public static GaSymMultivector CreateCopy(GaSymMultivector mv)
{
var resultMv = new GaSymMultivector(mv.GaSpaceDimension);
resultMv.TermsTree.FillFromTree(mv.TermsTree);
return(resultMv);
}
public static IEnumerable <GaSymMultivectorBiTerm> GetBiTermsForOp(this GaSymMultivector mv1, GaSymMultivector mv2)
{
var mvStack1 = mv1.TermsTree.CreateNodesStack();
var mvStack2 = mv2.TermsTree.CreateNodesStack();
var idStack1 = mv1.TermsTree.CreateNodeIDsStack();
var idStack2 = mv2.TermsTree.CreateNodeIDsStack();
while (mvStack1.Count > 0)
{
var node1 = mvStack1.Pop();
var node2 = mvStack2.Pop();
var id1 = idStack1.Pop();
var id2 = idStack2.Pop();
if (node1.IsLeafNode)
{
yield return(new GaSymMultivectorBiTerm(
(int)id1,
(int)id2,
node1.Value,
node2.Value
));
continue;
}
if (node1.HasChildNode0)
{
if (node2.HasChildNode0)
{
mvStack1.Push(node1.ChildNode0);
mvStack2.Push(node2.ChildNode0);
idStack1.Push(id1);
idStack2.Push(id2);
}
if (node2.HasChildNode1)
{
mvStack1.Push(node1.ChildNode0);
mvStack2.Push(node2.ChildNode1);
idStack1.Push(id1);
idStack2.Push(id2 | node2.ChildNode1.BitMask);
}
}
if (node1.HasChildNode1 && node2.HasChildNode0)
{
mvStack1.Push(node1.ChildNode1);
mvStack2.Push(node2.ChildNode0);
idStack1.Push(id1 | node1.ChildNode1.BitMask);
idStack2.Push(id2);
}
}
}
public static GaSymMultivector CreateCopy(GMacBinaryTree <Expr> termsTree)
{
var gaSpaceDimension = termsTree.TreeDepth.ToGaSpaceDimension();
var resultMv = new GaSymMultivector(gaSpaceDimension);
resultMv.TermsTree.FillFromTree(termsTree);
return(resultMv);
}
public static GaSymMultivector SetTerms(this GaSymMultivector mv, IEnumerable <KeyValuePair <int, Expr> > terms)
{
foreach (var term in terms)
{
mv.SetTermCoef(term.Key, term.Value);
}
return(mv);
}
public static IEnumerable <GaSymMultivectorBiTerm> GetBiTermsForSp(this GaSymMultivector mv1, GaSymMultivector mv2, GaSymMetricOrthogonal orthogonalMetric)
{
var mvStack1 = mv1.TermsTree.CreateNodesStack();
var mvStack2 = mv2.TermsTree.CreateNodesStack();
var idStack1 = mv1.TermsTree.CreateNodeIDsStack();
var idStack2 = mv2.TermsTree.CreateNodeIDsStack();
var metricStack = orthogonalMetric.RootNode.CreateNodesStack();
while (mvStack1.Count > 0)
{
var node1 = mvStack1.Pop();
var node2 = mvStack2.Pop();
var id1 = idStack1.Pop();
var id2 = idStack2.Pop();
var metricNode = metricStack.Pop();
if (node1.IsLeafNode)
{
yield return(new GaSymMultivectorBiTerm(
(int)id1,
(int)id2,
node1.Value,
node2.Value,
metricNode.Value
));
continue;
}
if (node1.HasChildNode0 && node2.HasChildNode0 && metricNode.HasChildNode0)
{
mvStack1.Push(node1.ChildNode0);
mvStack2.Push(node2.ChildNode0);
idStack1.Push(id1);
idStack2.Push(id2);
//0 and 0 = 0
metricStack.Push(metricNode.ChildNode0);
}
if (node1.HasChildNode1 && node2.HasChildNode1 && metricNode.HasChildNode1)
{
mvStack1.Push(node1.ChildNode1);
mvStack2.Push(node2.ChildNode1);
idStack1.Push(id1 | node1.ChildNode1.BitMask);
idStack2.Push(id2 | node2.ChildNode1.BitMask);
//1 and 1 = 1
metricStack.Push(metricNode.ChildNode1);
}
}
}
public GaSymMultivector GetOddPart()
{
var resultMv = new GaSymMultivector(GaSpaceDimension);
foreach (var term in NonZeroTerms.Where(t => (t.Key.BasisBladeGrade() & 1) == 1))
{
resultMv.SetTermCoef(term.Key, term.Value);
}
return(resultMv);
}
public static GaTreeMultivector ToTreeMultivector(this GaSymMultivector sparseMv)
{
var treeMv = GaTreeMultivector.CreateZero(sparseMv.GaSpaceDimension);
foreach (var term in sparseMv.NonZeroExprTerms)
{
treeMv[term.Key] = term.Value;
}
return(treeMv);
}
public static GaSymMultivector CreateMapped(GaSymMultivector mv, Func <Expr, Expr> scalarMap)
{
var resultMv = CreateZero(mv.GaSpaceDimension);
foreach (var term in mv.NonZeroExprTerms)
{
resultMv.SetTermCoef(term.Key, scalarMap(term.Value));
}
return(resultMv);
}
public GaSymMultivector GetPartByGrade(Func <int, bool> gradeSelectionFunc)
{
var resultMv = new GaSymMultivector(GaSpaceDimension);
foreach (var term in NonZeroTerms.Where(t => gradeSelectionFunc(t.Key.BasisBladeGrade())))
{
resultMv.SetTermCoef(term.Key, term.Value);
}
return(resultMv);
}
public GaSymMultivector GetVectorPart()
{
var mv = GaSymMultivector.CreateZero(GaSpaceDimension);
if (TermId.BasisBladeGrade() == 1)
{
mv.SetTermCoef(TermId, TermCoef);
}
return(mv);
}
public static GaSymMultivector CreateFromColumn(ISymbolicMatrix matrix, int col)
{
Debug.Assert(matrix.RowCount.IsValidGaSpaceDimension());
var mv = new GaSymMultivector(matrix.RowCount);
for (var index = 0; index < matrix.RowCount; index++)
{
mv.SetTermCoef(index, matrix[index, col]);
}
return(mv);
}
public static GaSymMultivector CreateVectorFromRow(ISymbolicMatrix matrix, int row)
{
var gaSpaceDim = matrix.ColumnCount.ToGaSpaceDimension();
var mv = new GaSymMultivector(gaSpaceDim);
for (var col = 0; col < matrix.ColumnCount; col++)
{
mv.SetTermCoef(1, col, matrix[row, col]);
}
return(mv);
}
public static GaSymMultivector CreateVectorFromColumn(ISymbolicMatrix matrix, int col)
{
var gaSpaceDim = matrix.RowCount.ToGaSpaceDimension();
var mv = new GaSymMultivector(gaSpaceDim);
for (var row = 0; row < matrix.RowCount; row++)
{
mv.SetTermCoef(1, row, matrix[row, col]);
}
return(mv);
}
public static GaSymMultivector CreateVectorFromScalars(Expr[] exprScalars)
{
var gaSpaceDim = exprScalars.Length.ToGaSpaceDimension();
var mv = new GaSymMultivector(gaSpaceDim);
for (var index = 0; index < exprScalars.Length; index++)
{
mv.SetTermCoef(1, index, exprScalars[index]);
}
return(mv);
}
public static GaSymMultivector CreateVectorFromColumn(Expr[,] matrix, int col)
{
var rowsCount = matrix.GetLength(0);
var gaSpaceDim = rowsCount.ToGaSpaceDimension();
var mv = new GaSymMultivector(gaSpaceDim);
for (var row = 0; row < rowsCount; row++)
{
mv.SetTermCoef(1, row, matrix[row, col]);
}
return(mv);
}
public static GaSymMultivector SetTerms(this GaSymMultivector mv, ISymbolicVector termsMv)
{
for (var id = 0; id < termsMv.Size; id++)
{
var coef = termsMv[id].Expression;
if (!coef.IsNullOrZero())
{
mv.SetTermCoef(id, coef);
}
}
return(mv);
}
public GaSymMultivector CliffConj()
{
var resultMv = new GaSymMultivector(GaSpaceDimension);
foreach (var term in NonZeroExprTerms)
{
resultMv.SetTermCoef(
term.Key,
term.Key.BasisBladeIdHasNegativeClifConj(),
term.Value
);
}
return(resultMv);
}
public static IGaSymMultivectorTemp ToTempMultivector(this IGaSymMultivector mv)
{
if (ReferenceEquals(mv, null))
{
return(null);
}
var tempMv = GaSymMultivector.CreateZeroTemp(mv.GaSpaceDimension);
foreach (var term in mv.NonZeroExprTerms)
{
tempMv.SetTermCoef(term.Key, term.Value);
}
return(tempMv);
}
public GaSymMultivector GetKVectorPart(int grade)
{
var resultMv = new GaSymMultivector(GaSpaceDimension);
if (grade < 0 || grade > VSpaceDimension)
{
return(resultMv);
}
foreach (var term in NonZeroTerms.Where(t => t.Key.BasisBladeGrade() == grade))
{
resultMv.SetTermCoef(term.Key, term.Value);
}
return(resultMv);
}
public IGaSymMultivector this[int id1]
{
get
{
IGaSymMultivector mv;
RootNode.TryGetLeafValue((ulong)id1, out mv);
return(mv);
}
set
{
RootNode.SetLeafValue(
(ulong)id1,
value ?? GaSymMultivector.CreateZero(TargetGaSpaceDimension)
);
}
}
public static GaSymMultivector CreateSymbolic(int gaSpaceDim, string baseCoefName, IEnumerable <int> idsList)
{
var resultMv = new GaSymMultivector(gaSpaceDim);
var vSpaceDim = gaSpaceDim.ToVSpaceDimension();
foreach (var id in idsList)
{
resultMv.SetTermCoef(
id,
MathematicaScalar.CreateSymbol(
SymbolicUtils.Cas,
baseCoefName + id.PatternToString(vSpaceDim)
));
}
return(resultMv);
}
public static GaSymMultivector CreateFromColumn(Expr[,] exprArray, int col)
{
var rows = exprArray.GetLength(0);
Debug.Assert(rows.IsValidGaSpaceDimension());
var mv = new GaSymMultivector(rows);
for (var row = 0; row < rows; row++)
{
var expr = exprArray[row, col];
if (!expr.IsNullOrZero())
{
mv.SetTermCoef(row, expr);
}
}
return(mv);
}
public static GaSymMultivector CreateFromRow(Expr[,] exprArray, int row)
{
var cols = exprArray.GetLength(1);
Debug.Assert(cols.IsValidGaSpaceDimension());
var mv = new GaSymMultivector(cols);
for (var col = 0; col < cols; col++)
{
var expr = exprArray[row, col];
if (!expr.IsNullOrZero())
{
mv.SetTermCoef(col, expr);
}
}
return(mv);
}
public Dictionary <int, GaSymMultivector> GetKVectorParts()
{
var kVectorsList = new Dictionary <int, GaSymMultivector>();
foreach (var term in NonZeroTerms)
{
GaSymMultivector mv;
var grade = term.Key.BasisBladeGrade();
if (kVectorsList.TryGetValue(grade, out mv) == false)
{
mv = new GaSymMultivector(GaSpaceDimension);
kVectorsList.Add(grade, mv);
}
mv.AddFactor(term.Key, term.Value);
}
return(kVectorsList);
}
public static GaSymMultivector CreatePseudoscalar(int gaSpaceDim, MathematicaScalar coef)
{
var resultMv = new GaSymMultivector(gaSpaceDim);
return(resultMv.SetTermCoef(gaSpaceDim - 1, coef.Expression));
}
public static GaSymMultivector CreateScalar(int gaSpaceDim, Expr coef)
{
var resultMv = new GaSymMultivector(gaSpaceDim);
return(resultMv.SetTermCoef(0, coef));
}
public static GaSymMultivector CreateUnitScalar(int gaSpaceDim)
{
var resultMv = new GaSymMultivector(gaSpaceDim);
return(resultMv.SetTermCoef(0, Expr.INT_ONE));
}
public static GaSymMultivector CreateBasisBlade(int gaSpaceDim, int id)
{
var resultMv = new GaSymMultivector(gaSpaceDim);
return(resultMv.SetTermCoef(id, Expr.INT_ONE));
}
public static IGaSymMultivectorTemp CreateCopyTemp(GaSymMultivector mv)
{
return(CreateZeroTemp(mv.GaSpaceDimension).SetTerms(mv));
}
public static bool IsNullOrNearNumericZero(this GaSymMultivector mv, double epsilon)
{
return(ReferenceEquals(mv, null) || mv.IsNearNumericZero(epsilon));
}