/// <summary>
/// Solves the system of linear equations.
/// </summary>
/// <param name="b">The vector b in A * x = b.</param>
/// <returns>The solution vector x.</returns>
public Double[,] Solve(Double[,] b)
{
var k = Restart;
var x = default(Double[, ]);
var converged = false;
var c = new Double[k - 1];
var s = new Double[k - 1];
var gamma = new Double[k + 1];
var iter = 0;
if (Guess == null)
{
Guess = new Double[b.GetLength(0), b.GetLength(1)];
}
if (Guess.GetLength(0) != b.GetLength(0) || Guess.GetLength(1) != b.GetLength(1))
{
throw new InvalidOperationException(ErrorMessages.DimensionMismatch);
}
var H = new Double[k + 1, k];
var V = new Double[Guess.GetLength(0), k];
do
{
var j = 0;
x = (Double[, ])Guess.Clone();
var r0 = Helpers.Subtract(b, Helpers.Multiply(Matrix, x));
var beta = Helpers.Norm(r0);
H.Initialize();
V.Initialize();
gamma.Initialize();
c.Initialize();
s.Initialize();
gamma[0] = beta;
Helpers.SetColumnVector(V, 1, Helpers.Multiply(r0, 1.0 / beta));
if (beta < Tolerance)
{
break;
}
do
{
iter++;
var Avj = Helpers.Multiply(Matrix, Helpers.GetColumnVector(V, j));
var sum = new Double[Avj.GetLength(0), Avj.GetLength(1)];
for (var m = 0; m <= j; m++)
{
var w = Helpers.GetColumnVector(V, m);
H[m, j] = Helpers.Reduce(w, Avj);
sum = Helpers.AddScaled(sum, H[m, j], w);
}
var wj = Helpers.Subtract(Avj, sum);
H[j + 1, j] = Helpers.Reduce(wj, wj);
Rotate(j, H, c, s, gamma);
if (Math.Abs(H[j + 1, j]) == 0.0)
{
j++;
converged = true;
break;
}
Helpers.SetColumnVector(V, j + 1, Helpers.Multiply(wj, 1.0 / H[j + 1, j]));
beta = Math.Abs(gamma[j]);
if (beta < Tolerance)
{
j++;
converged = true;
break;
}
j++;
}while (j < k);
var y = new Double[j];
for (var l = j; l >= 1; l--)
{
var sum = 0.0;
for (var m = l + 1; m <= j; m++)
{
sum += H[l, m] * y[m];
}
y[l] = (gamma[l] - sum) / H[l, l];
}
for (var l = 0; l < j; l++)
{
x = Helpers.AddScaled(x, y[l], Helpers.GetColumnVector(V, l));
}
if (converged)
{
break;
}
Guess = x;
}while (iter < MaxIterations);
return(x);
}
