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 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);
}
//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));
}