public bool Solve()
{
Iterations = 0;
int size = B.Length;
// Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
R = new double[size];
P = new double[size];
AP = new double[size];
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = new double[size];
}
Array.Clear(X, 0, X.Length);
Array.Copy(B, R, B.Length);
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] these were inside loop but they are constant!
double norm = BufferUtil.Dot(B, B);
double root1 = Math.Sqrt(norm);
// The first iteration.
double rho0 = BufferUtil.Dot(R, R);
// [RMS] If we were initialized w/ constraints already satisfied,
// then we are done! (happens for example in mesh deformations)
if (rho0 < MathUtil.ZeroTolerance * root1)
{
return(true);
}
Array.Copy(R, P, R.Length);
MultiplyF(P, AP);
double alpha = rho0 / BufferUtil.Dot(P, AP);
BufferUtil.MultiplyAdd(X, alpha, P);
BufferUtil.MultiplyAdd(R, -alpha, AP);
double rho1 = BufferUtil.Dot(R, R);
// The remaining iterations.
int iter;
for (iter = 1; iter < MaxIterations; ++iter)
{
double root0 = Math.Sqrt(rho1);
if (root0 <= MathUtil.ZeroTolerance * root1)
{
break;
}
double beta = rho1 / rho0;
UpdateP(P, beta, R);
MultiplyF(P, AP);
alpha = rho1 / BufferUtil.Dot(P, AP);
// can compute these two steps simultaneously
double RdotR = 0;
gParallel.Evaluate(
() => { BufferUtil.MultiplyAdd(X, alpha, P); },
() => { RdotR = BufferUtil.MultiplyAdd_GetSqrSum(R, -alpha, AP); }
);
rho0 = rho1;
rho1 = RdotR; // BufferUtil.Dot(R, R);
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
/// <summary>
/// standard CG solve
/// </summary>
public bool Solve()
{
Iterations = 0;
if (B == null || MultiplyF == null)
{
throw new Exception("SparseSymmetricCGMultipleRHS.Solve(): Must set B and MultiplyF!");
}
int NRHS = B.Length;
if (NRHS == 0)
{
throw new Exception("SparseSymmetricCGMultipleRHS.Solve(): Need at least one RHS vector in B");
}
int size = B[0].Length;
// Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
R = BufferUtil.AllocNxM(NRHS, size);
P = BufferUtil.AllocNxM(NRHS, size);
W = BufferUtil.AllocNxM(NRHS, size);
if (X == null || UseXAsInitialGuess == false)
{
if (X == null)
{
X = BufferUtil.AllocNxM(NRHS, size);
}
for (int j = 0; j < NRHS; ++j)
{
Array.Clear(X[j], 0, size);
Array.Copy(B[j], R[j], size);
}
}
else
{
// hopefully is X is a decent initialization...
InitializeR(R);
}
// [RMS] these were inside loop but they are constant!
double[] norm = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
norm[j] = BufferUtil.Dot(B[j], B[j]);
}
double[] root1 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
root1[j] = Math.Sqrt(norm[j]);
}
// The first iteration.
double[] rho0 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
rho0[j] = BufferUtil.Dot(R[j], R[j]);
}
// [RMS] If we were initialized w/ constraints already satisfied,
// then we are done! (happens for example in mesh deformations)
bool[] converged = new bool[NRHS];
int nconverged = 0;
for (int j = 0; j < NRHS; ++j)
{
converged[j] = rho0[j] < (ConvergeTolerance * root1[j]);
if (converged[j])
{
nconverged++;
}
}
if (nconverged == NRHS)
{
return(true);
}
for (int j = 0; j < NRHS; ++j)
{
Array.Copy(R[j], P[j], size);
}
MultiplyF(P, W);
double[] alpha = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
alpha[j] = rho0[j] / BufferUtil.Dot(P[j], W[j]);
}
for (int j = 0; j < NRHS; ++j)
{
BufferUtil.MultiplyAdd(X[j], alpha[j], P[j]);
}
for (int j = 0; j < NRHS; ++j)
{
BufferUtil.MultiplyAdd(R[j], -alpha[j], W[j]);
}
double[] rho1 = new double[NRHS];
for (int j = 0; j < NRHS; ++j)
{
rho1[j] = BufferUtil.Dot(R[j], R[j]);
}
double[] beta = new double[NRHS];
var rhs = Interval1i.Range(NRHS);
// The remaining iterations.
int iter;
for (iter = 1; iter < MaxIterations; ++iter)
{
bool done = true;
for (int j = 0; j < NRHS; ++j)
{
if (converged[j] == false)
{
double root0 = Math.Sqrt(rho1[j]);
if (root0 <= ConvergeTolerance * root1[j])
{
converged[j] = true;
}
}
if (converged[j] == false)
{
done = false;
}
}
if (done)
{
break;
}
for (int j = 0; j < NRHS; ++j)
{
beta[j] = rho1[j] / rho0[j];
}
UpdateP(P, beta, R, converged);
MultiplyF(P, W);
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
alpha[j] = rho1[j] / BufferUtil.Dot(P[j], W[j]);
}
});
// can do all these in parallel, but improvement is minimal
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
BufferUtil.MultiplyAdd(X[j], alpha[j], P[j]);
}
});
gParallel.ForEach(rhs, (j) =>
{
if (converged[j] == false)
{
rho0[j] = rho1[j];
rho1[j] = BufferUtil.MultiplyAdd_GetSqrSum(R[j], -alpha[j], W[j]);
}
});
}
//System.Console.WriteLine("{0} iterations", iter);
Iterations = iter;
return(iter < MaxIterations);
}
