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level2_real_impl.h
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#include "common.h"

// y = alpha*A*x + beta*y
int EIGEN_BLAS_FUNC(symv) (char *uplo, int *n, RealScalar *palpha, RealScalar *pa, int *lda, RealScalar *px, int *incx, RealScalar *pbeta, RealScalar *py, int *incy)
{
  Scalar* a = reinterpret_cast<Scalar*>(pa);
  Scalar* x = reinterpret_cast<Scalar*>(px);
  Scalar* y = reinterpret_cast<Scalar*>(py);
  Scalar alpha  = *reinterpret_cast<Scalar*>(palpha);
  Scalar beta   = *reinterpret_cast<Scalar*>(pbeta);

  // check arguments
  int info = 0;
  if(UPLO(*uplo)==INVALID)        info = 1;
  else if(*n<0)                   info = 2;
  else if(*lda<std::max(1,*n))    info = 5;
  else if(*incx==0)               info = 7;
  else if(*incy==0)               info = 10;
  if(info)
    return xerbla_(SCALAR_SUFFIX_UP"SYMV ",&info,6);

  if(*n==0)
    return 0;

  Scalar* actual_x = get_compact_vector(x,*n,*incx);
  Scalar* actual_y = get_compact_vector(y,*n,*incy);

  if(beta!=Scalar(1))
  {
    if(beta==Scalar(0)) vector(actual_y, *n).setZero();
    else                vector(actual_y, *n) *= beta;
  }

  // TODO performs a direct call to the underlying implementation function
       if(UPLO(*uplo)==UP) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Upper>() * (alpha * vector(actual_x,*n));
  else if(UPLO(*uplo)==LO) vector(actual_y,*n).noalias() += matrix(a,*n,*n,*lda).selfadjointView<Lower>() * (alpha * vector(actual_x,*n));

  if(actual_x!=x) delete[] actual_x;
  if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);

  return 1;
}

// C := alpha*x*x' + C
int EIGEN_BLAS_FUNC(syr)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pc, int *ldc)
{

//   typedef void (*functype)(int, const Scalar *, int, Scalar *, int, Scalar);
//   static functype func[2];

//   static bool init = false;
//   if(!init)
//   {
//     for(int k=0; k<2; ++k)
//       func[k] = 0;
//
//     func[UP] = (internal::selfadjoint_product<Scalar,ColMajor,ColMajor,false,UpperTriangular>::run);
//     func[LO] = (internal::selfadjoint_product<Scalar,ColMajor,ColMajor,false,LowerTriangular>::run);

//     init = true;
//   }

  Scalar* x = reinterpret_cast<Scalar*>(px);
  Scalar* c = reinterpret_cast<Scalar*>(pc);
  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);

  int info = 0;
  if(UPLO(*uplo)==INVALID)                                            info = 1;
  else if(*n<0)                                                       info = 2;
  else if(*incx==0)                                                   info = 5;
  else if(*ldc<std::max(1,*n))                                        info = 7;
  if(info)
    return xerbla_(SCALAR_SUFFIX_UP"SYR  ",&info,6);

  if(*n==0 || alpha==Scalar(0)) return 1;

  // if the increment is not 1, let's copy it to a temporary vector to enable vectorization
  Scalar* x_cpy = get_compact_vector(x,*n,*incx);

  Matrix<Scalar,Dynamic,Dynamic> m2(matrix(c,*n,*n,*ldc));
  
  // TODO check why this is not accurate enough for lapack tests
//   if(UPLO(*uplo)==LO)       matrix(c,*n,*n,*ldc).selfadjointView<Lower>().rankUpdate(vector(x_cpy,*n), alpha);
//   else if(UPLO(*uplo)==UP)  matrix(c,*n,*n,*ldc).selfadjointView<Upper>().rankUpdate(vector(x_cpy,*n), alpha);

  if(UPLO(*uplo)==LO)
    for(int j=0;j<*n;++j)
      matrix(c,*n,*n,*ldc).col(j).tail(*n-j) += alpha * x_cpy[j] * vector(x_cpy+j,*n-j);
  else
    for(int j=0;j<*n;++j)
      matrix(c,*n,*n,*ldc).col(j).head(j+1) += alpha * x_cpy[j] * vector(x_cpy,j+1);

  if(x_cpy!=x)  delete[] x_cpy;

  return 1;
}

// C := alpha*x*y' + alpha*y*x' + C
int EIGEN_BLAS_FUNC(syr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, int *ldc)
{
//   typedef void (*functype)(int, const Scalar *, int, const Scalar *, int, Scalar *, int, Scalar);
//   static functype func[2];
//
//   static bool init = false;
//   if(!init)
//   {
//     for(int k=0; k<2; ++k)
//       func[k] = 0;
//
//     func[UP] = (internal::selfadjoint_product<Scalar,ColMajor,ColMajor,false,UpperTriangular>::run);
//     func[LO] = (internal::selfadjoint_product<Scalar,ColMajor,ColMajor,false,LowerTriangular>::run);
//
//     init = true;
//   }

  Scalar* x = reinterpret_cast<Scalar*>(px);
  Scalar* y = reinterpret_cast<Scalar*>(py);
  Scalar* c = reinterpret_cast<Scalar*>(pc);
  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);

  int info = 0;
  if(UPLO(*uplo)==INVALID)                                            info = 1;
  else if(*n<0)                                                       info = 2;
  else if(*incx==0)                                                   info = 5;
  else if(*incy==0)                                                   info = 7;
  else if(*ldc<std::max(1,*n))                                        info = 9;
  if(info)
    return xerbla_(SCALAR_SUFFIX_UP"SYR2 ",&info,6);

  if(alpha==Scalar(0))
    return 1;

  Scalar* x_cpy = get_compact_vector(x,*n,*incx);
  Scalar* y_cpy = get_compact_vector(y,*n,*incy);

  // TODO perform direct calls to underlying implementation
  if(UPLO(*uplo)==LO)       matrix(c,*n,*n,*ldc).selfadjointView<Lower>().rankUpdate(vector(x_cpy,*n), vector(y_cpy,*n), alpha);
  else if(UPLO(*uplo)==UP)  matrix(c,*n,*n,*ldc).selfadjointView<Upper>().rankUpdate(vector(x_cpy,*n), vector(y_cpy,*n), alpha);

  if(x_cpy!=x)  delete[] x_cpy;
  if(y_cpy!=y)  delete[] y_cpy;

//   int code = UPLO(*uplo);
//   if(code>=2 || func[code]==0)
//     return 0;

//   func[code](*n, a, *inca, b, *incb, c, *ldc, alpha);
  return 1;
}

/**  DSBMV  performs the matrix-vector  operation
  *
  *     y := alpha*A*x + beta*y,
  *
  *  where alpha and beta are scalars, x and y are n element vectors and
  *  A is an n by n symmetric band matrix, with k super-diagonals.
  */
// int EIGEN_BLAS_FUNC(sbmv)( char *uplo, int *n, int *k, RealScalar *alpha, RealScalar *a, int *lda,
//                            RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
// {
//   return 1;
// }


/**  DSPMV  performs the matrix-vector operation
  *
  *     y := alpha*A*x + beta*y,
  *
  *  where alpha and beta are scalars, x and y are n element vectors and
  *  A is an n by n symmetric matrix, supplied in packed form.
  *
  */
// int EIGEN_BLAS_FUNC(spmv)(char *uplo, int *n, RealScalar *alpha, RealScalar *ap, RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
// {
//   return 1;
// }

/**  DSPR    performs the symmetric rank 1 operation
  *
  *     A := alpha*x*x' + A,
  *
  *  where alpha is a real scalar, x is an n element vector and A is an
  *  n by n symmetric matrix, supplied in packed form.
  */
// int EIGEN_BLAS_FUNC(spr)(char *uplo, int *n, Scalar *alpha, Scalar *x, int *incx, Scalar *ap)
// {
//   return 1;
// }

/**  DSPR2  performs the symmetric rank 2 operation
  *
  *     A := alpha*x*y' + alpha*y*x' + A,
  *
  *  where alpha is a scalar, x and y are n element vectors and A is an
  *  n by n symmetric matrix, supplied in packed form.
  */
// int EIGEN_BLAS_FUNC(spr2)(char *uplo, int *n, RealScalar *alpha, RealScalar *x, int *incx, RealScalar *y, int *incy, RealScalar *ap)
// {
//   return 1;
// }


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