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
));
}
protected virtual void ComputeMappingMatrix()
{
var matrixItems = new Expr[TargetGaSpaceDimension, DomainGaSpaceDimension];
for (var col = 0; col < DomainGaSpaceDimension; col++)
{
var mv = this[col];
if (mv.IsNullOrZero())
{
for (var row = 0; row < TargetGaSpaceDimension; row++)
{
matrixItems[row, col] = Expr.INT_ZERO;
}
continue;
}
for (var row = 0; row < TargetGaSpaceDimension; row++)
{
var scalar = mv[row];
matrixItems[row, col] =
scalar.IsNullOrZero()
? Expr.INT_ZERO
: scalar;
}
}
InternalMappingMatrix =
MathematicaMatrix.CreateFullMatrix(SymbolicUtils.Cas, matrixItems);
}
public static MathematicaMatrix ToMatrix(this IGaSymMapUnilinear linearMap)
{
return(MathematicaMatrix.CreateFullMatrix(
SymbolicUtils.Cas,
ToExprScalarsArray(linearMap)
));
}
public static GaSymOutermorphism CreateIdentity(int vSpaceDim)
{
return(new GaSymOutermorphism(
MathematicaMatrix.CreateIdentity(SymbolicUtils.Cas, vSpaceDim),
GaSymMapUnilinearIdentity.Create(vSpaceDim),
GaUnilinearMapImplementation.Identity
));
}
protected override void ComputeIpm()
{
var bvSig = _basisVectorsSignatures.Select(i => MathematicaScalar.Create(CasInterface, i));
var v = MathematicaVector.CreateFullVector(CasInterface, bvSig);
InnerProductMatrix = MathematicaMatrix.CreateDiagonal(v);
}
///Set the signature of the current frame to be defined by IPM
private GaFrame translate_Frame_Signature_IPM(ParseTreeNode node)
{
//Read the IPM symbolic matrix
var ipmMatrix = MathematicaMatrix.Create(Cas, GenUtils.Translate_StringLiteral(node.ChildNodes[0]));
if (ipmMatrix.IsSymmetric() == false || ipmMatrix.Rows != _vSpaceDim)
{
CompilationLog.RaiseGeneratorError <int>("Expecting a square symmetric matrix with " + _vSpaceDim + " rows", node.ChildNodes[0]);
}
return(GaFrame.CreateFromIpm(ipmMatrix));
}
public static void ConstructionTest()
{
TestUtils.AddTestStartingMessage("MathematicaMatrix Creation Test Started.");
var scalarsArray = new MathematicaScalar[2, 2];
scalarsArray[0, 0] = MathematicaScalar.Create(Cas, 2);
scalarsArray[0, 1] = MathematicaScalar.Create(Cas, -2);
scalarsArray[1, 0] = MathematicaScalar.Create(Cas, 3);
scalarsArray[1, 1] = MathematicaScalar.Create(Cas, 1);
var s = MathematicaMatrix.CreateFullMatrix(Cas, scalarsArray);
TestUtils.AddTest("Try create full matrix from array of scalars ... ", s);
s = MathematicaMatrix.CreateIdentity(Cas, 3);
TestUtils.AddTest("Try create full 3x3 identity matrix ... ", s);
s = MathematicaMatrix.CreateIdentity(Cas, 3, false);
TestUtils.AddTest("Try create sparse 3x3 identity matrix ... ", s);
var v = MathematicaVector.CreateFullVector(Cas, Cas.Constants.Zero, Cas.Constants.TwoPi, Cas.Constants.One);
s = MathematicaMatrix.CreateDiagonal(v);
TestUtils.AddTest("Try create full 3x3 diagonal matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateDiagonal(v, false);
TestUtils.AddTest("Try create sparse 3x3 diagonal matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateRowVector(v);
TestUtils.AddTest("Try create full row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateRowVector(v, false);
TestUtils.AddTest("Try create sparse row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateColumnVector(v);
TestUtils.AddTest("Try create full row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateColumnVector(v, false);
TestUtils.AddTest("Try create sparse row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateConstant(Cas.Constants.Pi, 2, 3);
TestUtils.AddTest("Try create 2x3 matrix with constant elements of Pi ... ", s);
s = MathematicaMatrix.Create(Cas, @"{{1, x}, {2, y}, {3, z}}");
TestUtils.AddTest("Try create matrix from expression text \"{{1, x}, {2, y}, {3, z}}\" ... ", s);
TestUtils.AddTestCompletionMessage("MathematicaMatrix Creation Test Completed.");
}
private void ComputeMultivectorTransformMatrix()
{
var matrixArray = new MathematicaScalar[CodomainGaSpaceDim, DomainGaSpaceDim];
for (var col = 0; col < DomainGaSpaceDim; col++)
{
var mv = _transformedBasisBlades[col];
foreach (var term in mv)
{
matrixArray[term.Key, col] = term.Value;
}
}
_multivectorTransformMatrix = MathematicaMatrix.CreateFullMatrix(CasInterface, matrixArray);
}
/// <summary>
/// Create a non orthogonal frame based on an asymmetric inner product matrix
/// </summary>
/// <param name="ipm"></param>
/// <returns></returns>
private static GaFrameNonOrthogonal CreateNonOrthogonalFromIpm(MathematicaMatrix ipm)
{
MathematicaVector eigenValues;
MathematicaMatrix eigenVectors;
if (ipm.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixColumns, out eigenValues, out eigenVectors) == false)
{
throw new GMacSymbolicException("Cannot obtain orthogonal eigen system of the given matrix");
}
var baseFrame = CreateOrthogonal(eigenValues);
var baseToDerivedOm = GaOuterMorphismFull.Create(eigenVectors);
var derivedToBaseOm = GaOuterMorphismFull.Create(eigenVectors.Transpose());
return(new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm));
}
//public GAOuterMorphismFull(ISymbolicMatrix vector_transform_matrix)
// : base(vector_transform_matrix.CAS)
//{
// int domain_ga_space_dim = GAUtils.GASpaceDim(vector_transform_matrix.Columns);
// int codomain_ga_space_dim = GAUtils.GASpaceDim(vector_transform_matrix.Rows);
// _TransformedBasisBlades = new Multivector[domain_ga_space_dim];
// _TransformedBasisBlades[0] = Multivector.CreateScalar(codomain_ga_space_dim, MathematicaScalar.Create(CAS, 1));
// for (int id = 1 ; id <= domain_ga_space_dim - 1)
// {
// if (GAUtils.is_ID_Vector(id))
// {
// _TransformedBasisBlades[id] = CreateFromMatrixColumn(vector_transform_matrix, GAUtils.ID_To_Index(id));
// }
// else
// {
// int id1, id2;
// GAUtils.SeparateIDs(id, out id1, out id2);
// _TransformedBasisBlades[id] = Multivector.OuterProduct(_TransformedBasisBlades[id1], _TransformedBasisBlades[id2]);
// }
// }
//}
private void ComputeVectorTransformMatrix()
{
var matrixArray = new MathematicaScalar[CodomainVSpaceDim, DomainVSpaceDim];
for (var col = 0; col < DomainVSpaceDim; col++)
{
var id = FrameUtils.BasisBladeId(1, col);
var mv = _transformedBasisBlades[id];
foreach (var term in mv)
{
var row = term.Key.BasisBladeIndex();
matrixArray[row, col] = term.Value;
}
}
_vectorTransformMatrix = MathematicaMatrix.CreateFullMatrix(CasInterface, matrixArray);
}
/// <summary>
/// Create a derived frame system where the derived frame is the reciprocal of the base frame
/// </summary>
/// <param name="baseFrame"></param>
/// <returns></returns>
public static GaSymMetricNonOrthogonal CreateReciprocalCbmFrameSystem(GaSymFrame baseFrame)
{
if (baseFrame.IsOrthogonal)
{
var cbmat = baseFrame.Ipm.Inverse();
var b2DOm = baseFrame.Ipm.ToOutermorphismTree();
var d2BOm = cbmat.ToOutermorphismTree();
var derivedFrame = CreateOrthogonal(cbmat.GetDiagonal());
return(new GaSymMetricNonOrthogonal(baseFrame, derivedFrame, d2BOm, b2DOm));
}
var cbmArray = new MathematicaScalar[baseFrame.VSpaceDimension, baseFrame.VSpaceDimension];
var mv2 = baseFrame.CreateInverseUnitPseudoScalar();
for (var i = 0; i < baseFrame.VSpaceDimension; i++)
{
var id = (1 << i) ^ baseFrame.MaxBasisBladeId;
var mv1 = GaSymMultivector.CreateTerm(baseFrame.GaSpaceDimension, id, SymbolicUtils.Constants.One);
var mv = baseFrame.Lcp[mv1, mv2];
foreach (var term in mv.NonZeroTerms)
{
var j = term.Key.BasisBladeIndex();
if ((i & 1) == 1)
{
cbmArray[i, j] = term.Value;
}
else
{
cbmArray[i, j] = -term.Value;
}
}
}
var cbm = MathematicaMatrix.CreateFullMatrix(SymbolicUtils.Cas, cbmArray);
return(CreateDerivedCbmFrameSystem(baseFrame, cbm));
}
public static GaSymMapUnilinearMatrix ToMatrixMap(this Dictionary <int, GaSymMultivector> basisBladeMaps, int domainVSpaceDim, int targetVSpaceDim)
{
var targetGaSpaceDim = targetVSpaceDim.ToGaSpaceDimension();
var zeroMvArray = new Expr[targetGaSpaceDim];
return(GaSymMapUnilinearMatrix.Create(
MathematicaMatrix.CreateFullMatrixFromColumns(
SymbolicUtils.Cas,
Enumerable
.Range(0, domainVSpaceDim.ToGaSpaceDimension())
.Select(
id =>
{
GaSymMultivector mv;
basisBladeMaps.TryGetValue(id, out mv);
return mv?.TermsToExprArray()
?? zeroMvArray;
}
)
)
));
}
///Set the signature of the current frame to a base frame with a change of basis matrix
private GaFrame translate_Frame_Signature_CBM(ParseTreeNode node)
{
var baseFrame =
(GMacFrame)GMacValueAccessGenerator.Translate_Direct(Context, node.ChildNodes[0], RoleNames.Frame);
if (baseFrame.VSpaceDimension != _vSpaceDim)
{
CompilationLog.RaiseGeneratorError <int>("Base frame must be of dimension " + _vSpaceDim, node.ChildNodes[0]);
}
var cbmMatrix = MathematicaMatrix.Create(Cas, GenUtils.Translate_StringLiteral(node.ChildNodes[1]));
if (cbmMatrix.IsInvertable() == false || cbmMatrix.Rows != _vSpaceDim)
{
CompilationLog.RaiseGeneratorError <int>("Expecting a square invertable matrix with " + _vSpaceDim + " rows", node.ChildNodes[1]);
}
_baseFrame = baseFrame;
var derivedFrameSystem = GaFrame.CreateDerivedCbmFrameSystem(baseFrame.AssociatedSymbolicFrame, cbmMatrix);
return(derivedFrameSystem.DerivedFrame);
}
public static GaSymFrameNonOrthogonal CreateConformal(int vSpaceDim)
{
VerifyVSpaceDim(vSpaceDim, 3);
var eSpaceDim = vSpaceDim - 2;
var listComposer = new ListComposer(",")
{
FinalPrefix = "{",
FinalSuffix = "}"
};
for (var i = 0; i < eSpaceDim; i++)
{
listComposer.Add(
(1 << i)
.PatternToSequence(vSpaceDim, "0", "1")
.Concatenate(",", "{", "}")
);
}
listComposer.Add(
"{" +
0.PatternToSequence(eSpaceDim, "0", "1").Concatenate(",") +
",0,-1}"
);
listComposer.Add(
"{" +
0.PatternToSequence(eSpaceDim, "0", "1").Concatenate(",") +
",-1,0}"
);
var ipm = MathematicaMatrix.Create(SymbolicUtils.Cas, listComposer.ToString());
return(CreateNonOrthogonalFromIpm(ipm));
}
public static string DescribeMatrix(MathematicaMatrix matrix)
{
return(matrix.ToString());
}
public MathematicaMatrix ToMathematicaSparseMatrix()
{
return(MathematicaMatrix.CreateIdentity(CasInterface, _size, false));
}
public MathematicaMatrix ToMathematicaFullMatrix()
{
return(MathematicaMatrix.CreateIdentity(CasInterface, _size));
}
public static void BasicOpsTest()
{
var s = MathematicaScalar.Create(Cas, -2);
var v = MathematicaVector.CreateFullVector(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
var m1 = MathematicaMatrix.Create(Cas, "RandomInteger[{-5, 5}, {3, 4}]");
var m2 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
var sm3 = MathematicaMatrix.Create(Cas, "SparseArray[{{1, 0, 0, 0}, {0, 2, 0, 4}, {0, 0, 0, 3}}]");
var sm4 = m2.ToMathematicaSparseMatrix();
TestUtils.AddTestStartingMessage("MathematicaMatrix Basic Operations Test Started.");
TestUtils.AddTest("Try get rows of full 3x4 matrix ... ", m1.RowCount);
TestUtils.AddTest("Try get columns of full 3x4 matrix ... ", m1.ColumnCount);
TestUtils.AddTest("Try get rows of sparse 3x4 matrix ... ", sm3.RowCount);
TestUtils.AddTest("Try get columns of sparse 3x4 matrix ... ", sm3.ColumnCount);
for (var i = 0; i < m1.RowCount; i++)
{
for (var j = 0; j < m1.ColumnCount; j++)
{
TestUtils.AddTest("Try get component (" + i + ", " + j + ") of full 3x4 matrix " + m1.ExpressionText + " ... ", m1[i, j]);
}
}
for (var i = 0; i < sm3.RowCount; i++)
{
for (var j = 0; j < sm3.ColumnCount; j++)
{
TestUtils.AddTest("Try get component (" + i + ", " + j + ") of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3[i, j]);
}
}
for (var i = 0; i < m1.RowCount; i++)
{
TestUtils.AddTest("Try get row " + i + " of full 3x4 matrix " + m1.ExpressionText + " ... ", m1.GetRow(i));
}
for (var i = 0; i < m1.ColumnCount; i++)
{
TestUtils.AddTest("Try get column " + i + " of full 3x4 matrix " + m1.ExpressionText + " ... ", m1.GetColumn(i));
}
for (var i = 0; i < sm3.RowCount; i++)
{
TestUtils.AddTest("Try get row " + i + " of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3.GetRow(i));
}
for (var i = 0; i < sm3.ColumnCount; i++)
{
TestUtils.AddTest("Try get column " + i + " of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3.GetColumn(i));
}
TestUtils.AddTest("Try get diagonal of full matrix " + m2.ExpressionText + " ... ", m2.GetDiagonal());
TestUtils.AddTest("Try get diagonal of sparse matrix " + sm4.ToMathematicaFullMatrix().ExpressionText + " ... ", sm4.GetDiagonal());
TestUtils.AddTest("Try negate matrix " + m2.ExpressionText + " ... ", -m2);
TestUtils.AddTest("Try add matrix " + m1.ExpressionText + " and " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", m1 + sm3);
TestUtils.AddTest("Try subtract matrix " + m1.ExpressionText + " and " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", m1 - sm3);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and " + m1.ToMathematicaFullMatrix().ExpressionText + " ... ", m2 * m1);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and scalar -2 ... ", m2 * s);
TestUtils.AddTest("Try multiply scalar -2 and matrix " + m2.ExpressionText + " ... ", s * m2);
TestUtils.AddTest("Try divide matrix " + m2.ExpressionText + " by scalar -2 ... ", m2 / s);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and vector " + v.ExpressionText + " ... ", m2.Times(v));
TestUtils.AddTest("Try multiply vector " + v.ExpressionText + " and matrix " + m2.ExpressionText + " ... ", v.Times(m2));
TestUtils.AddTest("Try transpose matrix " + m2.ExpressionText + " ... ", m2.Transpose());
TestUtils.AddTest("Try inverse matrix " + m2.ExpressionText + " ... ", m2.Inverse());
TestUtils.AddTest("Try inverse transpose matrix " + m2.ExpressionText + " ... ", m2.InverseTranspose());
m2 = MathematicaMatrix.Create(Cas, "{{1, -1, 0}, {-1, 2, -1}, {0, -1, 1}}");
TestUtils.AddTest("Try get eigen values (in a vector) of matrix " + m2.ExpressionText + " ... ", m2.EigenValues_InVector());
TestUtils.AddTest("Try get eigen values (in a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenValues_InDiagonalMatrix());
TestUtils.AddTest("Try get eigen vectors (as rows of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows));
TestUtils.AddTest("Try get eigen vectors (as columns of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.InMatrixColumns));
TestUtils.AddTest("Try get eigen vectors (as orthonormal rows of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixRows));
TestUtils.AddTest("Try get eigen vectors (as orthonormal columns of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixColumns));
MathematicaVector eval1;
MathematicaMatrix eval2;
MathematicaMatrix evec;
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system values (in a vector) of matrix " + m2.ExpressionText + " ... ", eval1);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval2, out evec);
TestUtils.AddTest("Try get eigen system values (in a matrix) of matrix " + m2.ExpressionText + " ... ", eval2);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as rows of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixColumns, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as columns of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as orthonormal rows of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixColumns, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as orthonormal columns of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
TestUtils.AddTestCompletionMessage("MathematicaMatrix Basic Operations Test Completed.");
}
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.");
}
/// <summary>
/// Create a derived frame system using a change of basis matrix for the basis vectors
/// </summary>
/// <param name="baseFrame">The base frame. It may be any kind of frame</param>
/// <param name="cbm">The 'Change Of Basis Vectors' matrix. It must be invertable</param>
/// <returns></returns>
public static GaSymMetricNonOrthogonal CreateDerivedCbmFrameSystem(GaSymFrame baseFrame, MathematicaMatrix cbm)
{
var baseIpm = baseFrame.Ipm.ToMathematicaMatrix();
var cbmTrans = (MathematicaMatrix)cbm.Transpose();
var cbmInverseTrans = (MathematicaMatrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedCba = cbmInverseTrans.ToOutermorphismTree();
var derivedToBaseCba = cbmTrans.ToOutermorphismTree();
if (ipm.IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.GetDiagonal());
return(new GaSymMetricNonOrthogonal(baseFrame, derivedFrame, derivedToBaseCba, baseToDerivedCba));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaSymFrameNonOrthogonal(baseFrame, ipm, derivedToBaseCba, baseToDerivedCba);
return(derivedFrame.NonOrthogonalMetric);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm.ToMathematicaMatrix());
return(gaFrame.NonOrthogonalMetric);
//return new DerivedFrameSystem(baseFrame, gaFrame, derivedToBaseOm, baseToDerivedOm);
}
public static void AddTest(string message, MathematicaMatrix result)
{
Log.AppendAtNewLine(message);
Log.AppendLine(DescribeMatrix(result));
Log.AppendLine();
}
protected override void ComputeIpm()
{
var v = MathematicaVector.CreateFullVector(CasInterface, BasisVectorsSignatures);
InnerProductMatrix = MathematicaMatrix.CreateDiagonal(v);
}
/// <summary>
/// Create a derived frame system using a change of basis matrix for the basis vectors
/// </summary>
/// <param name="baseFrame">The base frame. It may be any kind of frame</param>
/// <param name="cbm">The 'Change Of Basis Vectors' matrix. It must be invertable</param>
/// <returns></returns>
public static DerivedFrameSystem CreateDerivedCbmFrameSystem(GaFrame baseFrame, MathematicaMatrix cbm)
{
var baseIpm = baseFrame.Ipm.ToMathematicaMatrix();
var cbmTrans = (MathematicaMatrix)cbm.Transpose();
var cbmInverseTrans = (MathematicaMatrix)cbmTrans.Inverse();
var ipm = cbm * baseIpm * cbmTrans;
var baseToDerivedOm = GaOuterMorphismFull.Create(cbmInverseTrans);
var derivedToBaseOm = GaOuterMorphismFull.Create(cbmTrans);
if (ipm.IsDiagonal())
{
var derivedFrame = CreateOrthogonal(ipm.GetDiagonal());
return(new DerivedFrameSystem(baseFrame, derivedFrame, derivedToBaseOm, baseToDerivedOm));
}
if (baseFrame.IsOrthogonal)
{
var derivedFrame = new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
return(derivedFrame.Dfs);
}
var gaFrame =
//new GaFrameNonOrthogonal(baseFrame, ipm, derivedToBaseOm, baseToDerivedOm);
CreateNonOrthogonalFromIpm(ipm.ToMathematicaMatrix());
return(gaFrame.Dfs);
//return new DerivedFrameSystem(baseFrame, gaFrame, derivedToBaseOm, baseToDerivedOm);
}
public static void BasicOpsTest()
{
var v1 = MathematicaVector.CreateFullVector(Cas, Cas.Constants.Zero, Cas.Constants.One, Cas.Constants.TwoPi);
var v2 = MathematicaVector.Create(Cas, @"{-1, x, Sin[t]}");
var sv3 = MathematicaVector.Create(Cas, "SparseArray[{Rule[1, Pi], Rule[5, -1]}]");
var s = MathematicaScalar.Create(Cas, "x");
TestUtils.AddTestStartingMessage("MathematicaVector Basic Operations Test Started.");
TestUtils.AddTest("Try get size of full vector {-1, x, Sin[t]} ... ", v2.Size);
TestUtils.AddTest("Try get 1st component of full vector {-1, x, Sin[t]} ... ", v2[0]);
TestUtils.AddTest("Try get 2nd component of full vector {-1, x, Sin[t]} ... ", v2[1]);
TestUtils.AddTest("Try get 3rd component of full vector {-1, x, Sin[t]} ... ", v2[2]);
TestUtils.AddTest("Try get size of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.Size);
TestUtils.AddTest("Try get 1st component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[0]);
TestUtils.AddTest("Try get 3rd component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[2]);
TestUtils.AddTest("Try get 5th component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[4]);
TestUtils.AddTest("Try list components of full vector {-1, x, Sin[t]}", "");
var i = 0;
foreach (var scalar in v2)
{
TestUtils.AddTest(" Component " + i + " ... ", scalar);
i++;
}
TestUtils.AddTest("Try list components of sparse vector {Pi, 0, 0, 0, -1}", "");
i = 0;
foreach (var scalar in sv3)
{
TestUtils.AddTest(" Component " + i + " ... ", scalar);
i++;
}
TestUtils.AddTest("Try negate vector {-1, x, Sin[t]} ... ", -v2);
TestUtils.AddTest("Try add vectors {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 + v2);
TestUtils.AddTest("Try subtract vectors {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 - v2);
TestUtils.AddTest("Try find dot product of {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 * v2);
TestUtils.AddTest("Try find product of vector {-1, x, Sin[t]} with scalar x ... ", v2 * s);
TestUtils.AddTest("Try find product of scalar x with vector {-1, x, Sin[t]} ... ", s * v2);
TestUtils.AddTest("Try divide vector {-1, x, Sin[t]} by scalar x ... ", v2 / s);
TestUtils.AddTest("Try apply Norm to vector {0, 1, 2 Pi} ... ", v1.Norm());
TestUtils.AddTest("Try apply Norm2 to vector {0, 1, 2 Pi} ... ", v1.Norm2());
var m = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
TestUtils.AddTest("Try find product of vector {-1, x, Sin[t]} with matrix DiagonalMatrix[{1, Pi, -1}] ... ", v2.Times(m));
TestUtils.AddTest("Try apply ToMathematicaVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaVector());
TestUtils.AddTest("Try apply ToMathematicaFullVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaFullVector());
TestUtils.AddTest("Try apply ToMathematicaSparseVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaSparseVector());
TestUtils.AddTest("Try apply ToMathematicaVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaVector());
TestUtils.AddTest("Try apply ToMathematicaFullVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaFullVector());
TestUtils.AddTest("Try apply ToMathematicaSparseVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaSparseVector());
TestUtils.AddTestCompletionMessage("MathematicaVector Basic Operations Test Completed.");
}
