void ModelOBJ::CreateVertexTangentsBinormals( const MaterialGroupIterator & p_MatGroupIt, BIT_FLOAT32 * p_pTangents,
BIT_FLOAT32 * p_pBinormals, const BIT_UINT32 p_TriangleCount )
{
// Go through all the triangles
BIT_UINT32 ti = 0;
for( TriangleIterator it_tr = (*p_MatGroupIt)->Triangles.begin( ); it_tr != (*p_MatGroupIt)->Triangles.end( ); it_tr++ )
{
for( BIT_UINT32 vt = 0; vt < 3; vt++ )
{
Vector3_ui32 Indices( vt, ( vt + 1 ) % 3, ( vt + 2 ) % 3 );
const Vector3_f32 Vertex1 = m_VertexPositions[ (*it_tr).PositionIndices[ Indices.x ] ];
const Vector3_f32 Vertex2 = m_VertexPositions[ (*it_tr).PositionIndices[ Indices.y ] ];
const Vector3_f32 Vertex3 = m_VertexPositions[ (*it_tr).PositionIndices[ Indices.z ] ];
const Vector2_f32 Texture1 = m_TexturePositions[ (*it_tr).TextureIndices[ Indices.x ] ];
const Vector2_f32 Texture2 = m_TexturePositions[ (*it_tr).TextureIndices[ Indices.y ] ];
const Vector2_f32 Texture3 = m_TexturePositions[ (*it_tr).TextureIndices[ Indices.z ] ];
float x1 = Vertex2.x - Vertex1.x;
float x2 = Vertex3.x - Vertex1.x;
float y1 = Vertex2.y - Vertex1.y;
float y2 = Vertex3.y - Vertex1.y;
float z1 = Vertex2.z - Vertex1.z;
float z2 = Vertex3.z - Vertex1.z;
float s1 = Texture2.x - Texture1.x;
float s2 = Texture3.x - Texture1.x;
float t1 = Texture2.y - Texture1.y;
float t2 = Texture3.y - Texture1.y;
float r = 1.0f / ( s1 * t2 - s2 * t1 );
// Tangent
if( p_pTangents )
{
Vector3_f32 Tangent( (t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r,
(t2 * z1 - t1 * z2) * r );
Tangent.Normalize( );
p_pTangents[ ( ti * 9 ) + ( vt * 3 ) + 0 ] = Tangent.x;
p_pTangents[ ( ti * 9 ) + ( vt * 3 ) + 1 ] = Tangent.y;
p_pTangents[ ( ti * 9 ) + ( vt * 3 ) + 2 ] = Tangent.z;
}
// Binormal
if( p_pTangents )
{
Vector3_f32 Binormal( (s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r,
(s1 * z2 - s2 * z1) * r );
Binormal.Normalize( );
p_pBinormals[ ( ti * 9 ) + ( vt * 3 ) + 0 ] = Binormal.x;
p_pBinormals[ ( ti * 9 ) + ( vt * 3 ) + 1 ] = Binormal.y;
p_pBinormals[ ( ti * 9 ) + ( vt * 3 ) + 2 ] = Binormal.z;
}
}
// Increment the triangle index
ti++;
}
}
decltype(auto) a2t(const std::array<T, N>& a)
{
return a2t_impl(a, Indices());
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
// Initialize MPI and setup an Epetra communicator
MPI_Init(&argc,&argv);
Teuchos::RCP<Epetra_MpiComm> Comm = Teuchos::rcp( new Epetra_MpiComm(MPI_COMM_WORLD) );
#else
// If we aren't using MPI, then setup a serial communicator.
Teuchos::RCP<Epetra_SerialComm> Comm = Teuchos::rcp( new Epetra_SerialComm() );
#endif
bool success = false;
bool verbose = false;
try {
int i, epetra_ierr;
bool ierr, gerr = true;
// number of global elements
int dim = 100;
int blockSize = 5;
bool verbose = false;
if (argc>1) {
if (argv[1][0]=='-' && argv[1][1]=='v') {
verbose = true;
}
}
// Construct a Map that puts approximately the same number of
// equations on each processor.
Teuchos::RCP<Epetra_Map> Map = Teuchos::rcp( new Epetra_Map(dim, 0, *Comm) );
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map->NumMyElements();
std::vector<int> MyGlobalElements(NumMyElements);
Map->MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
// on this processor
std::vector<int> NumNz(NumMyElements);
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for (i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i]==0 || MyGlobalElements[i] == dim-1) {
NumNz[i] = 2;
}
else {
NumNz[i] = 3;
}
}
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, *Map, &NumNz[0]) );
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
std::vector<double> Values(2);
Values[0] = -1.0; Values[1] = -1.0;
std::vector<int> Indices(2);
double two = 2.0;
int NumEntries;
for (i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i]==0) {
Indices[0] = 1;
NumEntries = 1;
}
else if (MyGlobalElements[i] == dim-1) {
Indices[0] = dim-2;
NumEntries = 1;
}
else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
epetra_ierr = A->InsertGlobalValues(MyGlobalElements[i],NumEntries,&Values[0],&Indices[0]);
assert(epetra_ierr==0);
// Put in the diagonal entry
epetra_ierr = A->InsertGlobalValues(MyGlobalElements[i],1,&two,&MyGlobalElements[i]);
assert(epetra_ierr==0);
}
// Finish building the epetra matrix A
epetra_ierr = A->FillComplete();
assert(epetra_ierr==0);
// Create an Anasazi::EpetraSymOp from this Epetra_CrsMatrix
Teuchos::RCP<Anasazi::EpetraSymOp> op = Teuchos::rcp(new Anasazi::EpetraSymOp(A));
// Issue several useful typedefs;
typedef Anasazi::MultiVec<double> EMV;
typedef Anasazi::Operator<double> EOP;
// Create an Epetra_MultiVector for an initial vector to start the solver.
// Note that this needs to have the same number of columns as the blocksize.
Teuchos::RCP<Anasazi::EpetraMultiVec> ivec = Teuchos::rcp( new Anasazi::EpetraMultiVec(*Map, blockSize) );
ivec->Random();
// Create an output manager to handle the I/O from the solver
Teuchos::RCP<Anasazi::OutputManager<double> > MyOM = Teuchos::rcp( new Anasazi::BasicOutputManager<double>() );
if (verbose) {
MyOM->setVerbosity( Anasazi::Warnings );
}
// test the Epetra adapter multivector
ierr = Anasazi::TestMultiVecTraits<double,EMV>(MyOM,ivec);
gerr &= ierr;
if (ierr) {
MyOM->print(Anasazi::Warnings,"*** EpetraAdapter PASSED TestMultiVecTraits()\n");
}
else {
MyOM->print(Anasazi::Warnings,"*** EpetraAdapter FAILED TestMultiVecTraits() ***\n\n");
}
// test the Epetra adapter operator
ierr = Anasazi::TestOperatorTraits<double,EMV,EOP>(MyOM,ivec,op);
gerr &= ierr;
if (ierr) {
MyOM->print(Anasazi::Warnings,"*** EpetraAdapter PASSED TestOperatorTraits()\n");
}
else {
MyOM->print(Anasazi::Warnings,"*** EpetraAdapter FAILED TestOperatorTraits() ***\n\n");
}
success = gerr;
if (success) {
MyOM->print(Anasazi::Warnings,"End Result: TEST PASSED\n");
} else {
MyOM->print(Anasazi::Warnings,"End Result: TEST FAILED\n");
}
}
TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}
int main(int argc, char *argv[])
{
int ierr = 0, i;
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
bool success = false;
bool verbose = true;
try {
//int myRank = Comm.MyPID();
//int numGlobalElements = 10000000;
int numGlobalElements = 100;
Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("numGlobalElements",&numGlobalElements,"Global problem size.");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
throw -1;
}
Epetra_Map Map(numGlobalElements, 0, Comm);
int NumMyElements = Map.NumMyElements();
std::vector<int> MyGlobalElements(NumMyElements);
Map.MyGlobalElements(&MyGlobalElements[0]);
int NumNz = 3;
// std::vector<int> NumNz(NumMyElements);
// for (i=0; i<NumMyElements; i++)
// if (MyGlobalElements[i]==0 || MyGlobalElements[i] == numGlobalElements-1)
// NumNz[i] = 2;
// else
// NumNz[i] = 3;
// Epetra_CrsMatrix A(Copy, Map, &NumNz[0]);
MemoryUsageStart("Epetra");
PrintMemoryUsage("Initial memory usage", "epetra-init.heap");
Epetra_CrsMatrix A(Copy, Map, NumNz);
PrintMemoryUsage("Memory after CrsMatrix constructor", "epetra-after-ctor.heap");
std::vector<double> Values(2);
Values[0] = -1.0; Values[1] = -1.0;
std::vector<int> Indices(2);
double two = 2.0;
int NumEntries;
for (i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i]==0) {
Indices[0] = 1;
NumEntries = 1;
} else if (MyGlobalElements[i] == numGlobalElements-1) {
Indices[0] = numGlobalElements-2;
NumEntries = 1;
} else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
ierr = A.InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert(ierr==0);
// Put in the diagonal entry
ierr = A.InsertGlobalValues(MyGlobalElements[i], 1, &two, &MyGlobalElements[i]);
assert(ierr==0);
}
PrintMemoryUsage("Memory after InsertGlobalValues()", "epetra-after-insert.heap");
ierr = A.FillComplete();
assert(ierr == 0);
PrintMemoryUsage("Memory after FillComplete()", "epetra-after-fillcomplete.heap");
MemoryUsageStop();
success = true;
}
TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}
void BaseMesh::Split(float (*PositionFunction) (Vec3f &), BaseMesh &M1, BaseMesh &M2)
{
int i,vc=VertexCount(),ic=IndexCount();
MeshVertex *V = Vertices();
DWORD *I = Indices();
Vector<MeshVertex> NV1,NV2;
Vector<TriMeshFace> NT1,NT2;
SplitVMapper *VMap = new SplitVMapper[vc];
float Value;
for(i=0;i<vc;i++)
{
Value = PositionFunction(V[i].Pos);
if(Value < 0.0f)
{
VMap[i].Side = 0;
VMap[i].NVMap1 = NV1.Length();
VMap[i].NVMap2 = -1;
NV1.PushEnd(V[i]);
} else {
VMap[i].Side = 1;
VMap[i].NVMap1 = -1;
VMap[i].NVMap2 = NV2.Length();
NV2.PushEnd(V[i]);
}
}
int TSide[3];
TriMeshFace Tri;
int Oddball,State;
for(i=0;i<ic;i+=3)
{
TSide[0] = VMap[I[i]].Side;
TSide[1] = VMap[I[i+1]].Side;
TSide[2] = VMap[I[i+2]].Side;
if(TSide[0] && TSide[1] && TSide[2]) //all O2
{
Tri.I[0] = VMap[I[i]].NVMap2;
Tri.I[1] = VMap[I[i+1]].NVMap2;
Tri.I[2] = VMap[I[i+2]].NVMap2;
NT2.PushEnd(Tri);
} else if(!(TSide[0] || TSide[1] || TSide[2])) //all O1
{
Tri.I[0] = VMap[I[i]].NVMap1;
Tri.I[1] = VMap[I[i+1]].NVMap1;
Tri.I[2] = VMap[I[i+2]].NVMap1;
NT1.PushEnd(Tri);
} else {
if(TSide[0] && TSide[1]) {Oddball = 2; State = 1;}
if(TSide[0] && TSide[2]) {Oddball = 1; State = 1;}
if(TSide[1] && TSide[2]) {Oddball = 0; State = 1;}
if(!(TSide[0] || TSide[1])) {Oddball = 2; State = 2;}
if(!(TSide[0] || TSide[2])) {Oddball = 1; State = 2;}
if(!(TSide[1] || TSide[2])) {Oddball = 0; State = 2;}
if(State == 1) //Add to Obj2
{
if(VMap[I[i+Oddball]].NVMap2 == -1)
{
VMap[I[i+Oddball]].NVMap2 = NV2.Length();
NV2.PushEnd(V[I[i+Oddball]]);
}
Tri.I[0] = VMap[I[i]].NVMap2;
Tri.I[1] = VMap[I[i+1]].NVMap2;
Tri.I[2] = VMap[I[i+2]].NVMap2;
NT2.PushEnd(Tri);
} else { //Add to Obj1
if(VMap[I[i+Oddball]].NVMap1 == -1)
{
VMap[I[i+Oddball]].NVMap1 = NV1.Length();
NV1.PushEnd(V[I[i+Oddball]]);
}
Tri.I[0] = VMap[I[i]].NVMap1;
Tri.I[1] = VMap[I[i+1]].NVMap1;
Tri.I[2] = VMap[I[i+2]].NVMap1;
NT1.PushEnd(Tri);
}
}
}
delete[] VMap;
M1.Allocate(NV1.Length(),NT1.Length());
M2.Allocate(NV2.Length(),NT2.Length());
memcpy(M1.Vertices(), NV1.CArray(), M1.VertexCount() * sizeof(MeshVertex));
memcpy(M2.Vertices(), NV2.CArray(), M2.VertexCount() * sizeof(MeshVertex));
memcpy(M1.Indices(), NT1.CArray(), M1.IndexCount() * sizeof(DWORD));
memcpy(M2.Indices(), NT2.CArray(), M2.IndexCount() * sizeof(DWORD));
}
int main(int argc, char *argv[])
{
int i;
bool ierr, gerr;
gerr = true;
#ifdef HAVE_MPI
// Initialize MPI and setup an Epetra communicator
MPI_Init(&argc,&argv);
Teuchos::RCP<Epetra_MpiComm> Comm = Teuchos::rcp( new Epetra_MpiComm(MPI_COMM_WORLD) );
#else
// If we aren't using MPI, then setup a serial communicator.
Teuchos::RCP<Epetra_SerialComm> Comm = Teuchos::rcp( new Epetra_SerialComm() );
#endif
// number of global elements
const int dim = 100;
const int blockSize = 5;
bool verbose = false;
if (argc>1) {
if (argv[1][0]=='-' && argv[1][1]=='v') {
verbose = true;
}
}
// Create an output manager to handle the I/O from the solver
Teuchos::RCP<Anasazi::OutputManager<double> > MyOM = Teuchos::rcp( new Anasazi::BasicOutputManager<double>() );
if (verbose) {
MyOM->setVerbosity( Anasazi::Warnings );
}
#ifndef HAVE_EPETRA_THYRA
MyOM->stream(Anasazi::Warnings)
<< "Please configure Anasazi with:" << std::endl
<< "--enable-epetra-thyra" << std::endl
<< "--enable-anasazi-thyra" << std::endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
#endif
// Construct a Map that puts approximately the same number of
// equations on each processor.
Teuchos::RCP<Epetra_Map> Map = Teuchos::rcp( new Epetra_Map(dim, 0, *Comm) );
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map->NumMyElements();
std::vector<int> MyGlobalElements(NumMyElements);
Map->MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
// on this processor
std::vector<int> NumNz(NumMyElements);
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for (i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i]==0 || MyGlobalElements[i] == dim-1) {
NumNz[i] = 2;
}
else {
NumNz[i] = 3;
}
}
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, *Map, &NumNz[0]) );
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
std::vector<double> Values(2);
Values[0] = -1.0; Values[1] = -1.0;
std::vector<int> Indices(2);
double two = 2.0;
int NumEntries;
for (i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i]==0) {
Indices[0] = 1;
NumEntries = 1;
}
else if (MyGlobalElements[i] == dim-1) {
Indices[0] = dim-2;
NumEntries = 1;
}
else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
ierr = A->InsertGlobalValues(MyGlobalElements[i],NumEntries,&Values[0],&Indices[0]);
assert(ierr==0);
// Put in the diagonal entry
ierr = A->InsertGlobalValues(MyGlobalElements[i],1,&two,&MyGlobalElements[i]);
assert(ierr==0);
}
// Finish building the epetra matrix A
ierr = A->FillComplete();
assert(ierr==0);
#ifdef HAVE_EPETRA_THYRA
typedef Thyra::MultiVectorBase<double> TMVB;
typedef Thyra::LinearOpBase<double> TLOB;
// first, create a Thyra::VectorSpaceBase from an Epetra_Map using the Epetra-Thyra wrappers
Teuchos::RCP<const Thyra::VectorSpaceBase<double> > space = Thyra::create_VectorSpace(Map);
// then, create a Thyra::MultiVectorBase from the Thyra::VectorSpaceBase using Thyra creational functions
Teuchos::RCP<Thyra::MultiVectorBase<double> > thyra_ivec = Thyra::createMembers(space,blockSize);
// then, create a Thyra::LinearOpBase from the Epetra_CrsMatrix using the Epetra-Thyra wrappers
Teuchos::RCP<const Thyra::LinearOpBase<double> > thyra_op = Thyra::epetraLinearOp(A);
// test the Thyra multivector adapter
ierr = Anasazi::TestMultiVecTraits<double,TMVB>(MyOM,thyra_ivec);
gerr |= ierr;
if (ierr) {
MyOM->stream(Anasazi::Warnings) << "*** ThyraAdapter PASSED TestMultiVecTraits()" << std::endl;
}
else {
MyOM->stream(Anasazi::Warnings) << "*** ThyraAdapter FAILED TestMultiVecTraits() ***" << std::endl << std::endl;
}
// test the Thyra operator adapter
ierr = Anasazi::TestOperatorTraits<double,TMVB,TLOB>(MyOM,thyra_ivec,thyra_op);
gerr |= ierr;
if (ierr) {
MyOM->stream(Anasazi::Warnings) << "*** ThyraAdapter PASSED TestOperatorTraits()" << std::endl;
}
else {
MyOM->stream(Anasazi::Warnings) << "*** ThyraAdapter FAILED TestOperatorTraits() ***" << std::endl << std::endl;
}
#endif
#ifdef HAVE_MPI
MPI_Finalize();
#endif
if (gerr == false) {
MyOM->print(Anasazi::Warnings,"End Result: TEST FAILED\n");
return -1;
}
//
// Default return value
//
MyOM->print(Anasazi::Warnings,"End Result: TEST PASSED\n");
return 0;
}
//==============================================================================
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
// only one process
if (Comm.NumProc() != 1) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
if (Comm.MyPID() == 0)
cout << "Please run this test with one process only" << endl;
// return success not to break the tests
exit(EXIT_SUCCESS);
}
// ======================================================== //
// now create the famous "upper arrow" matrix, which //
// should be reordered as a "lower arrow". Sparsity pattern //
// will be printed on screen. //
// ======================================================== //
int NumPoints = 16;
#if !defined(EPETRA_NO_32BIT_GLOBAL_INDICES) || !defined(EPETRA_NO_64BIT_GLOBAL_INDICES)
Epetra_Map Map(-1,NumPoints,0,Comm);
#else
Epetra_Map Map;
#endif
std::vector<int> Indices(NumPoints);
std::vector<double> Values(NumPoints);
Teuchos::RefCountPtr<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy,Map,0) );
for (int i = 0 ; i < NumPoints ; ++i) {
int NumEntries;
if (i == 0) {
NumEntries = NumPoints;
for (int j = 0 ; j < NumPoints ; ++j) {
Indices[j] = j;
Values[j] = 1.0;
}
}
else {
NumEntries = 2;
Indices[0] = 0;
Indices[1] = i;
Values[0] = 1.0;
Values[1] = 1.0;
}
#if !defined(EPETRA_NO_32BIT_GLOBAL_INDICES) || !defined(EPETRA_NO_64BIT_GLOBAL_INDICES)
A->InsertGlobalValues(i, NumEntries, &Values[0], &Indices[0]);
#endif
}
A->FillComplete();
// print the sparsity to file, postscript format
////Ifpack_PrintSparsity(A,"OrigA.ps");
// create the reordering...
Teuchos::RefCountPtr<Ifpack_RCMReordering> Reorder = Teuchos::rcp( new Ifpack_RCMReordering() );
// and compute is on A
IFPACK_CHK_ERR(Reorder->Compute(*A));
// cout information
cout << *Reorder;
// create a reordered matrix
Ifpack_ReorderFilter ReordA(A, Reorder);
// print the sparsity to file, postscript format
////Ifpack_PrintSparsity(ReordA,"ReordA.ps");
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return(EXIT_SUCCESS);
}
T make() const {
using Indices = std::make_index_sequence<
std::tuple_size<tuple_type>::value
>;
return make_impl<T>(Indices());
}
int main(int argc, char *argv[]) {
int i, j, info;
const double one = 1.0;
const double zero = 0.0;
Teuchos::LAPACK<int,double> lapack;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
int MyPID = Comm.MyPID();
// Dimension of the matrix
int m = 500;
int n = 100;
// Construct a Map that puts approximately the same number of
// equations on each processor.
Epetra_Map RowMap(m, 0, Comm);
Epetra_Map ColMap(n, 0, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyRowElements = RowMap.NumMyElements();
std::vector<int> MyGlobalRowElements(NumMyRowElements);
RowMap.MyGlobalElements(&MyGlobalRowElements[0]);
/* We are building an m by n matrix with entries
A(i,j) = k*(si)*(tj - 1) if i <= j
= k*(tj)*(si - 1) if i > j
where si = i/(m+1) and tj = j/(n+1) and k = 1/(n+1).
*/
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, RowMap, n) );
// Compute coefficients for discrete integral operator
std::vector<double> Values(n);
std::vector<int> Indices(n);
double inv_mp1 = one/(m+1);
double inv_np1 = one/(n+1);
for (i=0; i<n; i++) { Indices[i] = i; }
for (i=0; i<NumMyRowElements; i++) {
//
for (j=0; j<n; j++) {
//
if ( MyGlobalRowElements[i] <= j ) {
Values[j] = inv_np1 * ( (MyGlobalRowElements[i]+one)*inv_mp1 ) * ( (j+one)*inv_np1 - one ); // k*(si)*(tj-1)
}
else {
Values[j] = inv_np1 * ( (j+one)*inv_np1 ) * ( (MyGlobalRowElements[i]+one)*inv_mp1 - one ); // k*(tj)*(si-1)
}
}
info = A->InsertGlobalValues(MyGlobalRowElements[i], n, &Values[0], &Indices[0]);
assert( info==0 );
}
// Finish up
info = A->FillComplete(ColMap, RowMap);
assert( info==0 );
info = A->OptimizeStorage();
assert( info==0 );
A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks
//************************************
// Start the block Arnoldi iteration
//***********************************
//
// Variables used for the Block Arnoldi Method
//
int nev = 4;
int blockSize = 1;
int numBlocks = 10;
int maxRestarts = 20;
int verbosity = Anasazi::Errors + Anasazi::Warnings + Anasazi::FinalSummary;
double tol = lapack.LAMCH('E');
std::string which = "LM";
//
// Create parameter list to pass into solver
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Num Blocks", numBlocks );
MyPL.set( "Maximum Restarts", maxRestarts );
MyPL.set( "Convergence Tolerance", tol );
typedef Anasazi::MultiVec<double> MV;
typedef Anasazi::Operator<double> OP;
// Create an Anasazi::EpetraMultiVec for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
Teuchos::RCP<Anasazi::EpetraMultiVec> ivec = Teuchos::rcp( new Anasazi::EpetraMultiVec(ColMap, blockSize) );
ivec->MvRandom();
// Call the constructor for the (A^T*A) operator
Teuchos::RCP<Anasazi::EpetraSymOp> Amat = Teuchos::rcp( new Anasazi::EpetraSymOp(A) );
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem =
Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(Amat, ivec) );
// Inform the eigenproblem that the matrix A is symmetric
MyProblem->setHermitian(true);
// Set the number of eigenvalues requested and the blocksize the solver should use
MyProblem->setNEV( nev );
// Inform the eigenproblem that you are finished passing it information
bool boolret = MyProblem->setProblem();
if (boolret != true) {
if (MyPID == 0) {
cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}
// Initialize the Block Arnoldi solver
Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);
// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
if (returnCode != Anasazi::Converged && MyPID==0) {
cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << endl;
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<double,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<double> > evals = sol.Evals;
int numev = sol.numVecs;
if (numev > 0) {
// Compute singular values/vectors and direct residuals.
//
// Compute singular values which are the square root of the eigenvalues
if (MyPID==0) {
cout<<"------------------------------------------------------"<<endl;
cout<<"Computed Singular Values: "<<endl;
cout<<"------------------------------------------------------"<<endl;
}
for (i=0; i<numev; i++) { evals[i].realpart = Teuchos::ScalarTraits<double>::squareroot( evals[i].realpart ); }
//
// Compute left singular vectors : u = Av/sigma
//
std::vector<double> tempnrm(numev), directnrm(numev);
std::vector<int> index(numev);
for (i=0; i<numev; i++) { index[i] = i; }
Anasazi::EpetraMultiVec Av(RowMap,numev), u(RowMap,numev);
Anasazi::EpetraMultiVec* evecs = dynamic_cast<Anasazi::EpetraMultiVec* >(sol.Evecs->CloneViewNonConst( index ));
Teuchos::SerialDenseMatrix<int,double> S(numev,numev);
A->Apply( *evecs, Av );
Av.MvNorm( tempnrm );
for (i=0; i<numev; i++) { S(i,i) = one/tempnrm[i]; };
u.MvTimesMatAddMv( one, Av, S, zero );
//
// Compute direct residuals : || Av - sigma*u ||
//
for (i=0; i<numev; i++) { S(i,i) = evals[i].realpart; }
Av.MvTimesMatAddMv( -one, u, S, one );
Av.MvNorm( directnrm );
if (MyPID==0) {
cout.setf(std::ios_base::right, std::ios_base::adjustfield);
cout<<std::setw(16)<<"Singular Value"
<<std::setw(20)<<"Direct Residual"
<<endl;
cout<<"------------------------------------------------------"<<endl;
for (i=0; i<numev; i++) {
cout<<std::setw(16)<<evals[i].realpart
<<std::setw(20)<<directnrm[i]
<<endl;
}
cout<<"------------------------------------------------------"<<endl;
}
}
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
return 0;
}
void GetVerticesIntoModel(Model3D& Model)
{
// Search for redundant vertices -- if there are any vertices to look for
if (FullVertexList.empty()) return;
// First, index-sort them
// Set up for index sorting by finding the position range
// (this code is a bit smarter than BG's 3DMF Mapper code for doing that);
// this is unnecessary for the other vertex data
GLfloat PosMin[3], PosMax[3];
for (int c=0; c<3; c++)
PosMin[c] = PosMax[c] = FullVertexList[0].Data[FullVertexData::POS_BASE+c];
int OldNumVertices = FullVertexList.size();
for (int k=0; k<OldNumVertices; k++)
{
GLfloat *Pos = FullVertexList[0].Data + FullVertexData::POS_BASE;
for (int c=0; c<3; c++)
{
GLfloat PC = Pos[c];
PosMin[c] = MIN(PosMin[c],PC);
PosMax[c] = MAX(PosMax[c],PC);
}
}
const GLfloat ThresholdConstant = 0.001;
for (int c=0; c<3; c++)
Thresholds[FullVertexData::POS_BASE+c] = ThresholdConstant*(PosMax[c]-PosMin[c]);
for (int c=0; c<2; c++)
Thresholds[FullVertexData::TC_BASE+c] = ThresholdConstant;
for (int c=0; c<3; c++)
Thresholds[FullVertexData::NORM_BASE+c] = ThresholdConstant;
for (int c=0; c<3; c++)
Thresholds[FullVertexData::COLOR_BASE+c] = ThresholdConstant;
// Now the actual sorting
vector<int> Indices(OldNumVertices);
for (int k=0; k<Indices.size(); k++)
Indices[k] = k;
// STL sort may be slow
qsort(&Indices[0],OldNumVertices,sizeof(int),CompareVertices);
// Set up vertex ranks in place; count the distinct vertices.
// Also, use the first one of a non-distinct set in sorted order
// as the new vertex
Model.VertIndices.resize(OldNumVertices);
vector<int> VertexSelect;
VertexSelect.resize(OldNumVertices);
int TopRank = 0;
int PrevIndex = Indices[0];
VertexSelect[TopRank] = PrevIndex;
Model.VertIndices[PrevIndex] = TopRank;
for (int k=1; k<OldNumVertices; k++)
{
int CurrIndex = Indices[k];
if (CompareVertices(&PrevIndex,&CurrIndex) != 0)
{
TopRank++;
VertexSelect[TopRank] = CurrIndex;
}
Model.VertIndices[CurrIndex] = TopRank;
PrevIndex = CurrIndex;
}
int NewNumVertices = TopRank + 1;
// Fill up the rest of model arrays
Model.Positions.resize(3*NewNumVertices);
GLfloat *PosPtr = &Model.Positions[0];
GLfloat *TCPtr = NULL;
if (TxtrCoordsPresent)
{
Model.TxtrCoords.resize(2*NewNumVertices);
TCPtr = &Model.TxtrCoords[0];
}
GLfloat *NormPtr = NULL;
if (NormalsPresent)
{
Model.Normals.resize(3*NewNumVertices);
NormPtr = &Model.Normals[0];
}
GLfloat *ColorPtr = NULL;
if (ColorsPresent)
{
Model.Colors.resize(3*NewNumVertices);
ColorPtr = &Model.Colors[0];
}
for (int k=0; k<NewNumVertices; k++)
{
FullVertexData& FullVertex = FullVertexList[VertexSelect[k]];
GLfloat *Pos = FullVertex.Data + FullVertexData::POS_BASE;
for (int c=0; c<3; c++)
*(PosPtr++) = *(Pos++);
if (TxtrCoordsPresent)
{
GLfloat *TC = FullVertex.Data + FullVertexData::TC_BASE;
for (int c=0; c<2; c++)
*(TCPtr++) = *(TC++);
}
if (NormalsPresent)
{
GLfloat *Norm = FullVertex.Data + FullVertexData::NORM_BASE;
for (int c=0; c<3; c++)
*(NormPtr++) = *(Norm++);
}
if (ColorsPresent)
{
GLfloat *Color = FullVertex.Data + FullVertexData::COLOR_BASE;
for (int c=0; c<3; c++)
*(ColorPtr++) = *(Color++);
}
}
// All done!
FullVertexList.clear();
}
void BaseMesh::TwoPatch()
{
Vector<MeshVertex> NewVertices; //list of new vertices in the mesh
Vector<TriMeshFace> NewFaces; //list of new faces in the mesh
UINT vc = VertexCount(), ic = IndexCount();
MeshVertex *V = Vertices();
DWORD *I = Indices();
Vector<MeshTwoPatchEdge>* HashVertices = new Vector<MeshTwoPatchEdge>[vc];
//HashVertices is a hash table that stores all edges incident on an edge.
//a given edge's location in the hash table is HashVertices[Q], where Q is the index
//of the smallest of the edge's two indices.
DWORD LocalTIndices[6]; //we take each face and add 3 new vertices in the middle of each edge.
//LocalTIndices represents these 6 vertices (the 3 new ones and the 3 origional ones.)
//these 6 vertices then become 4 triangles that exactly match the origional triangle.
DWORD VertexIndex; //the index of the vertex we're looking for
MeshVertex NewVertex; //the new vertex we're going to add to the mesh
TriMeshFace NewTriangle; //the new triangle we're going to add to the mesh
MeshTwoPatchEdge NewEdge; //the edge we're going to add to the hash table
for(UINT i = 0; i < vc; i++)
{
NewVertices.PushEnd(V[i]); //all old vertices will be in the new mesh
}
for(UINT i = 0; i < ic; i+=3)
{
LocalTIndices[0] = I[i+0];
LocalTIndices[1] = I[i+1];
LocalTIndices[2] = I[i+2]; //the origional 3 triangles are always in LocalTIndices
//now it remains to get the vertices at the middle of each edge
//if these aren't already in the mesh we just add a new vertex to the final mesh, otherwise we need to use our hash table to find
//their position in the mesh and use those indices.
for(UINT i2=0;i2<3;i2++)
{
int EdgeVtx1, EdgeVtx2; //the indices we're looking for
if(i2 == 0)
{
EdgeVtx1 = I[i+0];
EdgeVtx2 = I[i+1];
}
if(i2 == 1)
{
EdgeVtx1 = I[i+1];
EdgeVtx2 = I[i+2];
}
if(i2 == 2)
{
EdgeVtx1 = I[i+0];
EdgeVtx2 = I[i+2];
}
if(EdgeVtx2 < EdgeVtx1) Utility::Swap(EdgeVtx1, EdgeVtx2); //we want EdgeVtx1 to be the smallest
if(SearchTwoPatchEdge(HashVertices[EdgeVtx1], VertexIndex, EdgeVtx2)) //search for the corresponding edge to see if it's already in the mesh
{
LocalTIndices[3+i2] = VertexIndex; //if it is we just choose the found index as our entry in LocalTIndices. No need to add another vertex to the mesh; it's already there
} else
{
Interpolate(V[EdgeVtx1],V[EdgeVtx2],NewVertex,0.5f); //otherwise make a new vertex at the middle of the edge,
NewEdge.v2 = EdgeVtx2;
NewEdge.v1 = NewVertices.Length();
LocalTIndices[3+i2] = NewVertices.Length(); //this new vertex is our LocalTIndices entry
HashVertices[EdgeVtx1].PushEnd(NewEdge); //we need to add it to the hash table...
NewVertices.PushEnd(NewVertex); //and add it to the new mesh
}
}
//Now we have all 6 of our LocalTIndices. This was one triangle in the origional mesh and is now 4 triangles in the new mesh.
//we add those 4 new triangles now.
NewTriangle.I[0] = LocalTIndices[0];
NewTriangle.I[1] = LocalTIndices[3];
NewTriangle.I[2] = LocalTIndices[5];
NewFaces.PushEnd(NewTriangle);
NewTriangle.I[0] = LocalTIndices[3];
NewTriangle.I[1] = LocalTIndices[1];
NewTriangle.I[2] = LocalTIndices[4];
NewFaces.PushEnd(NewTriangle);
NewTriangle.I[0] = LocalTIndices[5];
NewTriangle.I[1] = LocalTIndices[4];
NewTriangle.I[2] = LocalTIndices[2];
NewFaces.PushEnd(NewTriangle);
NewTriangle.I[0] = LocalTIndices[5];
NewTriangle.I[1] = LocalTIndices[3];
NewTriangle.I[2] = LocalTIndices[4];
NewFaces.PushEnd(NewTriangle);
}
for(UINT i = 0; i <vc; i++)
{
HashVertices[i].FreeMemory();
}
delete[] HashVertices; //free the hash table up
Allocate(NewVertices.Length(), NewFaces.Length()); //allocate space for the new mesh (deleting the old mesh)
MeshVertex *VNew = Vertices();
DWORD *INew = Indices();
vc = VertexCount();
ic = IndexCount();
for(UINT i = 0; i < vc; i++)
{
VNew[i] = NewVertices[i];
}
for(UINT i = 0; i < ic / 3; i++)
{
INew[i * 3 + 0] = NewFaces[i].I[0];
INew[i * 3 + 1] = NewFaces[i].I[1];
INew[i * 3 + 2] = NewFaces[i].I[2];
}
}
Vect<float &> a2v(std::array<T, N>& a, int j)
{
return a2v_impl(a, j, Indices());
}
// ======================================================================
int Ifpack_PrintSparsity(const Epetra_RowMatrix& A, const char* InputFileName,
const int NumPDEEqns)
{
int ltit;
long long m,nc,nr,maxdim;
double lrmrgn,botmrgn,xtit,ytit,ytitof,fnstit,siz = 0.0;
double xl,xr, yb,yt, scfct,u2dot,frlw,delt,paperx;
bool square = false;
/*change square to .true. if you prefer a square frame around
a rectangular matrix */
double conv = 2.54;
char munt = 'E'; /* put 'E' for centimeters, 'U' for inches */
int ptitle = 0; /* position of the title, 0 under the drawing,
else above */
FILE* fp = NULL;
int NumMyRows;
//int NumMyCols;
long long NumGlobalRows;
long long NumGlobalCols;
int MyPID;
int NumProc;
char FileName[1024];
char title[1024];
const Epetra_Comm& Comm = A.Comm();
/* --------------------- execution begins ---------------------- */
if (strlen(A.Label()) != 0)
strcpy(title, A.Label());
else
sprintf(title, "%s", "matrix");
if (InputFileName == 0)
sprintf(FileName, "%s.ps", title);
else
strcpy(FileName, InputFileName);
MyPID = Comm.MyPID();
NumProc = Comm.NumProc();
NumMyRows = A.NumMyRows();
//NumMyCols = A.NumMyCols();
NumGlobalRows = A.NumGlobalRows64();
NumGlobalCols = A.NumGlobalCols64();
if (NumGlobalRows != NumGlobalCols)
IFPACK_CHK_ERR(-1); // never tested
/* to be changed for rect matrices */
maxdim = (NumGlobalRows>NumGlobalCols)?NumGlobalRows:NumGlobalCols;
maxdim /= NumPDEEqns;
m = 1 + maxdim;
nr = NumGlobalRows / NumPDEEqns + 1;
nc = NumGlobalCols / NumPDEEqns + 1;
if (munt == 'E') {
u2dot = 72.0/conv;
paperx = 21.0;
siz = 10.0;
}
else {
u2dot = 72.0;
paperx = 8.5*conv;
siz = siz*conv;
}
/* left and right margins (drawing is centered) */
lrmrgn = (paperx-siz)/2.0;
/* bottom margin : 2 cm */
botmrgn = 2.0;
/* c scaling factor */
scfct = siz*u2dot/m;
/* matrix frame line witdh */
frlw = 0.25;
/* font size for title (cm) */
fnstit = 0.5;
/* mfh 23 Jan 2013: title is always nonnull, since it's an array of
fixed nonzero length. The 'if' test thus results in a compiler
warning. */
/*if (title) ltit = strlen(title);*/
/*else ltit = 0;*/
ltit = strlen(title);
/* position of title : centered horizontally */
/* at 1.0 cm vertically over the drawing */
ytitof = 1.0;
xtit = paperx/2.0;
ytit = botmrgn+siz*nr/m + ytitof;
/* almost exact bounding box */
xl = lrmrgn*u2dot - scfct*frlw/2;
xr = (lrmrgn+siz)*u2dot + scfct*frlw/2;
yb = botmrgn*u2dot - scfct*frlw/2;
yt = (botmrgn+siz*nr/m)*u2dot + scfct*frlw/2;
if (ltit == 0) {
yt = yt + (ytitof+fnstit*0.70)*u2dot;
}
/* add some room to bounding box */
delt = 10.0;
xl = xl-delt;
xr = xr+delt;
yb = yb-delt;
yt = yt+delt;
/* correction for title under the drawing */
if ((ptitle == 0) && (ltit == 0)) {
ytit = botmrgn + fnstit*0.3;
botmrgn = botmrgn + ytitof + fnstit*0.7;
}
/* begin of output */
if (MyPID == 0) {
fp = fopen(FileName,"w");
fprintf(fp,"%s","%%!PS-Adobe-2.0\n");
fprintf(fp,"%s","%%Creator: IFPACK\n");
fprintf(fp,"%%%%BoundingBox: %f %f %f %f\n",
xl,yb,xr,yt);
fprintf(fp,"%s","%%EndComments\n");
fprintf(fp,"%s","/cm {72 mul 2.54 div} def\n");
fprintf(fp,"%s","/mc {72 div 2.54 mul} def\n");
fprintf(fp,"%s","/pnum { 72 div 2.54 mul 20 string ");
fprintf(fp,"%s","cvs print ( ) print} def\n");
fprintf(fp,"%s","/Cshow {dup stringwidth pop -2 div 0 rmoveto show} def\n");
/* we leave margins etc. in cm so it is easy to modify them if
needed by editing the output file */
fprintf(fp,"%s","gsave\n");
if (ltit != 0) {
fprintf(fp,"/Helvetica findfont %e cm scalefont setfont\n",
fnstit);
fprintf(fp,"%f cm %f cm moveto\n",
xtit,ytit);
fprintf(fp,"(%s) Cshow\n", title);
fprintf(fp,"%f cm %f cm translate\n",
lrmrgn,botmrgn);
}
fprintf(fp,"%f cm %d div dup scale \n",
siz, (int) m);
/* draw a frame around the matrix */
fprintf(fp,"%f setlinewidth\n",
frlw);
fprintf(fp,"%s","newpath\n");
fprintf(fp,"%s","0 0 moveto ");
if (square) {
printf("------------------- %d\n", (int) m);
fprintf(fp,"%d %d lineto\n",
(int) m, 0);
fprintf(fp,"%d %d lineto\n",
(int) m, (int) m);
fprintf(fp,"%d %d lineto\n",
0, (int) m);
}
else {
fprintf(fp,"%d %d lineto\n",
(int) nc, 0);
fprintf(fp,"%d %d lineto\n",
(int) nc, (int) nr);
fprintf(fp,"%d %d lineto\n",
0, (int) nr);
}
fprintf(fp,"%s","closepath stroke\n");
/* plotting loop */
fprintf(fp,"%s","1 1 translate\n");
fprintf(fp,"%s","0.8 setlinewidth\n");
fprintf(fp,"%s","/p {moveto 0 -.40 rmoveto \n");
fprintf(fp,"%s"," 0 .80 rlineto stroke} def\n");
fclose(fp);
}
int MaxEntries = A.MaxNumEntries();
std::vector<int> Indices(MaxEntries);
std::vector<double> Values(MaxEntries);
for (int pid = 0 ; pid < NumProc ; ++pid) {
if (pid == MyPID) {
fp = fopen(FileName,"a");
if( fp == NULL ) {
fprintf(stderr,"%s","ERROR\n");
exit(EXIT_FAILURE);
}
for (int i = 0 ; i < NumMyRows ; ++i) {
if (i % NumPDEEqns) continue;
int Nnz;
A.ExtractMyRowCopy(i,MaxEntries,Nnz,&Values[0],&Indices[0]);
long long grow = A.RowMatrixRowMap().GID64(i);
for (int j = 0 ; j < Nnz ; ++j) {
int col = Indices[j];
if (col % NumPDEEqns == 0) {
long long gcol = A.RowMatrixColMap().GID64(Indices[j]);
grow /= NumPDEEqns;
gcol /= NumPDEEqns;
fprintf(fp,"%lld %lld p\n",
gcol, NumGlobalRows - grow - 1);
}
}
}
fprintf(fp,"%s","%end of data for this process\n");
if( pid == NumProc - 1 )
fprintf(fp,"%s","showpage\n");
fclose(fp);
}
Comm.Barrier();
}
return(0);
}
int main(int argc, char *argv[])
{
int ierr = 0;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc, &argv);
int rank; // My process ID
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
int rank = 0;
Epetra_SerialComm Comm;
#endif
bool verbose = false;
// Check if we should print results to standard out
if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
int verbose_int = verbose ? 1 : 0;
Comm.Broadcast(&verbose_int, 1, 0);
verbose = verbose_int==1 ? true : false;
Comm.SetTracebackMode(0); // This should shut down any error traceback reporting
int MyPID = Comm.MyPID();
int NumProc = Comm.NumProc();
if(verbose && MyPID==0)
cout << Epetra_Version() << std::endl << std::endl;
if (verbose) cout << "Processor "<<MyPID<<" of "<< NumProc
<< " is alive."<<endl;
// unused: bool verbose1 = verbose;
// Redefine verbose to only print on PE 0
if(verbose && rank!=0)
verbose = false;
if (verbose) cout << "Test the memory management system of the class CrsMatrix (memory leak, invalid free)" << std::endl;
//
// Test 1: code initially proposed to illustrate bug #5499
//
if(Comm.NumProc() == 1) { // this is a sequential test
if (verbose) cout << "* Using Copy, ColMap, Variable number of indices per row and Static profile (cf. bug #5499)." << std::endl;
// Row Map
Epetra_Map RowMap(2LL, 0LL, Comm);
// ColMap
std::vector<long long> colids(2);
colids[0]=0;
colids[1]=1;
Epetra_Map ColMap(-1LL, 2, &colids[0], 0LL, Comm);
// NumEntriesPerRow
std::vector<int> NumEntriesPerRow(2);
NumEntriesPerRow[0]=2;
NumEntriesPerRow[1]=2;
// Test
Epetra_CrsMatrix A(Copy, RowMap, ColMap, &NumEntriesPerRow[0], true);
// Bug #5499 shows up because InsertGlobalValues() is not called (CrsMatrix::Values_ not allocated but freed)
A.FillComplete();
}
//
// Test 1 Bis: same as Test1, but without ColMap and variable number of indices per row. Does not seems to matter
//
if(Comm.NumProc() == 1) { // this is a sequential test
if (verbose) cout << "* Using Copy, Fixed number of indices per row and Static profile" << std::endl;
Epetra_Map RowMap(2LL, 0LL, Comm);
// Test
Epetra_CrsMatrix A(Copy, RowMap, 1, true);
// Bug #5499 shows up because InsertGlobalValues() is not called (CrsMatrix::Values_ not allocated but freed)
A.FillComplete();
}
//
// Test 2: same as Test 1 Bis but with one call to InsertGlobalValues.
//
if(Comm.NumProc() == 1) {
if (verbose) cout << "* Using Copy, Fixed number of indices per row and Static profile + InsertGlobalValues()." << std::endl;
Epetra_Map RowMap(2LL, 0LL, Comm);
// Test
Epetra_CrsMatrix A(Copy, RowMap, 1, true);
std::vector<long long> Indices(1);
std::vector<double> Values(1);
Values[0] = 2;
Indices[0] = 0;
A.InsertGlobalValues(0, 1, &Values[0], &Indices[0]); // Memory leak if CrsMatrix::Values not freed
A.FillComplete();
}
//
// Test 3: check if the patch is not introducing some obvious regression
//
if(Comm.NumProc() == 1) {
if (verbose) cout << "* Using Copy, Fixed number of indices per row and Dynamic profile" << std::endl;
Epetra_Map RowMap(2LL, 0LL, Comm);
// Test
Epetra_CrsMatrix A(Copy, RowMap, 1, false);
A.FillComplete();
}
//
// Test 4: idem but with one call to InsertGlobalValues.
//
if(Comm.NumProc() == 1) {
if (verbose) cout << "* Using Copy, Fixed number of indices per row and Dynamic profile + InsertGlobalValues()." << std::endl;
Epetra_Map RowMap(2LL, 0LL, Comm);
// Test
Epetra_CrsMatrix A(Copy, RowMap, 1, false);
std::vector<long long> Indices(1);
std::vector<double> Values(1);
Values[0] = 2;
Indices[0] = 0;
A.InsertGlobalValues(0, 1, &Values[0], &Indices[0]);
A.FillComplete();
}
if(Comm.NumProc() == 1) {
if (verbose) cout << "* Using Copy, Static Graph()." << std::endl;
Epetra_Map RowMap(1LL, 0LL, Comm);
// Test
Epetra_CrsGraph G(Copy, RowMap, 1);
std::vector<long long> Indices(1);
Indices[0] = 0;
G.InsertGlobalIndices(0, 1, &Indices[0]);
G.FillComplete();
Epetra_CrsMatrix A(Copy, G);
std::vector<double> Values(1);
Values[0] = 2;
A.ReplaceGlobalValues(0, 1, &Values[0], &Indices[0]);
A.FillComplete();
double norminf = A.NormInf();
if (verbose) cout << "** Inf Norm of Matrix = " << norminf << "." << std::endl;
cout << A << std::endl;
}
if(Comm.NumProc() == 1) {
if (verbose) cout << "* Using Copy, Fixed number of indices per row and static profile + InsertGlobalValues() for a single row." << std::endl;
Epetra_Map RowMap(1LL, 0LL, Comm);
// Test
Epetra_CrsMatrix A(Copy, RowMap, 1, true);
std::vector<long long> Indices(1);
std::vector<double> Values(1);
Values[0] = 2;
Indices[0] = 0;
A.InsertGlobalValues(0, 1, &Values[0], &Indices[0]);
A.FillComplete();
}
/*
if (bool) {
if (verbose) cout << endl << "tests FAILED" << endl << endl;
}
else {*/
if (verbose) cout << endl << "tests PASSED" << endl << endl;
/* } */
#ifdef EPETRA_MPI
MPI_Finalize();
#endif
return ierr;
}
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> >
Cross3D_Helmholtz_Pair(const Teuchos::RCP<const Map> & map,
const GlobalOrdinal nx, const GlobalOrdinal ny, const GlobalOrdinal nz,
const double h, const double delta,
const int PMLgridptsx_left, const int PMLgridptsx_right,
const int PMLgridptsy_left, const int PMLgridptsy_right,
const int PMLgridptsz_left, const int PMLgridptsz_right,
const double omega, const Scalar shift,
const int model) {
Teuchos::RCP<Matrix> ktx = MatrixTraits<Map,Matrix>::Build(map, 7);
Teuchos::RCP<Matrix> mtx = MatrixTraits<Map,Matrix>::Build(map, 1);
LocalOrdinal NumMyElements = map->getNodeNumElements();
Teuchos::ArrayView<const GlobalOrdinal> MyGlobalElements = map->getNodeElementList();
GlobalOrdinal left, right, bottom, top, front, back, center;
std::vector<Scalar> Values(7);
std::vector<GlobalOrdinal> Indices(7);
VelocityModel<Scalar,LocalOrdinal,GlobalOrdinal> velocitymodel(3,model);
double LBx, RBx, LBy, RBy, LBz, RBz, Dx, Dy, Dz;
Scalar sx_left, sx_center, sx_right;
Scalar sy_left, sy_center, sy_right;
Scalar sz_left, sz_center, sz_right;
Scalar c;
// Calculate some parameters
Dx = ((double) nx-1)*h;
Dy = ((double) ny-1)*h;
Dz = ((double) nz-1)*h;
LBx = ((double) PMLgridptsx_left)*h;
RBx = Dx-((double) PMLgridptsx_right)*h;
LBy = ((double) PMLgridptsy_left)*h;
RBy = Dy-((double) PMLgridptsy_right)*h;
LBz = ((double) PMLgridptsz_left)*h;
RBz = Dz-((double) PMLgridptsz_right)*h;
for (GlobalOrdinal i = 0; i < NumMyElements; ++i) {
// calculate PML functions
size_t numEntries = 0;
center = MyGlobalElements[i];
GetNeighboursCartesian3d(center, nx, ny, nz, left, right, front, back, bottom, top);
GetPMLvalues(center, nx, ny, nz, h, delta, Dx, Dy, Dz,
LBx, RBx, LBy, RBy, LBz, RBz,
sx_left, sx_center, sx_right,
sy_left, sy_center, sy_right,
sz_left, sz_center, sz_right);
// get velocity
GlobalOrdinal ixy, ix, iy, iz;
ixy = i % (nx * ny);
iz = (i - ixy) / (nx * ny);
ix = ixy % nx;
iy = (ixy - ix) / nx;
double xcoord, ycoord, zcoord;
xcoord=((double) ix)*h;
ycoord=((double) iy)*h;
zcoord=((double) iz)*h;
c = velocitymodel.getVelocity(xcoord,ycoord,zcoord);
if (left != -1) {
Indices[numEntries] = left;
Values [numEntries] = -(sy_center*sz_center/sx_center + sy_center*sz_center/sx_left)/2.0;
numEntries++;
}
if (right != -1) {
Indices[numEntries] = right;
Values [numEntries] = -(sy_center*sz_center/sx_center + sy_center*sz_center/sx_right)/2.0;
numEntries++;
}
if (front != -1) {
Indices[numEntries] = front;
Values [numEntries] = -(sx_center*sz_center/sy_center + sx_center*sz_center/sy_right)/2.0;
numEntries++;
}
if (back != -1) {
Indices[numEntries] = back;
Values [numEntries] = -(sx_center*sz_center/sy_center + sx_center*sz_center/sy_left)/2.0;
numEntries++;
}
if (bottom != -1) {
Indices[numEntries] = bottom;
Values [numEntries] = -(sx_center*sy_center/sz_center + sx_center*sy_center/sz_left)/2.0;
numEntries++;
}
if (top != -1) {
Indices[numEntries] = top;
Values [numEntries] = -(sx_center*sy_center/sz_center + sx_center*sy_center/sz_right)/2.0;
numEntries++;
}
// diagonal
Scalar z = (Scalar) 0.0;
for (size_t j = 0; j < numEntries; j++)
z -= Values[j];
Indices[numEntries] = center;
Values [numEntries] = z;
numEntries++;
Teuchos::ArrayView<GlobalOrdinal> iv(&Indices[0], numEntries);
Teuchos::ArrayView<Scalar> av(&Values[0], numEntries);
ktx->insertGlobalValues(center, iv, av);
mtx->insertGlobalValues(center,
Teuchos::tuple<GlobalOrdinal>(center),
Teuchos::tuple<Scalar>(h*h*sx_center*sy_center*sz_center/(c*c)) );
}
ktx->fillComplete();
mtx->fillComplete();
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> > system;
system=std::make_pair(ktx,mtx);
return system;
} //Cross3D_Helmholtz
status_t
Volume::Mount(const char* deviceName, uint32 flags)
{
// TODO: validate the FS in write mode as well!
#if (B_HOST_IS_LENDIAN && defined(BFS_BIG_ENDIAN_ONLY)) \
|| (B_HOST_IS_BENDIAN && defined(BFS_LITTLE_ENDIAN_ONLY))
// in big endian mode, we only mount read-only for now
flags |= B_MOUNT_READ_ONLY;
#endif
DeviceOpener opener(deviceName, (flags & B_MOUNT_READ_ONLY) != 0
? O_RDONLY : O_RDWR);
fDevice = opener.Device();
if (fDevice < B_OK)
RETURN_ERROR(fDevice);
if (opener.IsReadOnly())
fFlags |= VOLUME_READ_ONLY;
// read the superblock
if (Identify(fDevice, &fSuperBlock) != B_OK) {
FATAL(("invalid superblock!\n"));
return B_BAD_VALUE;
}
// initialize short hands to the superblock (to save byte swapping)
fBlockSize = fSuperBlock.BlockSize();
fBlockShift = fSuperBlock.BlockShift();
fAllocationGroupShift = fSuperBlock.AllocationGroupShift();
// check if the device size is large enough to hold the file system
off_t diskSize;
if (opener.GetSize(&diskSize, &fDeviceBlockSize) != B_OK)
RETURN_ERROR(B_ERROR);
if (diskSize < (NumBlocks() << BlockShift()))
RETURN_ERROR(B_BAD_VALUE);
// set the current log pointers, so that journaling will work correctly
fLogStart = fSuperBlock.LogStart();
fLogEnd = fSuperBlock.LogEnd();
if ((fBlockCache = opener.InitCache(NumBlocks(), fBlockSize)) == NULL)
return B_ERROR;
fJournal = new(std::nothrow) Journal(this);
if (fJournal == NULL)
return B_NO_MEMORY;
status_t status = fJournal->InitCheck();
if (status < B_OK) {
FATAL(("could not initialize journal: %s!\n", strerror(status)));
return status;
}
// replaying the log is the first thing we will do on this disk
status = fJournal->ReplayLog();
if (status != B_OK) {
FATAL(("Replaying log failed, data may be corrupted, volume "
"read-only.\n"));
fFlags |= VOLUME_READ_ONLY;
// TODO: if this is the boot volume, Bootscript will assume this
// is a CD...
// TODO: it would be nice to have a user visible alert instead
// of letting him just find this in the syslog.
}
status = fBlockAllocator.Initialize();
if (status != B_OK) {
FATAL(("could not initialize block bitmap allocator!\n"));
return status;
}
fRootNode = new(std::nothrow) Inode(this, ToVnode(Root()));
if (fRootNode != NULL && fRootNode->InitCheck() == B_OK) {
status = publish_vnode(fVolume, ToVnode(Root()), (void*)fRootNode,
&gBFSVnodeOps, fRootNode->Mode(), 0);
if (status == B_OK) {
// try to get indices root dir
if (!Indices().IsZero()) {
fIndicesNode = new(std::nothrow) Inode(this,
ToVnode(Indices()));
}
if (fIndicesNode == NULL
|| fIndicesNode->InitCheck() < B_OK
|| !fIndicesNode->IsContainer()) {
INFORM(("bfs: volume doesn't have indices!\n"));
if (fIndicesNode) {
// if this is the case, the index root node is gone bad,
// and BFS switch to read-only mode
fFlags |= VOLUME_READ_ONLY;
delete fIndicesNode;
fIndicesNode = NULL;
}
} else {
// we don't use the vnode layer to access the indices node
}
} else {
FATAL(("could not create root node: publish_vnode() failed!\n"));
delete fRootNode;
return status;
}
} else {
status = B_BAD_VALUE;
FATAL(("could not create root node!\n"));
return status;
}
// all went fine
opener.Keep();
return B_OK;
}
UINT64 BaseMesh::Hash64() const
{
return Utility::Hash64((const BYTE *)Vertices(), VertexCount() * sizeof(MeshVertex)) +
Utility::Hash64((const BYTE *)Indices(), IndexCount() * sizeof(DWORD));
}
// source point clouds are assumed to contain their normals
int ICP::registerModelToScene(const Mat& srcPC, const Mat& dstPC, double& residual, Matx44d& pose)
{
int n = srcPC.rows;
const bool useRobustReject = m_rejectionScale>0;
Mat srcTemp = srcPC.clone();
Mat dstTemp = dstPC.clone();
Vec3d meanSrc, meanDst;
computeMeanCols(srcTemp, meanSrc);
computeMeanCols(dstTemp, meanDst);
Vec3d meanAvg = 0.5 * (meanSrc + meanDst);
subtractColumns(srcTemp, meanAvg);
subtractColumns(dstTemp, meanAvg);
double distSrc = computeDistToOrigin(srcTemp);
double distDst = computeDistToOrigin(dstTemp);
double scale = (double)n / ((distSrc + distDst)*0.5);
srcTemp(cv::Range(0, srcTemp.rows), cv::Range(0,3)) *= scale;
dstTemp(cv::Range(0, dstTemp.rows), cv::Range(0,3)) *= scale;
Mat srcPC0 = srcTemp;
Mat dstPC0 = dstTemp;
// initialize pose
pose = Matx44d::eye();
Mat M = Mat::eye(4,4,CV_64F);
double tempResidual = 0;
// walk the pyramid
for (int level = m_numLevels-1; level >=0; level--)
{
const double impact = 2;
double div = pow((double)impact, (double)level);
//double div2 = div*div;
const int numSamples = cvRound((double)(n/(div)));
const double TolP = m_tolerance*(double)(level+1)*(level+1);
const int MaxIterationsPyr = cvRound((double)m_maxIterations/(level+1));
// Obtain the sampled point clouds for this level: Also rotates the normals
Mat srcPCT = transformPCPose(srcPC0, pose);
const int sampleStep = cvRound((double)n/(double)numSamples);
srcPCT = samplePCUniform(srcPCT, sampleStep);
/*
Tolga Birdal thinks that downsampling the scene points might decrease the accuracy.
Hamdi Sahloul, however, noticed that accuracy increased (pose residual decreased slightly).
*/
Mat dstPCS = samplePCUniform(dstPC0, sampleStep);
void* flann = indexPCFlann(dstPCS);
double fval_old=9999999999;
double fval_perc=0;
double fval_min=9999999999;
Mat Src_Moved = srcPCT.clone();
int i=0;
size_t numElSrc = (size_t)Src_Moved.rows;
int sizesResult[2] = {(int)numElSrc, 1};
float* distances = new float[numElSrc];
int* indices = new int[numElSrc];
Mat Indices(2, sizesResult, CV_32S, indices, 0);
Mat Distances(2, sizesResult, CV_32F, distances, 0);
// use robust weighting for outlier treatment
int* indicesModel = new int[numElSrc];
int* indicesScene = new int[numElSrc];
int* newI = new int[numElSrc];
int* newJ = new int[numElSrc];
Matx44d PoseX = Matx44d::eye();
while ( (!(fval_perc<(1+TolP) && fval_perc>(1-TolP))) && i<MaxIterationsPyr)
{
uint di=0, selInd = 0;
queryPCFlann(flann, Src_Moved, Indices, Distances);
for (di=0; di<numElSrc; di++)
{
newI[di] = di;
newJ[di] = indices[di];
}
if (useRobustReject)
{
int numInliers = 0;
float threshold = getRejectionThreshold(distances, Distances.rows, m_rejectionScale);
Mat acceptInd = Distances<threshold;
uchar *accPtr = (uchar*)acceptInd.data;
for (int l=0; l<acceptInd.rows; l++)
{
if (accPtr[l])
{
newI[numInliers] = l;
newJ[numInliers] = indices[l];
numInliers++;
}
}
numElSrc=numInliers;
}
// Step 2: Picky ICP
// Among the resulting corresponding pairs, if more than one scene point p_i
// is assigned to the same model point m_j, then select p_i that corresponds
// to the minimum distance
hashtable_int* duplicateTable = getHashtable(newJ, numElSrc, dstPCS.rows);
for (di=0; di<duplicateTable->size; di++)
{
hashnode_i *node = duplicateTable->nodes[di];
if (node)
{
// select the first node
size_t idx = reinterpret_cast<size_t>(node->data)-1, dn=0;
int dup = (int)node->key-1;
size_t minIdxD = idx;
float minDist = distances[idx];
while ( node )
{
idx = reinterpret_cast<size_t>(node->data)-1;
if (distances[idx] < minDist)
{
minDist = distances[idx];
minIdxD = idx;
}
node = node->next;
dn++;
}
indicesModel[ selInd ] = newI[ minIdxD ];
indicesScene[ selInd ] = dup ;
selInd++;
}
}
hashtableDestroy(duplicateTable);
if (selInd >= 6)
{
Mat Src_Match = Mat(selInd, srcPCT.cols, CV_64F);
Mat Dst_Match = Mat(selInd, srcPCT.cols, CV_64F);
for (di=0; di<selInd; di++)
{
const int indModel = indicesModel[di];
const int indScene = indicesScene[di];
const float *srcPt = srcPCT.ptr<float>(indModel);
const float *dstPt = dstPCS.ptr<float>(indScene);
double *srcMatchPt = Src_Match.ptr<double>(di);
double *dstMatchPt = Dst_Match.ptr<double>(di);
int ci=0;
for (ci=0; ci<srcPCT.cols; ci++)
{
srcMatchPt[ci] = (double)srcPt[ci];
dstMatchPt[ci] = (double)dstPt[ci];
}
}
Vec3d rpy, t;
minimizePointToPlaneMetric(Src_Match, Dst_Match, rpy, t);
if (cvIsNaN(cv::trace(rpy)) || cvIsNaN(cv::norm(t)))
break;
getTransformMat(rpy, t, PoseX);
Src_Moved = transformPCPose(srcPCT, PoseX);
double fval = cv::norm(Src_Match, Dst_Match)/(double)(Src_Moved.rows);
// Calculate change in error between iterations
fval_perc=fval/fval_old;
// Store error value
fval_old=fval;
if (fval < fval_min)
fval_min = fval;
}
else
break;
i++;
}
pose = PoseX * pose;
residual = tempResidual;
delete[] newI;
delete[] newJ;
delete[] indicesModel;
delete[] indicesScene;
delete[] distances;
delete[] indices;
tempResidual = fval_min;
destroyFlann(flann);
}
Matx33d Rpose;
Vec3d Cpose;
poseToRT(pose, Rpose, Cpose);
Cpose = Cpose / scale + meanAvg - Rpose * meanAvg;
rtToPose(Rpose, Cpose, pose);
residual = tempResidual;
return 0;
}
// ============================================================================
void
PrintStencil2D(const Epetra_CrsMatrix* Matrix,
const int nx, const int ny, int GID)
{
if (nx <= 0 || ny <= 0)
throw(Exception(__FILE__, __LINE__, "Input parameter not valid"));
if (GID == -1)
{
if (ny == 1)
GID = (int)(nx/2);
else
GID = (int)(nx*(ny/2) + nx/2);
}
int LID = Matrix->RowMatrixRowMap().LID(GID);
// only processor having this node will go on
if (LID == -1) return;
int MaxPerRow = Matrix->MaxNumEntries();
int NumEntriesRow; // local entries on each row
vector<double> Values(MaxPerRow);
vector<int> Indices(MaxPerRow);
int ierr = Matrix->ExtractMyRowCopy(LID, MaxPerRow, NumEntriesRow,
&Values[0], &Indices[0]);
if (ierr)
throw(Exception(__FILE__, __LINE__,
"Matrix->ExtractMyRowCopy() return an error"));
// cycle over nonzero elements, look for elements in positions that we
// can understand
int size = 5;
Epetra_IntSerialDenseMatrix SI(size, size);
Epetra_SerialDenseMatrix SV(size, size);
for (int i = 0 ; i < size ; ++i)
for (int j = 0 ; j < size ; ++j)
SV(i, j) = 0.0;
SI(0,0) = Matrix->RowMatrixColMap().LID(GID - 2 - 2 * nx);
SI(1,0) = Matrix->RowMatrixColMap().LID(GID - 1 - 2 * nx);
SI(2,0) = Matrix->RowMatrixColMap().LID(GID - 2 * nx);
SI(3,0) = Matrix->RowMatrixColMap().LID(GID + 1 - 2 * nx);
SI(4,0) = Matrix->RowMatrixColMap().LID(GID + 2 - 2 * nx);
SI(0,1) = Matrix->RowMatrixColMap().LID(GID - 2 - nx);
SI(1,1) = Matrix->RowMatrixColMap().LID(GID - 1 - nx);
SI(2,1) = Matrix->RowMatrixColMap().LID(GID - nx);
SI(3,1) = Matrix->RowMatrixColMap().LID(GID + 1 - nx);
SI(4,1) = Matrix->RowMatrixColMap().LID(GID + 2 - nx);
SI(0,2) = Matrix->RowMatrixColMap().LID(GID - 2);
SI(1,2) = Matrix->RowMatrixColMap().LID(GID - 1);
SI(2,2) = Matrix->RowMatrixColMap().LID(GID);
SI(3,2) = Matrix->RowMatrixColMap().LID(GID + 1);
SI(4,2) = Matrix->RowMatrixColMap().LID(GID + 2);
SI(0,3) = Matrix->RowMatrixColMap().LID(GID - 2 + nx);
SI(1,3) = Matrix->RowMatrixColMap().LID(GID - 1 + nx);
SI(2,3) = Matrix->RowMatrixColMap().LID(GID - nx);
SI(3,3) = Matrix->RowMatrixColMap().LID(GID + 1 + nx);
SI(4,3) = Matrix->RowMatrixColMap().LID(GID + 2 + nx);
SI(0,4) = Matrix->RowMatrixColMap().LID(GID - 2 + 2 * nx);
SI(1,4) = Matrix->RowMatrixColMap().LID(GID - 1 + 2 * nx);
SI(2,4) = Matrix->RowMatrixColMap().LID(GID - 2 * nx);
SI(3,4) = Matrix->RowMatrixColMap().LID(GID + 1 + 2 * nx);
SI(4,4) = Matrix->RowMatrixColMap().LID(GID + 2 + 2 * nx);
for (int i = 0 ; i < NumEntriesRow ; ++i)
{
// convert into block row
int LocalColID = Indices[i];
// look for known positions
for (int ix = 0 ; ix < size ; ++ix)
for (int iy = 0 ; iy < size ; ++iy)
if (SI(ix, iy) == LocalColID)
SV(ix,iy) = Values[i];
}
cout << "2D computational stencil at GID " << GID
<< " (grid is " << nx << " x " << ny << ")" << endl;
cout << endl;
for (int iy = 0 ; iy < size ; ++iy)
{
for (int ix = 0 ; ix < size ; ++ix)
{
cout << " " << std::setw(10) << SV(ix,iy);
}
cout << endl;
}
cout << endl;
}
//==========================================================================
int Ifpack_SPARSKIT::Compute()
{
if (!IsInitialized())
IFPACK_CHK_ERR(Initialize());
IsComputed_ = false;
// convert the matrix into SPARSKIT format. The matrix is then
// free'd after method Compute() returns.
// convert the matrix into CSR format. Note that nnz is an over-estimate,
// since it contains the nonzeros corresponding to external nodes as well.
int n = Matrix().NumMyRows();
int nnz = Matrix().NumMyNonzeros();
vector<double> a(nnz);
vector<int> ja(nnz);
vector<int> ia(n + 1);
const int MaxNumEntries = Matrix().MaxNumEntries();
vector<double> Values(MaxNumEntries);
vector<int> Indices(MaxNumEntries);
int count = 0;
ia[0] = 1;
for (int i = 0 ; i < n ; ++i)
{
int NumEntries;
int NumMyEntries = 0;
Matrix().ExtractMyRowCopy(i, MaxNumEntries, NumEntries, &Values[0],
&Indices[0]);
// NOTE: There might be some issues here with the ILU(0) if the column indices aren't sorted.
// The other factorizations are probably OK.
for (int j = 0 ; j < NumEntries ; ++j)
{
if (Indices[j] < n) // skip non-local columns
{
a[count] = Values[j];
ja[count] = Indices[j] + 1; // SPARSKIT is FORTRAN
++count;
++NumMyEntries;
}
}
ia[i + 1] = ia[i] + NumMyEntries;
}
if (mbloc_ == -1) mbloc_ = n;
int iwk;
if (Type_ == "ILUT" || Type_ == "ILUTP" || Type_ == "ILUD" ||
Type_ == "ILUDP")
iwk = nnz + 2 * lfil_ * n;
else if (Type_ == "ILUK")
iwk = (2 * lfil_ + 1) * nnz + 1;
else if (Type_ == "ILU0")
iwk = nnz+2;
int ierr = 0;
alu_.resize(iwk);
jlu_.resize(iwk);
ju_.resize(n + 1);
vector<int> jw(n + 1);
vector<double> w(n + 1);
if (Type_ == "ILUT")
{
jw.resize(2 * n);
F77_ILUT(&n, &a[0], &ja[0], &ia[0], &lfil_, &droptol_,
&alu_[0], &jlu_[0], &ju_[0], &iwk, &w[0], &jw[0], &ierr);
}
else if (Type_ == "ILUD")
{
jw.resize(2 * n);
F77_ILUD(&n, &a[0], &ja[0], &ia[0], &alph_, &tol_,
&alu_[0], &jlu_[0], &ju_[0], &iwk, &w[0], &jw[0], &ierr);
}
else if (Type_ == "ILUTP")
{
jw.resize(2 * n);
iperm_.resize(2 * n);
F77_ILUTP(&n, &a[0], &ja[0], &ia[0], &lfil_, &droptol_, &permtol_,
&mbloc_, &alu_[0], &jlu_[0], &ju_[0], &iwk, &w[0], &jw[0],
&iperm_[0], &ierr);
for (int i = 0 ; i < n ; ++i)
iperm_[i]--;
}
else if (Type_ == "ILUDP")
{
jw.resize(2 * n);
iperm_.resize(2 * n);
F77_ILUDP(&n, &a[0], &ja[0], &ia[0], &alph_, &droptol_, &permtol_,
&mbloc_, &alu_[0], &jlu_[0], &ju_[0], &n, &w[0], &jw[0],
&iperm_[0], &ierr);
for (int i = 0 ; i < n ; ++i)
iperm_[i]--;
}
else if (Type_ == "ILUK")
{
vector<int> levs(iwk);
jw.resize(3 * n);
F77_ILUK(&n, &a[0], &ja[0], &ia[0], &lfil_,
&alu_[0], &jlu_[0], &ju_[0], &levs[0], &iwk, &w[0], &jw[0], &ierr);
}
else if (Type_ == "ILU0")
{
// here w is only of size n
jw.resize(2 * n);
F77_ILU0(&n, &a[0], &ja[0], &ia[0],
&alu_[0], &jlu_[0], &ju_[0], &jw[0], &ierr);
}
IFPACK_CHK_ERR(ierr);
IsComputed_ = true;
return(0);
}
inline Result tuple_init( Tuple && t ) {
return etude::to_tuple( std::forward<Tuple>(t), Indices() );
}
//==============================================================================
int Ifpack_PointRelaxation::
ApplyInverseGS_RowMatrix(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
int NumVectors = X.NumVectors();
int Length = Matrix().MaxNumEntries();
vector<int> Indices(Length);
vector<double> Values(Length);
Teuchos::RefCountPtr< Epetra_MultiVector > Y2;
if (IsParallel_)
Y2 = Teuchos::rcp( new Epetra_MultiVector(Importer_->TargetMap(), NumVectors) );
else
Y2 = Teuchos::rcp( &Y, false );
// extract views (for nicer and faster code)
double** y_ptr, ** y2_ptr, ** x_ptr, *d_ptr;
X.ExtractView(&x_ptr);
Y.ExtractView(&y_ptr);
Y2->ExtractView(&y2_ptr);
Diagonal_->ExtractView(&d_ptr);
for (int j = 0; j < NumSweeps_ ; j++) {
// data exchange is here, once per sweep
if (IsParallel_)
IFPACK_CHK_ERR(Y2->Import(Y,*Importer_,Insert));
// FIXME: do I really need this code below?
if (NumVectors == 1) {
double* y0_ptr = y_ptr[0];
double* y20_ptr = y2_ptr[0];
double* x0_ptr = x_ptr[0];
if(!DoBackwardGS_){
/* Forward Mode */
for (int i = 0 ; i < NumMyRows_ ; ++i) {
int NumEntries;
int col;
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y20_ptr[col];
}
y20_ptr[i] += DampingFactor_ * d_ptr[i] * (x0_ptr[i] - dtemp);
}
}
else {
/* Backward Mode */
for (int i = NumMyRows_ - 1 ; i > -1 ; --i) {
int NumEntries;
int col;
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y20_ptr[i];
}
y20_ptr[i] += DampingFactor_ * d_ptr[i] * (x0_ptr[i] - dtemp);
}
}
// using Export() sounded quite expensive
if (IsParallel_)
for (int i = 0 ; i < NumMyRows_ ; ++i)
y0_ptr[i] = y20_ptr[i];
}
else {
if(!DoBackwardGS_){
/* Forward Mode */
for (int i = 0 ; i < NumMyRows_ ; ++i) {
int NumEntries;
int col;
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
for (int m = 0 ; m < NumVectors ; ++m) {
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y2_ptr[m][col];
}
y2_ptr[m][i] += DampingFactor_ * d_ptr[i] * (x_ptr[m][i] - dtemp);
}
}
}
else {
/* Backward Mode */
for (int i = NumMyRows_ - 1 ; i > -1 ; --i) {
int NumEntries;
int col;
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
for (int m = 0 ; m < NumVectors ; ++m) {
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y2_ptr[m][col];
}
y2_ptr[m][i] += DampingFactor_ * d_ptr[i] * (x_ptr[m][i] - dtemp);
}
}
}
// using Export() sounded quite expensive
if (IsParallel_)
for (int m = 0 ; m < NumVectors ; ++m)
for (int i = 0 ; i < NumMyRows_ ; ++i)
y_ptr[m][i] = y2_ptr[m][i];
}
}
ApplyInverseFlops_ += NumVectors * (4 * NumGlobalRows_ + 2 * NumGlobalNonzeros_);
return(0);
} //ApplyInverseGS_RowMatrix()
void BaseMesh::ClosedPlaneSplit(const Plane &P, BaseMesh &M1, BaseMesh &M2)
{
UINT VC = VertexCount(), IC = IndexCount();
MeshVertex *V = Vertices();
DWORD *I = Indices();
Vector<Vec3f> NewVertices[2];
Vector<TriMeshFace> NewFaces[2];
Vector<Vec2f> BoundaryVertices;
Vector<UINT> BoundaryIndices[2];
Vec3f OrthogonalBasis1, OrthogonalBasis2;
Vec3f::CompleteOrthonormalBasis(P.Normal(), OrthogonalBasis1, OrthogonalBasis2);
PerfectSplitVMapper *VMap = new PerfectSplitVMapper[VC];
for(UINT VertexIndex = 0; VertexIndex < VC; VertexIndex++)
{
Vec3f Pos = V[VertexIndex].Pos;
float Value = Plane::DotCoord(P, Pos);
if(Value < 0.0f)
{
VMap[VertexIndex].Side = 0;
VMap[VertexIndex].NVMap = NewVertices[0].Length();
NewVertices[0].PushEnd(Pos);
}
else
{
VMap[VertexIndex].Side = 1;
VMap[VertexIndex].NVMap = NewVertices[1].Length();
NewVertices[1].PushEnd(Pos);
}
}
for(UINT IndexIndex = 0; IndexIndex < IC; IndexIndex += 3)
{
int TSide[3];
TSide[0] = VMap[I[IndexIndex + 0]].Side;
TSide[1] = VMap[I[IndexIndex + 1]].Side;
TSide[2] = VMap[I[IndexIndex + 2]].Side;
DWORD LocalTriangleM1[6], LocalTriangleM2[6];
LocalTriangleM2[0] = LocalTriangleM1[0] = VMap[I[IndexIndex + 0]].NVMap;
LocalTriangleM2[1] = LocalTriangleM1[1] = VMap[I[IndexIndex + 1]].NVMap;
LocalTriangleM2[2] = LocalTriangleM1[2] = VMap[I[IndexIndex + 2]].NVMap;
UINT TriangleType = TSide[0] * 4 + TSide[1] * 2 + TSide[2] * 1;
for(UINT EdgeIndex = 0; EdgeIndex < 3; EdgeIndex++)
{
if(PerfectEdges[TriangleType][EdgeIndex])
{
Vec3f Vtx1 = V[I[IndexIndex + PerfectEdgeList[EdgeIndex][0]]].Pos;
Vec3f Vtx2 = V[I[IndexIndex + PerfectEdgeList[EdgeIndex][1]]].Pos;
Vec3f VtxIntersect = P.IntersectLine(Vtx1, Vtx2);
if(!Vec3f::WithinRect(VtxIntersect, Rectangle3f::ConstructFromTwoPoints(Vtx1, Vtx2)))
{
VtxIntersect = (Vtx1 + Vtx2) * 0.5f;
}
BoundaryVertices.PushEnd(Vec2f(Vec3f::Dot(VtxIntersect, OrthogonalBasis1), Vec3f::Dot(VtxIntersect, OrthogonalBasis2)));
LocalTriangleM1[3 + EdgeIndex] = NewVertices[0].Length();
BoundaryIndices[0].PushEnd(NewVertices[0].Length());
NewVertices[0].PushEnd(VtxIntersect);
LocalTriangleM2[3 + EdgeIndex] = NewVertices[1].Length();
BoundaryIndices[1].PushEnd(NewVertices[1].Length());
NewVertices[1].PushEnd(VtxIntersect);
}
}
for(UINT LocalTriangleIndex = 0; LocalTriangleIndex < 6; LocalTriangleIndex += 3)
{
if(M1Indices[TriangleType][LocalTriangleIndex] != -1)
{
TriMeshFace Tri;
Tri.I[0] = LocalTriangleM1[M1Indices[TriangleType][LocalTriangleIndex + 0]];
Tri.I[1] = LocalTriangleM1[M1Indices[TriangleType][LocalTriangleIndex + 1]];
Tri.I[2] = LocalTriangleM1[M1Indices[TriangleType][LocalTriangleIndex + 2]];
NewFaces[0].PushEnd(Tri);
}
if(M2Indices[TriangleType][LocalTriangleIndex] != -1)
{
TriMeshFace Tri;
Tri.I[0] = LocalTriangleM2[M2Indices[TriangleType][LocalTriangleIndex + 0]];
Tri.I[1] = LocalTriangleM2[M2Indices[TriangleType][LocalTriangleIndex + 1]];
Tri.I[2] = LocalTriangleM2[M2Indices[TriangleType][LocalTriangleIndex + 2]];
NewFaces[1].PushEnd(Tri);
}
}
}
#ifdef DELAUNAY_TRIANGULATOR
if(BoundaryVertices.Length() > 0)
{
Vector<DWORD> BoundaryTriangulation;
DelaunayTriangulator::Triangulate(BoundaryVertices, BoundaryTriangulation);
for(UINT TriangleIndex = 0; TriangleIndex < BoundaryTriangulation.Length() / 3; TriangleIndex++)
{
for(UINT MeshIndex = 0; MeshIndex < 2; MeshIndex++)
{
TriMeshFace Tri;
Vec3f V[3];
for(UINT LocalVertexIndex = 0; LocalVertexIndex < 3; LocalVertexIndex++)
{
Tri.I[LocalVertexIndex] = BoundaryIndices[MeshIndex][UINT(BoundaryTriangulation[TriangleIndex * 3 + LocalVertexIndex])];
V[LocalVertexIndex] = NewVertices[MeshIndex][UINT(Tri.I[LocalVertexIndex])];
}
//Utility::Swap(Tri.I[0], Tri.I[1]);
//if(Math::TriangleArea(V[0], V[1], V[2]) > 1e-5f)
{
NewFaces[MeshIndex].PushEnd(Tri);
}
}
}
}
#endif
delete[] VMap;
M1.SetGD(GetGD());
M2.SetGD(GetGD());
M1.Allocate(NewVertices[0].Length(), NewFaces[0].Length());
M2.Allocate(NewVertices[1].Length(), NewFaces[1].Length());
for(UINT VertexIndex = 0; VertexIndex < NewVertices[0].Length(); VertexIndex++)
{
M1.Vertices()[VertexIndex].Pos = NewVertices[0][VertexIndex];
}
for(UINT VertexIndex = 0; VertexIndex < NewVertices[1].Length(); VertexIndex++)
{
M2.Vertices()[VertexIndex].Pos = NewVertices[1][VertexIndex];
}
if(NewFaces[0].Length() > 0)
{
memcpy(M1.Indices(), NewFaces[0].CArray(), M1.IndexCount() * sizeof(DWORD));
}
if(NewFaces[1].Length() > 0)
{
memcpy(M2.Indices(), NewFaces[1].CArray(), M2.IndexCount() * sizeof(DWORD));
}
}
//==============================================================================
int Ifpack_PointRelaxation::
ApplyInverseSGS_RowMatrix(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
int NumVectors = X.NumVectors();
int Length = Matrix().MaxNumEntries();
vector<int> Indices(Length);
vector<double> Values(Length);
Teuchos::RefCountPtr< Epetra_MultiVector > Y2;
if (IsParallel_) {
Y2 = Teuchos::rcp( new Epetra_MultiVector(Importer_->TargetMap(), NumVectors) );
}
else
Y2 = Teuchos::rcp( &Y, false );
double** y_ptr, ** y2_ptr, ** x_ptr, *d_ptr;
X.ExtractView(&x_ptr);
Y.ExtractView(&y_ptr);
Y2->ExtractView(&y2_ptr);
Diagonal_->ExtractView(&d_ptr);
for (int iter = 0 ; iter < NumSweeps_ ; ++iter) {
// only one data exchange per sweep
if (IsParallel_)
IFPACK_CHK_ERR(Y2->Import(Y,*Importer_,Insert));
for (int i = 0 ; i < NumMyRows_ ; ++i) {
int NumEntries;
int col;
double diag = d_ptr[i];
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
for (int m = 0 ; m < NumVectors ; ++m) {
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y2_ptr[m][col];
}
y2_ptr[m][i] += DampingFactor_ * (x_ptr[m][i] - dtemp) * diag;
}
}
for (int i = NumMyRows_ - 1 ; i > -1 ; --i) {
int NumEntries;
int col;
double diag = d_ptr[i];
IFPACK_CHK_ERR(Matrix_->ExtractMyRowCopy(i, Length,NumEntries,
&Values[0], &Indices[0]));
for (int m = 0 ; m < NumVectors ; ++m) {
double dtemp = 0.0;
for (int k = 0 ; k < NumEntries ; ++k) {
col = Indices[k];
dtemp += Values[k] * y2_ptr[m][col];
}
y2_ptr[m][i] += DampingFactor_ * (x_ptr[m][i] - dtemp) * diag;
}
}
if (IsParallel_)
for (int m = 0 ; m < NumVectors ; ++m)
for (int i = 0 ; i < NumMyRows_ ; ++i)
y_ptr[m][i] = y2_ptr[m][i];
}
ApplyInverseFlops_ += NumVectors * (8 * NumGlobalRows_ + 4 * NumGlobalNonzeros_);
return(0);
}
int main(int argc, char *argv[]) {
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
bool testFailed;
bool boolret;
int MyPID = Comm.MyPID();
bool verbose = true;
bool debug = false;
std::string which("SM");
Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
cmdp.setOption("debug","nodebug",&debug,"Print debugging information.");
cmdp.setOption("sort",&which,"Targetted eigenvalues (SM,LM,SR,LR,SI,or LI).");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
typedef double ScalarType;
typedef Teuchos::ScalarTraits<ScalarType> ScalarTypeTraits;
typedef ScalarTypeTraits::magnitudeType MagnitudeType;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Anasazi::MultiVecTraits<ScalarType,MV> MVTraits;
typedef Anasazi::OperatorTraits<ScalarType,MV,OP> OpTraits;
// Dimension of the matrix
int nx = 10; // Discretization points in any one direction.
int NumGlobalElements = nx*nx; // Size of matrix nx*nx
// Construct a Map that puts approximately the same number of
// equations on each processor.
Epetra_Map Map(NumGlobalElements, 0, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map.NumMyElements();
std::vector<int> MyGlobalElements(NumMyElements);
Map.MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
// on this processor
std::vector<int> NumNz(NumMyElements);
/* We are building a matrix of block structure:
| T -I |
|-I T -I |
| -I T |
| ... -I|
| -I T|
where each block is dimension nx by nx and the matrix is on the order of
nx*nx. The block T is a tridiagonal matrix.
*/
for (int i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i] == 0 || MyGlobalElements[i] == NumGlobalElements-1 ||
MyGlobalElements[i] == nx-1 || MyGlobalElements[i] == nx*(nx-1) ) {
NumNz[i] = 3;
}
else if (MyGlobalElements[i] < nx || MyGlobalElements[i] > nx*(nx-1) ||
MyGlobalElements[i]%nx == 0 || (MyGlobalElements[i]+1)%nx == 0) {
NumNz[i] = 4;
}
else {
NumNz[i] = 5;
}
}
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, Map, &NumNz[0]) );
// Diffusion coefficient, can be set by user.
// When rho*h/2 <= 1, the discrete convection-diffusion operator has real eigenvalues.
// When rho*h/2 > 1, the operator has complex eigenvalues.
double rho = 2*(nx+1);
// Compute coefficients for discrete convection-diffution operator
const double one = 1.0;
std::vector<double> Values(4);
std::vector<int> Indices(4);
double h = one /(nx+1);
double h2 = h*h;
double c = 5.0e-01*rho/ h;
Values[0] = -one/h2 - c; Values[1] = -one/h2 + c; Values[2] = -one/h2; Values[3]= -one/h2;
double diag = 4.0 / h2;
int NumEntries, info;
for (int i=0; i<NumMyElements; i++)
{
if (MyGlobalElements[i]==0)
{
Indices[0] = 1;
Indices[1] = nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx*(nx-1))
{
Indices[0] = nx*(nx-1)+1;
Indices[1] = nx*(nx-2);
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx-1)
{
Indices[0] = nx-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = 2*nx-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == NumGlobalElements-1)
{
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = nx*(nx-1)-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] < nx)
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] > nx*(nx-1))
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i]%nx == 0)
{
Indices[0] = MyGlobalElements[i]+1;
Indices[1] = MyGlobalElements[i]-nx;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if ((MyGlobalElements[i]+1)%nx == 0)
{
Indices[0] = MyGlobalElements[i]-nx;
Indices[1] = MyGlobalElements[i]+nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
Indices[0] = MyGlobalElements[i]-1;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
Indices[3] = MyGlobalElements[i]+nx;
NumEntries = 4;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
// Put in the diagonal entry
info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
assert( info==0 );
}
// Finish up
info = A->FillComplete();
assert( info==0 );
A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks
//************************************
// Start the block Davidson iteration
//***********************************
//
// Variables used for the Generalized Davidson Method
//
int nev = 4;
int blockSize = 1;
int maxDim = 50;
int restartDim = 10;
int maxRestarts = 500;
double tol = 1e-10;
// Set verbosity level
int verbosity = Anasazi::Errors + Anasazi::Warnings;
if (verbose) {
verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
}
if (debug) {
verbosity += Anasazi::Debug;
}
//
// Create parameter list to pass into solver manager
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Maximum Subspace Dimension", maxDim);
MyPL.set( "Restart Dimension", restartDim);
MyPL.set( "Maximum Restarts", maxRestarts );
MyPL.set( "Convergence Tolerance", tol );
MyPL.set( "Relative Convergence Tolerance", true );
MyPL.set( "Initial Guess", "User" );
// Create an Epetra_MultiVector for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
Teuchos::RCP<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(Map, blockSize) );
ivec->Random();
// Create the eigenproblem.
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem = Teuchos::rcp(
new Anasazi::BasicEigenproblem<double,MV,OP>() );
MyProblem->setA(A);
MyProblem->setInitVec(ivec);
// Inform the eigenproblem that the operator A is non-Hermitian
MyProblem->setHermitian(false);
// Set the number of eigenvalues requested
MyProblem->setNEV( nev );
// Inform the eigenproblem that you are finishing passing it information
boolret = MyProblem->setProblem();
if (boolret != true) {
if (verbose && MyPID == 0) {
std::cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << std::endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}
// Initialize the Block Arnoldi solver
Anasazi::GeneralizedDavidsonSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);
// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
testFailed = false;
if (returnCode != Anasazi::Converged && MyPID==0 && verbose) {
testFailed = true;
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<ScalarType,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<ScalarType> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
std::vector<int> index = sol.index;
int numev = sol.numVecs;
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
int numritz = (int)evals.size();
std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
std::cout<<std::endl<< "Computed Ritz Values"<< std::endl;
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numritz; i++) {
std::cout<< std::setw(16) << evals[i].realpart
<< std::setw(16) << evals[i].imagpart
<< std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
if (numev > 0) {
// Compute residuals.
Teuchos::LAPACK<int,double> lapack;
std::vector<double> normA(numev);
// The problem is non-Hermitian.
int i=0;
std::vector<int> curind(1);
std::vector<double> resnorm(1), tempnrm(1);
Teuchos::RCP<MV> tempAevec;
Teuchos::RCP<const MV> evecr, eveci;
Epetra_MultiVector Aevec(Map,numev);
// Compute A*evecs
OpTraits::Apply( *A, *evecs, Aevec );
Teuchos::SerialDenseMatrix<int,double> Breal(1,1), Bimag(1,1);
while (i<numev) {
if (index[i]==0) {
// Get a view of the current eigenvector (evecr)
curind[0] = i;
evecr = MVTraits::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Compute A*evecr - lambda*evecr
Breal(0,0) = evals[i].realpart;
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
// Compute the norm of the residual and increment counter
MVTraits::MvNorm( *tempAevec, resnorm );
normA[i] = resnorm[0] / Teuchos::ScalarTraits<MagnitudeType>::magnitude( evals[i].realpart );
i++;
} else {
// Get a view of the real part of the eigenvector (evecr)
curind[0] = i;
evecr = MVTraits::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Get a view of the imaginary part of the eigenvector (eveci)
curind[0] = i+1;
eveci = MVTraits::CloneView( *evecs, curind );
// Set the eigenvalue into Breal and Bimag
Breal(0,0) = evals[i].realpart;
Bimag(0,0) = evals[i].imagpart;
// Compute A*evecr - evecr*lambdar + eveci*lambdai
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
MVTraits::MvTimesMatAddMv( 1.0, *eveci, Bimag, 1.0, *tempAevec );
MVTraits::MvNorm( *tempAevec, tempnrm );
// Get a copy of A*eveci
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Compute A*eveci - eveci*lambdar - evecr*lambdai
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Bimag, 1.0, *tempAevec );
MVTraits::MvTimesMatAddMv( -1.0, *eveci, Breal, 1.0, *tempAevec );
MVTraits::MvNorm( *tempAevec, resnorm );
// Compute the norms and scale by magnitude of eigenvalue
normA[i] = lapack.LAPY2( tempnrm[0], resnorm[0] ) /
lapack.LAPY2( evals[i].realpart, evals[i].imagpart );
normA[i+1] = normA[i];
i=i+2;
}
}
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
std::cout<<std::endl<< "Actual Residuals"<<std::endl;
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::setw(20) << "Direct Residual"<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int j=0; j<numev; j++) {
std::cout<< std::setw(16) << evals[j].realpart
<< std::setw(16) << evals[j].imagpart
<< std::setw(20) << normA[j] << std::endl;
if ( normA[j] > tol ) {
testFailed = true;
}
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
}
#ifdef EPETRA_MPI
MPI_Finalize();
#endif
if (testFailed) {
if (verbose && MyPID==0) {
std::cout << "End Result: TEST FAILED" << std::endl;
}
return -1;
}
//
// Default return value
//
if (verbose && MyPID==0) {
std::cout << "End Result: TEST PASSED" << std::endl;
}
return 0;
}
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> >
TriDiag_Helmholtz_Pair(const Teuchos::RCP<const Map> & map, const GlobalOrdinal nx,
const double h, const double omega, const Scalar shift) {
Teuchos::RCP<Matrix> ktx = MatrixTraits<Map,Matrix>::Build(map, 3);
Teuchos::RCP<Matrix> mtx = MatrixTraits<Map,Matrix>::Build(map, 1);
LocalOrdinal NumMyElements = map->getNodeNumElements();
Teuchos::ArrayView<const GlobalOrdinal> MyGlobalElements = map->getNodeElementList();
Teuchos::RCP<const Teuchos::Comm<int> > comm = map->getComm();
GlobalOrdinal NumGlobalElements = map->getGlobalNumElements();
GlobalOrdinal NumEntries;
LocalOrdinal nnz=2;
std::vector<Scalar> Values(nnz);
std::vector<GlobalOrdinal> Indices(nnz);
Scalar one = (Scalar) 1.0;
comm->barrier();
if (comm->getRank() == 0) {
std::cout << "starting global insert" << std::endl;
}
Teuchos::RCP<Teuchos::Time> timer = rcp(new Teuchos::Time("TriDiag global insert"));
timer->start(true);
for (LocalOrdinal i = 0; i < NumMyElements; ++i) {
if (MyGlobalElements[i] == 0) {
// off-diagonal for first row
Indices[0] = 1;
NumEntries = 1;
Values[0] = -one;
}
else if (MyGlobalElements[i] == NumGlobalElements - 1) {
// off-diagonal for last row
Indices[0] = NumGlobalElements - 2;
NumEntries = 1;
Values[0] = -one;
}
else {
// off-diagonal for internal row
Indices[0] = MyGlobalElements[i] - 1;
Indices[1] = MyGlobalElements[i] + 1;
Values[0] = -one;
Values[1] = -one;
NumEntries = 2;
}
// put the off-diagonal entries
// Xpetra wants ArrayViews (sigh)
Teuchos::ArrayView<Scalar> av(&Values[0],NumEntries);
Teuchos::ArrayView<GlobalOrdinal> iv(&Indices[0],NumEntries);
ktx->insertGlobalValues(MyGlobalElements[i], iv, av);
// Put in the diagonal entry
mtx->insertGlobalValues(MyGlobalElements[i],
Teuchos::tuple<GlobalOrdinal>(MyGlobalElements[i]),
Teuchos::tuple<Scalar>(h*h) );
}
timer->stop();
timer = rcp(new Teuchos::Time("TriDiag fillComplete"));
timer->start(true);
ktx->fillComplete();
mtx->fillComplete();
timer->stop();
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> > system;
system=std::make_pair(ktx,mtx);
return system;
} //TriDiag_Helmholtz
//==============================================================================
int Ifpack_GreedyPartitioner::ComputePartitions()
{
std::vector<int> ElementsPerPart(NumLocalParts());
std::vector<int> Count(NumLocalParts());
for (int i = 0 ; i < NumLocalParts() ; ++i)
Count[i] = 0;
// define how many nodes have to be put on each part
int div = NumMyRows() / NumLocalParts();
int mod = NumMyRows() % NumLocalParts();
for (int i = 0 ; i < NumLocalParts() ; ++i) {
Count[i] = 0;
ElementsPerPart[i] = div;
if (i < mod) ElementsPerPart[i]++;
}
for( int i=0 ; i<NumMyRows() ; ++i ) {
Partition_[i] = -1;
}
int NumEntries;
std::vector<int> Indices(MaxNumEntries());
// load root node for partition 0
int CurrentPartition = 0;
int TotalCount = 0;
// filter singletons and empty rows, put all of them in partition 0
for (int i = 0 ; i < NumMyRows() ; ++i) {
NumEntries = 0;
int ierr = Graph_->ExtractMyRowCopy(i, MaxNumEntries(),
NumEntries, &Indices[0]);
IFPACK_CHK_ERR(ierr);
if (NumEntries <= 1) {
Partition_[i] = 0;
TotalCount++;
}
}
if (TotalCount)
CurrentPartition = 1;
std::vector<int> ThisLevel(1);
ThisLevel[0] = RootNode_;
// be sure that RootNode is not a singleton or empty row
if (Partition_[RootNode_] != -1) {
// look for another RN
for (int i = 0 ; i < NumMyRows() ; ++i)
if (Partition_[i] == -1) {
ThisLevel[0] = i;
break;
}
}
else {
Partition_[RootNode_] = CurrentPartition;
}
// now aggregate the non-empty and non-singleton rows
while (ThisLevel.size()) {
std::vector<int> NextLevel;
for (unsigned int i = 0 ; i < ThisLevel.size() ; ++i) {
int CurrentNode = ThisLevel[i];
int ierr = Graph_->ExtractMyRowCopy(CurrentNode, MaxNumEntries(),
NumEntries, &Indices[0]);
IFPACK_CHK_ERR(ierr);
if (NumEntries <= 1)
continue;
for (int j = 0 ; j < NumEntries ; ++j) {
int NextNode = Indices[j];
if (NextNode >= NumMyRows()) continue;
if (Partition_[NextNode] == -1) {
// this is a free node
NumLocalParts_ = CurrentPartition + 1;
Partition_[NextNode] = CurrentPartition;
++Count[CurrentPartition];
++TotalCount;
NextLevel.push_back(NextNode);
}
}
} // for (i)
// check whether change partition or not
if (Count[CurrentPartition] >= ElementsPerPart[CurrentPartition])
++CurrentPartition;
// swap next and this
ThisLevel.resize(0);
for (unsigned int i = 0 ; i < NextLevel.size() ; ++i)
ThisLevel.push_back(NextLevel[i]);
if (ThisLevel.size() == 0 && (TotalCount != NumMyRows())) {
// need to look for new RootNode, do this in a simple way
for (int i = 0 ; i < NumMyRows() ; i++) {
if (Partition_[i] == -1)
ThisLevel.push_back(i);
break;
}
}
} // while (ok)
return(0);
}
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> >
Cross2D_Helmholtz_Pair(const Teuchos::RCP<const Map> & map,
const GlobalOrdinal nx, const GlobalOrdinal ny,
const double h, const double delta,
const int PMLgridptsx_left, const int PMLgridptsx_right,
const int PMLgridptsy_left, const int PMLgridptsy_right,
const double omega, const Scalar shift,
const int model) {
Teuchos::RCP<Matrix> ktx = MatrixTraits<Map,Matrix>::Build(map, 5);
Teuchos::RCP<Matrix> mtx = MatrixTraits<Map,Matrix>::Build(map, 1);
LocalOrdinal NumMyElements = map->getNodeNumElements();
Teuchos::ArrayView<const GlobalOrdinal> MyGlobalElements = map->getNodeElementList();
GlobalOrdinal left, right, lower, upper, center;
LocalOrdinal nnz=5;
std::vector<Scalar> Values(nnz);
std::vector<GlobalOrdinal> Indices(nnz);
VelocityModel<Scalar,LocalOrdinal,GlobalOrdinal> velocitymodel(2,model);
double LBx, RBx, LBy, RBy, Dx, Dy;
Scalar sx_left, sx_center, sx_right;
Scalar sy_left, sy_center, sy_right;
Scalar c;
// Calculate some parameters
Dx = ((double) nx-1)*h;
Dy = ((double) ny-1)*h;
LBx = ((double) PMLgridptsx_left)*h;
RBx = Dx-((double) PMLgridptsx_right)*h;
LBy = ((double) PMLgridptsy_left)*h;
RBy = Dy-((double) PMLgridptsy_right)*h;
for (LocalOrdinal i = 0; i < NumMyElements; ++i) {
// calculate PML functions
size_t numEntries = 0;
center = MyGlobalElements[i];
GetNeighboursCartesian2d(center, nx, ny, left, right, lower, upper);
GetPMLvalues(center, nx, ny, h, delta,
Dx, Dy, LBx, RBx, LBy, RBy,
sx_left, sx_center, sx_right,
sy_left, sy_center, sy_right);
// get velocity
GlobalOrdinal ix, iy;
ix = i % nx;
iy = (i - ix) / nx;
double xcoord, ycoord;
xcoord=((double) ix)*h;
ycoord=((double) iy)*h;
c = velocitymodel.getVelocity(xcoord,ycoord,0.0);
if (left != -1) {
Indices[numEntries] = left;
Values [numEntries] = -(sy_center/sx_center + sy_center/sx_left)/2.0;
numEntries++;
}
if (right != -1) {
Indices[numEntries] = right;
Values [numEntries] = -(sy_center/sx_center + sy_center/sx_right)/2.0;
numEntries++;
}
if (lower != -1) {
Indices[numEntries] = lower;
Values [numEntries] = -(sx_center/sy_center + sx_center/sy_left)/2.0;
numEntries++;
}
if (upper != -1) {
Indices[numEntries] = upper;
Values [numEntries] = -(sx_center/sy_center + sx_center/sy_right)/2.0;
numEntries++;
}
// diagonal
Scalar z = (Scalar) 0.0;
for (size_t j = 0; j < numEntries; j++)
z -= Values[j];
Indices[numEntries] = center;
Values [numEntries] = z;
numEntries++;
Teuchos::ArrayView<GlobalOrdinal> iv(&Indices[0], numEntries);
Teuchos::ArrayView<Scalar> av(&Values[0], numEntries);
ktx->insertGlobalValues(center, iv, av);
mtx->insertGlobalValues(center,
Teuchos::tuple<GlobalOrdinal>(center),
Teuchos::tuple<Scalar>(h*h*sx_center*sy_center/(c*c)) );
}
ktx->fillComplete();
mtx->fillComplete();
std::pair< Teuchos::RCP<Matrix>, Teuchos::RCP<Matrix> > system;
system=std::make_pair(ktx,mtx);
return system;
} //Cross2D_Helmholtz
int main(int argc, char *argv[])
{
int ierr = 0, i, forierr = 0;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
int rank; // My process ID
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
int rank = 0;
Epetra_SerialComm Comm;
#endif
bool verbose = false;
// Check if we should print results to standard out
if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
int verbose_int = verbose ? 1 : 0;
Comm.Broadcast(&verbose_int, 1, 0);
verbose = verbose_int==1 ? true : false;
// char tmp;
// if (rank==0) cout << "Press any key to continue..."<< endl;
// if (rank==0) cin >> tmp;
// Comm.Barrier();
Comm.SetTracebackMode(0); // This should shut down any error traceback reporting
int MyPID = Comm.MyPID();
int NumProc = Comm.NumProc();
if(verbose && MyPID==0)
cout << Epetra_Version() << endl << endl;
if (verbose) cout << "Processor "<<MyPID<<" of "<< NumProc
<< " is alive."<<endl;
// Redefine verbose to only print on PE 0
if(verbose && rank!=0)
verbose = false;
int NumMyEquations = 10000;
int NumGlobalEquations = (NumMyEquations * NumProc) + EPETRA_MIN(NumProc,3);
if(MyPID < 3)
NumMyEquations++;
// Construct a Map that puts approximately the same Number of equations on each processor
Epetra_Map Map(NumGlobalEquations, NumMyEquations, 0, Comm);
// Get update list and number of local equations from newly created Map
vector<int> MyGlobalElements(Map.NumMyElements());
Map.MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation on this processor
vector<int> NumNz(NumMyEquations);
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for(i = 0; i < NumMyEquations; i++)
if((MyGlobalElements[i] == 0) || (MyGlobalElements[i] == NumGlobalEquations - 1))
NumNz[i] = 1;
else
NumNz[i] = 2;
// Create a Epetra_Matrix
Epetra_CrsMatrix A(Copy, Map, &NumNz[0]);
EPETRA_TEST_ERR(A.IndicesAreGlobal(),ierr);
EPETRA_TEST_ERR(A.IndicesAreLocal(),ierr);
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
vector<double> Values(2);
Values[0] = -1.0;
Values[1] = -1.0;
vector<int> Indices(2);
double two = 2.0;
int NumEntries;
forierr = 0;
for(i = 0; i < NumMyEquations; i++) {
if(MyGlobalElements[i] == 0) {
Indices[0] = 1;
NumEntries = 1;
}
else if (MyGlobalElements[i] == NumGlobalEquations-1) {
Indices[0] = NumGlobalEquations-2;
NumEntries = 1;
}
else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
forierr += !(A.InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0])==0);
forierr += !(A.InsertGlobalValues(MyGlobalElements[i], 1, &two, &MyGlobalElements[i])>0); // Put in the diagonal entry
}
EPETRA_TEST_ERR(forierr,ierr);
// Finish up
A.FillComplete();
A.OptimizeStorage();
Epetra_JadMatrix JadA(A);
Epetra_JadMatrix JadA1(A);
Epetra_JadMatrix JadA2(A);
// Create vectors for Power method
Epetra_Vector q(Map);
Epetra_Vector z(Map);
z.Random();
Epetra_Vector resid(Map);
Epetra_Flops flopcounter;
A.SetFlopCounter(flopcounter);
q.SetFlopCounter(A);
z.SetFlopCounter(A);
resid.SetFlopCounter(A);
JadA.SetFlopCounter(A);
JadA1.SetFlopCounter(A);
JadA2.SetFlopCounter(A);
if (verbose) cout << "=======================================" << endl
<< "Testing Jad using CrsMatrix as input..." << endl
<< "=======================================" << endl;
A.ResetFlops();
powerMethodTests(A, JadA, Map, q, z, resid, verbose);
// Increase diagonal dominance
if (verbose) cout << "\n\nIncreasing the magnitude of first diagonal term and solving again\n\n"
<< endl;
if (A.MyGlobalRow(0)) {
int numvals = A.NumGlobalEntries(0);
vector<double> Rowvals(numvals);
vector<int> Rowinds(numvals);
A.ExtractGlobalRowCopy(0, numvals, numvals, &Rowvals[0], &Rowinds[0]); // Get A[0,0]
for (i=0; i<numvals; i++) if (Rowinds[i] == 0) Rowvals[i] *= 10.0;
A.ReplaceGlobalValues(0, numvals, &Rowvals[0], &Rowinds[0]);
}
JadA.UpdateValues(A);
A.ResetFlops();
powerMethodTests(A, JadA, Map, q, z, resid, verbose);
if (verbose) cout << "================================================================" << endl
<< "Testing Jad using Jad matrix as input matrix for construction..." << endl
<< "================================================================" << endl;
JadA1.ResetFlops();
powerMethodTests(JadA1, JadA2, Map, q, z, resid, verbose);
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
return ierr ;
}
void BaseMesh::CreateSphere(float radius, int slices, int stacks)
{
Allocate(slices * (stacks - 1) + 2,slices * 2 * (stacks - 1)); //allocate space for the angular splits
float PI_Stacks = Math::PIf / float(stacks);
float PI2_Slices = 2.0f * Math::PIf / float(slices);
float Theta, Phi,CosP,SinP;
int i,i2,vc=0,ic=0;
MeshVertex *V = Vertices();
DWORD *I = Indices();
MeshVertex MVtx(Vec3f::Origin, Vec3f::Origin, RGBColor::White, Vec2f::Origin);
for(i=1;i < stacks;i++)
{
Phi = float(i) * PI_Stacks;
CosP = cosf(Phi);
SinP = sinf(Phi);
for(i2=0;i2 < slices;i2++)
{
Theta = float(i2) * PI2_Slices;
MVtx.Pos = Vec3f(radius * cosf(Theta) * SinP, radius * sinf(Theta) * SinP, radius * CosP); //create the new vertex
V[vc++] = MVtx; //add the vertex to the mesh
}
}
//add the top and bottom vertices to the mesh
int TopVertex = vc,BottomVertex = vc+1;
MVtx.Pos = Vec3f(0.0f,0.0f,radius);
V[vc++] = MVtx;
MVtx.Pos = Vec3f(0.0f,0.0f,-radius);
V[vc++] = MVtx;
//add the top and bottom triangles (all triangles involving the TopVertex and BottomVertex)
int ip1,i2p1;
for(i=0;i < slices;i++)
{
ip1 = i + 1;
if(ip1 == slices) ip1 = 0;
I[ic++] = i;
I[ic++] = TopVertex; //top triangle
I[ic++] = ip1;
I[ic++] = ip1 + (stacks - 2) * slices;
I[ic++] = BottomVertex; //bottom triangle
I[ic++] = i + (stacks - 2) * slices;
}
//add all the remaining triangles
for(i=0;i < stacks - 2;i++)
{
for(i2=0;i2 < slices;i2++)
{
i2p1 = i2 + 1;
if(i2p1 == slices) i2p1 = 0;
I[ic++] = (i+1) * slices + i2;
I[ic++] = i * slices + i2;
I[ic++] = i * slices + i2p1;
I[ic++] = (i+1) * slices + i2;
I[ic++] = i * slices + i2p1;
I[ic++] = (i+1) * slices + i2p1;
}
}
GenerateNormals();
}