public SolveResult BiCGSTAB(int n, int nnz, float[] csrValA, int[] csrRowA, int[] csrColA, float[] x, float[] b, float[] ax, float[] r0, float[] r, float[] v, float[] p, float[] s, float[] t, float threshold = 0.000001f, int maxIterate = 1000)
{
SolveResult result = new SolveResult();
float l0 = 1.0f, alpha = 1.0f, w0 = 1.0f;
float l1, beta, w1;
float bn = blas.NRM2(b);
int k = 1;
float minusOne = 1.0f;
float one = 1.0f;
float zero = 0.0f;
blas.COPY(b, r0);
sparse.CSRMV(n, n, nnz, ref minusOne, csrValA, csrRowA, csrColA, x, ref one, r0);
blas.COPY(r0, r);
SetValue(n, v, 0.0f);
SetValue(n, p, 0.0f);
double residual = 0.0;
while (true)
{
l1 = blas.DOT(r0, r);
beta = (l1 / l0) * (alpha / w0);
// Update p
blas.AXPY(-w0, v, p);
blas.SCAL(beta, p);
blas.AXPY(1.0f, r, p);
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, p, ref zero, v);
// Update v
alpha = l1 / blas.DOT(r0, v);
blas.COPY(r, s);
blas.AXPY(-alpha, v, s);
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, s, ref zero, t);
w1 = blas.DOT(t, s) / blas.DOT(t, t);
// Update x
blas.AXPY(alpha, p, x);
blas.AXPY(w1, s, x);
// Update r
blas.COPY(s, r);
blas.AXPY(-w1, t, r);
//reidual = blas.NRM2(r) / bn;
residual = blas.NRM2(s);
if (k > maxIterate)
{
result.IterateCount = k;
result.IsSuccess = false;
result.LastError = residual;
return result;
}
if (residual <= threshold)
{
result.IterateCount = k;
result.IsSuccess = true;
result.LastError = residual;
return result;
}
k++;
w0 = w1;
l0 = l1;
}
}
public SolveResult CGPreconditioned(
int n, int nnz, float[] csrValA, int[] csrRowA, int[] csrColA, float[] dx, float[] db,
float[] csrValICP, int[] csrRowICP, int[] csrColICP,
float[] dy, float[] dp, float[] domega, float[] zm1, float[] zm2, float[] rm2, float tolerence = 0.0001f, int maxIterate = 300)
{
SolveResult result = new SolveResult();
// Make Incomplete Cholesky Preconditioner.
gpu.Launch().DefineLower(n, csrRowICP, csrColICP);
gpu.Launch(n, 1).CopyAIntoH(n, csrValA, csrRowA, csrValICP, csrRowICP);
gpu.Launch(n, 1).ConstructH(n, csrValICP, csrRowICP);
cusparseMatDescr descrM = new cusparseMatDescr();
descrM.MatrixType = cusparseMatrixType.Triangular;
descrM.FillMode = cusparseFillMode.Lower;
descrM.IndexBase = cusparseIndexBase.Zero;
descrM.DiagType = cusparseDiagType.NonUnit;
cusparseSolveAnalysisInfo info = new cusparseSolveAnalysisInfo();
sparse.CreateSolveAnalysisInfo(ref info);
cusparseSolveAnalysisInfo infoTrans = new cusparseSolveAnalysisInfo();
sparse.CreateSolveAnalysisInfo(ref infoTrans);
sparse.CSRSV_ANALYSIS(n, nnz, csrValICP, csrRowICP, csrColICP, cusparseOperation.NonTranspose, info, descrM);
sparse.CSRSV_ANALYSIS(n, nnz, csrValICP, csrRowICP, csrColICP, cusparseOperation.Transpose, infoTrans, descrM);
int k = 0;
float r1 = blas.DOT(db, db);
float alpha, beta;
float identityFloat = 1.0f;
float zeroFloat = 0.0f;
while (true)
{
sparse.CSRSV_SOLVE(n, ref identityFloat, csrValICP, csrRowICP, csrColICP, db, dy, cusparseOperation.NonTranspose, info, descrM);
sparse.CSRSV_SOLVE(n, ref identityFloat, csrValICP, csrRowICP, csrColICP, dy, zm1, cusparseOperation.Transpose, infoTrans, descrM);
k++;
if (k == 1)
{
blas.COPY(zm1, dp);
}
else
{
beta = blas.DOT(db, zm1) / blas.DOT(rm2, zm2);
blas.SCAL(beta, dp);
blas.AXPY(1.0f, zm1, dp);
}
sparse.CSRMV(n, n, nnz, ref identityFloat, csrValA, csrRowA, csrColA, dp, ref zeroFloat, domega);
alpha = blas.DOT(db, zm1) / blas.DOT(dp, domega);
blas.AXPY(alpha, dp, dx);
blas.COPY(db, rm2);
blas.COPY(zm1, zm2);
blas.AXPY(-alpha, domega, db);
r1 = blas.DOT(db, db);
if (r1 <= tolerence * tolerence)
{
result.IsSuccess = true;
result.IterateCount = k;
result.LastError = r1;
break;
}
if (k > maxIterate)
{
result.IsSuccess = false;
result.IterateCount = k;
result.LastError = r1;
break;
}
}
return result;
}
public SolveResult CG(
int n, int nnz, double[] csrValA, int[] csrRowA, int[] csrColA,
double[] dx, double[] db, double[] dp, double[] dAx, double tolerence = 0.00001f, int maxIterate = 300)
{
SolveResult result = new SolveResult();
int k; // Iterate count.
double a, b, r0, r1;
double zero = 0.0;
double one = 1.0;
if (blas.DOT(db, db) == 0.0)
{
SetValue(n, dx, 0);
result.IsSuccess = true;
return result;
}
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, dx, ref zero, dAx);
blas.AXPY(-1.0f, dAx, db);
r1 = blas.DOT(db, db);
k = 1;
r0 = 0;
while (true)
{
if (k > 1)
{
b = r1 / r0;
blas.SCAL(b, dp);
blas.AXPY(1.0f, db, dp);
}
else
{
blas.COPY(db, dp);
}
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, dp, ref zero, dAx);
a = r1 / blas.DOT(dp, dAx);
blas.AXPY(a, dp, dx);
blas.AXPY(-a, dAx, db);
r0 = r1;
r1 = blas.DOT(db, db);
k++;
if (r1 <= tolerence * tolerence)
{
result.IsSuccess = true;
result.LastError = r1;
result.IterateCount = k;
break;
}
if (k > maxIterate)
{
result.IsSuccess = false;
result.LastError = r1;
result.IterateCount = k;
break;
}
}
return result;
}
public SolveResult BiCGSTAB(int n, int nnz, float[] csrValA, int[] csrRowA, int[] csrColA, float[] x, float[] b, float[] ax, float[] r0, float[] r, float[] v, float[] p, float[] s, float[] t, float threshold = 0.000001f, int maxIterate = 1000)
{
SolveResult result = new SolveResult();
float l0 = 1.0f, alpha = 1.0f, w0 = 1.0f;
float l1, beta, w1;
float bn = blas.NRM2(b);
int k = 1;
float minusOne = 1.0f;
float one = 1.0f;
float zero = 0.0f;
blas.COPY(b, r0);
sparse.CSRMV(n, n, nnz, ref minusOne, csrValA, csrRowA, csrColA, x, ref one, r0);
blas.COPY(r0, r);
SetValue(n, v, 0.0f);
SetValue(n, p, 0.0f);
double residual = 0.0;
while (true)
{
l1 = blas.DOT(r0, r);
beta = (l1 / l0) * (alpha / w0);
// Update p
blas.AXPY(-w0, v, p);
blas.SCAL(beta, p);
blas.AXPY(1.0f, r, p);
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, p, ref zero, v);
// Update v
alpha = l1 / blas.DOT(r0, v);
blas.COPY(r, s);
blas.AXPY(-alpha, v, s);
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, s, ref zero, t);
w1 = blas.DOT(t, s) / blas.DOT(t, t);
// Update x
blas.AXPY(alpha, p, x);
blas.AXPY(w1, s, x);
// Update r
blas.COPY(s, r);
blas.AXPY(-w1, t, r);
//reidual = blas.NRM2(r) / bn;
residual = blas.NRM2(s);
if (k > maxIterate)
{
result.IterateCount = k;
result.IsSuccess = false;
result.LastError = residual;
return(result);
}
if (residual <= threshold)
{
result.IterateCount = k;
result.IsSuccess = true;
result.LastError = residual;
return(result);
}
k++;
w0 = w1;
l0 = l1;
}
}
public SolveResult CGPreconditioned(
int n, int nnz, float[] csrValA, int[] csrRowA, int[] csrColA, float[] dx, float[] db,
float[] csrValICP, int[] csrRowICP, int[] csrColICP,
float[] dy, float[] dp, float[] domega, float[] zm1, float[] zm2, float[] rm2, float tolerence = 0.0001f, int maxIterate = 300)
{
SolveResult result = new SolveResult();
// Make Incomplete Cholesky Preconditioner.
gpu.Launch().DefineLower(n, csrRowICP, csrColICP);
gpu.Launch(n, 1).CopyAIntoH(n, csrValA, csrRowA, csrValICP, csrRowICP);
gpu.Launch(n, 1).ConstructH(n, csrValICP, csrRowICP);
cusparseMatDescr descrM = new cusparseMatDescr();
descrM.MatrixType = cusparseMatrixType.Triangular;
descrM.FillMode = cusparseFillMode.Lower;
descrM.IndexBase = cusparseIndexBase.Zero;
descrM.DiagType = cusparseDiagType.NonUnit;
cusparseSolveAnalysisInfo info = new cusparseSolveAnalysisInfo();
sparse.CreateSolveAnalysisInfo(ref info);
cusparseSolveAnalysisInfo infoTrans = new cusparseSolveAnalysisInfo();
sparse.CreateSolveAnalysisInfo(ref infoTrans);
sparse.CSRSV_ANALYSIS(n, nnz, csrValICP, csrRowICP, csrColICP, cusparseOperation.NonTranspose, info, descrM);
sparse.CSRSV_ANALYSIS(n, nnz, csrValICP, csrRowICP, csrColICP, cusparseOperation.Transpose, infoTrans, descrM);
int k = 0;
float r1 = blas.DOT(db, db);
float alpha, beta;
float identityFloat = 1.0f;
float zeroFloat = 0.0f;
while (true)
{
sparse.CSRSV_SOLVE(n, ref identityFloat, csrValICP, csrRowICP, csrColICP, db, dy, cusparseOperation.NonTranspose, info, descrM);
sparse.CSRSV_SOLVE(n, ref identityFloat, csrValICP, csrRowICP, csrColICP, dy, zm1, cusparseOperation.Transpose, infoTrans, descrM);
k++;
if (k == 1)
{
blas.COPY(zm1, dp);
}
else
{
beta = blas.DOT(db, zm1) / blas.DOT(rm2, zm2);
blas.SCAL(beta, dp);
blas.AXPY(1.0f, zm1, dp);
}
sparse.CSRMV(n, n, nnz, ref identityFloat, csrValA, csrRowA, csrColA, dp, ref zeroFloat, domega);
alpha = blas.DOT(db, zm1) / blas.DOT(dp, domega);
blas.AXPY(alpha, dp, dx);
blas.COPY(db, rm2);
blas.COPY(zm1, zm2);
blas.AXPY(-alpha, domega, db);
r1 = blas.DOT(db, db);
if (r1 <= tolerence * tolerence)
{
result.IsSuccess = true;
result.IterateCount = k;
result.LastError = r1;
break;
}
if (k > maxIterate)
{
result.IsSuccess = false;
result.IterateCount = k;
result.LastError = r1;
break;
}
}
return(result);
}
public SolveResult CG(
int n, int nnz, double[] csrValA, int[] csrRowA, int[] csrColA,
double[] dx, double[] db, double[] dp, double[] dAx, double tolerence = 0.00001f, int maxIterate = 300)
{
SolveResult result = new SolveResult();
int k; // Iterate count.
double a, b, r0, r1;
double zero = 0.0;
double one = 1.0;
if (blas.DOT(db, db) == 0.0)
{
SetValue(n, dx, 0);
result.IsSuccess = true;
return(result);
}
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, dx, ref zero, dAx);
blas.AXPY(-1.0f, dAx, db);
r1 = blas.DOT(db, db);
k = 1;
r0 = 0;
while (true)
{
if (k > 1)
{
b = r1 / r0;
blas.SCAL(b, dp);
blas.AXPY(1.0f, db, dp);
}
else
{
blas.COPY(db, dp);
}
sparse.CSRMV(n, n, nnz, ref one, csrValA, csrRowA, csrColA, dp, ref zero, dAx);
a = r1 / blas.DOT(dp, dAx);
blas.AXPY(a, dp, dx);
blas.AXPY(-a, dAx, db);
r0 = r1;
r1 = blas.DOT(db, db);
k++;
if (r1 <= tolerence * tolerence)
{
result.IsSuccess = true;
result.LastError = r1;
result.IterateCount = k;
break;
}
if (k > maxIterate)
{
result.IsSuccess = false;
result.LastError = r1;
result.IterateCount = k;
break;
}
}
return(result);
}