double
do_time_teuchos_double_gemm(unsigned int m, unsigned int n, unsigned int k,
unsigned int nloop)
{
Sacado::Random<double> urand(0.0, 1.0);
Teuchos::BLAS<int,double> blas;
std::vector<double> A(m*k), B(k*n), C(m*n);
for (unsigned int j=0; j<k; j++)
for (unsigned int i=0; i<m; i++)
A[i+j*m] = urand.number();
for (unsigned int j=0; j<n; j++)
for (unsigned int i=0; i<k; i++)
B[i+j*k] = urand.number();
for (unsigned int j=0; j<n; j++)
for (unsigned int i=0; i<m; i++)
C[i+j*m] = urand.number();
double alpha = urand.number();
double beta = urand.number();
Teuchos::Time timer("Teuchos Double GEMM", false);
timer.start(true);
for (unsigned int j=0; j<nloop; j++) {
blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, m, n, k, alpha, &A[0], m,
&B[0], k, beta, &C[0], m);
}
timer.stop();
return timer.totalElapsedTime() / nloop;
}
static void
GEMM (const Teuchos::ETransp transA,
const Teuchos::ETransp transB,
const Scalar& alpha,
const View<const Scalar**, LayoutLeft, DeviceType>& A,
const View<const Scalar**, LayoutLeft, DeviceType>& B,
const Scalar& beta,
const View<Scalar**, LayoutLeft, DeviceType>& C)
{
const int n = static_cast<int> (C.dimension_1 ());
const int lda = static_cast<int> (Impl::getStride2DView (A));
Teuchos::BLAS<int,Scalar> blas;
// For some BLAS implementations (e.g., MKL), GEMM when B has
// one column may be signficantly less efficient than GEMV.
if (n == 1 && transB == Teuchos::NO_TRANS) {
blas.GEMV (transA, A.dimension_0 (), A.dimension_1 (),
alpha, A.ptr_on_device (), lda,
B.ptr_on_device (), static_cast<int> (1),
beta, C.ptr_on_device (), static_cast<int> (1));
}
else {
const int m = static_cast<int> (C.dimension_0 ());
const int k = static_cast<int> (transA == Teuchos::NO_TRANS ?
A.dimension_1 () : A.dimension_0 ());
const int ldb = static_cast<int> (Impl::getStride2DView (B));
const int ldc = static_cast<int> (Impl::getStride2DView (C));
blas.GEMM (transA, transB, m, n, k, alpha,
A.ptr_on_device(), lda,
B.ptr_on_device(), ldb,
beta, C.ptr_on_device(), ldc);
}
}
KOKKOS_INLINE_FUNCTION
int
Gemm<Trans::ConjTranspose,Trans::NoTranspose,
AlgoGemm::ExternalBlas,Variant::One>
::invoke(PolicyType &policy,
MemberType &member,
const ScalarType alpha,
DenseExecViewTypeA &A,
DenseExecViewTypeB &B,
const ScalarType beta,
DenseExecViewTypeC &C) {
// static_assert( Kokkos::Impl::is_same<
// typename DenseMatrixTypeA::space_type,
// typename DenseMatrixTypeB::space_type
// >::value &&
// Kokkos::Impl::is_same<
// typename DenseMatrixTypeB::space_type,
// typename DenseMatrixTypeC::space_type
// >::value,
// "Space type of input matrices does not match" );
if (member.team_rank() == 0) {
#if \
defined( HAVE_SHYLUTACHO_TEUCHOS ) && \
defined( KOKKOS_ACTIVE_EXECUTION_MEMORY_SPACE_HOST )
typedef typename DenseExecViewTypeA::ordinal_type ordinal_type;
typedef typename DenseExecViewTypeA::value_type value_type;
Teuchos::BLAS<ordinal_type,value_type> blas;
const ordinal_type m = C.NumRows();
const ordinal_type n = C.NumCols();
const ordinal_type k = B.NumRows();
if (m > 0 && n > 0 && k > 0)
blas.GEMM(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS,
m, n, k,
alpha,
A.ValuePtr(), A.BaseObject().ColStride(),
B.ValuePtr(), B.BaseObject().ColStride(),
beta,
C.ValuePtr(), C.BaseObject().ColStride());
#else
TACHO_TEST_FOR_ABORT( true, MSG_NOT_HAVE_PACKAGE("Teuchos") );
#endif
}
return 0;
}
double
do_time_teuchos_fad_gemm(unsigned int m, unsigned int n, unsigned int k,
unsigned int ndot, unsigned int nloop)
{
Sacado::Random<double> urand(0.0, 1.0);
Teuchos::BLAS<int,FadType> blas;
std::vector<FadType> A(m*k), B(k*n), C(m*n);
for (unsigned int j=0; j<k; j++) {
for (unsigned int i=0; i<m; i++) {
A[i+j*m] = FadType(ndot, urand.number());
for (unsigned int l=0; l<ndot; l++)
A[i+j*m].fastAccessDx(l) = urand.number();
}
}
for (unsigned int j=0; j<n; j++) {
for (unsigned int i=0; i<k; i++) {
B[i+j*k] = FadType(ndot, urand.number());
for (unsigned int l=0; l<ndot; l++)
B[i+j*k].fastAccessDx(l) = urand.number();
}
}
for (unsigned int j=0; j<n; j++) {
for (unsigned int i=0; i<m; i++) {
C[i+j*m] = FadType(ndot, urand.number());
for (unsigned int l=0; l<ndot; l++)
C[i+j*m].fastAccessDx(l) = urand.number();
}
}
FadType alpha(ndot, urand.number());
FadType beta(ndot, urand.number());
for (unsigned int l=0; l<ndot; l++) {
alpha.fastAccessDx(l) = urand.number();
beta.fastAccessDx(l) = urand.number();
}
Teuchos::Time timer("Teuchos Fad GEMM", false);
timer.start(true);
for (unsigned int j=0; j<nloop; j++) {
blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, m, n, k, alpha, &A[0], m,
&B[0], k, beta, &C[0], m);
}
timer.stop();
return timer.totalElapsedTime() / nloop;
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node, LocalMatOps>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
Ppattern_ = Ppattern;
const RCP<const Map> uniqueMap = Ppattern_->getDomainMap();
const RCP<const Map> nonUniqueMap = Ppattern_->getColMap();
RCP<const Import> importer = ImportFactory::Build(uniqueMap, nonUniqueMap);
const size_t NSDim = Bc.getNumVectors();
X_ = MultiVectorFactory::Build(nonUniqueMap, NSDim);
X_->doImport(Bc, *importer, Xpetra::INSERT);
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
Teuchos::SerialDenseVector<LO,SC> BcRow(NSDim, false);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false);
for (size_t j = 0; j < nnz; j++) {
for (size_t k = 0; k < NSDim; k++)
BcRow[k] = X_->getData(k)[indices[j]];
Teuchos::setCol(BcRow, (LO)j, locX);
}
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false);
Teuchos::BLAS<LO,SC> blas;
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
Teuchos::ScalarTraits<SC>::one(), locX.values(), locX.stride(),
locX.values(), locX.stride(), Teuchos::ScalarTraits<SC>::zero(),
XXtInv_[i].values(), XXtInv_[i].stride());
Teuchos::LAPACK<LO,SC> lapack;
LO info, lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
lapack.GETRF(NSDim, NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), &info);
lapack.GETRI(NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
static void
GEMM (const Teuchos::ETransp transA,
const Teuchos::ETransp transB,
const double& alpha,
const View<const double**, LayoutLeft, DeviceType>& A,
const View<const double**, LayoutLeft, DeviceType>& B,
const double& beta,
const View<double**, LayoutLeft, DeviceType>& C)
{
const int n = static_cast<int> (C.dimension_1 ());
// For some BLAS implementations (e.g., MKL), GEMM when B has
// one column may be signficantly less efficient than GEMV.
if (n == 1 && transB == Teuchos::NO_TRANS) {
char trans = 'N';
if (transA == Teuchos::TRANS) {
trans = 'T';
}
else if (transA == Teuchos::CONJ_TRANS) {
trans = 'C';
}
auto B_0 = Kokkos::subview (B, Kokkos::ALL (), 0);
auto C_0 = Kokkos::subview (C, Kokkos::ALL (), 0);
KokkosBlas::gemv (&trans, alpha, A, B_0, beta, C_0);
}
else {
const int m = static_cast<int> (C.dimension_0 ());
const int k = static_cast<int> (transA == Teuchos::NO_TRANS ? A.dimension_1 () : A.dimension_0 ());
const int lda = static_cast<int> (Impl::getStride2DView (A));
const int ldb = static_cast<int> (Impl::getStride2DView (B));
const int ldc = static_cast<int> (Impl::getStride2DView (C));
Teuchos::BLAS<int,double> blas;
blas.GEMM (transA, transB, m, n, k, alpha,
A.ptr_on_device(), lda,
B.ptr_on_device(), ldb,
beta, C.ptr_on_device(), ldc);
}
}
int main(int argc, char *argv[]) {
Kokkos::initialize();
//Check number of arguments
if (argc < 4) {
std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
std::cout <<"Usage:\n\n";
std::cout <<" ./Intrepid_example_Drivers_Example_06.exe deg NX NY verbose\n\n";
std::cout <<" where \n";
std::cout <<" int deg - polynomial degree to be used (assumed > 1) \n";
std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n";
std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n";
std::cout <<" verbose (optional) - any character, indicates verbose output \n\n";
exit(1);
}
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 2)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Example: Apply Stiffness Matrix for |\n" \
<< "| Poisson Equation on Quadrilateral Mesh |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
// ************************************ GET INPUTS **************************************
int deg = atoi(argv[1]); // polynomial degree to use
int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1)
int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1)
// *********************************** CELL TOPOLOGY **********************************
// Get cell topology for base hexahedron
typedef shards::CellTopology CellTopology;
CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
// Get dimensions
int numNodesPerElem = quad_4.getNodeCount();
int spaceDim = quad_4.getDimension();
// *********************************** GENERATE MESH ************************************
*outStream << "Generating mesh ... \n\n";
*outStream << " NX" << " NY\n";
*outStream << std::setw(5) << NX <<
std::setw(5) << NY << "\n\n";
// Print mesh information
int numElems = NX*NY;
int numNodes = (NX+1)*(NY+1);
*outStream << " Number of Elements: " << numElems << " \n";
*outStream << " Number of Nodes: " << numNodes << " \n\n";
// Square
double leftX = 0.0, rightX = 1.0;
double leftY = 0.0, rightY = 1.0;
// Mesh spacing
double hx = (rightX-leftX)/((double)NX);
double hy = (rightY-leftY)/((double)NY);
// Get nodal coordinates
FieldContainer<double> nodeCoord(numNodes, spaceDim);
FieldContainer<int> nodeOnBoundary(numNodes);
int inode = 0;
for (int j=0; j<NY+1; j++) {
for (int i=0; i<NX+1; i++) {
nodeCoord(inode,0) = leftX + (double)i*hx;
nodeCoord(inode,1) = leftY + (double)j*hy;
if (j==0 || i==0 || j==NY || i==NX){
nodeOnBoundary(inode)=1;
}
else {
nodeOnBoundary(inode)=0;
}
inode++;
}
}
#define DUMP_DATA
#ifdef DUMP_DATA
// Print nodal coords
ofstream fcoordout("coords.dat");
for (int i=0; i<numNodes; i++) {
fcoordout << nodeCoord(i,0) <<" ";
fcoordout << nodeCoord(i,1) <<"\n";
}
fcoordout.close();
#endif
// Element to Node map
// We'll keep it around, but this is only the DOFMap if you are in the lowest order case.
FieldContainer<int> elemToNode(numElems, numNodesPerElem);
int ielem = 0;
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
elemToNode(ielem,0) = (NX + 1)*j + i;
elemToNode(ielem,1) = (NX + 1)*j + i + 1;
elemToNode(ielem,2) = (NX + 1)*(j + 1) + i + 1;
elemToNode(ielem,3) = (NX + 1)*(j + 1) + i;
ielem++;
}
}
#ifdef DUMP_DATA
// Output connectivity
ofstream fe2nout("elem2node.dat");
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
int ielem = i + j * NX;
for (int m=0; m<numNodesPerElem; m++){
fe2nout << elemToNode(ielem,m) <<" ";
}
fe2nout <<"\n";
}
}
fe2nout.close();
#endif
// ************************************ CUBATURE **************************************
*outStream << "Getting cubature ... \n\n";
// Get numerical integration points and weights
DefaultCubatureFactory<double> cubFactory;
int cubDegree = 2*deg;
Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(quad_4, cubDegree);
int cubDim = quadCub->getDimension();
int numCubPoints = quadCub->getNumPoints();
FieldContainer<double> cubPoints(numCubPoints, cubDim);
FieldContainer<double> cubWeights(numCubPoints);
quadCub->getCubature(cubPoints, cubWeights);
// ************************************** BASIS ***************************************
*outStream << "Getting basis ... \n\n";
// Define basis
Basis_HGRAD_QUAD_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL);
int numFieldsG = quadHGradBasis.getCardinality();
FieldContainer<double> quadGVals(numFieldsG, numCubPoints);
FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim);
// Evaluate basis values and gradients at cubature points
quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE);
quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD);
// create the local-global mapping for higher order elements
FieldContainer<int> ltgMapping(numElems,numFieldsG);
const int numDOF = (NX*deg+1)*(NY*deg+1);
ielem=0;
for (int j=0;j<NY;j++) {
for (int i=0;i<NX;i++) {
const int start = deg * j * ( NX * deg + 1 ) + i * deg;
// loop over local dof on this cell
int local_dof_cur=0;
for (int vertical=0;vertical<=deg;vertical++) {
for (int horizontal=0;horizontal<=deg;horizontal++) {
ltgMapping(ielem,local_dof_cur) = start + vertical*(NX*deg+1)+horizontal;
local_dof_cur++;
}
}
ielem++;
}
}
#ifdef DUMP_DATA
// Output ltg mapping
// ofstream ltgout("ltg.dat");
// for (int j=0; j<NY; j++) {
// for (int i=0; i<NX; i++) {
// int ielem = i + j * NX;
// for (int m=0; m<numFieldsG; m++){
// ltgout << ltgMapping(ielem,m) <<" ";
// }
// ltgout <<"\n";
// }
// }
// ltgout.close();
#endif
// ******** CREATE A SINGLE STIFFNESS MATRIX, WHICH IS REPLICATED ON ALL ELEMENTS *********
*outStream << "Applying stiffness matrix and right hand side ... \n\n";
// Settings and data structures for mass and stiffness matrices
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = 1;
// Container for nodes
FieldContainer<double> refQuadNodes(numCells, numNodesPerElem, spaceDim);
// Containers for Jacobian
FieldContainer<double> refQuadJacobian(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> refQuadJacobInv(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> refQuadJacobDet(numCells, numCubPoints);
// Containers for element HGRAD stiffness matrix
FieldContainer<double> localStiffMatrix(numCells, numFieldsG, numFieldsG);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> quadGradsTransformed(numCells, numFieldsG, numCubPoints, spaceDim);
FieldContainer<double> quadGradsTransformedWeighted(numCells, numFieldsG, numCubPoints, spaceDim);
// Containers for right hand side vectors
FieldContainer<double> rhsData(numCells, numCubPoints);
FieldContainer<double> localRHS(numCells, numFieldsG);
FieldContainer<double> quadGValsTransformed(numCells, numFieldsG, numCubPoints);
FieldContainer<double> quadGValsTransformedWeighted(numCells, numFieldsG, numCubPoints);
// Container for cubature points in physical space
FieldContainer<double> physCubPoints(numCells, numCubPoints, cubDim);
// Global arrays in Epetra format
Epetra_SerialComm Comm;
Epetra_Map globalMapG(numDOF, 0, Comm);
Epetra_FEVector u(globalMapG);
Epetra_FEVector Ku(globalMapG);
u.Random();
std::cout << "About to start ref element matrix\n";
// ************************** Compute element HGrad stiffness matrices *******************************
refQuadNodes(0,0,0) = 0.0;
refQuadNodes(0,0,1) = 0.0;
refQuadNodes(0,1,0) = hx;
refQuadNodes(0,1,1) = 0.0;
refQuadNodes(0,2,0) = hx;
refQuadNodes(0,2,1) = hy;
refQuadNodes(0,3,0) = 0.0;
refQuadNodes(0,3,1) = hy;
// Compute cell Jacobians, their inverses and their determinants
CellTools::setJacobian(refQuadJacobian, cubPoints, refQuadNodes, quad_4);
CellTools::setJacobianInv(refQuadJacobInv, refQuadJacobian );
CellTools::setJacobianDet(refQuadJacobDet, refQuadJacobian );
// transform from [-1,1]^2 to [0,hx]x[0,hy]
fst::HGRADtransformGRAD<double>(quadGradsTransformed, refQuadJacobInv, quadGrads);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, refQuadJacobDet, cubWeights);
// multiply values with weighted measure
fst::multiplyMeasure<double>(quadGradsTransformedWeighted,
weightedMeasure, quadGradsTransformed);
// integrate to compute element stiffness matrix
fst::integrate<double>(localStiffMatrix,
quadGradsTransformed, quadGradsTransformedWeighted, COMP_BLAS);
std::cout << "Finished with reference element matrix\n";
// now we will scatter global degrees of freedom, apply the local stiffness matrix
// with BLAS, and then gather the results
FieldContainer<double> uScattered(numElems,numFieldsG);
FieldContainer<double> KuScattered(numElems,numFieldsG);
// to extract info from u
u.GlobalAssemble();
Epetra_Time multTimer(Comm);
Ku.PutScalar(0.0);
Ku.GlobalAssemble();
double *uVals = u[0];
double *KuVals = Ku[0];
Teuchos::BLAS<int,double> blas;
Epetra_Time scatterTime(Comm);
std::cout << "Scattering\n";
// Scatter
for (int k=0; k<numElems; k++)
{
for (int i=0;i<numFieldsG;i++)
{
uScattered(k,i) = uVals[ltgMapping(k,i)];
}
}
const double scatTime = scatterTime.ElapsedTime();
std::cout << "Scattered in time " << scatTime << "\n";
Epetra_Time blasTimer(Comm);
blas.GEMM(Teuchos::NO_TRANS , Teuchos::NO_TRANS ,
numFieldsG , numElems, numFieldsG ,
1.0 ,
&localStiffMatrix(0,0,0) ,
numFieldsG ,
&uScattered(0,0) ,
numFieldsG ,
0.0 ,
&KuScattered(0,0) ,
numFieldsG );
const double blasTime = blasTimer.ElapsedTime();
std::cout << "Element matrices applied in " << blasTime << "\n";
Epetra_Time gatherTimer(Comm);
// Gather
for (int k=0;k<numElems;k++)
{
for (int i=0;i<numFieldsG;i++)
{
KuVals[ltgMapping(k,i)] += KuScattered(k,i);
}
}
const double gatherTime = gatherTimer.ElapsedTime();
std::cout << "Gathered in " << gatherTime << "\n";
const double applyTime = gatherTime + blasTime + scatTime;
std::cout << "Time to do matrix-free product: " << applyTime << std::endl;
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return 0;
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
const size_t NSDim = Bc.getNumVectors();
Ppattern_ = Ppattern;
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
RCP<const Import> importer = Ppattern_->getImporter();
X_ = MultiVectorFactory::Build(Ppattern_->getColMap(), NSDim);
if (!importer.is_null())
X_->doImport(Bc, *importer, Xpetra::INSERT);
else
*X_ = Bc;
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
SC zero = Teuchos::ScalarTraits<SC>::zero();
SC one = Teuchos::ScalarTraits<SC>::one();
Teuchos::BLAS <LO,SC> blas;
Teuchos::LAPACK<LO,SC> lapack;
LO lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false/*zeroOut*/);
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
if (NSDim == 1) {
SC d = zero;
for (size_t j = 0; j < nnz; j++)
d += Xval[0][indices[j]] * Xval[0][indices[j]];
XXtInv(0,0) = one/d;
} else {
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false/*zeroOut*/);
for (size_t j = 0; j < nnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][indices[j]];
// XXtInv_ = (locX*locX^T)^{-1}
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
one, locX.values(), locX.stride(),
locX.values(), locX.stride(),
zero, XXtInv.values(), XXtInv.stride());
LO info;
// Compute LU factorization using partial pivoting with row exchanges
lapack.GETRF(NSDim, NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), &info);
// Use the computed factorization to compute the inverse
lapack.GETRI(NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
}
KOKKOS_INLINE_FUNCTION
int exampleDenseTrsmMKL(const OrdinalType mmin,
const OrdinalType mmax,
const OrdinalType minc,
const OrdinalType k,
const bool verbose) {
typedef ValueType value_type;
typedef OrdinalType ordinal_type;
typedef SizeType size_type;
typedef DenseMatrixBase<value_type,ordinal_type,size_type,SpaceType,MemoryTraits> DenseMatrixBaseType;
int r_val = 0;
Kokkos::Impl::Timer timer;
double t = 0.0;
cout << "DenseGemmMKL:: test matrices "
<<":: mmin = " << mmin << " , mmax = " << mmax << " , minc = " << minc << " , k = "<< k << endl;
ostringstream os;
os.precision(3);
os << scientific;
for (ordinal_type m=mmin;m<=mmax;m+=minc) {
os.str("");
DenseMatrixBaseType AA("AA", m, m), BB("BB", m, k), BC("BC", m, k);
// setup upper triangular
for (ordinal_type j=0;j<AA.NumCols();++j) {
AA.Value(j,j) = 10.0;
for (ordinal_type i=0;i<j;++i)
AA.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
}
// setup one and right hand side is going to be overwritten by the product of AB
for (ordinal_type j=0;j<BB.NumCols();++j)
for (ordinal_type i=0;i<BB.NumRows();++i)
BB.Value(i,j) = 1.0;
Teuchos::BLAS<ordinal_type,value_type> blas;
blas.GEMM(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS,
m, k, m,
1.0,
AA.ValuePtr(), AA.ColStride(),
BB.ValuePtr(), BB.ColStride(),
0.0,
BC.ValuePtr(), BC.ColStride());
BB.copy(BC);
const double flop = get_flop_trsm_upper<value_type>(m, k);
os << "DenseTrsmMKL:: m = " << m << " k = " << k;
{
timer.reset();
Teuchos::BLAS<ordinal_type,value_type> blas;
const ordinal_type mm = AA.NumRows();
const ordinal_type nn = BB.NumCols();
blas.TRSM(Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::CONJ_TRANS,
Teuchos::NON_UNIT_DIAG,
mm, nn,
1.0,
AA.ValuePtr(), AA.ColStride(),
BB.ValuePtr(), BB.ColStride());
t = timer.seconds();
os << ":: MKL Performance = " << (flop/t/1.0e9) << " [GFLOPs] ";
}
cout << os.str() << endl;
}
return r_val;
}
void
randomGlobalMatrix (Generator* const pGenerator,
MatrixViewType& A_local,
const typename Teuchos::ScalarTraits< typename MatrixViewType::scalar_type >::magnitudeType singular_values[],
MessengerBase< typename MatrixViewType::ordinal_type >* const ordinalMessenger,
MessengerBase< typename MatrixViewType::scalar_type >* const scalarMessenger)
{
using Teuchos::NO_TRANS;
using std::vector;
typedef typename MatrixViewType::ordinal_type ordinal_type;
typedef typename MatrixViewType::scalar_type scalar_type;
const bool b_local_debug = false;
const int rootProc = 0;
const int nprocs = ordinalMessenger->size();
const int myRank = ordinalMessenger->rank();
Teuchos::BLAS<ordinal_type, scalar_type> blas;
const ordinal_type nrowsLocal = A_local.nrows();
const ordinal_type ncols = A_local.ncols();
// Theory: Suppose there are P processors. Proc q wants an m_q by n
// component of the matrix A, which we write as A_q. On Proc 0, we
// generate random m_q by n orthogonal matrices Q_q (in explicit
// form), and send Q_q to Proc q. The m by n matrix [Q_0; Q_1; ...;
// Q_{P-1}] is not itself orthogonal. However, the m by n matrix
// Q = [Q_0 / P; Q_1 / P; ...; Q_{P-1} / P] is orthogonal:
//
// \sum_{q = 0}^{P-1} (Q_q^T * Q_q) / P = I.
if (myRank == rootProc)
{
typedef Random::MatrixGenerator< ordinal_type, scalar_type, Generator > matgen_type;
matgen_type matGen (*pGenerator);
// Generate a random ncols by ncols upper triangular matrix
// R with the given singular values.
Matrix< ordinal_type, scalar_type > R (ncols, ncols, scalar_type(0));
matGen.fill_random_R (ncols, R.get(), R.lda(), singular_values);
// Broadcast R to all the processors.
scalarMessenger->broadcast (R.get(), ncols*ncols, rootProc);
// Generate (for myself) a random nrowsLocal x ncols
// orthogonal matrix, stored in explicit form.
Matrix< ordinal_type, scalar_type > Q_local (nrowsLocal, ncols);
matGen.explicit_Q (nrowsLocal, ncols, Q_local.get(), Q_local.lda());
// Scale the (local) orthogonal matrix by the number of
// processors P, to make the columns of the global matrix Q
// orthogonal. (Otherwise the norm of each column will be P
// instead of 1.)
const scalar_type P = static_cast< scalar_type > (nprocs);
// Do overflow check. If casting P back to scalar_type
// doesn't produce the same value as nprocs, the cast
// overflowed. We take the real part, because scalar_type
// might be complex.
if (nprocs != static_cast<int> (Teuchos::ScalarTraits<scalar_type>::real (P)))
throw std::runtime_error ("Casting nprocs to Scalar failed");
scaleMatrix (Q_local, P);
// A_local := Q_local * R
blas.GEMM (NO_TRANS, NO_TRANS, nrowsLocal, ncols, ncols,
scalar_type(1), Q_local.get(), Q_local.lda(),
R.get(), R.lda(),
scalar_type(0), A_local.get(), A_local.lda());
for (int recvProc = 1; recvProc < nprocs; ++recvProc)
{
// Ask the receiving processor how big (i.e., how many rows)
// its local component of the matrix is.
ordinal_type nrowsRemote = 0;
ordinalMessenger->recv (&nrowsRemote, 1, recvProc, 0);
if (b_local_debug)
{
std::ostringstream os;
os << "For Proc " << recvProc << ": local block is "
<< nrowsRemote << " by " << ncols << std::endl;
std::cerr << os.str();
}
// Make sure Q_local is big enough to hold the data for
// the current receiver proc.
Q_local.reshape (nrowsRemote, ncols);
// Compute a random nrowsRemote * ncols orthogonal
// matrix Q_local, for the current receiving processor.
matGen.explicit_Q (nrowsRemote, ncols, Q_local.get(), Q_local.lda());
// Send Q_local to the current receiving processor.
scalarMessenger->send (Q_local.get(), nrowsRemote*ncols, recvProc, 0);
}
}
else
{
// Receive the R factor from Proc 0. There's only 1 R
// factor for all the processes.
Matrix< ordinal_type, scalar_type > R (ncols, ncols, scalar_type (0));
scalarMessenger->broadcast (R.get(), ncols*ncols, rootProc);
// Q_local (nrows_local by ncols, random orthogonal matrix)
// will be received from Proc 0, where it was generated.
const ordinal_type recvSize = nrowsLocal * ncols;
Matrix< ordinal_type, scalar_type > Q_local (nrowsLocal, ncols);
// Tell Proc 0 how many rows there are in the random orthogonal
// matrix I want to receive from Proc 0.
ordinalMessenger->send (&nrowsLocal, 1, rootProc, 0);
// Receive the orthogonal matrix from Proc 0.
scalarMessenger->recv (Q_local.get(), recvSize, rootProc, 0);
// Scale the (local) orthogonal matrix by the number of
// processors, to make the global matrix Q orthogonal.
const scalar_type P = static_cast< scalar_type > (nprocs);
// Do overflow check. If casting P back to scalar_type
// doesn't produce the same value as nprocs, the cast
// overflowed. We take the real part, because scalar_type
// might be complex.
if (nprocs != static_cast<int> (Teuchos::ScalarTraits<scalar_type>::real (P)))
throw std::runtime_error ("Casting nprocs to Scalar failed");
scaleMatrix (Q_local, P);
// A_local := Q_local * R
blas.GEMM (NO_TRANS, NO_TRANS, nrowsLocal, ncols, ncols,
scalar_type(1), Q_local.get(), Q_local.lda(),
R.get(), R.lda(),
scalar_type(0), A_local.get(), A_local.lda());
}
}
int main(int argc, char **argv)
{
const unsigned int n = 5;
Sacado::Fad::Vector<unsigned int, FadType> A(n*n,0),B(n,n), C(n,n);
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
A[i+j*n] = FadType(Teuchos::ScalarTraits<double>::random());
B[i] = FadType(n, Teuchos::ScalarTraits<double>::random());
for (unsigned int j=0; j<n; j++)
B[i].fastAccessDx(j) = Teuchos::ScalarTraits<double>::random();
C[i] = 0.0;
}
double *a = A.vals();
double *b = B.vals();
double *bdx = B.dx();
std::vector<double> c(n), cdx(n*n);
Teuchos::BLAS<int,double> blas;
blas.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &a[0], n, &b[0], 1, 0.0, &c[0], 1);
blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, n, n, n, 1.0, &a[0], n, &bdx[0], n, 0.0, &cdx[0], n);
// Teuchos::BLAS<int,FadType> blas_fad;
// blas_fad.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &A[0], n, &B[0], 1, 0.0, &C[0], 1);
Teuchos::BLAS<int,FadType> sacado_fad_blas(false);
sacado_fad_blas.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &A[0], n, &B[0], 1, 0.0, &C[0], 1);
// Print the results
int p = 4;
int w = p+7;
std::cout.setf(std::ios::scientific);
std::cout.precision(p);
std::cout << "BLAS GEMV calculation:" << std::endl;
std::cout << "a = " << std::endl;
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << a[i+j*n];
std::cout << std::endl;
}
std::cout << "b = " << std::endl;
for (unsigned int i=0; i<n; i++) {
std::cout << " " << std::setw(w) << b[i];
}
std::cout << std::endl;
std::cout << "bdot = " << std::endl;
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << bdx[i+j*n];
std::cout << std::endl;
}
std::cout << "c = " << std::endl;
for (unsigned int i=0; i<n; i++) {
std::cout << " " << std::setw(w) << c[i];
}
std::cout << std::endl;
std::cout << "cdot = " << std::endl;
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << cdx[i+j*n];
std::cout << std::endl;
}
std::cout << std::endl << std::endl;
std::cout << "FAD BLAS GEMV calculation:" << std::endl;
std::cout << "A.val() (should = a) = " << std::endl;
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << A[i+j*n].val();
std::cout << std::endl;
}
std::cout << "B.val() (should = b) = " << std::endl;
for (unsigned int i=0; i<n; i++) {
std::cout << " " << std::setw(w) << B[i].val();
}
std::cout << std::endl;
std::cout << "B.dx() (should = bdot) = " << std::endl;
double *Bdx = B.dx();
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << Bdx[i+j*n];
std::cout << std::endl;
}
std::cout << "C.val() (should = c) = " << std::endl;
for (unsigned int i=0; i<n; i++) {
std::cout << " " << std::setw(w) << C[i].val();
}
std::cout << std::endl;
std::cout << "C.dx() (should = cdot) = " << std::endl;
double *Cdx = C.dx();
for (unsigned int i=0; i<n; i++) {
for (unsigned int j=0; j<n; j++)
std::cout << " " << std::setw(w) << Cdx[i+j*n];
std::cout << std::endl;
}
double tol = 1.0e-14;
bool failed = false;
for (unsigned int i=0; i<n; i++) {
if (std::fabs(C[i].val() - c[i]) > tol)
failed = true;
for (unsigned int j=0; j<n; j++) {
if (std::fabs(C[i].dx(j) - cdx[i+j*n]) > tol)
failed = true;
}
}
if (!failed) {
std::cout << "\nExample passed!" << std::endl;
return 0;
}
else {
std::cout <<"\nSomething is wrong, example failed!" << std::endl;
return 1;
}
}