/// <summary>
/// Calculates the Cholesky factorization of the matrix. Will throw <see cref="IndefiniteMatrixException"/> if the
/// matrix is not positive definite.
/// </summary>
/// <returns></returns>
public CholeskyPacked FactorCholesky()
{
var factor = CholeskyPacked.Factorize(Order, data);
Definiteness = DefiniteProperty.PositiveDefinite; // An exception would have been thrown otherwise.
return(factor);
}
private static void TestDeterminant(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// positive definite
var A = SymmetricMatrix.CreateFromArray(SymmPosDef10by10.Matrix);
CholeskyPacked factorization = A.FactorCholesky();
double detComputed = factorization.CalcDeterminant();
comparer.AssertEqual(SymmPosDef10by10.Determinant, detComputed);
});
}
private static void TestInversion(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// positive definite
var A = SymmetricMatrix.CreateFromArray(SymmPosDef10by10.Matrix);
var inverseAExpected = Matrix.CreateFromArray(SymmPosDef10by10.Inverse);
CholeskyPacked factorization = A.FactorCholesky();
SymmetricMatrix inverseAComputed = factorization.Invert(true);
comparer.AssertEqual(inverseAExpected, inverseAComputed);
});
}
private static void TestSystemSolution(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// positive definite
var A = SymmetricMatrix.CreateFromArray(SymmPosDef10by10.Matrix);
var b = Vector.CreateFromArray(SymmPosDef10by10.Rhs);
var xExpected = Vector.CreateFromArray(SymmPosDef10by10.Lhs);
CholeskyPacked factorization = A.FactorCholesky();
Vector xComputed = factorization.SolveLinearSystem(b);
comparer.AssertEqual(xExpected, xComputed);
});
}
private static void TestFactorization(LinearAlgebraProviderChoice providers)
{
TestSettings.RunMultiproviderTest(providers, delegate()
{
// positive definite
var A1 = SymmetricMatrix.CreateFromArray(SymmPosDef10by10.Matrix);
var expectedU1 = Matrix.CreateFromArray(SymmPosDef10by10.FactorU);
CholeskyPacked factorization1 = A1.FactorCholesky();
TriangularUpper computedU1 = factorization1.GetFactorU();
comparer.AssertEqual(expectedU1, computedU1);
// singular
var A2 = SymmetricMatrix.CreateFromArray(SquareSingular10by10.Matrix);
Assert.Throws <IndefiniteMatrixException>(() => A2.FactorCholesky());
});
}
