSpaceDimension, idsList);
var subspace = frame.DefineSubspace(subspaceName, subspaceSignature);
subspace.AddCodeLocation(Context.GetCodeLocation(frame.ParseNode));
return(subspace);
}
public Expr this[int grade, int index] => this[GMacMathUtils.BasisBladeId(grade, index)];
public double this[int grade, int index] => _termsArray[GMacMathUtils.BasisBladeId(grade, index)];
public Expr this[int grade, int index] => _coefsArray[GMacMathUtils.BasisBladeId(grade, index)].Simplify();
public GMacMultivectorBinding UnBindCoef(int grade, int index)
{
_patternDictionary.Remove(GMacMathUtils.BasisBladeId(grade, index));
return(this);
}
public string BasisBladeName(int grade, int index)
{
return(AssociatedFrame.BasisVectorNames.ConcatenateUsingPattern(
GMacMathUtils.BasisBladeId(grade, index), "E0", "^"
));
}
internal AstFrameBasisBlade(GMacFrame frame, int grade, int index)
{
AssociatedMultivector = frame.MultivectorType;
BasisBladeId = GMacMathUtils.BasisBladeId(grade, index);
}
public IGaSymMultivector this[int grade1, int index1] => this[GMacMathUtils.BasisBladeId(grade1, index1)];