/// <summary>
/// computes the inner product of this array and another array <paramref name="other"/>.
/// </summary>
/// <param name="other">
/// must be of the same size a this array
/// </param>
/// <returns></returns>
public double InnerProduct(MultidimensionalArray other)
{
if (this.Dimension != other.Dimension)
{
throw new ArgumentException("mismatch in number of dimensions");
}
int D = this.Dimension;
for (int k = 0; k < D; k++)
{
if (this.GetLength(k) != other.GetLength(k))
{
throw new ArgumentException("mismatch in dimension " + k);
}
}
if (this.IsContinious && other.IsContinious)
{
unsafe
{
fixed(double *pStorageThis = this.m_Storage, pStorageOther = other.m_Storage)
{
return(BLAS.ddot(this.Length, pStorageThis, 1, pStorageOther, 1));
}
}
}
else
{
double acc = 0;
this.ApplyAll(delegate(int[] index, ref double entry) {
acc += entry * other[index];
});
return(acc);
}
}
void __AddSol(ref double[] X)
{
Debug.Assert(SolHistory.Count == MxxHistory.Count);
Debug.Assert(X.Length == OpMatrix._RowPartitioning.LocalLength);
int L = X.Length;
int KrylovDim = SolHistory.Count;
double[] Mxx = new double[L];
OpMatrix.SpMV(1.0, X, 0.0, Mxx);
for (int i = 0; i < KrylovDim; i++)
{
Debug.Assert(!object.ReferenceEquals(Mxx, MxxHistory[i]));
double beta = BLAS.ddot(L, Mxx, 1, MxxHistory[i], 1).MPISum();
BLAS.daxpy(L, -beta, SolHistory[i], 1, X, 1);
BLAS.daxpy(L, -beta, MxxHistory[i], 1, Mxx, 1);
}
double gamma = 1.0 / Mxx.L2NormPow2().MPISum().Sqrt();
//double gamma = 1.0 / BLAS.dnrm2(L, Mxx, 1).Pow2().MPISum().Sqrt();
BLAS.dscal(L, gamma, Mxx, 1);
BLAS.dscal(L, gamma, X, 1);
SolHistory.Add(X);
MxxHistory.Add(Mxx);
X = null;
}
double MinimizeResidual(double[] outX, double[] Sol0, double[] Res0, double[] outRes, bool diagnosis = false)
{
using (new FuncTrace()) {
Debug.Assert(SolHistory.Count == MxxHistory.Count);
Debug.Assert(outX.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(Sol0.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(Res0.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(outRes.Length == m_MgOperator.Mapping.LocalLength);
int KrylovDim = SolHistory.Count;
int L = outX.Length;
double[] alpha = new double[KrylovDim];
for (int i = 0; i < KrylovDim; i++)
{
//alpha[i] = GenericBlas.InnerProd(MxxHistory[i], Res0).MPISum();
alpha[i] = BLAS.ddot(L, MxxHistory[i], 1, Res0, 1);
}
alpha = alpha.MPISum();
Array.Copy(Sol0, outX, L);
Array.Copy(Res0, outRes, L);
for (int i = 0; i < KrylovDim; i++)
{
//outX.AccV(alpha[i], SolHistory[i]);
//outRes.AccV(-alpha[i], MxxHistory[i]);
BLAS.daxpy(L, alpha[i], SolHistory[i], 1, outX, 1);
BLAS.daxpy(L, -alpha[i], MxxHistory[i], 1, outRes, 1);
}
double ResNorm = BLAS.dnrm2(L, outRes, 1).Pow2().MPISum().Sqrt();
//Console.WriteLine("OrthonormalizationMultigrid: minimizing ofer " + KrylovDim + " vectors");
return(ResNorm);
/* we cannot do the following
* // since the 'MxxHistory' vectors form an orthonormal system,
* // the L2-norm is the L2-Norm of the 'alpha'-coordinates (Parceval's equality)
* return alpha.L2Norm();
*/
}
}
void AddSolCore(ref double[] X)
{
Debug.Assert(SolHistory.Count == MxxHistory.Count);
Debug.Assert(X.Length == OpMatrix._RowPartitioning.LocalLength);
int L = X.Length;
int KrylovDim = SolHistory.Count;
double[] Mxx = new double[L];
OpMatrix.SpMV(1.0, X, 0.0, Mxx);
//double NormInitial = Mxx.MPI_L2Norm();
for (int jj = 0; jj < 2; jj++) // re-orthogonalisation, loop-limit to 2; See book of Saad, p 162, section 6.3.2
{
for (int i = 0; i < KrylovDim; i++)
{
Debug.Assert(!object.ReferenceEquals(Mxx, MxxHistory[i]));
double beta = BLAS.ddot(L, Mxx, 1, MxxHistory[i], 1).MPISum();
BLAS.daxpy(L, -beta, SolHistory[i], 1, X, 1);
BLAS.daxpy(L, -beta, MxxHistory[i], 1, Mxx, 1);
}
//double NormAfter = Mxx.MPI_L2Norm();
//Console.WriteLine(" orthonormalization norm reduction: " + (NormAfter/NormInitial));
double gamma = 1.0 / Mxx.L2NormPow2().MPISum().Sqrt();
//double gamma = 1.0 / BLAS.dnrm2(L, Mxx, 1).Pow2().MPISum().Sqrt();
BLAS.dscal(L, gamma, Mxx, 1);
BLAS.dscal(L, gamma, X, 1);
}
SolHistory.Add(X);
MxxHistory.Add(Mxx);
X = null;
}
double MinimizeResidual(double[] outX, double[] Sol0, double[] Res0, double[] outRes, bool diagnosis = false)
{
using (new FuncTrace()) {
Debug.Assert(SolHistory.Count == MxxHistory.Count);
Debug.Assert(outX.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(Sol0.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(Res0.Length == m_MgOperator.Mapping.LocalLength);
Debug.Assert(outRes.Length == m_MgOperator.Mapping.LocalLength);
int KrylovDim = SolHistory.Count;
int L = outX.Length;
double[] alpha = new double[KrylovDim];
for (int i = 0; i < KrylovDim; i++)
{
//alpha[i] = GenericBlas.InnerProd(MxxHistory[i], Res0).MPISum();
alpha[i] = BLAS.ddot(L, MxxHistory[i], 1, Res0, 1);
}
alpha = alpha.MPISum();
//outX.SetV(Sol0);
//outRes.SetV(Res0);
Array.Copy(Sol0, outX, L);
Array.Copy(Res0, outRes, L);
for (int i = 0; i < KrylovDim; i++)
{
//outX.AccV(alpha[i], SolHistory[i]);
//outRes.AccV(-alpha[i], MxxHistory[i]);
BLAS.daxpy(L, alpha[i], SolHistory[i], 1, outX, 1);
BLAS.daxpy(L, -alpha[i], MxxHistory[i], 1, outRes, 1);
}
double ResNorm = BLAS.dnrm2(L, outRes, 1).Pow2().MPISum().Sqrt();
/*
* if(ResNorm < Tolerance) {
* alpha.SaveToStream(Console.Out, m_MgOperator.BaseGridProblemMapping.MPI_Comm);
*
* alpha.SaveToTextFile("ConvScheisse.txt", m_MgOperator.BaseGridProblemMapping.MPI_Comm);
* }
*/
/*
* if (diagnosis) {
* for (int i = 0; i < KrylovDim; i++) {
* Console.WriteLine(" s " + alpha[KrylovDim - i - 1]);
*
* }
* }
*/
return(ResNorm);
/* we cannot do the following
* // since the 'MxxHistory' vectors form an orthonormal system,
* // the L2-norm is the L2-Norm of the 'alpha'-coordinates (Parceval's equality)
* return alpha.L2Norm();
*/
}
}
