public static GaSymOutermorphism Create(ISymbolicMatrix vectorsMappingMatrix, GaUnilinearMapImplementation multivectorsMappingKind)
{
if (multivectorsMappingKind == GaUnilinearMapImplementation.Identity)
{
var vSpaceDim = vectorsMappingMatrix.ColumnCount;
return(new GaSymOutermorphism(
MathematicaMatrix.CreateIdentity(SymbolicUtils.Cas, vSpaceDim),
GaSymMapUnilinearIdentity.Create(vSpaceDim),
GaUnilinearMapImplementation.Identity
));
}
var mvMappingDictionaryDict = vectorsMappingMatrix.ToOutermorphismDictionary();
GaSymMapUnilinear multivectorsMap;
switch (multivectorsMappingKind)
{
case GaUnilinearMapImplementation.Array:
multivectorsMap = mvMappingDictionaryDict.ToArrayMap(
vectorsMappingMatrix.ColumnCount,
vectorsMappingMatrix.RowCount
);
break;
case GaUnilinearMapImplementation.Hash:
multivectorsMap = mvMappingDictionaryDict.ToHashMap(
vectorsMappingMatrix.ColumnCount,
vectorsMappingMatrix.RowCount
);
break;
case GaUnilinearMapImplementation.Matrix:
multivectorsMap = mvMappingDictionaryDict.ToMatrixMap(
vectorsMappingMatrix.ColumnCount,
vectorsMappingMatrix.RowCount
);
break;
case GaUnilinearMapImplementation.CoefSums:
multivectorsMap = mvMappingDictionaryDict.ToCoefSumsMap(
vectorsMappingMatrix.ColumnCount,
vectorsMappingMatrix.RowCount
);
break;
default:
multivectorsMap = mvMappingDictionaryDict.ToTreeMap(
vectorsMappingMatrix.ColumnCount,
vectorsMappingMatrix.RowCount
);
break;
}
return(new GaSymOutermorphism(
vectorsMappingMatrix,
multivectorsMap,
multivectorsMappingKind
));
}
public static GaSymOutermorphism CreateIdentity(int vSpaceDim)
{
return(new GaSymOutermorphism(
MathematicaMatrix.CreateIdentity(SymbolicUtils.Cas, vSpaceDim),
GaSymMapUnilinearIdentity.Create(vSpaceDim),
GaUnilinearMapImplementation.Identity
));
}
public static void IsOpsTest()
{
TestUtils.AddTestStartingMessage("MathematicaMatrix 'Is' Operations Test Started.");
var m1 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.Zero, Cas.Constants.One, Cas.Constants.TwoPi);
TestUtils.AddTest("Try apply IsZero() to full diagonal matrix {0, 1, 2 Pi} ... ", m1.IsZero());
var sm1 = m1.ToMathematicaSparseMatrix();
TestUtils.AddTest("Try apply IsZero() to sparse diagonal matrix {0, 1, 2 Pi} ... ", sm1.IsZero());
m1 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.Zero, Cas.Constants.Zero, Cas.Constants.Zero);
TestUtils.AddTest("Try apply IsZero() to full diagonal matrix {0, 0, 0} ... ", m1.IsZero());
sm1 = m1.ToMathematicaSparseMatrix();
TestUtils.AddTest("Try apply IsZero() to sparse diagonal matrix {0, 0, 0} ... ", sm1.IsZero());
m1 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.Zero, Cas.Constants.One, Cas.Constants.TwoPi);
TestUtils.AddTest("Try apply IsIdentity() to full diagonal matrix {0, 1, 2 Pi} ... ", m1.IsIdentity());
sm1 = m1.ToMathematicaSparseMatrix();
TestUtils.AddTest("Try apply IsIdentity() to sparse diagonal matrix {0, 1, 2 Pi} ... ", sm1.IsIdentity());
m1 = MathematicaMatrix.CreateIdentity(Cas, 4);
TestUtils.AddTest("Try apply IsIdentity() to full 4x4 Identity matrix ... ", m1.IsIdentity());
sm1 = m1.ToMathematicaSparseMatrix();
TestUtils.AddTest("Try apply IsIdentity() to sparse 4x4 Identity matrix ... ", sm1.IsIdentity());
m1 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.Zero, Cas.Constants.One, Cas.Constants.TwoPi);
TestUtils.AddTest("Try apply IsDiagonal() to full diagonal matrix {0, 1, 2 Pi} ... ", m1.IsDiagonal());
sm1 = m1.ToMathematicaSparseMatrix();
TestUtils.AddTest("Try apply IsDiagonal() to sparse diagonal matrix {0, 1, 2 Pi} ... ", sm1.IsDiagonal());
m1 = MathematicaMatrix.CreateConstant(Cas.Constants.Pi, 5, 5);
TestUtils.AddTest("Try apply IsDiagonal() to full 5x5 matrix with non-zero elements ... ", m1.IsDiagonal());
sm1 = MathematicaMatrix.Create(Cas, "SparseArray[RandomInteger[1, {5, 5}]]");
TestUtils.AddTest("Try apply IsDiagonal() to sparse 5x5 matrix " + sm1.ToMathematicaFullMatrix().ExpressionText + " ... ", sm1.IsDiagonal());
m1 = MathematicaMatrix.Create(Cas, "RandomInteger[3, {5, 5}]");
m1 = m1 * m1.Transpose().ToMathematicaMatrix();
TestUtils.AddTest("Try apply IsSymmetric() to full 5x5 symmetric matrix " + m1.ExpressionText + " ... ", m1.IsSymmetric());
TestUtils.AddTest("Try apply IsSymmetric() to sparse 5x5 matrix " + sm1.ToMathematicaFullMatrix().ExpressionText + " ... ", sm1.IsSymmetric());
m1 = MathematicaMatrix.Create(Cas, "RandomInteger[{-10, 10}, {5, 5}]");
TestUtils.AddTest("Try apply IsInvertable() to full 5x5 matrix " + m1.ExpressionText + " ... ", m1.IsInvertable());
sm1 = MathematicaMatrix.Create(Cas, "SparseArray[RandomInteger[1, {5, 5}]]");
TestUtils.AddTest("Try apply IsInvertable() to sparse 5x5 matrix " + sm1.ToMathematicaFullMatrix().ExpressionText + " ... ", sm1.IsInvertable());
m1 = MathematicaMatrix.Create(Cas, "RandomInteger[3, {5, 5}]");
m1 = m1 * m1.Transpose().ToMathematicaMatrix();
TestUtils.AddTest("Try apply IsOrthogonal() to full 5x5 symmetric matrix " + m1.ExpressionText + " ... ", m1.IsOrthogonal());
TestUtils.AddTest("Try apply IsOrthogonal() to sparse 5x5 matrix " + sm1.ToMathematicaFullMatrix().ExpressionText + " ... ", sm1.IsOrthogonal());
m1 = MathematicaMatrix.Create(Cas, Cas[Mfs.Orthogonalize[m1.Expression]]);
TestUtils.AddTest("Try apply IsOrthogonal() to full 5x5 symmetric matrix " + m1.ExpressionText + " ... ", m1.IsOrthogonal());
sm1 = MathematicaMatrix.Create(Cas, Cas[Mfs.SparseArray[Mfs.Orthogonalize[sm1.Expression]]]);
TestUtils.AddTest("Try apply IsOrthogonal() to sparse 5x5 matrix " + sm1.ToMathematicaFullMatrix().ExpressionText + " ... ", sm1.IsOrthogonal());
TestUtils.AddTestCompletionMessage("MathematicaMatrix 'Is' Operations Test Completed.");
}