public static GaMultivector OuterProduct(this GaMultivector mv1, GaMultivector mv2)
{
if (mv1.GaSpaceDim != mv2.GaSpaceDim)
{
throw new GMacSymbolicException("Multivector size mismatch");
}
var terms1 = mv1.ToStringsDictionary();
var terms2 = mv2.ToStringsDictionary();
var accumExprDict = new Dictionary <int, ListComposer>();
foreach (var term1 in terms1)
{
var id1 = term1.Key;
var coef1 = term1.Value;
foreach (var term2 in terms2.FilterTermsForOp(id1))
{
var id2 = term2.Key;
var coef2 = term2.Value;
var resultId = id1 ^ id2;
var resultCoefDelta =
Times(coef1, coef2, FrameUtils.IsNegativeEGp(id1, id2));
accumExprDict.AddTerm(resultId, resultCoefDelta);
}
}
return(accumExprDict.ToMultivector(mv1.GaSpaceDim));
}
//TODO: This requires more acceleration (try to build the expressions then evaluate once per basis blade id for result_mv)
//private GAMultivectorCoefficients BilinearProduct(GAMultivectorCoefficients mv1, GAMultivectorCoefficients mv2, Func<int, int, bool> term_discard_function)
//{
// if (mv1.GASpaceDim != mv2.GASpaceDim || mv1.GASpaceDim != GASpaceDim)
// throw new GMacSymbolicException("Multivector size mismatch");
// GAMultivectorCoefficients mv = GAMultivectorCoefficients.CreateZero(mv1.GASpaceDim);
// foreach (var term1 in mv1)
// {
// int id1 = term1.Key;
// MathematicaScalar coef1 = term1.Value;
// foreach (var term2 in mv2.FilterTermsUsing(id1, term_discard_function))
// {
// int id2 = term2.Key;
// MathematicaScalar coef2 = term2.Value;
// int id = id1 ^ id2;
// if (GAUtils.IDs_To_EGP_Sign(id1, id2))
// mv[id] -= coef1 * coef2 * _BasisBladesSignatures[id];
// else
// mv[id] += coef1 * coef2 * _BasisBladesSignatures[id];
// }
// }
// return mv;
//}
private GaMultivector BilinearProduct(GaMultivector mv1, GaMultivector mv2, Func <int, int, bool> termDiscardFunction)
{
if (mv1.GaSpaceDim != mv2.GaSpaceDim || mv1.GaSpaceDim != GaSpaceDimension)
{
throw new GMacSymbolicException("Multivector size mismatch");
}
var terms1 = mv1.ToStringsDictionary();
var terms2 = mv2.ToStringsDictionary();
var accumExprDict = new Dictionary <int, ListComposer>();
foreach (var term1 in terms1)
{
var id1 = term1.Key;
var coef1 = term1.Value;
foreach (var term2 in terms2.FilterTermsUsing(id1, termDiscardFunction))
{
var id2 = term2.Key;
var coef2 = term2.Value;
var resultId = id1 ^ id2;
var sigId = id1 & id2;
var resultCoefDelta =
EuclideanUtils.Times(
coef1,
coef2,
_basisBladesSignatures[sigId].MathExpr.ToString(),
FrameUtils.IsNegativeEGp(id1, id2)
);
accumExprDict.AddTerm(resultId, resultCoefDelta);
}
}
return(accumExprDict.ToMultivector(mv1.GaSpaceDim));
}
//TODO: This requires more acceleration (try to build the expressions then evaluate once per basis blade id for result_mv)
//public override GAMultivectorCoefficients Transform(GAMultivectorCoefficients mv1)
//{
// if (mv1.GASpaceDim != this.DomainGASpaceDim)
// throw new GMacSymbolicException("Multivector GA space dimension does not agree with domain GA space dimension");
// GAMultivectorCoefficients result_mv = GAMultivectorCoefficients.CreateZero(CodomainGASpaceDim);
// foreach (var term1 in mv1)
// {
// var coef1 = term1.Value;
// var mv2 = _TransformedBasisBlades[term1.Key];
// foreach (var term2 in mv2)
// {
// var coef2 = term2.Value;
// var result_id = term2.Key;
// result_mv[result_id] += coef1 * coef2;
// }
// }
// return result_mv;
//}
public override GaMultivector Transform(GaMultivector mv1)
{
if (mv1.GaSpaceDim != DomainGaSpaceDim)
{
throw new GMacSymbolicException("Multivector GA space dimension does not agree with domain GA space dimension");
}
var accumExprDict = new Dictionary <int, ListComposer>();
var terms1 = mv1.ToStringsDictionary();
foreach (var term1 in terms1)
{
var terms2 = _transformedBasisBlades[term1.Key].ToStringsDictionary();
foreach (var term2 in terms2)
{
accumExprDict.AddTerm(term2.Key, EuclideanUtils.Times(term1.Value, term2.Value));
}
}
return(accumExprDict.ToMultivector(CodomainGaSpaceDim));
}
