public OptVector Solve(
OptVector[] A,
OptVector b,
OptVector startX,
int nIter)
{
OptVector[] normA = A;
OptVector normb = b;
if (!OptVector.Equals(A, OptVector.Transpose(A)))
{
OptVector[] At = OptVector.Transpose(A);
normA = OptVector.Mult(At, A);
normb = OptVector.Mult(At, b);
}
OptVector rNew = normb - OptVector.Mult(normA, startX);
OptVector p = rNew;
OptVector x = new OptVector(startX);
double r2Old = rNew * rNew;
double alpha = 1.0;
double beta = 1.0;
for (int i = 0; i < nIter; i++)
{
alpha = GetAlpha(normA, p, r2Old);
x = x + alpha * p;
rNew = rNew - alpha * OptVector.Mult(normA, p);
double r2New = rNew * rNew;
if (r2New < Precision)
{
return(x);
}
beta = GetBeta(r2New, r2Old);
p = rNew + beta * p;
r2Old = r2New;
}
return(x);
}
public OptVector Solve(
OptVector[] A,
OptVector b,
OptVector startX,
int nIter)
{
OptVector[] symmA = A;
OptVector normb = b;
//Symmetrize matrix
if (CheckSymmetry)
{
OptVector[] At = OptVector.Transpose(A);
if (!OptVector.Equals(A, At))
{
symmA = OptVector.Mult(At, A);
normb = OptVector.Mult(At, b);
}
}
OptVector v0 = new OptVector(b.Count);
OptVector v1 = normb - OptVector.Mult(symmA, startX);
double beta1 = v1.Length();
double betaN = 0.0;
double n = beta1;
double c0 = 1.0;
double c1 = 1.0;
double s0 = 0.0;
double s1 = 0.0;
OptVector w0 = new OptVector(v1.Count);
OptVector w_1 = new OptVector(v1.Count);
OptVector x = new OptVector(startX);
for (int i = 0; i < nIter; i++)
{
//Calculate Lanczos Vectors
OptVector v = (1.0 / beta1) * v1;
OptVector Av = OptVector.Mult(symmA, v);
double alpha = v * Av;
v1 = Av - alpha * v - beta1 * v0;
betaN = v1.Length();
//Calculate QR factors
double lambda = c1 * alpha - c0 * s1 * beta1;
double p1 = Math.Sqrt(lambda * lambda + betaN * betaN);
double p2 = s1 * alpha + c0 * c1 * beta1;
double p3 = s0 * beta1;
//Calculate New Givens Rotations
c0 = c1;
c1 = lambda / p1;
s0 = s1;
s1 = betaN / p1;
//Update Solution
OptVector w = (1.0 / p1) * (v - p3 * w_1 - p2 * w0);
x = x + c1 * n * w;
n = -s1 * n;
residual = Math.Abs(n);
if (residual < precisionConst)
{
break;
}
beta1 = betaN;
v0 = v;
w_1 = w0;
w0 = w;
}
return(x);
}
