C++ BLAS::GEMM方法代码示例

double
do_time_teuchos_double_gemm(unsigned int m, unsigned int n, unsigned int k,
			    unsigned int nloop)
{
  Sacado::Random<double> urand(0.0, 1.0);
  Teuchos::BLAS<int,double> blas;

  std::vector<double> A(m*k), B(k*n), C(m*n);
  for (unsigned int j=0; j<k; j++)
    for (unsigned int i=0; i<m; i++)
      A[i+j*m] = urand.number();
  for (unsigned int j=0; j<n; j++)
    for (unsigned int i=0; i<k; i++)
    B[i+j*k] = urand.number();
  for (unsigned int j=0; j<n; j++)
    for (unsigned int i=0; i<m; i++)
      C[i+j*m] = urand.number();
  double alpha = urand.number();
  double beta = urand.number();
  
  Teuchos::Time timer("Teuchos Double GEMM", false);
  timer.start(true);
  for (unsigned int j=0; j<nloop; j++) {
    blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, m, n, k, alpha, &A[0], m, 
	      &B[0], k, beta, &C[0], m);
  }
  timer.stop();

  return timer.totalElapsedTime() / nloop;
}

    static void
    GEMM (const Teuchos::ETransp transA,
          const Teuchos::ETransp transB,
          const Scalar& alpha,
          const View<const Scalar**, LayoutLeft, DeviceType>& A,
          const View<const Scalar**, LayoutLeft, DeviceType>& B,
          const Scalar& beta,
          const View<Scalar**, LayoutLeft, DeviceType>& C)
    {
      const int n = static_cast<int> (C.dimension_1 ());
      const int lda = static_cast<int> (Impl::getStride2DView (A));
      Teuchos::BLAS<int,Scalar> blas;

      // For some BLAS implementations (e.g., MKL), GEMM when B has
      // one column may be signficantly less efficient than GEMV.
      if (n == 1 && transB == Teuchos::NO_TRANS) {
        blas.GEMV (transA, A.dimension_0 (), A.dimension_1 (),
                   alpha, A.ptr_on_device (), lda,
                   B.ptr_on_device (), static_cast<int> (1),
                   beta, C.ptr_on_device (), static_cast<int> (1));
      }
      else {
        const int m = static_cast<int> (C.dimension_0 ());
        const int k = static_cast<int> (transA == Teuchos::NO_TRANS ?
                                        A.dimension_1 () : A.dimension_0 ());
        const int ldb = static_cast<int> (Impl::getStride2DView (B));
        const int ldc = static_cast<int> (Impl::getStride2DView (C));

        blas.GEMM (transA, transB, m, n, k, alpha,
                   A.ptr_on_device(), lda,
                   B.ptr_on_device(), ldb,
                   beta, C.ptr_on_device(), ldc);
      }
    }

  KOKKOS_INLINE_FUNCTION
  int
  Gemm<Trans::ConjTranspose,Trans::NoTranspose,
       AlgoGemm::ExternalBlas,Variant::One>
  ::invoke(PolicyType &policy,
           MemberType &member,
           const ScalarType alpha,
           DenseExecViewTypeA &A,
           DenseExecViewTypeB &B,
           const ScalarType beta,
           DenseExecViewTypeC &C) {
    // static_assert( Kokkos::Impl::is_same<
    //                typename DenseMatrixTypeA::space_type,
    //                typename DenseMatrixTypeB::space_type
    //                >::value && 
    //                Kokkos::Impl::is_same<
    //                typename DenseMatrixTypeB::space_type,
    //                typename DenseMatrixTypeC::space_type
    //                >::value,
    //                "Space type of input matrices does not match" );
    
    if (member.team_rank() == 0) {
#if                                                     \
  defined( HAVE_SHYLUTACHO_TEUCHOS ) &&                 \
  defined( KOKKOS_ACTIVE_EXECUTION_MEMORY_SPACE_HOST )
      typedef typename DenseExecViewTypeA::ordinal_type ordinal_type;
      typedef typename DenseExecViewTypeA::value_type   value_type;

      Teuchos::BLAS<ordinal_type,value_type> blas;
      
      const ordinal_type m = C.NumRows();
      const ordinal_type n = C.NumCols();
      const ordinal_type k = B.NumRows();

      if (m > 0 && n > 0 && k > 0)
        blas.GEMM(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS,
                  m, n, k,
                  alpha,
                  A.ValuePtr(), A.BaseObject().ColStride(),
                  B.ValuePtr(), B.BaseObject().ColStride(),
                  beta,
                  C.ValuePtr(), C.BaseObject().ColStride());
#else
    TACHO_TEST_FOR_ABORT( true, MSG_NOT_HAVE_PACKAGE("Teuchos") );        
#endif
    } 

    return 0;
  }

double
do_time_teuchos_fad_gemm(unsigned int m, unsigned int n, unsigned int k,
			 unsigned int ndot, unsigned int nloop)
{
  Sacado::Random<double> urand(0.0, 1.0);
  Teuchos::BLAS<int,FadType> blas;

  std::vector<FadType> A(m*k), B(k*n), C(m*n);
  for (unsigned int j=0; j<k; j++) {
    for (unsigned int i=0; i<m; i++) {
      A[i+j*m] = FadType(ndot, urand.number());
      for (unsigned int l=0; l<ndot; l++)
      	A[i+j*m].fastAccessDx(l) = urand.number();
    }
  }
  for (unsigned int j=0; j<n; j++) {
    for (unsigned int i=0; i<k; i++) {
      B[i+j*k] = FadType(ndot, urand.number());
      for (unsigned int l=0; l<ndot; l++)
	B[i+j*k].fastAccessDx(l) = urand.number();
    }
  }
  for (unsigned int j=0; j<n; j++) {
    for (unsigned int i=0; i<m; i++) {
      C[i+j*m] = FadType(ndot, urand.number());
      for (unsigned int l=0; l<ndot; l++)
	C[i+j*m].fastAccessDx(l) = urand.number();
    }
  }
  FadType alpha(ndot, urand.number());
  FadType beta(ndot, urand.number());
  for (unsigned int l=0; l<ndot; l++) {
    alpha.fastAccessDx(l) = urand.number();
    beta.fastAccessDx(l) = urand.number();
  }
  
  Teuchos::Time timer("Teuchos Fad GEMM", false);
  timer.start(true);
  for (unsigned int j=0; j<nloop; j++) {
    blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, m, n, k, alpha, &A[0], m, 
	      &B[0], k, beta, &C[0], m);
  }
  timer.stop();

  return timer.totalElapsedTime() / nloop;
}

    static void
    GEMM (const Teuchos::ETransp transA,
          const Teuchos::ETransp transB,
          const double& alpha,
          const View<const double**, LayoutLeft, DeviceType>& A,
          const View<const double**, LayoutLeft, DeviceType>& B,
          const double& beta,
          const View<double**, LayoutLeft, DeviceType>& C)
    {
      const int n = static_cast<int> (C.dimension_1 ());

      // For some BLAS implementations (e.g., MKL), GEMM when B has
      // one column may be signficantly less efficient than GEMV.
      if (n == 1 && transB == Teuchos::NO_TRANS) {
        char trans = 'N';
        if (transA == Teuchos::TRANS) {
          trans = 'T';
        }
        else if (transA == Teuchos::CONJ_TRANS) {
          trans = 'C';
        }
        auto B_0 = Kokkos::subview (B, Kokkos::ALL (), 0);
        auto C_0 = Kokkos::subview (C, Kokkos::ALL (), 0);
        KokkosBlas::gemv (&trans, alpha, A, B_0, beta, C_0);
      }
      else {
        const int m = static_cast<int> (C.dimension_0 ());
        const int k = static_cast<int> (transA == Teuchos::NO_TRANS ? A.dimension_1 () : A.dimension_0 ());
        const int lda = static_cast<int> (Impl::getStride2DView (A));
        const int ldb = static_cast<int> (Impl::getStride2DView (B));
        const int ldc = static_cast<int> (Impl::getStride2DView (C));

        Teuchos::BLAS<int,double> blas;
        blas.GEMM (transA, transB, m, n, k, alpha,
                   A.ptr_on_device(), lda,
                   B.ptr_on_device(), ldb,
                   beta, C.ptr_on_device(), ldc);
      }
    }

//.........这里部分代码省略.........
  refQuadNodes(0,0,1) = 0.0;
  refQuadNodes(0,1,0) = hx;
  refQuadNodes(0,1,1) = 0.0;
  refQuadNodes(0,2,0) = hx;
  refQuadNodes(0,2,1) = hy;
  refQuadNodes(0,3,0) = 0.0;
  refQuadNodes(0,3,1) = hy;

  // Compute cell Jacobians, their inverses and their determinants
  CellTools::setJacobian(refQuadJacobian, cubPoints, refQuadNodes, quad_4);
  CellTools::setJacobianInv(refQuadJacobInv, refQuadJacobian );
  CellTools::setJacobianDet(refQuadJacobDet, refQuadJacobian );
  
  // transform from [-1,1]^2 to [0,hx]x[0,hy]
  fst::HGRADtransformGRAD<double>(quadGradsTransformed, refQuadJacobInv, quadGrads);
      
  // compute weighted measure
  fst::computeCellMeasure<double>(weightedMeasure, refQuadJacobDet, cubWeights);

  // multiply values with weighted measure
  fst::multiplyMeasure<double>(quadGradsTransformedWeighted,
			       weightedMeasure, quadGradsTransformed);

  // integrate to compute element stiffness matrix
  fst::integrate<double>(localStiffMatrix,
			 quadGradsTransformed, quadGradsTransformedWeighted, COMP_BLAS);

  std::cout << "Finished with reference element matrix\n";

  
  // now we will scatter global degrees of freedom, apply the local stiffness matrix 
  // with BLAS, and then gather the results
  FieldContainer<double> uScattered(numElems,numFieldsG);
  FieldContainer<double> KuScattered(numElems,numFieldsG);

  // to extract info from u

  u.GlobalAssemble();

  Epetra_Time multTimer(Comm);

  Ku.PutScalar(0.0);
  Ku.GlobalAssemble();

  double *uVals = u[0];
  double *KuVals = Ku[0];

  Teuchos::BLAS<int,double> blas;
  Epetra_Time scatterTime(Comm);
  std::cout << "Scattering\n";
  // Scatter
  for (int k=0; k<numElems; k++) 
    {
      for (int i=0;i<numFieldsG;i++) 
	{
	  uScattered(k,i) = uVals[ltgMapping(k,i)];
	}
    }
  const double scatTime = scatterTime.ElapsedTime();
  std::cout << "Scattered in time " << scatTime << "\n";

  Epetra_Time blasTimer(Comm);
  blas.GEMM(Teuchos::NO_TRANS , Teuchos::NO_TRANS , 
	    numFieldsG , numElems, numFieldsG  , 
	    1.0 , 
	    &localStiffMatrix(0,0,0) , 
	    numFieldsG ,
	    &uScattered(0,0) , 
	    numFieldsG , 
	    0.0 , 
	     &KuScattered(0,0) , 
	    numFieldsG );
  const double blasTime = blasTimer.ElapsedTime();
  std::cout << "Element matrices applied in " << blasTime << "\n";

  Epetra_Time gatherTimer(Comm);
  // Gather
  for (int k=0;k<numElems;k++)
    {
      for (int i=0;i<numFieldsG;i++)
	{
	  KuVals[ltgMapping(k,i)] += KuScattered(k,i);
	}
    }

  const double gatherTime = gatherTimer.ElapsedTime();
  std::cout << "Gathered in " << gatherTime << "\n";
  

  const double applyTime = gatherTime + blasTime + scatTime;
  std::cout << "Time to do matrix-free product: " << applyTime << std::endl;
  
  
  std::cout << "End Result: TEST PASSED\n";
  
  // reset format state of std::cout
  std::cout.copyfmt(oldFormatState);
 Kokkos::finalize(); 
  return 0;
}

  void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
    const size_t NSDim = Bc.getNumVectors();

    Ppattern_ = Ppattern;

    size_t numRows = Ppattern_->getNodeNumRows();
    XXtInv_.resize(numRows);

    RCP<const Import> importer = Ppattern_->getImporter();

    X_ = MultiVectorFactory::Build(Ppattern_->getColMap(), NSDim);
    if (!importer.is_null())
      X_->doImport(Bc, *importer, Xpetra::INSERT);
    else
      *X_ = Bc;

    std::vector<const SC*> Xval(NSDim);
    for (size_t j = 0; j < NSDim; j++)
      Xval[j] = X_->getData(j).get();

    SC zero = Teuchos::ScalarTraits<SC>::zero();
    SC one  = Teuchos::ScalarTraits<SC>::one();

    Teuchos::BLAS  <LO,SC> blas;
    Teuchos::LAPACK<LO,SC> lapack;
    LO lwork = 3*NSDim;
    ArrayRCP<LO> IPIV(NSDim);
    ArrayRCP<SC> WORK(lwork);

    for (size_t i = 0; i < numRows; i++) {
      Teuchos::ArrayView<const LO> indices;
      Ppattern_->getLocalRowView(i, indices);

      size_t nnz = indices.size();

      XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false/*zeroOut*/);
      Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];

      if (NSDim == 1) {
        SC d = zero;
        for (size_t j = 0; j < nnz; j++)
          d += Xval[0][indices[j]] * Xval[0][indices[j]];
        XXtInv(0,0) = one/d;

      } else {
        Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false/*zeroOut*/);
        for (size_t j = 0; j < nnz; j++)
          for (size_t k = 0; k < NSDim; k++)
            locX(k,j) = Xval[k][indices[j]];

        // XXtInv_ = (locX*locX^T)^{-1}
        blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
                   one,   locX.values(),   locX.stride(),
                          locX.values(),   locX.stride(),
                  zero, XXtInv.values(), XXtInv.stride());

        LO info;
        // Compute LU factorization using partial pivoting with row exchanges
        lapack.GETRF(NSDim, NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), &info);
        // Use the computed factorization to compute the inverse
        lapack.GETRI(NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), WORK.get(), lwork, &info);
      }
    }
  }

  KOKKOS_INLINE_FUNCTION
  int exampleDenseTrsmMKL(const OrdinalType mmin,
                          const OrdinalType mmax,
                          const OrdinalType minc,
                          const OrdinalType k,
                          const bool verbose) {
    typedef ValueType   value_type;
    typedef OrdinalType ordinal_type;
    typedef SizeType    size_type;

    typedef DenseMatrixBase<value_type,ordinal_type,size_type,SpaceType,MemoryTraits> DenseMatrixBaseType;

    int r_val = 0;

    Kokkos::Impl::Timer timer;
    double t = 0.0;

    cout << "DenseGemmMKL:: test matrices "
         <<":: mmin = " << mmin << " , mmax = " << mmax << " , minc = " << minc << " , k = "<< k << endl;

    ostringstream os;
    os.precision(3);
    os << scientific;

    for (ordinal_type m=mmin;m<=mmax;m+=minc) {
      os.str("");

      DenseMatrixBaseType AA("AA", m, m), BB("BB", m, k), BC("BC", m, k);
      
      // setup upper triangular
      for (ordinal_type j=0;j<AA.NumCols();++j) {
        AA.Value(j,j) = 10.0;
        for (ordinal_type i=0;i<j;++i)
          AA.Value(i,j) = 2.0*((value_type)rand()/(RAND_MAX)) - 1.0;
      }

      // setup one and right hand side is going to be overwritten by the product of AB
      for (ordinal_type j=0;j<BB.NumCols();++j)
        for (ordinal_type i=0;i<BB.NumRows();++i)
          BB.Value(i,j) = 1.0;

      Teuchos::BLAS<ordinal_type,value_type> blas;

      blas.GEMM(Teuchos::CONJ_TRANS, Teuchos::NO_TRANS,
                m, k, m,
                1.0,
                AA.ValuePtr(), AA.ColStride(),
                BB.ValuePtr(), BB.ColStride(),
                0.0,
                BC.ValuePtr(), BC.ColStride());
      BB.copy(BC);

      const double flop = get_flop_trsm_upper<value_type>(m, k);

      os << "DenseTrsmMKL:: m = " << m << " k = " << k;
      {
        timer.reset();
        Teuchos::BLAS<ordinal_type,value_type> blas;

        const ordinal_type mm = AA.NumRows();
        const ordinal_type nn = BB.NumCols();

        blas.TRSM(Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::CONJ_TRANS,
                  Teuchos::NON_UNIT_DIAG,
                  mm, nn,
                  1.0,
                  AA.ValuePtr(), AA.ColStride(),
                  BB.ValuePtr(), BB.ColStride());
        t = timer.seconds();
        os << ":: MKL Performance = " << (flop/t/1.0e9) << " [GFLOPs]  ";
      }
      cout << os.str() << endl;
    }

    return r_val;
  }

    void
    randomGlobalMatrix (Generator* const pGenerator,
                        MatrixViewType& A_local,
                        const typename Teuchos::ScalarTraits< typename MatrixViewType::scalar_type >::magnitudeType singular_values[],
                        MessengerBase< typename MatrixViewType::ordinal_type >* const ordinalMessenger,
                        MessengerBase< typename MatrixViewType::scalar_type >* const scalarMessenger)
    {
      using Teuchos::NO_TRANS;
      using std::vector;
      typedef typename MatrixViewType::ordinal_type ordinal_type;
      typedef typename MatrixViewType::scalar_type scalar_type;


      const bool b_local_debug = false;

      const int rootProc = 0;
      const int nprocs = ordinalMessenger->size();
      const int myRank = ordinalMessenger->rank();
      Teuchos::BLAS<ordinal_type, scalar_type> blas;

      const ordinal_type nrowsLocal = A_local.nrows();
      const ordinal_type ncols = A_local.ncols();

      // Theory: Suppose there are P processors.  Proc q wants an m_q by n
      // component of the matrix A, which we write as A_q.  On Proc 0, we
      // generate random m_q by n orthogonal matrices Q_q (in explicit
      // form), and send Q_q to Proc q.  The m by n matrix [Q_0; Q_1; ...;
      // Q_{P-1}] is not itself orthogonal.  However, the m by n matrix
      // Q = [Q_0 / P; Q_1 / P; ...; Q_{P-1} / P] is orthogonal:
      //
      // \sum_{q = 0}^{P-1} (Q_q^T * Q_q) / P = I.

      if (myRank == rootProc)
        {
          typedef Random::MatrixGenerator< ordinal_type, scalar_type, Generator > matgen_type;
          matgen_type matGen (*pGenerator);

          // Generate a random ncols by ncols upper triangular matrix
          // R with the given singular values.
          Matrix< ordinal_type, scalar_type > R (ncols, ncols, scalar_type(0));
          matGen.fill_random_R (ncols, R.get(), R.lda(), singular_values);

          // Broadcast R to all the processors.
          scalarMessenger->broadcast (R.get(), ncols*ncols, rootProc);

          // Generate (for myself) a random nrowsLocal x ncols
          // orthogonal matrix, stored in explicit form.
          Matrix< ordinal_type, scalar_type > Q_local (nrowsLocal, ncols);
          matGen.explicit_Q (nrowsLocal, ncols, Q_local.get(), Q_local.lda());

          // Scale the (local) orthogonal matrix by the number of
          // processors P, to make the columns of the global matrix Q
          // orthogonal.  (Otherwise the norm of each column will be P
          // instead of 1.)
          const scalar_type P = static_cast< scalar_type > (nprocs);
          // Do overflow check.  If casting P back to scalar_type
          // doesn't produce the same value as nprocs, the cast
          // overflowed.  We take the real part, because scalar_type
          // might be complex.
          if (nprocs != static_cast<int> (Teuchos::ScalarTraits<scalar_type>::real (P)))
            throw std::runtime_error ("Casting nprocs to Scalar failed");

          scaleMatrix (Q_local, P);

          // A_local := Q_local * R
          blas.GEMM (NO_TRANS, NO_TRANS, nrowsLocal, ncols, ncols,
                     scalar_type(1), Q_local.get(), Q_local.lda(),
                     R.get(), R.lda(),
                     scalar_type(0), A_local.get(), A_local.lda());

          for (int recvProc = 1; recvProc < nprocs; ++recvProc)
            {
              // Ask the receiving processor how big (i.e., how many rows)
              // its local component of the matrix is.
              ordinal_type nrowsRemote = 0;
              ordinalMessenger->recv (&nrowsRemote, 1, recvProc, 0);

              if (b_local_debug)
                {
                  std::ostringstream os;
                  os << "For Proc " << recvProc << ": local block is "
                     << nrowsRemote << " by " << ncols << std::endl;
                  std::cerr << os.str();
                }

              // Make sure Q_local is big enough to hold the data for
              // the current receiver proc.
              Q_local.reshape (nrowsRemote, ncols);

              // Compute a random nrowsRemote * ncols orthogonal
              // matrix Q_local, for the current receiving processor.
              matGen.explicit_Q (nrowsRemote, ncols, Q_local.get(), Q_local.lda());

              // Send Q_local to the current receiving processor.
              scalarMessenger->send (Q_local.get(), nrowsRemote*ncols, recvProc, 0);
            }
        }
      else
        {
          // Receive the R factor from Proc 0.  There's only 1 R
//.........这里部分代码省略.........

int main(int argc, char **argv)
{
  const unsigned int n = 5;
  Sacado::Fad::Vector<unsigned int, FadType> A(n*n,0),B(n,n), C(n,n);
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      A[i+j*n] = FadType(Teuchos::ScalarTraits<double>::random());
    B[i] = FadType(n, Teuchos::ScalarTraits<double>::random());
    for (unsigned int j=0; j<n; j++)
      B[i].fastAccessDx(j) = Teuchos::ScalarTraits<double>::random();
    C[i] = 0.0;
  }

  double *a = A.vals();
  double *b = B.vals();
  double *bdx = B.dx();
  std::vector<double> c(n), cdx(n*n);

  Teuchos::BLAS<int,double> blas;
  blas.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &a[0], n, &b[0], 1, 0.0, &c[0], 1);
  blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, n, n, n, 1.0, &a[0], n, &bdx[0], n, 0.0, &cdx[0], n);

  // Teuchos::BLAS<int,FadType> blas_fad;
  // blas_fad.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &A[0], n, &B[0], 1, 0.0, &C[0], 1);

  Teuchos::BLAS<int,FadType> sacado_fad_blas(false);
  sacado_fad_blas.GEMV(Teuchos::NO_TRANS, n, n, 1.0, &A[0], n, &B[0], 1, 0.0, &C[0], 1);

  // Print the results
  int p = 4;
  int w = p+7;
  std::cout.setf(std::ios::scientific);
  std::cout.precision(p);

  std::cout << "BLAS GEMV calculation:" << std::endl;
  std::cout << "a = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << a[i+j*n];
    std::cout << std::endl;
  }
  std::cout << "b = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    std::cout << " " << std::setw(w) << b[i];
  }
  std::cout << std::endl;
  std::cout << "bdot = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << bdx[i+j*n];
    std::cout << std::endl;
  }
  std::cout << "c = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    std::cout << " " << std::setw(w) << c[i];
  }
  std::cout << std::endl;
  std::cout << "cdot = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << cdx[i+j*n];
    std::cout << std::endl;
  }
  std::cout << std::endl << std::endl;

  std::cout << "FAD BLAS GEMV calculation:" << std::endl;
  std::cout << "A.val() (should = a) = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << A[i+j*n].val();
    std::cout << std::endl;
  }
  std::cout << "B.val() (should = b) = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    std::cout << " " << std::setw(w) << B[i].val();
  }
  std::cout << std::endl;
  std::cout << "B.dx() (should = bdot) = " << std::endl;
  double *Bdx = B.dx();
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << Bdx[i+j*n];
    std::cout << std::endl;
  }
  std::cout << "C.val() (should = c) = " << std::endl;
  for (unsigned int i=0; i<n; i++) {
    std::cout << " " << std::setw(w) << C[i].val();
  }
  std::cout << std::endl;
  std::cout << "C.dx() (should = cdot) = " << std::endl;
  double *Cdx = C.dx();
  for (unsigned int i=0; i<n; i++) {
    for (unsigned int j=0; j<n; j++)
      std::cout << " " << std::setw(w) << Cdx[i+j*n];
    std::cout << std::endl;
  }

  double tol = 1.0e-14;
  bool failed = false;
  for (unsigned int i=0; i<n; i++) {
//.........这里部分代码省略.........