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.");
}
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 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.");
}