///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.");
}
///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 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.");
}