shared_ptr<Epetra_CrsMatrix> sparseCholesky(const Epetra_CrsMatrix &mat) {
// Note: we assume the matrix mat is symmetric and positive-definite
size_t size = mat.NumGlobalCols();
if (mat.NumGlobalRows() != size)
throw std::invalid_argument("sparseCholesky(): matrix must be square");
int *rowOffsets = 0;
int *colIndices = 0;
double *values = 0;
mat.ExtractCrsDataPointers(rowOffsets, colIndices, values);
Epetra_SerialComm comm;
Epetra_LocalMap rowMap(static_cast<int>(size), 0 /* index_base */, comm);
Epetra_LocalMap columnMap(static_cast<int>(size), 0 /* index_base */, comm);
shared_ptr<Epetra_CrsMatrix> result = boost::make_shared<Epetra_CrsMatrix>(
Copy, rowMap, columnMap, mat.GlobalMaxNumEntries());
arma::Mat<double> localMat;
arma::Mat<double> localCholesky;
std::vector<bool> processed(size, false);
for (size_t r = 0; r < size; ++r) {
if (processed[r])
continue;
int localSize = rowOffsets[r + 1] - rowOffsets[r];
localMat.set_size(localSize, localSize);
localMat.fill(0.);
localCholesky.set_size(localSize, localSize);
for (int s = 0; s < localSize; ++s) {
int row = colIndices[rowOffsets[r] + s];
for (int c = 0; c < localSize; ++c) {
int col = colIndices[rowOffsets[row] + c];
if (col != colIndices[rowOffsets[r] + c])
throw std::invalid_argument("sparseCholesky(): matrix is not "
"block-diagonal");
localMat(s, c) = values[rowOffsets[row] + c];
}
}
assert(arma::norm(localMat - localMat.t(), "fro") <
1e-12 * arma::norm(localMat, "fro"));
localCholesky = arma::chol(localMat); // localCholesky: U
for (int s = 0; s < localSize; ++s) {
int row = colIndices[rowOffsets[r] + s];
processed[row] = true;
#ifndef NDEBUG
int errorCode =
#endif
result->InsertGlobalValues(row, s + 1 /* number of values */,
localCholesky.colptr(s),
colIndices + rowOffsets[r]);
assert(errorCode == 0);
}
}
result->FillComplete(columnMap, rowMap);
return result;
}
bool CrsMatrixInfo( const Epetra_CrsMatrix & A,
ostream & os )
{
int MyPID = A.Comm().MyPID();
// take care that matrix is already trasformed
bool IndicesAreGlobal = A.IndicesAreGlobal();
if( IndicesAreGlobal == true ) {
if( MyPID == 0 ) {
os << "WARNING : matrix must be transformed to local\n";
os << " before calling CrsMatrixInfo\n";
os << " Now returning...\n";
}
return false;
}
int NumGlobalRows = A.NumGlobalRows();
int NumGlobalNonzeros = A.NumGlobalNonzeros();
int NumGlobalCols = A.NumGlobalCols();
double NormInf = A.NormInf();
double NormOne = A.NormOne();
int NumGlobalDiagonals = A.NumGlobalDiagonals();
int GlobalMaxNumEntries = A.GlobalMaxNumEntries();
int IndexBase = A.IndexBase();
bool StorageOptimized = A.StorageOptimized();
bool LowerTriangular = A.LowerTriangular();
bool UpperTriangular = A.UpperTriangular();
bool NoDiagonal = A.NoDiagonal();
// these variables identifies quantities I have to compute,
// since not provided by Epetra_CrsMatrix
double MyFrobeniusNorm( 0.0 ), FrobeniusNorm( 0.0 );
double MyMinElement( DBL_MAX ), MinElement( DBL_MAX );
double MyMaxElement( DBL_MIN ), MaxElement( DBL_MIN );
double MyMinAbsElement( DBL_MAX ), MinAbsElement( DBL_MAX );
double MyMaxAbsElement( 0.0 ), MaxAbsElement( 0.0 );
int NumMyRows = A.NumMyRows();
int * NzPerRow = new int[NumMyRows];
int Row; // iterator on rows
int Col; // iterator on cols
int MaxNumEntries = A.MaxNumEntries();
double * Values = new double[MaxNumEntries];
int * Indices = new int[MaxNumEntries];
double Element, AbsElement; // generic nonzero element and its abs value
int NumEntries;
double * Diagonal = new double [NumMyRows];
// SumOffDiagonal is the sum of absolute values for off-diagonals
double * SumOffDiagonal = new double [NumMyRows];
for( Row=0 ; Row<NumMyRows ; ++Row ) {
SumOffDiagonal[Row] = 0.0;
}
int * IsDiagonallyDominant = new int [NumMyRows];
int GlobalRow;
// cycle over all matrix elements
for( Row=0 ; Row<NumMyRows ; ++Row ) {
GlobalRow = A.GRID(Row);
NzPerRow[Row] = A.NumMyEntries(Row);
A.ExtractMyRowCopy(Row,NzPerRow[Row],NumEntries,Values,Indices);
for( Col=0 ; Col<NumEntries ; ++Col ) {
Element = Values[Col];
AbsElement = abs(Element);
if( Element<MyMinElement ) MyMinElement = Element;
if( Element>MyMaxElement ) MyMaxElement = Element;
if( AbsElement<MyMinAbsElement ) MyMinAbsElement = AbsElement;
if( AbsElement>MyMaxAbsElement ) MyMaxAbsElement = AbsElement;
if( Indices[Col] == Row ) Diagonal[Row] = Element;
else
SumOffDiagonal[Row] += abs(Element);
MyFrobeniusNorm += pow(Element,2);
}
}
// analise storage per row
int MyMinNzPerRow( NumMyRows ), MinNzPerRow( NumMyRows );
int MyMaxNzPerRow( 0 ), MaxNzPerRow( 0 );
for( Row=0 ; Row<NumMyRows ; ++Row ) {
if( NzPerRow[Row]<MyMinNzPerRow ) MyMinNzPerRow=NzPerRow[Row];
if( NzPerRow[Row]>MyMaxNzPerRow ) MyMaxNzPerRow=NzPerRow[Row];
}
// a test to see if matrix is diagonally-dominant
int MyDiagonalDominance( 0 ), DiagonalDominance( 0 );
int MyWeakDiagonalDominance( 0 ), WeakDiagonalDominance( 0 );
for( Row=0 ; Row<NumMyRows ; ++Row ) {
if( abs(Diagonal[Row])>SumOffDiagonal[Row] )
++MyDiagonalDominance;
else if( abs(Diagonal[Row])==SumOffDiagonal[Row] )
++MyWeakDiagonalDominance;
}
// reduction operations
A.Comm().SumAll(&MyFrobeniusNorm, &FrobeniusNorm, 1);
A.Comm().MinAll(&MyMinElement, &MinElement, 1);
A.Comm().MaxAll(&MyMaxElement, &MaxElement, 1);
A.Comm().MinAll(&MyMinAbsElement, &MinAbsElement, 1);
A.Comm().MaxAll(&MyMaxAbsElement, &MaxAbsElement, 1);
A.Comm().MinAll(&MyMinNzPerRow, &MinNzPerRow, 1);
A.Comm().MaxAll(&MyMaxNzPerRow, &MaxNzPerRow, 1);
A.Comm().SumAll(&MyDiagonalDominance, &DiagonalDominance, 1);
A.Comm().SumAll(&MyWeakDiagonalDominance, &WeakDiagonalDominance, 1);
// free memory
delete Values;
delete Indices;
delete Diagonal;
delete SumOffDiagonal;
delete IsDiagonallyDominant;
delete NzPerRow;
// simply no output for MyPID>0, only proc 0 write on os
if( MyPID != 0 ) return true;
os << "*** general Information about the matrix\n";
os << "Number of Global Rows = " << NumGlobalRows << endl;
os << "Number of Global Cols = " << NumGlobalCols << endl;
os << "is the matrix square = " <<
((NumGlobalRows==NumGlobalCols)?"yes":"no") << endl;
os << "||A||_\\infty = " << NormInf << endl;
os << "||A||_1 = " << NormOne << endl;
os << "||A||_F = " << sqrt(FrobeniusNorm) << endl;
os << "Number of nonzero diagonal entries = "
<< NumGlobalDiagonals
<< "( " << 1.0* NumGlobalDiagonals/NumGlobalRows*100
<< " %)\n";
os << "Nonzero per row : min = " << MinNzPerRow
<< " average = " << 1.0*NumGlobalNonzeros/NumGlobalRows
<< " max = " << MaxNzPerRow << endl;
os << "Maximum number of nonzero elements/row = "
<< GlobalMaxNumEntries << endl;
os << "min( a_{i,j} ) = " << MinElement << endl;
os << "max( a_{i,j} ) = " << MaxElement << endl;
os << "min( abs(a_{i,j}) ) = " << MinAbsElement << endl;
os << "max( abs(a_{i,j}) ) = " << MaxAbsElement << endl;
os << "Number of diagonal dominant rows = " << DiagonalDominance
<< " (" << 100.0*DiagonalDominance/NumGlobalRows << " % of total)\n";
os << "Number of weakly diagonal dominant rows = "
<< WeakDiagonalDominance
<< " (" << 100.0*WeakDiagonalDominance/NumGlobalRows << " % of total)\n";
os << "*** Information about the Trilinos storage\n";
os << "Base Index = " << IndexBase << endl;
os << "is storage optimized = "
<< ((StorageOptimized==true)?"yes":"no") << endl;
os << "are indices global = "
<< ((IndicesAreGlobal==true)?"yes":"no") << endl;
os << "is matrix lower triangular = "
<< ((LowerTriangular==true)?"yes":"no") << endl;
os << "is matrix upper triangular = "
<< ((UpperTriangular==true)?"yes":"no") << endl;
os << "are there diagonal entries = "
<< ((NoDiagonal==false)?"yes":"no") << endl;
return true;
}
// rebuild a single subblock Epetra_CrsMatrix
void rebuildSubBlock(int i,int j,const Epetra_CrsMatrix & A,const std::vector<std::pair<int,RCP<Epetra_Map> > > & subMaps,Epetra_CrsMatrix & mat)
{
// get the number of variables families
int numVarFamily = subMaps.size();
TEUCHOS_ASSERT(i>=0 && i<numVarFamily);
TEUCHOS_ASSERT(j>=0 && j<numVarFamily);
TEUCHOS_ASSERT(mat.Filled());
const Epetra_Map & gRowMap = *subMaps[i].second;
const Epetra_Map & rowMap = *Teuchos::get_extra_data<RCP<Epetra_Map> >(subMaps[i].second,"contigMap");
int colFamilyCnt = subMaps[j].first;
// compute the number of global variables
// and the row and column block offset
int numGlobalVars = 0;
int rowBlockOffset = 0;
int colBlockOffset = 0;
for(int k=0;k<numVarFamily;k++) {
numGlobalVars += subMaps[k].first;
// compute block offsets
if(k<i) rowBlockOffset += subMaps[k].first;
if(k<j) colBlockOffset += subMaps[k].first;
}
// copy all global rows to here
Epetra_Import import(gRowMap,A.RowMap());
Epetra_CrsMatrix localA(Copy,gRowMap,0);
localA.Import(A,import,Insert);
// clear out the old matrix
mat.PutScalar(0.0);
// get entry information
int numMyRows = rowMap.NumMyElements();
int maxNumEntries = A.GlobalMaxNumEntries();
// for extraction
std::vector<int> indices(maxNumEntries);
std::vector<double> values(maxNumEntries);
// for insertion
std::vector<int> colIndices(maxNumEntries);
std::vector<double> colValues(maxNumEntries);
// insert each row into subblock
// let FillComplete handle column distribution
for(int localRow=0;localRow<numMyRows;localRow++) {
int numEntries = -1;
int globalRow = gRowMap.GID(localRow);
int contigRow = rowMap.GID(localRow);
TEUCHOS_ASSERT(globalRow>=0);
TEUCHOS_ASSERT(contigRow>=0);
// extract a global row copy
int err = localA.ExtractGlobalRowCopy(globalRow, maxNumEntries, numEntries, &values[0], &indices[0]);
TEUCHOS_ASSERT(err==0);
int numOwnedCols = 0;
for(int localCol=0;localCol<numEntries;localCol++) {
int globalCol = indices[localCol];
// determinate which block this column ID is in
int block = globalCol / numGlobalVars;
bool inFamily = true;
// test the beginning of the block
inFamily &= (block*numGlobalVars+colBlockOffset <= globalCol);
inFamily &= ((block*numGlobalVars+colBlockOffset+colFamilyCnt) > globalCol);
// is this column in the variable family
if(inFamily) {
int familyOffset = globalCol-(block*numGlobalVars+colBlockOffset);
colIndices[numOwnedCols] = block*colFamilyCnt + familyOffset;
colValues[numOwnedCols] = values[localCol];
numOwnedCols++;
}
}
// insert it into the new matrix
mat.SumIntoGlobalValues(contigRow,numOwnedCols,&colValues[0],&colIndices[0]);
}
}
// int
// main(int argc, char * argv[])
TEUCHOS_UNIT_TEST(tALOperator, test)
{
// Build communicator
#ifdef HAVE_MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
// Get process information
int myPID = Comm.MyPID();
out << "MPI_PID = " << myPID << ", UNIX_PID = " << getpid() << std::endl;
// Maps.
int dim = 2, numVel = 3, numPre = 2, errCode;
Epetra_Map mapVel(numVel, 0, Comm), mapPre(numPre, 0, Comm);
Epetra_Map mapAll(numVel * dim + numPre, 0, Comm);
// Reorder.
std::vector<int> reorderedVec;
int numMyLen = mapVel.NumMyElements();
int * myGlb;
myGlb = mapVel.MyGlobalElements();
for(int i = 0; i < dim; i++)
for(int j = 0; j < numMyLen; j++)
reorderedVec.push_back(myGlb[j] + numVel * i);
numMyLen = mapPre.NumMyElements();
myGlb = mapPre.MyGlobalElements();
for(int j = 0; j < numMyLen; j++)
reorderedVec.push_back(myGlb[j] + numVel * dim);
Teuchos::RCP < Epetra_Map > mapReorder = Teuchos::rcp(
new Epetra_Map(-1, reorderedVec.size(), &reorderedVec[0], 0, Comm));
Teuchos::RCP < Epetra_Import > importReorder = Teuchos::rcp(new Epetra_Import(*mapReorder, mapAll));
std::vector<std::vector<int> > blockedVec;
numMyLen = mapVel.NumMyElements();
myGlb = mapVel.MyGlobalElements();
for(int i = 0; i < dim; i++)
{
reorderedVec.clear();
for(int j = 0; j < numMyLen; j++)
reorderedVec.push_back(myGlb[j] + numVel * i);
blockedVec.push_back(reorderedVec);
}
numMyLen = mapPre.NumMyElements();
myGlb = mapPre.MyGlobalElements();
reorderedVec.clear();
for(int j = 0; j < numMyLen; j++)
reorderedVec.push_back(myGlb[j] + numVel * dim);
blockedVec.push_back(reorderedVec);
// Read matrices and vector.
Epetra_CrsMatrix *ptrMat = 0, *ptrMp = 0;
TEUCHOS_ASSERT(EpetraExt::MatrixMarketFileToCrsMatrix("data/tOpMat.mm", mapAll, ptrMat)==0);
TEUCHOS_ASSERT(EpetraExt::MatrixMarketFileToCrsMatrix("data/tOpMp.mm", mapPre, ptrMp)==0);
LinearOp lpMp = Thyra::epetraLinearOp(Teuchos::rcpFromRef(*ptrMp));
// This vector is computed by Matlab for comparison.
Epetra_Vector *ptrExact = 0;
TEUCHOS_ASSERT(EpetraExt::MatrixMarketFileToVector("data/tOpRhs.mm", mapAll, ptrExact)==0);
// Reorder matrix.
RCP < Epetra_CrsMatrix > mat = Teuchos::rcp(new Epetra_CrsMatrix(Copy, *mapReorder, ptrMat->GlobalMaxNumEntries()));
errCode = mat->Import(*ptrMat, *importReorder, Insert);
errCode = mat->FillComplete();
// Build augmented Lagrangian-based operator.
Teko::NS::ALOperator al(blockedVec, mat, lpMp);
// Initialize vectors.
Epetra_Vector x(*mapReorder, false), b(*mapReorder, false);
x.PutScalar(1.0);
b.PutScalar(0.0);
// Apply operator.
al.Apply(x, b);
// Compare computed vector and exact vector.
b.Update(-1.0, *ptrExact, 1.0);
double norm2;
b.Norm2(&norm2);
if(norm2 < 1.0e-15)
{
out << "Test:ALOperator: Passed." << std::endl;
errCode = 0;
}
else
{
out << "Test:ALOperator: Failed." << std::endl;
errCode = -1;
}
delete ptrMat;
delete ptrMp;
delete ptrExact;
TEST_ASSERT(errCode==0);
}
