int Epetra_PETScAIJMatrix::Multiply(bool TransA,
const Epetra_MultiVector& X,
Epetra_MultiVector& Y) const
{
(void)TransA;
int NumVectors = X.NumVectors();
if (NumVectors!=Y.NumVectors()) EPETRA_CHK_ERR(-1); // X and Y must have same number of vectors
double ** xptrs;
double ** yptrs;
X.ExtractView(&xptrs);
Y.ExtractView(&yptrs);
if (RowMatrixImporter()!=0) {
if (ImportVector_!=0) {
if (ImportVector_->NumVectors()!=NumVectors) { delete ImportVector_; ImportVector_= 0;}
}
if (ImportVector_==0) ImportVector_ = new Epetra_MultiVector(RowMatrixColMap(),NumVectors);
ImportVector_->Import(X, *RowMatrixImporter(), Insert);
ImportVector_->ExtractView(&xptrs);
}
double *vals=0;
int length;
Vec petscX, petscY;
int ierr;
for (int i=0; i<NumVectors; i++) {
# ifdef HAVE_MPI
ierr=VecCreateMPIWithArray(Comm_->Comm(),X.MyLength(),X.GlobalLength(),xptrs[i],&petscX); CHKERRQ(ierr);
ierr=VecCreateMPIWithArray(Comm_->Comm(),Y.MyLength(),Y.GlobalLength(),yptrs[i],&petscY); CHKERRQ(ierr);
# else //FIXME untested
ierr=VecCreateSeqWithArray(Comm_->Comm(),X.MyLength(),X.GlobalLength(),xptrs[i],&petscX); CHKERRQ(ierr);
ierr=VecCreateSeqWithArray(Comm_->Comm(),Y.MyLength(),Y.GlobalLength(),yptrs[i],&petscY); CHKERRQ(ierr);
# endif
ierr = MatMult(Amat_,petscX,petscY);CHKERRQ(ierr);
ierr = VecGetArray(petscY,&vals);CHKERRQ(ierr);
ierr = VecGetLocalSize(petscY,&length);CHKERRQ(ierr);
for (int j=0; j<length; j++) yptrs[i][j] = vals[j];
ierr = VecRestoreArray(petscY,&vals);CHKERRQ(ierr);
}
VecDestroy(petscX); VecDestroy(petscY);
double flops = NumGlobalNonzeros();
flops *= 2.0;
flops *= (double) NumVectors;
UpdateFlops(flops);
return(0);
} //Multiply()
int writeMultiVector(FILE * handle, const Epetra_MultiVector & A, bool mmFormat) {
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;
for (int j=0; j<numVectors; j++) {
for (int i=0; i<length; i++) {
double val = A[j][i];
if (mmFormat)
fprintf(handle, "%22.16e\n", val);
else
fprintf(handle, "%22.16e ", val);
}
if (!mmFormat) fprintf(handle, "%s", "\n");
}
}
int ierrGlobal;
comm.MinAll(&ierr, &ierrGlobal, 1); // If any processor has -1, all return -1
return(ierrGlobal);
}
// =============================================================================
void
VIO::EpetraMesh::Writer::
setValues( const Epetra_MultiVector & x,
const Teuchos::Array<std::string> & scalarsNames
)
{
unsigned int numVecs = x.NumVectors();
unsigned int numVariables = x.GlobalLength();
unsigned int numNodes = mesh_->getNodesMap()->NumGlobalElements();
// make sure the sizes match the mesh
if ( !mesh_.is_null() )
TEUCHOS_ASSERT_EQUALITY( numVariables, 2*numNodes );
// cast into a vtkUnstructuredGrid
vtkSmartPointer<vtkUnstructuredGrid> vtkMesh =
dynamic_cast<vtkUnstructuredGrid*> ( vtkDataSet_.GetPointer() );
TEUCHOS_ASSERT_INEQUALITY( 0, !=, vtkMesh );
// get scalarsNames, and insert default names if empty
Teuchos::Array<std::string> scNames ( scalarsNames );
if ( scNames.empty() )
{
scNames.resize ( numVecs );
for ( int vec=0; vec<numVecs; vec++ )
scNames[vec] = "x" + EpetraExt::toString ( vec );
}
// fill the scalar field
vtkSmartPointer<vtkDoubleArray> scalars =
vtkSmartPointer<vtkDoubleArray>::New();
// real and imaginary part
scalars->SetNumberOfComponents ( 2 );
for ( int vec=0; vec<numVecs; vec++ )
{
scalars->SetName ( scNames[vec].c_str() );
for ( int k=0; k<numNodes; k++ )
{
// const unsigned int dof_id = libmeshMesh_->node(k).dof_number(0,k,0);
scalars->InsertNextValue ( x[vec][2*k] );
scalars->InsertNextValue ( x[vec][2*k+1] );
}
vtkMesh->GetPointData()->AddArray ( scalars );
}
return;
}
// Convert a Epetra_MultiVector with assumed block structure dictated by the
// vector space into a Thyra::MultiVectorBase object.
// const Teuchos::RCP<const Thyra::MultiVectorBase<double> > blockEpetraToThyra(const Epetra_MultiVector & e,const Teuchos::RCP<const Thyra::VectorSpaceBase<double> > & vs)
void blockEpetraToThyra(const Epetra_MultiVector & epetraX,const Teuchos::Ptr<Thyra::MultiVectorBase<double> > & thyraX)
{
TEUCHOS_ASSERT(thyraX->range()->dim()==epetraX.GlobalLength());
// extract local information from the Epetra_MultiVector
int leadingDim=0,numVectors=0,localDim=0;
double * epetraData=0;
epetraX.ExtractView(&epetraData,&leadingDim);
numVectors = epetraX.NumVectors();
blockEpetraToThyra(numVectors,epetraData,leadingDim,thyraX.ptr(),localDim);
TEUCHOS_ASSERT(localDim==epetraX.MyLength());
}
// ============================================================================
void EpetraExt::XMLWriter::
Write(const std::string& Label, const Epetra_MultiVector& MultiVector)
{
TEUCHOS_TEST_FOR_EXCEPTION(IsOpen_ == false, std::logic_error,
"No file has been opened");
int Length = MultiVector.GlobalLength();
int NumVectors = MultiVector.NumVectors();
if (Comm_.MyPID() == 0)
{
std::ofstream of(FileName_.c_str(), std::ios::app);
of << "<MultiVector Label=\"" << Label
<< "\" Length=\"" << Length << '"'
<< " NumVectors=\"" << NumVectors << '"'
<< " Type=\"double\">" << std::endl;
}
for (int iproc = 0; iproc < Comm_.NumProc(); iproc++)
{
if (iproc == Comm_.MyPID())
{
std::ofstream of(FileName_.c_str(), std::ios::app);
of.precision(15);
for (int i = 0; i < MultiVector.MyLength(); ++i)
{
for (int j = 0; j < NumVectors; ++j)
of << std::setiosflags(std::ios::scientific) << MultiVector[j][i] << " ";
of << std::endl;
}
of.close();
}
Comm_.Barrier();
}
if (Comm_.MyPID() == 0)
{
std::ofstream of(FileName_.c_str(), std::ios::app);
of << "</MultiVector>" << std::endl;
of.close();
}
}
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);
}
// Convert a Thyra::MultiVectorBase object to a Epetra_MultiVector object with
// the map defined by the Epetra_Map.
// const Teuchos::RCP<const Epetra_MultiVector>
// blockThyraToEpetra(const Teuchos::RCP<const Thyra::MultiVectorBase<double> > & tX,const RCP<const Epetra_Map> & map)
void blockThyraToEpetra(const Teuchos::RCP<const Thyra::MultiVectorBase<double> > & thyraX,Epetra_MultiVector & epetraX)
{
// build an Epetra_MultiVector object
int numVectors = thyraX->domain()->dim();
// make sure the number of vectors are the same
TEUCHOS_ASSERT(numVectors==epetraX.NumVectors());
TEUCHOS_ASSERT(thyraX->range()->dim()==epetraX.GlobalLength());
// extract local information from the Epetra_MultiVector
int leadingDim=0,localDim=0;
double * epetraData=0;
epetraX.ExtractView(&epetraData,&leadingDim);
// perform recursive copy
blockThyraToEpetra(numVectors,epetraData,leadingDim,thyraX,localDim);
// sanity check
TEUCHOS_ASSERT(localDim==epetraX.Map().NumMyElements());
}
int MultiVectorToMatrixMarketFile( const char *filename, const Epetra_MultiVector & A,
const char * matrixName,
const char *matrixDescription,
bool writeHeader) {
int M = A.GlobalLength();
int N = A.NumVectors();
FILE * handle = 0;
if (A.Map().Comm().MyPID()==0) { // Only PE 0 does this section
handle = fopen(filename,"w");
if (!handle) return(-1);
MM_typecode matcode;
mm_initialize_typecode(&matcode);
mm_set_matrix(&matcode);
mm_set_array(&matcode);
mm_set_real(&matcode);
if (writeHeader==true) { // Only write header if requested (true by default)
if (mm_write_banner(handle, matcode)) return(-1);
if (matrixName!=0) fprintf(handle, "%% \n%% %s\n", matrixName);
if (matrixDescription!=0) fprintf(handle, "%% %s\n%% \n", matrixDescription);
if (mm_write_mtx_array_size(handle, M, N)) return(-1);
}
}
if (MultiVectorToMatrixMarketHandle(handle, A)) return(-1); // Everybody calls this routine
if (A.Map().Comm().MyPID()==0) // Only PE 0 opened a file
if (fclose(handle)) return(-1);
return(0);
}
int main(int argc, char** argv) {
int fail = 0, dim=0;
#ifdef HAVE_MPI
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &localProc);
MPI_Comm_size(MPI_COMM_WORLD, &numProcs);
const Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
const Epetra_SerialComm Comm;
#endif
// =============================================================
// get command line options
// =============================================================
Teuchos::CommandLineProcessor clp(false,true);
std::string *inputFile = new std::string("simple.coords");
bool verbose = false;
clp.setOption( "f", inputFile, "Name of coordinate input file");
clp.setOption( "v", "q", &verbose,
"Display coordinates and weights before and after partitioning.");
Teuchos::CommandLineProcessor::EParseCommandLineReturn parse_return =
clp.parse(argc,argv);
if( parse_return == Teuchos::CommandLineProcessor::PARSE_HELP_PRINTED){
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}
if( parse_return != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL ) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 1;
}
// =============================================================
// Open file of coordinates and distribute them across processes
// so they are unbalanced.
// =============================================================
Epetra_MultiVector *mv = ispatest::file2multivector(Comm, *inputFile);
if (!mv || ((dim = mv->NumVectors()) < 1)){
if (localProc == 0)
std::cerr << "Invalid input file " << *inputFile << std::endl;
exit(1);
}
if (localProc == 0){
std::cerr << "Found input file " << *inputFile << ", " ;
std::cerr << dim << " dimensional coordinates" << std::endl;
}
delete inputFile;
int base = mv->Map().IndexBase();
int globalSize = mv->GlobalLength();
int myShare = 0;
int n = numProcs - 1;
if (n){
if (localProc < n){
int oneShare = globalSize / n;
int leftOver = globalSize - (n * oneShare);
myShare = oneShare + ((localProc < leftOver) ? 1 : 0);
}
}
else{
myShare = globalSize;
}
Epetra_BlockMap unbalancedMap(globalSize, myShare, 1, base, mv->Map().Comm());
Epetra_Import importer(unbalancedMap, mv->Map());
Epetra_MultiVector umv(unbalancedMap, dim);
umv.Import(*mv, importer, Insert);
delete mv;
Teuchos::RCP<const Epetra_MultiVector> coords =
Teuchos::rcp(new const Epetra_MultiVector(umv));
// =============================================================
// Create some different coordinate weight vectors
// =============================================================
Epetra_MultiVector *unitWgts = ispatest::makeWeights(coords->Map(), &ispatest::unitWeights);
Epetra_MultiVector *veeWgts = ispatest::makeWeights(coords->Map(), &ispatest::veeWeights);
Epetra_MultiVector *altWgts = ispatest::makeWeights(coords->Map(), &ispatest::alternateWeights);
Teuchos::RCP<const Epetra_MultiVector> unit_weights_rcp = Teuchos::rcp(unitWgts);
Teuchos::RCP<const Epetra_MultiVector> vee_weights_rcp = Teuchos::rcp(veeWgts);
Teuchos::RCP<const Epetra_MultiVector> alt_weights_rcp = Teuchos::rcp(altWgts);
if (localProc == 0){
std::cerr << "Unit weights: Each object has weight 1.0" << std::endl;
std::cerr << "V weights: Low and high GIDs have high weights, center GIDs have low weights" << std::endl;
std::cerr << "Alternate weights: Objects on even rank processes have one weight, on odd another weight" << std::endl;
std::cerr << std::endl;
}
// ======================================================================
// Create a parameter list for Zoltan, and one for internal partitioning
// ======================================================================
Teuchos::ParameterList internalParams;
internalParams.set("PARTITIONING_METHOD", "SIMPLE_LINEAR");
Teuchos::ParameterList zoltanParams;
Teuchos::ParameterList sublist = zoltanParams.sublist("ZOLTAN");
//sublist.set("DEBUG_LEVEL", "1"); // Zoltan will print out parameters
//sublist.set("DEBUG_LEVEL", "5"); // proc 0 will trace Zoltan calls
//sublist.set("DEBUG_MEMORY", "2"); // Zoltan will trace alloc & free
// =============================================================
// Run some tests
// =============================================================
zoltanParams.set("PARTITIONING METHOD", "RCB");
if (localProc == 0){
std::cerr << "RCB - unit weights" << std::endl;
}
fail = run_test(coords, unit_weights_rcp, zoltanParams);
if (fail) goto failure;
if (localProc == 0){
std::cerr << "PASS" << std::endl << std::endl;
}
// *************************************************************
if (localProc == 0){
std::cerr << "HSFC - V weights" << std::endl;
}
zoltanParams.set("PARTITIONING METHOD", "HSFC");
fail = run_test(coords, vee_weights_rcp, zoltanParams);
if (fail) goto failure;
if (localProc == 0){
std::cerr << "PASS" << std::endl << std::endl;
}
// *************************************************************
if (localProc == 0){
std::cerr << "RIB - alternate weights" << std::endl;
}
zoltanParams.set("PARTITIONING METHOD", "RIB");
fail = run_test(coords, alt_weights_rcp, zoltanParams);
if (fail) goto failure;
if (localProc == 0){
std::cerr << "PASS" << std::endl << std::endl;
}
// *************************************************************
if (localProc == 0){
std::cerr << "RIB - no weights supplied" << std::endl;
}
zoltanParams.set("PARTITIONING METHOD", "RIB");
fail = run_test(coords, zoltanParams);
if (fail) goto failure;
if (localProc == 0){
std::cerr << "PASS" << std::endl << std::endl;
}
// *************************************************************
goto done;
failure:
if (localProc == 0){
std::cerr << "FAIL: test failed" << std::endl;
}
done:
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return fail;
}
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 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 BuildMatrixTests (Epetra_MultiVector & C,
const char TransA, const char TransB,
const double alpha,
Epetra_MultiVector& A,
Epetra_MultiVector& B,
const double beta,
Epetra_MultiVector& C_GEMM ) {
// For given values of TransA, TransB, alpha and beta, a (possibly
// zero) filled Epetra_MultiVector C, and allocated
// Epetra_MultiVectors A, B and C_GEMM this routine will generate values for
// Epetra_MultiVectors A, B and C_GEMM such that, if A, B and (this) are
// used with GEMM in this class, the results should match the results
// generated by this routine.
// Test for Strided multivectors (required for GEMM ops)
if (!A.ConstantStride() ||
!B.ConstantStride() ||
!C_GEMM.ConstantStride() ||
!C.ConstantStride()) return(-1); // Error
int i, j;
double fi, fj; // Used for casting loop variables to floats
// Get a view of the MultiVectors
double *Ap = 0;
double *Bp = 0;
double *Cp = 0;
double *C_GEMMp = 0;
int A_nrows = A.MyLength();
int A_ncols = A.NumVectors();
int B_nrows = B.MyLength();
int B_ncols = B.NumVectors();
int C_nrows = C.MyLength();
int C_ncols = C.NumVectors();
int A_Stride = 0;
int B_Stride = 0;
int C_Stride = 0;
int C_GEMM_Stride = 0;
A.ExtractView(&Ap, &A_Stride);
B.ExtractView(&Bp, &B_Stride);
C.ExtractView(&Cp, &C_Stride);
C_GEMM.ExtractView(&C_GEMMp, &C_GEMM_Stride);
// Define some useful constants
int opA_ncols = (TransA=='N') ? A.NumVectors() : A.MyLength();
int opB_nrows = (TransB=='N') ? B.MyLength() : B.NumVectors();
int C_global_inner_dim = (TransA=='N') ? A.NumVectors() : A.GlobalLength();
bool A_is_local = (!A.DistributedGlobal());
bool B_is_local = (!B.DistributedGlobal());
bool C_is_local = (!C.DistributedGlobal());
int A_IndexBase = A.Map().IndexBase();
int B_IndexBase = B.Map().IndexBase();
// Build two new maps that we can use for defining global equation indices below
Epetra_Map * A_Map = new Epetra_Map(-1, A_nrows, A_IndexBase, A.Map().Comm());
Epetra_Map * B_Map = new Epetra_Map(-1, B_nrows, B_IndexBase, B.Map().Comm());
int* A_MyGlobalElements = new int[A_nrows];
A_Map->MyGlobalElements(A_MyGlobalElements);
int* B_MyGlobalElements = new int[B_nrows];
B_Map->MyGlobalElements(B_MyGlobalElements);
// Check for compatible dimensions
if (C.MyLength() != C_nrows ||
opA_ncols != opB_nrows ||
C.NumVectors() != C_ncols ||
C.MyLength() != C_GEMM.MyLength() ||
C.NumVectors() != C_GEMM.NumVectors() ) {
delete A_Map;
delete B_Map;
delete [] A_MyGlobalElements;
delete [] B_MyGlobalElements;
return(-2); // Return error
}
bool Case1 = ( A_is_local && B_is_local && C_is_local); // Case 1 above
bool Case2 = (!A_is_local && !B_is_local && C_is_local && TransA=='T' );// Case 2
bool Case3 = (!A_is_local && B_is_local && !C_is_local && TransA=='N');// Case 3
// Test for meaningful cases
if (!(Case1 || Case2 || Case3)) {
delete A_Map;
delete B_Map;
delete [] A_MyGlobalElements;
delete [] B_MyGlobalElements;
return(-3); // Meaningless case
}
/* Fill A, B and C with values as follows:
If A_is_local is false:
A(i,j) = A_MyGlobalElements[i]*j, i=1,...,numLocalEquations, j=1,...,NumVectors
else
A(i,j) = i*j, i=1,...,numLocalEquations, j=1,...,NumVectors
If B_is_local is false:
B(i,j) = 1/(A_MyGlobalElements[i]*j), i=1,...,numLocalEquations, j=1,...,NumVectors
else
B(i,j) = 1/(i*j), i=1,...,numLocalEquations, j=1,...,NumVectors
In addition, scale each entry by GlobalLength for A and
1/GlobalLength for B--keeps the magnitude of entries in check
C_GEMM will depend on A_is_local and B_is_local. Three cases:
1) A_is_local true and B_is_local true:
C_GEMM will be local replicated and equal to A*B = i*NumVectors/j
2) A_is_local false and B_is_local false
C_GEMM will be local replicated = A(trans)*B(i,j) = i*numGlobalEquations/j
3) A_is_local false B_is_local true
C_GEMM will distributed global and equals A*B = A_MyGlobalElements[i]*NumVectors/j
*/
// Define a scalar to keep magnitude of entries reasonable
double sf = C_global_inner_dim;
double sfinv = 1.0/sf;
// Define A depending on A_is_local
if (A_is_local)
{
for (j = 0; j <A_ncols ; j++)
for (i = 0; i<A_nrows; i++)
{
fi = i+1; // Get float version of i and j, offset by 1.
fj = j+1;
Ap[i + A_Stride*j] = (fi*sfinv)*fj;
}
}
else
{
for (j = 0; j <A_ncols ; j++)
for (i = 0; i<A_nrows; i++)
{
fi = A_MyGlobalElements[i]+1; // Get float version of i and j, offset by 1.
fj = j+1;
Ap[i + A_Stride*j] = (fi*sfinv)*fj;
}
}
// Define B depending on TransB and B_is_local
if (B_is_local)
{
for (j = 0; j <B_ncols ; j++)
for (i = 0; i<B_nrows; i++)
{
fi = i+1; // Get float version of i and j, offset by 1.
fj = j+1;
Bp[i + B_Stride*j] = 1.0/((fi*sfinv)*fj);
}
}
else
{
for (j = 0; j <B_ncols ; j++)
for (i = 0; i<B_nrows; i++)
{
fi = B_MyGlobalElements[i]+1; // Get float version of i and j, offset by 1.
fj = j+1;
Bp[i + B_Stride*j] = 1.0/((fi*sfinv)*fj);
}
}
// Define C_GEMM depending on A_is_local and B_is_local. C_GEMM is also a
// function of alpha, beta, TransA, TransB:
// C_GEMM = alpha*A(TransA)*B(TransB) + beta*C_GEMM
if (Case1)
{
for (j = 0; j <C_ncols ; j++)
for (i = 0; i<C_nrows; i++)
{
// Get float version of i and j, offset by 1.
fi = (i+1)*C_global_inner_dim;
fj = j+1;
C_GEMMp[i + C_GEMM_Stride*j] = alpha * (fi/fj)
+ beta * Cp[i + C_Stride*j];
}
}
else if (Case2)
{
for (j = 0; j <C_ncols ; j++)
for (i = 0; i<C_nrows; i++)
{
// Get float version of i and j, offset by 1.
fi = (i+1)*C_global_inner_dim;
fj = j+1;
C_GEMMp[i + C_GEMM_Stride*j] = alpha * (fi/fj)
+ beta * Cp[i + C_Stride*j];
}
}
else
{
for (j = 0; j <C_ncols ; j++)
for (i = 0; i<C_nrows; i++)
{
// Get float version of i and j.
fi = (A_MyGlobalElements[i]+1)*C_global_inner_dim;
fj = j+1;
C_GEMMp[i + C_GEMM_Stride*j] = alpha * (fi/fj)
+ beta * Cp[i + C_Stride*j];
}
}
delete A_Map;
delete B_Map;
delete [] A_MyGlobalElements;
delete [] B_MyGlobalElements;
return(0);
}
int BuildMultiVectorTests (Epetra_MultiVector & C, const double alpha,
Epetra_MultiVector& A,
Epetra_MultiVector& sqrtA,
Epetra_MultiVector& B,
Epetra_MultiVector& C_alphaA,
Epetra_MultiVector& C_alphaAplusB,
Epetra_MultiVector& C_plusB,
double* const dotvec_AB,
double* const norm1_A,
double* const norm2_sqrtA,
double* const norminf_A,
double* const normw_A,
Epetra_MultiVector& Weights,
double* const minval_A,
double* const maxval_A,
double* const meanval_A ) {
// For given values alpha and a (possibly zero) filled
// Epetra_MultiVector (the this object), allocated double * arguments dotvec_AB,
// norm1_A, and norm2_A, and allocated Epetra_MultiVectors A, sqrtA,
// B, C_alpha, C_alphaAplusB and C_plusB, this method will generate values for
// Epetra_MultiVectors A, B and all of the additional arguments on
// the list above such that, if A, B and (this) are used with the methods in
// this class, the results should match the results generated by this routine.
// Specifically, the results in dotvec_AB should match those from a call to
// A.dotProd (B,dotvec). Similarly for other routines.
int i,j;
double fi, fj; // Used for casting loop variables to floats
// Define some useful constants
int A_nrows = A.MyLength();
int A_ncols = A.NumVectors();
int sqrtA_nrows = sqrtA.MyLength();
int sqrtA_ncols = sqrtA.NumVectors();
int B_nrows = B.MyLength();
int B_ncols = B.NumVectors();
double **Ap = 0;
double **sqrtAp = 0;
double **Bp = 0;
double **Cp = 0;
double **C_alphaAp = 0;
double **C_alphaAplusBp = 0;
double **C_plusBp = 0;
double **Weightsp = 0;
A.ExtractView(&Ap);
sqrtA.ExtractView(&sqrtAp);
B.ExtractView(&Bp);
C.ExtractView(&Cp);
C_alphaA.ExtractView(&C_alphaAp);
C_alphaAplusB.ExtractView(&C_alphaAplusBp);
C_plusB.ExtractView(&C_plusBp);
Weights.ExtractView(&Weightsp);
bool A_is_local = (A.MyLength() == A.GlobalLength());
bool B_is_local = (B.MyLength() == B.GlobalLength());
bool C_is_local = (C.MyLength() == C.GlobalLength());
int A_IndexBase = A.Map().IndexBase();
int B_IndexBase = B.Map().IndexBase();
// Build two new maps that we can use for defining global equation indices below
Epetra_Map * A_Map = new Epetra_Map(-1, A_nrows, A_IndexBase, A.Map().Comm());
Epetra_Map * B_Map = new Epetra_Map(-1, B_nrows, B_IndexBase, B.Map().Comm());
int* A_MyGlobalElements = new int[A_nrows];
A_Map->MyGlobalElements(A_MyGlobalElements);
int* B_MyGlobalElements = new int[B_nrows];
B_Map->MyGlobalElements(B_MyGlobalElements);
// Check for compatible dimensions
if (C.MyLength() != A_nrows ||
A_nrows != B_nrows ||
C.NumVectors() != A_ncols ||
A_ncols != B_ncols ||
sqrtA_nrows != A_nrows ||
sqrtA_ncols != A_ncols ||
C.MyLength() != C_alphaA.MyLength() ||
C.NumVectors() != C_alphaA.NumVectors() ||
C.MyLength() != C_alphaAplusB.MyLength() ||
C.NumVectors() != C_alphaAplusB.NumVectors() ||
C.MyLength() != C_plusB.MyLength() ||
C.NumVectors() != C_plusB.NumVectors() ) return(-2); // Return error
bool Case1 = ( A_is_local && B_is_local && C_is_local); // Case 1
bool Case2 = (!A_is_local && !B_is_local && !C_is_local);// Case 2
// Test for meaningful cases
if (!(Case1 || Case2)) return(-3); // Meaningless case
/* Fill A and B with values as follows:
If A_is_local is false:
A(i,j) = A_MyGlobalElements[i]*j, i=1,...,numLocalEquations, j=1,...,NumVectors
else
A(i,j) = i*j, i=1,...,numLocalEquations, j=1,...,NumVectors
If B_is_local is false:
B(i,j) = 1/(A_MyGlobalElements[i]*j), i=1,...,numLocalEquations, j=1,...,NumVectors
else
B(i,j) = 1/(i*j), i=1,...,numLocalEquations, j=1,...,NumVectors
In addition, scale each entry by GlobalLength for A and
1/GlobalLength for B--keeps the magnitude of entries in check
*/
//Define scale factor
double sf = A.GlobalLength();
double sfinv = 1.0/sf;
// Define A
if (A_is_local)
{
for (j = 0; j <A_ncols ; j++)
{
for (i = 0; i<A_nrows; i++)
{
fi = i+1; // Get float version of i and j, offset by 1.
fj = j+1;
Ap[j][i] = (fi*sfinv)*fj;
sqrtAp[j][i] = std::sqrt(Ap[j][i]);
}
}
}
else
{
for (j = 0; j <A_ncols ; j++)
{
for (i = 0; i<A_nrows; i++)
{
fi = A_MyGlobalElements[i]+1; // Get float version of i and j, offset by 1.
fj = j+1;
Ap[j][i] = (fi*sfinv)*fj;
sqrtAp[j][i] = std::sqrt(Ap[j][i]);
}
}
}
// Define B depending on TransB and B_is_local
if (B_is_local)
{
for (j = 0; j <B_ncols ; j++)
{
for (i = 0; i<B_nrows; i++)
{
fi = i+1; // Get float version of i and j, offset by 1.
fj = j+1;
Bp[j][i] = 1.0/((fi*sfinv)*fj);
}
}
}
else
{
for (j = 0; j <B_ncols ; j++)
{
for (i = 0; i<B_nrows; i++)
{
fi = B_MyGlobalElements[i]+1; // Get float version of i and j, offset by 1.
fj = j+1;
Bp[j][i] = 1.0/((fi*sfinv)*fj);
}
}
}
// Generate C_alphaA = alpha * A
for (j = 0; j <A_ncols ; j++)
for (i = 0; i<A_nrows; i++)
C_alphaAp[j][i] = alpha * Ap[j][i];
// Generate C_alphaA = alpha * A + B
for (j = 0; j <A_ncols ; j++)
for (i = 0; i<A_nrows; i++)
C_alphaAplusBp[j][i] = alpha * Ap[j][i] + Bp[j][i];
// Generate C_plusB = this + B
for (j = 0; j <A_ncols ; j++)
for (i = 0; i<A_nrows; i++)
C_plusBp[j][i] = Cp[j][i] + Bp[j][i];
// Generate dotvec_AB. Because B(i,j) = 1/A(i,j), dotvec[i] = C.GlobalLength()
for (i=0; i< A.NumVectors(); i++) dotvec_AB[i] = C.GlobalLength();
// For the next two results we want to be careful how we do arithmetic
// to avoid very large numbers.
// We are computing sfinv*(C.GlobalLength()*(C.GlobalLength()+1)/2)
double result = C.GlobalLength();
result *= sfinv;
result /= 2.0;
result *= (double)(C.GlobalLength()+1);
// Generate norm1_A. Can use formula for sum of first n integers.
for (i=0; i< A.NumVectors(); i++)
// m1_A[i] = (i+1)*C.GlobalLength()*(C.GlobalLength()+1)/2;
norm1_A[i] = result * ((double) (i+1));
// Generate norm2_sqrtA. Can use formula for sum of first n integers.
for (i=0; i< A.NumVectors(); i++)
// norm2_sqrtA[i] = std::sqrt((double) ((i+1)*C.GlobalLength()*(C.GlobalLength()+1)/2));
norm2_sqrtA[i] = std::sqrt(result * ((double) (i+1)));
// Generate norminf_A, minval_A, maxval_A, meanval_A.
for (i=0; i< A.NumVectors(); i++)
{
norminf_A[i] = (double) (i+1);
minval_A[i] = (double) (i+1)/ (double) A.GlobalLength();
maxval_A[i] = (double) (i+1);
meanval_A[i] = norm1_A[i]/((double) (A.GlobalLength()));
}
// Define weights and expected weighted norm
for (i=0; i< A.NumVectors(); i++)
{
double ip1 = (double) i+1;
normw_A[i] = ip1;
for (j=0; j<A_nrows; j++) Weightsp[i][j] = Ap[i][j]/ip1;
}
delete A_Map;
delete B_Map;
delete [] A_MyGlobalElements;
delete [] B_MyGlobalElements;
return(0);
}