int powerMethodTests(Epetra_RowMatrix & A, Epetra_RowMatrix & JadA, Epetra_Map & Map,
Epetra_Vector & q, Epetra_Vector & z, Epetra_Vector & resid, bool verbose) {
// variable needed for iteration
double lambda = 0.0;
// int niters = 10000;
int niters = 300;
double tolerance = 1.0e-2;
int ierr = 0;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Iterate
Epetra_Time timer(Map.Comm());
double startTime = timer.ElapsedTime();
EPETRA_TEST_ERR(power_method(false, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
double elapsed_time = timer.ElapsedTime() - startTime;
double total_flops = q.Flops();
double MFLOPs = total_flops/elapsed_time/1000000.0;
double lambdaref = lambda;
double flopsref = total_flops;
if (verbose)
cout << "\n\nTotal MFLOPs for reference first solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
lambda = 0.0;
startTime = timer.ElapsedTime();
EPETRA_TEST_ERR(power_method(false, JadA, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime() - startTime;
total_flops = q.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for candidate first solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
EPETRA_TEST_ERR(checkValues(lambda,lambdaref," No-transpose Power Method result", verbose),ierr);
EPETRA_TEST_ERR(checkValues(total_flops,flopsref," No-transpose Power Method flop count", verbose),ierr);
/////////////////////////////////////////////////////////////////////////////////////////////////
// Solve transpose problem
if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
<< endl;
// Iterate
lambda = 0.0;
startTime = timer.ElapsedTime();
EPETRA_TEST_ERR(power_method(true, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime() - startTime;
total_flops = q.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
lambdaref = lambda;
flopsref = total_flops;
if (verbose)
cout << "\n\nTotal MFLOPs for reference transpose solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
lambda = 0.0;
startTime = timer.ElapsedTime();
EPETRA_TEST_ERR(power_method(true, JadA, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime() - startTime;
total_flops = q.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for candidate transpose solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
EPETRA_TEST_ERR(checkValues(lambda,lambdaref,"Transpose Power Method result", verbose),ierr);
EPETRA_TEST_ERR(checkValues(total_flops,flopsref,"Transpose Power Method flop count", verbose),ierr);
EPETRA_TEST_ERR(check(A, JadA, verbose),ierr);
return(0);
}
int main(int argc, char *argv[])
{
int ierr = 0, i;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
Epetra_SerialComm Comm;
#endif
int MyPID = Comm.MyPID();
int NumProc = Comm.NumProc();
bool verbose = (MyPID==0);
if (verbose)
cout << Epetra_Version() << endl << endl;
cout << Comm << endl;
// Get the number of local equations from the command line
if (argc!=2)
{
if (verbose)
cout << "Usage: " << argv[0] << " number_of_equations" << endl;
std::exit(1);
}
long long NumGlobalElements = std::atoi(argv[1]);
if (NumGlobalElements < NumProc)
{
if (verbose)
cout << "numGlobalBlocks = " << NumGlobalElements
<< " cannot be < number of processors = " << NumProc << endl;
std::exit(1);
}
// Construct a Map that puts approximately the same number of
// equations on each processor.
Epetra_Map Map(NumGlobalElements, 0LL, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map.NumMyElements();
std::vector<long long> MyGlobalElements(NumMyElements);
Map.MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
// on this processor
std::vector<int> NumNz(NumMyElements);
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for (i=0; i<NumMyElements; i++)
if (MyGlobalElements[i]==0 || MyGlobalElements[i] == NumGlobalElements-1)
NumNz[i] = 2;
else
NumNz[i] = 3;
// Create a Epetra_Matrix
Epetra_CrsMatrix A(Copy, Map, &NumNz[0]);
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
std::vector<double> Values(2);
Values[0] = -1.0; Values[1] = -1.0;
std::vector<long long> Indices(2);
double two = 2.0;
int NumEntries;
for (i=0; i<NumMyElements; i++)
{
if (MyGlobalElements[i]==0)
{
Indices[0] = 1;
NumEntries = 1;
}
else if (MyGlobalElements[i] == NumGlobalElements-1)
{
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
}
else
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
ierr = A.InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert(ierr==0);
// Put in the diagonal entry
ierr = A.InsertGlobalValues(MyGlobalElements[i], 1, &two, &MyGlobalElements[i]);
assert(ierr==0);
}
// Finish up
ierr = A.FillComplete();
assert(ierr==0);
// Create vectors for Power method
// variable needed for iteration
double lambda = 0.0;
int niters = (int) NumGlobalElements*10;
double tolerance = 1.0e-2;
// Iterate
Epetra_Flops counter;
A.SetFlopCounter(counter);
Epetra_Time timer(Comm);
ierr += power_method(A, lambda, niters, tolerance, verbose);
double elapsed_time = timer.ElapsedTime();
double total_flops =counter.Flops();
double MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for first solve = " << MFLOPs << endl<< endl;
// Increase diagonal dominance
if (verbose)
cout << "\nIncreasing magnitude of first diagonal term, solving again\n\n"
<< endl;
if (A.MyGlobalRow(0)) {
int numvals = A.NumGlobalEntries(0);
std::vector<double> Rowvals(numvals);
std::vector<long long> Rowinds(numvals);
A.ExtractGlobalRowCopy(0, numvals, numvals, &Rowvals[0], &Rowinds[0]); // Get A[0,0]
for (i=0; i<numvals; i++) if (Rowinds[i] == 0) Rowvals[i] *= 10.0;
A.ReplaceGlobalValues(0, numvals, &Rowvals[0], &Rowinds[0]);
}
// Iterate (again)
lambda = 0.0;
timer.ResetStartTime();
counter.ResetFlops();
ierr += power_method(A, lambda, niters, tolerance, verbose);
elapsed_time = timer.ElapsedTime();
total_flops = counter.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for second solve = " << MFLOPs << endl<< endl;
// Release all objects
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
/* end main
*/
return ierr ;
}
int powerMethodTests(CT_Epetra_RowMatrix_ID_t & A, CT_Epetra_RowMatrix_ID_t & JadA,
CT_Epetra_Map_ID_Flex_t & Map, CT_Epetra_Vector_ID_Flex_t & q,
CT_Epetra_Vector_ID_Flex_t & z, CT_Epetra_Vector_ID_Flex_t & resid, bool verbose) {
// variable needed for iteration
double lambda = 0.0;
// int niters = 10000;
int niters = 300;
double tolerance = 1.0e-2;
int ierr = 0;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Iterate
CT_Epetra_Comm_ID_t Comm = Epetra_BlockMap_Comm(Map.Epetra_BlockMap);
CT_Epetra_Time_ID_t timer = Epetra_Time_Create(Comm);
Epetra_Comm_Destroy(&Comm);
double startTime = Epetra_Time_ElapsedTime(timer);
EPETRA_TEST_ERR(power_method(FALSE, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
double elapsed_time = Epetra_Time_ElapsedTime(timer) - startTime;
double total_flops = Epetra_CompObject_Flops(q.Epetra_CompObject);
double MFLOPs = total_flops/elapsed_time/1000000.0;
double lambdaref = lambda;
double flopsref = total_flops;
if (verbose)
cout << "\n\nTotal MFLOPs for reference first solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
lambda = 0.0;
startTime = Epetra_Time_ElapsedTime(timer);
EPETRA_TEST_ERR(power_method(FALSE, JadA, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = Epetra_Time_ElapsedTime(timer) - startTime;
total_flops = Epetra_CompObject_Flops(q.Epetra_CompObject);
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for candidate first solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
EPETRA_TEST_ERR(checkValues(lambda,lambdaref," No-transpose Power Method result", verbose),ierr);
EPETRA_TEST_ERR(checkValues(total_flops,flopsref," No-transpose Power Method flop count", verbose),ierr);
/////////////////////////////////////////////////////////////////////////////////////////////////
// Solve transpose problem
if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
<< endl;
// Iterate
lambda = 0.0;
startTime = Epetra_Time_ElapsedTime(timer);
EPETRA_TEST_ERR(power_method(TRUE, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = Epetra_Time_ElapsedTime(timer) - startTime;
total_flops = Epetra_CompObject_Flops(q.Epetra_CompObject);
MFLOPs = total_flops/elapsed_time/1000000.0;
lambdaref = lambda;
flopsref = total_flops;
if (verbose)
cout << "\n\nTotal MFLOPs for reference transpose solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
lambda = 0.0;
startTime = Epetra_Time_ElapsedTime(timer);
EPETRA_TEST_ERR(power_method(TRUE, JadA, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = Epetra_Time_ElapsedTime(timer) - startTime;
total_flops = Epetra_CompObject_Flops(q.Epetra_CompObject);
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose)
cout << "\n\nTotal MFLOPs for candidate transpose solve = " << MFLOPs << endl
<< "Total FLOPS = " <<total_flops <<endl<<endl;
EPETRA_TEST_ERR(checkValues(lambda,lambdaref,"Transpose Power Method result", verbose),ierr);
EPETRA_TEST_ERR(checkValues(total_flops,flopsref,"Transpose Power Method flop count", verbose),ierr);
EPETRA_TEST_ERR(check(A, JadA, verbose),ierr);
return(0);
}
int main(int argc, char *argv[])
{
int ierr = 0, forierr = 0;
bool debug = false;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
int rank; // My process ID
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
int rank = 0;
Epetra_SerialComm Comm;
#endif
bool verbose = false;
// Check if we should print results to standard out
if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
int verbose_int = verbose ? 1 : 0;
Comm.Broadcast(&verbose_int, 1, 0);
verbose = verbose_int==1 ? true : false;
// char tmp;
// if (rank==0) cout << "Press any key to continue..."<< std::endl;
// if (rank==0) cin >> tmp;
// Comm.Barrier();
Comm.SetTracebackMode(0); // This should shut down any error traceback reporting
int MyPID = Comm.MyPID();
int NumProc = Comm.NumProc();
if(verbose && MyPID==0)
cout << Epetra_Version() << std::endl << std::endl;
if (verbose) cout << "Processor "<<MyPID<<" of "<< NumProc
<< " is alive."<<endl;
bool verbose1 = verbose;
// Redefine verbose to only print on PE 0
if(verbose && rank!=0)
verbose = false;
int NumMyEquations = 10000;
int NumGlobalEquations = (NumMyEquations * NumProc) + EPETRA_MIN(NumProc,3);
if(MyPID < 3)
NumMyEquations++;
// Construct a Map that puts approximately the same Number of equations on each processor
Epetra_Map Map(NumGlobalEquations, NumMyEquations, 0, Comm);
// Get update list and number of local equations from newly created Map
int* MyGlobalElements = new int[Map.NumMyElements()];
Map.MyGlobalElements(MyGlobalElements);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation on this processor
int* NumNz = new int[NumMyEquations];
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for (int i = 0; i < NumMyEquations; i++)
if((MyGlobalElements[i] == 0) || (MyGlobalElements[i] == NumGlobalEquations - 1))
NumNz[i] = 1;
else
NumNz[i] = 2;
// Create a Epetra_Matrix
Epetra_CrsMatrix A(Copy, Map, NumNz);
EPETRA_TEST_ERR(A.IndicesAreGlobal(),ierr);
EPETRA_TEST_ERR(A.IndicesAreLocal(),ierr);
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
double* Values = new double[2];
Values[0] = -1.0;
Values[1] = -1.0;
int* Indices = new int[2];
double two = 2.0;
int NumEntries;
forierr = 0;
for (int i = 0; i < NumMyEquations; i++) {
if(MyGlobalElements[i] == 0) {
Indices[0] = 1;
NumEntries = 1;
}
else if (MyGlobalElements[i] == NumGlobalEquations-1) {
Indices[0] = NumGlobalEquations-2;
NumEntries = 1;
}
else {
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
NumEntries = 2;
}
forierr += !(A.InsertGlobalValues(MyGlobalElements[i], NumEntries, Values, Indices)==0);
forierr += !(A.InsertGlobalValues(MyGlobalElements[i], 1, &two, MyGlobalElements+i)>0); // Put in the diagonal entry
}
EPETRA_TEST_ERR(forierr,ierr);
int * indexOffsetTmp;
int * indicesTmp;
double * valuesTmp;
// Finish up
EPETRA_TEST_ERR(!(A.IndicesAreGlobal()),ierr);
EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==-1),ierr); // Should fail
EPETRA_TEST_ERR(!(A.FillComplete(false)==0),ierr);
EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==-1),ierr); // Should fail
EPETRA_TEST_ERR(!(A.IndicesAreLocal()),ierr);
EPETRA_TEST_ERR(A.StorageOptimized(),ierr);
A.OptimizeStorage();
EPETRA_TEST_ERR(!(A.StorageOptimized()),ierr);
EPETRA_TEST_ERR(!(A.ExtractCrsDataPointers(indexOffsetTmp, indicesTmp, valuesTmp)==0),ierr); // Should succeed
const Epetra_CrsGraph & GofA = A.Graph();
EPETRA_TEST_ERR((indicesTmp!=GofA[0] || valuesTmp!=A[0]),ierr); // Extra check to see if operator[] is consistent
EPETRA_TEST_ERR(A.UpperTriangular(),ierr);
EPETRA_TEST_ERR(A.LowerTriangular(),ierr);
int NumMyNonzeros = 3 * NumMyEquations;
if(A.LRID(0) >= 0)
NumMyNonzeros--; // If I own first global row, then there is one less nonzero
if(A.LRID(NumGlobalEquations-1) >= 0)
NumMyNonzeros--; // If I own last global row, then there is one less nonzero
EPETRA_TEST_ERR(check(A, NumMyEquations, NumGlobalEquations, NumMyNonzeros, 3*NumGlobalEquations-2,
MyGlobalElements, verbose),ierr);
forierr = 0;
for (int i = 0; i < NumMyEquations; i++)
forierr += !(A.NumGlobalEntries(MyGlobalElements[i])==NumNz[i]+1);
EPETRA_TEST_ERR(forierr,ierr);
forierr = 0;
for (int i = 0; i < NumMyEquations; i++)
forierr += !(A.NumMyEntries(i)==NumNz[i]+1);
EPETRA_TEST_ERR(forierr,ierr);
if (verbose) cout << "\n\nNumEntries function check OK" << std::endl<< std::endl;
EPETRA_TEST_ERR(check_graph_sharing(Comm),ierr);
// Create vectors for Power method
Epetra_Vector q(Map);
Epetra_Vector z(Map);
Epetra_Vector resid(Map);
// variable needed for iteration
double lambda = 0.0;
// int niters = 10000;
int niters = 200;
double tolerance = 1.0e-1;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Iterate
Epetra_Flops flopcounter;
A.SetFlopCounter(flopcounter);
q.SetFlopCounter(A);
z.SetFlopCounter(A);
resid.SetFlopCounter(A);
Epetra_Time timer(Comm);
EPETRA_TEST_ERR(power_method(false, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
double elapsed_time = timer.ElapsedTime();
double total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
double MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose) cout << "\n\nTotal MFLOPs for first solve = " << MFLOPs << std::endl<< std::endl;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Solve transpose problem
if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
<< std::endl;
// Iterate
lambda = 0.0;
flopcounter.ResetFlops();
timer.ResetStartTime();
EPETRA_TEST_ERR(power_method(true, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime();
total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose) cout << "\n\nTotal MFLOPs for transpose solve = " << MFLOPs << std::endl<< endl;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Increase diagonal dominance
if (verbose) cout << "\n\nIncreasing the magnitude of first diagonal term and solving again\n\n"
<< endl;
if (A.MyGlobalRow(0)) {
int numvals = A.NumGlobalEntries(0);
double * Rowvals = new double [numvals];
int * Rowinds = new int [numvals];
A.ExtractGlobalRowCopy(0, numvals, numvals, Rowvals, Rowinds); // Get A[0,0]
for (int i=0; i<numvals; i++) if (Rowinds[i] == 0) Rowvals[i] *= 10.0;
A.ReplaceGlobalValues(0, numvals, Rowvals, Rowinds);
delete [] Rowvals;
delete [] Rowinds;
}
// Iterate (again)
lambda = 0.0;
flopcounter.ResetFlops();
timer.ResetStartTime();
EPETRA_TEST_ERR(power_method(false, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime();
total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose) cout << "\n\nTotal MFLOPs for second solve = " << MFLOPs << endl<< endl;
/////////////////////////////////////////////////////////////////////////////////////////////////
// Solve transpose problem
if (verbose) cout << "\n\nUsing transpose of matrix and solving again (should give same result).\n\n"
<< endl;
// Iterate (again)
lambda = 0.0;
flopcounter.ResetFlops();
timer.ResetStartTime();
EPETRA_TEST_ERR(power_method(true, A, q, z, resid, &lambda, niters, tolerance, verbose),ierr);
elapsed_time = timer.ElapsedTime();
total_flops = A.Flops() + q.Flops() + z.Flops() + resid.Flops();
MFLOPs = total_flops/elapsed_time/1000000.0;
if (verbose) cout << "\n\nTotal MFLOPs for tranpose of second solve = " << MFLOPs << endl<< endl;
if (verbose) cout << "\n\n*****Testing constant entry constructor" << endl<< endl;
Epetra_CrsMatrix AA(Copy, Map, 5);
if (debug) Comm.Barrier();
double dble_one = 1.0;
for (int i=0; i< NumMyEquations; i++) AA.InsertGlobalValues(MyGlobalElements[i], 1, &dble_one, MyGlobalElements+i);
// Note: All processors will call the following Insert routines, but only the processor
// that owns it will actually do anything
int One = 1;
if (AA.MyGlobalRow(0)) {
EPETRA_TEST_ERR(!(AA.InsertGlobalValues(0, 0, &dble_one, &One)==0),ierr);
}
else EPETRA_TEST_ERR(!(AA.InsertGlobalValues(0, 1, &dble_one, &One)==-1),ierr);
EPETRA_TEST_ERR(!(AA.FillComplete(false)==0),ierr);
EPETRA_TEST_ERR(AA.StorageOptimized(),ierr);
EPETRA_TEST_ERR(!(AA.UpperTriangular()),ierr);
EPETRA_TEST_ERR(!(AA.LowerTriangular()),ierr);
if (debug) Comm.Barrier();
EPETRA_TEST_ERR(check(AA, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
MyGlobalElements, verbose),ierr);
if (debug) Comm.Barrier();
forierr = 0;
for (int i=0; i<NumMyEquations; i++) forierr += !(AA.NumGlobalEntries(MyGlobalElements[i])==1);
EPETRA_TEST_ERR(forierr,ierr);
if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
if (debug) Comm.Barrier();
if (verbose) cout << "\n\n*****Testing copy constructor" << endl<< endl;
Epetra_CrsMatrix B(AA);
EPETRA_TEST_ERR(check(B, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
MyGlobalElements, verbose),ierr);
forierr = 0;
for (int i=0; i<NumMyEquations; i++) forierr += !(B.NumGlobalEntries(MyGlobalElements[i])==1);
EPETRA_TEST_ERR(forierr,ierr);
if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
if (debug) Comm.Barrier();
if (verbose) cout << "\n\n*****Testing local view constructor" << endl<< endl;
Epetra_CrsMatrix BV(View, AA.RowMap(), AA.ColMap(), 0);
forierr = 0;
int* Inds;
double* Vals;
for (int i = 0; i < NumMyEquations; i++) {
forierr += !(AA.ExtractMyRowView(i, NumEntries, Vals, Inds)==0);
forierr += !(BV.InsertMyValues(i, NumEntries, Vals, Inds)==0);
}
BV.FillComplete(false);
EPETRA_TEST_ERR(check(BV, NumMyEquations, NumGlobalEquations, NumMyEquations, NumGlobalEquations,
MyGlobalElements, verbose),ierr);
forierr = 0;
for (int i=0; i<NumMyEquations; i++) forierr += !(BV.NumGlobalEntries(MyGlobalElements[i])==1);
EPETRA_TEST_ERR(forierr,ierr);
if (verbose) cout << "\n\nNumEntries function check OK" << endl<< endl;
if (debug) Comm.Barrier();
if (verbose) cout << "\n\n*****Testing post construction modifications" << endl<< endl;
EPETRA_TEST_ERR(!(B.InsertGlobalValues(0, 1, &dble_one, &One)==-2),ierr);
// Release all objects
delete [] NumNz;
delete [] Values;
delete [] Indices;
delete [] MyGlobalElements;
if (verbose1) {
// Test ostream << operator (if verbose1)
// Construct a Map that puts 2 equations on each PE
int NumMyElements1 = 2;
int NumMyEquations1 = NumMyElements1;
int NumGlobalEquations1 = NumMyEquations1*NumProc;
Epetra_Map Map1(-1, NumMyElements1, 0, Comm);
// Get update list and number of local equations from newly created Map
int * MyGlobalElements1 = new int[Map1.NumMyElements()];
Map1.MyGlobalElements(MyGlobalElements1);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation on this processor
int * NumNz1 = new int[NumMyEquations1];
// We are building a tridiagonal matrix where each row has (-1 2 -1)
// So we need 2 off-diagonal terms (except for the first and last equation)
for (int i=0; i<NumMyEquations1; i++)
if (MyGlobalElements1[i]==0 || MyGlobalElements1[i] == NumGlobalEquations1-1)
NumNz1[i] = 1;
else
NumNz1[i] = 2;
// Create a Epetra_Matrix
Epetra_CrsMatrix A1(Copy, Map1, NumNz1);
// Add rows one-at-a-time
// Need some vectors to help
// Off diagonal Values will always be -1
double *Values1 = new double[2];
Values1[0] = -1.0; Values1[1] = -1.0;
int *Indices1 = new int[2];
double two1 = 2.0;
int NumEntries1;
forierr = 0;
for (int i=0; i<NumMyEquations1; i++)
{
if (MyGlobalElements1[i]==0)
{
Indices1[0] = 1;
NumEntries1 = 1;
}
else if (MyGlobalElements1[i] == NumGlobalEquations1-1)
{
Indices1[0] = NumGlobalEquations1-2;
NumEntries1 = 1;
}
else
{
Indices1[0] = MyGlobalElements1[i]-1;
Indices1[1] = MyGlobalElements1[i]+1;
NumEntries1 = 2;
}
forierr += !(A1.InsertGlobalValues(MyGlobalElements1[i], NumEntries1, Values1, Indices1)==0);
forierr += !(A1.InsertGlobalValues(MyGlobalElements1[i], 1, &two1, MyGlobalElements1+i)>0); // Put in the diagonal entry
}
EPETRA_TEST_ERR(forierr,ierr);
delete [] Indices1;
delete [] Values1;
// Finish up
EPETRA_TEST_ERR(!(A1.FillComplete(false)==0),ierr);
// Test diagonal extraction function
Epetra_Vector checkDiag(Map1);
EPETRA_TEST_ERR(!(A1.ExtractDiagonalCopy(checkDiag)==0),ierr);
forierr = 0;
for (int i=0; i<NumMyEquations1; i++) forierr += !(checkDiag[i]==two1);
EPETRA_TEST_ERR(forierr,ierr);
// Test diagonal replacement method
forierr = 0;
for (int i=0; i<NumMyEquations1; i++) checkDiag[i]=two1*two1;
EPETRA_TEST_ERR(forierr,ierr);
EPETRA_TEST_ERR(!(A1.ReplaceDiagonalValues(checkDiag)==0),ierr);
Epetra_Vector checkDiag1(Map1);
EPETRA_TEST_ERR(!(A1.ExtractDiagonalCopy(checkDiag1)==0),ierr);
forierr = 0;
for (int i=0; i<NumMyEquations1; i++) forierr += !(checkDiag[i]==checkDiag1[i]);
EPETRA_TEST_ERR(forierr,ierr);
if (verbose) cout << "\n\nDiagonal extraction and replacement OK.\n\n" << endl;
double orignorm = A1.NormOne();
EPETRA_TEST_ERR(!(A1.Scale(4.0)==0),ierr);
EPETRA_TEST_ERR(!(A1.NormOne()!=orignorm),ierr);
if (verbose) cout << "\n\nMatrix scale OK.\n\n" << endl;
if (verbose) cout << "\n\nPrint out tridiagonal matrix, each part on each processor.\n\n" << endl;
cout << A1 << endl;
// Release all objects
delete [] NumNz1;
delete [] MyGlobalElements1;
}
if (verbose) cout << "\n\n*****Testing LeftScale and RightScale" << endl << endl;
int NumMyElements2 = 7;
int NumMyRows2 = 1;//This value should not be changed without editing the
// code below.
Epetra_Map RowMap(-1,NumMyRows2,0,Comm);
Epetra_Map ColMap(NumMyElements2,NumMyElements2,0,Comm);
// The DomainMap needs to be different from the ColMap for the test to
// be meaningful.
Epetra_Map DomainMap(NumMyElements2,0,Comm);
int NumMyRangeElements2 = 0;
// We need to distribute the elements differently for the range map also.
if (MyPID % 2 == 0)
NumMyRangeElements2 = NumMyRows2*2; //put elements on even number procs
if (NumProc % 2 == 1 && MyPID == NumProc-1)
NumMyRangeElements2 = NumMyRows2; //If number of procs is odd, put
// the last NumMyElements2 elements on the last proc
Epetra_Map RangeMap(-1,NumMyRangeElements2,0,Comm);
Epetra_CrsMatrix A2(Copy,RowMap,ColMap,NumMyElements2);
double * Values2 = new double[NumMyElements2];
int * Indices2 = new int[NumMyElements2];
for (int i=0; i<NumMyElements2; i++) {
Values2[i] = i+MyPID;
Indices2[i]=i;
}
A2.InsertMyValues(0,NumMyElements2,Values2,Indices2);
A2.FillComplete(DomainMap,RangeMap,false);
Epetra_CrsMatrix A2copy(A2);
double * RowLeftScaleValues = new double[NumMyRows2];
double * ColRightScaleValues = new double[NumMyElements2];
int RowLoopLength = RowMap.MaxMyGID()-RowMap.MinMyGID()+1;
for (int i=0; i<RowLoopLength; i++)
RowLeftScaleValues[i] = (i + RowMap.MinMyGID() ) % 2 + 1;
// For the column map, all procs own all elements
for (int i=0; i<NumMyElements2;i++)
ColRightScaleValues[i] = i % 2 + 1;
int RangeLoopLength = RangeMap.MaxMyGID()-RangeMap.MinMyGID()+1;
double * RangeLeftScaleValues = new double[RangeLoopLength];
int DomainLoopLength = DomainMap.MaxMyGID()-DomainMap.MinMyGID()+1;
double * DomainRightScaleValues = new double[DomainLoopLength];
for (int i=0; i<RangeLoopLength; i++)
RangeLeftScaleValues[i] = 1.0/((i + RangeMap.MinMyGID() ) % 2 + 1);
for (int i=0; i<DomainLoopLength;i++)
DomainRightScaleValues[i] = 1.0/((i + DomainMap.MinMyGID() ) % 2 + 1);
Epetra_Vector xRow(View,RowMap,RowLeftScaleValues);
Epetra_Vector xCol(View,ColMap,ColRightScaleValues);
Epetra_Vector xRange(View,RangeMap,RangeLeftScaleValues);
Epetra_Vector xDomain(View,DomainMap,DomainRightScaleValues);
double A2infNorm = A2.NormInf();
double A2oneNorm = A2.NormOne();
if (verbose1) cout << A2;
EPETRA_TEST_ERR(A2.LeftScale(xRow),ierr);
double A2infNorm1 = A2.NormInf();
double A2oneNorm1 = A2.NormOne();
bool ScalingBroke = false;
if (A2infNorm1>2*A2infNorm||A2infNorm1<A2infNorm) {
EPETRA_TEST_ERR(-31,ierr);
ScalingBroke = true;
}
if (A2oneNorm1>2*A2oneNorm||A2oneNorm1<A2oneNorm) {
EPETRA_TEST_ERR(-32,ierr);
ScalingBroke = true;
}
if (verbose1) cout << A2;
EPETRA_TEST_ERR(A2.RightScale(xCol),ierr);
double A2infNorm2 = A2.NormInf();
double A2oneNorm2 = A2.NormOne();
if (A2infNorm2>=2*A2infNorm1||A2infNorm2<=A2infNorm1) {
EPETRA_TEST_ERR(-33,ierr);
ScalingBroke = true;
}
if (A2oneNorm2>2*A2oneNorm1||A2oneNorm2<=A2oneNorm1) {
EPETRA_TEST_ERR(-34,ierr);
ScalingBroke = true;
}
if (verbose1) cout << A2;
EPETRA_TEST_ERR(A2.RightScale(xDomain),ierr);
double A2infNorm3 = A2.NormInf();
double A2oneNorm3 = A2.NormOne();
// The last two scaling ops cancel each other out
if (A2infNorm3!=A2infNorm1) {
EPETRA_TEST_ERR(-35,ierr)
ScalingBroke = true;
}
if (A2oneNorm3!=A2oneNorm1) {
EPETRA_TEST_ERR(-36,ierr)
ScalingBroke = true;
}
if (verbose1) cout << A2;
EPETRA_TEST_ERR(A2.LeftScale(xRange),ierr);
double A2infNorm4 = A2.NormInf();
double A2oneNorm4 = A2.NormOne();
// The 4 scaling ops all cancel out
if (A2infNorm4!=A2infNorm) {
EPETRA_TEST_ERR(-37,ierr)
ScalingBroke = true;
}
if (A2oneNorm4!=A2oneNorm) {
EPETRA_TEST_ERR(-38,ierr)
ScalingBroke = true;
}
//
// Now try changing the values underneath and make sure that
// telling one process about the change causes NormInf() and
// NormOne() to recompute the norm on all processes.
//
double *values;
int num_my_rows = A2.NumMyRows() ;
int num_entries;
for ( int i=0 ; i< num_my_rows; i++ ) {
EPETRA_TEST_ERR( A2.ExtractMyRowView( i, num_entries, values ), ierr );
for ( int j = 0 ; j <num_entries; j++ ) {
values[j] *= 2.0;
}
}
if ( MyPID == 0 )
A2.SumIntoGlobalValues( 0, 0, 0, 0 ) ;
double A2infNorm5 = A2.NormInf();
double A2oneNorm5 = A2.NormOne();
if (A2infNorm5!=2.0 * A2infNorm4) {
EPETRA_TEST_ERR(-39,ierr)
ScalingBroke = true;
}
if (A2oneNorm5!= 2.0 * A2oneNorm4) {
EPETRA_TEST_ERR(-40,ierr)
ScalingBroke = true;
}
//
// Restore the values underneath
//
for ( int i=0 ; i< num_my_rows; i++ ) {
EPETRA_TEST_ERR( A2.ExtractMyRowView( i, num_entries, values ), ierr );
for ( int j = 0 ; j <num_entries; j++ ) {
values[j] /= 2.0;
}
}
if (verbose1) cout << A2;
if (ScalingBroke) {
if (verbose) cout << endl << "LeftScale and RightScale tests FAILED" << endl << endl;
}
else {
if (verbose) cout << endl << "LeftScale and RightScale tests PASSED" << endl << endl;
}
Comm.Barrier();
if (verbose) cout << "\n\n*****Testing InvRowMaxs and InvColMaxs" << endl << endl;
if (verbose1) cout << A2 << endl;
EPETRA_TEST_ERR(A2.InvRowMaxs(xRow),ierr);
EPETRA_TEST_ERR(A2.InvRowMaxs(xRange),ierr);
if (verbose1) cout << xRow << endl << xRange << endl;
if (verbose) cout << "\n\n*****Testing InvRowSums and InvColSums" << endl << endl;
bool InvSumsBroke = false;
// Works!
EPETRA_TEST_ERR(A2.InvRowSums(xRow),ierr);
if (verbose1) cout << xRow;
EPETRA_TEST_ERR(A2.LeftScale(xRow),ierr);
float A2infNormFloat = A2.NormInf();
if (verbose1) cout << A2 << endl;
if (fabs(1.0-A2infNormFloat) > 1.e-5) {
EPETRA_TEST_ERR(-41,ierr);
InvSumsBroke = true;
}
// Works
int expectedcode = 1;
if (Comm.NumProc()>1) expectedcode = 0;
EPETRA_TEST_ERR(!(A2.InvColSums(xDomain)==expectedcode),ierr); // This matrix has a single row, the first column has a zero, so a warning is issued.
if (verbose1) cout << xDomain << endl;
EPETRA_TEST_ERR(A2.RightScale(xDomain),ierr);
float A2oneNormFloat2 = A2.NormOne();
if (verbose1) cout << A2;
if (fabs(1.0-A2oneNormFloat2)>1.e-5) {
EPETRA_TEST_ERR(-42,ierr)
InvSumsBroke = true;
}
// Works!
EPETRA_TEST_ERR(A2.InvRowSums(xRange),ierr);
if (verbose1) cout << xRange;
EPETRA_TEST_ERR(A2.LeftScale(xRange),ierr);
float A2infNormFloat2 = A2.NormInf(); // We use a float so that rounding error
// will not prevent the sum from being 1.0.
if (verbose1) cout << A2;
if (fabs(1.0-A2infNormFloat2)>1.e-5) {
cout << "InfNorm should be = 1, but InfNorm = " << A2infNormFloat2 << endl;
EPETRA_TEST_ERR(-43,ierr);
InvSumsBroke = true;
}
// Doesn't work - may not need this test because column ownership is not unique
/* EPETRA_TEST_ERR(A2.InvColSums(xCol),ierr);
cout << xCol;
EPETRA_TEST_ERR(A2.RightScale(xCol),ierr);
float A2oneNormFloat = A2.NormOne();
cout << A2;
if (fabs(1.0-A2oneNormFloat)>1.e-5) {
EPETRA_TEST_ERR(-44,ierr);
InvSumsBroke = true;
}
*/
delete [] ColRightScaleValues;
delete [] DomainRightScaleValues;
if (verbose) cout << "Begin partial sum testing." << endl;
// Test with a matrix that has partial sums for a subset of the rows
// on multiple processors. (Except for the serial case, of course.)
int NumMyRows3 = 2; // Changing this requires further changes below
int * myGlobalElements = new int[NumMyRows3];
for (int i=0; i<NumMyRows3; i++) myGlobalElements[i] = MyPID+i;
Epetra_Map RowMap3(NumProc*2, NumMyRows3, myGlobalElements, 0, Comm);
int NumMyElements3 = 5;
Epetra_CrsMatrix A3(Copy, RowMap3, NumMyElements3);
double * Values3 = new double[NumMyElements3];
int * Indices3 = new int[NumMyElements3];
for (int i=0; i < NumMyElements3; i++) {
Values3[i] = (int) (MyPID + (i+1));
Indices3[i]=i;
}
for (int i=0; i<NumMyRows3; i++) {
A3.InsertGlobalValues(myGlobalElements[i],NumMyElements3,Values3,Indices3);
}
Epetra_Map RangeMap3(NumProc+1, 0, Comm);
Epetra_Map DomainMap3(NumMyElements3, 0, Comm);
EPETRA_TEST_ERR(A3.FillComplete(DomainMap3, RangeMap3,false),ierr);
if (verbose1) cout << A3;
Epetra_Vector xRange3(RangeMap3,false);
Epetra_Vector xDomain3(DomainMap3,false);
EPETRA_TEST_ERR(A3.InvRowSums(xRange3),ierr);
if (verbose1) cout << xRange3;
EPETRA_TEST_ERR(A3.LeftScale(xRange3),ierr);
float A3infNormFloat = A3.NormInf();
if (verbose1) cout << A3;
if (1.0!=A3infNormFloat) {
cout << "InfNorm should be = 1, but InfNorm = " << A3infNormFloat <<endl;
EPETRA_TEST_ERR(-61,ierr);
InvSumsBroke = true;
}
// we want to take the transpose of our matrix and fill in different values.
int NumMyColumns3 = NumMyRows3;
Epetra_Map ColMap3cm(RowMap3);
Epetra_Map RowMap3cm(A3.ColMap());
Epetra_CrsMatrix A3cm(Copy,RowMap3cm,ColMap3cm,NumProc+1);
double *Values3cm = new double[NumMyColumns3];
int * Indices3cm = new int[NumMyColumns3];
for (int i=0; i<NumMyColumns3; i++) {
Values3cm[i] = MyPID + i + 1;
Indices3cm[i]= i + MyPID;
}
for (int ii=0; ii<NumMyElements3; ii++) {
A3cm.InsertGlobalValues(ii, NumMyColumns3, Values3cm, Indices3cm);
}
// The DomainMap and the RangeMap from the last test will work fine for
// the RangeMap and DomainMap, respectively, but I will make copies to
// avaoid confusion when passing what looks like a DomainMap where we
// need a RangeMap and vice vera.
Epetra_Map RangeMap3cm(DomainMap3);
Epetra_Map DomainMap3cm(RangeMap3);
EPETRA_TEST_ERR(A3cm.FillComplete(DomainMap3cm,RangeMap3cm),ierr);
if (verbose1) cout << A3cm << endl;
// Again, we can copy objects from the last example.
//Epetra_Vector xRange3cm(xDomain3); //Don't use at this time
Epetra_Vector xDomain3cm(DomainMap3cm,false);
EPETRA_TEST_ERR(A3cm.InvColSums(xDomain3cm),ierr);
if (verbose1) cout << xDomain3cm << endl;
EPETRA_TEST_ERR(A3cm.RightScale(xDomain3cm),ierr);
float A3cmOneNormFloat = A3cm.NormOne();
if (verbose1) cout << A3cm << endl;
if (1.0!=A3cmOneNormFloat) {
cout << "OneNorm should be = 1, but OneNorm = " << A3cmOneNormFloat << endl;
EPETRA_TEST_ERR(-62,ierr);
InvSumsBroke = true;
}
if (verbose) cout << "End partial sum testing" << endl;
if (verbose) cout << "Begin replicated testing" << endl;
// We will now view the shared row as a repliated row, rather than one
// that has partial sums of its entries on mulitple processors.
// We will reuse much of the data used for the partial sum tesitng.
Epetra_Vector xRow3(RowMap3,false);
Epetra_CrsMatrix A4(Copy, RowMap3, NumMyElements3);
for (int ii=0; ii < NumMyElements3; ii++) {
Values3[ii] = (int)((ii*.6)+1.0);
}
for (int ii=0; ii<NumMyRows3; ii++) {
A4.InsertGlobalValues(myGlobalElements[ii],NumMyElements3,Values3,Indices3);
}
EPETRA_TEST_ERR(A4.FillComplete(DomainMap3, RangeMap3,false),ierr);
if (verbose1) cout << A4 << endl;
// The next two lines should be expanded into a verifiable test.
EPETRA_TEST_ERR(A4.InvRowMaxs(xRow3),ierr);
EPETRA_TEST_ERR(A4.InvRowMaxs(xRange3),ierr);
if (verbose1) cout << xRow3 << xRange3;
EPETRA_TEST_ERR(A4.InvRowSums(xRow3),ierr);
if (verbose1) cout << xRow3;
EPETRA_TEST_ERR(A4.LeftScale(xRow3),ierr);
float A4infNormFloat = A4.NormInf();
if (verbose1) cout << A4;
if (2.0!=A4infNormFloat && NumProc != 1) {
if (verbose1) cout << "InfNorm should be = 2 (because one column is replicated on two processors and NormOne() does not handle replication), but InfNorm = " << A4infNormFloat <<endl;
EPETRA_TEST_ERR(-63,ierr);
InvSumsBroke = true;
}
else if (1.0!=A4infNormFloat && NumProc == 1) {
if (verbose1) cout << "InfNorm should be = 1, but InfNorm = " << A4infNormFloat <<endl;
EPETRA_TEST_ERR(-63,ierr);
InvSumsBroke = true;
}
Epetra_Vector xCol3cm(ColMap3cm,false);
Epetra_CrsMatrix A4cm(Copy, RowMap3cm, ColMap3cm, NumProc+1);
//Use values from A3cm
for (int ii=0; ii<NumMyElements3; ii++) {
A4cm.InsertGlobalValues(ii,NumMyColumns3,Values3cm,Indices3cm);
}
EPETRA_TEST_ERR(A4cm.FillComplete(DomainMap3cm, RangeMap3cm,false),ierr);
if (verbose1) cout << A4cm << endl;
// The next two lines should be expanded into a verifiable test.
EPETRA_TEST_ERR(A4cm.InvColMaxs(xCol3cm),ierr);
EPETRA_TEST_ERR(A4cm.InvColMaxs(xDomain3cm),ierr);
if (verbose1) cout << xCol3cm << xDomain3cm;
EPETRA_TEST_ERR(A4cm.InvColSums(xCol3cm),ierr);
if (verbose1) cout << xCol3cm << endl;
EPETRA_TEST_ERR(A4cm.RightScale(xCol3cm),ierr);
float A4cmOneNormFloat = A4cm.NormOne();
if (verbose1) cout << A4cm << endl;
if (2.0!=A4cmOneNormFloat && NumProc != 1) {
if (verbose1) cout << "OneNorm should be = 2 (because one column is replicated on two processors and NormOne() does not handle replication), but OneNorm = " << A4cmOneNormFloat << endl;
EPETRA_TEST_ERR(-64,ierr);
InvSumsBroke = true;
}
else if (1.0!=A4cmOneNormFloat && NumProc == 1) {
if (verbose1) cout << "OneNorm should be = 1, but OneNorm = " << A4infNormFloat <<endl;
EPETRA_TEST_ERR(-64,ierr);
InvSumsBroke = true;
}
if (verbose) cout << "End replicated testing" << endl;
if (InvSumsBroke) {
if (verbose) cout << endl << "InvRowSums tests FAILED" << endl << endl;
}
else
if (verbose) cout << endl << "InvRowSums tests PASSED" << endl << endl;
A3cm.PutScalar(2.0);
int nnz_A3cm = A3cm.Graph().NumGlobalNonzeros();
double check_frobnorm = sqrt(nnz_A3cm*4.0);
double frobnorm = A3cm.NormFrobenius();
bool frobnorm_test_failed = false;
if (fabs(check_frobnorm-frobnorm) > 5.e-5) {
frobnorm_test_failed = true;
}
if (frobnorm_test_failed) {
if (verbose) std::cout << "Frobenius-norm test FAILED."<<std::endl;
EPETRA_TEST_ERR(-65, ierr);
}
delete [] Values2;
delete [] Indices2;
delete [] myGlobalElements;
delete [] Values3;
delete [] Indices3;
delete [] Values3cm;
delete [] Indices3cm;
delete [] RangeLeftScaleValues;
delete [] RowLeftScaleValues;
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
/* end main
*/
return ierr ;
}
void country_graph_coloring(int seed, SparseMatrix A, int **p, real *norm_1){
int n = A->m, i, j, jj;
SparseMatrix L, A2;
int *ia = A->ia, *ja = A->ja;
int a = -1.;
real nrow;
real *v = NULL;
real norm1[2], norm2[2], norm11[2], norm22[2], norm = n;
real pi, pj;
int improved = TRUE;
assert(A->m == A->n);
A2 = SparseMatrix_symmetrize(A, TRUE);
ia = A2->ia; ja = A2->ja;
/* Laplacian */
L = SparseMatrix_new(n, n, 1, MATRIX_TYPE_REAL, FORMAT_COORD);
for (i = 0; i < n; i++){
nrow = 0.;
for (j = ia[i]; j < ia[i+1]; j++){
jj = ja[j];
if (jj != i){
nrow ++;
L = SparseMatrix_coordinate_form_add_entries(L, 1, &i, &jj, &a);
}
}
L = SparseMatrix_coordinate_form_add_entries(L, 1, &i, &i, &nrow);
}
L = SparseMatrix_from_coordinate_format(L);
/* largest eigen vector */
{
int maxit = 100;
real tol = 0.00001;
power_method(L, seed, maxit, tol, &v);
}
vector_ordering(n, v, p, TRUE);
/* swapping */
while (improved){
improved = FALSE; norm = n;
for (i = 0; i < n; i++){
get_local_12_norm(n, i, ia, ja, *p, norm1);
for (j = 0; j < n; j++){
if (j == i) continue;
get_local_12_norm(n, j, ia, ja, *p, norm2);
norm = MIN(norm, norm2[0]);
pi = (*p)[i]; pj = (*p)[j];
(*p)[i] = pj;
(*p)[j] = pi;
get_local_12_norm(n, i, ia, ja, *p, norm11);
get_local_12_norm(n, j, ia, ja, *p, norm22);
if (MIN(norm11[0],norm22[0]) > MIN(norm1[0],norm2[0])){
// ||
//(MIN(norm11[0],norm22[0]) == MIN(norm1[0],norm2[0]) && norm11[1]+norm22[1] > norm1[1]+norm2[1])) {
improved = TRUE;
norm1[0] = norm11[0];
norm1[1] = norm11[1];
continue;
}
(*p)[i] = pi;
(*p)[j] = pj;
}
}
if (Verbose) {
get_12_norm(n, ia, ja, *p, norm1);
fprintf(stderr, "norm = %f", norm);
fprintf(stderr, "norm1 = %f, norm2 = %f\n", norm1[0], norm1[1]);
}
}
get_12_norm(n, ia, ja, *p, norm1);
*norm_1 = norm1[0];
if (A2 != A) SparseMatrix_delete(A2);
SparseMatrix_delete(L);
}
void test01 ( void )
/******************************************************************************/
/*
Purpose:
TEST01 uses POWER_METHOD on the Fibonacci2 matrix.
Discussion:
This matrix, despite having a single dominant eigenvalue, will generally
converge only very slowly under the power method. This has to do with
the fact that the matrix has only 3 eigenvectors.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
20 July 2008
Author:
John Burkardt
*/
{
double *a;
double cos_x1x2;
double ctime;
double ctime1;
double ctime2;
int i;
int it_max;
int it_num;
double lambda;
int n = 50;
double norm;
double phi;
int seed;
double sin_x1x2;
double tol;
double *x;
double *x2;
a = fibonacci2 ( n );
seed = 123456789;
x = r8vec_uniform_01 ( n, &seed );
it_max = 300;
tol = 0.000001;
phi = ( 1.0 + sqrt ( 5.0 ) ) / 2.0;
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " Use the power method on the Fibonacci2 matrix.\n" );
printf ( "\n" );
printf ( " Matrix order N = %d\n", n );
printf ( " Maximum iterations = %d\n", it_max );
printf ( " Error tolerance = %e\n", tol );
ctime1 = cpu_time ( );
power_method ( n, a, x, it_max, tol, &lambda, &it_num );
ctime2 = cpu_time ( );
ctime = ctime2 - ctime1;
printf ( "\n" );
printf ( " Number of iterations = %d\n", it_num );
printf ( " CPU time = %f\n", ctime );
printf ( " Estimated eigenvalue = %24.16f\n", lambda );
printf ( " Correct value = %24.16f\n", phi );
printf ( " Error = %e\n", r8_abs ( lambda - phi ) );
/*
X2 is the exact eigenvector.
*/
x2 = ( double * ) malloc ( n * sizeof ( double ) );
x2[0] = 1.0;
for ( i = 1; i < n; i++ )
{
x2[i] = phi * x2[i-1];
}
norm = r8vec_norm_l2 ( n, x2 );
for ( i = 0; i < n; i++ )
{
x2[i] = x2[i] / norm;
}
/*
The sine of the angle between X and X2 is a measure of error.
*/
cos_x1x2 = r8vec_dot ( n, x, x2 );
sin_x1x2 = sqrt ( ( 1.0 - cos_x1x2 ) * ( 1.0 + cos_x1x2 ) );
printf ( "\n" );
printf ( " Sine of angle between true and estimated vectors = %e\n", sin_x1x2 );
free ( a );
free ( x );
free ( x2 );
return;
}
