void
LOCA::Epetra::CompactWYOp::applyCompactWY(const Epetra_MultiVector& x,
Epetra_MultiVector& result_x,
Epetra_MultiVector& result_p) const
{
// Compute Y_x^T*x
result_p.Multiply('T', 'N', 1.0, *Y_x, x, 0.0);
// Compute T*(Y_x^T*x)
dblas.TRMM(Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::NO_TRANS,
Teuchos::NON_UNIT_DIAG, result_p.MyLength(),
result_p.NumVectors(), 1.0, T.Values(), T.MyLength(),
result_p.Values(), result_p.MyLength());
// Compute x = x + Y_x*T*(Y_x^T*x)
result_x = x;
result_x.Multiply('N', 'N', 1.0, *Y_x, result_p, 1.0);
// Compute result_p = Y_p*T*(Y_x^T*x)
dblas.TRMM(Teuchos::LEFT_SIDE, Teuchos::LOWER_TRI, Teuchos::NO_TRANS,
Teuchos::UNIT_DIAG, result_p.MyLength(),
result_p.NumVectors(), 1.0, Y_p.Values(), Y_p.MyLength(),
result_p.Values(), result_p.MyLength());
}
int
Stokhos::MeanBasedPreconditioner::
ApplyInverse(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
int myBlockRows = epetraCijk->numMyRows();
if (!use_block_apply) {
EpetraExt::BlockMultiVector sg_input(View, *base_map, Input);
EpetraExt::BlockMultiVector sg_result(View, *base_map, Result);
for (int i=0; i<myBlockRows; i++) {
mean_prec->ApplyInverse(*(sg_input.GetBlock(i)),
*(sg_result.GetBlock(i)));
}
}
else {
int m = Input.NumVectors();
Epetra_MultiVector input_block(
View, *base_map, Input.Values(), base_map->NumMyElements(),
m*myBlockRows);
Epetra_MultiVector result_block(
View, *base_map, Result.Values(), base_map->NumMyElements(),
m*myBlockRows);
mean_prec->ApplyInverse(input_block, result_block);
}
return 0;
}
int
Stokhos::ApproxJacobiPreconditioner::
ApplyInverse(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Approximate Jacobi Time");
#endif
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values()) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
int m = input->NumVectors();
if (rhs_block == Teuchos::null || rhs_block->NumVectors() != m)
rhs_block =
Teuchos::rcp(new EpetraExt::BlockMultiVector(*base_map, *sg_map, m));
// Extract blocks
EpetraExt::BlockMultiVector input_block(View, *base_map, *input);
EpetraExt::BlockMultiVector result_block(View, *base_map, Result);
int myBlockRows = epetraCijk->numMyRows();
result_block.PutScalar(0.0);
for (int iter=0; iter<num_iter; iter++) {
// Compute RHS
if (iter == 0)
rhs_block->Update(1.0, input_block, 0.0);
else {
mat_free_op->Apply(result_block, *rhs_block);
rhs_block->Update(1.0, input_block, -1.0);
}
// Apply deterministic preconditioner
for(int i=0; i<myBlockRows; i++) {
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total AJ Deterministic Preconditioner Time");
#endif
mean_prec->ApplyInverse(*(rhs_block->GetBlock(i)),
*(result_block.GetBlock(i)));
}
}
if (made_copy)
delete input;
return 0;
}
int EpetraOperator::ApplyInverse(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const {
try {
// There is no rcpFromRef(const T&), so we need to do const_cast
const Xpetra::EpetraMultiVector eX(rcpFromRef(const_cast<Epetra_MultiVector&>(X)));
Xpetra::EpetraMultiVector eY(rcpFromRef(Y));
// Generally, we assume two different vectors, but AztecOO uses a single vector
if (X.Values() == Y.Values()) {
// X and Y point to the same memory, use an additional vector
RCP<Xpetra::EpetraMultiVector> tmpY = Teuchos::rcp(new Xpetra::EpetraMultiVector(eY.getMap(), eY.getNumVectors()));
// InitialGuessIsZero in MueLu::Hierarchy.Iterate() does not zero out components, it
// only assumes that user provided an already zeroed out vector
bool initialGuessZero = true;
tmpY->putScalar(0.0);
// apply one V-cycle as preconditioner
Hierarchy_->Iterate(eX, 1, *tmpY, initialGuessZero);
// deep copy solution from MueLu
eY.update(1.0, *tmpY, 0.0);
} else {
// X and Y point to different memory, pass the vectors through
// InitialGuessIsZero in MueLu::Hierarchy.Iterate() does not zero out components, it
// only assumes that user provided an already zeroed out vector
bool initialGuessZero = true;
eY.putScalar(0.0);
Hierarchy_->Iterate(eX, 1, eY, initialGuessZero);
}
} catch (std::exception& e) {
//TODO: error msg directly on std::cerr?
std::cerr << "Caught an exception in MueLu::EpetraOperator::ApplyInverse():" << std::endl
<< e.what() << std::endl;
return -1;
}
return 0;
}
int DoCopyMultiVector(double** matlabApr, const Epetra_MultiVector& A) {
int ierr = 0;
int length = A.GlobalLength();
int numVectors = A.NumVectors();
const Epetra_Comm & comm = A.Map().Comm();
if (comm.MyPID()!=0) {
if (A.MyLength()!=0) ierr = -1;
}
else {
if (length!=A.MyLength()) ierr = -1;
double* matlabAvalues = *matlabApr;
double* Aptr = A.Values();
memcpy((void *)matlabAvalues, (void *)Aptr, sizeof(*Aptr) * length * numVectors);
*matlabApr += length;
}
int ierrGlobal;
comm.MinAll(&ierr, &ierrGlobal, 1); // If any processor has -1, all return -1
return(ierrGlobal);
}
int ARPACKm3::reSolve(int numEigen, Epetra_MultiVector &Q, double *lambda, int startingEV) {
// Computes eigenvalues and the corresponding eigenvectors
// of the generalized eigenvalue problem
//
// K X = M X Lambda
//
// using ARPACK (mode 3).
//
// The convergence test is provided by ARPACK.
//
// Note that if M is not specified, then K X = X Lambda is solved.
// (using the mode for generalized eigenvalue problem).
//
// Input variables:
//
// numEigen (integer) = Number of eigenmodes requested
//
// Q (Epetra_MultiVector) = Initial search space
// The number of columns of Q defines the size of search space (=NCV).
// The rows of X are distributed across processors.
// As a rule of thumb in ARPACK User's guide, NCV >= 2*numEigen.
// At exit, the first numEigen locations contain the eigenvectors requested.
//
// lambda (array of doubles) = Converged eigenvalues
// The length of this array is equal to the number of columns in Q.
// At exit, the first numEigen locations contain the eigenvalues requested.
//
// startingEV (integer) = Number of eigenmodes already stored in Q
// A linear combination of these vectors is made to define the starting
// vector, placed in resid.
//
// Return information on status of computation
//
// info >= 0 >> Number of converged eigenpairs at the end of computation
//
// // Failure due to input arguments
//
// info = - 1 >> The stiffness matrix K has not been specified.
// info = - 2 >> The maps for the matrix K and the matrix M differ.
// info = - 3 >> The maps for the matrix K and the preconditioner P differ.
// info = - 4 >> The maps for the vectors and the matrix K differ.
// info = - 5 >> Q is too small for the number of eigenvalues requested.
// info = - 6 >> Q is too small for the computation parameters.
//
// info = - 8 >> numEigen must be smaller than the dimension of the matrix.
//
// info = - 30 >> MEMORY
//
// See ARPACK documentation for the meaning of INFO
if (numEigen <= startingEV) {
return numEigen;
}
int info = myVerify.inputArguments(numEigen, K, M, 0, Q, minimumSpaceDimension(numEigen));
if (info < 0)
return info;
int myPid = MyComm.MyPID();
int localSize = Q.MyLength();
int NCV = Q.NumVectors();
int knownEV = 0;
if (NCV > Q.GlobalLength()) {
if (numEigen >= Q.GlobalLength()) {
cerr << endl;
cerr << " !! The number of requested eigenvalues must be smaller than the dimension";
cerr << " of the matrix !!\n";
cerr << endl;
return -8;
}
NCV = Q.GlobalLength();
}
int localVerbose = verbose*(myPid == 0);
// Define data for ARPACK
highMem = (highMem > currentSize()) ? highMem : currentSize();
int ido = 0;
int lwI = 22 + NCV;
int *wI = new (nothrow) int[lwI];
if (wI == 0) {
return -30;
}
memRequested += sizeof(int)*lwI/(1024.0*1024.0);
int *iparam = wI;
int *ipntr = wI + 11;
int *select = wI + 22;
int lworkl = NCV*(NCV+8);
int lwD = lworkl + 4*localSize;
double *wD = new (nothrow) double[lwD];
if (wD == 0) {
delete[] wI;
return -30;
}
memRequested += sizeof(double)*(4*localSize+lworkl)/(1024.0*1024.0);
double *pointer = wD;
double *workl = pointer;
pointer = pointer + lworkl;
double *resid = pointer;
pointer = pointer + localSize;
double *workd = pointer;
double *v = Q.Values();
highMem = (highMem > currentSize()) ? highMem : currentSize();
double sigma = 0.0;
if (startingEV > 0) {
// Define the initial starting vector
memset(resid, 0, localSize*sizeof(double));
for (int jj = 0; jj < startingEV; ++jj)
for (int ii = 0; ii < localSize; ++ii)
resid[ii] += v[ii + jj*localSize];
info = 1;
}
iparam[1-1] = 1;
iparam[3-1] = maxIterEigenSolve;
iparam[7-1] = 3;
// The fourth parameter forces to use the convergence test provided by ARPACK.
// This requires a customization of ARPACK (provided by R. Lehoucq).
iparam[4-1] = 0;
Epetra_Vector v1(View, Q.Map(), workd);
Epetra_Vector v2(View, Q.Map(), workd + localSize);
Epetra_Vector v3(View, Q.Map(), workd + 2*localSize);
double *vTmp = new (nothrow) double[localSize];
if (vTmp == 0) {
delete[] wI;
delete[] wD;
return -30;
}
memRequested += sizeof(double)*localSize/(1024.0*1024.0);
highMem = (highMem > currentSize()) ? highMem : currentSize();
if (localVerbose > 0) {
cout << endl;
cout << " *|* Problem: ";
if (M)
cout << "K*Q = M*Q D ";
else
cout << "K*Q = Q D ";
cout << endl;
cout << " *|* Algorithm = ARPACK (mode 3)" << endl;
cout << " *|* Number of requested eigenvalues = " << numEigen << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
cout << " *|* Tolerance for convergence = " << tolEigenSolve << endl;
if (startingEV > 0)
cout << " *|* User-defined starting vector (Combination of " << startingEV << " vectors)\n";
cout << "\n -- Start iterations -- \n";
}
#ifdef EPETRA_MPI
Epetra_MpiComm *MPIComm = dynamic_cast<Epetra_MpiComm *>(const_cast<Epetra_Comm*>(&MyComm));
#endif
timeOuterLoop -= MyWatch.WallTime();
while (ido != 99) {
highMem = (highMem > currentSize()) ? highMem : currentSize();
#ifdef EPETRA_MPI
if (MPIComm)
callFortran.PSAUPD(MPIComm->Comm(), &ido, 'G', localSize, which, numEigen, tolEigenSolve,
resid, NCV, v, localSize, iparam, ipntr, workd, workl, lworkl, &info, localVerbose);
else
callFortran.SAUPD(&ido, 'G', localSize, which, numEigen, tolEigenSolve, resid, NCV, v,
localSize, iparam, ipntr, workd, workl, lworkl, &info, localVerbose);
#else
callFortran.SAUPD(&ido, 'G', localSize, which, numEigen, tolEigenSolve, resid, NCV, v,
localSize, iparam, ipntr, workd, workl, lworkl, &info, localVerbose);
#endif
if (ido == -1) {
// Apply the mass matrix
v3.ResetView(workd + ipntr[0] - 1);
v1.ResetView(vTmp);
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(v3, v1);
else
memcpy(v1.Values(), v3.Values(), localSize*sizeof(double));
timeMassOp += MyWatch.WallTime();
massOp += 1;
// Solve the stiffness problem
v2.ResetView(workd + ipntr[1] - 1);
timeStifOp -= MyWatch.WallTime();
K->ApplyInverse(v1, v2);
timeStifOp += MyWatch.WallTime();
stifOp += 1;
continue;
} // if (ido == -1)
if (ido == 1) {
// Solve the stiffness problem
v1.ResetView(workd + ipntr[2] - 1);
v2.ResetView(workd + ipntr[1] - 1);
timeStifOp -= MyWatch.WallTime();
K->ApplyInverse(v1, v2);
timeStifOp += MyWatch.WallTime();
stifOp += 1;
continue;
} // if (ido == 1)
if (ido == 2) {
// Apply the mass matrix
v1.ResetView(workd + ipntr[0] - 1);
v2.ResetView(workd + ipntr[1] - 1);
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(v1, v2);
else
memcpy(v2.Values(), v1.Values(), localSize*sizeof(double));
timeMassOp += MyWatch.WallTime();
massOp += 1;
continue;
} // if (ido == 2)
} // while (ido != 99)
timeOuterLoop += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
if (info < 0) {
if (myPid == 0) {
cerr << endl;
cerr << " Error with DSAUPD, info = " << info << endl;
cerr << endl;
}
}
else {
// Compute the eigenvectors
timePostProce -= MyWatch.WallTime();
#ifdef EPETRA_MPI
if (MPIComm)
callFortran.PSEUPD(MPIComm->Comm(), 1, 'A', select, lambda, v, localSize, sigma, 'G',
localSize, which, numEigen, tolEigenSolve, resid, NCV, v, localSize, iparam, ipntr,
workd, workl, lworkl, &info);
else
callFortran.SEUPD(1, 'A', select, lambda, v, localSize, sigma, 'G', localSize, which,
numEigen, tolEigenSolve, resid, NCV, v, localSize, iparam, ipntr, workd, workl,
lworkl, &info);
#else
callFortran.SEUPD(1, 'A', select, lambda, v, localSize, sigma, 'G', localSize, which,
numEigen, tolEigenSolve, resid, NCV, v, localSize, iparam, ipntr, workd, workl,
lworkl, &info);
#endif
timePostProce += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
// Treat the error
if (info != 0) {
if (myPid == 0) {
cerr << endl;
cerr << " Error with DSEUPD, info = " << info << endl;
cerr << endl;
}
}
} // if (info < 0)
if (info == 0) {
outerIter = iparam[3-1];
knownEV = iparam[5-1];
orthoOp = iparam[11-1];
}
delete[] wI;
delete[] wD;
delete[] vTmp;
return (info == 0) ? knownEV : info;
}
int BlockDACG::reSolve(int numEigen, Epetra_MultiVector &Q, double *lambda, int startingEV) {
// Computes the smallest eigenvalues and the corresponding eigenvectors
// of the generalized eigenvalue problem
//
// K X = M X Lambda
//
// using a Block Deflation Accelerated Conjugate Gradient algorithm.
//
// Note that if M is not specified, then K X = X Lambda is solved.
//
// Ref: P. Arbenz & R. Lehoucq, "A comparison of algorithms for modal analysis in the
// absence of a sparse direct method", SNL, Technical Report SAND2003-1028J
// With the notations of this report, the coefficient beta is defined as
// diag( H^T_{k} G_{k} ) / diag( H^T_{k-1} G_{k-1} )
//
// Input variables:
//
// numEigen (integer) = Number of eigenmodes requested
//
// Q (Epetra_MultiVector) = Converged eigenvectors
// The number of columns of Q must be equal to numEigen + blockSize.
// The rows of Q are distributed across processors.
// At exit, the first numEigen columns contain the eigenvectors requested.
//
// lambda (array of doubles) = Converged eigenvalues
// At input, it must be of size numEigen + blockSize.
// At exit, the first numEigen locations contain the eigenvalues requested.
//
// startingEV (integer) = Number of existing converged eigenmodes
//
// Return information on status of computation
//
// info >= 0 >> Number of converged eigenpairs at the end of computation
//
// // Failure due to input arguments
//
// info = - 1 >> The stiffness matrix K has not been specified.
// info = - 2 >> The maps for the matrix K and the matrix M differ.
// info = - 3 >> The maps for the matrix K and the preconditioner P differ.
// info = - 4 >> The maps for the vectors and the matrix K differ.
// info = - 5 >> Q is too small for the number of eigenvalues requested.
// info = - 6 >> Q is too small for the computation parameters.
//
// info = - 10 >> Failure during the mass orthonormalization
//
// info = - 20 >> Error in LAPACK during the local eigensolve
//
// info = - 30 >> MEMORY
//
// Check the input parameters
if (numEigen <= startingEV) {
return startingEV;
}
int info = myVerify.inputArguments(numEigen, K, M, Prec, Q, numEigen + blockSize);
if (info < 0)
return info;
int myPid = MyComm.MyPID();
// Get the weight for approximating the M-inverse norm
Epetra_Vector *vectWeight = 0;
if (normWeight) {
vectWeight = new Epetra_Vector(View, Q.Map(), normWeight);
}
int knownEV = startingEV;
int localVerbose = verbose*(myPid==0);
// Define local block vectors
//
// MX = Working vectors (storing M*X if M is specified, else pointing to X)
// KX = Working vectors (storing K*X)
//
// R = Residuals
//
// H = Preconditioned residuals
//
// P = Search directions
// MP = Working vectors (storing M*P if M is specified, else pointing to P)
// KP = Working vectors (storing K*P)
int xr = Q.MyLength();
Epetra_MultiVector X(View, Q, numEigen, blockSize);
X.Random();
int tmp;
tmp = (M == 0) ? 5*blockSize*xr : 7*blockSize*xr;
double *work1 = new (nothrow) double[tmp];
if (work1 == 0) {
if (vectWeight)
delete vectWeight;
info = -30;
return info;
}
memRequested += sizeof(double)*tmp/(1024.0*1024.0);
highMem = (highMem > currentSize()) ? highMem : currentSize();
double *tmpD = work1;
Epetra_MultiVector KX(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector MX(View, Q.Map(), (M) ? tmpD : X.Values(), xr, blockSize);
tmpD = (M) ? tmpD + xr*blockSize : tmpD;
Epetra_MultiVector R(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector H(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector P(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector KP(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector MP(View, Q.Map(), (M) ? tmpD : P.Values(), xr, blockSize);
// Define arrays
//
// theta = Store the local eigenvalues (size: 2*blockSize)
// normR = Store the norm of residuals (size: blockSize)
//
// oldHtR = Store the previous H_i^T*R_i (size: blockSize)
// currentHtR = Store the current H_i^T*R_i (size: blockSize)
//
// MM = Local mass matrix (size: 2*blockSize x 2*blockSize)
// KK = Local stiffness matrix (size: 2*blockSize x 2*blockSize)
//
// S = Local eigenvectors (size: 2*blockSize x 2*blockSize)
int lwork2;
lwork2 = 5*blockSize + 12*blockSize*blockSize;
double *work2 = new (nothrow) double[lwork2];
if (work2 == 0) {
if (vectWeight)
delete vectWeight;
delete[] work1;
info = -30;
return info;
}
highMem = (highMem > currentSize()) ? highMem : currentSize();
tmpD = work2;
double *theta = tmpD;
tmpD = tmpD + 2*blockSize;
double *normR = tmpD;
tmpD = tmpD + blockSize;
double *oldHtR = tmpD;
tmpD = tmpD + blockSize;
double *currentHtR = tmpD;
tmpD = tmpD + blockSize;
memset(currentHtR, 0, blockSize*sizeof(double));
double *MM = tmpD;
tmpD = tmpD + 4*blockSize*blockSize;
double *KK = tmpD;
tmpD = tmpD + 4*blockSize*blockSize;
double *S = tmpD;
memRequested += sizeof(double)*lwork2/(1024.0*1024.0);
// Define an array to store the residuals history
if (localVerbose > 2) {
resHistory = new (nothrow) double[maxIterEigenSolve*blockSize];
if (resHistory == 0) {
if (vectWeight)
delete vectWeight;
delete[] work1;
delete[] work2;
info = -30;
return info;
}
historyCount = 0;
}
// Miscellaneous definitions
bool reStart = false;
numRestart = 0;
int localSize;
int twoBlocks = 2*blockSize;
int nFound = blockSize;
int i, j;
if (localVerbose > 0) {
cout << endl;
cout << " *|* Problem: ";
if (M)
cout << "K*Q = M*Q D ";
else
cout << "K*Q = Q D ";
if (Prec)
cout << " with preconditioner";
cout << endl;
cout << " *|* Algorithm = DACG (block version)" << endl;
cout << " *|* Size of blocks = " << blockSize << endl;
cout << " *|* Number of requested eigenvalues = " << numEigen << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
cout << " *|* Tolerance for convergence = " << tolEigenSolve << endl;
cout << " *|* Norm used for convergence: ";
if (normWeight)
cout << "weighted L2-norm with user-provided weights" << endl;
else
cout << "L^2-norm" << endl;
if (startingEV > 0)
cout << " *|* Input converged eigenvectors = " << startingEV << endl;
cout << "\n -- Start iterations -- \n";
}
timeOuterLoop -= MyWatch.WallTime();
for (outerIter = 1; outerIter <= maxIterEigenSolve; ++outerIter) {
highMem = (highMem > currentSize()) ? highMem : currentSize();
if ((outerIter == 1) || (reStart == true)) {
reStart = false;
localSize = blockSize;
if (nFound > 0) {
Epetra_MultiVector X2(View, X, blockSize-nFound, nFound);
Epetra_MultiVector MX2(View, MX, blockSize-nFound, nFound);
Epetra_MultiVector KX2(View, KX, blockSize-nFound, nFound);
// Apply the mass matrix to X
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(X2, MX2);
timeMassOp += MyWatch.WallTime();
massOp += nFound;
if (knownEV > 0) {
// Orthonormalize X against the known eigenvectors with Gram-Schmidt
// Note: Use R as a temporary work space
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
timeOrtho -= MyWatch.WallTime();
info = modalTool.massOrthonormalize(X, MX, M, copyQ, nFound, 0, R.Values());
timeOrtho += MyWatch.WallTime();
// Exit the code if the orthogonalization did not succeed
if (info < 0) {
info = -10;
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
return info;
}
}
// Apply the stiffness matrix to X
timeStifOp -= MyWatch.WallTime();
K->Apply(X2, KX2);
timeStifOp += MyWatch.WallTime();
stifOp += nFound;
} // if (nFound > 0)
} // if ((outerIter == 1) || (reStart == true))
else {
// Apply the preconditioner on the residuals
if (Prec != 0) {
timePrecOp -= MyWatch.WallTime();
Prec->ApplyInverse(R, H);
timePrecOp += MyWatch.WallTime();
precOp += blockSize;
}
else {
memcpy(H.Values(), R.Values(), xr*blockSize*sizeof(double));
}
// Compute the product H^T*R
timeSearchP -= MyWatch.WallTime();
memcpy(oldHtR, currentHtR, blockSize*sizeof(double));
H.Dot(R, currentHtR);
// Define the new search directions
if (localSize == blockSize) {
P.Scale(-1.0, H);
localSize = twoBlocks;
} // if (localSize == blockSize)
else {
bool hasZeroDot = false;
for (j = 0; j < blockSize; ++j) {
if (oldHtR[j] == 0.0) {
hasZeroDot = true;
break;
}
callBLAS.SCAL(xr, currentHtR[j]/oldHtR[j], P.Values() + j*xr);
}
if (hasZeroDot == true) {
// Restart the computation when there is a null dot product
if (localVerbose > 0) {
cout << endl;
cout << " !! Null dot product -- Restart the search space !!\n";
cout << endl;
}
if (blockSize == 1) {
X.Random();
nFound = blockSize;
}
else {
Epetra_MultiVector Xinit(View, X, j, blockSize-j);
Xinit.Random();
nFound = blockSize - j;
} // if (blockSize == 1)
reStart = true;
numRestart += 1;
info = 0;
continue;
}
callBLAS.AXPY(xr*blockSize, -1.0, H.Values(), P.Values());
} // if (localSize == blockSize)
timeSearchP += MyWatch.WallTime();
// Apply the mass matrix on P
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(P, MP);
timeMassOp += MyWatch.WallTime();
massOp += blockSize;
if (knownEV > 0) {
// Orthogonalize P against the known eigenvectors
// Note: Use R as a temporary work space
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
timeOrtho -= MyWatch.WallTime();
modalTool.massOrthonormalize(P, MP, M, copyQ, blockSize, 1, R.Values());
timeOrtho += MyWatch.WallTime();
}
// Apply the stiffness matrix to P
timeStifOp -= MyWatch.WallTime();
K->Apply(P, KP);
timeStifOp += MyWatch.WallTime();
stifOp += blockSize;
} // if ((outerIter == 1) || (reStart == true))
// Form "local" mass and stiffness matrices
// Note: Use S as a temporary workspace
timeLocalProj -= MyWatch.WallTime();
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, KX.Values(), xr,
KK, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, MX.Values(), xr,
MM, localSize, S);
if (localSize > blockSize) {
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, KP.Values(), xr,
KK + blockSize*localSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, P.Values(), xr, KP.Values(), xr,
KK + blockSize*localSize + blockSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, MP.Values(), xr,
MM + blockSize*localSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, P.Values(), xr, MP.Values(), xr,
MM + blockSize*localSize + blockSize, localSize, S);
} // if (localSize > blockSize)
timeLocalProj += MyWatch.WallTime();
// Perform a spectral decomposition
timeLocalSolve -= MyWatch.WallTime();
int nevLocal = localSize;
info = modalTool.directSolver(localSize, KK, localSize, MM, localSize, nevLocal,
S, localSize, theta, localVerbose,
(blockSize == 1) ? 1: 0);
timeLocalSolve += MyWatch.WallTime();
if (info < 0) {
// Stop when spectral decomposition has a critical failure
break;
}
// Check for restarting
if ((theta[0] < 0.0) || (nevLocal < blockSize)) {
if (localVerbose > 0) {
cout << " Iteration " << outerIter;
cout << "- Failure for spectral decomposition - RESTART with new random search\n";
}
if (blockSize == 1) {
X.Random();
nFound = blockSize;
}
else {
Epetra_MultiVector Xinit(View, X, 1, blockSize-1);
Xinit.Random();
nFound = blockSize - 1;
} // if (blockSize == 1)
reStart = true;
numRestart += 1;
info = 0;
continue;
} // if ((theta[0] < 0.0) || (nevLocal < blockSize))
if ((localSize == twoBlocks) && (nevLocal == blockSize)) {
for (j = 0; j < nevLocal; ++j)
memcpy(S + j*blockSize, S + j*twoBlocks, blockSize*sizeof(double));
localSize = blockSize;
}
// Check the direction of eigenvectors
// Note: This sign check is important for convergence
for (j = 0; j < nevLocal; ++j) {
double coeff = S[j + j*localSize];
if (coeff < 0.0)
callBLAS.SCAL(localSize, -1.0, S + j*localSize);
}
// Compute the residuals
timeResidual -= MyWatch.WallTime();
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KX.Values(), xr,
S, localSize, 0.0, R.Values(), xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KP.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
for (j = 0; j < blockSize; ++j)
callBLAS.SCAL(localSize, theta[j], S + j*localSize);
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, -1.0, MX.Values(), xr,
S, localSize, 1.0, R.Values(), xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, -1.0, MP.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
for (j = 0; j < blockSize; ++j)
callBLAS.SCAL(localSize, 1.0/theta[j], S + j*localSize);
timeResidual += MyWatch.WallTime();
// Compute the norms of the residuals
timeNorm -= MyWatch.WallTime();
if (vectWeight)
R.NormWeighted(*vectWeight, normR);
else
R.Norm2(normR);
// Scale the norms of residuals with the eigenvalues
// Count the converged eigenvectors
nFound = 0;
for (j = 0; j < blockSize; ++j) {
normR[j] = (theta[j] == 0.0) ? normR[j] : normR[j]/theta[j];
if (normR[j] < tolEigenSolve)
nFound += 1;
}
timeNorm += MyWatch.WallTime();
// Store the residual history
if (localVerbose > 2) {
memcpy(resHistory + historyCount*blockSize, normR, blockSize*sizeof(double));
historyCount += 1;
}
// Print information on current iteration
if (localVerbose > 0) {
cout << " Iteration " << outerIter << " - Number of converged eigenvectors ";
cout << knownEV + nFound << endl;
}
if (localVerbose > 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
cout.precision(2);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Ritz eigenvalue " << i;
cout.setf((fabs(theta[i]) < 0.01) ? ios::scientific : ios::fixed, ios::floatfield);
cout << " = " << theta[i] << endl;
}
cout << endl;
}
if (nFound == 0) {
// Update the spaces
// Note: Use H as a temporary work space
timeLocalUpdate -= MyWatch.WallTime();
memcpy(H.Values(), X.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, X.Values(), xr);
memcpy(H.Values(), KX.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, KX.Values(), xr);
if (M) {
memcpy(H.Values(), MX.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, MX.Values(), xr);
}
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, X.Values(), xr);
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KP.Values(), xr,
S + blockSize, localSize, 1.0, KX.Values(), xr);
if (M) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, MP.Values(), xr,
S + blockSize, localSize, 1.0, MX.Values(), xr);
}
} // if (localSize == twoBlocks)
timeLocalUpdate += MyWatch.WallTime();
// When required, monitor some orthogonalities
if (verbose > 2) {
if (knownEV == 0) {
accuracyCheck(&X, &MX, &R, 0, (localSize>blockSize) ? &P : 0);
}
else {
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
accuracyCheck(&X, &MX, &R, ©Q, (localSize>blockSize) ? &P : 0);
}
} // if (verbose > 2)
continue;
} // if (nFound == 0)
// Order the Ritz eigenvectors by putting the converged vectors at the beginning
int firstIndex = blockSize;
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
while (firstIndex < nFound) {
for (j = firstIndex; j < blockSize; ++j) {
if (normR[j] < tolEigenSolve) {
// Swap the j-th and firstIndex-th position
callFortran.SWAP(localSize, S + j*localSize, 1, S + firstIndex*localSize, 1);
callFortran.SWAP(1, theta + j, 1, theta + firstIndex, 1);
callFortran.SWAP(1, normR + j, 1, normR + firstIndex, 1);
break;
}
} // for (j = firstIndex; j < blockSize; ++j)
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
} // while (firstIndex < nFound)
// Copy the converged eigenvalues
memcpy(lambda + knownEV, theta, nFound*sizeof(double));
// Convergence test
if (knownEV + nFound >= numEigen) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, X.Values(), xr,
S, localSize, 0.0, R.Values(), xr);
if (localSize > blockSize) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
memcpy(Q.Values() + knownEV*xr, R.Values(), nFound*xr*sizeof(double));
knownEV += nFound;
if (localVerbose == 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
}
break;
}
// Store the converged eigenvalues and eigenvectors
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, X.Values(), xr,
S, localSize, 0.0, Q.Values() + knownEV*xr, xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, Q.Values() + knownEV*xr, xr);
}
knownEV += nFound;
// Define the restarting vectors
timeRestart -= MyWatch.WallTime();
int leftOver = (nevLocal < blockSize + nFound) ? nevLocal - nFound : blockSize;
double *Snew = S + nFound*localSize;
memcpy(H.Values(), X.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, X.Values(), xr);
memcpy(H.Values(), KX.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, KX.Values(), xr);
if (M) {
memcpy(H.Values(), MX.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, MX.Values(), xr);
}
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, P.Values(), xr,
Snew+blockSize, localSize, 1.0, X.Values(), xr);
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, KP.Values(), xr,
Snew+blockSize, localSize, 1.0, KX.Values(), xr);
if (M) {
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, MP.Values(), xr,
Snew+blockSize, localSize, 1.0, MX.Values(), xr);
}
} // if (localSize == twoBlocks)
if (nevLocal < blockSize + nFound) {
// Put new random vectors at the end of the block
Epetra_MultiVector Xtmp(View, X, leftOver, blockSize - leftOver);
Xtmp.Random();
}
else {
nFound = 0;
} // if (nevLocal < blockSize + nFound)
reStart = true;
timeRestart += MyWatch.WallTime();
} // for (outerIter = 1; outerIter <= maxIterEigenSolve; ++outerIter)
timeOuterLoop += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
// Clean memory
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
// Sort the eigenpairs
timePostProce -= MyWatch.WallTime();
if ((info == 0) && (knownEV > 0)) {
mySort.sortScalars_Vectors(knownEV, lambda, Q.Values(), Q.MyLength());
}
timePostProce += MyWatch.WallTime();
return (info == 0) ? knownEV : info;
}
int BlockPCGSolver::Solve(const Epetra_MultiVector &X, Epetra_MultiVector &Y, int blkSize) const {
int xrow = X.MyLength();
int xcol = X.NumVectors();
int ycol = Y.NumVectors();
int info = 0;
int localVerbose = verbose*(MyComm.MyPID() == 0);
double *valX = X.Values();
int NB = 3 + callLAPACK.ILAENV(1, "hetrd", "u", blkSize);
int lworkD = (blkSize > NB) ? blkSize*blkSize : NB*blkSize;
int wSize = 4*blkSize*xrow + 3*blkSize + 2*blkSize*blkSize + lworkD;
bool useY = true;
if (ycol % blkSize != 0) {
// Allocate an extra block to store the solutions
wSize += blkSize*xrow;
useY = false;
}
if (lWorkSpace < wSize) {
delete[] workSpace;
workSpace = new (std::nothrow) double[wSize];
if (workSpace == 0) {
info = -1;
return info;
}
lWorkSpace = wSize;
} // if (lWorkSpace < wSize)
double *pointer = workSpace;
// Array to store the matrix PtKP
double *PtKP = pointer;
pointer = pointer + blkSize*blkSize;
// Array to store coefficient matrices
double *coeff = pointer;
pointer = pointer + blkSize*blkSize;
// Workspace array
double *workD = pointer;
pointer = pointer + lworkD;
// Array to store the eigenvalues of P^t K P
double *da = pointer;
pointer = pointer + blkSize;
// Array to store the norms of right hand sides
double *initNorm = pointer;
pointer = pointer + blkSize;
// Array to store the norms of residuals
double *resNorm = pointer;
pointer = pointer + blkSize;
// Array to store the residuals
double *valR = pointer;
pointer = pointer + xrow*blkSize;
Epetra_MultiVector R(View, X.Map(), valR, xrow, blkSize);
// Array to store the preconditioned residuals
double *valZ = pointer;
pointer = pointer + xrow*blkSize;
Epetra_MultiVector Z(View, X.Map(), valZ, xrow, blkSize);
// Array to store the search directions
double *valP = pointer;
pointer = pointer + xrow*blkSize;
Epetra_MultiVector P(View, X.Map(), valP, xrow, blkSize);
// Array to store the image of the search directions
double *valKP = pointer;
pointer = pointer + xrow*blkSize;
Epetra_MultiVector KP(View, X.Map(), valKP, xrow, blkSize);
// Pointer to store the solutions
double *valSOL = (useY == true) ? Y.Values() : pointer;
int iRHS;
for (iRHS = 0; iRHS < xcol; iRHS += blkSize) {
int numVec = (iRHS + blkSize < xcol) ? blkSize : xcol - iRHS;
// Set the initial residuals to the right hand sides
if (numVec < blkSize) {
R.Random();
}
memcpy(valR, valX + iRHS*xrow, numVec*xrow*sizeof(double));
// Set the initial guess to zero
valSOL = (useY == true) ? Y.Values() + iRHS*xrow : valSOL;
Epetra_MultiVector SOL(View, X.Map(), valSOL, xrow, blkSize);
SOL.PutScalar(0.0);
int ii = 0;
int iter = 0;
int nFound = 0;
R.Norm2(initNorm);
if (localVerbose > 1) {
std::cout << std::endl;
std::cout << " Vectors " << iRHS << " to " << iRHS + numVec - 1 << std::endl;
if (localVerbose > 2) {
std::fprintf(stderr,"\n");
for (ii = 0; ii < numVec; ++ii) {
std::cout << " ... Initial Residual Norm " << ii << " = " << initNorm[ii] << std::endl;
}
std::cout << std::endl;
}
}
// Iteration loop
for (iter = 1; iter <= iterMax; ++iter) {
// Apply the preconditioner
if (Prec)
Prec->ApplyInverse(R, Z);
else
Z = R;
// Define the new search directions
if (iter == 1) {
P = Z;
}
else {
// Compute P^t K Z
callBLAS.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS, blkSize, blkSize, xrow, 1.0, KP.Values(), xrow, Z.Values(), xrow,
0.0, workD, blkSize);
MyComm.SumAll(workD, coeff, blkSize*blkSize);
// Compute the coefficient (P^t K P)^{-1} P^t K Z
callBLAS.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS, blkSize, blkSize, blkSize, 1.0, PtKP, blkSize, coeff, blkSize,
0.0, workD, blkSize);
for (ii = 0; ii < blkSize; ++ii)
callBLAS.SCAL(blkSize, da[ii], workD + ii, blkSize);
callBLAS.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, blkSize, blkSize, blkSize, 1.0, PtKP, blkSize, workD, blkSize,
0.0, coeff, blkSize);
// Update the search directions
// Note: Use KP as a workspace
memcpy(KP.Values(), P.Values(), xrow*blkSize*sizeof(double));
callBLAS.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, xrow, blkSize, blkSize, 1.0, KP.Values(), xrow, coeff, blkSize,
0.0, P.Values(), xrow);
P.Update(1.0, Z, -1.0);
} // if (iter == 1)
K->Apply(P, KP);
// Compute P^t K P
callBLAS.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS, blkSize, blkSize, xrow, 1.0, P.Values(), xrow, KP.Values(), xrow,
0.0, workD, blkSize);
MyComm.SumAll(workD, PtKP, blkSize*blkSize);
// Eigenvalue decomposition of P^t K P
callLAPACK.SYEV('V', 'U', blkSize, PtKP, blkSize, da, workD, lworkD, &info);
if (info) {
// Break the loop as spectral decomposition failed
break;
} // if (info)
// Compute the pseudo-inverse of the eigenvalues
for (ii = 0; ii < blkSize; ++ii) {
TEUCHOS_TEST_FOR_EXCEPTION(da[ii] < 0.0, std::runtime_error, "Negative "
"eigenvalue for P^T K P: da[" << ii << "] = "
<< da[ii] << ".");
da[ii] = (da[ii] == 0.0) ? 0.0 : 1.0/da[ii];
} // for (ii = 0; ii < blkSize; ++ii)
// Compute P^t R
callBLAS.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS, blkSize, blkSize, xrow, 1.0, P.Values(), xrow, R.Values(), xrow,
0.0, workD, blkSize);
MyComm.SumAll(workD, coeff, blkSize*blkSize);
// Compute the coefficient (P^t K P)^{-1} P^t R
callBLAS.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS, blkSize, blkSize, blkSize, 1.0, PtKP, blkSize, coeff, blkSize,
0.0, workD, blkSize);
for (ii = 0; ii < blkSize; ++ii)
callBLAS.SCAL(blkSize, da[ii], workD + ii, blkSize);
callBLAS.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, blkSize, blkSize, blkSize, 1.0, PtKP, blkSize, workD, blkSize,
0.0, coeff, blkSize);
// Update the solutions
callBLAS.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, xrow, blkSize, blkSize, 1.0, P.Values(), xrow, coeff, blkSize,
1.0, valSOL, xrow);
// Update the residuals
callBLAS.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, xrow, blkSize, blkSize, -1.0, KP.Values(), xrow, coeff, blkSize,
1.0, R.Values(), xrow);
// Check convergence
R.Norm2(resNorm);
nFound = 0;
for (ii = 0; ii < numVec; ++ii) {
if (resNorm[ii] <= tolCG*initNorm[ii])
nFound += 1;
}
if (localVerbose > 1) {
std::cout << " Vectors " << iRHS << " to " << iRHS + numVec - 1;
std::cout << " -- Iteration " << iter << " -- " << nFound << " converged vectors\n";
if (localVerbose > 2) {
std::cout << std::endl;
for (ii = 0; ii < numVec; ++ii) {
std::cout << " ... ";
std::cout.width(5);
std::cout << ii << " ... Residual = ";
std::cout.precision(2);
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout << resNorm[ii] << " ... Right Hand Side = " << initNorm[ii] << std::endl;
}
std::cout << std::endl;
}
}
if (nFound == numVec) {
break;
}
} // for (iter = 1; iter <= maxIter; ++iter)
if (useY == false) {
// Copy the solutions back into Y
memcpy(Y.Values() + xrow*iRHS, valSOL, numVec*xrow*sizeof(double));
}
numSolve += nFound;
if (nFound == numVec) {
minIter = (iter < minIter) ? iter : minIter;
maxIter = (iter > maxIter) ? iter : maxIter;
sumIter += iter;
}
} // for (iRHS = 0; iRHS < xcol; iRHS += blkSize)
return info;
}
int BlockPCGSolver::Solve(const Epetra_MultiVector &X, Epetra_MultiVector &Y) const {
int info = 0;
int localVerbose = verbose*(MyComm.MyPID() == 0);
int xr = X.MyLength();
int wSize = 3*xr;
if (lWorkSpace < wSize) {
if (workSpace)
delete[] workSpace;
workSpace = new (std::nothrow) double[wSize];
if (workSpace == 0) {
info = -1;
return info;
}
lWorkSpace = wSize;
} // if (lWorkSpace < wSize)
double *pointer = workSpace;
Epetra_Vector r(View, X.Map(), pointer);
pointer = pointer + xr;
Epetra_Vector p(View, X.Map(), pointer);
pointer = pointer + xr;
// Note: Kp and z uses the same memory space
Epetra_Vector Kp(View, X.Map(), pointer);
Epetra_Vector z(View, X.Map(), pointer);
double tmp;
double initNorm = 0.0, rNorm = 0.0, newRZ = 0.0, oldRZ = 0.0, alpha = 0.0;
double tolSquare = tolCG*tolCG;
memcpy(r.Values(), X.Values(), xr*sizeof(double));
tmp = callBLAS.DOT(xr, r.Values(), 1, r.Values(), 1);
MyComm.SumAll(&tmp, &initNorm, 1);
Y.PutScalar(0.0);
if (localVerbose > 1) {
std::cout << std::endl;
std::cout << " --- PCG Iterations --- " << std::endl;
}
int iter;
for (iter = 1; iter <= iterMax; ++iter) {
if (Prec) {
Prec->ApplyInverse(r, z);
}
else {
memcpy(z.Values(), r.Values(), xr*sizeof(double));
}
if (iter == 1) {
tmp = callBLAS.DOT(xr, r.Values(), 1, z.Values(), 1);
MyComm.SumAll(&tmp, &newRZ, 1);
memcpy(p.Values(), z.Values(), xr*sizeof(double));
}
else {
oldRZ = newRZ;
tmp = callBLAS.DOT(xr, r.Values(), 1, z.Values(), 1);
MyComm.SumAll(&tmp, &newRZ, 1);
p.Update(1.0, z, newRZ/oldRZ);
}
K->Apply(p, Kp);
tmp = callBLAS.DOT(xr, p.Values(), 1, Kp.Values(), 1);
MyComm.SumAll(&tmp, &alpha, 1);
alpha = newRZ/alpha;
TEUCHOS_TEST_FOR_EXCEPTION(alpha <= 0.0, std::runtime_error,
" !!! Non-positive value for p^TKp (" << alpha << ") !!!");
callBLAS.AXPY(xr, alpha, p.Values(), 1, Y.Values(), 1);
alpha *= -1.0;
callBLAS.AXPY(xr, alpha, Kp.Values(), 1, r.Values(), 1);
// Check convergence
tmp = callBLAS.DOT(xr, r.Values(), 1, r.Values(), 1);
MyComm.SumAll(&tmp, &rNorm, 1);
if (localVerbose > 1) {
std::cout << " Iter. " << iter;
std::cout.precision(4);
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout << " Residual reduction " << std::sqrt(rNorm/initNorm) << std::endl;
}
if (rNorm <= tolSquare*initNorm)
break;
} // for (iter = 1; iter <= iterMax; ++iter)
if (localVerbose == 1) {
std::cout << std::endl;
std::cout << " --- End of PCG solve ---" << std::endl;
std::cout << " Iter. " << iter;
std::cout.precision(4);
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout << " Residual reduction " << std::sqrt(rNorm/initNorm) << std::endl;
std::cout << std::endl;
}
if (localVerbose > 1) {
std::cout << std::endl;
}
numSolve += 1;
minIter = (iter < minIter) ? iter : minIter;
maxIter = (iter > maxIter) ? iter : maxIter;
sumIter += iter;
return info;
}
int Davidson::reSolve(int numEigen, Epetra_MultiVector &Q, double *lambda, int startingEV) {
// Computes the smallest eigenvalues and the corresponding eigenvectors
// of the generalized eigenvalue problem
//
// K X = M X Lambda
//
// using a generalized Davidson algorithm
//
// Note that if M is not specified, then K X = X Lambda is solved.
//
// Input variables:
//
// numEigen (integer) = Number of eigenmodes requested
//
// Q (Epetra_MultiVector) = Converged eigenvectors
// The number of columns of Q must be at least numEigen + blockSize.
// The rows of Q are distributed across processors.
// At exit, the first numEigen columns contain the eigenvectors requested.
//
// lambda (array of doubles) = Converged eigenvalues
// At input, it must be of size numEigen + blockSize.
// At exit, the first numEigen locations contain the eigenvalues requested.
//
// startingEV (integer) = Number of existing converged eigenvectors
// We assume that the user has check the eigenvectors and
// their M-orthonormality.
//
// Return information on status of computation
//
// info >= 0 >> Number of converged eigenpairs at the end of computation
//
// // Failure due to input arguments
//
// info = - 1 >> The stiffness matrix K has not been specified.
// info = - 2 >> The maps for the matrix K and the matrix M differ.
// info = - 3 >> The maps for the matrix K and the preconditioner P differ.
// info = - 4 >> The maps for the vectors and the matrix K differ.
// info = - 5 >> Q is too small for the number of eigenvalues requested.
// info = - 6 >> Q is too small for the computation parameters.
//
// info = - 8 >> The number of blocks is too small for the number of eigenvalues.
//
// info = - 10 >> Failure during the mass orthonormalization
//
// info = - 30 >> MEMORY
//
// Check the input parameters
if (numEigen <= startingEV) {
return startingEV;
}
int info = myVerify.inputArguments(numEigen, K, M, Prec, Q, minimumSpaceDimension(numEigen));
if (info < 0)
return info;
int myPid = MyComm.MyPID();
if (numBlock*blockSize < numEigen) {
if (myPid == 0) {
cerr << endl;
cerr << " !!! The space dimension (# of blocks x size of blocks) must be greater than ";
cerr << " the number of eigenvalues !!!\n";
cerr << " Number of blocks = " << numBlock << endl;
cerr << " Size of blocks = " << blockSize << endl;
cerr << " Number of eigenvalues = " << numEigen << endl;
cerr << endl;
}
return -8;
}
// Get the weight for approximating the M-inverse norm
Epetra_Vector *vectWeight = 0;
if (normWeight) {
vectWeight = new Epetra_Vector(View, Q.Map(), normWeight);
}
int knownEV = startingEV;
int localVerbose = verbose*(myPid==0);
// Define local block vectors
//
// MX = Working vectors (storing M*X if M is specified, else pointing to X)
// KX = Working vectors (storing K*X)
//
// R = Residuals
int xr = Q.MyLength();
int dimSearch = blockSize*numBlock;
Epetra_MultiVector X(View, Q, 0, dimSearch + blockSize);
if (knownEV > 0) {
Epetra_MultiVector copyX(View, Q, knownEV, blockSize);
copyX.Random();
}
else {
X.Random();
}
int tmp;
tmp = (M == 0) ? 2*blockSize*xr : 3*blockSize*xr;
double *work1 = new (nothrow) double[tmp];
if (work1 == 0) {
if (vectWeight)
delete vectWeight;
info = -30;
return info;
}
memRequested += sizeof(double)*tmp/(1024.0*1024.0);
highMem = (highMem > currentSize()) ? highMem : currentSize();
double *tmpD = work1;
Epetra_MultiVector KX(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector MX(View, Q.Map(), (M) ? tmpD : X.Values(), xr, blockSize);
tmpD = (M) ? tmpD + xr*blockSize : tmpD;
Epetra_MultiVector R(View, Q.Map(), tmpD, xr, blockSize);
// Define arrays
//
// theta = Store the local eigenvalues (size: dimSearch)
// normR = Store the norm of residuals (size: blockSize)
//
// KK = Local stiffness matrix (size: dimSearch x dimSearch)
//
// S = Local eigenvectors (size: dimSearch x dimSearch)
//
// tmpKK = Local workspace (size: blockSize x blockSize)
int lwork2 = blockSize + dimSearch + 2*dimSearch*dimSearch + blockSize*blockSize;
double *work2 = new (nothrow) double[lwork2];
if (work2 == 0) {
if (vectWeight)
delete vectWeight;
delete[] work1;
info = -30;
return info;
}
memRequested += sizeof(double)*lwork2/(1024.0*1024.0);
highMem = (highMem > currentSize()) ? highMem : currentSize();
tmpD = work2;
double *theta = tmpD;
tmpD = tmpD + dimSearch;
double *normR = tmpD;
tmpD = tmpD + blockSize;
double *KK = tmpD;
tmpD = tmpD + dimSearch*dimSearch;
memset(KK, 0, dimSearch*dimSearch*sizeof(double));
double *S = tmpD;
tmpD = tmpD + dimSearch*dimSearch;
double *tmpKK = tmpD;
// Define an array to store the residuals history
if (localVerbose > 2) {
resHistory = new (nothrow) double[maxIterEigenSolve*blockSize];
spaceSizeHistory = new (nothrow) int[maxIterEigenSolve];
if ((resHistory == 0) || (spaceSizeHistory == 0)) {
if (vectWeight)
delete vectWeight;
delete[] work1;
delete[] work2;
info = -30;
return info;
}
historyCount = 0;
}
// Miscellaneous definitions
bool reStart = false;
numRestart = 0;
bool criticalExit = false;
int bStart = 0;
int offSet = 0;
numBlock = (dimSearch/blockSize) - (knownEV/blockSize);
int nFound = blockSize;
int i, j;
if (localVerbose > 0) {
cout << endl;
cout << " *|* Problem: ";
if (M)
cout << "K*Q = M*Q D ";
else
cout << "K*Q = Q D ";
if (Prec)
cout << " with preconditioner";
cout << endl;
cout << " *|* Algorithm = Davidson algorithm (block version)" << endl;
cout << " *|* Size of blocks = " << blockSize << endl;
cout << " *|* Largest size of search space = " << numBlock*blockSize << endl;
cout << " *|* Number of requested eigenvalues = " << numEigen << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
cout << " *|* Tolerance for convergence = " << tolEigenSolve << endl;
cout << " *|* Norm used for convergence: ";
if (vectWeight)
cout << "weighted L2-norm with user-provided weights" << endl;
else
cout << "L^2-norm" << endl;
if (startingEV > 0)
cout << " *|* Input converged eigenvectors = " << startingEV << endl;
cout << "\n -- Start iterations -- \n";
}
int maxBlock = (dimSearch/blockSize) - (knownEV/blockSize);
timeOuterLoop -= MyWatch.WallTime();
outerIter = 0;
while (outerIter <= maxIterEigenSolve) {
highMem = (highMem > currentSize()) ? highMem : currentSize();
int nb;
for (nb = bStart; nb < maxBlock; ++nb) {
outerIter += 1;
if (outerIter > maxIterEigenSolve)
break;
int localSize = nb*blockSize;
Epetra_MultiVector Xcurrent(View, X, localSize + knownEV, blockSize);
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(Xcurrent, MX);
timeMassOp += MyWatch.WallTime();
massOp += blockSize;
// Orthonormalize X against the known eigenvectors and the previous vectors
// Note: Use R as a temporary work space
timeOrtho -= MyWatch.WallTime();
if (nb == bStart) {
if (nFound > 0) {
if (knownEV == 0) {
info = modalTool.massOrthonormalize(Xcurrent, MX, M, Q, nFound, 2, R.Values());
}
else {
Epetra_MultiVector copyQ(View, X, 0, knownEV + localSize);
info = modalTool.massOrthonormalize(Xcurrent, MX, M, copyQ, nFound, 0, R.Values());
}
}
nFound = 0;
}
else {
Epetra_MultiVector copyQ(View, X, 0, knownEV + localSize);
info = modalTool.massOrthonormalize(Xcurrent, MX, M, copyQ, blockSize, 0, R.Values());
}
timeOrtho += MyWatch.WallTime();
// Exit the code when the number of vectors exceeds the space dimension
if (info < 0) {
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
return -10;
}
timeStifOp -= MyWatch.WallTime();
K->Apply(Xcurrent, KX);
timeStifOp += MyWatch.WallTime();
stifOp += blockSize;
// Check the orthogonality properties of X
if (verbose > 2) {
if (knownEV + localSize == 0)
accuracyCheck(&Xcurrent, &MX, 0);
else {
Epetra_MultiVector copyQ(View, X, 0, knownEV + localSize);
accuracyCheck(&Xcurrent, &MX, ©Q);
}
if (localVerbose > 0)
cout << endl;
} // if (verbose > 2)
// Define the local stiffness matrix
// Note: S is used as a workspace
timeLocalProj -= MyWatch.WallTime();
for (j = 0; j <= nb; ++j) {
callBLAS.GEMM('T', 'N', blockSize, blockSize, xr,
1.0, X.Values()+(knownEV+j*blockSize)*xr, xr, KX.Values(), xr,
0.0, tmpKK, blockSize);
MyComm.SumAll(tmpKK, S, blockSize*blockSize);
int iC;
for (iC = 0; iC < blockSize; ++iC) {
double *Kpointer = KK + localSize*dimSearch + j*blockSize + iC*dimSearch;
memcpy(Kpointer, S + iC*blockSize, blockSize*sizeof(double));
}
}
timeLocalProj += MyWatch.WallTime();
// Perform a spectral decomposition
timeLocalSolve -= MyWatch.WallTime();
int nevLocal = localSize + blockSize;
info = modalTool.directSolver(localSize+blockSize, KK, dimSearch, 0, 0,
nevLocal, S, dimSearch, theta, localVerbose, 10);
timeLocalSolve += MyWatch.WallTime();
if (info != 0) {
// Stop as spectral decomposition has a critical failure
if (info < 0) {
criticalExit = true;
break;
}
// Restart as spectral decomposition failed
if (localVerbose > 0) {
cout << " Iteration " << outerIter;
cout << "- Failure for spectral decomposition - RESTART with new random search\n";
}
reStart = true;
numRestart += 1;
timeRestart -= MyWatch.WallTime();
Epetra_MultiVector Xinit(View, X, knownEV, blockSize);
Xinit.Random();
timeRestart += MyWatch.WallTime();
nFound = blockSize;
bStart = 0;
break;
} // if (info != 0)
// Update the search space
// Note: Use KX as a workspace
timeLocalUpdate -= MyWatch.WallTime();
callBLAS.GEMM('N', 'N', xr, blockSize, localSize+blockSize, 1.0, X.Values()+knownEV*xr, xr,
S, dimSearch, 0.0, KX.Values(), xr);
timeLocalUpdate += MyWatch.WallTime();
// Apply the mass matrix for the next block
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(KX, MX);
timeMassOp += MyWatch.WallTime();
massOp += blockSize;
// Apply the stiffness matrix for the next block
timeStifOp -= MyWatch.WallTime();
K->Apply(KX, R);
timeStifOp += MyWatch.WallTime();
stifOp += blockSize;
// Form the residuals
timeResidual -= MyWatch.WallTime();
if (M) {
for (j = 0; j < blockSize; ++j) {
callBLAS.AXPY(xr, -theta[j], MX.Values() + j*xr, R.Values() + j*xr);
}
}
else {
// Note KX contains the updated block
for (j = 0; j < blockSize; ++j) {
callBLAS.AXPY(xr, -theta[j], KX.Values() + j*xr, R.Values() + j*xr);
}
}
timeResidual += MyWatch.WallTime();
residual += blockSize;
// Compute the norm of residuals
timeNorm -= MyWatch.WallTime();
if (vectWeight) {
R.NormWeighted(*vectWeight, normR);
}
else {
R.Norm2(normR);
}
// Scale the norms of residuals with the eigenvalues
// Count the number of converged eigenvectors
nFound = 0;
for (j = 0; j < blockSize; ++j) {
normR[j] = (theta[j] == 0.0) ? normR[j] : normR[j]/theta[j];
if (normR[j] < tolEigenSolve)
nFound += 1;
} // for (j = 0; j < blockSize; ++j)
timeNorm += MyWatch.WallTime();
// Store the residual history
if (localVerbose > 2) {
memcpy(resHistory + historyCount*blockSize, normR, blockSize*sizeof(double));
spaceSizeHistory[historyCount] = localSize + blockSize;
historyCount += 1;
}
maxSpaceSize = (maxSpaceSize > localSize+blockSize) ? maxSpaceSize : localSize+blockSize;
sumSpaceSize += localSize + blockSize;
// Print information on current iteration
if (localVerbose > 0) {
cout << " Iteration " << outerIter << " - Number of converged eigenvectors ";
cout << knownEV + nFound << endl;
} // if (localVerbose > 0)
if (localVerbose > 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
cout.precision(2);
for (i=0; i<nevLocal; ++i) {
cout << " Iteration " << outerIter << " - Ritz eigenvalue " << i;
cout.setf((fabs(theta[i]) < 0.01) ? ios::scientific : ios::fixed, ios::floatfield);
cout << " = " << theta[i] << endl;
}
cout << endl;
}
// Exit the loop to treat the converged eigenvectors
if (nFound > 0) {
nb += 1;
offSet = 0;
break;
}
// Apply the preconditioner on the residuals
// Note: Use KX as a workspace
if (maxBlock == 1) {
if (Prec) {
timePrecOp -= MyWatch.WallTime();
Prec->ApplyInverse(R, Xcurrent);
timePrecOp += MyWatch.WallTime();
precOp += blockSize;
}
else {
memcpy(Xcurrent.Values(), R.Values(), blockSize*xr*sizeof(double));
}
timeRestart -= MyWatch.WallTime();
Xcurrent.Update(1.0, KX, -1.0);
timeRestart += MyWatch.WallTime();
break;
} // if (maxBlock == 1)
if (nb == maxBlock - 1) {
nb += 1;
break;
}
Epetra_MultiVector Xnext(View, X, knownEV+localSize+blockSize, blockSize);
if (Prec) {
timePrecOp -= MyWatch.WallTime();
Prec->ApplyInverse(R, Xnext);
timePrecOp += MyWatch.WallTime();
precOp += blockSize;
}
else {
memcpy(Xnext.Values(), R.Values(), blockSize*xr*sizeof(double));
}
} // for (nb = bStart; nb < maxBlock; ++nb)
if (outerIter > maxIterEigenSolve)
break;
if (reStart == true) {
reStart = false;
continue;
}
if (criticalExit == true)
break;
// Store the final converged eigenvectors
if (knownEV + nFound >= numEigen) {
for (j = 0; j < blockSize; ++j) {
if (normR[j] < tolEigenSolve) {
memcpy(X.Values() + knownEV*xr, KX.Values() + j*xr, xr*sizeof(double));
lambda[knownEV] = theta[j];
knownEV += 1;
}
}
if (localVerbose == 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
}
break;
} // if (knownEV + nFound >= numEigen)
// Treat the particular case of 1 block
if (maxBlock == 1) {
if (nFound > 0) {
double *Xpointer = X.Values() + (knownEV+nFound)*xr;
nFound = 0;
for (j = 0; j < blockSize; ++j) {
if (normR[j] < tolEigenSolve) {
memcpy(X.Values() + knownEV*xr, KX.Values() + j*xr, xr*sizeof(double));
lambda[knownEV] = theta[j];
knownEV += 1;
nFound += 1;
}
else {
memcpy(Xpointer + (j-nFound)*xr, KX.Values() + j*xr, xr*sizeof(double));
}
}
Epetra_MultiVector Xnext(View, X, knownEV + blockSize - nFound, nFound);
Xnext.Random();
}
else {
nFound = blockSize;
}
continue;
}
// Define the restarting block when maxBlock > 1
if (nFound > 0) {
int firstIndex = blockSize;
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
while (firstIndex < nFound) {
for (j = firstIndex; j < blockSize; ++j) {
if (normR[j] < tolEigenSolve) {
// Swap the j-th and firstIndex-th position
callFortran.SWAP(nb*blockSize, S + j*dimSearch, 1, S + firstIndex*dimSearch, 1);
callFortran.SWAP(1, theta + j, 1, theta + firstIndex, 1);
callFortran.SWAP(1, normR + j, 1, normR + firstIndex, 1);
break;
}
} // for (j = firstIndex; j < blockSize; ++j)
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
} // while (firstIndex < nFound)
// Copy the converged eigenvalues
memcpy(lambda + knownEV, theta, nFound*sizeof(double));
} // if (nFound > 0)
// Define the restarting size
bStart = ((nb - offSet) > 2) ? (nb - offSet)/2 : 0;
// Define the restarting space and local stiffness
timeRestart -= MyWatch.WallTime();
memset(KK, 0, nb*blockSize*dimSearch*sizeof(double));
for (j = 0; j < bStart*blockSize; ++j) {
KK[j + j*dimSearch] = theta[j + nFound];
}
// Form the restarting space
int oldCol = nb*blockSize;
int newCol = nFound + (bStart+1)*blockSize;
newCol = (newCol > oldCol) ? oldCol : newCol;
callFortran.GEQRF(oldCol, newCol, S, dimSearch, theta, R.Values(), xr*blockSize, &info);
callFortran.ORMQR('R', 'N', xr, oldCol, newCol, S, dimSearch, theta,
X.Values()+knownEV*xr, xr, R.Values(), blockSize*xr, &info);
timeRestart += MyWatch.WallTime();
if (nFound == 0)
offSet += 1;
knownEV += nFound;
maxBlock = (dimSearch/blockSize) - (knownEV/blockSize);
// Put random vectors if the Rayleigh Ritz vectors are not enough
newCol = nFound + (bStart+1)*blockSize;
if (newCol > oldCol) {
Epetra_MultiVector Xnext(View, X, knownEV+blockSize-nFound, nFound);
Xnext.Random();
continue;
}
nFound = 0;
} // while (outerIter <= maxIterEigenSolve)
timeOuterLoop += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
// Clean memory
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
// Sort the eigenpairs
timePostProce -= MyWatch.WallTime();
if ((info == 0) && (knownEV > 0)) {
mySort.sortScalars_Vectors(knownEV, lambda, Q.Values(), Q.MyLength());
}
timePostProce += MyWatch.WallTime();
return (info == 0) ? knownEV : info;
}
int
Stokhos::ApproxSchurComplementPreconditioner::
ApplyInverse(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Approximate Schur Complement Time");
#endif
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values()) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
// Allocate temporary storage
int m = input->NumVectors();
if (rhs_block == Teuchos::null || rhs_block->NumVectors() != m)
rhs_block =
Teuchos::rcp(new EpetraExt::BlockMultiVector(*base_map, *sg_map, m));
if (tmp == Teuchos::null || tmp->NumVectors() != m*max_num_mat_vec)
tmp = Teuchos::rcp(new Epetra_MultiVector(*base_map,
m*max_num_mat_vec));
j_ptr.resize(m*max_num_mat_vec);
mj_indices.resize(m*max_num_mat_vec);
// Extract blocks
EpetraExt::BlockMultiVector input_block(View, *base_map, *input);
EpetraExt::BlockMultiVector result_block(View, *base_map, Result);
result_block.PutScalar(0.0);
// Set right-hand-side to input_block
rhs_block->Update(1.0, input_block, 0.0);
// At level l, linear system has the structure
// [ A_{l-1} B_l ][ u_l^{l-1} ] = [ r_l^{l-1} ]
// [ C_l D_l ][ u_l^l ] [ r_l^l ]
for (int l=P; l>=1; l--) {
// Compute D_l^{-1} r_l^l
divide_diagonal_block(block_indices[l], block_indices[l+1],
*rhs_block, result_block);
// Compute r_l^{l-1} = r_l^{l-1} - B_l D_l^{-1} r_l^l
multiply_block(upper_block_Cijk[l], -1.0, result_block, *rhs_block);
}
// Solve A_0 u_0 = r_0
divide_diagonal_block(0, 1, *rhs_block, result_block);
for (int l=1; l<=P; l++) {
// Compute r_l^l - C_l*u_l^{l-1}
multiply_block(lower_block_Cijk[l], -1.0, result_block, *rhs_block);
// Compute D_l^{-1} (r_l^l - C_l*u_l^{l-1})
divide_diagonal_block(block_indices[l], block_indices[l+1],
*rhs_block, result_block);
}
if (made_copy)
delete input;
return 0;
}
int
Stokhos::MatrixFreeOperator::
Apply(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: SG Operator Apply()");
#endif
// Note for transpose:
// The stochastic matrix is symmetric, however the matrix blocks may not
// be. So the algorithm here is the same whether we are using the transpose
// or not. We just apply the transpose of the blocks in the case of
// applying the global transpose, and make sure the imported Input
// vectors use the right map.
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values() && !is_stoch_parallel) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
// Initialize
Result.PutScalar(0.0);
const Epetra_Map* input_base_map = domain_base_map.get();
const Epetra_Map* result_base_map = range_base_map.get();
if (useTranspose == true) {
input_base_map = range_base_map.get();
result_base_map = domain_base_map.get();
}
// Allocate temporary storage
int m = Input.NumVectors();
if (useTranspose == false &&
(tmp == Teuchos::null || tmp->NumVectors() != m*max_num_mat_vec))
tmp = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
else if (useTranspose == true &&
(tmp_trans == Teuchos::null ||
tmp_trans->NumVectors() != m*max_num_mat_vec))
tmp_trans = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
Epetra_MultiVector *tmp_result;
if (useTranspose == false)
tmp_result = tmp.get();
else
tmp_result = tmp_trans.get();
// Map input into column map
const Epetra_MultiVector *tmp_col;
if (!is_stoch_parallel)
tmp_col = input;
else {
if (useTranspose == false) {
if (input_col == Teuchos::null || input_col->NumVectors() != m)
input_col = Teuchos::rcp(new Epetra_MultiVector(*global_col_map, m));
input_col->Import(*input, *col_importer, Insert);
tmp_col = input_col.get();
}
else {
if (input_col_trans == Teuchos::null ||
input_col_trans->NumVectors() != m)
input_col_trans =
Teuchos::rcp(new Epetra_MultiVector(*global_col_map_trans, m));
input_col_trans->Import(*input, *col_importer_trans, Insert);
tmp_col = input_col_trans.get();
}
}
// Extract blocks
EpetraExt::BlockMultiVector sg_input(View, *input_base_map, *tmp_col);
EpetraExt::BlockMultiVector sg_result(View, *result_base_map, Result);
for (int i=0; i<input_block.size(); i++)
input_block[i] = sg_input.GetBlock(i);
for (int i=0; i<result_block.size(); i++)
result_block[i] = sg_result.GetBlock(i);
// Apply block SG operator via
// w_i =
// \sum_{j=0}^P \sum_{k=0}^L J_k v_j < \psi_i \psi_j \psi_k > / <\psi_i^2>
// for i=0,...,P where P = expansion_size, L = num_blocks, w_j is the jth
// input block, w_i is the ith result block, and J_k is the kth block operator
// k_begin and k_end are initialized in the constructor
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
for (Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
int k = index(k_it);
Cijk_type::kj_iterator j_begin = Cijk->j_begin(k_it);
Cijk_type::kj_iterator j_end = Cijk->j_end(k_it);
int nj = Cijk->num_j(k_it);
if (nj > 0) {
Teuchos::Array<double*> j_ptr(nj*m);
Teuchos::Array<int> mj_indices(nj*m);
int l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (int mm=0; mm<m; mm++) {
j_ptr[l*m+mm] = (*input_block[j])[mm];
mj_indices[l*m+mm] = l*m+mm;
}
l++;
}
Epetra_MultiVector input_tmp(View, *input_base_map, &j_ptr[0], nj*m);
Epetra_MultiVector result_tmp(View, *tmp_result, &mj_indices[0], nj*m);
if (use_block_apply) {
(*block_ops)[k].Apply(input_tmp, result_tmp);
}
else {
for (int jj=0; jj<nj*m; jj++)
(*block_ops)[k].Apply(*(input_tmp(jj)), *(result_tmp(jj)));
}
l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
i_it != Cijk->i_end(j_it); ++i_it) {
int i = index(i_it);
double c = value(i_it);
if (scale_op) {
int i_gid;
if (useTranspose)
i_gid = epetraCijk->GCID(j);
else
i_gid = epetraCijk->GRID(i);
c /= norms[i_gid];
}
for (int mm=0; mm<m; mm++)
(*result_block[i])(mm)->Update(c, *result_tmp(l*m+mm), 1.0);
}
l++;
}
}
}
// Destroy blocks
for (int i=0; i<input_block.size(); i++)
input_block[i] = Teuchos::null;
for (int i=0; i<result_block.size(); i++)
result_block[i] = Teuchos::null;
if (made_copy)
delete input;
return 0;
}
int ModifiedARPACKm3::reSolve(int numEigen, Epetra_MultiVector &Q, double *lambda,
int startingEV, const Epetra_MultiVector *orthoVec) {
// Computes the smallest eigenvalues and the corresponding eigenvectors
// of the generalized eigenvalue problem
//
// K X = M X Lambda
//
// using ModifiedARPACK (mode 3).
//
// The convergence test is performed outisde of ARPACK
//
// || Kx - Mx lambda || < tol*lambda
//
// The norm ||.|| can be specified by the user through the array normWeight.
// By default, the L2 Euclidean norm is used.
//
// Note that if M is not specified, then K X = X Lambda is solved.
// (using the mode for generalized eigenvalue problem).
//
// Input variables:
//
// numEigen (integer) = Number of eigenmodes requested
//
// Q (Epetra_MultiVector) = Initial search space
// The number of columns of Q defines the size of search space (=NCV).
// The rows of X are distributed across processors.
// As a rule of thumb in ARPACK User's guide, NCV >= 2*numEigen.
// At exit, the first numEigen locations contain the eigenvectors requested.
//
// lambda (array of doubles) = Converged eigenvalues
// The length of this array is equal to the number of columns in Q.
// At exit, the first numEigen locations contain the eigenvalues requested.
//
// startingEV (integer) = Number of eigenmodes already stored in Q
// A linear combination of these vectors is made to define the starting
// vector, placed in resid.
//
// orthoVec (Pointer to Epetra_MultiVector) = Space to be orthogonal to
// The computation is performed in the orthogonal of the space spanned
// by the columns vectors in orthoVec.
//
// Return information on status of computation
//
// info >= 0 >> Number of converged eigenpairs at the end of computation
//
// // Failure due to input arguments
//
// info = - 1 >> The stiffness matrix K has not been specified.
// info = - 2 >> The maps for the matrix K and the matrix M differ.
// info = - 3 >> The maps for the matrix K and the preconditioner P differ.
// info = - 4 >> The maps for the vectors and the matrix K differ.
// info = - 5 >> Q is too small for the number of eigenvalues requested.
// info = - 6 >> Q is too small for the computation parameters.
//
// info = - 8 >> numEigen must be smaller than the dimension of the matrix.
//
// info = - 30 >> MEMORY
//
// See ARPACK documentation for the meaning of INFO
if (numEigen <= startingEV) {
return numEigen;
}
int info = myVerify.inputArguments(numEigen, K, M, 0, Q, minimumSpaceDimension(numEigen));
if (info < 0)
return info;
int myPid = MyComm.MyPID();
int localSize = Q.MyLength();
int NCV = Q.NumVectors();
int knownEV = 0;
if (NCV > Q.GlobalLength()) {
if (numEigen >= Q.GlobalLength()) {
cerr << endl;
cerr << " !! The number of requested eigenvalues must be smaller than the dimension";
cerr << " of the matrix !!\n";
cerr << endl;
return -8;
}
NCV = Q.GlobalLength();
}
// Get the weight for approximating the M-inverse norm
Epetra_Vector *vectWeight = 0;
if (normWeight) {
vectWeight = new Epetra_Vector(View, Q.Map(), normWeight);
}
int localVerbose = verbose*(myPid == 0);
// Define data for ARPACK
//
// UH (10/17/03) Note that workl is also used
// * to store the eigenvectors of the tridiagonal matrix
// * as a workspace for DSTEQR
// * as a workspace for recovering the global eigenvectors
highMem = (highMem > currentSize()) ? highMem : currentSize();
int ido = 0;
int lwI = 22;
int *wI = new (nothrow) int[lwI];
if (wI == 0) {
if (vectWeight)
delete vectWeight;
return -30;
}
memRequested += sizeof(int)*lwI/(1024.0*1024.0);
int *iparam = wI;
int *ipntr = wI + 11;
int lworkl = NCV*(NCV+8);
int lwD = lworkl + 4*localSize;
double *wD = new (nothrow) double[lwD];
if (wD == 0) {
if (vectWeight)
delete vectWeight;
delete[] wI;
return -30;
}
memRequested += sizeof(double)*(4*localSize+lworkl)/(1024.0*1024.0);
double *pointer = wD;
double *workl = pointer;
pointer = pointer + lworkl;
double *resid = pointer;
pointer = pointer + localSize;
double *workd = pointer;
double *v = Q.Values();
highMem = (highMem > currentSize()) ? highMem : currentSize();
if (startingEV > 0) {
// Define the initial starting vector
memset(resid, 0, localSize*sizeof(double));
for (int jj = 0; jj < startingEV; ++jj)
for (int ii = 0; ii < localSize; ++ii)
resid[ii] += v[ii + jj*localSize];
info = 1;
}
iparam[1-1] = 1;
iparam[3-1] = maxIterEigenSolve;
iparam[7-1] = 3;
// The fourth parameter forces to use the convergence test provided by ARPACK.
// This requires a customization of ARPACK (provided by R. Lehoucq).
iparam[4-1] = 1;
Epetra_Vector v1(View, Q.Map(), workd);
Epetra_Vector v2(View, Q.Map(), workd + localSize);
Epetra_Vector v3(View, Q.Map(), workd + 2*localSize);
// Define further storage for the new residual check
// Use a block of vectors to compute the residuals more quickly.
// Note that workd could be used if memory becomes an issue.
int loopZ = (NCV > 10) ? 10 : NCV;
int lwD2 = localSize + 2*NCV-1 + NCV;
lwD2 += (M) ? 3*loopZ*localSize : 2*loopZ*localSize;
double *wD2 = new (nothrow) double[lwD2];
if (wD2 == 0) {
if (vectWeight)
delete vectWeight;
delete[] wI;
delete[] wD;
return -30;
}
memRequested += sizeof(double)*lwD2/(1024.0*1024.0);
pointer = wD2;
// vTmp is used when ido = -1
double *vTmp = pointer;
pointer = pointer + localSize;
// dd and ee stores the tridiagonal matrix.
// Note that DSTEQR destroys the contents of the input arrays.
double *dd = pointer;
pointer = pointer + NCV;
double *ee = pointer;
pointer = pointer + NCV-1;
double *vz = pointer;
pointer = pointer + loopZ*localSize;
Epetra_MultiVector approxEV(View, Q.Map(), vz, localSize, loopZ);
double *kvz = pointer;
pointer = pointer + loopZ*localSize;
Epetra_MultiVector KapproxEV(View, Q.Map(), kvz, localSize, loopZ);
double *mvz = (M) ? pointer : vz;
pointer = (M) ? pointer + loopZ*localSize : pointer;
Epetra_MultiVector MapproxEV(View, Q.Map(), mvz, localSize, loopZ);
double *normR = pointer;
// zz contains the eigenvectors of the tridiagonal matrix.
// workt is a workspace for DSTEQR.
// Note that zz and workt will use parts of workl.
double *zz, *workt;
highMem = (highMem > currentSize()) ? highMem : currentSize();
// Define an array to store the residuals history
if (localVerbose > 2) {
resHistory = new (nothrow) double[maxIterEigenSolve*NCV];
if (resHistory == 0) {
if (vectWeight)
delete vectWeight;
delete[] wI;
delete[] wD;
delete[] wD2;
return -30;
}
historyCount = 0;
}
highMem = (highMem > currentSize()) ? highMem : currentSize();
if (localVerbose > 0) {
cout << endl;
cout << " *|* Problem: ";
if (M)
cout << "K*Q = M*Q D ";
else
cout << "K*Q = Q D ";
cout << endl;
cout << " *|* Algorithm = ARPACK (Mode 3, modified such that user checks convergence)" << endl;
cout << " *|* Number of requested eigenvalues = " << numEigen << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
cout << " *|* Tolerance for convergence = " << tolEigenSolve << endl;
if (startingEV > 0)
cout << " *|* User-defined starting vector (Combination of " << startingEV << " vectors)\n";
cout << " *|* Norm used for convergence: ";
if (normWeight)
cout << "weighted L2-norm with user-provided weights" << endl;
else
cout << "L^2-norm" << endl;
if (orthoVec)
cout << " *|* Size of orthogonal subspace = " << orthoVec->NumVectors() << endl;
cout << "\n -- Start iterations -- \n";
}
#ifdef EPETRA_MPI
Epetra_MpiComm *MPIComm = dynamic_cast<Epetra_MpiComm *>(const_cast<Epetra_Comm*>(&MyComm));
#endif
timeOuterLoop -= MyWatch.WallTime();
while (ido != 99) {
highMem = (highMem > currentSize()) ? highMem : currentSize();
#ifdef EPETRA_MPI
if (MPIComm)
callFortran.PSAUPD(MPIComm->Comm(), &ido, 'G', localSize, "LM", numEigen, tolEigenSolve,
resid, NCV, v, localSize, iparam, ipntr, workd, workl, lworkl, &info, 0);
else
callFortran.SAUPD(&ido, 'G', localSize, "LM", numEigen, tolEigenSolve, resid, NCV, v,
localSize, iparam, ipntr, workd, workl, lworkl, &info, 0);
#else
callFortran.SAUPD(&ido, 'G', localSize, "LM", numEigen, tolEigenSolve, resid, NCV, v,
localSize, iparam, ipntr, workd, workl, lworkl, &info, 0);
#endif
if (ido == -1) {
// Apply the mass matrix
v3.ResetView(workd + ipntr[0] - 1);
v1.ResetView(vTmp);
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(v3, v1);
else
memcpy(v1.Values(), v3.Values(), localSize*sizeof(double));
timeMassOp += MyWatch.WallTime();
massOp += 1;
if ((orthoVec) && (verbose > 3)) {
// Check the orthogonality
double maxDot = myVerify.errorOrthogonality(orthoVec, &v1, 0);
if (myPid == 0) {
cout << " Maximum Euclidean dot product against orthogonal space (Before Solve) = ";
cout << maxDot << endl;
}
}
// Solve the stiffness problem
v2.ResetView(workd + ipntr[1] - 1);
timeStifOp -= MyWatch.WallTime();
K->ApplyInverse(v1, v2);
timeStifOp += MyWatch.WallTime();
stifOp += 1;
// Project the solution vector if needed
// Note: Use mvz as workspace
if (orthoVec) {
Epetra_Vector Mv2(View, v2.Map(), mvz);
if (M)
M->Apply(v2, Mv2);
else
memcpy(Mv2.Values(), v2.Values(), localSize*sizeof(double));
modalTool.massOrthonormalize(v2, Mv2, M, *orthoVec, 1, 1);
}
if ((orthoVec) && (verbose > 3)) {
// Check the orthogonality
double maxDot = myVerify.errorOrthogonality(orthoVec, &v2, M);
if (myPid == 0) {
cout << " Maximum M-dot product against orthogonal space (After Solve) = ";
cout << maxDot << endl;
}
}
continue;
} // if (ido == -1)
if (ido == 1) {
// Solve the stiffness problem
v1.ResetView(workd + ipntr[2] - 1);
v2.ResetView(workd + ipntr[1] - 1);
if ((orthoVec) && (verbose > 3)) {
// Check the orthogonality
double maxDot = myVerify.errorOrthogonality(orthoVec, &v1, 0);
if (myPid == 0) {
cout << " Maximum Euclidean dot product against orthogonal space (Before Solve) = ";
cout << maxDot << endl;
}
}
timeStifOp -= MyWatch.WallTime();
K->ApplyInverse(v1, v2);
timeStifOp += MyWatch.WallTime();
stifOp += 1;
// Project the solution vector if needed
// Note: Use mvz as workspace
if (orthoVec) {
Epetra_Vector Mv2(View, v2.Map(), mvz);
if (M)
M->Apply(v2, Mv2);
else
memcpy(Mv2.Values(), v2.Values(), localSize*sizeof(double));
modalTool.massOrthonormalize(v2, Mv2, M, *orthoVec, 1, 1);
}
if ((orthoVec) && (verbose > 3)) {
// Check the orthogonality
double maxDot = myVerify.errorOrthogonality(orthoVec, &v2, M);
if (myPid == 0) {
cout << " Maximum M-dot product against orthogonal space (After Solve) = ";
cout << maxDot << endl;
}
}
continue;
} // if (ido == 1)
if (ido == 2) {
// Apply the mass matrix
v1.ResetView(workd + ipntr[0] - 1);
v2.ResetView(workd + ipntr[1] - 1);
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(v1, v2);
else
memcpy(v2.Values(), v1.Values(), localSize*sizeof(double));
timeMassOp += MyWatch.WallTime();
massOp += 1;
continue;
} // if (ido == 2)
if (ido == 4) {
timeResidual -= MyWatch.WallTime();
// Copy the main diagonal of T
memcpy(dd, workl + NCV + ipntr[4] - 1, NCV*sizeof(double));
// Copy the lower diagonal of T
memcpy(ee, workl + ipntr[4], (NCV-1)*sizeof(double));
// Compute the eigenpairs of the tridiagonal matrix
zz = workl + 4*NCV;
workt = workl + 4*NCV + NCV*NCV;
callFortran.STEQR('I', NCV, dd, ee, zz, NCV, workt, &info);
if (info != 0) {
if (localVerbose > 0) {
cerr << endl;
cerr << " Error with DSTEQR, info = " << info << endl;
cerr << endl;
}
break;
}
// dd contains the eigenvalues in ascending order
// Check the residual of the proposed eigenvectors of (K, M)
int ii, jz;
iparam[4] = 0;
for (jz = 0; jz < NCV; jz += loopZ) {
int colZ = (jz + loopZ < NCV) ? loopZ : NCV - jz;
callBLAS.GEMM('N', 'N', localSize, colZ, NCV, 1.0, v, localSize,
zz + jz*NCV, NCV, 0.0, vz, localSize);
// Form the residuals
if (M)
M->Apply(approxEV, MapproxEV);
K->Apply(approxEV, KapproxEV);
for (ii = 0; ii < colZ; ++ii) {
callBLAS.AXPY(localSize, -1.0/dd[ii+jz], MapproxEV.Values() + ii*localSize,
KapproxEV.Values() + ii*localSize);
}
// Compute the norms of the residuals
if (vectWeight) {
KapproxEV.NormWeighted(*vectWeight, normR + jz);
}
else {
KapproxEV.Norm2(normR + jz);
}
// Scale the norms of residuals with the eigenvalues
for (ii = 0; ii < colZ; ++ii) {
normR[ii+jz] = normR[ii+jz]*dd[ii+jz];
}
// Put the number of converged pairs in iparam[5-1]
for (ii=0; ii<colZ; ++ii) {
if (normR[ii+jz] < tolEigenSolve)
iparam[4] += 1;
}
}
timeResidual += MyWatch.WallTime();
numResidual += NCV;
outerIter += 1;
if (localVerbose > 0) {
cout << " Iteration " << outerIter;
cout << " - Number of converged eigenvalues " << iparam[4] << endl;
}
if (localVerbose > 2) {
memcpy(resHistory + historyCount, normR, NCV*sizeof(double));
historyCount += NCV;
}
if (localVerbose > 1) {
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (ii=0; ii < NCV; ++ii) {
cout << " Iteration " << outerIter;
cout << " - Scaled Norm of Residual " << ii << " = " << normR[ii] << endl;
}
cout << endl;
cout.precision(2);
for (ii = 0; ii < NCV; ++ii) {
cout << " Iteration " << outerIter << " - Ritz eigenvalue " << ii;
cout.setf((fabs(dd[ii]) > 100) ? ios::scientific : ios::fixed, ios::floatfield);
cout << " = " << 1.0/dd[ii] << endl;
}
cout << endl;
}
} // if (ido == 4)
} // while (ido != 99)
timeOuterLoop += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
if (info < 0) {
if (myPid == 0) {
cerr << endl;
cerr << " Error with DSAUPD, info = " << info << endl;
cerr << endl;
}
}
else {
// Get the eigenvalues
timePostProce -= MyWatch.WallTime();
int ii, jj;
double *pointer = workl + 4*NCV + NCV*NCV;
for (ii=0; ii < localSize; ii += 3) {
int nRow = (ii + 3 < localSize) ? 3 : localSize - ii;
for (jj=0; jj<NCV; ++jj)
memcpy(pointer + jj*nRow, v + ii + jj*localSize, nRow*sizeof(double));
callBLAS.GEMM('N', 'N', nRow, NCV, NCV, 1.0, pointer, nRow, zz, NCV,
0.0, Q.Values() + ii, localSize);
}
// Put the converged eigenpairs at the beginning
knownEV = 0;
for (ii=0; ii < NCV; ++ii) {
if (normR[ii] < tolEigenSolve) {
lambda[knownEV] = 1.0/dd[ii];
memcpy(Q.Values()+knownEV*localSize, Q.Values()+ii*localSize, localSize*sizeof(double));
knownEV += 1;
if (knownEV == Q.NumVectors())
break;
}
}
// Sort the eigenpairs
if (knownEV > 0) {
mySort.sortScalars_Vectors(knownEV, lambda, Q.Values(), localSize);
}
timePostProce += MyWatch.WallTime();
} // if (info < 0)
if (info == 0) {
orthoOp = iparam[11-1];
}
delete[] wI;
delete[] wD;
delete[] wD2;
if (vectWeight)
delete vectWeight;
return (info == 0) ? knownEV : info;
}
int
Stokhos::ApproxGaussSeidelPreconditioner::
ApplyInverse(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Approximate Gauss-Seidel Time");
#endif
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values()) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
int m = input->NumVectors();
if (mat_vec_tmp == Teuchos::null || mat_vec_tmp->NumVectors() != m)
mat_vec_tmp = Teuchos::rcp(new Epetra_MultiVector(*base_map, m));
if (rhs_block == Teuchos::null || rhs_block->NumVectors() != m)
rhs_block =
Teuchos::rcp(new EpetraExt::BlockMultiVector(*base_map, *sg_map, m));
// Extract blocks
EpetraExt::BlockMultiVector input_block(View, *base_map, *input);
EpetraExt::BlockMultiVector result_block(View, *base_map, Result);
result_block.PutScalar(0.0);
int k_limit = sg_poly->size();
if (only_use_linear)
k_limit = sg_poly->basis()->dimension() + 1;
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
rhs_block->Update(1.0, input_block, 0.0);
for (Cijk_type::i_iterator i_it=Cijk->i_begin();
i_it!=Cijk->i_end(); ++i_it) {
int i = index(i_it);
Teuchos::RCP<Epetra_MultiVector> res_i = result_block.GetBlock(i);
{
// Apply deterministic preconditioner
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total AGS Deterministic Preconditioner Time");
#endif
mean_prec->ApplyInverse(*(rhs_block->GetBlock(i)), *res_i);
}
int i_gid = epetraCijk->GRID(i);
for (Cijk_type::ik_iterator k_it = Cijk->k_begin(i_it);
k_it != Cijk->k_end(i_it); ++k_it) {
int k = index(k_it);
if (k!=0 && k<k_limit) {
bool do_mat_vec = false;
for (Cijk_type::ikj_iterator j_it = Cijk->j_begin(k_it);
j_it != Cijk->j_end(k_it); ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
if (j_gid > i_gid) {
bool on_proc = epetraCijk->myGRID(j_gid);
if (on_proc) {
do_mat_vec = true;
break;
}
}
}
if (do_mat_vec) {
(*sg_poly)[k].Apply(*res_i, *mat_vec_tmp);
for (Cijk_type::ikj_iterator j_it = Cijk->j_begin(k_it);
j_it != Cijk->j_end(k_it); ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
double c = value(j_it);
if (scale_op) {
if (useTranspose)
c /= norms[i_gid];
else
c /= norms[j_gid];
}
if (j_gid > i_gid) {
bool on_proc = epetraCijk->myGRID(j_gid);
if (on_proc) {
rhs_block->GetBlock(j)->Update(-c, *mat_vec_tmp, 1.0);
}
}
}
}
}
}
}
// For symmetric Gauss-Seidel
if (symmetric) {
for (Cijk_type::i_reverse_iterator i_it= Cijk->i_rbegin();
i_it!=Cijk->i_rend(); ++i_it) {
int i = index(i_it);
Teuchos::RCP<Epetra_MultiVector> res_i = result_block.GetBlock(i);
{
// Apply deterministic preconditioner
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total AGS Deterministic Preconditioner Time");
#endif
mean_prec->ApplyInverse(*(rhs_block->GetBlock(i)), *res_i);
}
int i_gid = epetraCijk->GRID(i);
for (Cijk_type::ik_iterator k_it = Cijk->k_begin(i_it);
k_it != Cijk->k_end(i_it); ++k_it) {
int k = index(k_it);
if (k!=0 && k<k_limit) {
bool do_mat_vec = false;
for (Cijk_type::ikj_iterator j_it = Cijk->j_begin(k_it);
j_it != Cijk->j_end(k_it); ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
if (j_gid < i_gid) {
bool on_proc = epetraCijk->myGRID(j_gid);
if (on_proc) {
do_mat_vec = true;
break;
}
}
}
if (do_mat_vec) {
(*sg_poly)[k].Apply(*res_i, *mat_vec_tmp);
for (Cijk_type::ikj_iterator j_it = Cijk->j_begin(k_it);
j_it != Cijk->j_end(k_it); ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
double c = value(j_it);
if (scale_op)
c /= norms[j_gid];
if (j_gid < i_gid) {
bool on_proc = epetraCijk->myGRID(j_gid);
if (on_proc) {
rhs_block->GetBlock(j)->Update(-c, *mat_vec_tmp, 1.0);
}
}
}
}
}
}
}
}
if (made_copy)
delete input;
return 0;
}
int
Stokhos::KLMatrixFreeOperator::
Apply(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values() && !is_stoch_parallel) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
// Initialize
Result.PutScalar(0.0);
const Epetra_Map* input_base_map = domain_base_map.get();
const Epetra_Map* result_base_map = range_base_map.get();
if (useTranspose == true) {
input_base_map = range_base_map.get();
result_base_map = domain_base_map.get();
}
// Allocate temporary storage
int m = Input.NumVectors();
if (useTranspose == false &&
(tmp == Teuchos::null || tmp->NumVectors() != m*max_num_mat_vec))
tmp = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
else if (useTranspose == true &&
(tmp_trans == Teuchos::null ||
tmp_trans->NumVectors() != m*max_num_mat_vec))
tmp_trans = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
Epetra_MultiVector *tmp_result;
if (useTranspose == false)
tmp_result = tmp.get();
else
tmp_result = tmp_trans.get();
// Map input into column map
const Epetra_MultiVector *tmp_col;
if (!is_stoch_parallel)
tmp_col = input;
else {
if (useTranspose == false) {
if (input_col == Teuchos::null || input_col->NumVectors() != m)
input_col = Teuchos::rcp(new Epetra_MultiVector(*global_col_map, m));
input_col->Import(*input, *col_importer, Insert);
tmp_col = input_col.get();
}
else {
if (input_col_trans == Teuchos::null ||
input_col_trans->NumVectors() != m)
input_col_trans =
Teuchos::rcp(new Epetra_MultiVector(*global_col_map_trans, m));
input_col_trans->Import(*input, *col_importer_trans, Insert);
tmp_col = input_col_trans.get();
}
}
// Extract blocks
EpetraExt::BlockMultiVector sg_input(View, *input_base_map, *tmp_col);
EpetraExt::BlockMultiVector sg_result(View, *result_base_map, Result);
for (int i=0; i<input_block.size(); i++)
input_block[i] = sg_input.GetBlock(i);
for (int i=0; i<result_block.size(); i++)
result_block[i] = sg_result.GetBlock(i);
int N = result_block[0]->MyLength();
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
int d = sg_basis->dimension();
Teuchos::Array<double> zero(d), one(d);
for(int j = 0; j<d; j++) {
zero[j] = 0.0;
one[j] = 1.0;
}
Teuchos::Array< double > phi_0(expansion_size), phi_1(expansion_size);
sg_basis->evaluateBases(zero, phi_0);
sg_basis->evaluateBases(one, phi_1);
// k_begin and k_end are initialized in the constructor
for (Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
Cijk_type::kj_iterator j_begin = Cijk->j_begin(k_it);
Cijk_type::kj_iterator j_end = Cijk->j_end(k_it);
int k = index(k_it);
int nj = Cijk->num_j(k_it);
if (nj > 0) {
Teuchos::Array<double*> j_ptr(nj*m);
Teuchos::Array<int> mj_indices(nj*m);
int l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (int mm=0; mm<m; mm++) {
j_ptr[l*m+mm] = input_block[j]->Values()+mm*N;
mj_indices[l*m+mm] = l*m+mm;
}
l++;
}
Epetra_MultiVector input_tmp(View, *input_base_map, &j_ptr[0], nj*m);
Epetra_MultiVector result_tmp(View, *tmp_result, &mj_indices[0], nj*m);
(*block_ops)[k].Apply(input_tmp, result_tmp);
l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
for (Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
i_it != Cijk->i_end(j_it); ++i_it) {
int i = index(i_it);
int i_gid = epetraCijk->GRID(i);
double c = value(i_it);
if (k == 0)
c /= phi_0[0];
else {
c /= phi_1[k];
if (i_gid == j_gid)
c -= phi_0[k]/(phi_1[k]*phi_0[0])*norms[i_gid];
}
if (scale_op) {
if (useTranspose)
c /= norms[j_gid];
else
c /= norms[i_gid];
}
for (int mm=0; mm<m; mm++)
(*result_block[i])(mm)->Update(c, *result_tmp(l*m+mm), 1.0);
}
l++;
}
}
}
// Destroy blocks
for (int i=0; i<input_block.size(); i++)
input_block[i] = Teuchos::null;
for (int i=0; i<result_block.size(); i++)
result_block[i] = Teuchos::null;
if (made_copy)
delete input;
return 0;
}
// ============================================================================
int ML_Epetra::MatrixFreePreconditioner::
Compute(const Epetra_CrsGraph& Graph, Epetra_MultiVector& NullSpace)
{
Epetra_Time TotalTime(Comm());
const int NullSpaceDim = NullSpace.NumVectors();
// get parameters from the list
std::string PrecType = List_.get("prec: type", "hybrid");
std::string SmootherType = List_.get("smoother: type", "Jacobi");
std::string ColoringType = List_.get("coloring: type", "JONES_PLASSMAN");
int PolynomialDegree = List_.get("smoother: degree", 3);
std::string DiagonalColoringType = List_.get("diagonal coloring: type", "JONES_PLASSMAN");
int MaximumIterations = List_.get("eigen-analysis: max iters", 10);
std::string EigenType_ = List_.get("eigen-analysis: type", "cg");
double boost = List_.get("eigen-analysis: boost for lambda max", 1.0);
int OutputLevel = List_.get("ML output", -47);
if (OutputLevel == -47) OutputLevel = List_.get("output", 10);
omega_ = List_.get("smoother: damping", omega_);
ML_Set_PrintLevel(OutputLevel);
bool LowMemory = List_.get("low memory", true);
double AllocationFactor = List_.get("AP allocation factor", 0.5);
verbose_ = (MyPID() == 0 && ML_Get_PrintLevel() > 5);
// ================ //
// check parameters //
// ================ //
if (PrecType == "presmoother only")
PrecType_ = ML_MFP_PRESMOOTHER_ONLY;
else if (PrecType == "hybrid")
PrecType_ = ML_MFP_HYBRID;
else if (PrecType == "additive")
PrecType_ = ML_MFP_ADDITIVE;
else
ML_CHK_ERR(-3); // not recognized
if (SmootherType == "none")
SmootherType_ = ML_MFP_NONE;
else if (SmootherType == "Jacobi")
SmootherType_ = ML_MFP_JACOBI;
else if (SmootherType == "block Jacobi")
SmootherType_ = ML_MFP_BLOCK_JACOBI;
else if (SmootherType == "Chebyshev")
SmootherType_ = ML_MFP_CHEBY;
else
ML_CHK_ERR(-4); // not recognized
if (AllocationFactor <= 0.0)
ML_CHK_ERR(-1); // should be positive
// =============================== //
// basic checkings and some output //
// =============================== //
int OperatorDomainPoints = Operator_.OperatorDomainMap().NumGlobalPoints();
int OperatorRangePoints = Operator_.OperatorRangeMap().NumGlobalPoints();
int GraphBlockRows = Graph.NumGlobalBlockRows();
int GraphNnz = Graph.NumGlobalNonzeros();
NumPDEEqns_ = OperatorRangePoints / GraphBlockRows;
NumMyBlockRows_ = Graph.NumMyBlockRows();
if (OperatorDomainPoints != OperatorRangePoints)
ML_CHK_ERR(-1); // only square matrices
if (OperatorRangePoints % NumPDEEqns_ != 0)
ML_CHK_ERR(-2); // num PDEs seems not constant
if (verbose_)
{
ML_print_line("=",78);
std::cout << "*** " << std::endl;
std::cout << "*** ML_Epetra::MatrixFreePreconditioner" << std::endl;
std::cout << "***" << std::endl;
std::cout << "Number of rows and columns = " << OperatorDomainPoints << std::endl;
std::cout << "Number of rows per processor = " << OperatorDomainPoints / Comm().NumProc()
<< " (on average)" << std::endl;
std::cout << "Number of rows in the graph = " << GraphBlockRows << std::endl;
std::cout << "Number of nonzeros in the graph = " << GraphNnz << std::endl;
std::cout << "Processors used in computation = " << Comm().NumProc() << std::endl;
std::cout << "Number of PDE equations = " << NumPDEEqns_ << std::endl;
std::cout << "Null space dimension = " << NullSpaceDim << std::endl;
std::cout << "Preconditioner type = " << PrecType << std::endl;
std::cout << "Smoother type = " << SmootherType << std::endl;
std::cout << "Coloring type = " << ColoringType << std::endl;
std::cout << "Allocation factor = " << AllocationFactor << std::endl;
std::cout << "Number of V-cycles for C = " << List_.sublist("ML list").get("cycle applications", 1) << std::endl;
std::cout << std::endl;
}
ResetStartTime();
// ==================================== //
// compute the inverse of the diagonal, //
// control that no elements are zero. //
// ==================================== //
for (int i = 0; i < InvPointDiagonal_->MyLength(); ++i)
if ((*InvPointDiagonal_)[i] != 0.0)
(*InvPointDiagonal_)[i] = 1.0 / (*InvPointDiagonal_)[i];
// ========================================================= //
// Setup the smoother. I need to extract the block diagonal //
// only if block Jacobi is used. For Chebyshev, I scale with //
// the point diagonal only. In this latter case, I need to //
// compute lambda_max of the scaled operator. //
// ========================================================= //
// probes for the block diagonal of the matrix.
if (SmootherType_ == ML_MFP_JACOBI ||
SmootherType_ == ML_MFP_NONE)
{
// do-nothing here
}
else if (SmootherType_ == ML_MFP_BLOCK_JACOBI)
{
if (verbose_);
std::cout << "Diagonal coloring type = " << DiagonalColoringType << std::endl;
ML_CHK_ERR(GetBlockDiagonal(Graph, DiagonalColoringType));
AddAndResetStartTime("block diagonal construction", true);
}
else if (SmootherType_ == ML_MFP_CHEBY)
{
double lambda_min = 0.0;
double lambda_max = 0.0;
Teuchos::ParameterList IFPACKList;
if (EigenType_ == "power-method")
{
ML_CHK_ERR(Ifpack_Chebyshev::PowerMethod(Operator_, *InvPointDiagonal_,
MaximumIterations, lambda_max));
}
else if(EigenType_ == "cg")
{
ML_CHK_ERR(Ifpack_Chebyshev::CG(Operator_, *InvPointDiagonal_,
MaximumIterations, lambda_min,
lambda_max));
}
else
ML_CHK_ERR(-1); // not recognized
if (verbose_)
{
std::cout << "Using Chebyshev smoother of degree " << PolynomialDegree << std::endl;
std::cout << "Estimating eigenvalues using " << EigenType_ << std::endl;
std::cout << "lambda_min = " << lambda_min << ", ";
std::cout << "lambda_max = " << lambda_max << std::endl;
}
IFPACKList.set("chebyshev: min eigenvalue", lambda_min);
IFPACKList.set("chebyshev: max eigenvalue", boost * lambda_max);
// FIXME: this allocates a new std::vector inside
IFPACKList.set("chebyshev: operator inv diagonal", InvPointDiagonal_.get());
IFPACKList.set("chebyshev: degree", PolynomialDegree);
PreSmoother_ = rcp(new Ifpack_Chebyshev((Epetra_Operator*)(&Operator_)));
if (PreSmoother_.get() == 0) ML_CHK_ERR(-1); // memory error?
IFPACKList.set("chebyshev: zero starting solution", true);
ML_CHK_ERR(PreSmoother_->SetParameters(IFPACKList));
ML_CHK_ERR(PreSmoother_->Initialize());
ML_CHK_ERR(PreSmoother_->Compute());
PostSmoother_ = rcp(new Ifpack_Chebyshev((Epetra_Operator*)(&Operator_)));
if (PostSmoother_.get() == 0) ML_CHK_ERR(-1); // memory error?
IFPACKList.set("chebyshev: zero starting solution", false);
ML_CHK_ERR(PostSmoother_->SetParameters(IFPACKList));
ML_CHK_ERR(PostSmoother_->Initialize());
ML_CHK_ERR(PostSmoother_->Compute());
}
// ========================================================= //
// building P and R for block graph. This is done by working //
// on the Graph_ object. Support is provided for local //
// aggregation schemes only so that all is basically local. //
// Then, build the block graph coarse problem. //
// ========================================================= //
// ML wrapper for Graph_
ML_Operator* Graph_ML = ML_Operator_Create(Comm_ML());
ML_Operator_WrapEpetraCrsGraph(const_cast<Epetra_CrsGraph*>(&Graph), Graph_ML);
ML_Aggregate* BlockAggr_ML = 0;
ML_Operator* BlockPtent_ML = 0, *BlockRtent_ML = 0,* CoarseGraph_ML = 0;
if (verbose_) std::cout << std::endl;
ML_CHK_ERR(Coarsen(Graph_ML, &BlockAggr_ML, &BlockPtent_ML, &BlockRtent_ML,
&CoarseGraph_ML));
if (verbose_) std::cout << std::endl;
Epetra_CrsMatrix* GraphCoarse;
ML_CHK_ERR(ML_Operator2EpetraCrsMatrix(CoarseGraph_ML, GraphCoarse));
// used later to estimate the entries in AP
ML_Operator* CoarseAP_ML = ML_Operator_Create(Comm_ML());
ML_2matmult(Graph_ML, BlockPtent_ML, CoarseAP_ML, ML_CSR_MATRIX);
int AP_MaxNnzRow, itmp = CoarseAP_ML->max_nz_per_row;
Comm().MaxAll(&itmp, &AP_MaxNnzRow, 1);
ML_Operator_Destroy(&CoarseAP_ML);
int NumAggregates = BlockPtent_ML->invec_leng;
ML_Operator_Destroy(&BlockRtent_ML);
ML_Operator_Destroy(&CoarseGraph_ML);
AddAndResetStartTime("construction of block C, R, and P", true);
if (verbose_) std::cout << std::endl;
// ================================================== //
// coloring of block graph: //
// - color of block row `i' is given by `ColorMap[i]' //
// - number of colors is ColorMap.NumColors(). //
// ================================================== //
ResetStartTime();
CrsGraph_MapColoring* MapColoringTransform;
if (ColoringType == "JONES_PLASSMAN")
MapColoringTransform = new CrsGraph_MapColoring (CrsGraph_MapColoring::JONES_PLASSMAN,
0, false, 0);
else if (ColoringType == "PSEUDO_PARALLEL")
MapColoringTransform = new CrsGraph_MapColoring (CrsGraph_MapColoring::PSEUDO_PARALLEL,
0, false, 0);
else if (ColoringType == "GREEDY")
MapColoringTransform = new CrsGraph_MapColoring (CrsGraph_MapColoring::GREEDY,
0, false, 0);
else if (ColoringType == "LUBY")
MapColoringTransform = new CrsGraph_MapColoring (CrsGraph_MapColoring::LUBY,
0, false, 0);
else
ML_CHK_ERR(-1);
Epetra_MapColoring* ColorMap = &(*MapColoringTransform)(const_cast<Epetra_CrsGraph&>(GraphCoarse->Graph()));
// move the information from ColorMap to std::vector Colors
const int NumColors = ColorMap->MaxNumColors();
RefCountPtr<Epetra_IntSerialDenseVector> Colors = rcp(new Epetra_IntSerialDenseVector(GraphCoarse->Graph().NumMyRows()));
for (int i = 0; i < GraphCoarse->Graph().NumMyRows(); ++i)
(*Colors)[i] = (*ColorMap)[i];
delete MapColoringTransform;
delete ColorMap; ColorMap = 0;
delete GraphCoarse;
AddAndResetStartTime("coarse graph coloring", true);
if (verbose_) std::cout << std::endl;
// get some other information about the aggregates, to be used
// in the QR factorization of the null space. NodesOfAggregate
// contains the local ID of block rows contained in each aggregate.
// FIXME: make it faster
std::vector< std::vector<int> > NodesOfAggregate(NumAggregates);
for (int i = 0; i < Graph.NumMyBlockRows(); ++i)
{
int AID = BlockAggr_ML->aggr_info[0][i];
NodesOfAggregate[AID].push_back(i);
}
int MaxAggrSize = 0;
for (int i = 0; i < NumAggregates; ++i)
{
const int& MySize = NodesOfAggregate[i].size();
if (MySize > MaxAggrSize) MaxAggrSize = MySize;
}
// collect aggregate information, and mark all nodes that are
// connected with each aggregate. These nodes will have a possible
// nonzero entry after the matrix-matrix product between the Operator_
// and the tentative prolongator.
std::vector<vector<int> > aggregates(NumAggregates);
std::vector<int>::iterator iter;
for (int i = 0; i < NumAggregates; ++i)
aggregates[i].reserve(MaxAggrSize);
for (int i = 0; i < Graph.NumMyBlockRows(); ++i)
{
int AID = BlockAggr_ML->aggr_info[0][i];
int NumEntries;
int* Indices;
Graph.ExtractMyRowView(i, NumEntries, Indices);
for (int k = 0; k < NumEntries; ++k)
{
// FIXME: use hash??
const int& GCID = Graph.ColMap().GID(Indices[k]);
iter = find(aggregates[AID].begin(), aggregates[AID].end(), GCID);
if (iter == aggregates[AID].end())
aggregates[AID].push_back(GCID);
}
}
int* BlockNodeList = Graph.ColMap().MyGlobalElements();
// finally get rid of the ML_Aggregate structure.
ML_Aggregate_Destroy(&BlockAggr_ML);
const Epetra_Map& FineMap = Operator_.OperatorDomainMap();
Epetra_Map CoarseMap(-1, NumAggregates * NullSpaceDim, 0, Comm());
RefCountPtr<Epetra_Map> BlockNodeListMap =
rcp(new Epetra_Map(-1, Graph.ColMap().NumMyElements(),
BlockNodeList, 0, Comm()));
std::vector<int> NodeList(Graph.ColMap().NumMyElements() * NumPDEEqns_);
for (int i = 0; i < Graph.ColMap().NumMyElements(); ++i)
for (int m = 0; m < NumPDEEqns_; ++m)
NodeList[i * NumPDEEqns_ + m] = BlockNodeList[i] * NumPDEEqns_ + m;
RefCountPtr<Epetra_Map> NodeListMap =
rcp(new Epetra_Map(-1, NodeList.size(), &NodeList[0], 0, Comm()));
AddAndResetStartTime("data structures", true);
// ====================== //
// process the null space //
// ====================== //
// CHECKME
Epetra_MultiVector NewNullSpace(CoarseMap, NullSpaceDim);
NewNullSpace.PutScalar(0.0);
if (NullSpaceDim == 1)
{
double* ns_ptr = NullSpace.Values();
for (int AID = 0; AID < NumAggregates; ++AID)
{
double dtemp = 0.0;
for (int j = 0; j < (int) (NodesOfAggregate[AID].size()); j++)
for (int m = 0; m < NumPDEEqns_; ++m)
{
const int& pos = NodesOfAggregate[AID][j] * NumPDEEqns_ + m;
dtemp += (ns_ptr[pos] * ns_ptr[pos]);
}
dtemp = std::sqrt(dtemp);
NewNullSpace[0][AID] = dtemp;
dtemp = 1.0 / dtemp;
for (int j = 0; j < (int) (NodesOfAggregate[AID].size()); j++)
for (int m = 0; m < NumPDEEqns_; ++m)
ns_ptr[NodesOfAggregate[AID][j] * NumPDEEqns_ + m] *= dtemp;
}
}
else
{
// FIXME
std::vector<double> qr_ptr(MaxAggrSize * NumPDEEqns_ * MaxAggrSize * NumPDEEqns_);
std::vector<double> tmp_ptr(MaxAggrSize * NumPDEEqns_ * NullSpaceDim);
std::vector<double> work(NullSpaceDim);
int info;
for (int AID = 0; AID < NumAggregates; ++AID)
{
int MySize = NodesOfAggregate[AID].size();
int MyFullSize = NodesOfAggregate[AID].size() * NumPDEEqns_;
int lwork = NullSpaceDim;
for (int k = 0; k < NullSpaceDim; ++k)
for (int j = 0; j < MySize; ++j)
for (int m = 0; m < NumPDEEqns_; ++m)
qr_ptr[k * MyFullSize + j * NumPDEEqns_ + m] =
NullSpace[k][NodesOfAggregate[AID][j] * NumPDEEqns_ + m];
DGEQRF_F77(&MyFullSize, (int*)&NullSpaceDim, &qr_ptr[0],
&MyFullSize, &tmp_ptr[0], &work[0], &lwork, &info);
ML_CHK_ERR(info);
if (work[0] > lwork) work.resize((int) work[0]);
// the upper triangle of qr_tmp is now R, so copy that into the
// new nullspace
for (int j = 0; j < NullSpaceDim; j++)
for (int k = j; k < NullSpaceDim; k++)
NewNullSpace[k][AID * NullSpaceDim + j] = qr_ptr[j + MyFullSize * k];
// to get this block of P, need to run qr_tmp through another LAPACK
// function:
DORGQR_F77(&MyFullSize, (int*)&NullSpaceDim, (int*)&NullSpaceDim,
&qr_ptr[0], &MyFullSize, &tmp_ptr[0], &work[0], &lwork, &info);
ML_CHK_ERR(info); // dgeqtr returned a non-zero
if (work[0] > lwork) work.resize((int) work[0]);
// insert the Q block into the null space
for (int k = 0; k < NullSpaceDim; ++k)
for (int j = 0; j < MySize; ++j)
for (int m = 0; m < NumPDEEqns_; ++m)
{
int LRID = NodesOfAggregate[AID][j] * NumPDEEqns_ + m;
double& val = qr_ptr[k * MyFullSize + j * NumPDEEqns_ + m];
NullSpace[k][LRID] = val;
}
}
}
AddAndResetStartTime("null space setup", true);
if (verbose_)
std::cout << "Number of colors on processor " << Comm().MyPID() << " = "
<< NumColors << std::endl;
if (verbose_)
std::cout << "Maximum number of colors = " << NumColors << std::endl;
RefCountPtr<Epetra_FECrsMatrix> AP;
// try to get a good estimate of the nonzeros per row.
// This is a compromize between efficiency -- that is, reduce
// the memory allocation processes, and memory usage -- that, is
// overestimating can actually kill the code. Basically, this is
// all junk due to our dear friend, the Cray XT3.
AP = rcp(new Epetra_FECrsMatrix(Copy, FineMap, (int)
(AllocationFactor * AP_MaxNnzRow * NullSpaceDim)));
if (AP.get() == 0) throw(-1);
if (!LowMemory)
{
// ================================================= //
// allocate one big chunk of memory, and use View //
// to create Epetra_MultiVectors. Note that //
// NumColors * NullSpace can indeed be a quite large //
// value. To reduce the memory consumption, both //
// ColoredAP and ExtColoredAP use the same memory //
// array. //
// ================================================= //
Epetra_MultiVector* ColoredP;
std::vector<double> ColoredAP_ptr;
try
{
ColoredP = new Epetra_MultiVector(FineMap, NumColors * NullSpaceDim);
ColoredAP_ptr.resize(NumColors * NullSpaceDim * NodeListMap->NumMyPoints());
}
catch (std::exception& rhs)
{
catch_message("the allocation of ColoredP", rhs.what(), __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
catch (...)
{
catch_message("the allocation of ColoredP", "", __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
int ColoredAP_LDA = NodeListMap->NumMyPoints();
ColoredP->PutScalar(0.0);
for (int i = 0; i < BlockPtent_ML->outvec_leng; ++i)
{
int allocated = 1;
int NumEntries;
int Indices;
double Values;
int ierr = ML_Operator_Getrow(BlockPtent_ML, 1 ,&i, allocated,
&Indices,&Values,&NumEntries);
if (ierr < 0)
ML_CHK_ERR(-1);
assert (NumEntries == 1); // this is the block P
const int& Color = (*Colors)[Indices] - 1;
for (int k = 0; k < NumPDEEqns_; ++k)
for (int j = 0; j < NullSpaceDim; ++j)
(*ColoredP)[(Color * NullSpaceDim + j)][i * NumPDEEqns_ + k] =
NullSpace[j][i * NumPDEEqns_ + k];
}
ML_Operator_Destroy(&BlockPtent_ML);
Epetra_MultiVector ColoredAP(View, Operator_.OperatorRangeMap(),
&ColoredAP_ptr[0], ColoredAP_LDA,
NumColors * NullSpaceDim);
// move ColoredAP into ColoredP. This should not be required.
// but I prefer to skip strange games with View pointers
Operator_.Apply(*ColoredP, ColoredAP);
*ColoredP = ColoredAP;
// FIXME: only if NumProc > 1
Epetra_MultiVector ExtColoredAP(View, *NodeListMap,
&ColoredAP_ptr[0], ColoredAP_LDA,
NumColors * NullSpaceDim);
try
{
Epetra_Import Importer(*NodeListMap, Operator_.OperatorRangeMap());
ExtColoredAP.Import(*ColoredP, Importer, Insert);
}
catch (std::exception& rhs)
{
catch_message("importing of ExtColoredAP", rhs.what(), __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
catch (...)
{
catch_message("importing of ExtColoredAP", "", __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
delete ColoredP;
AddAndResetStartTime("computation of AP", true);
// populate the actual AP operator, skip some controls to make it faster
for (int i = 0; i < NumAggregates; ++i)
{
for (int j = 0; j < (int) (aggregates[i].size()); ++j)
{
int GRID = aggregates[i][j];
int LRID = BlockNodeListMap->LID(GRID); // this is the block ID
//assert (LRID != -1);
int GCID = CoarseMap.GID(i * NullSpaceDim);
//assert (GCID != -1);
int color = (*Colors)[i] - 1;
for (int k = 0; k < NumPDEEqns_; ++k)
for (int j = 0; j < NullSpaceDim; ++j)
{
double val = ExtColoredAP[color * NullSpaceDim + j][LRID * NumPDEEqns_ + k];
if (val != 0.0)
{
int GRID2 = GRID * NumPDEEqns_ + k;
int GCID2 = GCID + j;
AP->InsertGlobalValues(1, &GRID2, 1, &GCID2, &val);
//if (ierr < 0) ML_CHK_ERR(ierr);
}
}
}
}
}
else
{
// =============================================================== //
// apply the operator one color at-a-time. This requires NumColors //
// cycles over BlockPtent. However, the memory requirements are //
// drastically reduced. As for low-memory == false, both ColoredAP //
// and ExtColoredAP point to the same memory location. //
// =============================================================== //
if (verbose_)
std::cout << "Using low-memory computation for AP" << std::endl;
Epetra_MultiVector ColoredP(FineMap, NullSpaceDim);
std::vector<double> ColoredAP_ptr;
try
{
ColoredAP_ptr.resize(NullSpaceDim * NodeListMap->NumMyPoints());
}
catch (std::exception& rhs)
{
catch_message("resizing of ColoredAP_pt", rhs.what(), __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
catch (...)
{
catch_message("resizing of ColoredAP_pt", "", __FILE__, __LINE__);
ML_CHK_ERR(-1);
}
Epetra_MultiVector ColoredAP(View, Operator_.OperatorRangeMap(),
&ColoredAP_ptr[0], NodeListMap->NumMyPoints(),
NullSpaceDim);
Epetra_MultiVector ExtColoredAP(View, *NodeListMap,
&ColoredAP_ptr[0], NodeListMap->NumMyPoints(),
NullSpaceDim);
Epetra_Import Importer(*NodeListMap, Operator_.OperatorRangeMap());
for (int ic = 0; ic < NumColors; ++ic)
{
if (ML_Get_PrintLevel() > 8 && Comm().MyPID() == 0)
{
if (ic % 20 == 0)
std::cout << "Processing color " << flush;
std::cout << ic << " " << flush;
if (ic % 20 == 19 || ic == NumColors - 1)
std::cout << std::endl;
if (ic == NumColors - 1) std::cout << std::endl;
}
ColoredP.PutScalar(0.0);
for (int i = 0; i < BlockPtent_ML->outvec_leng; ++i)
{
int allocated = 1;
int NumEntries;
int Indices;
double Values;
int ierr = ML_Operator_Getrow(BlockPtent_ML, 1 ,&i, allocated,
&Indices,&Values,&NumEntries);
if (ierr < 0 || // something strange in getrow
NumEntries != 1) // this is the block P
ML_CHK_ERR(-1);
const int& Color = (*Colors)[Indices] - 1;
if (Color != ic)
continue; // skip this color for this cycle
for (int k = 0; k < NumPDEEqns_; ++k)
for (int j = 0; j < NullSpaceDim; ++j)
ColoredP[j][i * NumPDEEqns_ + k] =
NullSpace[j][i * NumPDEEqns_ + k];
}
Operator_.Apply(ColoredP, ColoredAP);
ColoredP = ColoredAP; // just to be safe
ExtColoredAP.Import(ColoredP, Importer, Insert);
// populate the actual AP operator, skip some controls to make it faster
std::vector<int> InsertCols(NullSpaceDim * NumPDEEqns_);
std::vector<double> InsertValues(NullSpaceDim * NumPDEEqns_);
for (int i = 0; i < NumAggregates; ++i)
{
for (int j = 0; j < (int) (aggregates[i].size()); ++j)
{
int GRID = aggregates[i][j];
int LRID = BlockNodeListMap->LID(GRID); // this is the block ID
//assert (LRID != -1);
int GCID = CoarseMap.GID(i * NullSpaceDim);
//assert (GCID != -1);
int color = (*Colors)[i] - 1;
if (color != ic) continue;
for (int k = 0; k < NumPDEEqns_; ++k)
{
int count = 0;
int GRID2 = GRID * NumPDEEqns_ + k;
for (int j = 0; j < NullSpaceDim; ++j)
{
double val = ExtColoredAP[j][LRID * NumPDEEqns_ + k];
if (val != 0.0)
{
InsertCols[count] = GCID + j;
InsertValues[count] = val;
++count;
}
}
AP->InsertGlobalValues(1, &GRID2, count, &InsertCols[0],
&InsertValues[0]);
}
}
}
}
ML_Operator_Destroy(&BlockPtent_ML);
}
aggregates.resize(0);
BlockNodeListMap = Teuchos::null;
NodeListMap = Teuchos::null;
Colors = Teuchos::null;
AP->GlobalAssemble(false);
AP->FillComplete(CoarseMap, FineMap);
#if 0
try
{
AP->OptimizeStorage();
}
catch(...)
{
// a memory error was reported, typically ReportError.
// We just continue with fingers crossed.
}
#endif
AddAndResetStartTime("computation of the final AP", true);
ML_Operator* AP_ML = ML_Operator_Create(Comm_ML());
ML_Operator_WrapEpetraMatrix(AP.get(), AP_ML);
// ======== //
// create R //
// ======== //
std::vector<int> REntries(NumAggregates * NullSpaceDim);
for (int AID = 0; AID < NumAggregates; ++AID)
{
for (int m = 0; m < NullSpaceDim; ++m)
REntries[AID * NullSpaceDim + m] = NodesOfAggregate[AID].size() * NumPDEEqns_;
}
R_ = rcp(new Epetra_CrsMatrix(Copy, CoarseMap, &REntries[0], true));
REntries.resize(0);
for (int AID = 0; AID < NumAggregates; ++AID)
{
const int& MySize = NodesOfAggregate[AID].size();
// FIXME: make it faster
for (int j = 0; j < MySize; ++j)
for (int m = 0; m < NumPDEEqns_; ++m)
for (int k = 0; k < NullSpaceDim; ++k)
{
int LCID = NodesOfAggregate[AID][j] * NumPDEEqns_ + m;
int GCID = FineMap.GID(LCID);
assert (GCID != -1);
double& val = NullSpace[k][LCID];
int GRID = CoarseMap.GID(AID * NullSpaceDim + k);
int ierr = R_->InsertGlobalValues(GRID, 1, &val, &GCID);
if (ierr < 0)
ML_CHK_ERR(-1);
}
}
NodesOfAggregate.resize(0);
R_->FillComplete(FineMap, CoarseMap);
#if 0
try
{
R_->OptimizeStorage();
}
catch(...)
{
// a memory error was reported, typically ReportError.
// We just continue with fingers crossed.
}
#endif
ML_Operator* R_ML = ML_Operator_Create(Comm_ML());
ML_Operator_WrapEpetraMatrix(R_.get(), R_ML);
AddAndResetStartTime("computation of R", true);
// ======== //
// Create C //
// ======== //
C_ML_ = ML_Operator_Create(Comm_ML());
ML_2matmult(R_ML, AP_ML, C_ML_, ML_MSR_MATRIX);
ML_Operator_Destroy(&AP_ML);
ML_Operator_Destroy(&R_ML);
AP = Teuchos::null;
C_ = rcp(new ML_Epetra::RowMatrix(C_ML_, &Comm(), false));
assert (R_->OperatorRangeMap().SameAs(C_->OperatorDomainMap()));
TotalTime.ResetStartTime();
AddAndResetStartTime("computation of C", true);
if (verbose_)
{
std::cout << "Matrix-free preconditioner built. Now building solver for C..." << std::endl;
}
Teuchos::ParameterList& sublist = List_.sublist("ML list");
sublist.set("PDE equations", NullSpaceDim);
sublist.set("null space: type", "pre-computed");
sublist.set("null space: dimension", NewNullSpace.NumVectors());
sublist.set("null space: vectors", NewNullSpace.Values());
MLP_ = rcp(new MultiLevelPreconditioner(*C_, sublist, true));
assert (MLP_.get() != 0);
IsComputed_ = true;
AddAndResetStartTime("computation of the preconditioner for C", true);
if (verbose_)
{
std::cout << std::endl;
std::cout << "Total CPU time for construction (all included) = ";
std::cout << TotalCPUTime() << std::endl;
ML_print_line("=",78);
}
return(0);
}
