// ============================================================================
void
Solve(const Epetra_RowMatrix* Matrix, const Epetra_MultiVector* LHS,
const Epetra_MultiVector* RHS)
{
if (Matrix->Comm().NumProc() != 1)
throw(Exception(__FILE__, __LINE__,
"Solve() works only in serial"));
if (LHS->NumVectors() != RHS->NumVectors())
throw(Exception(__FILE__, __LINE__,
"number of vectors in multivectors not consistent"));
if(Matrix->NumGlobalRows64() > std::numeric_limits<int>::max())
throw(Exception(__FILE__, __LINE__,
"Matrix->NumGlobalRows64() > std::numeric_limits<int>::max()"));
int n = static_cast<int>(Matrix->NumGlobalRows64());
int NumVectors = LHS->NumVectors();
Epetra_SerialDenseMatrix DenseMatrix;
DenseMatrix.Shape(n, n);
for (int i = 0 ; i < n ; ++i)
for (int j = 0 ; j < n ; ++j)
DenseMatrix(i,j) = 0.0;
// allocate storage to extract matrix rows.
int Length = Matrix->MaxNumEntries();
vector<double> Values(Length);
vector<int> Indices(Length);
for (int j = 0 ; j < Matrix->NumMyRows() ; ++j)
{
int NumEntries;
int ierr = Matrix->ExtractMyRowCopy(j, Length, NumEntries,
&Values[0], &Indices[0]);
for (int k = 0 ; k < NumEntries ; ++k)
DenseMatrix(j,Indices[k]) = Values[k];
}
Epetra_SerialDenseMatrix DenseX(n, NumVectors);
Epetra_SerialDenseMatrix DenseB(n, NumVectors);
for (int i = 0 ; i < n ; ++i)
for (int j = 0 ; j < NumVectors ; ++j)
DenseB(i,j) = (*RHS)[j][i];
Epetra_SerialDenseSolver DenseSolver;
DenseSolver.SetMatrix(DenseMatrix);
DenseSolver.SetVectors(DenseX,DenseB);
DenseSolver.Factor();
DenseSolver.Solve();
for (int i = 0 ; i < n ; ++i)
for (int j = 0 ; j < NumVectors ; ++j)
(*LHS)[j][i] = DenseX(i,j);
}
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 ;
}
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 ;
}
// main driver
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc, &argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
if (Comm.NumProc() != 2) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return(0);
}
int NumMyElements = 0; // NODES assigned to this processor
int NumMyExternalElements = 0; // nodes used by this proc, but not hosted
int NumMyTotalElements = 0;
int FE_NumMyElements = 0; // TRIANGLES assigned to this processor
int * MyGlobalElements = 0; // nodes assigned to this processor
Epetra_IntSerialDenseMatrix T; // store the grid connectivity
int MyPID=Comm.MyPID();
cout << MyPID << endl;
switch( MyPID ) {
case 0:
NumMyElements = 3;
NumMyExternalElements = 2;
NumMyTotalElements = NumMyElements + NumMyExternalElements;
FE_NumMyElements = 3;
MyGlobalElements = new int[NumMyTotalElements];
MyGlobalElements[0] = 0;
MyGlobalElements[1] = 4;
MyGlobalElements[2] = 3;
MyGlobalElements[3] = 1;
MyGlobalElements[4] = 5;
break;
case 1:
NumMyElements = 3;
NumMyExternalElements = 2;
NumMyTotalElements = NumMyElements + NumMyExternalElements;
FE_NumMyElements = 3;
MyGlobalElements = new int[NumMyTotalElements];
MyGlobalElements[0] = 1;
MyGlobalElements[1] = 2;
MyGlobalElements[2] = 5;
MyGlobalElements[3] = 0;
MyGlobalElements[4] = 4;
break;
}
// build Map corresponding to update
Epetra_Map Map(-1,NumMyElements,MyGlobalElements,0,Comm);
// vector containing coordinates BEFORE exchanging external nodes
Epetra_Vector CoordX_noExt(Map);
Epetra_Vector CoordY_noExt(Map);
switch( MyPID ) {
case 0:
T.Shape(3,FE_NumMyElements);
// fill x-coordinates
CoordX_noExt[0] = 0.0;
CoordX_noExt[1] = 1.0;
CoordX_noExt[2] = 0.0;
// fill y-coordinates
CoordY_noExt[0] = 0.0;
CoordY_noExt[1] = 1.0;
CoordY_noExt[2] = 1.0;
// fill connectivity
T(0,0) = 0; T(0,1) = 4; T(0,2) = 3;
T(1,0) = 0; T(1,1) = 1; T(1,2) = 4;
T(2,0) = 4; T(2,1) = 1; T(2,2) = 5;
break;
case 1:
T.Shape(3,FE_NumMyElements);
// fill x-coordinates
CoordX_noExt[0] = 1.0;
CoordX_noExt[1] = 2.0;
CoordX_noExt[2] = 2.0;
// fill y-coordinates
CoordY_noExt[0] = 0.0;
CoordY_noExt[1] = 0.0;
CoordY_noExt[2] = 1.0;
// fill connectivity
T(0,0) = 0; T(0,1) = 1; T(0,2) = 4;
T(1,0) = 1; T(1,1) = 5; T(1,2) = 4;
T(2,0) = 1; T(2,1) = 2; T(2,2) = 5;
break;
}
// - - - - - - - - - - - - - - - - - - - - //
// E X T E R N A L N O D E S S E T U P //
// - - - - - - - - - - - - - - - - - - - - //
// build target map to exchange the valus of external nodes
Epetra_Map TargetMap(-1,NumMyTotalElements,
MyGlobalElements, 0, Comm);
// !@# rename Map -> SourceMap ?????
Epetra_Import Importer(TargetMap,Map);
Epetra_Vector CoordX(TargetMap);
Epetra_Vector CoordY(TargetMap);
CoordX.Import(CoordX_noExt,Importer,Insert);
CoordY.Import(CoordY_noExt,Importer,Insert);
// now CoordX_noExt and CoordY_noExt are no longer required
// NOTE: better to construct CoordX and CoordY as MultiVector
// - - - - - - - - - - - - //
// M A T R I X S E T U P //
// - - - - - - - - - - - - //
// build the CRS matrix corresponding to the grid
// some vectors are allocated
const int MaxNnzRow = 5;
Epetra_CrsMatrix A(Copy,Map,MaxNnzRow);
int Element, MyRow, GlobalRow, GlobalCol, i, j, k;
Epetra_IntSerialDenseMatrix Struct; // temp to create the matrix connectivity
Struct.Shape(NumMyElements,MaxNnzRow);
for( i=0 ; i<NumMyElements ; ++i )
for( j=0 ; j<MaxNnzRow ; ++j )
Struct(i,j) = -1;
// cycle over all the finite elements
for( Element=0 ; Element<FE_NumMyElements ; ++Element ) {
// cycle over each row
for( i=0 ; i<3 ; ++i ) {
// get the global and local number of this row
GlobalRow = T(Element,i);
MyRow = A.LRID(GlobalRow);
if( MyRow != -1 ) { // only rows stored on this proc
// cycle over the columns
for( j=0 ; j<3 ; ++j ) {
// get the global number only of this column
GlobalCol = T(Element,j);
// look if GlobalCol was already put in Struct
for( k=0 ; k<MaxNnzRow ; ++k ) {
if( Struct(MyRow,k) == GlobalCol ||
Struct(MyRow,k) == -1 ) break;
}
if( Struct(MyRow,k) == -1 ) { // new entry
Struct(MyRow,k) = GlobalCol;
} else if( Struct(MyRow,k) != GlobalCol ) {
// maybe not enough space has beenn allocated
cerr << "ERROR: not enough space for element "
<< GlobalRow << "," << GlobalCol << endl;
return( 0 );
}
}
}
}
}
int * Indices = new int [MaxNnzRow];
double * Values = new double [MaxNnzRow];
for( i=0 ; i<MaxNnzRow ; ++i ) Values[i] = 0.0;
// now use Struct to fill build the matrix structure
for( int Row=0 ; Row<NumMyElements ; ++Row ) {
int Length = 0;
for( int j=0 ; j<MaxNnzRow ; ++j ) {
if( Struct(Row,j) == -1 ) break;
Indices[Length] = Struct(Row,j);
Length++;
}
GlobalRow = MyGlobalElements[Row];
A.InsertGlobalValues(GlobalRow, Length, Values, Indices);
}
// replace global numbering with local one in T
for( int Element=0 ; Element<FE_NumMyElements ; ++Element ) {
for( int i=0 ; i<3 ; ++i ) {
int global = T(Element,i);
int local = find(MyGlobalElements,NumMyTotalElements,
global);
if( global == -1 ) {
cerr << "ERROR\n";
return( EXIT_FAILURE );
}
T(Element,i) = local;
}
}
// - - - - - - - - - - - - - - //
// M A T R I X F I L L - I N //
// - - - - - - - - - - - - - - //
// room for the local matrix
Epetra_SerialDenseMatrix Ke;
Ke.Shape(3,3);
// now fill the matrix
for( int Element=0 ; Element<FE_NumMyElements ; ++Element ) {
// variables used inside
int GlobalRow;
int MyRow;
int GlobalCol;
double x_triangle[3];
double y_triangle[3];
// get the spatial coordinate of each local node
for( int i=0 ; i<3 ; ++i ) {
MyRow = T(Element,i);
y_triangle[i] = CoordX[MyRow];
x_triangle[i] = CoordY[MyRow];
}
// compute the local matrix for Element
compute_loc_matrix( x_triangle, y_triangle,Ke );
// insert it in the global one
// cycle over each row
for( int i=0 ; i<3 ; ++i ) {
// get the global and local number of this row
MyRow = T(Element,i);
if( MyRow < NumMyElements ) {
for( int j=0 ; j<3 ; ++j ) {
// get global column number
GlobalRow = MyGlobalElements[MyRow];
GlobalCol = MyGlobalElements[T(Element,j)];
A.SumIntoGlobalValues(GlobalRow,1,&(Ke(i,j)),&GlobalCol);
}
}
}
}
A.FillComplete();
// - - - - - - - - - - - - - //
// R H S & S O L U T I O N //
// - - - - - - - - - - - - - //
Epetra_Vector x(Map), b(Map);
x.Random(); b.PutScalar(0.0);
// Solution can be obtained using Aztecoo
// free memory before leaving
delete MyGlobalElements;
delete Indices;
delete Values;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return( EXIT_SUCCESS );
} /* main */