//==============================================================================
int Ifpack_Chebyshev::
ApplyInverse(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
if (!IsComputed())
IFPACK_CHK_ERR(-3);
if (PolyDegree_ == 0)
return 0;
int nVec = X.NumVectors();
int len = X.MyLength();
if (nVec != Y.NumVectors())
IFPACK_CHK_ERR(-2);
Time_->ResetStartTime();
// AztecOO gives X and Y pointing to the same memory location,
// need to create an auxiliary vector, Xcopy
Teuchos::RefCountPtr<const Epetra_MultiVector> Xcopy;
if (X.Pointers()[0] == Y.Pointers()[0])
Xcopy = Teuchos::rcp( new Epetra_MultiVector(X) );
else
Xcopy = Teuchos::rcp( &X, false );
double **xPtr = 0, **yPtr = 0;
Xcopy->ExtractView(&xPtr);
Y.ExtractView(&yPtr);
#ifdef HAVE_IFPACK_EPETRAEXT
EpetraExt_PointToBlockDiagPermute* IBD=0;
if (UseBlockMode_) IBD=&*InvBlockDiagonal_;
#endif
//--- Do a quick solve when the matrix is identity
double *invDiag=0;
if(!UseBlockMode_) invDiag=InvDiagonal_->Values();
if ((LambdaMin_ == 1.0) && (LambdaMax_ == LambdaMin_)) {
#ifdef HAVE_IFPACK_EPETRAEXT
if(UseBlockMode_) IBD->ApplyInverse(*Xcopy,Y);
else
#endif
if (nVec == 1) {
double *yPointer = yPtr[0], *xPointer = xPtr[0];
for (int i = 0; i < len; ++i)
yPointer[i] = xPointer[i]*invDiag[i];
}
else {
int i, k;
for (i = 0; i < len; ++i) {
double coeff = invDiag[i];
for (k = 0; k < nVec; ++k)
yPtr[k][i] = xPtr[k][i] * coeff;
}
} // if (nVec == 1)
return 0;
} // if ((LambdaMin_ == 1.0) && (LambdaMax_ == LambdaMin_))
//--- Initialize coefficients
// Note that delta stores the inverse of ML_Cheby::delta
double alpha = LambdaMax_ / EigRatio_;
double beta = 1.1 * LambdaMax_;
double delta = 2.0 / (beta - alpha);
double theta = 0.5 * (beta + alpha);
double s1 = theta * delta;
//--- Define vectors
// In ML_Cheby, V corresponds to pAux and W to dk
Epetra_MultiVector V(X);
Epetra_MultiVector W(X);
#ifdef HAVE_IFPACK_EPETRAEXT
Epetra_MultiVector Temp(X);
#endif
double *vPointer = V.Values(), *wPointer = W.Values();
double oneOverTheta = 1.0/theta;
int i, j, k;
//--- If solving normal equations, multiply RHS by A^T
if(SolveNormalEquations_){
Apply_Transpose(Operator_,Y,V);
Y=V;
}
// Do the smoothing when block scaling is turned OFF
// --- Treat the initial guess
if (ZeroStartingSolution_ == false) {
Operator_->Apply(Y, V);
// Compute W = invDiag * ( X - V )/ Theta
#ifdef HAVE_IFPACK_EPETRAEXT
if(UseBlockMode_) {
Temp.Update(oneOverTheta,X,-oneOverTheta,V,0.0);
IBD->ApplyInverse(Temp,W);
// Perform additional matvecs for normal equations
// CMS: Testing this only in block mode FOR NOW
if(SolveNormalEquations_){
IBD->ApplyInverse(W,Temp);
Apply_Transpose(Operator_,Temp,W);
}
}
else
#endif
if (nVec == 1) {
double *xPointer = xPtr[0];
for (i = 0; i < len; ++i)
wPointer[i] = invDiag[i] * (xPointer[i] - vPointer[i]) * oneOverTheta;
}
else {
for (i = 0; i < len; ++i) {
double coeff = invDiag[i]*oneOverTheta;
double *wi = wPointer + i, *vi = vPointer + i;
for (k = 0; k < nVec; ++k) {
*wi = (xPtr[k][i] - (*vi)) * coeff;
wi = wi + len; vi = vi + len;
}
}
} // if (nVec == 1)
// Update the vector Y
Y.Update(1.0, W, 1.0);
}
else {
// Compute W = invDiag * X / Theta
#ifdef HAVE_IFPACK_EPETRAEXT
if(UseBlockMode_) {
IBD->ApplyInverse(X,W);
// Perform additional matvecs for normal equations
// CMS: Testing this only in block mode FOR NOW
if(SolveNormalEquations_){
IBD->ApplyInverse(W,Temp);
Apply_Transpose(Operator_,Temp,W);
}
W.Scale(oneOverTheta);
Y.Update(1.0, W, 0.0);
}
else
#endif
if (nVec == 1) {
double *xPointer = xPtr[0];
for (i = 0; i < len; ++i){
wPointer[i] = invDiag[i] * xPointer[i] * oneOverTheta;
}
memcpy(yPtr[0], wPointer, len*sizeof(double));
}
else {
for (i = 0; i < len; ++i) {
double coeff = invDiag[i]*oneOverTheta;
double *wi = wPointer + i;
for (k = 0; k < nVec; ++k) {
*wi = xPtr[k][i] * coeff;
wi = wi + len;
}
}
for (k = 0; k < nVec; ++k)
memcpy(yPtr[k], wPointer + k*len, len*sizeof(double));
} // if (nVec == 1)
} // if (ZeroStartingSolution_ == false)
//--- Apply the polynomial
double rhok = 1.0/s1, rhokp1;
double dtemp1, dtemp2;
int degreeMinusOne = PolyDegree_ - 1;
if (nVec == 1) {
double *xPointer = xPtr[0];
for (k = 0; k < degreeMinusOne; ++k) {
Operator_->Apply(Y, V);
rhokp1 = 1.0 / (2.0*s1 - rhok);
dtemp1 = rhokp1 * rhok;
dtemp2 = 2.0 * rhokp1 * delta;
rhok = rhokp1;
// Compute W = dtemp1 * W
W.Scale(dtemp1);
// Compute W = W + dtemp2 * invDiag * ( X - V )
#ifdef HAVE_IFPACK_EPETRAEXT
if(UseBlockMode_) {
//NTS: We can clobber V since it will be reset in the Apply
V.Update(dtemp2,X,-dtemp2);
IBD->ApplyInverse(V,Temp);
// Perform additional matvecs for normal equations
// CMS: Testing this only in block mode FOR NOW
if(SolveNormalEquations_){
IBD->ApplyInverse(V,Temp);
Apply_Transpose(Operator_,Temp,V);
}
W.Update(1.0,Temp,1.0);
}
else{
#endif
for (i = 0; i < len; ++i)
wPointer[i] += dtemp2* invDiag[i] * (xPointer[i] - vPointer[i]);
#ifdef HAVE_IFPACK_EPETRAEXT
}
#endif
// Update the vector Y
Y.Update(1.0, W, 1.0);
} // for (k = 0; k < degreeMinusOne; ++k)
}
else {
for (k = 0; k < degreeMinusOne; ++k) {
Operator_->Apply(Y, V);
rhokp1 = 1.0 / (2.0*s1 - rhok);
dtemp1 = rhokp1 * rhok;
dtemp2 = 2.0 * rhokp1 * delta;
rhok = rhokp1;
// Compute W = dtemp1 * W
W.Scale(dtemp1);
// Compute W = W + dtemp2 * invDiag * ( X - V )
#ifdef HAVE_IFPACK_EPETRAEXT
if(UseBlockMode_) {
//We can clobber V since it will be reset in the Apply
V.Update(dtemp2,X,-dtemp2);
IBD->ApplyInverse(V,Temp);
// Perform additional matvecs for normal equations
// CMS: Testing this only in block mode FOR NOW
if(SolveNormalEquations_){
IBD->ApplyInverse(V,Temp);
Apply_Transpose(Operator_,Temp,V);
}
W.Update(1.0,Temp,1.0);
}
else{
#endif
for (i = 0; i < len; ++i) {
double coeff = invDiag[i]*dtemp2;
double *wi = wPointer + i, *vi = vPointer + i;
for (j = 0; j < nVec; ++j) {
*wi += (xPtr[j][i] - (*vi)) * coeff;
wi = wi + len; vi = vi + len;
}
}
#ifdef HAVE_IFPACK_EPETRAEXT
}
#endif
// Update the vector Y
Y.Update(1.0, W, 1.0);
} // for (k = 0; k < degreeMinusOne; ++k)
} // if (nVec == 1)
// Flops are updated in each of the following.
++NumApplyInverse_;
ApplyInverseTime_ += Time_->ElapsedTime();
return(0);
}
int Ifpack_SORa::ApplyInverse(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const{
if(!IsComputed_) return -1;
Time_.ResetStartTime();
bool initial_guess_is_zero=false;
int NumMyRows=W_->NumMyRows();
int NumVectors = X.NumVectors();
Epetra_MultiVector Temp(A_->RowMatrixRowMap(),NumVectors);
double omega=GetOmega();
// need to create an auxiliary vector, Xcopy
Teuchos::RefCountPtr<const Epetra_MultiVector> Xcopy;
if (X.Pointers()[0] == Y.Pointers()[0]){
Xcopy = Teuchos::rcp( new Epetra_MultiVector(X) );
// Since the user didn't give us anything better, our initial guess is zero.
Y.Scale(0.0);
initial_guess_is_zero=true;
}
else
Xcopy = Teuchos::rcp( &X, false );
Teuchos::RefCountPtr< Epetra_MultiVector > T2;
// Note: Assuming that the matrix has an importer. Ifpack_PointRelaxation doesn't do this, but given that
// I have a CrsMatrix, I'm probably OK.
// Note: This is the lazy man's version sacrificing a few extra flops for avoiding if statements to determine
// if things are on or off processor.
// Note: T2 must be zero'd out
if (IsParallel_ && W_->Importer()) T2 = Teuchos::rcp( new Epetra_MultiVector(W_->Importer()->TargetMap(),NumVectors,true));
else T2 = Teuchos::rcp( new Epetra_MultiVector(A_->RowMatrixRowMap(),NumVectors,true));
// Pointer grabs
int* rowptr,*colind;
double *values;
double **t_ptr,** y_ptr, ** t2_ptr, **x_ptr,*d_ptr;
T2->ExtractView(&t2_ptr);
Y.ExtractView(&y_ptr);
Temp.ExtractView(&t_ptr);
Xcopy->ExtractView(&x_ptr);
Wdiag_->ExtractView(&d_ptr);
IFPACK_CHK_ERR(W_->ExtractCrsDataPointers(rowptr,colind,values));
for(int i=0; i<NumSweeps_; i++){
// Calculate b-Ax
if(!initial_guess_is_zero || i > 0) {
A_->Apply(Y,Temp);
Temp.Update(1.0,*Xcopy,-1.0);
}
else
Temp.Update(1.0,*Xcopy,0.0);
// Note: The off-processor entries of T2 never get touched (they're always zero) and the other entries are updated
// in this sweep before they are used, so we don't need to reset T2 to zero here.
// Do backsolve & update
// x = x + W^{-1} (b - A x)
for(int j=0; j<NumMyRows; j++){
double diag=d_ptr[j];
for (int m=0 ; m<NumVectors; m++) {
double dtmp=0.0;
// Note: Since the diagonal is in the matrix, we need to zero that entry of T2 here to make sure it doesn't contribute.
t2_ptr[m][j]=0.0;
for(int k=rowptr[j];k<rowptr[j+1];k++){
dtmp+= values[k]*t2_ptr[m][colind[k]];
}
// Yes, we need to update both of these.
t2_ptr[m][j] = (t_ptr[m][j]- dtmp)/diag;
y_ptr[m][j] += omega*t2_ptr[m][j];
}
}
}
// Counter update
NumApplyInverse_++;
ApplyInverseTime_ += Time_.ElapsedTime();
return 0;
}