/usr/include/openmeeg/integrator.h is in libopenmeeg-dev 2.0.0.dfsg-5.1ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 | /*
Project Name : OpenMEEG
© INRIA and ENPC (contributors: Geoffray ADDE, Maureen CLERC, Alexandre
GRAMFORT, Renaud KERIVEN, Jan KYBIC, Perrine LANDREAU, Théodore PAPADOPOULO,
Emmanuel OLIVI
Maureen.Clerc.AT.sophia.inria.fr, keriven.AT.certis.enpc.fr,
kybic.AT.fel.cvut.cz, papadop.AT.sophia.inria.fr)
The OpenMEEG software is a C++ package for solving the forward/inverse
problems of electroencephalography and magnetoencephalography.
This software is governed by the CeCILL-B license under French law and
abiding by the rules of distribution of free software. You can use,
modify and/ or redistribute the software under the terms of the CeCILL-B
license as circulated by CEA, CNRS and INRIA at the following URL
"http://www.cecill.info".
As a counterpart to the access to the source code and rights to copy,
modify and redistribute granted by the license, users are provided only
with a limited warranty and the software's authors, the holders of the
economic rights, and the successive licensors have only limited
liability.
In this respect, the user's attention is drawn to the risks associated
with loading, using, modifying and/or developing or reproducing the
software by the user in light of its specific status of free software,
that may mean that it is complicated to manipulate, and that also
therefore means that it is reserved for developers and experienced
professionals having in-depth computer knowledge. Users are therefore
encouraged to load and test the software's suitability as regards their
requirements in conditions enabling the security of their systems and/or
data to be ensured and, more generally, to use and operate it in the
same conditions as regards security.
The fact that you are presently reading this means that you have had
knowledge of the CeCILL-B license and that you accept its terms.
*/
#ifndef OPENMEEG_INTEGRATOR_H
#define OPENMEEG_INTEGRATOR_H
#include <cmath>
#include <iostream>
#include "vect3.h"
#include "triangle.h"
#include "mesh3.h"
namespace OpenMEEG {
// light class containing d Vect3
template <int d>
class OPENMEEG_EXPORT Vect3array
{
private:
Vect3 t[d];
public:
Vect3array() {};
inline Vect3array(double x) {
for (int i=0;i<d;i++)
t[i]=Vect3(x);
}
inline Vect3array<d> operator*(double x) const {
Vect3array<d> r;
for (int i=0;i<d;i++)
r.t[i]=t[i]*x;
return r;
}
inline Vect3 operator()(int i) const { return t[i]; }
inline Vect3& operator()(int i) { return t[i]; }
};
template <int d>
inline void multadd (Vect3array<d> &target, const double scale, const Vect3array<d> &incr)
{
for (int i=0;i<d;i++) {
target(i) = target(i) + scale*incr(i);
}
}
inline void multadd (double &target, const double scale, const double incr)
{
target += scale*incr;
}
inline void multadd (Vect3 &target, const double scale, const Vect3 &incr)
{
target = target + scale*incr;
}
// Quadrature rules are from Marc Bonnet's book: Equations integrales..., Appendix B.3
static const double cordBars[4][16][4]=
{
//parameters for N=3
{
{0.166666666666667,0.166666666666667,0.666666666666667,0.166666666666667},
{0.166666666666667,0.666666666666667,0.166666666666667,0.166666666666667},
{0.666666666666667,0.166666666666667,0.166666666666667,0.166666666666667},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0}
}
,
// parameters for N=6
{
{0.445948490915965,0.445948490915965,0.10810301816807,0.111690794839005},
{0.445948490915965,0.10810301816807,0.445948490915965,0.111690794839005},
{0.10810301816807,0.445948490915965,0.445948490915965,0.111690794839005},
{0.091576213509771,0.091576213509771,0.81684757298045796,0.054975871827661},
{0.091576213509771,0.81684757298045796,0.091576213509771,0.054975871827661},
{0.816847572980458,0.091576213509771,0.091576213509771,0.054975871827661},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0}
}
,
// parameters for N=7
{
{0.333333333333333,0.333333333333333,0.333333333333333,0.1125},
{0.470142064105115,0.470142064105115,0.059715871789770,0.066197076394253},
{0.470142064105115,0.059715871789770,0.470142064105115,0.066197076394253},
{0.059715871789770,0.470142064105115,0.470142064105115,0.066197076394253},
{0.101286507323456,0.101286507323456,0.79742698535308798,0.062969590272414},
{0.101286507323456,0.7974269853530880,0.101286507323456,0.062969590272414},
{0.797426985353088,0.101286507323456,0.101286507323456,0.062969590272414},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0}
}
,
// parameters for N=16
{
{0.333333333333333,0.333333333333333,0.3333333333333333,0.072157803838893},
{0.081414823414554,0.459292588292722,0.459292588292722,0.047545817133642},
{0.459292588292722,0.081414823414554,0.459292588292722,0.047545817133642},
{0.459292588292722,0.459292588292722,0.081414823414554,0.047545817133642},
{0.898905543365937,0.050547228317031,0.050547228317031,0.016229248811599},
{0.050547228317031,0.898905543365937,0.050547228317031,0.016229248811599},
{0.050547228317031,0.050547228317031,0.898905543365937,0.016229248811599},
{0.658861384496479,0.170569307751760,0.17056930775176099,0.051608685267359},
{0.170569307751760,0.658861384496479,0.17056930775176099,0.051608685267359},
{0.170569307751760,0.17056930775176099,0.658861384496479,0.051608685267359},
{0.008394777409957,0.728492392955404,0.263112829634639,0.013615157087217},
{0.728492392955404,0.008394777409957,0.263112829634639,0.013615157087217},
{0.728492392955404,0.263112829634639,0.008394777409957,0.013615157087217},
{0.008394777409957,0.263112829634639,0.728492392955404,0.013615157087217},
{0.263112829634639,0.008394777409957,0.728492392955404,0.013615157087217},
{0.263112829634639,0.728492392955404,0.008394777409957,0.013615157087217}
}
}; // end of gaussTriangleParams
static const int nbPts[4]={3,6,7,16};
template<class T,class I>
class OPENMEEG_EXPORT Integrator
{
private:
int order;
public:
inline Integrator() {setOrder(3);}
inline Integrator(int ord) {setOrder(ord);}
inline ~Integrator() {}
inline void setOrder(int n)
{
if(n>=0 && n<4) order=n;
else {std::cout<<"Unavailable Gauss Order: "<<n<<std::endl; order = (n<1)?order=1:order;}
}
virtual inline T integrate ( const I &fc, const Triangle& Trg ,const Mesh& M)
{
Vect3 sommets[3]={M.getPt(Trg.s1()),M.getPt(Trg.s2()),M.getPt(Trg.s3())};
return triangle_integration(fc,sommets);
}
protected:
inline T triangle_integration( const I &fc, Vect3 *vertices)
{// compute double area of triangle defined by vertices
Vect3 crossprod=(vertices[1]-vertices[0])^(vertices[2]-vertices[0]);
double S = crossprod.norm();
T result = 0;
static Vect3 zero(0.0,0.0,0.0);
for(int i=0;i<nbPts[order];i++)
{
Vect3 v=zero;
for(int j=0;j<3;j++) {
v.multadd(cordBars[order][i][j],vertices[j]);
}
multadd(result,cordBars[order][i][3],fc.f(v));
}
return result*S;
}
};
template<class T,class I>
class OPENMEEG_EXPORT AdaptiveIntegrator : public Integrator<T,I>
{
public:
inline AdaptiveIntegrator() : tolerance(0.0001) {}
inline AdaptiveIntegrator(double tol) : tolerance(tol) {}
inline ~AdaptiveIntegrator() {}
inline double norm(double a) {
return fabs(a);
}
inline double norm(Vect3 a) {
return a.norm();
}
virtual inline T integrate(const I &fc, const Triangle& Trg ,const Mesh& M)
{
int n=0;
Vect3 vertices[3]={M.getPt(Trg.s1()),M.getPt(Trg.s2()),M.getPt(Trg.s3())};
T I0=this->triangle_integration(fc,vertices);
return adaptive_integration(fc,vertices,I0,n);
}
private:
double tolerance;
inline T adaptive_integration(const I &fc,const Vect3 *vertices,T I0,int n)
{
Vect3 newpoint0(0.0,0.0,0.0);
multadd(newpoint0,0.5,vertices[0]);
multadd(newpoint0,0.5,vertices[1]);
Vect3 newpoint1(0.0,0.0,0.0);
multadd(newpoint1,0.5,vertices[1]);
multadd(newpoint1,0.5,vertices[2]);
Vect3 newpoint2(0.0,0.0,0.0);
multadd(newpoint2,0.5,vertices[2]);
multadd(newpoint2,0.5,vertices[0]);
Vect3 vertices1[3]={vertices[0],newpoint0,newpoint2};
Vect3 vertices2[3]={vertices[1],newpoint1,newpoint0};
Vect3 vertices3[3]={vertices[2],newpoint2,newpoint1};
Vect3 vertices4[3]={newpoint0,newpoint1,newpoint2};
T I1=this->triangle_integration(fc,vertices1);
T I2=this->triangle_integration(fc,vertices2);
T I3=this->triangle_integration(fc,vertices3);
T I4=this->triangle_integration(fc,vertices4);
T sum=I1+I2+I3+I4;
if (norm(I0-sum)>tolerance*norm(I0)){
n=n+1;
if (n<10) {
I1 = adaptive_integration(fc,vertices1,I1,n);
I2 = adaptive_integration(fc,vertices2,I2,n);
I3 = adaptive_integration(fc,vertices3,I3,n);
I4 = adaptive_integration(fc,vertices4,I4,n);
I0 = I1+I2+I3+I4;
}
}
return I0;
}
};
}
#endif //! OPENMEEG_INTEGRATOR_H
|