cxx_main_qr_solver.cpp

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#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_SerialDenseHelpers.hpp"
#include "Teuchos_SerialQRDenseSolver.hpp"
#include "Teuchos_ScalarTraits.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_Version.hpp"
 
using Teuchos::ScalarTraits;
using Teuchos::LAPACK;
using Teuchos::SerialDenseMatrix;
using Teuchos::SerialDenseVector;
 
#define OTYPE int
#ifdef HAVE_TEUCHOS_COMPLEX
#define STYPE std::complex<double>
#else
#define STYPE double
#endif
 
// SCALARMAX defines the maximum positive value (with a little leeway) generated for matrix and vector elements and scalars:
// random numbers in [-SCALARMAX, SCALARMAX] will be generated.
#ifdef HAVE_TEUCHOS_COMPLEX
#define SCALARMAX  STYPE(10,0)
#else
#define SCALARMAX  STYPE(10)
#endif
 
template<typename TYPE>
int PrintTestResults(std::string, TYPE, TYPE, bool);
 
int ReturnCodeCheck(std::string, int, int, bool);
 
typedef SerialDenseVector<OTYPE, STYPE> DVector;
typedef SerialDenseMatrix<OTYPE, STYPE> DMatrix;
 
// Returns ScalarTraits<TYPE>::random() (the input parameters are ignored)
template<typename TYPE>
TYPE GetRandom(TYPE, TYPE);
 
// Returns a random integer between the two input parameters, inclusive
template<>
int GetRandom(int, int);
 
// Returns a random double between the two input parameters, plus or minus a random number between 0 and 1
template<>
double GetRandom(double, double);
 
template<typename T>
std::complex<T> GetRandom( std::complex<T>, std::complex<T> );
 
// Generates random matrices and vectors using GetRandom()
Teuchos::RCP<DMatrix> GetRandomMatrix(int m, int n);
Teuchos::RCP<DVector> GetRandomVector(int n);
 
// Compares the difference between two vectors using relative euclidean norms
// Returns 1 if the comparison failed, the relative difference is greater than the tolerance.
int CompareVectors(const SerialDenseVector<OTYPE,STYPE>& Vector1,
                   const SerialDenseVector<OTYPE,STYPE>& Vector2,
                   ScalarTraits<STYPE>::magnitudeType Tolerance );
 
int main(int argc, char* argv[])
{
  typedef ScalarTraits<STYPE>::magnitudeType MagnitudeType;
 
  Teuchos::LAPACK<OTYPE,STYPE> L;
 
  int n=8, m=12;
  MagnitudeType tol = 1e-12*ScalarTraits<MagnitudeType>::one();
 
  bool verbose = 0;
  if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
 
  if (verbose)
    std::cout << Teuchos::Teuchos_Version() << std::endl << std::endl;
 
  int numberFailedTests = 0;
  int returnCode = 0;
  std::string testName = "", testType = "";
 
#ifdef HAVE_TEUCHOS_COMPLEX
  testType = "COMPLEX";
#else
  testType = "REAL";
#endif
 
  if (verbose) std::cout<<std::endl<<"********** CHECKING TEUCHOS SERIAL QR SOLVER - " << testType << "-VALUED **********"<<std::endl<<std::endl;
 
  // Create dense matrix and vector.
  Teuchos::RCP<DMatrix> A1 = GetRandomMatrix(m,n);
  Teuchos::RCP<DVector> x1 = GetRandomVector(n);
  Teuchos::RCP<DVector> x1t = GetRandomVector(m);
  DVector xhat(n), b(m), xhatt(m);
 
  // Compute the right-hand side vector using multiplication.
  returnCode = b.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A1, *x1, ScalarTraits<STYPE>::zero());
  testName = "Generating right-hand side vector using A*x, where x is a random vector:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
#ifdef HAVE_TEUCHOS_COMPLEX
  DVector bct(n);
  returnCode = bct.multiply(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A1, *x1t, ScalarTraits<STYPE>::zero());
  testName = "Generating right-hand side vector using A^H*x, where x is a random vector:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
#else
  DVector bt(n);
  returnCode = bt.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A1, *x1t, ScalarTraits<STYPE>::zero());
  testName = "Generating right-hand side vector using A^T*x, where x is a random vector:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
#endif
  DVector bp, bp2;
  Teuchos::RCP<DMatrix> Q;
  DVector tmp(n), tmp2(m);
 
  // Fill the solution vector with zeros.
  xhat.putScalar( ScalarTraits<STYPE>::zero() );
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
 
  // Create a serial dense solver.
  Teuchos::SerialQRDenseSolver<OTYPE, STYPE> solver1;
 
  // Pass in matrix and vectors
  solver1.setMatrix( A1 );
  solver1.setVectors( Teuchos::rcp( &xhat, false ), Teuchos::rcp( &b, false ) );
 
  // Test1:  Simple factor and solve
  returnCode = solver1.factor();
  testName = "Simple solve: factor() random A:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  returnCode = solver1.formQ();
  testName = "Simple solve: formQ() random A:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
  // Non-transpose solve
  returnCode = solver1.solve();
  testName = "Simple solve: solve() random A (NO_TRANS):";
  numberFailedTests += CompareVectors( *x1, xhat, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  testName = "Simple solve: multiplyQ(TRANS) solveR (NO_TRANS) random A (NO_TRANS):";
  bp = b;
  returnCode = solver1.multiplyQ( Teuchos::TRANS, bp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  for (OTYPE i=0; i<n; i++) {tmp(i) = bp(i);}
  returnCode = solver1.solveR( Teuchos::NO_TRANS, tmp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  numberFailedTests += CompareVectors( tmp, xhat, tol );
 
#ifdef HAVE_TEUCHOS_COMPLEX
  testName = "Simple solve: formQ() solve with explicit Q implicit R random A (NO_TRANS):";
  Q = solver1.getQ();
  bp.multiply(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS, 1.0, *Q, b, 0.0);
  for (OTYPE i=0; i<n; i++) {tmp(i) = bp(i);}
  returnCode = solver1.solveR( Teuchos::NO_TRANS, tmp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  numberFailedTests += CompareVectors( tmp, xhat, tol );
  testName = "Simple solve: formQ() solve with explicit Q explicit R random A (NO_TRANS):";
  Q = solver1.getQ();
  returnCode = solver1.formR();
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  bp.multiply(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS, 1.0, *Q, b, 0.0);
  for (OTYPE i=0; i<n; i++) {tmp(i) = bp(i);}
  returnCode = solver1.solveR( Teuchos::NO_TRANS, tmp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  numberFailedTests += CompareVectors( tmp, xhat, tol );
#else
  testName = "Simple solve: formQ() solve with explicit Q random A (NO_TRANS):";
  Q = solver1.getQ();
  bp.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, *Q, b, 0.0);
  for (OTYPE i=0; i<n; i++) {tmp(i) = bp(i);}
  returnCode = solver1.solveR( Teuchos::NO_TRANS, tmp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  numberFailedTests += CompareVectors( tmp, xhat, tol );
  testName = "Simple solve: formQ() solve with explicit Q explicit R random A (NO_TRANS):";
  Q = solver1.getQ();
  returnCode = solver1.formR();
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  bp.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, *Q, b, 0.0);
  for (OTYPE i=0; i<n; i++) {tmp(i) = bp(i);}
  returnCode = solver1.solveR( Teuchos::NO_TRANS, tmp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  numberFailedTests += CompareVectors( tmp, xhat, tol );
#endif
 
#ifdef HAVE_TEUCHOS_COMPLEX
  // Conjugate tranpose solve (can be done after factorization, since factorization doesn't depend on this)
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
  solver1.setVectors( Teuchos::rcp( &xhatt, false ), Teuchos::rcp( &bct, false ) );
  solver1.solveWithTransposeFlag( Teuchos::CONJ_TRANS );
  returnCode = solver1.solve();
  testName = "Simple solve: solve() random A (CONJ_TRANS):";
  if (m == n)
    numberFailedTests += CompareVectors( *x1t, xhatt, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  testName = "Simple solve: solveR (NO_TRANS) multiplyQ(TRANS) random A (CONJ_TRANS):";
  bp = bct;
  returnCode = solver1.solveR( Teuchos::TRANS, bp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  for (OTYPE i=0; i<n; i++) {tmp2(i) = bp(i);}
  returnCode = solver1.multiplyQ( Teuchos::NO_TRANS, tmp2 );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  if (m == n)
    numberFailedTests += CompareVectors(*x1t, tmp2, tol );
  numberFailedTests += CompareVectors( tmp2, xhatt, tol );
  testName = "Simple solve: formQ() solve with explicit Q random A (CONJ_TRANS):";
  bp = bct;
  Q = solver1.getQ();
  returnCode = solver1.solveR( Teuchos::TRANS, bp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  tmp2.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, *Q, bp, 0.0);
  if (m == n)
    numberFailedTests += CompareVectors(*x1t, tmp2, tol );
  numberFailedTests += CompareVectors( tmp2, xhatt, tol );
 
#else
  // Tranpose solve (can be done after factorization, since factorization doesn't depend on this)
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
  solver1.setVectors( Teuchos::rcp( &xhatt, false ), Teuchos::rcp( &bt, false ) );
  solver1.solveWithTransposeFlag( Teuchos::TRANS );
  returnCode = solver1.solve();
  testName = "Simple solve: solve() random A (TRANS):";
  if (m == n)
    numberFailedTests += CompareVectors( *x1t, xhatt, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  bp = bt;
  testName = "Simple solve: solveR multiplyQ(TRANS) (NO_TRANS) random A (TRANS):";
  returnCode = solver1.solveR( Teuchos::TRANS, bp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  for (OTYPE i=0; i<n; i++) {tmp2(i) = bp(i);}
  returnCode = solver1.multiplyQ( Teuchos::NO_TRANS, tmp2 );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  if (m == n)
    numberFailedTests += CompareVectors(*x1t, tmp2, tol );
  numberFailedTests += CompareVectors( tmp2, xhatt, tol );
  testName = "Simple solve: formQ() solve with explicit Q random A (CONJ_TRANS):";
  bp = bt;
  Q = solver1.getQ();
  returnCode = solver1.solveR( Teuchos::TRANS, bp );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
  tmp2.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, *Q, bp, 0.0);
  if (m == n)
    numberFailedTests += CompareVectors(*x1t, tmp2, tol );
  numberFailedTests += CompareVectors( tmp2, xhatt, tol );
 
#endif
 
  // Test2:  Solve with matrix equilibration.
 
  // Create random linear system
  Teuchos::RCP<DMatrix> A2 = GetRandomMatrix(m,n);
  Teuchos::RCP<DVector> x2 = GetRandomVector(n);
  Teuchos::RCP<DVector> x2t = GetRandomVector(m);
 
  // Create LHS through multiplication with A2
  xhat.putScalar( ScalarTraits<STYPE>::zero() );
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
  b.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A2, *x2, ScalarTraits<STYPE>::zero());
#ifdef HAVE_TEUCHOS_COMPLEX
  bct.multiply(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A2, *x2t, ScalarTraits<STYPE>::zero());
#else
  bt.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, ScalarTraits<STYPE>::one() , *A2, *x2t, ScalarTraits<STYPE>::zero());
#endif
 
  // Create a serial dense solver.
  Teuchos::SerialQRDenseSolver<OTYPE, STYPE> solver2;
  solver2.factorWithEquilibration( true );
 
  // Pass in matrix and vectors
  MagnitudeType safeMin = ScalarTraits<STYPE>::sfmin();
  MagnitudeType prec = ScalarTraits<STYPE>::prec();
  STYPE sOne  = ScalarTraits<STYPE>::one();
  MagnitudeType smlnum = ScalarTraits<STYPE>::magnitude(safeMin/prec);
  MagnitudeType bignum = ScalarTraits<STYPE>::magnitude(sOne/smlnum);
  (void) bignum; // Silence "unused variable" compiler warning.
  MagnitudeType smlnum2 = smlnum/2;
  (void) smlnum2; // Silence "unused variable" compiler warning.
  MagnitudeType anorm = ScalarTraits<STYPE>::magnitude(ScalarTraits<STYPE>::zero());
  for (OTYPE j = 0; j < A2->numCols(); j++) {
    for (OTYPE i = 0; i < A2->numRows(); i++) {
      anorm = TEUCHOS_MAX( anorm, ScalarTraits<STYPE>::magnitude((*A2)(i,j)) );
    }
  }
  OTYPE BW = 0;
  (void) BW; // Silence "unused variable" compiler warning.
  OTYPE info = 0;
  (void) info; // Silence "unused variable" compiler warning.
  // TODO: fix scaling test
  //  L.LASCL(Teuchos::ETypeChar[Teuchos::FULL], BW, BW, anorm, smlnum2, A2->numRows(), A2->numCols(), A2->values(), A2->stride(), &info);
  solver2.setMatrix( A2 );
  solver2.setVectors( Teuchos::rcp( &xhat, false ), Teuchos::rcp( &b, false ) );
 
  Teuchos::RCP<DMatrix> A2bak = Teuchos::rcp( new DMatrix( Teuchos::Copy, *A2 ) );
  Teuchos::RCP<DVector> b2bak = Teuchos::rcp( new DVector( Teuchos::Copy, b ) );
 
  // Factor and solve with matrix equilibration.
  returnCode = solver2.factor();
  testName = "Solve with matrix equilibration: factor() random A:";
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
  // Non-transpose solve
  returnCode = solver2.solve();
  testName = "Solve with matrix equilibration: solve() random A (NO_TRANS):";
  numberFailedTests += CompareVectors( *x2, xhat, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
#ifdef HAVE_TEUCHOS_COMPLEX
  // Conjugate tranpose solve (can be done after factorization, since factorization doesn't depend on this)
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
  solver2.setVectors( Teuchos::rcp( &xhatt, false ), Teuchos::rcp( &bct, false ) );
  solver2.solveWithTransposeFlag( Teuchos::CONJ_TRANS );
  returnCode = solver2.solve();
  testName = "Solve with matrix equilibration: solve() random A (CONJ_TRANS):";
  if (m == n)
    numberFailedTests += CompareVectors( *x2t, xhatt, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
#else
  // Tranpose solve (can be done after factorization, since factorization doesn't depend on this)
  xhatt.putScalar( ScalarTraits<STYPE>::zero() );
  solver2.setVectors( Teuchos::rcp( &xhatt, false ), Teuchos::rcp( &bt, false ) );
  solver2.solveWithTransposeFlag( Teuchos::TRANS );
  returnCode = solver2.solve();
  testName = "Solve with matrix equilibration: solve() random A (TRANS):";
  if (m == n)
    numberFailedTests += CompareVectors( *x2t, xhatt, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
#endif
 
  // Non-transpose solve without call to factor.
  xhat.putScalar( ScalarTraits<STYPE>::zero() );
  solver2.setMatrix( A2bak );
  solver2.setVectors( Teuchos::rcp( &xhat, false ), b2bak );
  solver2.solveWithTransposeFlag( Teuchos::NO_TRANS );
  returnCode = solver2.solve();
  testName = "Solve with matrix equilibration: solve() without factor() random A (NO_TRANS):";
  numberFailedTests += CompareVectors( *x2, xhat, tol );
  numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
 
  //
  // If a test failed output the number of failed tests.
  //
  if(numberFailedTests > 0)
  {
            if (verbose) {
                std::cout << "Number of failed tests: " << numberFailedTests << std::endl;
                std::cout << "End Result: TEST FAILED" << std::endl;
                return -1;
            }
        }
  if(numberFailedTests == 0)
    std::cout << "End Result: TEST PASSED" << std::endl;
 
  return 0;
}
 
template<typename TYPE>
int PrintTestResults(std::string testName, TYPE calculatedResult, TYPE expectedResult, bool verbose)
{
  int result;
  if(calculatedResult == expectedResult)
    {
      if(verbose) std::cout << testName << " successful." << std::endl;
      result = 0;
    }
  else
    {
      if(verbose) std::cout << testName << " unsuccessful." << std::endl;
      result = 1;
    }
  return result;
}
 
int ReturnCodeCheck(std::string testName, int returnCode, int expectedResult, bool verbose)
{
  int result;
  if(expectedResult == 0)
    {
      if(returnCode == 0)
        {
          if(verbose) std::cout << testName << " test successful." << std::endl;
          result = 0;
        }
      else
        {
          if(verbose) std::cout << testName << " test unsuccessful. Return code was " << returnCode << "." << std::endl;
          result = 1;
        }
    }
  else
    {
      if(returnCode != 0)
        {
          if(verbose) std::cout << testName << " test successful -- failed as expected." << std::endl;
          result = 0;
        }
      else
        {
          if(verbose) std::cout << testName << " test unsuccessful -- did not fail as expected. Return code was " << returnCode << "." << std::endl;
          result = 1;
        }
    }
  return result;
}
 
template<typename TYPE>
TYPE GetRandom(TYPE Low, TYPE High)
{
  return ((TYPE)((double)((1.0 * ScalarTraits<int>::random()) / RAND_MAX) * (High - Low + 1)) + Low);
}
 
template<typename T>
std::complex<T> GetRandom( std::complex<T> Low, std::complex<T> High)
{
  T lowMag = Low.real();
  T highMag = High.real();
  T real = (T)(((1.0 * ScalarTraits<int>::random()) / RAND_MAX) * (highMag - lowMag + ScalarTraits<T>::one())) + lowMag;
  T imag = (T)(((1.0 * ScalarTraits<int>::random()) / RAND_MAX) * (highMag - lowMag + ScalarTraits<T>::one())) + lowMag;
  return std::complex<T>( real, imag );
}
 
template<>
int GetRandom(int Low, int High)
{
  return ((int)((double)((1.0 * ScalarTraits<int>::random()) / RAND_MAX) * (High - Low + 1)) + Low);
}
 
template<>
double GetRandom(double Low, double High)
{
  return (((double)((1.0 * ScalarTraits<int>::random()) / RAND_MAX) * (High - Low + 1)) + Low + ScalarTraits<double>::random());
}
 
Teuchos::RCP<DMatrix> GetRandomMatrix(int m, int n)
{
  Teuchos::RCP<DMatrix> newmat = Teuchos::rcp( new DMatrix(m,n) );
 
  // Fill dense matrix with random entries.
  for (int i=0; i<m; i++)
    for (int j=0; j<n; j++) {
      (*newmat)(i,j) = GetRandom(-SCALARMAX, SCALARMAX);
    }
  return newmat;
}
 
Teuchos::RCP<DVector> GetRandomVector(int n)
{
  Teuchos::RCP<DVector> newvec = Teuchos::rcp( new DVector( n ) );
 
  // Fill dense vector with random entries.
  for (int i=0; i<n; i++) {
    (*newvec)(i) = GetRandom(-SCALARMAX, SCALARMAX);
  }
 
  return newvec;
}
 
/*  Function:  CompareVectors
    Purpose:   Compares the difference between two vectors using relative euclidean-norms, i.e. ||v_1-v_2||_2/||v_2||_2
*/
int CompareVectors(const SerialDenseVector<OTYPE,STYPE>& Vector1,
                   const SerialDenseVector<OTYPE,STYPE>& Vector2,
                   ScalarTraits<STYPE>::magnitudeType Tolerance )
{
  typedef ScalarTraits<STYPE>::magnitudeType MagnitudeType;
 
  SerialDenseVector<OTYPE,STYPE> diff( Vector1 );
  diff -= Vector2;
 
  MagnitudeType norm_diff = diff.normFrobenius();
  MagnitudeType norm_v2 = Vector2.normFrobenius();
  MagnitudeType temp = norm_diff;
  if (norm_v2 != ScalarTraits<MagnitudeType>::zero())
    temp /= norm_v2;
 
  if (temp > Tolerance)
    return 1;
  else
    return 0;
}