private static void TestSystemSolutionFullUpper()
{
int n = SymmPosDef10by10.Order;
var A = Matrix.CreateFromArray(SymmPosDef10by10.Matrix);
var b = SymmPosDef10by10.Rhs;
var xExpected = SymmPosDef10by10.Lhs;
// Factorization
CholeskyFactorizations.FactorizeFullUpper2(A.NumColumns, A, pivotTolerance);
// Forward substitution
var x1Computed = new double[n];
var x2Computed = new double[n];
CholeskyFactorizations.ForwardSubstitutionFullUpper(n, A, b, x1Computed);
CholeskyFactorizations.ForwardSubstitutionFullUpper(n, A, b, x2Computed);
// Back substitution - column / vector version
CholeskyFactorizations.BackSubstitutionFullUpper1(n, A, x1Computed);
comparer.AssertEqual(xExpected, x1Computed);
// Back substitution - dot version
CholeskyFactorizations.BackSubstitutionFullUpper2(n, A, x2Computed);
comparer.AssertEqual(xExpected, x2Computed);
}
/// <summary>
/// Performs the operation: <paramref name="result"/> = generalized_inverse(A) * <paramref name="vector"/>
/// </summary>
/// <param name="vector">The vector that will be multiplied. Its <see cref="IIndexable1D.Length"/> must be equal to
/// <see cref="IIndexable2D.NumRows"/> of the original matrix A.
/// </param>
/// <param name="result">
/// Output vector that will be overwritten with the solution of the linear system. Its <see cref="IIndexable1D.Length"/>
/// must be equal to <see cref="IIndexable2D.NumColumns"/> of the original matrix A.
/// </param>
/// <exception cref="NonMatchingDimensionsException">
/// Thrown if <paramref name="vector"/> or <paramref name="result"/> violate the described constraints.
/// </exception>
/// <exception cref="IndefiniteMatrixException">
/// Thrown if the original skyline matrix turns out to not be symmetric positive semi-definite.
/// </exception>
public void MultiplyGeneralizedInverseMatrixTimesVector(Vector vector, Vector result)
{
Preconditions.CheckSystemSolutionDimensions(Order, vector.Length);
Preconditions.CheckMultiplicationDimensions(Order, result.Length);
// TODO: Is this correct?
CholeskyFactorizations.ForwardSubstitutionFullUpper(Order, upperFactorized, vector.RawData, result.RawData);
CholeskyFactorizations.BackSubstitutionFullUpper1(Order, upperFactorized, result.RawData);
}