public GMRESResult solve(Vector b, Vector x0 = null)
{
GMRESResult result = solveImpl(b, x0);
Utils.QL_REQUIRE(result.Errors.Last() < relTol_, () => "could not converge");
return(result);
}
public GMRESResult solveWithRestart(int restart, Vector b, Vector x0 = null)
{
GMRESResult result = solveImpl(b, x0);
List <double> errors = result.Errors;
for (int i = 0; i < restart - 1 && result.Errors.Last() >= relTol_; ++i)
{
result = solveImpl(b, result.X);
errors.AddRange(result.Errors);
}
Utils.QL_REQUIRE(errors.Last() < relTol_, () => "could not converge");
result.Errors = errors;
return(result);
}
protected GMRESResult solveImpl(Vector b, Vector x0)
{
double bn = Vector.Norm2(b);
GMRESResult result;
if (bn.IsEqual(0.0))
{
result = new GMRESResult(new InitializedList <double>(1, 0.0), b);
return(result);
}
Vector x = !x0.empty() ? x0 : new Vector(b.size(), 0.0);
Vector r = b - A_(x);
double g = Vector.Norm2(r);
if (g / bn < relTol_)
{
result = new GMRESResult(new InitializedList <double>(1, g / bn), x);
return(result);
}
List <Vector> v = new InitializedList <Vector>(1, r / g);
List <Vector> h = new InitializedList <Vector>(1, new Vector(maxIter_, 0.0));
List <double> c = new List <double>(maxIter_ + 1),
s = new List <double>(maxIter_ + 1),
z = new List <double>(maxIter_ + 1);
z[0] = g;
List <double> errors = new InitializedList <double>(1, g / bn);
for (int j = 0; j < maxIter_ && errors.Last() >= relTol_; ++j)
{
h.Add(new Vector(maxIter_, 0.0));
Vector w = A_((M_ != null) ? M_(v[j]) : v[j]);
for (int i = 0; i <= j; ++i)
{
h[i][j] = Vector.DotProduct(w, v[i]);
w -= h[i][j] * v[i];
}
h[j + 1][j] = Vector.Norm2(w);
if (h[j + 1][j] < Const.QL_EPSILON * Const.QL_EPSILON)
{
break;
}
v.Add(w / h[j + 1][j]);
for (int i = 0; i < j; ++i)
{
double h0 = c[i] * h[i][j] + s[i] * h[i + 1][j];
double h1 = -s[i] * h[i][j] + c[i] * h[i + 1][j];
h[i][j] = h0;
h[i + 1][j] = h1;
}
double nu = Math.Sqrt((h[j][j]) * (h[j][j])
+ (h[j + 1][j]) * (h[j + 1][j]));
c[j] = h[j][j] / nu;
s[j] = h[j + 1][j] / nu;
h[j][j] = nu;
h[j + 1][j] = 0.0;
z[j + 1] = -s[j] * z[j];
z[j] = c[j] * z[j];
errors.Add(Math.Abs(z[j + 1] / bn));
}
int k = v.Count - 1;
Vector y = new Vector(k, 0.0);
y[k - 1] = z[k - 1] / h[k - 1][k - 1];
for (int i = k - 2; i >= 0; --i)
{
y[i] = (z[i] - h[i].inner_product(
i + 1, k, i + 1, y, 0.0)) / h[i][i];
}
Vector xm = new Vector(x.Count, 0.0);
for (int i = 0; i < x.Count; i++)
{
xm[i] = v[i].inner_product(0, k, 0, y, 0.0);
}
xm = x + ((M_ != null) ? M_(xm) : xm);
result = new GMRESResult(errors, xm);
return(result);
}