text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra. Eigen itself is part of the KDE project.
  //
  // Copyright (C) 2008 Gael Guennebaud <g.gael@free.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/.
  
  #ifndef EIGEN_GSL_HELPER
  #define EIGEN_GSL_HELPER
  
  #include <Eigen/Core>
  
  #include <gsl/gsl_blas.h>
  #include <gsl/gsl_multifit.h>
  #include <gsl/gsl_eigen.h>
  #include <gsl/gsl_linalg.h>
  #include <gsl/gsl_complex.h>
  #include <gsl/gsl_complex_math.h>
  
  namespace Eigen {
  
  template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> struct GslTraits
  {
    typedef gsl_matrix* Matrix;
    typedef gsl_vector* Vector;
    static Matrix createMatrix(int rows, int cols) { return gsl_matrix_alloc(rows,cols); }
    static Vector createVector(int size) { return gsl_vector_alloc(size); }
    static void free(Matrix& m) { gsl_matrix_free(m); m=0; }
    static void free(Vector& m) { gsl_vector_free(m); m=0; }
    static void prod(const Matrix& m, const Vector& v, Vector& x) { gsl_blas_dgemv(CblasNoTrans,1,m,v,0,x); }
    static void cholesky(Matrix& m) { gsl_linalg_cholesky_decomp(m); }
    static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_cholesky_solve(m,b,x); }
    static void eigen_symm(const Matrix& m, Vector& eval, Matrix& evec)
    {
      gsl_eigen_symmv_workspace * w = gsl_eigen_symmv_alloc(m->size1);
      Matrix a = createMatrix(m->size1, m->size2);
      gsl_matrix_memcpy(a, m);
      gsl_eigen_symmv(a,eval,evec,w);
      gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
      gsl_eigen_symmv_free(w);
      free(a);
    }
    static void eigen_symm_gen(const Matrix& m, const Matrix& _b, Vector& eval, Matrix& evec)
    {
      gsl_eigen_gensymmv_workspace * w = gsl_eigen_gensymmv_alloc(m->size1);
      Matrix a = createMatrix(m->size1, m->size2);
      Matrix b = createMatrix(_b->size1, _b->size2);
      gsl_matrix_memcpy(a, m);
      gsl_matrix_memcpy(b, _b);
      gsl_eigen_gensymmv(a,b,eval,evec,w);
      gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
      gsl_eigen_gensymmv_free(w);
      free(a);
    }
  };
  
  template<typename Scalar> struct GslTraits<Scalar,true>
  {
    typedef gsl_matrix_complex* Matrix;
    typedef gsl_vector_complex* Vector;
    static Matrix createMatrix(int rows, int cols) { return gsl_matrix_complex_alloc(rows,cols); }
    static Vector createVector(int size) { return gsl_vector_complex_alloc(size); }
    static void free(Matrix& m) { gsl_matrix_complex_free(m); m=0; }
    static void free(Vector& m) { gsl_vector_complex_free(m); m=0; }
    static void cholesky(Matrix& m) { gsl_linalg_complex_cholesky_decomp(m); }
    static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_complex_cholesky_solve(m,b,x); }
    static void prod(const Matrix& m, const Vector& v, Vector& x)
    { gsl_blas_zgemv(CblasNoTrans,gsl_complex_rect(1,0),m,v,gsl_complex_rect(0,0),x); }
    static void eigen_symm(const Matrix& m, gsl_vector* &eval, Matrix& evec)
    {
      gsl_eigen_hermv_workspace * w = gsl_eigen_hermv_alloc(m->size1);
      Matrix a = createMatrix(m->size1, m->size2);
      gsl_matrix_complex_memcpy(a, m);
      gsl_eigen_hermv(a,eval,evec,w);
      gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
      gsl_eigen_hermv_free(w);
      free(a);
    }
    static void eigen_symm_gen(const Matrix& m, const Matrix& _b, gsl_vector* &eval, Matrix& evec)
    {
      gsl_eigen_genhermv_workspace * w = gsl_eigen_genhermv_alloc(m->size1);
      Matrix a = createMatrix(m->size1, m->size2);
      Matrix b = createMatrix(_b->size1, _b->size2);
      gsl_matrix_complex_memcpy(a, m);
      gsl_matrix_complex_memcpy(b, _b);
      gsl_eigen_genhermv(a,b,eval,evec,w);
      gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
      gsl_eigen_genhermv_free(w);
      free(a);
    }
  };
  
  template<typename MatrixType>
  void convert(const MatrixType& m, gsl_matrix* &res)
  {
  //   if (res)
  //     gsl_matrix_free(res);
    res = gsl_matrix_alloc(m.rows(), m.cols());
    for (int i=0 ; i<m.rows() ; ++i)
      for (int j=0 ; j<m.cols(); ++j)
        gsl_matrix_set(res, i, j, m(i,j));
  }
  
  template<typename MatrixType>
  void convert(const gsl_matrix* m, MatrixType& res)
  {
    res.resize(int(m->size1), int(m->size2));
    for (int i=0 ; i<res.rows() ; ++i)
      for (int j=0 ; j<res.cols(); ++j)
        res(i,j) = gsl_matrix_get(m,i,j);
  }
  
  template<typename VectorType>
  void convert(const VectorType& m, gsl_vector* &res)
  {
    if (res) gsl_vector_free(res);
    res = gsl_vector_alloc(m.size());
    for (int i=0 ; i<m.size() ; ++i)
        gsl_vector_set(res, i, m[i]);
  }
  
  template<typename VectorType>
  void convert(const gsl_vector* m, VectorType& res)
  {
    res.resize (m->size);
    for (int i=0 ; i<res.rows() ; ++i)
      res[i] = gsl_vector_get(m, i);
  }
  
  template<typename MatrixType>
  void convert(const MatrixType& m, gsl_matrix_complex* &res)
  {
    res = gsl_matrix_complex_alloc(m.rows(), m.cols());
    for (int i=0 ; i<m.rows() ; ++i)
      for (int j=0 ; j<m.cols(); ++j)
      {
        gsl_matrix_complex_set(res, i, j,
          gsl_complex_rect(m(i,j).real(), m(i,j).imag()));
      }
  }
  
  template<typename MatrixType>
  void convert(const gsl_matrix_complex* m, MatrixType& res)
  {
    res.resize(int(m->size1), int(m->size2));
    for (int i=0 ; i<res.rows() ; ++i)
      for (int j=0 ; j<res.cols(); ++j)
        res(i,j) = typename MatrixType::Scalar(
          GSL_REAL(gsl_matrix_complex_get(m,i,j)),
          GSL_IMAG(gsl_matrix_complex_get(m,i,j)));
  }
  
  template<typename VectorType>
  void convert(const VectorType& m, gsl_vector_complex* &res)
  {
    res = gsl_vector_complex_alloc(m.size());
    for (int i=0 ; i<m.size() ; ++i)
        gsl_vector_complex_set(res, i, gsl_complex_rect(m[i].real(), m[i].imag()));
  }
  
  template<typename VectorType>
  void convert(const gsl_vector_complex* m, VectorType& res)
  {
    res.resize(m->size);
    for (int i=0 ; i<res.rows() ; ++i)
      res[i] = typename VectorType::Scalar(
          GSL_REAL(gsl_vector_complex_get(m, i)),
          GSL_IMAG(gsl_vector_complex_get(m, i)));
  }
  
  }
  
  #endif // EIGEN_GSL_HELPER
  