// ======================================================================
bool BasicTest(string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A,bool backward, bool reorder=false)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
double starting_residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
// Set up the list
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: sweeps",2550);
List.set("relaxation: type", PrecType);
if(backward) List.set("relaxation: backward mode",backward);
// Reordering if needed
int NumRows=A->NumMyRows();
std::vector<int> RowList(NumRows);
if(reorder) {
for(int i=0; i<NumRows; i++)
RowList[i]=i;
List.set("relaxation: number of local smoothing indices",NumRows);
List.set("relaxation: local smoothing indices",RowList.size()>0? &RowList[0] : (int*)0);
}
Ifpack_PointRelaxation Point(&*A);
Point.SetParameters(List);
Point.Compute();
// use the preconditioner as solver, with 1550 iterations
Point.ApplyInverse(RHS,LHS);
// compute the real residual
double residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
if (A->Comm().MyPID() == 0 && verbose)
cout << "||A * x - b||_2 (scaled) = " << residual / starting_residual << endl;
// Jacobi is very slow to converge here
if (residual / starting_residual < 1e-2) {
if (verbose)
cout << "BasicTest Test passed" << endl;
return(true);
}
else {
if (verbose)
cout << "BasicTest Test failed!" << endl;
return(false);
}
}
bool Test(const Teuchos::RefCountPtr<Epetra_RowMatrix>& Matrix, Teuchos::ParameterList& List)
{
int NumVectors = 1;
bool UseTranspose = false;
Epetra_MultiVector LHS(Matrix->OperatorDomainMap(),NumVectors);
Epetra_MultiVector RHS(Matrix->OperatorRangeMap(),NumVectors);
Epetra_MultiVector LHSexact(Matrix->OperatorDomainMap(),NumVectors);
LHS.PutScalar(0.0);
LHSexact.Random();
Matrix->Multiply(UseTranspose,LHSexact,RHS);
Epetra_LinearProblem Problem(&*Matrix,&LHS,&RHS);
Teuchos::RefCountPtr<T> Prec;
Prec = Teuchos::rcp( new T(&*Matrix) );
assert(Prec != Teuchos::null);
IFPACK_CHK_ERR(Prec->SetParameters(List));
IFPACK_CHK_ERR(Prec->Initialize());
IFPACK_CHK_ERR(Prec->Compute());
// create the AztecOO solver
AztecOO AztecOOSolver(Problem);
// specify solver
AztecOOSolver.SetAztecOption(AZ_solver,AZ_gmres);
AztecOOSolver.SetAztecOption(AZ_output,32);
AztecOOSolver.SetPrecOperator(&*Prec);
// solver. The solver should converge in one iteration,
// or maximum two (numerical errors)
AztecOOSolver.Iterate(1550,1e-8);
cout << *Prec;
vector<double> Norm(NumVectors);
LHS.Update(1.0,LHSexact,-1.0);
LHS.Norm2(&Norm[0]);
for (int i = 0 ; i < NumVectors ; ++i) {
cout << "Norm[" << i << "] = " << Norm[i] << endl;
if (Norm[i] > 1e-3)
return(false);
}
return(true);
}
// ======================================================================
int AllSingle(const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, Teuchos::RCP<Epetra_MultiVector> coord)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: type", "symmetric Gauss-Seidel");
List.set("relaxation: sweeps",1);
List.set("partitioner: overlap",0);
List.set("partitioner: type", "line");
List.set("partitioner: line detection threshold",1.0);
List.set("partitioner: x-coordinates",&(*coord)[0][0]);
List.set("partitioner: y-coordinates",&(*coord)[1][0]);
List.set("partitioner: z-coordinates",(double*) 0);
RHS.PutScalar(1.0);
LHS.PutScalar(0.0);
Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Prec(&*A);
Prec.SetParameters(List);
Prec.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
if (verbose)
AztecOOSolver.SetAztecOption(AZ_output,32);
else
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Prec);
AztecOOSolver.Iterate(2550,1e-5);
printf(" AllSingle iters %d \n",AztecOOSolver.NumIters());
return(AztecOOSolver.NumIters());
}
QString CEdge::DisplayParse( StringToString* filter )
{
QString parse = LHS() + "( ";
if( m_Daughters.count() )
{
CEdge* daughter;
for( daughter = m_Daughters.first(); daughter; daughter = m_Daughters.next() )
{
parse += daughter->DisplayParse( filter );
parse += " ";
}
}
else
{
if( filter ) parse += Filter( filter, RHS() );
else parse += RHS();
parse += " ";
}
return parse + ")";
}
// ======================================================================
int CompareLineSmootherEntries(const Teuchos::RefCountPtr<Epetra_RowMatrix>& A)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: type", "symmetric Gauss-Seidel");
List.set("relaxation: sweeps",1);
List.set("partitioner: overlap",0);
List.set("partitioner: type", "line");
List.set("partitioner: line mode","matrix entries");
List.set("partitioner: line detection threshold",10.0);
RHS.PutScalar(1.0);
LHS.PutScalar(0.0);
Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Prec(&*A);
Prec.SetParameters(List);
Prec.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
if (verbose)
AztecOOSolver.SetAztecOption(AZ_output,32);
else
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Prec);
AztecOOSolver.Iterate(2550,1e-5);
return(AztecOOSolver.NumIters());
}
// ======================================================================
int CompareBlockOverlap(const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, int Overlap)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: type", "Jacobi");
List.set("relaxation: sweeps",1);
List.set("partitioner: overlap", Overlap);
List.set("partitioner: type", "linear");
List.set("partitioner: local parts", 16);
RHS.PutScalar(1.0);
LHS.PutScalar(0.0);
Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Prec(&*A);
Prec.SetParameters(List);
Prec.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
if (verbose)
AztecOOSolver.SetAztecOption(AZ_output,32);
else
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Prec);
AztecOOSolver.Iterate(1550,1e-5);
return(AztecOOSolver.NumIters());
}
// ======================================================================
bool TestContainer(string Type, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A)
{
int NumVectors = 3;
int NumMyRows = A->NumMyRows();
Epetra_MultiVector LHS_exact(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS_exact.Random(); LHS.PutScalar(0.0);
A->Multiply(false, LHS_exact, RHS);
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
if (verbose) {
cout << "Container type = " << Type << endl;
cout << "NumMyRows = " << NumMyRows << ", NumVectors = " << NumVectors << endl;
}
LHS.PutScalar(0.0);
Teuchos::RefCountPtr<Ifpack_Container> Container;
if (Type == "dense")
Container = Teuchos::rcp( new Ifpack_DenseContainer(A->NumMyRows(), NumVectors) );
else
Container = Teuchos::rcp( new Ifpack_SparseContainer<Ifpack_Amesos>(A->NumMyRows(), NumVectors) );
assert (Container != Teuchos::null);
IFPACK_CHK_ERR(Container->Initialize());
// set as ID all the local rows of A
for (int i = 0 ; i < A->NumMyRows() ; ++i)
Container->ID(i) = i;
// extract submatrix (in this case, the entire matrix)
// and complete setup
IFPACK_CHK_ERR(Container->Compute(*A));
// set the RHS and LHS
for (int i = 0 ; i < A->NumMyRows() ; ++i)
for (int j = 0 ; j < NumVectors ; ++j) {
Container->RHS(i,j) = RHS[j][i];
Container->LHS(i,j) = LHS[j][i];
}
// set parameters (empty for dense containers)
Teuchos::ParameterList List;
List.set("amesos: solver type", Type);
IFPACK_CHK_ERR(Container->SetParameters(List));
// solve the linear system
IFPACK_CHK_ERR(Container->ApplyInverse());
// get the computed solution, store it in LHS
for (int i = 0 ; i < A->NumMyRows() ; ++i)
for (int j = 0 ; j < NumVectors ; ++j) {
LHS[j][i] = Container->LHS(i,j);
}
double residual = Galeri::ComputeNorm(&LHS, &LHS_exact);
if (A->Comm().MyPID() == 0 && verbose) {
cout << "||x_exact - x||_2 = " << residual << endl;
cout << *Container;
}
bool passed = false;
if (residual < 1e-5)
passed = true;
return(passed);
}
void EventLoop(CCam & Camera1)
{
bool quitit=false;
SDL_Event event;
SDL_MouseMotionEvent event2;
SDL_keysym *whatkey;
bool mousedown=false;
// Go to while(!quitit) to see what happens once data set up
// Go to Render Scene for graphics bit
bool exitnow=false;
double xunit,yunit,zunit;
xunit=1.0;yunit=1.0;zunit=1.0;
// if_stream opens for input
// of_stream opens for output
// f_stream opens for both
//
string filename ="Sphere4.dat";
ifstream file_in;
file_in.open(filename.c_str());
file_in >> n_nodes >> ntri;
cout << n_nodes << " number of nodes" << endl;
cout << ntri<< " number of triangles" << endl;
cout << "read next line\n";
cout << "start read loop\n";
Triangles=(Triangle*)calloc(ntri, sizeof(Triangle));
NodeV=(D3Dvec*)calloc(n_nodes, sizeof(D3Dvec));
//initiales
char quad, otherquad;
int id,l,m,n;
double x,y,z;
for(int i=0; i<ntri;i++){
file_in >>l;
file_in >>m;
file_in >>n;
file_in >>quad;
// same resuly of file_in >> l >>m >>n;
Triangles[i]=Triangle(); //initialise
Triangles[i].SetTri(l,m,n);
Triangles[i].SetQuad(quad);
}
for(int i=0; i<ntri;i++){
file_in >> l >> m >> n;
Triangles[i].SetNeighb(l,m,n);
}
for(int i=0; i < n_nodes; i++){
NodeV[i]=D3Dvec();
file_in >> x >> y >> z;
NodeV[i].SetVec(x,y,z);
}
istart=0;
istop=ntri;
/**********************************************************************************
Calculate Metric Tensor
**********************************************************************************/
double **Gmetric;
Gmetric =(double**)calloc( ntri, sizeof( double[3] ) );
if(!Gmetric){ cout << "Memory Failed for Gmetric " << endl; exit(0);}
// 2D vectors in each triangle
double **avec, **bvec;
avec=(double**)calloc( ntri, sizeof(double[2]) );
if(!avec){ cout << "Memory Failed for avec" << endl; exit(0);}
bvec=(double**)calloc( ntri, sizeof(double[2]) );
if(!bvec){ cout << "Memory Failed for bvec" << endl; exit(0);}
double avecdash[2], bvecdash[2];
double avecdash_new[2], bvecdash_new[2];
D3Dvec Ve1,Ve2,VOrig; //origin and edge vectors
Ve1=D3Dvec(); Ve2=D3Dvec(); VOrig=D3Dvec(); //Initialise
D3Dvec Unit_i, Unit_j, Unit_k;
Unit_i=D3Dvec(); Unit_j=D3Dvec(); Unit_k=D3Dvec();
int i1,i2,i3;
double rad=-1;
for(int i=0; i<ntri; i++){
Gmetric[i]=new double[3]; //initialise
i1=Triangles[i].Get1();
i2=Triangles[i].Get2();
i3=Triangles[i].Get3();
x=NodeV[i1].GetX();
y=NodeV[i1].GetY();
z=NodeV[i1].GetZ();
VOrig.SetVec(x,y,z);
x=NodeV[i2].GetX()-VOrig.GetX();
y=NodeV[i2].GetY()-VOrig.GetY();
z=NodeV[i2].GetZ()-VOrig.GetZ();
Ve1.SetVec(x,y,z);
x=NodeV[i3].GetX()-VOrig.GetX();
y=NodeV[i3].GetY()-VOrig.GetY();
z=NodeV[i3].GetZ()-VOrig.GetZ();
Ve2.SetVec(x,y,z);
Gmetric[i][0]=Ve1.Dot(Ve1);
Gmetric[i][1]=Ve1.Dot(Ve2);
Gmetric[i][2]=Ve2.Dot(Ve2);
rad=Gmetric[i][0];
rad=sqrt(rad)*6370.;
// local cartesians
Unit_i=Ve1;
Normalise(Unit_i);
Unit_k=Ve1*Ve2;
Normalise(Unit_k);
Unit_j=Unit_k*Unit_i;
avec[i]=new double[2];
bvec[i]=new double[2];
avec[i][0]=Unit_i.Dot(Ve1);
avec[i][1]=0.0;
bvec[i][0]=Unit_i.Dot(Ve2);
bvec[i][1]=Unit_j.Dot(Ve2);
}
/**********************************************************************************
GEODESIC- start point
**********************************************************************************/
// Now for a geodesic !
//
int Tstart0=56;
int Tstart, TNext;
double xO,yO,zO;
double x1,y1,z1;
double x2,y2,z2;
double x3,y3,z3;
char qStart,qNext;
double d1, d2, lambda;
double d1dash,d2dash;
double ds_total, ds_squared;
double alpha_start, beta_start;
double alphaTstart, betaTstart;
//values of lambda to hit the line alpha=0, beta=0, alpha+beta=1
double Tol1=0.000001;
// if fabs(d) less than this it lands on edge miles
// away or never at all
double Tol2=1e-8; //possibility that we land on a corner
double alpha_e1, beta_e1;
double alpha_e2, beta_e2;
double alpha_e3, beta_e3;
bool land_e1, land_e2, land_e3;
double lambda_edge1, lambda_edge2, lambda_edge3;
int Node1, Node2, Node3;
double alphaNext,betaNext;
double alpha_p, beta_p, alpha_q, beta_q;
double alpha_p_dash, beta_p_dash, alpha_q_dash, beta_q_dash;
double CosTheta,SinTheta,Theta,Phi;
double adot_adash, adot_bdash, bdot_adash, bdot_bdash;
double W1,W2,X1,X2,Y1,Y2,Z1,Z2,Det;
double ex1,why1,ex2,why3;
unsigned int ndim;
int kount=0;
Tstart=Tstart0;
alpha_start=0.25, beta_start=0.25;
d1=.25; d2=0.19;
bool start_e1, start_e2, start_e3;
start_e1=false; //assume that for first triangle
start_e2=false; //we don't start off on an edge
start_e3=false; //change for instance, if we have alpha_start=0
/**********************************************************************************
GEODESIC- Propagate
**********************************************************************************/
while(ds_total < 6.3 && kount < GeoPos){
if(kount==GeoPos-1){
cout <<"Last One! " << endl;
}
Node1=Triangles[Tstart].Get1();
Node2=Triangles[Tstart].Get2();
Node3=Triangles[Tstart].Get3();
D3Dvec Rnode1,Rnode2;
Rnode1=D3Dvec(); Rnode2=D3Dvec();
xO=NodeV[Node1].GetX();
yO=NodeV[Node1].GetY();
zO=NodeV[Node1].GetZ();
VOrig.SetVec(xO,yO,zO);
x1=NodeV[Node2].GetX();
y1=NodeV[Node2].GetY();
z1=NodeV[Node2].GetZ();
Rnode1.SetVec(x1,y1,z1);
x2=NodeV[Node3].GetX();
y2=NodeV[Node3].GetY();
z2=NodeV[Node3].GetZ();
Rnode2.SetVec(x2,y2,z2);
Ve1=Rnode1-VOrig;
Ve2=Rnode2-VOrig;
x3=VOrig.GetX()+alpha_start*Ve1.GetX()+beta_start*Ve2.GetX();
y3=VOrig.GetY()+alpha_start*Ve1.GetY()+beta_start*Ve2.GetY();
z3=VOrig.GetZ()+alpha_start*Ve1.GetZ()+beta_start*Ve2.GetZ();
Geodesy[kount]=new D3Dvec();
Geodesy[kount].SetX(x3);
Geodesy[kount].SetY(y3);
Geodesy[kount].SetZ(z3);
cout << Geodesy[kount].GetX() << " "
<< Geodesy[kount].GetY()
<< " " << Geodesy[kount].GetZ()
<< " kount=" << kount <<
" Tstart=" << Tstart << endl;
kount++;
land_e1=false; land_e2=false; land_e3=false;
//alpha_start + d1 lambda=0 lands on edge2;
//beta_start+ d2 lambda=0 lands on edge1;
if( fabs(d1) > Tol1){lambda_edge1=-beta_start/d2; land_e1=true;}
if( fabs(d2) > Tol1){lambda_edge2=-alpha_start/d1; land_e2=true;}
if( fabs(d2+d2) > Tol1)
{lambda_edge3=(1.0-alpha_start-beta_start)/(d1+d2);
land_e3=true;}
cout << "d1=" << d1 << endl;
cout << "d2=" << d2 << endl;
cout << "alpha_s=" << alpha_start << endl;
cout << "beta_s=" << beta_start << endl;
alpha_e1=alpha_start+lambda_edge1*d1;
beta_e1=beta_start+lambda_edge1*d2;
alpha_e2=alpha_start+lambda_edge2*d1;
beta_e2=beta_start+lambda_edge2*d2;
alpha_e3=alpha_start+lambda_edge3*d1;
beta_e3=beta_start+lambda_edge3*d2;
ndim=2;
Dmatrix Mat(ndim,ndim); //creates 4 by 3 on the heap.
Dvector RHS(ndim);
Dvector LHS(ndim);
if( (fabs(alpha_e1) < Tol2) && (fabs(beta_e1) <Tol2) ){
// set it safely on edge 1
alpha_e1=2.*Tol2;
beta_e1=0.0;
}
if( (fabs(1.0-alpha_e1) < Tol2) && (fabs(beta_e1) <Tol2) ){
// set it safely on edge 1
alpha_e1=1.0-2.0*Tol2;
beta_e1=0.0;
}
if( (fabs(alpha_e2) < Tol2) && (fabs(beta_e2) <Tol2) ){
// set it safely on edge 2
alpha_e2=0.0;
beta_e2=2.0*Tol2;
}
if( (fabs(1.0-beta_e2) < Tol2) && (fabs(alpha_e2) <Tol2) ){
// set it safely on edge 2
alpha_e2=0.0;
beta_e2=1.0-2.0*Tol2;
}
if( (fabs(1.0-alpha_e3-beta_e3) < Tol2) ){
if(fabs(alpha_e3) < Tol2){
// set it safely on edge 3
alpha_e3=2.0*Tol2;
beta_e3=1.0-alpha_e3;
}
if(fabs(beta_e3) < Tol2){
// set it safely on edge 3
beta_e3=2.0*Tol2;
alpha_e3=1.0-beta_e3;
}
}
/* cout << "e1 " << alpha_e1 << " L e1=" << lambda_edge1 << endl;
cout << "e2 " << beta_e2 << " L_e2=" << lambda_edge2 << endl;
cout << "a e3 " << alpha_e3 << " L_e3=" << lambda_edge3 << endl;
cout << "b e3 " << beta_e3 << endl; */
if(lambda_edge1 <0.0 || alpha_e1 < 0.0 || alpha_e1 > 1.0)land_e1=false;
if(lambda_edge2 <0.0 || beta_e2 < 0.0 || beta_e2 > 1.0)land_e2=false;
if(lambda_edge3 <0.0 || alpha_e3 < 0.0 || alpha_e3 > 1.0)land_e3=false;
if(lambda_edge3 <0.0 || beta_e3 < 0.0 || beta_e3 > 1.0)land_e3=false;
cout << land_e1 << land_e2 << land_e3 << " edges 1 2 and 3" << endl;
// Normally we land on two edges!
// We start it some point in the start triangle
// proceed to the edge, but now we start at an edge
//
if(start_e1)land_e1=false;
if(start_e2)land_e2=false;
if(start_e3)land_e3=false;
start_e1=false;
start_e2=false;
start_e3=false;
if(land_e1){
//beta_e1=0
ds_squared=
Gmetric[Tstart][0]*(alpha_e1-alpha_start)*(alpha_e1-alpha_start)
-2.0*Gmetric[Tstart][1]*(alpha_e1-alpha_start)*beta_start
+Gmetric[Tstart][2]*beta_start*beta_start;
ds_total=ds_total+sqrt(ds_squared);
}
if(land_e2){
//alpha_e1=0
ds_squared=
Gmetric[Tstart][0]*alpha_start*alpha_start
-2.0*Gmetric[Tstart][1]*alpha_start*(beta_e2-beta_start)
+Gmetric[Tstart][2]*(beta_e2-beta_start)*(beta_e2-beta_start);
ds_total=ds_total+sqrt(ds_squared);
}
if(land_e3){
ds_squared=
Gmetric[Tstart][0]*(alpha_e3-alpha_start)*(alpha_e3-alpha_start)
+2.0*Gmetric[Tstart][1]*(alpha_e3-alpha_start)*(beta_e3-beta_start)
+Gmetric[Tstart][2]*(beta_e3-beta_start)*(beta_e3-beta_start);
ds_total=ds_total+sqrt(ds_squared);
}
if( land_e1 )TNext=Triangles[Tstart].GetN1();
if( land_e2 )TNext=Triangles[Tstart].GetN2();
if( land_e3 )TNext=Triangles[Tstart].GetN3();
avecdash[0]=avec[TNext][0];
avecdash[1]=avec[TNext][1];
bvecdash[0]=bvec[TNext][0];
bvecdash[1]=bvec[TNext][1];
qStart=Triangles[Tstart].GetQuad();
qNext=Triangles[TNext].GetQuad();
// edge 1 always crosses into an edge 1 in the opposite sense
if(land_e1){
alphaNext=1.0-alpha_e1;
betaNext=0.0;
start_e1=true;
alpha_p=0.0; //edge 1
beta_p=0.0;
alpha_q=1.0;
beta_q=0.0;
alpha_p_dash=alpha_q; // same edge, opposite sense
beta_p_dash=beta_q;
alpha_q_dash=alpha_p;
beta_q_dash=beta_p;
}
// If the neighbour on edge 2 is in a different quad
// it lands on edge 3, otherwise minus edge 2
if(land_e2){
alpha_p=0.0;
beta_p=0.0;
alpha_q=0.0;
beta_q=1.0;
if(qNext==qStart){
//crosses to edge 2 of neighbour- opposite sense
betaNext=1.0-beta_e2;
alphaNext=0.0;
start_e2=true;
alpha_p_dash=alpha_q;
beta_p_dash=beta_q;
alpha_q_dash=alpha_p;
beta_q_dash=beta_p;
}
else
{
//crosses to edge 3 of neighbour- same sense.
alphaNext=1.0-beta_e2;
betaNext=beta_e2;
start_e3=true;
alpha_p_dash=1.0;
beta_p_dash=0.0;
alpha_q_dash=0.0;
beta_q_dash=1.0;
}
}
if(land_e3){
alpha_p=1.0;
beta_p=0.0;
alpha_q=0.0;
beta_q=1.0;
if(qNext==qStart){
//crosses to edge 3 of neighbour- opposite sense.
alphaNext=1.0-alpha_e3;
betaNext=alpha_e3;
alpha_p_dash=alpha_q;
beta_p_dash=beta_q;
alpha_q_dash=alpha_p;
beta_q_dash=beta_p;
start_e3=true;
}
else
{
//crosses to edge 2 of neighbour -- has same sense
alphaNext=0;
betaNext=beta_e3;
alpha_p_dash=0.0;
beta_p_dash=0.0;
alpha_q_dash=0.0;
beta_q_dash=1.0;
start_e2=true;
}
}
cout << "ds_total=" << ds_total << endl;
X1=alpha_p_dash*avecdash[0]+beta_p_dash*bvecdash[0];
X2=alpha_p_dash*avecdash[1]+beta_p_dash*bvecdash[1];
Y1=alpha_p*avec[Tstart][0]+beta_p*bvec[Tstart][0];
Y2=alpha_p*avec[Tstart][1]+beta_p*bvec[Tstart][1];
W1=alpha_q_dash*avecdash[0]+beta_q_dash*bvecdash[0];
W2=alpha_q_dash*avecdash[1]+beta_q_dash*bvecdash[1];
Z1=alpha_q*avec[Tstart][0]+beta_q*bvec[Tstart][0];
Z2=alpha_q*avec[Tstart][1]+beta_q*bvec[Tstart][1];
Det=(W2-X2)*(W2-X2)+(W1-X1)*(W1-X1);
unsigned int ir,ic,ir1,ir2;
ir=0; ic=0;
Mat(ir,ic)=W1-X1;
ir=0; ic=1;
Mat(ir,ic)=W2-X2;
ir=1; ic=0;
Mat(ir,ic)=-(W2-X2);
ir=1; ic=1;
Mat(ir,ic)=W1-X1;
Mat=Mat/Det;
ir=0;
RHS(ir)=Z1-Y1;
ir=1;
RHS(ir)=Z2-Y2;
LHS=Mat*RHS;
ir=0;
CosTheta=LHS(ir);
ir=1;
SinTheta=LHS(ir);
// cout << "cos and sin "<< CosTheta << " " << SinTheta << endl;
// cout << "cossq+sinsq=" << CosTheta*CosTheta+SinTheta*SinTheta << endl;
avecdash_new[0]=
avecdash[0]*CosTheta-avecdash[1]*SinTheta;
avecdash_new[1]=
avecdash[0]*SinTheta+avecdash[1]*CosTheta;
bvecdash_new[0]=
bvecdash[0]*CosTheta-bvecdash[1]*SinTheta;
bvecdash_new[1]=
bvecdash[0]*SinTheta+bvecdash[1]*CosTheta;
adot_adash=avec[Tstart][0]*avecdash_new[0]
+avec[Tstart][1]*avecdash_new[1];
adot_bdash=avec[Tstart][0]*bvecdash_new[0]
+avec[Tstart][1]*bvecdash_new[1];
bdot_adash=bvec[Tstart][0]*avecdash_new[0]
+bvec[Tstart][1]*avecdash_new[1];
bdot_bdash=bvec[Tstart][0]*bvecdash_new[0]
+bvec[Tstart][1]*bvecdash_new[1];
/*
cout << adot_adash << " a dot adash " <<
avec[Tstart][0]*avecdash_new[0]+
avec[Tstart][1]*avecdash_new[1] << endl;
cout << adot_bdash << " a dot bdash " <<
avec[Tstart][0]*bvecdash_new[0]+
avec[Tstart][1]*bvecdash_new[1] << endl;
cout << bdot_adash << " b dot adash " <<
bvec[Tstart][0]*avecdash_new[0]+
bvec[Tstart][1]*avecdash_new[1] << endl;
cout << bdot_bdash << " b dot bdash " <<
bvec[Tstart][0]*bvecdash_new[0]+
bvec[Tstart][1]*bvecdash_new[1] << endl;
*/
// The next couts all check out
/* cout << " a dot a " <<
avec[Tstart][0]*avec[Tstart][0]+
avec[Tstart][1]*avec[Tstart][1] << endl;
cout << " b dot b " <<
bvec[Tstart][0]*bvec[Tstart][0]+
bvec[Tstart][1]*bvec[Tstart][1] << endl;
cout << " a dot a in Next " <<
avec[TNext][0]*avec[TNext][0]+
avec[TNext][1]*avec[TNext][1] << endl;
cout << bdot_bdash << " b dot b in Next " <<
bvec[TNext][0]*bvec[TNext][0]+
bvec[TNext][1]*bvec[TNext][1] << endl;
cout << "a " << avec[Tstart][0]
<< " " << avec[Tstart][1] << endl;
cout << "b " << bvec[Tstart][0]
<< " " << bvec[Tstart][1] << endl;
*/
/*
cout << "a dash " << avecdash[0]
<< " " << avecdash[1] << endl;
cout << "b dash " << bvecdash[0]
<< " " << bvecdash[1] << endl;
*/
/* cout << "a dash rotate " << avecdash_new[0]
<< " " << avecdash_new[1] << endl;
cout << "b dash rotate " << bvecdash_new[0]
<< " " << bvecdash_new[1] << endl;
*/
ir=0;ic=0;
Mat(ir,ic)=Gmetric[Tstart][2];
ir=0;ic=1;
Mat(ir,ic)=-Gmetric[Tstart][1];
ir=1;ic=0;
Mat(ir,ic)=-Gmetric[Tstart][1];
ir=1;ic=1;
Mat(ir,ic)=Gmetric[Tstart][0];
Det=Gmetric[Tstart][0]*Gmetric[Tstart][2]
-Gmetric[Tstart][1]*Gmetric[Tstart][1];
Mat=Mat/Det;
ir=0;
RHS(ir)=adot_adash;
ir=1;
RHS(ir)=bdot_adash;
LHS=Mat*RHS;
ir=0;
x1=LHS(ir);
ir=1;
y1=LHS(ir);
ir=0;
RHS(ir)=adot_bdash;
ir=1;
RHS(ir)=bdot_bdash;
LHS=Mat*RHS;
ir=0;
x2=LHS(ir);
ir=1;
y2=LHS(ir);
//check adash=x1 a + y1 b, bdash=x2 a+ y2 b
cout << x1*avec[Tstart][0]+y1*bvec[Tstart][0]
<< " " << avecdash_new[0] << endl;
cout << x1*avec[Tstart][1]+y1*bvec[Tstart][1]
<< " " << avecdash_new[1] << endl;
cout << x2*avec[Tstart][0]+y2*bvec[Tstart][0]
<< " " << bvecdash_new[0] << endl;
cout << x2*avec[Tstart][1]+y2*bvec[Tstart][1]
<< " " << bvecdash_new[1] << endl;
ir=0;ic=0;
Mat(ir,ic)=y2;
ir=0;ic=1;
Mat(ir,ic)=-x2;
ir=1;ic=0;
Mat(ir,ic)=-y1;
ir=1;ic=1;
Mat(ir,ic)=x1;
Det=x1*y2-x2*y1;
Mat=Mat/Det;
cout << "M11=" << y2/Det << " M12=" << -x2/Det << endl;
cout << "M21=" << -y1/Det << " M12=" << x1/Det << endl;
ir=0;
RHS(ir)=d1;
ir=1;
RHS(ir)=d2;
LHS=Mat*RHS;
ir=0;
d1dash=LHS(ir);
ir=1;
d2dash=LHS(ir);
// We have finally arrived in TNext, which will be the new Tstart;
Tstart=TNext;
alpha_start=alphaNext;
beta_start=betaNext;
d1=d1dash;
d2=d2dash;
} //end while ds_total
Geokount=kount;
cout << "Geokount=" << Geokount << endl;
while(!quitit){
while(SDL_PollEvent(&event)){
switch(event.type){
case SDL_QUIT:
quitit=true;
break;
case SDL_MOUSEBUTTONDOWN:
mousedown=true;
break;
case SDL_MOUSEBUTTONUP:
mousedown=false;
break;
case SDL_MOUSEMOTION:
if(mousedown){
if(MouseOn)Camera1.MouseView();}
else{
if(MouseOn)Camera1.MouseLookAt(); }
break;
case SDL_KEYDOWN:
whatkey=&event.key.keysym;
HandleKeyPress(whatkey);
break;
case SDL_KEYUP:
whatkey=&event.key.keysym;
HandleKeyRelease(whatkey);
default:
break;
} // end of case
} //end of inner loop
CheckMove(Camera1);
RenderScene(Camera1);
} //end of outer loop
}
int main(int argc, char *argv[])
{
int ierr = 0, i, j, k;
#ifdef EPETRA_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
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;
if(verbose && Comm.MyPID()==0)
std::cout << Epetra_Version() << std::endl << std::endl;
int rank = Comm.MyPID();
// char tmp;
// if (rank==0) std::cout << "Press any key to continue..."<< std::endl;
// if (rank==0) cin >> tmp;
// Comm.Barrier();
Comm.SetTracebackMode(0); // This should shut down any error traceback reporting
if (verbose) std::cout << Comm << std::endl;
// bool verbose1 = verbose;
// Redefine verbose to only print on PE 0
if (verbose && rank!=0) verbose = false;
int N = 20;
int NRHS = 4;
double * A = new double[N*N];
double * A1 = new double[N*N];
double * X = new double[(N+1)*NRHS];
double * X1 = new double[(N+1)*NRHS];
int LDX = N+1;
int LDX1 = N+1;
double * B = new double[N*NRHS];
double * B1 = new double[N*NRHS];
int LDB = N;
int LDB1 = N;
int LDA = N;
int LDA1 = LDA;
double OneNorm1;
bool Upper = false;
Epetra_SerialSpdDenseSolver solver;
Epetra_SerialSymDenseMatrix * Matrix;
for (int kk=0; kk<2; kk++) {
for (i=1; i<=N; i++) {
GenerateHilbert(A, LDA, i);
OneNorm1 = 0.0;
for (j=1; j<=i; j++) OneNorm1 += 1.0/((double) j); // 1-Norm = 1 + 1/2 + ...+1/n
if (kk==0) {
Matrix = new Epetra_SerialSymDenseMatrix(View, A, LDA, i);
LDA1 = LDA;
}
else {
Matrix = new Epetra_SerialSymDenseMatrix(Copy, A, LDA, i);
LDA1 = i;
}
GenerateHilbert(A1, LDA1, i);
if (kk==1) {
solver.FactorWithEquilibration(true);
Matrix->SetUpper();
Upper = true;
solver.SolveToRefinedSolution(false);
}
for (k=0; k<NRHS; k++)
for (j=0; j<i; j++) {
B[j+k*LDB] = 1.0/((double) (k+3)*(j+3));
B1[j+k*LDB1] = B[j+k*LDB1];
}
Epetra_SerialDenseMatrix Epetra_B(View, B, LDB, i, NRHS);
Epetra_SerialDenseMatrix Epetra_X(View, X, LDX, i, NRHS);
solver.SetMatrix(*Matrix);
solver.SetVectors(Epetra_X, Epetra_B);
ierr = check(solver, A1, LDA1, i, NRHS, OneNorm1, B1, LDB1, X1, LDX1, Upper, verbose);
assert (ierr>-1);
delete Matrix;
if (ierr!=0) {
if (verbose) std::cout << "Factorization failed due to bad conditioning. This is normal if SCOND is small."
<< std::endl;
break;
}
}
}
delete [] A;
delete [] A1;
delete [] X;
delete [] X1;
delete [] B;
delete [] B1;
/////////////////////////////////////////////////////////////////////
// Now test norms and scaling functions
/////////////////////////////////////////////////////////////////////
Epetra_SerialSymDenseMatrix D;
double ScalarA = 2.0;
int DM = 10;
int DN = 10;
D.Shape(DM);
for (j=0; j<DN; j++)
for (i=0; i<DM; i++) D[j][i] = (double) (1+i+j*DM) ;
//std::cout << D << std::endl;
double NormInfD_ref = (double)(DM*(DN*(DN+1))/2);
double NormOneD_ref = NormInfD_ref;
double NormInfD = D.NormInf();
double NormOneD = D.NormOne();
if (verbose) {
std::cout << " *** Before scaling *** " << std::endl
<< " Computed one-norm of test matrix = " << NormOneD << std::endl
<< " Expected one-norm = " << NormOneD_ref << std::endl
<< " Computed inf-norm of test matrix = " << NormInfD << std::endl
<< " Expected inf-norm = " << NormInfD_ref << std::endl;
}
D.Scale(ScalarA); // Scale entire D matrix by this value
//std::cout << D << std::endl;
NormInfD = D.NormInf();
NormOneD = D.NormOne();
if (verbose) {
std::cout << " *** After scaling *** " << std::endl
<< " Computed one-norm of test matrix = " << NormOneD << std::endl
<< " Expected one-norm = " << NormOneD_ref*ScalarA << std::endl
<< " Computed inf-norm of test matrix = " << NormInfD << std::endl
<< " Expected inf-norm = " << NormInfD_ref*ScalarA << std::endl;
}
/////////////////////////////////////////////////////////////////////
// Now test for larger system, both correctness and performance.
/////////////////////////////////////////////////////////////////////
N = 2000;
NRHS = 5;
LDA = N;
LDB = N;
LDX = N;
if (verbose) std::cout << "\n\nComputing factor of an " << N << " x " << N << " SPD matrix...Please wait.\n\n" << std::endl;
// Define A and X
A = new double[LDA*N];
X = new double[LDB*NRHS];
for (j=0; j<N; j++) {
for (k=0; k<NRHS; k++) X[j+k*LDX] = 1.0/((double) (j+5+k));
for (i=0; i<N; i++) {
if (i==j) A[i+j*LDA] = 100.0 + i;
else A[i+j*LDA] = -1.0/((double) (i+10)*(j+10));
}
}
// Define Epetra_SerialDenseMatrix object
Epetra_SerialSymDenseMatrix BigMatrix(Copy, A, LDA, N);
Epetra_SerialSymDenseMatrix OrigBigMatrix(View, A, LDA, N);
Epetra_SerialSpdDenseSolver BigSolver;
BigSolver.FactorWithEquilibration(true);
BigSolver.SetMatrix(BigMatrix);
// Time factorization
Epetra_Flops counter;
BigSolver.SetFlopCounter(counter);
Epetra_Time Timer(Comm);
double tstart = Timer.ElapsedTime();
ierr = BigSolver.Factor();
if (ierr!=0 && verbose) std::cout << "Error in factorization = "<<ierr<< std::endl;
assert(ierr==0);
double time = Timer.ElapsedTime() - tstart;
double FLOPS = counter.Flops();
double MFLOPS = FLOPS/time/1000000.0;
if (verbose) std::cout << "MFLOPS for Factorization = " << MFLOPS << std::endl;
// Define Left hand side and right hand side
Epetra_SerialDenseMatrix LHS(View, X, LDX, N, NRHS);
Epetra_SerialDenseMatrix RHS;
RHS.Shape(N,NRHS); // Allocate RHS
// Compute RHS from A and X
Epetra_Flops RHS_counter;
RHS.SetFlopCounter(RHS_counter);
tstart = Timer.ElapsedTime();
RHS.Multiply('L', 1.0, OrigBigMatrix, LHS, 0.0); // Symmetric Matrix-multiply
time = Timer.ElapsedTime() - tstart;
Epetra_SerialDenseMatrix OrigRHS = RHS;
FLOPS = RHS_counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) std::cout << "MFLOPS to build RHS (NRHS = " << NRHS <<") = " << MFLOPS << std::endl;
// Set LHS and RHS and solve
BigSolver.SetVectors(LHS, RHS);
tstart = Timer.ElapsedTime();
ierr = BigSolver.Solve();
if (ierr==1 && verbose) std::cout << "LAPACK guidelines suggest this matrix might benefit from equilibration." << std::endl;
else if (ierr!=0 && verbose) std::cout << "Error in solve = "<<ierr<< std::endl;
assert(ierr>=0);
time = Timer.ElapsedTime() - tstart;
FLOPS = BigSolver.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) std::cout << "MFLOPS for Solve (NRHS = " << NRHS <<") = " << MFLOPS << std::endl;
double * resid = new double[NRHS];
bool OK = Residual(N, NRHS, A, LDA, BigSolver.X(), BigSolver.LDX(),
OrigRHS.A(), OrigRHS.LDA(), resid);
if (verbose) {
if (!OK) std::cout << "************* Residual do not meet tolerance *************" << std::endl;
for (i=0; i<NRHS; i++)
std::cout << "Residual[" << i <<"] = "<< resid[i] << std::endl;
std::cout << std::endl;
}
// Solve again using the Epetra_SerialDenseVector class for LHS and RHS
Epetra_SerialDenseVector X2;
Epetra_SerialDenseVector B2;
X2.Size(BigMatrix.N());
B2.Size(BigMatrix.M());
int length = BigMatrix.N();
{for (int kk=0; kk<length; kk++) X2[kk] = ((double ) kk)/ ((double) length);} // Define entries of X2
RHS_counter.ResetFlops();
B2.SetFlopCounter(RHS_counter);
tstart = Timer.ElapsedTime();
B2.Multiply('N', 'N', 1.0, OrigBigMatrix, X2, 0.0); // Define B2 = A*X2
time = Timer.ElapsedTime() - tstart;
Epetra_SerialDenseVector OrigB2 = B2;
FLOPS = RHS_counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) std::cout << "MFLOPS to build single RHS = " << MFLOPS << std::endl;
// Set LHS and RHS and solve
BigSolver.SetVectors(X2, B2);
tstart = Timer.ElapsedTime();
ierr = BigSolver.Solve();
time = Timer.ElapsedTime() - tstart;
if (ierr==1 && verbose) std::cout << "LAPACK guidelines suggest this matrix might benefit from equilibration." << std::endl;
else if (ierr!=0 && verbose) std::cout << "Error in solve = "<<ierr<< std::endl;
assert(ierr>=0);
FLOPS = counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) std::cout << "MFLOPS to solve single RHS = " << MFLOPS << std::endl;
OK = Residual(N, 1, A, LDA, BigSolver.X(), BigSolver.LDX(), OrigB2.A(),
OrigB2.LDA(), resid);
if (verbose) {
if (!OK) std::cout << "************* Residual do not meet tolerance *************" << std::endl;
std::cout << "Residual = "<< resid[0] << std::endl;
}
delete [] resid;
delete [] A;
delete [] X;
///////////////////////////////////////////////////
// Now test default constructor and index operators
///////////////////////////////////////////////////
N = 5;
Epetra_SerialSymDenseMatrix C; // Implicit call to default constructor, should not need to call destructor
C.Shape(5); // Make it 5 by 5
double * C1 = new double[N*N];
GenerateHilbert(C1, N, N); // Generate Hilber matrix
C1[1+2*N] = 1000.0; // Make matrix nonsymmetric
// Fill values of C with Hilbert values
for (i=0; i<N; i++)
for (j=0; j<N; j++)
C(i,j) = C1[i+j*N];
// Test if values are correctly written and read
for (i=0; i<N; i++)
for (j=0; j<N; j++) {
assert(C(i,j) == C1[i+j*N]);
assert(C(i,j) == C[j][i]);
}
if (verbose)
std::cout << "Default constructor and index operator check OK. Values of Hilbert matrix = "
<< std::endl << C << std::endl
<< "Values should be 1/(i+j+1), except value (1,2) should be 1000" << std::endl;
delete [] C1;
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
/* end main
*/
return ierr ;
}
QRect CEdge::drawTree( Q3Canvas* canvas, int left, int depth, StringToString* filter )
{
int X_PADDING = 10;
int Y_SPACING = 30;
// int X_MARGIN = 10; unused variable 'X_Margin'
int Y_MARGIN = 10;
//================================================
Q3CanvasItem* edge = new Q3CanvasText( LHS(), canvas ),
* leaf = NULL;
Q3CanvasLine* line;
m_CanvasItems.clear();
m_CanvasItems.append( edge );
int myLeft = left,
myTop = ( depth * Y_SPACING ) + Y_MARGIN,
myCenterX,
myBottom,
childCenterX,
childLeft,
childTop,
shiftAmount;
Q3ValueList<QRect> daughterBoundingRectangles;
Q3ValueList<QRect>::iterator it;
QRect myBoundingRect, rectangle;
myBoundingRect.setTop( myTop );
myBoundingRect.setLeft( myLeft );
myBoundingRect.setBottom( myTop + edge->boundingRect().height() - 1 );
myBoundingRect.setRight( myLeft + edge->boundingRect().width() - 1 );
int count = 0;
// bool first = TRUE; unused variable 'first'
CEdge* daughter;
for( daughter = m_Daughters.first(); daughter; daughter = m_Daughters.next() )
{
daughterBoundingRectangles.append( rectangle );
daughterBoundingRectangles[count] = daughter->drawTree( canvas, left, depth + 1, filter );
// Adjust left position based on bounding rectangle of last daughter
left = daughterBoundingRectangles[count].right() + X_PADDING;
count++;
}
if( m_Daughters.isEmpty() )
{
// Create leaf node
childLeft = myLeft;
childTop = ( ( depth + 1 ) * Y_SPACING ) + Y_MARGIN;
leaf = new Q3CanvasText( Filter( filter, RHS() ), canvas );
m_CanvasItems.append( leaf );
leaf->move( childLeft, childTop );
leaf->show();
// Adjust my bounding rect
if( leaf->boundingRect().right() > myBoundingRect.right() ) myBoundingRect.setRight( leaf->boundingRect().right() );
myBoundingRect.setBottom( leaf->boundingRect().bottom() );
}
else
{
for( it = daughterBoundingRectangles.begin(); it != daughterBoundingRectangles.end(); ++it )
{
// Adjust my bounding rect
if( (*it).right() > myBoundingRect.right() ) myBoundingRect.setRight( (*it).right() );
if( (*it).bottom() > myBoundingRect.bottom() ) myBoundingRect.setBottom( (*it).bottom() );
}
}
if( myBoundingRect.width() == edge->boundingRect().width() )
{
// Shift all children to the right
if( m_Daughters.isEmpty() )
{
shiftAmount = int (( myBoundingRect.width() - leaf->boundingRect().width() ) / 2.0);
leaf->move( leaf->boundingRect().left() + shiftAmount, leaf->boundingRect().top() );
leaf->show();
}
else
{
shiftAmount = int (( myBoundingRect.width() - ( daughterBoundingRectangles.last().right() - daughterBoundingRectangles.first().left() ) ) / 2.0);
for( daughter = m_Daughters.first(); daughter; daughter = m_Daughters.next() )
{
daughter->shiftTree( canvas, shiftAmount, 0 );
}
for( it = daughterBoundingRectangles.begin(); it != daughterBoundingRectangles.end(); ++it )
{
// Adjust the bounding rect position
(*it).setLeft( (*it).left() + shiftAmount );
(*it).setRight( (*it).right() + shiftAmount );
}
}
}
else myLeft = ( myBoundingRect.right() - ( myBoundingRect.width() / 2 ) ) - ( edge->boundingRect().width() / 2 );
if( myLeft < myBoundingRect.left() ) myLeft = myBoundingRect.left();
edge->move( myLeft, myTop );
// Draw lines to daughter nodes
if( m_Daughters.isEmpty() )
{
myCenterX = edge->boundingRect().center().x();
myBottom = edge->boundingRect().bottom();
childCenterX = leaf->boundingRect().center().x();
childTop = leaf->boundingRect().top();
if( myCenterX - childCenterX == 1 || myCenterX - childCenterX == -1 ) myCenterX = childCenterX;
line = new Q3CanvasLine( canvas );
line->setPoints( myCenterX, myBottom, childCenterX, childTop );
line->show();
m_CanvasItems.append( line );
}
else
{
Q3ValueList<QRect>::iterator it;
for( it = daughterBoundingRectangles.begin(); it != daughterBoundingRectangles.end(); ++it )
{
myCenterX = edge->boundingRect().center().x();
myBottom = edge->boundingRect().bottom();
childCenterX = (*it).center().x();
childTop = (*it).top();
if( myCenterX - childCenterX == 1 || myCenterX - childCenterX == -1 ) myCenterX = childCenterX;
line = new Q3CanvasLine( canvas );
line->setPoints( myCenterX, myBottom, childCenterX, childTop );
line->show();
m_CanvasItems.append( line );
}
}
edge->show();
canvas->update();
return myBoundingRect;
}
// ======================================================================
bool KrylovTest(string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, bool backward, bool reorder=false)
{
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
// Set up the list
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: type", PrecType);
if(backward) List.set("relaxation: backward mode",backward);
// Reordering if needed
int NumRows=A->NumMyRows();
std::vector<int> RowList(NumRows);
if(reorder) {
for(int i=0; i<NumRows; i++)
RowList[i]=i;
List.set("relaxation: number of local smoothing indices",NumRows);
List.set("relaxation: local smoothing indices",RowList.size()>0? &RowList[0] : (int*)0);
}
int Iters1, Iters10;
if (verbose) {
cout << "Krylov test: Using " << PrecType
<< " with AztecOO" << endl;
}
// ============================================== //
// get the number of iterations with 1 sweep only //
// ============================================== //
{
List.set("relaxation: sweeps",1);
Ifpack_PointRelaxation Point(&*A);
Point.SetParameters(List);
Point.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Point);
AztecOOSolver.Iterate(2550,1e-5);
double TrueResidual = AztecOOSolver.TrueResidual();
// some output
if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
cout << "Norm of the true residual = " << TrueResidual << endl;
}
Iters1 = AztecOOSolver.NumIters();
}
// ======================================================== //
// now re-run with 10 sweeps, solver should converge faster
// ======================================================== //
{
List.set("relaxation: sweeps",10);
Ifpack_PointRelaxation Point(&*A);
Point.SetParameters(List);
Point.Compute();
LHS.PutScalar(0.0);
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Point);
AztecOOSolver.Iterate(2550,1e-5);
double TrueResidual = AztecOOSolver.TrueResidual();
// some output
if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
cout << "Norm of the true residual = " << TrueResidual << endl;
}
Iters10 = AztecOOSolver.NumIters();
}
if (verbose) {
cout << "Iters_1 = " << Iters1 << ", Iters_10 = " << Iters10 << endl;
cout << "(second number should be smaller than first one)" << endl;
}
if (Iters10 > Iters1) {
if (verbose)
cout << "KrylovTest TEST FAILED!" << endl;
return(false);
}
else {
if (verbose)
cout << "KrylovTest TEST PASSED" << endl;
return(true);
}
}
// A second pass deriving better H from previous H is worthwhile.
// More such passes gain nothing for the extra compute time.
//
void MHmgphy::HmgphyFromHmgphy( vector<double> &X, int nTr )
{
double sc = 2 * max( gW, gH );
int nvars = nTr * NX;
printf( "Hmg: %d unknowns; %d constraints.\n",
nvars, vAllC.size() );
vector<double> RHS( nvars, 0.0 );
vector<LHSCol> LHS( nvars );
X.resize( nvars );
// Apply previous final results at highest level, once only
SetUniteLayer( LHS, RHS, sc );
// Get the Homographies A
vector<double> A;
HmgphyFromAffine( A, nTr );
// SetPointPairs: H(pi) = A(pj)
double fz = 1.0;
int nc = vAllC.size();
for( int i = 0; i < nc; ++i ) {
const Constraint &C = vAllC[i];
if( !C.used || !C.inlier )
continue;
// H(p1) = A(p2)
{
int j = vRgn[C.r1].itr * NX;
double x1 = C.p1.x * fz / sc,
y1 = C.p1.y * fz / sc,
x2,
y2;
Point g2 = C.p2;
L2GPoint( g2, A, vRgn[C.r2].itr );
x2 = g2.x / sc;
y2 = g2.y / sc;
double v[5] = { x1, y1, fz, -x1*x2, -y1*x2 };
int i1[5] = { j, j+1, j+2, j+6, j+7 },
i2[5] = { j+3, j+4, j+5, j+6, j+7 };
AddConstraint( LHS, RHS, 5, i1, v, x2 * fz );
v[3] = -x1*y2;
v[4] = -y1*y2;
AddConstraint( LHS, RHS, 5, i2, v, y2 * fz );
}
// H(p2) = A(p1)
{
int j = vRgn[C.r2].itr * NX;
double x1 = C.p2.x * fz / sc,
y1 = C.p2.y * fz / sc,
x2,
y2;
Point g2 = C.p1;
L2GPoint( g2, A, vRgn[C.r1].itr );
x2 = g2.x / sc;
y2 = g2.y / sc;
double v[5] = { x1, y1, fz, -x1*x2, -y1*x2 };
int i1[5] = { j, j+1, j+2, j+6, j+7 },
i2[5] = { j+3, j+4, j+5, j+6, j+7 };
AddConstraint( LHS, RHS, 5, i1, v, x2 * fz );
v[3] = -x1*y2;
v[4] = -y1*y2;
AddConstraint( LHS, RHS, 5, i2, v, y2 * fz );
}
}
// Solve
WriteSolveRead( X, LHS, RHS, "H-FrmH", nproc, false );
PrintMagnitude( X );
RescaleAll( X, sc );
}
int main(int argc, char *argv[])
{
// initialize MPI and Epetra communicator
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
Teuchos::ParameterList GaleriList;
// The problem is defined on a 2D grid, global size is nx * nx.
int nx = 30;
GaleriList.set("nx", nx);
GaleriList.set("ny", nx * Comm.NumProc());
GaleriList.set("mx", 1);
GaleriList.set("my", Comm.NumProc());
Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap64("Cartesian2D", Comm, GaleriList) );
Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
// =============================================================== //
// B E G I N N I N G O F I F P A C K C O N S T R U C T I O N //
// =============================================================== //
Teuchos::ParameterList List;
// builds an Ifpack_AdditiveSchwarz. This is templated with
// the local solvers, in this case Ifpack_BlockRelaxation.
// Ifpack_BlockRelaxation requires as a templated a container
// class. A container defines
// how to store the diagonal blocks. Two choices are available:
// Ifpack_DenseContainer (to store them as dense block,
// than use LAPACK' factorization to apply the inverse of
// each block), of Ifpack_SparseContainer (to store
// the diagonal block as Epetra_CrsMatrix's).
//
// Here, we use Ifpack_SparseContainer, which in turn is
// templated with the class to use to apply the inverse
// of each block. For example, we can use Ifpack_Amesos.
// We still have to decide the overlap among the processes,
// and the overlap among the blocks. The two values
// can be different. The overlap among the blocks is
// considered only if block Jacobi is used.
int OverlapProcs = 2;
int OverlapBlocks = 0;
// define the block below to use dense containers
#if 0
Ifpack_AdditiveSchwarz<Ifpack_BlockRelaxation<Ifpack_DenseContainer> > Prec(A, OverlapProcs);
#else
Ifpack_AdditiveSchwarz<Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > > Prec(&*A, OverlapProcs);
#endif
List.set("relaxation: type", "symmetric Gauss-Seidel");
List.set("partitioner: overlap", OverlapBlocks);
#ifdef HAVE_IFPACK_METIS
// use METIS to create the blocks. This requires --enable-ifpack-metis.
// If METIS is not installed, the user may select "linear".
List.set("partitioner: type", "metis");
#else
// or a simple greedy algorithm is METIS is not enabled
List.set("partitioner: type", "greedy");
#endif
// defines here the number of local blocks. If 1,
// and only one process is used in the computation, then
// the preconditioner must converge in one iteration.
List.set("partitioner: local parts", 4);
// sets the parameters
IFPACK_CHK_ERR(Prec.SetParameters(List));
// initialize the preconditioner.
IFPACK_CHK_ERR(Prec.Initialize());
// Builds the preconditioners.
IFPACK_CHK_ERR(Prec.Compute());
// =================================================== //
// E N D O F I F P A C K C O N S T R U C T I O N //
// =================================================== //
// At this point, we need some additional objects
// to define and solve the linear system.
// defines LHS and RHS
Epetra_Vector LHS(A->OperatorDomainMap());
Epetra_Vector RHS(A->OperatorDomainMap());
LHS.PutScalar(0.0);
RHS.Random();
// need an Epetra_LinearProblem to define AztecOO solver
Epetra_LinearProblem Problem(&*A,&LHS,&RHS);
// now we can allocate the AztecOO solver
AztecOO Solver(Problem);
// specify solver
Solver.SetAztecOption(AZ_solver,AZ_cg);
Solver.SetAztecOption(AZ_output,32);
// HERE WE SET THE IFPACK PRECONDITIONER
Solver.SetPrecOperator(&Prec);
// .. and here we solve
// NOTE: with one process, the solver must converge in
// one iteration.
Solver.Iterate(1550,1e-5);
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return(EXIT_SUCCESS);
}
// Experiment to use approximations H(pi) = T(pj). In practice
// translations lack the accuracy of affines and are always an
// inferior starting point for homographies.
//
void MHmgphy::HmgphyFromTrans( vector<double> &X, int nTr )
{
double sc = 2 * max( gW, gH );
int nvars = nTr * NX;
printf( "Hmg: %d unknowns; %d constraints.\n",
nvars, vAllC.size() );
vector<double> RHS( nvars, 0.0 );
vector<LHSCol> LHS( nvars );
X.resize( nvars );
// Get the pure translations T
MTrans M;
vector<double> T;
M.SetModelParams( gW, gH, -1, -1, -1, -1,
nproc, -1, NULL, NULL, zs );
M.SolveSystem( T, nTr );
// SetPointPairs: H(pi) = T(pj)
double fz = 1.0;
int nc = vAllC.size();
for( int i = 0; i < nc; ++i ) {
const Constraint &C = vAllC[i];
if( !C.used || !C.inlier )
continue;
// H(p1) = T(p2)
{
int j = vRgn[C.r1].itr * NX,
k = vRgn[C.r2].itr * 2;
double x1 = C.p1.x * fz / sc,
y1 = C.p1.y * fz / sc,
x2 = (C.p2.x + T[k ]) / sc,
y2 = (C.p2.y + T[k+1]) / sc;
double v[5] = { x1, y1, fz, -x1*x2, -y1*x2 };
int i1[5] = { j, j+1, j+2, j+6, j+7 },
i2[5] = { j+3, j+4, j+5, j+6, j+7 };
AddConstraint( LHS, RHS, 5, i1, v, x2 * fz );
v[3] = -x1*y2;
v[4] = -y1*y2;
AddConstraint( LHS, RHS, 5, i2, v, y2 * fz );
}
// H(p2) = T(p1)
{
int j = vRgn[C.r2].itr * NX,
k = vRgn[C.r1].itr * 2;
double x1 = C.p2.x * fz / sc,
y1 = C.p2.y * fz / sc,
x2 = (C.p1.x + T[k ]) / sc,
y2 = (C.p1.y + T[k+1]) / sc;
double v[5] = { x1, y1, fz, -x1*x2, -y1*x2 };
int i1[5] = { j, j+1, j+2, j+6, j+7 },
i2[5] = { j+3, j+4, j+5, j+6, j+7 };
AddConstraint( LHS, RHS, 5, i1, v, x2 * fz );
v[3] = -x1*y2;
v[4] = -y1*y2;
AddConstraint( LHS, RHS, 5, i2, v, y2 * fz );
}
}
// Solve
WriteSolveRead( X, LHS, RHS, "H-FrmT", nproc, false );
PrintMagnitude( X );
RescaleAll( X, sc );
}
// Like AffineFromAffine, try another pass of scaffold refinement.
//
void MAffine::AffineFromAffine2( vector<double> &X, int nTr )
{
double sc = 2 * max( gW, gH );
int nvars = nTr * NX;
printf( "Aff: %d unknowns; %d constraints.\n",
nvars, vAllC.size() );
vector<double> RHS( nvars, 0.0 );
vector<LHSCol> LHS( nvars );
X.resize( nvars );
// Get the Affines A
vector<double> A;
AffineFromAffine( A, nTr );
// SetPointPairs: A(pi) = A(pj)
double fz = 1.0;
int nc = vAllC.size();
for( int i = 0; i < nc; ++i ) {
const Constraint &C = vAllC[i];
if( !C.used || !C.inlier )
continue;
// A(p1) = A(p2)
{
int j = vRgn[C.r1].itr * NX;
double x1 = C.p1.x * fz / sc,
y1 = C.p1.y * fz / sc,
x2,
y2;
Point g2 = C.p2;
L2GPoint( g2, A, vRgn[C.r2].itr );
x2 = g2.x * fz / sc;
y2 = g2.y * fz / sc;
double v[3] = { x1, y1, fz };
int i1[3] = { j, j+1, j+2 },
i2[3] = { j+3, j+4, j+5 };
AddConstraint( LHS, RHS, 3, i1, v, x2 );
AddConstraint( LHS, RHS, 3, i2, v, y2 );
}
// A(p2) = T(p1)
{
int j = vRgn[C.r2].itr * NX;
double x1 = C.p2.x * fz / sc,
y1 = C.p2.y * fz / sc,
x2,
y2;
Point g2 = C.p1;
L2GPoint( g2, A, vRgn[C.r1].itr );
x2 = g2.x * fz / sc;
y2 = g2.y * fz / sc;
double v[3] = { x1, y1, fz };
int i1[3] = { j, j+1, j+2 },
i2[3] = { j+3, j+4, j+5 };
AddConstraint( LHS, RHS, 3, i1, v, x2 );
AddConstraint( LHS, RHS, 3, i2, v, y2 );
}
}
// Solve
//SolveWithSquareness( X, LHS, RHS, nTr );
//SolveWithUnitMag( X, LHS, RHS, nTr );
WriteSolveRead( X, LHS, RHS, "A-FrmA2", nproc, false );
PrintMagnitude( X );
RescaleAll( X, sc );
}
// This method for solving montages omits calling SetPointPairs
// to assert A1(p1) - A2(p2). Rather, we only set approximations
// A(pi) = T(pj). This isn't nearly as accurate as the current
// favorite AffineFromTransWt, which combines SetPointPairs with
// downweighted scaffold constraints A(pi) = T(pj).
//
// Rather than give up on this method, I also tried to improve
// results by a series of scaffold refinements. That is, first
// get T's, use those to get A's, use those to get better A's
// do that again. The result of that slowly converges toward
// AffineFromTransWt but a great computaion cost. These iterative
// experiment snippets follow.
//
void MAffine::AffineFromTrans( vector<double> &X, int nTr )
{
double sc = 2 * max( gW, gH );
int nvars = nTr * NX;
printf( "Aff: %d unknowns; %d constraints.\n",
nvars, vAllC.size() );
vector<double> RHS( nvars, 0.0 );
vector<LHSCol> LHS( nvars );
X.resize( nvars );
// Get the pure translations T
MTrans M;
vector<double> T;
M.SetModelParams( gW, gH, -1, -1, -1, -1,
nproc, -1, NULL, NULL, zs );
M.SolveSystem( T, nTr );
// SetPointPairs: A(pi) = T(pj)
int nc = vAllC.size();
for( int i = 0; i < nc; ++i ) {
const Constraint &C = vAllC[i];
if( !C.used || !C.inlier )
continue;
// A(p1) = T(p2)
{
int j = vRgn[C.r1].itr * NX,
k = vRgn[C.r2].itr * 2;
double x1 = C.p1.x * scaf_strength / sc,
y1 = C.p1.y * scaf_strength / sc,
x2 = (C.p2.x + T[k ]) * scaf_strength / sc,
y2 = (C.p2.y + T[k+1]) * scaf_strength / sc;
double v[3] = { x1, y1, scaf_strength };
int i1[3] = { j, j+1, j+2 },
i2[3] = { j+3, j+4, j+5 };
AddConstraint( LHS, RHS, 3, i1, v, x2 );
AddConstraint( LHS, RHS, 3, i2, v, y2 );
}
// A(p2) = T(p1)
{
int j = vRgn[C.r2].itr * NX,
k = vRgn[C.r1].itr * 2;
double x1 = C.p2.x * scaf_strength / sc,
y1 = C.p2.y * scaf_strength / sc,
x2 = (C.p1.x + T[k ]) * scaf_strength / sc,
y2 = (C.p1.y + T[k+1]) * scaf_strength / sc;
double v[3] = { x1, y1, scaf_strength };
int i1[3] = { j, j+1, j+2 },
i2[3] = { j+3, j+4, j+5 };
AddConstraint( LHS, RHS, 3, i1, v, x2 );
AddConstraint( LHS, RHS, 3, i2, v, y2 );
}
}
// Solve
//SolveWithSquareness( X, LHS, RHS, nTr );
//SolveWithUnitMag( X, LHS, RHS, nTr );
WriteSolveRead( X, LHS, RHS, "A-FrmT", nproc, false );
PrintMagnitude( X );
RescaleAll( X, sc );
}
int main(int argc, char *argv[])
{
// initialize MPI and Epetra communicator
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
Teuchos::ParameterList GaleriList;
// The problem is defined on a 2D grid, global size is nx * nx.
int nx = 30;
GaleriList.set("nx", nx);
GaleriList.set("ny", nx * Comm.NumProc());
GaleriList.set("mx", 1);
GaleriList.set("my", Comm.NumProc());
Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap64("Cartesian2D", Comm, GaleriList) );
Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
// =============================================================== //
// B E G I N N I N G O F I F P A C K C O N S T R U C T I O N //
// =============================================================== //
Teuchos::ParameterList List;
// builds an Ifpack_AdditiveSchwarz. This is templated with
// the local solvers, in this case Ifpack_ICT. Note that any
// other Ifpack_Preconditioner-derived class can be used
// instead of Ifpack_ICT.
// In this example the overlap is zero. Use
// Prec(A,OverlapLevel) for the general case.
Ifpack_AdditiveSchwarz<Ifpack_ICT> Prec(&*A);
// `1.0' means that the factorization should approximatively
// keep the same number of nonzeros per row of the original matrix.
List.set("fact: ict level-of-fill", 1.0);
// no modifications on the diagonal
List.set("fact: absolute threshold", 0.0);
List.set("fact: relative threshold", 1.0);
List.set("fact: relaxation value", 0.0);
// matrix `laplace_2d_bc' is not symmetric because of the way
// boundary conditions are imposed. We can filter the singletons,
// (that is, Dirichlet nodes) and end up with a symmetric
// matrix (as ICT requires).
List.set("schwarz: filter singletons", true);
// sets the parameters
IFPACK_CHK_ERR(Prec.SetParameters(List));
// initialize the preconditioner. At this point the matrix must
// have been FillComplete()'d, but actual values are ignored.
IFPACK_CHK_ERR(Prec.Initialize());
// Builds the preconditioners, by looking for the values of
// the matrix.
IFPACK_CHK_ERR(Prec.Compute());
// =================================================== //
// E N D O F I F P A C K C O N S T R U C T I O N //
// =================================================== //
// At this point, we need some additional objects
// to define and solve the linear system.
// defines LHS and RHS
Epetra_Vector LHS(A->OperatorDomainMap());
Epetra_Vector RHS(A->OperatorDomainMap());
LHS.PutScalar(0.0);
RHS.Random();
// need an Epetra_LinearProblem to define AztecOO solver
Epetra_LinearProblem Problem(&*A,&LHS,&RHS);
// now we can allocate the AztecOO solver
AztecOO Solver(Problem);
// specify solver
Solver.SetAztecOption(AZ_solver,AZ_cg_condnum);
Solver.SetAztecOption(AZ_output,32);
// HERE WE SET THE IFPACK PRECONDITIONER
Solver.SetPrecOperator(&Prec);
// .. and here we solve
// NOTE: with one process, the solver must converge in
// one iteration.
Solver.Iterate(1550,1e-5);
// Prints out some information about the preconditioner
cout << Prec;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return (EXIT_SUCCESS);
}
//==========================================================================
int Ifpack_ICT::Compute()
{
if (!IsInitialized())
IFPACK_CHK_ERR(Initialize());
Time_.ResetStartTime();
IsComputed_ = false;
NumMyRows_ = A_.NumMyRows();
int Length = A_.MaxNumEntries();
vector<int> RowIndices(Length);
vector<double> RowValues(Length);
bool distributed = (Comm().NumProc() > 1)?true:false;
if (distributed)
{
SerialComm_ = Teuchos::rcp(new Epetra_SerialComm);
SerialMap_ = Teuchos::rcp(new Epetra_Map(NumMyRows_, 0, *SerialComm_));
assert (SerialComm_.get() != 0);
assert (SerialMap_.get() != 0);
}
else
SerialMap_ = Teuchos::rcp(const_cast<Epetra_Map*>(&A_.RowMatrixRowMap()), false);
int RowNnz;
#ifdef IFPACK_FLOPCOUNTERS
double flops = 0.0;
#endif
H_ = Teuchos::rcp(new Epetra_CrsMatrix(Copy,*SerialMap_,0));
if (H_.get() == 0)
IFPACK_CHK_ERR(-5); // memory allocation error
// get A(0,0) element and insert it (after sqrt)
IFPACK_CHK_ERR(A_.ExtractMyRowCopy(0,Length,RowNnz,
&RowValues[0],&RowIndices[0]));
// skip off-processor elements
if (distributed)
{
int count = 0;
for (int i = 0 ;i < RowNnz ; ++i)
{
if (RowIndices[i] < NumMyRows_){
RowIndices[count] = RowIndices[i];
RowValues[count] = RowValues[i];
++count;
}
else
continue;
}
RowNnz = count;
}
// modify diagonal
double diag_val = 0.0;
for (int i = 0 ;i < RowNnz ; ++i) {
if (RowIndices[i] == 0) {
double& v = RowValues[i];
diag_val = AbsoluteThreshold() * EPETRA_SGN(v) +
RelativeThreshold() * v;
break;
}
}
diag_val = sqrt(diag_val);
int diag_idx = 0;
EPETRA_CHK_ERR(H_->InsertGlobalValues(0,1,&diag_val, &diag_idx));
// The 10 is just a small constant to limit collisons as the actual keys
// we store are the indices and not integers
// [0..A_.MaxNumEntries()*LevelofFill()].
Ifpack_HashTable Hash( 10 * A_.MaxNumEntries() * LevelOfFill(), 1);
// start factorization for line 1
for (int row_i = 1 ; row_i < NumMyRows_ ; ++row_i) {
// get row `row_i' of the matrix
IFPACK_CHK_ERR(A_.ExtractMyRowCopy(row_i,Length,RowNnz,
&RowValues[0],&RowIndices[0]));
// skip off-processor elements
if (distributed)
{
int count = 0;
for (int i = 0 ;i < RowNnz ; ++i)
{
if (RowIndices[i] < NumMyRows_){
RowIndices[count] = RowIndices[i];
RowValues[count] = RowValues[i];
++count;
}
else
continue;
}
RowNnz = count;
}
// number of nonzeros in this row are defined as the nonzeros
// of the matrix, plus the level of fill
int LOF = (int)(LevelOfFill() * RowNnz);
if (LOF == 0) LOF = 1;
// convert line `row_i' into hash for fast access
Hash.reset();
double h_ii = 0.0;
for (int i = 0 ; i < RowNnz ; ++i) {
if (RowIndices[i] == row_i) {
double& v = RowValues[i];
h_ii = AbsoluteThreshold() * EPETRA_SGN(v) + RelativeThreshold() * v;
}
else if (RowIndices[i] < row_i)
{
Hash.set(RowIndices[i], RowValues[i], true);
}
}
// form element (row_i, col_j)
// I start from the first row that has a nonzero column
// index in row_i.
for (int col_j = RowIndices[0] ; col_j < row_i ; ++col_j) {
double h_ij = 0.0, h_jj = 0.0;
// note: get() returns 0.0 if col_j is not found
h_ij = Hash.get(col_j);
// get pointers to row `col_j'
int* ColIndices;
double* ColValues;
int ColNnz;
H_->ExtractGlobalRowView(col_j, ColNnz, ColValues, ColIndices);
for (int k = 0 ; k < ColNnz ; ++k) {
int col_k = ColIndices[k];
if (col_k == col_j)
h_jj = ColValues[k];
else {
double xxx = Hash.get(col_k);
if (xxx != 0.0)
{
h_ij -= ColValues[k] * xxx;
#ifdef IFPACK_FLOPCOUNTERS
flops += 2.0;
#endif
}
}
}
h_ij /= h_jj;
if (IFPACK_ABS(h_ij) > DropTolerance_)
{
Hash.set(col_j, h_ij);
}
#ifdef IFPACK_FLOPCOUNTERS
// only approx
ComputeFlops_ += 2.0 * flops + 1.0;
#endif
}
int size = Hash.getNumEntries();
vector<double> AbsRow(size);
int count = 0;
// +1 because I use the extra position for diagonal in insert
vector<int> keys(size + 1);
vector<double> values(size + 1);
Hash.arrayify(&keys[0], &values[0]);
for (int i = 0 ; i < size ; ++i)
{
AbsRow[i] = IFPACK_ABS(values[i]);
}
count = size;
double cutoff = 0.0;
if (count > LOF) {
nth_element(AbsRow.begin(), AbsRow.begin() + LOF, AbsRow.begin() + count,
std::greater<double>());
cutoff = AbsRow[LOF];
}
for (int i = 0 ; i < size ; ++i)
{
h_ii -= values[i] * values[i];
}
if (h_ii < 0.0) h_ii = 1e-12;;
h_ii = sqrt(h_ii);
#ifdef IFPACK_FLOPCOUNTERS
// only approx, + 1 == sqrt
ComputeFlops_ += 2 * size + 1;
#endif
double DiscardedElements = 0.0;
count = 0;
for (int i = 0 ; i < size ; ++i)
{
if (IFPACK_ABS(values[i]) > cutoff)
{
values[count] = values[i];
keys[count] = keys[i];
++count;
}
else
DiscardedElements += values[i];
}
if (RelaxValue() != 0.0) {
DiscardedElements *= RelaxValue();
h_ii += DiscardedElements;
}
values[count] = h_ii;
keys[count] = row_i;
++count;
H_->InsertGlobalValues(row_i, count, &(values[0]), (int*)&(keys[0]));
}
IFPACK_CHK_ERR(H_->FillComplete());
#if 0
// to check the complete factorization
Epetra_Vector LHS(Matrix().RowMatrixRowMap());
Epetra_Vector RHS1(Matrix().RowMatrixRowMap());
Epetra_Vector RHS2(Matrix().RowMatrixRowMap());
Epetra_Vector RHS3(Matrix().RowMatrixRowMap());
LHS.Random();
Matrix().Multiply(false,LHS,RHS1);
H_->Multiply(true,LHS,RHS2);
H_->Multiply(false,RHS2,RHS3);
RHS1.Update(-1.0, RHS3, 1.0);
cout << endl;
cout << RHS1;
#endif
int MyNonzeros = H_->NumGlobalNonzeros();
Comm().SumAll(&MyNonzeros, &GlobalNonzeros_, 1);
IsComputed_ = true;
#ifdef IFPACK_FLOPCOUNTERS
double TotalFlops; // sum across all the processors
A_.Comm().SumAll(&flops, &TotalFlops, 1);
ComputeFlops_ += TotalFlops;
#endif
++NumCompute_;
ComputeTime_ += Time_.ElapsedTime();
return(0);
}
void MeshEnergy::GetKappa( const std::vector<int>& C, const std::vector<double>& phi,
std::valarray<double>& kappa)
{
// kappa: divergence of normal
// dy^2 * dxx - 2dxdydxy + dx^2dyy / ( dx^2 + dy^2 )^(3/2)
vtkPoints* verts = meshdata->polydata->GetPoints();
for( ::size_t k_ = 0; k_ < C.size(); k_++ )\
{
int k = C[k_];
std::vector<double> nhat(3);
nhat[0] = meshdata->nx[k]; // these are normal to surface; the nx_ are the contour normals
nhat[1] = meshdata->ny[k];
nhat[2] = meshdata->nz[k];
// step 1. create the rotation matrix that orients the current normal as [0,0,1]'.
double phiang = atan2( nhat[0], nhat[1] );
std::vector<double> rotate1(9);
rotate1[0] = cos(phiang); rotate1[1] = -sin(phiang); rotate1[2] = 0;
rotate1[3] = sin(phiang); rotate1[4] = cos(phiang); rotate1[5] = 0;
rotate1[6] = 0; rotate1[7] = 0; rotate1[8] = 1.0;
std::vector<double> nhat_a(3);
pkmult( nhat, rotate1, nhat_a );
double ytilde = nhat_a[1];
double theta = M_PI_2 - atan2(nhat[2],ytilde);
std::vector<double> rotate2(9);
rotate2[0] = 1.0; rotate2[1] = 0; rotate2[2] = 0;
rotate2[3] = 0; rotate2[4] = cos(theta); rotate2[5] = -sin(theta);
rotate2[6] = 0; rotate2[7] = sin(theta); rotate2[8] = cos(theta);
std::vector<double> nhat_b(3);
pkmult( nhat_a, rotate2, nhat_b );
// nhat_b should now be [0 0 1]'
double thispt[3];
verts->GetPoint( k, thispt );
// apply rotate2 * rotate1 to each *translated* neighbor of this k-th point
::size_t num_neigh = meshdata->adj[k].myNeighbs.size();
double vec[3];
std::vector<double> vv(3);
std::vector<double> vv_(3);
std::valarray<double> xdata(num_neigh);
std::valarray<double> ydata(num_neigh);
std::valarray<double> zdata(num_neigh);
// step 2. create temporary set of std::vectors as copies of neighboring points
// translated to origin
// step 3. apply the rotation to all these points
for (::size_t i = 0; i < num_neigh; i++ )
{
int idx = meshdata->adj[k].myNeighbs[i];
verts->GetPoint( idx, vec );
vv[0] = vec[0] - thispt[0];
vv[1] = vec[1] - thispt[1];
vv[2] = vec[2] - thispt[2];
pkmult( vv, rotate1, vv_ );
pkmult( vv_, rotate2, vv );
xdata[i] = vv[0];
ydata[i] = vv[1];
zdata[i] = phi[idx] - phi[k]; //vv[2];
// zero reference phi at the vertex where we are forming tangent plane
}
/*if( abs(zdata).min() < 1e-6 )
continue;*/
// step 4. find first derivatives
double phi_x = 0.0;
double phi_y = 0.0;
{
std::valarray<double> RHS(2);
std::valarray<double> ATA(4);
ATA[0] = (xdata * xdata).sum();
ATA[1] = (xdata * ydata).sum();
ATA[2] = ATA[1];
ATA[3] = (ydata * ydata).sum();
RHS[0] = (xdata * zdata).sum();
RHS[1] = (ydata * zdata).sum();
int maxits = 1000;
std::valarray<double> ab = RHS; // initial guess
std::valarray<double> LHS(2);
pkmult2( ab, ATA, LHS );
double res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
double tol = 1e-8;
int iter = 0;
while( iter < maxits && res > tol )
{
iter++;
ab[0] = (RHS[0] - ( ab[1]*ATA[1] ) )/ ATA[0];
ab[1] = (RHS[1] - ( ab[0]*ATA[2] ) )/ ATA[3];
pkmult2( ab, ATA, LHS );
res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
}
phi_x = ab[0];
phi_y = ab[1];
}
// step 4. find least-squares fit for phi(x,y) = ax^2 + bxy + cy^2
// to get second derivatives
std::valarray<double> RHS(3); // A'z
RHS[0] = ( xdata * xdata * zdata ).sum();
RHS[1] = ( xdata * ydata * zdata ).sum();
RHS[2] = ( ydata * ydata * zdata ).sum();
double tik_delta = 1e-1 * abs(RHS).min();
std::vector<double> ATA(9); // A'A
ATA[0] = tik_delta + (xdata * xdata * xdata * xdata).sum();
ATA[1] = (xdata * xdata * xdata * ydata).sum();
ATA[2] = (xdata * xdata * ydata * ydata).sum();
ATA[3] = (xdata * ydata * xdata * xdata).sum();
ATA[4] = tik_delta + (xdata * ydata * xdata * ydata).sum();
ATA[5] = (xdata * ydata * ydata * ydata).sum();
ATA[6] = (ydata * ydata * xdata * xdata).sum();
ATA[7] = (ydata * ydata * xdata * ydata).sum();
ATA[8] = tik_delta + (ydata * ydata * ydata * ydata).sum();
int maxits = 1000;
std::valarray<double> abc = RHS; // initial guess
std::valarray<double> LHS(3);
pkmult( abc, ATA, LHS );
double res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
double tol = 1e-8;
int iter = 0;
while( iter < maxits && res > tol )
{
iter++;
abc[0] = (RHS[0] - ( abc[1]*ATA[1] + abc[2]*ATA[2] ) )/ ATA[0];
abc[1] = (RHS[1] - ( abc[0]*ATA[3] + abc[2]*ATA[5] ) )/ ATA[4];
abc[2] = (RHS[2] - ( abc[0]*ATA[6] + abc[1]*ATA[7] ) )/ ATA[8];
pkmult( abc, ATA, LHS );
res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
}
// step 5. get the derivatives from quadratic form
double phi_xx = 2*abc[0];
double phi_xy = abc[1];
double phi_yy = 2*abc[2];
kappa[k_] = phi_y * phi_y * phi_xx - 2 * phi_x * phi_y * phi_xy + phi_x * phi_x * phi_yy;
if( abs(phi_x) + abs(phi_y) > 1e-9 )
{
kappa[k_] /= pow( (phi_x*phi_x + phi_y*phi_y), 1.5 );
}
}
}
int main(int argc, char *argv[])
{
// initialize MPI and Epetra communicator
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
Teuchos::ParameterList GaleriList;
// The problem is defined on a 2D grid, global size is nx * nx.
int nx = 30;
GaleriList.set("nx", nx);
GaleriList.set("ny", nx * Comm.NumProc());
GaleriList.set("mx", 1);
GaleriList.set("my", Comm.NumProc());
Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap("Cartesian2D", Comm, GaleriList) );
Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
// =============================================================== //
// B E G I N N I N G O F I F P A C K C O N S T R U C T I O N //
// =============================================================== //
Teuchos::ParameterList List;
// allocates an IFPACK factory. No data is associated
// to this object (only method Create()).
Ifpack Factory;
// create the preconditioner. For valid PrecType values,
// please check the documentation
std::string PrecType = "Amesos";
int OverlapLevel = 2; // must be >= 0. If Comm.NumProc() == 1,
// it is ignored.
Teuchos::RefCountPtr<Ifpack_Preconditioner> Prec = Teuchos::rcp( Factory.Create(PrecType, &*A, OverlapLevel) );
assert(Prec != Teuchos::null);
// specify the Amesos solver to be used.
// If the selected solver is not available,
// IFPACK will try to use Amesos' KLU (which is usually always
// compiled). Amesos' serial solvers are:
// "Amesos_Klu", "Amesos_Umfpack", "Amesos_Superlu"
List.set("amesos: solver type", "Amesos_Klu");
// sets the parameters
IFPACK_CHK_ERR(Prec->SetParameters(List));
// initialize the preconditioner. At this point the matrix must
// have been FillComplete()'d, but actual values are ignored.
// At this call, Amesos will perform the symbolic factorization.
IFPACK_CHK_ERR(Prec->Initialize());
// Builds the preconditioners, by looking for the values of
// the matrix. At this call, Amesos will perform the
// numeric factorization.
IFPACK_CHK_ERR(Prec->Compute());
// =================================================== //
// E N D O F I F P A C K C O N S T R U C T I O N //
// =================================================== //
// At this point, we need some additional objects
// to define and solve the linear system.
// defines LHS and RHS
Epetra_Vector LHS(A->OperatorDomainMap());
Epetra_Vector RHS(A->OperatorDomainMap());
// solution is constant
LHS.PutScalar(1.0);
// now build corresponding RHS
A->Apply(LHS,RHS);
// now randomize the solution
RHS.Random();
// need an Epetra_LinearProblem to define AztecOO solver
Epetra_LinearProblem Problem(&*A,&LHS,&RHS);
// now we can allocate the AztecOO solver
AztecOO Solver(Problem);
// specify solver
Solver.SetAztecOption(AZ_solver,AZ_gmres);
Solver.SetAztecOption(AZ_output,32);
// HERE WE SET THE IFPACK PRECONDITIONER
Solver.SetPrecOperator(&*Prec);
// .. and here we solve
// NOTE: with one process, the solver must converge in
// one iteration.
Solver.Iterate(1550,1e-8);
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return(EXIT_SUCCESS);
}
void MeshEnergy::GetNormalsTangentPlane( const std::vector<int>& C, const std::vector<double>& phi,
std::valarray<double>& ne1, std::valarray<double>& ne2,
MeshData* vtkNotUsed(meshdata))
{
vtkPoints* verts = meshdata->polydata->GetPoints();
for( ::size_t k_ = 0; k_ < C.size(); k_++ )
{
int k = C[k_];
std::vector<double> nhat(3);
nhat[0] = meshdata->nx[k]; // these are normal to surface; the nx_ are the contour normals
nhat[1] = meshdata->ny[k];
nhat[2] = meshdata->nz[k];
// step 1. create the rotation matrix that orients the current normal as [0,0,1]'.
double phiang = atan2( nhat[0], nhat[1] );
std::vector<double> rotate1(9);
rotate1[0] = cos(phiang); rotate1[1] = -sin(phiang); rotate1[2] = 0;
rotate1[3] = sin(phiang); rotate1[4] = cos(phiang); rotate1[5] = 0;
rotate1[6] = 0; rotate1[7] = 0; rotate1[8] = 1.0;
std::vector<double> nhat_a(3);
pkmult( nhat, rotate1, nhat_a );
double ytilde = nhat_a[1];
double theta = M_PI_2 - atan2(nhat[2],ytilde);
std::vector<double> rotate2(9);
rotate2[0] = 1.0; rotate2[1] = 0; rotate2[2] = 0;
rotate2[3] = 0; rotate2[4] = cos(theta); rotate2[5] = -sin(theta);
rotate2[6] = 0; rotate2[7] = sin(theta); rotate2[8] = cos(theta);
std::vector<double> nhat_b(3);
pkmult( nhat_a, rotate2, nhat_b );
// nhat_b should now be [0 0 1]'
double thispt[3];
verts->GetPoint( k, thispt );
// apply rotate2 * rotate1 to each *translated* neighbor of this k-th point
::size_t num_neigh = meshdata->adj[k].myNeighbs.size();
double vec[3];
std::vector<double> vv(3);
std::vector<double> vv_(3);
std::valarray<double> xdata(num_neigh);
std::valarray<double> ydata(num_neigh);
std::valarray<double> zdata(num_neigh);
// step 2. create temporary set of std::vectors as copies of neighboring points
// translated to origin
// step 3. apply the rotation to all these points
for ( ::size_t i = 0; i < num_neigh; i++ )
{
int idx = meshdata->adj[k].myNeighbs[i];
verts->GetPoint( idx, vec );
vv[0] = vec[0] - thispt[0];
vv[1] = vec[1] - thispt[1];
vv[2] = vec[2] - thispt[2];
pkmult( vv, rotate1, vv_ );
pkmult( vv_, rotate2, vv );
xdata[i] = vv[0];
ydata[i] = vv[1];
zdata[i] = phi[idx] - phi[k]; //vv[2];
// zero reference phi at the vertex where we are forming tangent plane
}
/*if( abs(zdata).min() < 1e-6 )
continue;*/
// step 4. find least-squares fit for H(x,y) = ax + by
std::valarray<double> RHS(2);
std::valarray<double> ATA(4);
ATA[0] = (xdata * xdata).sum();
ATA[1] = (xdata * ydata).sum();
ATA[2] = ATA[1];
ATA[3] = (ydata * ydata).sum();
RHS[0] = (xdata * zdata).sum();
RHS[1] = (ydata * zdata).sum();
int maxits = 1000;
std::valarray<double> ab = RHS; // initial guess
std::valarray<double> LHS(2);
pkmult2( ab, ATA, LHS );
double res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
double tol = 1e-8;
int iter = 0;
while( iter < maxits && res > tol )
{
iter++;
ab[0] = (RHS[0] - ( ab[1]*ATA[1] ) )/ ATA[0];
ab[1] = (RHS[1] - ( ab[0]*ATA[2] ) )/ ATA[3];
pkmult2( ab, ATA, LHS );
res = sqrt( ( (LHS - RHS)*(LHS - RHS) ).sum() );
}
ne1[k_] = ab[0] / sqrt( (ab*ab).sum() );
ne2[k_] = ab[1] / sqrt( (ab*ab).sum() );
// step 5. differentiate the plane along principal directions
}
}
// ======================================================================
bool ComparePointAndBlock(string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, int sweeps)
{
Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
LHS.PutScalar(0.0); RHS.Random();
Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
// Set up the list
Teuchos::ParameterList List;
List.set("relaxation: damping factor", 1.0);
List.set("relaxation: type", PrecType);
List.set("relaxation: sweeps",sweeps);
List.set("partitioner: type", "linear");
List.set("partitioner: local parts", A->NumMyRows());
int ItersPoint, ItersBlock;
// ================================================== //
// get the number of iterations with point relaxation //
// ================================================== //
{
RHS.PutScalar(1.0);
LHS.PutScalar(0.0);
Ifpack_PointRelaxation Point(&*A);
Point.SetParameters(List);
Point.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
if (verbose)
AztecOOSolver.SetAztecOption(AZ_output,32);
else
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Point);
AztecOOSolver.Iterate(2550,1e-2);
double TrueResidual = AztecOOSolver.TrueResidual();
ItersPoint = AztecOOSolver.NumIters();
// some output
if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
cout << "Iterations = " << ItersPoint << endl;
cout << "Norm of the true residual = " << TrueResidual << endl;
}
}
// ================================================== //
// get the number of iterations with block relaxation //
// ================================================== //
{
RHS.PutScalar(1.0);
LHS.PutScalar(0.0);
Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Block(&*A);
Block.SetParameters(List);
Block.Compute();
// set AztecOO solver object
AztecOO AztecOOSolver(Problem);
AztecOOSolver.SetAztecOption(AZ_solver,Solver);
if (verbose)
AztecOOSolver.SetAztecOption(AZ_output,32);
else
AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
AztecOOSolver.SetPrecOperator(&Block);
AztecOOSolver.Iterate(2550,1e-2);
double TrueResidual = AztecOOSolver.TrueResidual();
ItersBlock = AztecOOSolver.NumIters();
// some output
if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
cout << "Iterations " << ItersBlock << endl;
cout << "Norm of the true residual = " << TrueResidual << endl;
}
}
int diff = ItersPoint - ItersBlock;
if (diff < 0) diff = -diff;
if (diff > 10)
{
if (verbose)
cout << "ComparePointandBlock TEST FAILED!" << endl;
return(false);
}
else {
if (verbose)
cout << "ComparePointandBlock TEST PASSED" << endl;
return(true);
}
}
int main(int argc, char *argv[])
{
int ierr = 0, i, j, k;
bool debug = false;
#ifdef EPETRA_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
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;
if (verbose && Comm.MyPID()==0)
cout << Epetra_Version() << endl << endl;
int rank = Comm.MyPID();
// 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
if (verbose) cout << Comm <<endl;
// bool verbose1 = verbose;
// Redefine verbose to only print on PE 0
if (verbose && rank!=0) verbose = false;
int N = 20;
int NRHS = 4;
double * A = new double[N*N];
double * A1 = new double[N*N];
double * X = new double[(N+1)*NRHS];
double * X1 = new double[(N+1)*NRHS];
int LDX = N+1;
int LDX1 = N+1;
double * B = new double[N*NRHS];
double * B1 = new double[N*NRHS];
int LDB = N;
int LDB1 = N;
int LDA = N;
int LDA1 = LDA;
double OneNorm1;
bool Transpose = false;
Epetra_SerialDenseSolver solver;
Epetra_SerialDenseMatrix * Matrix;
for (int kk=0; kk<2; kk++) {
for (i=1; i<=N; i++) {
GenerateHilbert(A, LDA, i);
OneNorm1 = 0.0;
for (j=1; j<=i; j++) OneNorm1 += 1.0/((double) j); // 1-Norm = 1 + 1/2 + ...+1/n
if (kk==0) {
Matrix = new Epetra_SerialDenseMatrix(View, A, LDA, i, i);
LDA1 = LDA;
}
else {
Matrix = new Epetra_SerialDenseMatrix(Copy, A, LDA, i, i);
LDA1 = i;
}
GenerateHilbert(A1, LDA1, i);
if (kk==1) {
solver.FactorWithEquilibration(true);
solver.SolveWithTranspose(true);
Transpose = true;
solver.SolveToRefinedSolution(true);
}
for (k=0; k<NRHS; k++)
for (j=0; j<i; j++) {
B[j+k*LDB] = 1.0/((double) (k+3)*(j+3));
B1[j+k*LDB1] = B[j+k*LDB1];
}
Epetra_SerialDenseMatrix Epetra_B(View, B, LDB, i, NRHS);
Epetra_SerialDenseMatrix Epetra_X(View, X, LDX, i, NRHS);
solver.SetMatrix(*Matrix);
solver.SetVectors(Epetra_X, Epetra_B);
ierr = check(solver, A1, LDA1, i, NRHS, OneNorm1, B1, LDB1, X1, LDX1, Transpose, verbose);
assert (ierr>-1);
delete Matrix;
if (ierr!=0) {
if (verbose) cout << "Factorization failed due to bad conditioning. This is normal if RCOND is small."
<< endl;
break;
}
}
}
delete [] A;
delete [] A1;
delete [] X;
delete [] X1;
delete [] B;
delete [] B1;
/////////////////////////////////////////////////////////////////////
// Now test norms and scaling functions
/////////////////////////////////////////////////////////////////////
Epetra_SerialDenseMatrix D;
double ScalarA = 2.0;
int DM = 10;
int DN = 8;
D.Shape(DM, DN);
for (j=0; j<DN; j++)
for (i=0; i<DM; i++) D[j][i] = (double) (1+i+j*DM) ;
//cout << D << endl;
double NormInfD_ref = (double)(DM*(DN*(DN+1))/2);
double NormOneD_ref = (double)((DM*DN*(DM*DN+1))/2 - (DM*(DN-1)*(DM*(DN-1)+1))/2 );
double NormInfD = D.NormInf();
double NormOneD = D.NormOne();
if (verbose) {
cout << " *** Before scaling *** " << endl
<< " Computed one-norm of test matrix = " << NormOneD << endl
<< " Expected one-norm = " << NormOneD_ref << endl
<< " Computed inf-norm of test matrix = " << NormInfD << endl
<< " Expected inf-norm = " << NormInfD_ref << endl;
}
D.Scale(ScalarA); // Scale entire D matrix by this value
NormInfD = D.NormInf();
NormOneD = D.NormOne();
if (verbose) {
cout << " *** After scaling *** " << endl
<< " Computed one-norm of test matrix = " << NormOneD << endl
<< " Expected one-norm = " << NormOneD_ref*ScalarA << endl
<< " Computed inf-norm of test matrix = " << NormInfD << endl
<< " Expected inf-norm = " << NormInfD_ref*ScalarA << endl;
}
/////////////////////////////////////////////////////////////////////
// Now test that A.Multiply(false, x, y) produces the same result
// as y.Multiply('N','N', 1.0, A, x, 0.0).
/////////////////////////////////////////////////////////////////////
N = 10;
int M = 10;
LDA = N;
Epetra_SerialDenseMatrix smallA(N, M, false);
Epetra_SerialDenseMatrix x(N, 1, false);
Epetra_SerialDenseMatrix y1(N, 1, false);
Epetra_SerialDenseMatrix y2(N, 1, false);
for(i=0; i<N; ++i) {
for(j=0; j<M; ++j) {
smallA(i,j) = 1.0*i+2.0*j+1.0;
}
x(i,0) = 1.0;
y1(i,0) = 0.0;
y2(i,0) = 0.0;
}
//quick check of operator==
if (x == y1) {
if (verbose) cout << "err in Epetra_SerialDenseMatrix::operator==, "
<< "erroneously returned true." << std::endl;
return(-1);
}
//quick check of operator!=
if (x != x) {
if (verbose) cout << "err in Epetra_SerialDenseMatrix::operator==, "
<< "erroneously returned true." << std::endl;
return(-1);
}
int err1 = smallA.Multiply(false, x, y1);
int err2 = y2.Multiply('N','N', 1.0, smallA, x, 0.0);
if (err1 != 0 || err2 != 0) {
if (verbose) cout << "err in Epetra_SerialDenseMatrix::Multiply"<<endl;
return(err1+err2);
}
for(i=0; i<N; ++i) {
if (y1(i,0) != y2(i,0)) {
if (verbose) cout << "different versions of Multiply don't match."<<endl;
return(-99);
}
}
/////////////////////////////////////////////////////////////////////
// Now test for larger system, both correctness and performance.
/////////////////////////////////////////////////////////////////////
N = 2000;
NRHS = 5;
LDA = N;
LDB = N;
LDX = N;
if (verbose) cout << "\n\nComputing factor of an " << N << " x " << N << " general matrix...Please wait.\n\n" << endl;
// Define A and X
A = new double[LDA*N];
X = new double[LDB*NRHS];
for (j=0; j<N; j++) {
for (k=0; k<NRHS; k++) X[j+k*LDX] = 1.0/((double) (j+5+k));
for (i=0; i<N; i++) {
if (i==((j+2)%N)) A[i+j*LDA] = 100.0 + i;
else A[i+j*LDA] = -11.0/((double) (i+5)*(j+2));
}
}
// Define Epetra_SerialDenseMatrix object
Epetra_SerialDenseMatrix BigMatrix(Copy, A, LDA, N, N);
Epetra_SerialDenseMatrix OrigBigMatrix(View, A, LDA, N, N);
Epetra_SerialDenseSolver BigSolver;
BigSolver.FactorWithEquilibration(true);
BigSolver.SetMatrix(BigMatrix);
// Time factorization
Epetra_Flops counter;
BigSolver.SetFlopCounter(counter);
Epetra_Time Timer(Comm);
double tstart = Timer.ElapsedTime();
ierr = BigSolver.Factor();
if (ierr!=0 && verbose) cout << "Error in factorization = "<<ierr<< endl;
assert(ierr==0);
double time = Timer.ElapsedTime() - tstart;
double FLOPS = counter.Flops();
double MFLOPS = FLOPS/time/1000000.0;
if (verbose) cout << "MFLOPS for Factorization = " << MFLOPS << endl;
// Define Left hand side and right hand side
Epetra_SerialDenseMatrix LHS(View, X, LDX, N, NRHS);
Epetra_SerialDenseMatrix RHS;
RHS.Shape(N,NRHS); // Allocate RHS
// Compute RHS from A and X
Epetra_Flops RHS_counter;
RHS.SetFlopCounter(RHS_counter);
tstart = Timer.ElapsedTime();
RHS.Multiply('N', 'N', 1.0, OrigBigMatrix, LHS, 0.0);
time = Timer.ElapsedTime() - tstart;
Epetra_SerialDenseMatrix OrigRHS = RHS;
FLOPS = RHS_counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) cout << "MFLOPS to build RHS (NRHS = " << NRHS <<") = " << MFLOPS << endl;
// Set LHS and RHS and solve
BigSolver.SetVectors(LHS, RHS);
tstart = Timer.ElapsedTime();
ierr = BigSolver.Solve();
if (ierr==1 && verbose) cout << "LAPACK guidelines suggest this matrix might benefit from equilibration." << endl;
else if (ierr!=0 && verbose) cout << "Error in solve = "<<ierr<< endl;
assert(ierr>=0);
time = Timer.ElapsedTime() - tstart;
FLOPS = BigSolver.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) cout << "MFLOPS for Solve (NRHS = " << NRHS <<") = " << MFLOPS << endl;
double * resid = new double[NRHS];
bool OK = Residual(N, NRHS, A, LDA, BigSolver.Transpose(), BigSolver.X(), BigSolver.LDX(),
OrigRHS.A(), OrigRHS.LDA(), resid);
if (verbose) {
if (!OK) cout << "************* Residual do not meet tolerance *************" << endl;
for (i=0; i<NRHS; i++)
cout << "Residual[" << i <<"] = "<< resid[i] << endl;
cout << endl;
}
// Solve again using the Epetra_SerialDenseVector class for LHS and RHS
Epetra_SerialDenseVector X2;
Epetra_SerialDenseVector B2;
X2.Size(BigMatrix.N());
B2.Size(BigMatrix.M());
int length = BigMatrix.N();
{for (int kk=0; kk<length; kk++) X2[kk] = ((double ) kk)/ ((double) length);} // Define entries of X2
RHS_counter.ResetFlops();
B2.SetFlopCounter(RHS_counter);
tstart = Timer.ElapsedTime();
B2.Multiply('N', 'N', 1.0, OrigBigMatrix, X2, 0.0); // Define B2 = A*X2
time = Timer.ElapsedTime() - tstart;
Epetra_SerialDenseVector OrigB2 = B2;
FLOPS = RHS_counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) cout << "MFLOPS to build single RHS = " << MFLOPS << endl;
// Set LHS and RHS and solve
BigSolver.SetVectors(X2, B2);
tstart = Timer.ElapsedTime();
ierr = BigSolver.Solve();
time = Timer.ElapsedTime() - tstart;
if (ierr==1 && verbose) cout << "LAPACK guidelines suggest this matrix might benefit from equilibration." << endl;
else if (ierr!=0 && verbose) cout << "Error in solve = "<<ierr<< endl;
assert(ierr>=0);
FLOPS = counter.Flops();
MFLOPS = FLOPS/time/1000000.0;
if (verbose) cout << "MFLOPS to solve single RHS = " << MFLOPS << endl;
OK = Residual(N, 1, A, LDA, BigSolver.Transpose(), BigSolver.X(), BigSolver.LDX(), OrigB2.A(),
OrigB2.LDA(), resid);
if (verbose) {
if (!OK) cout << "************* Residual do not meet tolerance *************" << endl;
cout << "Residual = "<< resid[0] << endl;
}
delete [] resid;
delete [] A;
delete [] X;
///////////////////////////////////////////////////
// Now test default constructor and index operators
///////////////////////////////////////////////////
N = 5;
Epetra_SerialDenseMatrix C; // Implicit call to default constructor, should not need to call destructor
C.Shape(5,5); // Make it 5 by 5
double * C1 = new double[N*N];
GenerateHilbert(C1, N, N); // Generate Hilber matrix
C1[1+2*N] = 1000.0; // Make matrix nonsymmetric
// Fill values of C with Hilbert values
for (i=0; i<N; i++)
for (j=0; j<N; j++)
C(i,j) = C1[i+j*N];
// Test if values are correctly written and read
for (i=0; i<N; i++)
for (j=0; j<N; j++) {
assert(C(i,j) == C1[i+j*N]);
assert(C(i,j) == C[j][i]);
}
if (verbose)
cout << "Default constructor and index operator check OK. Values of Hilbert matrix = "
<< endl << C << endl
<< "Values should be 1/(i+j+1), except value (1,2) should be 1000" << endl;
delete [] C1;
// now test sized/shaped constructor
Epetra_SerialDenseMatrix shapedMatrix(10, 12);
assert(shapedMatrix.M() == 10);
assert(shapedMatrix.N() == 12);
for(i = 0; i < 10; i++)
for(j = 0; j < 12; j++)
assert(shapedMatrix(i, j) == 0.0);
Epetra_SerialDenseVector sizedVector(20);
assert(sizedVector.Length() == 20);
for(i = 0; i < 20; i++)
assert(sizedVector(i) == 0.0);
if (verbose)
cout << "Shaped/sized constructors check OK." << endl;
// test Copy/View mode in op= and cpy ctr
int temperr = 0;
temperr = matrixAssignment(verbose, debug);
if(verbose && temperr == 0)
cout << "Operator = checked OK." << endl;
EPETRA_TEST_ERR(temperr, ierr);
temperr = matrixCpyCtr(verbose, debug);
if(verbose && temperr == 0)
cout << "Copy ctr checked OK." << endl;
EPETRA_TEST_ERR(temperr, ierr);
// Test some vector methods
Epetra_SerialDenseVector v1(3);
v1[0] = 1.0;
v1[1] = 3.0;
v1[2] = 2.0;
Epetra_SerialDenseVector v2(3);
v2[0] = 2.0;
v2[1] = 1.0;
v2[2] = -2.0;
temperr = 0;
if (v1.Norm1()!=6.0) temperr++;
if (fabs(sqrt(14.0)-v1.Norm2())>1.0e-6) temperr++;
if (v1.NormInf()!=3.0) temperr++;
if(verbose && temperr == 0)
cout << "Vector Norms checked OK." << endl;
temperr = 0;
if (v1.Dot(v2)!=1.0) temperr++;
if(verbose && temperr == 0)
cout << "Vector Dot product checked OK." << endl;
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
/* end main
*/
return ierr ;
}
double Ifpack_Condest(const Ifpack_Preconditioner& IFP,
const Ifpack_CondestType CT,
const int MaxIters,
const double Tol,
Epetra_RowMatrix* Matrix)
{
double ConditionNumberEstimate = -1.0;
if (CT == Ifpack_Cheap) {
// Create a vector with all values equal to one
Epetra_Vector Ones(IFP.OperatorDomainMap());
Ones.PutScalar(1.0);
// Create the vector of results
Epetra_Vector OnesResult(IFP.OperatorRangeMap());
// Compute the effect of the solve on the vector of ones
IFPACK_CHK_ERR(IFP.ApplyInverse(Ones, OnesResult));
// Make all values non-negative
IFPACK_CHK_ERR(OnesResult.Abs(OnesResult));
// Get the maximum value across all processors
IFPACK_CHK_ERR(OnesResult.MaxValue(&ConditionNumberEstimate));
}
else if (CT == Ifpack_CG) {
#ifdef HAVE_IFPACK_AZTECOO
if (Matrix == 0)
Matrix = (Epetra_RowMatrix*)&(IFP.Matrix());
Epetra_Vector LHS(IFP.OperatorDomainMap());
LHS.PutScalar(0.0);
Epetra_Vector RHS(IFP.OperatorRangeMap());
RHS.Random();
Epetra_LinearProblem Problem;
Problem.SetOperator(Matrix);
Problem.SetLHS(&LHS);
Problem.SetRHS(&RHS);
AztecOO Solver(Problem);
Solver.SetAztecOption(AZ_output,AZ_none);
Solver.SetAztecOption(AZ_solver,AZ_cg_condnum);
Solver.Iterate(MaxIters,Tol);
const double* status = Solver.GetAztecStatus();
ConditionNumberEstimate = status[AZ_condnum];
#endif
} else if (CT == Ifpack_GMRES) {
#ifdef HAVE_IFPACK_AZTECOO
if (Matrix == 0)
Matrix = (Epetra_RowMatrix*)&(IFP.Matrix());
Epetra_Vector LHS(IFP.OperatorDomainMap());
LHS.PutScalar(0.0);
Epetra_Vector RHS(IFP.OperatorRangeMap());
RHS.Random();
Epetra_LinearProblem Problem;
Problem.SetOperator(Matrix);
Problem.SetLHS(&LHS);
Problem.SetRHS(&RHS);
AztecOO Solver(Problem);
Solver.SetAztecOption(AZ_solver,AZ_gmres_condnum);
Solver.SetAztecOption(AZ_output,AZ_none);
// the following can be problematic for large problems,
// but any restart would destroy useful information about
// the condition number.
Solver.SetAztecOption(AZ_kspace,MaxIters);
Solver.Iterate(MaxIters,Tol);
const double* status = Solver.GetAztecStatus();
ConditionNumberEstimate = status[AZ_condnum];
#endif
}
return(ConditionNumberEstimate);
}
vector<T> matrix<T>::solve(vector<T> RHS)
{
#ifdef _DEBUG
if (this->dims[0] != this->dims[1])
FatalErrorST("Can only use Gaussian elimination on a square matrix.");
#endif
// Gaussian elimination with full pivoting
// not to be used where speed is paramount
vector<T> vec(this->dims[0]);
vector<T> solution(this->dims[0]);
vector<int> swap_0(this->dims[0],1);
vector<int> swap_1(this->dims[0],1);
vector<T> tmpRow(this->dims[0]);
matrix<T> LHS(*this);
// setup swap arrays
for(uint i=0; i<this->dims[0]; i++) {
swap_0[i]=i;
swap_1[i]=i;
}
// make triangular
for(uint k=0; k<this->dims[0]-1; k++) {
T max = 0;
T mag;
// find pivot
int pivot_i = 0;
int pivot_j = 0;
for(uint i=k; i<this->dims[0]; i++) {
for(uint j=k; j<this->dims[0]; j++) {
mag = LHS(i,j)*LHS(i,j);
if(mag>max) {
pivot_i = i;
pivot_j = j;
max = mag;
}
}
}
// swap the swap arrays
int itemp_0 = swap_0[k];
swap_0[k] = swap_0[pivot_i];
swap_0[pivot_i] = itemp_0;
itemp_0 = swap_1[k];
swap_1[k] = swap_1[pivot_j];
swap_1[pivot_j] = itemp_0;
// swap the columns
for(uint i=0; i<this->dims[0]; i++) {
tmpRow[i] = LHS(i,pivot_j);
LHS(i,pivot_j) = LHS(i,k);
LHS(i,k) = tmpRow[i];
}
// swap the rows
for(uint j=0; j<this->dims[0]; j++) {
tmpRow[j] = LHS(pivot_i,j);
LHS(pivot_i,j) = LHS(k,j);
LHS(k,j) = tmpRow[j];
}
T tmp = RHS[pivot_i];
RHS[pivot_i] = RHS[k];
RHS[k] = tmp;
// subtraction
for(uint i=k+1; i<this->dims[0]; i++) {
T first = LHS(i,k);
RHS[i] = RHS[i] - first/LHS(k,k)*RHS[k];
for(uint j=k; j<this->dims[0]; j++)
LHS(i,j) = LHS(i,j) - (first/LHS(k,k))*LHS(k,j);
}
// exact zero
for(uint j=0; j<k+1; j++) {
for(uint i=j+1; i<this->dims[0]; i++) {
LHS(i,j)=0.0;
}
}
}
// back substitute
for(int i=(int)this->dims[0]-1; i>=0; i--) {
T dtemp_0 = 0.0;
for(uint k = i+1; k<this->dims[0]; k++) {
dtemp_0 = dtemp_0 + (LHS(i,k)*vec[k]);
}
vec[i] = (RHS[i]-dtemp_0)/LHS(i,i);
}
// swap solution rows
for(uint i=0; i<this->dims[0]; i++)
solution[swap_1[i]] = vec[i];
return solution;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
Teuchos::ParameterList GaleriList;
// The problem is defined on a 2D grid, global size is nx * nx.
int nx = 30;
GaleriList.set("n", nx * nx);
GaleriList.set("nx", nx);
GaleriList.set("ny", nx);
Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap64("Linear", Comm, GaleriList) );
Teuchos::RefCountPtr<Epetra_RowMatrix> A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
// =============================================================== //
// B E G I N N I N G O F I F P A C K C O N S T R U C T I O N //
// =============================================================== //
Teuchos::ParameterList List;
// allocates an IFPACK factory. No data is associated
// to this object (only method Create()).
Ifpack Factory;
// create the preconditioner. For valid PrecType values,
// please check the documentation
string PrecType = "ILU"; // incomplete LU
int OverlapLevel = 1; // must be >= 0. If Comm.NumProc() == 1,
// it is ignored.
Teuchos::RefCountPtr<Ifpack_Preconditioner> Prec = Teuchos::rcp( Factory.Create(PrecType, &*A, OverlapLevel) );
assert(Prec != Teuchos::null);
// specify parameters for ILU
List.set("fact: drop tolerance", 1e-9);
List.set("fact: level-of-fill", 1);
// the combine mode is on the following:
// "Add", "Zero", "Insert", "InsertAdd", "Average", "AbsMax"
// Their meaning is as defined in file Epetra_CombineMode.h
List.set("schwarz: combine mode", "Add");
// sets the parameters
IFPACK_CHK_ERR(Prec->SetParameters(List));
// initialize the preconditioner. At this point the matrix must
// have been FillComplete()'d, but actual values are ignored.
IFPACK_CHK_ERR(Prec->Initialize());
// Builds the preconditioners, by looking for the values of
// the matrix.
IFPACK_CHK_ERR(Prec->Compute());
// =================================================== //
// E N D O F I F P A C K C O N S T R U C T I O N //
// =================================================== //
// At this point, we need some additional objects
// to define and solve the linear system.
// defines LHS and RHS
Epetra_Vector LHS(A->OperatorDomainMap());
Epetra_Vector RHS(A->OperatorDomainMap());
// solution is constant
LHS.PutScalar(1.0);
// now build corresponding RHS
A->Apply(LHS,RHS);
// now randomize the solution
RHS.Random();
// need an Epetra_LinearProblem to define AztecOO solver
Epetra_LinearProblem Problem(&*A,&LHS,&RHS);
// now we can allocate the AztecOO solver
AztecOO Solver(Problem);
// specify solver
Solver.SetAztecOption(AZ_solver,AZ_gmres);
Solver.SetAztecOption(AZ_output,32);
// HERE WE SET THE IFPACK PRECONDITIONER
Solver.SetPrecOperator(&*Prec);
// .. and here we solve
Solver.Iterate(1550,1e-8);
cout << *Prec;
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return(EXIT_SUCCESS);
}
int main(int argc, char *argv[])
{
int Nnodes=32*32; /* Total number of nodes in the problem.*/
/* 'Nnodes' must be a perfect square. */
struct user_partition Edge_Partition = {NULL, NULL,0,0,NULL,0,0,0},
Node_Partition = {NULL, NULL,0,0,NULL,0,0,0};
int proc_config[AZ_PROC_SIZE];
#ifdef ML_MPI
MPI_Init(&argc,&argv);
#endif
AZ_set_proc_config(proc_config, COMMUNICATOR);
ML_Comm* comm;
ML_Comm_Create(&comm);
Node_Partition.Nglobal = Nnodes;
Edge_Partition.Nglobal = Node_Partition.Nglobal*2;
user_partition_nodes(&Node_Partition);
user_partition_edges(&Edge_Partition, &Node_Partition);
AZ_MATRIX * AZ_Ke = user_Ke_build(&Edge_Partition);
AZ_MATRIX * AZ_Kn = user_Kn_build(&Node_Partition);
// convert (put wrappers) from Aztec matrices to ML_Operator's
ML_Operator * ML_Ke, * ML_Kn, * ML_Tmat;
ML_Ke = ML_Operator_Create( comm );
ML_Kn = ML_Operator_Create( comm );
AZ_convert_aztec_matrix_2ml_matrix(AZ_Ke,ML_Ke,proc_config);
AZ_convert_aztec_matrix_2ml_matrix(AZ_Kn,ML_Kn,proc_config);
ML_Tmat = user_T_build(&Edge_Partition, &Node_Partition,
ML_Kn, comm);
Epetra_CrsMatrix * Epetra_Kn, * Epetra_Ke, * Epetra_T;
int MaxNumNonzeros;
double CPUTime;
ML_Operator2EpetraCrsMatrix(ML_Ke,Epetra_Ke,
MaxNumNonzeros,
true,CPUTime);
ML_Operator2EpetraCrsMatrix(ML_Kn,
Epetra_Kn,MaxNumNonzeros,
true,CPUTime);
ML_Operator2EpetraCrsMatrix(ML_Tmat,Epetra_T,MaxNumNonzeros,
true,CPUTime);
Teuchos::ParameterList MLList;
ML_Epetra::SetDefaults("maxwell", MLList);
MLList.set("ML output", 0);
MLList.set("aggregation: type", "Uncoupled");
MLList.set("coarse: max size", 30);
MLList.set("aggregation: threshold", 0.0);
MLList.set("coarse: type", "Amesos-KLU");
ML_Epetra::MultiLevelPreconditioner * MLPrec =
new ML_Epetra::MultiLevelPreconditioner(*Epetra_Ke, *Epetra_T, *Epetra_Kn,
MLList);
Epetra_Vector LHS(Epetra_Ke->DomainMap()); LHS.Random();
Epetra_Vector RHS(Epetra_Ke->DomainMap()); RHS.PutScalar(1.0);
Epetra_LinearProblem Problem(Epetra_Ke,&LHS,&RHS);
AztecOO solver(Problem);
solver.SetPrecOperator(MLPrec);
solver.SetAztecOption(AZ_solver, AZ_cg_condnum);
solver.SetAztecOption(AZ_output, 32);
solver.Iterate(500, 1e-8);
// ========================= //
// compute the real residual //
// ========================= //
Epetra_Vector RHScomp(Epetra_Ke->DomainMap());
int ierr;
ierr = Epetra_Ke->Multiply(false, LHS, RHScomp);
assert(ierr==0);
Epetra_Vector resid(Epetra_Ke->DomainMap());
ierr = resid.Update(1.0, RHS, -1.0, RHScomp, 0.0);
assert(ierr==0);
double residual;
ierr = resid.Norm2(&residual);
assert(ierr==0);
if (proc_config[AZ_node] == 0) {
std::cout << std::endl;
std::cout << "==> Residual = " << residual << std::endl;
std::cout << std::endl;
}
// =============== //
// C L E A N U P //
// =============== //
delete MLPrec; // destroy phase prints out some information
delete Epetra_Kn;
delete Epetra_Ke;
delete Epetra_T;
ML_Operator_Destroy( &ML_Ke );
ML_Operator_Destroy( &ML_Kn );
ML_Comm_Destroy( &comm );
if (Edge_Partition.my_local_ids != NULL) free(Edge_Partition.my_local_ids);
if (Node_Partition.my_local_ids != NULL) free(Node_Partition.my_local_ids);
if (Node_Partition.my_global_ids != NULL) free(Node_Partition.my_global_ids);
if (Edge_Partition.my_global_ids != NULL) free(Edge_Partition.my_global_ids);
if (Node_Partition.needed_external_ids != NULL)
free(Node_Partition.needed_external_ids);
if (Edge_Partition.needed_external_ids != NULL)
free(Edge_Partition.needed_external_ids);
if (AZ_Ke!= NULL) {
AZ_free(AZ_Ke->bindx);
AZ_free(AZ_Ke->val);
AZ_free(AZ_Ke->data_org);
AZ_matrix_destroy(&AZ_Ke);
}
if (AZ_Kn!= NULL) {
AZ_free(AZ_Kn->bindx);
AZ_free(AZ_Kn->val);
AZ_free(AZ_Kn->data_org);
AZ_matrix_destroy(&AZ_Kn);
}
ML_Operator_Destroy(&ML_Tmat);
if (residual > 1e-5) {
std::cout << "`MultiLevelPreconditioner_Maxwell.exe' failed!" << std::endl;
exit(EXIT_FAILURE);
}
#ifdef ML_MPI
MPI_Finalize();
#endif
if (proc_config[AZ_node] == 0)
std::cout << "`MultiLevelPreconditioner_Maxwell.exe' passed!" << std::endl;
exit(EXIT_SUCCESS);
}
