public GaNumMultivector GetNumBlade(int gaSpaceDim, int grade)
{
var vSpaceDim = gaSpaceDim.ToVSpaceDimension();
if (grade < 0 || grade > vSpaceDim)
{
return(GaNumMultivector.CreateZero(gaSpaceDim));
}
if (grade <= 1 || grade >= vSpaceDim - 1)
{
return(GetNumKVector(gaSpaceDim, grade));
}
var mv = GetNumVector(gaSpaceDim);
grade--;
while (grade > 0)
{
var v = GetNumVector(gaSpaceDim);
var mv1 = mv.Op(v);
if (mv1.IsZero())
{
continue;
}
mv = mv1;
grade--;
}
return(mv);
}
public GaNumMultivector GetNumTerm(int gaSpaceDim, int basisBladeId, double minValue, double maxValue)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
mv.SetTermCoef(basisBladeId, GetScalar(minValue, maxValue));
return(mv);
}
public GaNumMultivector GetNumTerm(int gaSpaceDim, int grade, int index, double minValue, double maxValue)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
var basisBladeId = GMacMathUtils.BasisBladeId(grade, index);
mv.SetTermCoef(basisBladeId, GetScalar(minValue, maxValue));
return(mv);
}
public GaNumMultivector ToMultivector()
{
var mv = GaNumMultivector.CreateZero(GaSpaceDimension);
foreach (var term in _termsDictionary.Where(p => !p.Value.IsNearZero()))
{
mv.SetTermCoef(term.Key, term.Value);
}
return(mv);
}
public override IGaNumMultivector this[int id1]
{
get
{
IGaNumMultivector basisBladeMv;
_basisBladeMaps.TryGetValue(id1, out basisBladeMv);
return(basisBladeMv
?? GaNumMultivector.CreateZero(TargetGaSpaceDimension));
}
}
public override IGaNumMultivector this[int id1, int id2, int id3]
{
get
{
IGaNumMultivector basisBladeMv;
return
(!_basisBladesMaps.TryGetValue(id1, id2, id3, out basisBladeMv) || ReferenceEquals(basisBladeMv, null)
? GaNumMultivector.CreateZero(TargetGaSpaceDimension)
: basisBladeMv);
}
}
public GaNumMultivector GetNumVector(int gaSpaceDim)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in GMacMathUtils.BasisBladeIDsOfGrade(mv.VSpaceDimension, 1))
{
mv.SetTermCoef(basisBladeId, GetScalar());
}
return(mv);
}
public GaNumMultivector GetNumKVector(int gaSpaceDim, int grade, double minValue, double maxValue)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in GMacMathUtils.BasisBladeIDsOfGrade(mv.VSpaceDimension, grade))
{
mv.SetTermCoef(basisBladeId, GetScalar(minValue, maxValue));
}
return(mv);
}
public GaNumMultivector GetNumMultivectorByTerms(int gaSpaceDim, IEnumerable <int> basisBladeIDs)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in basisBladeIDs)
{
mv.SetTermCoef(basisBladeId, GetScalar());
}
return(mv);
}
public GaNumMultivector GetNumMultivectorFull(int gaSpaceDim, double minValue, double maxValue)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
for (var basisBladeId = 0; basisBladeId < gaSpaceDim; basisBladeId++)
{
mv.SetTermCoef(basisBladeId, GetScalar(minValue, maxValue));
}
return(mv);
}
public override IGaNumMultivector this[int id1, int id2]
{
get
{
IGaNumMultivector resultMv;
_basisBladesMaps.TryGetValue(id1, id2, out resultMv);
return(resultMv
?? GaNumMultivector.CreateZero(TargetGaSpaceDimension));
}
}
public void Setup()
{
_randGen = new GMacRandomGenerator(10);
_frame = GaNumFrame.CreateConformal(5);
//_frame.SelectBilinearProductsImplementation(ProductsImplementation);
_mv1 = _randGen.GetNumMultivectorFull(_frame.GaSpaceDimension);
_mv2 = _mv1.Terms.ToDictionary(t => t.Key, t => t.Value);
_mv3 = GaNumMultivector.CreateZero(_frame.GaSpaceDimension);
//_mv4 = new Dictionary<int, double>();
//_mv5 = new double[_frame.GaSpaceDimension];
}
public GaNumMultivector GetVectorPart()
{
var mv = GaNumMultivector.CreateZero(GaSpaceDimension);
foreach (var id in GMacMathUtils.BasisVectorIDs(VSpaceDimension))
{
var coef = this[id];
if (!coef.IsNearZero())
{
mv.SetTermCoef(id, coef);
}
}
return(mv);
}
public GaNumMultivector GetNumMultivectorByGrades(int gaSpaceDim, params int[] grades)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
var basisBladeIDs =
GMacMathUtils.BasisBladeIDsOfGrades(
mv.VSpaceDimension,
grades
);
foreach (var basisBladeId in basisBladeIDs)
{
mv.SetTermCoef(basisBladeId, GetScalar());
}
return(mv);
}
public static Dictionary <int, GaNumMultivector> ToOutermorphismDictionary(this Dictionary <int, IGaNumMultivector> linearVectorMaps, int domainVSpaceDim, int targetVSpaceDim)
{
var domainGaSpaceDim =
domainVSpaceDim.ToGaSpaceDimension();
var targetGaSpaceDim =
targetVSpaceDim.ToGaSpaceDimension();
var omMapDict = new Dictionary <int, GaNumMultivector>();
//Add unit scalar as the image of the 0-basis blade
omMapDict.Add(0, GaNumMultivector.CreateUnitScalar(targetGaSpaceDim));
for (var id = 1; id <= domainGaSpaceDim - 1; id++)
{
GaNumMultivector basisBladeImage;
if (id.IsValidBasisVectorId())
{
//Add images of vector basis blades
IGaNumMultivector mv;
linearVectorMaps.TryGetValue(id.BasisBladeIndex(), out mv);
basisBladeImage = mv?.GetVectorPart()
?? GaNumMultivector.CreateZero(targetGaSpaceDim);
}
else
{
//Add images of a higher dimensional basis blade using the outer product
//of the images of two lower dimensional basis blades
int id1, id2;
id.SplitBySmallestBasicPattern(out id1, out id2);
basisBladeImage =
omMapDict[id1].Op(omMapDict[id2]);
}
if (!basisBladeImage.IsZero())
{
omMapDict.Add(id, basisBladeImage);
}
}
return(omMapDict);
}
public GaNumMultivector ToMultivector()
{
var mv = GaNumMultivector.CreateZero(GaSpaceDimension);
var id = 0;
foreach (var coef in _termsArray)
{
if (!coef.IsNearZero())
{
mv.SetTermCoef(id, coef);
}
id++;
}
return(mv);
}
