/usr/include/vmmlib/jacobi_solver.hpp is in libvmmlib-dev 1.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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* VMMLib - Vector & Matrix Math Lib
*
* @author Jonas Boesch
* @author Stefan Eilemann
* @author Renato Pajarola
* @author Andrew Willmott ( VL )
*
* @license revised BSD license, check LICENSE
*
* parts of the source code of VMMLib were inspired by David Eberly's
* Wild Magic and Andrew Willmott's VL.
*
*/
#ifndef __VMML__JACOBI_SOLVER__HPP__
#define __VMML__JACOBI_SOLVER__HPP__
#include <vmmlib/vmmlib.hpp>
#include <cmath>
#include <cassert>
namespace vmml
{
/*
* This function computes the eigenvalues and eigenvectors of a 3x3 matrix.
*
* @param a matrix to be diagonalized.
* @param d eigenvalues of A.
* @param v matrix whose columns are the normalized eigenvectors of A.
* @param rotationCount number of Jacobi rotations required.
* @return true if the transformation has been done. False if not.
*
*
* modified from numerical recipies for n=3 and float values
*
*/
template < typename T >
bool solve_jacobi_3x3(
matrix< 3, 3, T >& a,
vector< 3, T >& d,
matrix< 3, 3, T >& v,
size_t& rotationCount )
{
identity( v );
vector< 3, T > b, z;
for ( size_t i = 0; i < 3; ++i )
{
b[i] = d[i] = a( i,i );
z[i] = 0.0;
}
T t, theta, s, c, tau;
size_t rot = 0;
for ( size_t i = 1; i <= 150; ++i )
{
T sm = 0.0;
for ( size_t ip = 0; ip < 2; ++ip ) // < n-1
{
for ( size_t iq = ip + 1; iq < 3; ++iq ) // < n
{
sm += fabs( a( iq, ip ) );
}
}
if ( sm == 0.0 )
{
rotationCount = rot;
return true;
}
T tresh = ( i < 4 ) ? 0.2 * sm / 9.0 : 0.0;
for ( ssize_t ip = 0; ip < 2; ++ip ) // ip < n - 1
{
for ( ssize_t iq = ip + 1; iq < 3; ++iq )
{
T g = 100.0 * fabs( a( iq,ip ) );
// this has to be fabs( x ) + g == fabs( x ) and NOT
// g == 0.0 because of floating point evilness
// ( inaccuracies when comparing (anyfloat) to 0.0 )
if ( i > 4
&& fabs( d[ip] ) + g == fabs( d[ip] )
&& fabs( d[iq] ) + g == fabs( d[iq] )
)
{
a( iq, ip ) = 0.0;
}
else
{
if ( fabs( a( iq, iq ) ) > tresh )
{
T h = d[iq] - d[ip];
if ( fabs( h ) + g == fabs( h ) )
{
if ( h != 0.0 )
t = ( a( iq, ip ) ) / h;
else
t = 0.0;
}
else
{
if( a( iq, ip ) != 0.0 )
theta = 0.5 * h / ( a( iq, ip ) );
else
theta = 0.0;
t = 1.0 / ( fabs( theta ) + sqrt( 1.0 + theta * theta ) );
if ( theta < 0.0 )
t = -t;
}
c = 1.0 / sqrt( 1 + t * t );
s = t * c;
tau = s / ( 1.0 + c );
h = t * a( iq, ip );
z[ip] -= h;
z[iq] += h;
d[ip] -= h;
d[iq] += h;
a( iq, ip ) = 0.0;
for ( ssize_t j = 0; j <= ip - 1; ++j )
{
g = a( ip, j );
h = a( iq, j );
a( ip, j ) = g - s * ( h + g * tau );
a( iq, j ) = h + s * ( g - h * tau );
}
for ( ssize_t j = ip + 1; j <= iq - 1; ++j )
{
g = a( j, ip );
h = a( iq, j );
a( j, ip ) = g - s * ( h + g * tau );
a( iq, j ) = h + s * ( g - h * tau );
}
for ( size_t j = iq + 1; j < 3; ++j )
{
g = a( j, ip );
h = a( j, iq );
a( j, ip ) = g - s * ( h + g * tau );
a( j, iq ) = h + s * ( g - h * tau );
}
for ( size_t j = 0; j < 3; ++j )
{
g = v( ip, j );
h = v( iq, j );
v( ip, j ) = g - s * ( h + g * tau );
v( iq, j ) = h + s * ( g - h * tau );
}
++rot;
}
}
}
}
for ( size_t ip = 0; ip < 3; ++ip )
{
b[ip] += z[ip];
d[ip] = b[ip];
z[ip] = 0.0;
}
}
return false;
}
} // namespace vmml
#endif
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