public static bool ComplexSolvePreconditionedBiCGSTAB(
out System.Numerics.Complex[] X,
ComplexSparseMatrix A, System.Numerics.Complex[] B, ComplexSparseMatrix LU,
double convRatioTolerance)
{
System.Diagnostics.Debug.Assert(A.RowLength == A.ColumnLength);
int n = A.RowLength;
System.Diagnostics.Debug.Assert(B.Length == n);
double convRatio = convRatioTolerance;
double tolerance = convRatio;
const int maxIter = IvyFEM.Linear.Constants.MaxIter;
System.Numerics.Complex[] r = new System.Numerics.Complex[n];
System.Numerics.Complex[] r0 = new System.Numerics.Complex[n];
System.Numerics.Complex[] x = new System.Numerics.Complex[n];
System.Numerics.Complex[] p = new System.Numerics.Complex[n];
System.Numerics.Complex[] s = new System.Numerics.Complex[n];
System.Numerics.Complex[] Mp = new System.Numerics.Complex[n];
System.Numerics.Complex[] Ms = new System.Numerics.Complex[n];
int iter = 0;
B.CopyTo(r, 0);
double sqInvNorm0;
{
double sqNorm0 = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
if (sqNorm0 < IvyFEM.Constants.PrecisionLowerLimit)
{
convRatio = 0;
X = x;
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
return(true);
}
sqInvNorm0 = 1.0 / sqNorm0;
}
r.CopyTo(r0, 0);
r.CopyTo(p, 0);
for (iter = 0; iter < maxIter; iter++)
{
ComplexSolveLU(out Mp, LU, p);
System.Numerics.Complex r0r = IvyFEM.Lapack.Functions.zdotc(r0, r);
System.Numerics.Complex[] AMp = A * Mp;
System.Numerics.Complex alpha;
{
System.Numerics.Complex denominator = IvyFEM.Lapack.Functions.zdotc(r0, AMp);
alpha = r0r / denominator;
}
s = IvyFEM.Lapack.Functions.zaxpy(-alpha, AMp, r);
ComplexSolveLU(out Ms, LU, s);
System.Numerics.Complex[] AMs = A * Ms;
System.Numerics.Complex omega;
{
System.Numerics.Complex denominator = IvyFEM.Lapack.Functions.zdotc(AMs, AMs);
System.Numerics.Complex numerator = IvyFEM.Lapack.Functions.zdotc(s, AMs);
omega = numerator / denominator;
}
x = IvyFEM.Lapack.Functions.zaxpy(alpha, Mp, x);
x = IvyFEM.Lapack.Functions.zaxpy(omega, Ms, x);
r = IvyFEM.Lapack.Functions.zaxpy(-omega, AMs, s);
{
double sqNorm = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
if (sqNorm * sqInvNorm0 < tolerance * tolerance)
{
convRatio = Math.Sqrt(sqNorm * sqInvNorm0);
X = x;
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
return(true);
}
}
System.Numerics.Complex beta;
{
System.Numerics.Complex r0rPrev = r0r;
r0r = IvyFEM.Lapack.Functions.zdotc(r0, r);
beta = (r0r * alpha) / (r0rPrev * omega);
}
p = IvyFEM.Lapack.Functions.zaxpy(beta, p, r);
p = IvyFEM.Lapack.Functions.zaxpy(-beta * omega, AMp, p);
}
{
double sqNormRes = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
convRatio = Math.Sqrt(sqNormRes * sqInvNorm0);
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
X = x;
}
System.Diagnostics.Debug.WriteLine("Not converged");
return(false);
}
public static bool ComplexSolveNoPreconCOCG(
out System.Numerics.Complex[] X,
ComplexSparseMatrix A, System.Numerics.Complex[] B,
double convRatioTolerance)
{
System.Diagnostics.Debug.Assert(A.RowLength == A.ColumnLength);
int n = A.RowLength;
System.Diagnostics.Debug.Assert(B.Length == n);
double convRatio = convRatioTolerance;
double convRatioTol = convRatio;
const int maxIter = IvyFEM.Linear.Constants.MaxIter;
System.Numerics.Complex[] r = new System.Numerics.Complex[n];
System.Numerics.Complex[] x = new System.Numerics.Complex[n];
System.Numerics.Complex[] p = new System.Numerics.Complex[n];
int iter = 0;
B.CopyTo(r, 0);
double sqInvNorm0;
{
double sqNorm0 = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
if (sqNorm0 < IvyFEM.Constants.PrecisionLowerLimit)
{
convRatio = 0;
X = x;
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
return(true);
}
sqInvNorm0 = 1.0 / sqNorm0;
}
r.CopyTo(p, 0);
System.Numerics.Complex rr = IvyFEM.Lapack.Functions.zdotu(r, r);
for (iter = 0; iter < maxIter; iter++)
{
System.Numerics.Complex[] Ap = A * p;
System.Numerics.Complex alpha;
{
System.Numerics.Complex pAp = IvyFEM.Lapack.Functions.zdotu(p, Ap);
alpha = rr / pAp;
}
r = IvyFEM.Lapack.Functions.zaxpy(-alpha, Ap, r);
x = IvyFEM.Lapack.Functions.zaxpy(alpha, p, x);
{
double sqNorm = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
if (sqNorm * sqInvNorm0 < convRatioTol * convRatioTol)
{
convRatio = Math.Sqrt(sqNorm * sqInvNorm0);
X = x;
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
return(true);
}
}
System.Numerics.Complex rrPrev = rr;
rr = IvyFEM.Lapack.Functions.zdotu(r, r);
System.Numerics.Complex beta = rr / rrPrev;
p = IvyFEM.Lapack.Functions.zaxpy(beta, p, r);
}
{
double sqNormRes = IvyFEM.Lapack.Functions.zdotc(r, r).Real;
convRatio = Math.Sqrt(sqNormRes * sqInvNorm0);
System.Diagnostics.Debug.WriteLine("iter = " + iter + " norm: " + convRatio);
X = x;
}
System.Diagnostics.Debug.WriteLine("Not converged");
return(false);
}
