private static void CheckSystemSolution2()
{
Skip.IfNot(TestSettings.TestSuiteSparse, TestSettings.MessageWhenSkippingSuiteSparse);
int order = SparsePosDef10by10.Order;
// Build the matrices and right hand sides
var dense = Matrix.CreateFromArray(SparsePosDef10by10.Matrix);
//var skyline = SkylineMatrix.CreateFromArrays(order, SparsePositiveDefinite.skylineValues,
// SparsePositiveDefinite.skylineDiagOffsets, false);
//var dok = DOKSymmetricColMajor.CreateFromSparseMatrix(skyline);
var dok = DokSymmetric.CreateEmpty(order);
for (int j = 0; j < order; ++j)
{
for (int i = 0; i <= j; ++i)
{
if (dense[i, j] != 0)
{
dok[i, j] = dense[i, j];
}
}
}
Vector b = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
Matrix B = Matrix.CreateFromArray(SquareInvertible10by10.Matrix);
// Solve using dense algebra
CholeskyFull chol = dense.FactorCholesky(false);
Matrix U = chol.GetFactorU();
Matrix L = U.Transpose();
Vector xSolveExpect = chol.SolveLinearSystem(b);
Matrix XSolveExpect = dense.Invert() * B;
Vector xBackExpect = U.Invert() * b;
Matrix XBackExpect = U.Invert() * B;
Vector xForwardExpect = L.Invert() * b;
Matrix XForwardExpect = L.Invert() * B;
// Solve using SuiteSparse
var(values, rowIndices, colOffsets) = dok.BuildSymmetricCscArrays(true);
CholeskySuiteSparse factor = CholeskySuiteSparse.Factorize(order, values.Length, values, rowIndices, colOffsets,
true);
Vector xSolveComput = factor.SolveLinearSystem(b);
Matrix XSolveComput = factor.SolveLinearSystems(B);
Vector xBackComput = factor.BackSubstitution(b);
Matrix XBackComput = factor.BackSubstitutions(B);
Vector xForwardComput = factor.ForwardSubstitution(b);
Matrix XForwardComput = factor.ForwardSubstitutions(B);
Vector xSolveComput2 = factor.BackSubstitution(factor.ForwardSubstitution(b));
// Check results
comparer.AssertEqual(xSolveExpect, xSolveComput);
comparer.AssertEqual(XSolveExpect, XSolveComput);
comparer.AssertEqual(xBackExpect, xBackComput);
comparer.AssertEqual(XBackExpect, XBackComput);
comparer.AssertEqual(xForwardExpect, xForwardComput);
comparer.AssertEqual(XForwardExpect, XForwardComput);
}
private static void TestFactorization(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// positive definite
var A1 = Matrix.CreateFromArray(SymmPosDef10by10.Matrix);
var expectedU1 = Matrix.CreateFromArray(SymmPosDef10by10.FactorU);
CholeskyFull factorization1 = A1.FactorCholesky(true);
Matrix computedU1 = factorization1.GetFactorU();
comparer.AssertEqual(expectedU1, computedU1);
// singular
var A2 = Matrix.CreateFromArray(SquareSingular10by10.Matrix);
Assert.Throws <IndefiniteMatrixException>(() => A2.FactorCholesky(true));
});
}