public AMatrix <MatrixDataType> Solve(AMatrix <MatrixDataType> A, AMatrix <MatrixDataType> b, AMatrix <MatrixDataType> x0, int max_iter)
{
// [solution, solutions, errors, norms] = gmres_simple(A, b, x0, kmax, chosen_solution)
AMatrix <MatrixDataType> x = x0;
AMatrix <MatrixDataType> r = b - (A * x);
double rho0 = r.L2Norm();
if (rho0 == 0)
{
return(x0);
}
List <int> REPEATED = new List <int>();
List <AMatrix <MatrixDataType> > solutions = new List <AMatrix <MatrixDataType> >();
solutions.Add(x.Transpose());
List <double> errors = new List <double>();
errors.Add(rho0);
List <double> norms = new List <double>();
norms.Add(x.L2Norm());
// scale tol for relative residual reduction
AMatrix <MatrixDataType> H = algebra.CreateZeros(1, 0);
AMatrix <MatrixDataType> V = r / rho0;
AMatrix <MatrixDataType> gamma = this.algebra.CreateZeros(1, 1);
gamma.SetElement(0, 0, 1);
double nu = 1;
for (int iteration = 0; iteration < max_iter; iteration++)
{
Tuple <AMatrix <MatrixDataType>, AMatrix <MatrixDataType> > tuple = ArnoldiStep(A, V, H, REPEATED, -1);
V = tuple.Item1;
H = tuple.Item2;
// compute the nul vector of H'
AMatrix <MatrixDataType> gk = ((gamma * H.GetColumnSection(0, iteration + 1, iteration)) / H.GetElement(iteration + 1, iteration));
gamma = gamma.AppendColumns(gk * -1.0);
// Compute the residual norm
nu = nu + (gk.Transpose() * gk).GetElement();
errors.Add(rho0 / Math.Sqrt(nu));
// compute explicit residual every step
int k1 = H.ColumnCount;
AMatrix <MatrixDataType> e = this.algebra.CreateZeros(iteration + 2, 1);
e.SetElement(0, 0, 1);
AMatrix <MatrixDataType> y = simple_solver.Solve(H, e);
AMatrix <MatrixDataType> x1 = V.GetColumns(0, iteration + 1) * (y * rho0);
solutions.Add(x1);
norms.Add(x1.L2Norm());
}
return(solutions[solutions.Count - 1]);
// compute the approximate solution
//solution = solutions(chosen_solution,:);
}
public IFunction <double, double> GetIRF(double[] signal)
{
AMatrix <MatrixType> weights = solver.Solve(forward_matrix, algebra.Create(signal, true));
return(new FunctionWeigthed <double, double>(new AlgebraRealFloat64(), basis_function_list, weights.ToArray1DFloat64()));
}