text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #include "common.h"
  
  struct scalar_norm1_op {
    typedef RealScalar result_type;
    EIGEN_EMPTY_STRUCT_CTOR(scalar_norm1_op)
    inline RealScalar operator() (const Scalar& a) const { return numext::norm1(a); }
  };
  namespace Eigen {
    namespace internal {
      template<> struct functor_traits<scalar_norm1_op >
      {
        enum { Cost = 3 * NumTraits<Scalar>::AddCost, PacketAccess = 0 };
      };
    }
  }
  
  // computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum
  // res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n
  RealScalar EIGEN_CAT(EIGEN_CAT(REAL_SCALAR_SUFFIX,SCALAR_SUFFIX),asum_)(int *n, RealScalar *px, int *incx)
  {
  //   std::cerr << "__asum " << *n << " " << *incx << "\n";
    Complex* x = reinterpret_cast<Complex*>(px);
  
    if(*n<=0) return 0;
  
    if(*incx==1)  return make_vector(x,*n).unaryExpr<scalar_norm1_op>().sum();
    else          return make_vector(x,*n,std::abs(*incx)).unaryExpr<scalar_norm1_op>().sum();
  }
  
  // computes a dot product of a conjugated vector with another vector.
  int EIGEN_BLAS_FUNC(dotcw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)
  {
  //   std::cerr << "_dotc " << *n << " " << *incx << " " << *incy << "\n";
    Scalar* res = reinterpret_cast<Scalar*>(pres);
  
    if(*n<=0)
    {
      *res = Scalar(0);
      return 0;
    }
  
    Scalar* x = reinterpret_cast<Scalar*>(px);
    Scalar* y = reinterpret_cast<Scalar*>(py);
  
    if(*incx==1 && *incy==1)    *res = (make_vector(x,*n).dot(make_vector(y,*n)));
    else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,*incy)));
    else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,*incy)));
    else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,-*incy).reverse()));
    else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,-*incy).reverse()));
    return 0;
  }
  
  // computes a vector-vector dot product without complex conjugation.
  int EIGEN_BLAS_FUNC(dotuw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)
  {
    Scalar* res = reinterpret_cast<Scalar*>(pres);
  
    if(*n<=0)
    {
      *res = Scalar(0);
      return 0;
    }
  
    Scalar* x = reinterpret_cast<Scalar*>(px);
    Scalar* y = reinterpret_cast<Scalar*>(py);
  
    if(*incx==1 && *incy==1)    *res = (make_vector(x,*n).cwiseProduct(make_vector(y,*n))).sum();
    else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,*incy))).sum();
    else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,*incy))).sum();
    else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
    else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
    return 0;
  }
  
  RealScalar EIGEN_CAT(EIGEN_CAT(REAL_SCALAR_SUFFIX,SCALAR_SUFFIX),nrm2_)(int *n, RealScalar *px, int *incx)
  {
  //   std::cerr << "__nrm2 " << *n << " " << *incx << "\n";
    if(*n<=0) return 0;
  
    Scalar* x = reinterpret_cast<Scalar*>(px);
  
    if(*incx==1)
      return make_vector(x,*n).stableNorm();
  
    return make_vector(x,*n,*incx).stableNorm();
  }
  
  int EIGEN_CAT(EIGEN_CAT(SCALAR_SUFFIX,REAL_SCALAR_SUFFIX),rot_)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)
  {
    if(*n<=0) return 0;
  
    Scalar* x = reinterpret_cast<Scalar*>(px);
    Scalar* y = reinterpret_cast<Scalar*>(py);
    RealScalar c = *pc;
    RealScalar s = *ps;
  
    StridedVectorType vx(make_vector(x,*n,std::abs(*incx)));
    StridedVectorType vy(make_vector(y,*n,std::abs(*incy)));
  
    Reverse<StridedVectorType> rvx(vx);
    Reverse<StridedVectorType> rvy(vy);
  
    // TODO implement mixed real-scalar rotations
         if(*incx<0 && *incy>0) internal::apply_rotation_in_the_plane(rvx, vy, JacobiRotation<Scalar>(c,s));
    else if(*incx>0 && *incy<0) internal::apply_rotation_in_the_plane(vx, rvy, JacobiRotation<Scalar>(c,s));
    else                        internal::apply_rotation_in_the_plane(vx, vy,  JacobiRotation<Scalar>(c,s));
  
    return 0;
  }
  
  int EIGEN_CAT(EIGEN_CAT(SCALAR_SUFFIX,REAL_SCALAR_SUFFIX),scal_)(int *n, RealScalar *palpha, RealScalar *px, int *incx)
  {
    if(*n<=0) return 0;
  
    Scalar* x = reinterpret_cast<Scalar*>(px);
    RealScalar alpha = *palpha;
  
  //   std::cerr << "__scal " << *n << " " << alpha << " " << *incx << "\n";
  
    if(*incx==1)  make_vector(x,*n) *= alpha;
    else          make_vector(x,*n,std::abs(*incx)) *= alpha;
  
    return 0;
  }
  