/usr/include/CGAL/eigen.h is in libcgal-dev 4.2-5ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); 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.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Bruno Levy, Pierre Alliez
#ifndef CGAL_EIGEN_H
#define CGAL_EIGEN_H
#include <cmath>
namespace CGAL {
namespace internal {
template <class FT>
void eigen_symmetric(const FT *mat,
const int n,
FT *eigen_vectors,
FT *eigen_values,
const int MAX_ITER = 100)
{
static const FT EPSILON = (FT)0.00001;
// number of entries in mat
int nn = (n*(n+1))/2;
// copy matrix
FT *a = new FT[nn];
int ij;
for(ij=0; ij<nn; ij++)
a[ij] = mat[ij];
// Fortran-porting
a--;
// init diagonalization matrix as the unit matrix
FT *v = new FT[n*n];
ij = 0;
int i;
for(i=0; i<n; i++)
for(int j=0; j<n; j++)
if(i==j)
v[ij++] = 1.0;
else
v[ij++] = 0.0;
// Fortran-porting
v--;
// compute weight of the non diagonal terms
ij = 1;
FT a_norm = 0.0;
for(i=1; i<=n; i++)
for(int j=1; j<=i; j++)
{
if( i!=j )
{
FT a_ij = a[ij];
a_norm += a_ij * a_ij;
}
ij++;
}
if(a_norm != 0.0)
{
FT a_normEPS = a_norm * EPSILON;
FT thr = a_norm;
// rotations
int nb_iter = 0;
while(thr > a_normEPS && nb_iter < MAX_ITER)
{
nb_iter++;
FT thr_nn = thr / nn;
for(int l=1; l< n; l++)
{
for(int m=l+1; m<=n; m++)
{
// compute sinx and cosx
int lq = (l*l-l)/2;
int mq = (m*m-m)/2;
int lm = l + mq;
FT a_lm = a[lm];
FT a_lm_2 = a_lm * a_lm;
if(a_lm_2 < thr_nn)
continue;
int ll = l + lq;
int mm = m + mq;
FT a_ll = a[ll];
FT a_mm = a[mm];
FT delta = a_ll - a_mm;
FT x;
if(delta == 0.0)
x = (FT) - CGAL_PI / 4;
else
x = (FT)(- std::atan( (a_lm+a_lm) / delta ) / 2.0);
FT sinx = std::sin(x);
FT cosx = std::cos(x);
FT sinx_2 = sinx * sinx;
FT cosx_2 = cosx * cosx;
FT sincos = sinx * cosx;
// rotate L and M columns
int ilv = n*(l-1);
int imv = n*(m-1);
int i;
for( i=1; i<=n;i++ )
{
if( (i!=l) && (i!=m) )
{
int iq = (i*i-i)/2;
int im;
if( i<m )
im = i + mq;
else
im = m + iq;
FT a_im = a[im];
int il;
if( i<l )
il = i + lq;
else
il = l + iq;
FT a_il = a[il];
a[il] = a_il * cosx - a_im * sinx;
a[im] = a_il * sinx + a_im * cosx;
}
ilv++;
imv++;
FT v_ilv = v[ilv];
FT v_imv = v[imv];
v[ilv] = cosx * v_ilv - sinx * v_imv;
v[imv] = sinx * v_ilv + cosx * v_imv;
}
x = a_lm * sincos;
x += x;
a[ll] = a_ll * cosx_2 + a_mm * sinx_2 - x;
a[mm] = a_ll * sinx_2 + a_mm * cosx_2 + x;
a[lm] = 0.0;
thr = CGAL::abs(thr - a_lm_2);
}
}
}
}
// convert indices and copy eigen values
a++;
for(i=0; i<n; i++)
{
int k = i + (i*(i+1))/2;
eigen_values[i] = a[k];
}
delete [] a;
// sort eigen values and vectors
int *index = new int[n];
for(i=0; i<n; i++)
index[i] = i;
for(i=0; i<(n-1); i++)
{
FT x = eigen_values[i];
int k = i;
for(int j=i+1; j<n; j++)
if(x < eigen_values[j])
{
k = j;
x = eigen_values[j];
}
eigen_values[k] = eigen_values[i];
eigen_values[i] = x;
int jj = index[k];
index[k] = index[i];
index[i] = jj;
}
// save eigen vectors
v++; // back to C++
ij = 0;
for(int k=0; k<n; k++ )
{
int ik = index[k]*n;
for(int i=0; i<n; i++)
eigen_vectors[ij++] = v[ik++];
}
delete [] v;
delete [] index;
}
} // end namespace internal
} //namespace CGAL
#endif // CGAL_EIGEN_H
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