public static GaPoTNumFrame CreateGramSchmidtFrame(int vectorsCount, int refVectorIndex, out GaPoTNumFrame kirchhoffFrame)
{
kirchhoffFrame = CreateKirchhoffFrame(vectorsCount, refVectorIndex);
var uPseudoScalar = new GaPoTNumMultivector()
.SetTerm(
(1 << vectorsCount) - 1,
1.0d
);
var cFrame = kirchhoffFrame.GetOrthogonalFrame(true);
cFrame.AppendVector(
-GaPoTNumUtils
.OuterProduct(cFrame)
.Gp(uPseudoScalar.CliffordConjugate())
.GetVectorPart()
);
Debug.Assert(
cFrame.IsOrthonormal()
);
Debug.Assert(
CreateBasisFrame(vectorsCount).HasSameHandedness(cFrame)
);
return(cFrame);
}
public GaPoTNumMultivector Sp(GaPoTNumMultivector mv2)
{
var result = new GaPoTNumMultivector();
foreach (var term1 in _termsDictionary.Values)
{
if (!mv2._termsDictionary.TryGetValue(term1.IDsPattern, out var term2))
{
continue;
}
var value = term1.Value * term2.Value;
if (value == 0)
{
continue;
}
if (GaPoTNumUtils.ComputeIsNegativeEGp(term1.IDsPattern, term2.IDsPattern))
{
value = -value;
}
result.AddTerm(new GaPoTNumMultivectorTerm(0, value));
}
return(result);
}
public GaPoTNumBiversor GetTermPart(int id1, int id2)
{
(id1, id2) = GaPoTNumUtils.ValidateBiversorTermIDs(id1, id2);
return(new GaPoTNumBiversor(
_termsDictionary.Values.Where(t => t.TermId1 == id1 && t.TermId2 == id2)
));
}
public double GetTermValue(int id1, int id2)
{
(id1, id2) = GaPoTNumUtils.ValidateBiversorTermIDs(id1, id2);
return(_termsDictionary
.Values
.Where(t => t.TermId1 == id1 && t.TermId2 == id2)
.Select(v => v.Value)
.Sum());
}
public GaPoTNumMultivectorTerm Gp(GaPoTNumMultivectorTerm term2)
{
var term1 = this;
var idsPattern = term1.IDsPattern ^ term2.IDsPattern;
var value = term1.Value * term2.Value;
if (value == 0.0d)
{
return(new GaPoTNumMultivectorTerm(idsPattern, 0.0d));
}
if (GaPoTNumUtils.ComputeIsNegativeEGp(term1.IDsPattern, term2.IDsPattern))
{
value = -value;
}
return(new GaPoTNumMultivectorTerm(idsPattern, value));
}