Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2012-2023 The plumed team
3 : (see the PEOPLE file at the root of the distribution for a list of names)
4 :
5 : See http://www.plumed.org for more information.
6 :
7 : This file is part of plumed, version 2.
8 :
9 : plumed is free software: you can redistribute it and/or modify
10 : it under the terms of the GNU Lesser General Public License as published by
11 : the Free Software Foundation, either version 3 of the License, or
12 : (at your option) any later version.
13 :
14 : plumed is distributed in the hope that it will be useful,
15 : but WITHOUT ANY WARRANTY; without even the implied warranty of
16 : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 : GNU Lesser General Public License for more details.
18 :
19 : You should have received a copy of the GNU Lesser General Public License
20 : along with plumed. If not, see <http://www.gnu.org/licenses/>.
21 : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
22 : #include "KernelFunctions.h"
23 : #include "IFile.h"
24 : #include <iostream>
25 : #include <cmath>
26 :
27 : namespace PLMD {
28 :
29 : //+PLUMEDOC INTERNAL kernelfunctions
30 : /*
31 : Functions that are used to construct histograms
32 :
33 : Constructing histograms is something you learned to do relatively early in life. You perform an experiment a number of times,
34 : count the number of times each result comes up and then draw a bar graph that describes how often each of the results came up.
35 : This only works when there are a finite number of possible results. If the result a number between 0 and 1 the bar chart is
36 : less easy to draw as there are as many possible results as there are numbers between zero and one - an infinite number.
37 : To resolve this problem we replace probability, \f$P\f$ with probability density, \f$\pi\f$, and write the probability of getting
38 : a number between \f$a\f$ and \f$b\f$ as:
39 :
40 : \f[
41 : P = \int_{a}^b \textrm{d}x \pi(x)
42 : \f]
43 :
44 : To calculate probability densities from a set of results we use a process called kernel density estimation.
45 : Histograms are accumulated by adding up kernel functions, \f$K\f$, with finite spatial extent, that integrate to one.
46 : These functions are centered on each of the \f$n\f$-dimensional data points, \f$\mathbf{x}_i\f$. The overall effect of this
47 : is that each result we obtain in our experiments contributes to the probability density in a finite sized region of the space.
48 :
49 : Expressing all this mathematically in kernel density estimation we write the probability density as:
50 :
51 : \f[
52 : \pi(\mathbf{x}) = \sum_i K\left[ (\mathbf{x} - \mathbf{x}_i)^T \Sigma (\mathbf{x} - \mathbf{x}_i) \right]
53 : \f]
54 :
55 : where \f$\Sigma\f$ is an \f$n \times n\f$ matrix called the bandwidth that controls the spatial extent of
56 : the kernel. Whenever we accumulate a histogram (e.g. in \ref HISTOGRAM or in \ref METAD) we use this
57 : technique.
58 :
59 : There is thus some flexibility in the particular function we use for \f$K[\mathbf{r}]\f$ in the above.
60 : The following variants are available.
61 :
62 : <table align=center frame=void width=95%% cellpadding=5%%>
63 : <tr>
64 : <td> TYPE </td> <td> FUNCTION </td>
65 : </tr> <tr>
66 : <td> gaussian </td> <td> \f$f(r) = \frac{1}{(2 \pi)^{n} \sqrt{|\Sigma^{-1}|}} \exp\left(-0.5 r^2 \right)\f$ </td>
67 : </tr> <tr>
68 : <td> truncated-gaussian </td> <td> \f$f(r) = \frac{1}{(2 \pi)^{n} \sqrt{|\Sigma^{-1}|} \left(\frac{\mathrm{erf}(-6.25/sqrt{2}) - \mathrm{erf}(-6.25/sqrt{2})}{2}\right)^n} \exp\left(-0.5 r^2 \right)\f$ </td>
69 : </tr> <tr>
70 : <td> triangular </td> <td> \f$f(r) = \frac{3}{V} ( 1 - | r | )H(1-|r|) \f$ </td>
71 : </tr> <tr>
72 : <td> uniform </td> <td> \f$f(r) = \frac{1}{V}H(1-|r|)\f$ </td>
73 : </tr>
74 : </table>
75 :
76 : In the above \f$H(y)\f$ is a function that is equal to one when \f$y>0\f$ and zero when \f$y \le 0\f$. \f$n\f$ is
77 : the dimensionality of the vector \f$\mathbf{x}\f$ and \f$V\f$ is the volume of an ellipse in an \f$n\f$ dimensional
78 : space which is given by:
79 :
80 : \f{eqnarray*}{
81 : V &=& | \Sigma^{-1} | \frac{ \pi^{\frac{n}{2}} }{\left( \frac{n}{2} \right)! } \qquad \textrm{for even} \quad n \\
82 : V &=& | \Sigma^{-1} | \frac{ 2^{\frac{n+1}{2}} \pi^{\frac{n-1}{2}} }{ n!! }
83 : \f}
84 :
85 : In \ref METAD the normalization constants are ignored so that the value of the function at \f$r=0\f$ is equal
86 : to one. In addition in \ref METAD we must be able to differentiate the bias in order to get forces. This limits
87 : the kernels we can use in this method. Notice also that Gaussian kernels should have infinite support. When used
88 : with grids, however, they are assumed to only be non-zero over a finite range. The difference between the
89 : truncated-gaussian and regular gaussian is that the truncated gaussian is scaled so that its integral over the grid
90 : is equal to one when it is normalized. The integral of a regular gaussian when it is evaluated on a grid will be
91 : slightly less that one because of the truncation of a function that should have infinite support.
92 : */
93 : //+ENDPLUMEDOC
94 :
95 0 : KernelFunctions::KernelFunctions( const std::string& input ) {
96 :
97 0 : if(!dp2cutoffNoStretch()) {
98 0 : stretchA=dp2cutoffA;
99 0 : stretchB=dp2cutoffB;
100 : }
101 :
102 0 : std::vector<std::string> data=Tools::getWords(input);
103 0 : std::string name=data[0];
104 : data.erase(data.begin());
105 :
106 : std::vector<double> at;
107 0 : bool foundc = Tools::parseVector(data,"CENTER",at);
108 0 : if(!foundc) plumed_merror("failed to find center keyword in definition of kernel");
109 : std::vector<double> sig;
110 0 : bool founds = Tools::parseVector(data,"SIGMA",sig);
111 0 : if(!founds) plumed_merror("failed to find sigma keyword in definition of kernel");
112 :
113 0 : bool multi=false; Tools::parseFlag(data,"MULTIVARIATE",multi);
114 0 : bool vonmises=false; Tools::parseFlag(data,"VON-MISSES",vonmises);
115 0 : if( center.size()==1 && multi ) plumed_merror("one dimensional kernel cannot be multivariate");
116 0 : if( center.size()==1 && vonmises ) plumed_merror("one dimensional kernal cannot be von-misses");
117 0 : if( center.size()==1 && sig.size()!=1 ) plumed_merror("size mismatch between center size and sigma size");
118 0 : if( multi && center.size()>1 && sig.size()!=0.5*center.size()*(center.size()-1) ) plumed_merror("size mismatch between center size and sigma size");
119 0 : if( !multi && center.size()>1 && sig.size()!=center.size() ) plumed_merror("size mismatch between center size and sigma size");
120 :
121 : double h;
122 0 : bool foundh = Tools::parse(data,"HEIGHT",h);
123 0 : if( !foundh) h=1.0;
124 :
125 0 : if( multi ) setData( at, sig, name, "MULTIVARIATE", h );
126 0 : else if( vonmises ) setData( at, sig, name, "VON-MISSES", h );
127 0 : else setData( at, sig, name, "DIAGONAL", h );
128 0 : }
129 :
130 5563 : KernelFunctions::KernelFunctions( const std::vector<double>& at, const std::vector<double>& sig, const std::string& type, const std::string& mtype, const double& w ) {
131 :
132 5563 : if(!dp2cutoffNoStretch()) {
133 5563 : stretchA=dp2cutoffA;
134 5563 : stretchB=dp2cutoffB;
135 : }
136 :
137 5563 : setData( at, sig, type, mtype, w );
138 5563 : }
139 :
140 0 : KernelFunctions::KernelFunctions( const KernelFunctions* in ):
141 0 : dtype(in->dtype),
142 0 : ktype(in->ktype),
143 0 : center(in->center),
144 0 : width(in->width),
145 0 : height(in->height)
146 : {
147 0 : if(!dp2cutoffNoStretch()) {
148 0 : stretchA=dp2cutoffA;
149 0 : stretchB=dp2cutoffB;
150 : }
151 0 : }
152 :
153 5563 : void KernelFunctions::setData( const std::vector<double>& at, const std::vector<double>& sig, const std::string& type, const std::string& mtype, const double& w ) {
154 :
155 5563 : height=w;
156 16688 : center.resize( at.size() ); for(unsigned i=0; i<at.size(); ++i) center[i]=at[i];
157 21056 : width.resize( sig.size() ); for(unsigned i=0; i<sig.size(); ++i) width[i]=sig[i];
158 5563 : if( mtype=="MULTIVARIATE" ) dtype=multi;
159 1195 : else if( mtype=="VON-MISSES" ) dtype=vonmises;
160 1195 : else if( mtype=="DIAGONAL" ) dtype=diagonal;
161 0 : else plumed_merror(mtype + " is not a valid metric type");
162 :
163 : // Setup the kernel type
164 11126 : if(type=="GAUSSIAN" || type=="gaussian" ) {
165 0 : ktype=gaussian;
166 11126 : } else if(type=="STRETCHED-GAUSSIAN" || type=="stretched-gaussian" ) {
167 5563 : ktype=stretchedgaussian;
168 0 : } else if(type=="TRUNCATED-GAUSSIAN" || type=="truncated-gaussian" ) {
169 0 : ktype=truncatedgaussian;
170 0 : } else if(type=="UNIFORM" || type=="uniform") {
171 0 : ktype=uniform;
172 0 : } else if(type=="TRIANGULAR" || type=="triangular") {
173 0 : ktype=triangular;
174 : } else {
175 0 : plumed_merror(type+" is an invalid kernel type\n");
176 : }
177 5563 : }
178 :
179 0 : void KernelFunctions::normalize( const std::vector<Value*>& myvals ) {
180 :
181 : double det=1.;
182 : unsigned ncv=ndim();
183 0 : if(dtype==diagonal) {
184 0 : for(unsigned i=0; i<width.size(); ++i) det*=width[i]*width[i];
185 0 : } else if(dtype==multi) {
186 0 : Matrix<double> mymatrix( getMatrix() ), myinv( ncv, ncv );
187 0 : Invert(mymatrix,myinv); double logd;
188 0 : logdet( myinv, logd );
189 0 : det=std::exp(logd);
190 : }
191 0 : if( dtype==diagonal || dtype==multi ) {
192 : double volume;
193 0 : if( ktype==gaussian || ktype==stretchedgaussian ) {
194 0 : volume=pow( 2*pi, 0.5*ncv ) * pow( det, 0.5 );
195 0 : } else if( ktype==truncatedgaussian ) {
196 : // This makes it so the gaussian integrates to one over the range over which it has support
197 : const double DP2CUTOFF=std::sqrt(6.25);
198 0 : volume=pow( 2*pi, 0.5*ncv ) * pow( det, 0.5 ) * pow( 0.5 * ( erf(DP2CUTOFF) - erf(-DP2CUTOFF) ), ncv);
199 0 : } else if( ktype==uniform || ktype==triangular ) {
200 0 : if( ncv%2==1 ) {
201 : double dfact=1;
202 0 : for(unsigned i=1; i<ncv; i+=2) dfact*=static_cast<double>(i);
203 0 : volume=( pow( pi, (ncv-1)/2 ) ) * ( pow( 2., (ncv+1)/2 ) ) / dfact;
204 : } else {
205 : double fact=1.;
206 0 : for(unsigned i=1; i<ncv/2; ++i) fact*=static_cast<double>(i);
207 0 : volume=pow( pi,ncv/2 ) / fact;
208 : }
209 0 : if(ktype==uniform) volume*=det;
210 0 : else if(ktype==triangular) volume*=det / 3.;
211 : } else {
212 0 : plumed_merror("not a valid kernel type");
213 : }
214 0 : height /= volume;
215 0 : return;
216 : }
217 0 : plumed_assert( dtype==vonmises && ktype==gaussian );
218 : // Now calculate determinant for aperiodic variables
219 : unsigned naper=0;
220 0 : for(unsigned i=0; i<ncv; ++i) {
221 0 : if( !myvals[i]->isPeriodic() ) naper++;
222 : }
223 : // Now construct sub matrix
224 : double volume=1;
225 0 : if( naper>0 ) {
226 : unsigned isub=0;
227 0 : Matrix<double> mymatrix( getMatrix() ), mysub( naper, naper );
228 0 : for(unsigned i=0; i<ncv; ++i) {
229 0 : if( myvals[i]->isPeriodic() ) continue;
230 : unsigned jsub=0;
231 0 : for(unsigned j=0; j<ncv; ++j) {
232 0 : if( myvals[j]->isPeriodic() ) continue;
233 0 : mysub( isub, jsub ) = mymatrix( i, j ); jsub++;
234 : }
235 0 : isub++;
236 : }
237 : Matrix<double> myisub( naper, naper ); double logd;
238 0 : Invert( mysub, myisub ); logdet( myisub, logd );
239 0 : det=std::exp(logd);
240 0 : volume=pow( 2*pi, 0.5*ncv ) * pow( det, 0.5 );
241 : }
242 :
243 : // Calculate volume of periodic variables
244 : unsigned nper=0;
245 0 : for(unsigned i=0; i<ncv; ++i) {
246 0 : if( myvals[i]->isPeriodic() ) nper++;
247 : }
248 :
249 : // Now construct sub matrix
250 0 : if( nper>0 ) {
251 : unsigned isub=0;
252 0 : Matrix<double> mymatrix( getMatrix() ), mysub( nper, nper );
253 0 : for(unsigned i=0; i<ncv; ++i) {
254 0 : if( !myvals[i]->isPeriodic() ) continue;
255 : unsigned jsub=0;
256 0 : for(unsigned j=0; j<ncv; ++j) {
257 0 : if( !myvals[j]->isPeriodic() ) continue;
258 0 : mysub( isub, jsub ) = mymatrix( i, j ); jsub++;
259 : }
260 0 : isub++;
261 : }
262 : Matrix<double> eigvec( nper, nper );
263 0 : std::vector<double> eigval( nper );
264 0 : diagMat( mysub, eigval, eigvec );
265 : unsigned iper=0; volume=1;
266 0 : for(unsigned i=0; i<ncv; ++i) {
267 0 : if( myvals[i]->isPeriodic() ) {
268 0 : volume *= myvals[i]->getMaxMinusMin()*Tools::bessel0(eigval[iper])*std::exp(-eigval[iper]);
269 0 : iper++;
270 : }
271 : }
272 : }
273 0 : height /= volume;
274 : }
275 :
276 10033 : double KernelFunctions::getCutoff( const double& width ) const {
277 : const double DP2CUTOFF=6.25;
278 10033 : if( ktype==gaussian || ktype==truncatedgaussian || ktype==stretchedgaussian ) return std::sqrt(2.0*DP2CUTOFF)*width;
279 0 : else if(ktype==triangular ) return width;
280 0 : else if(ktype==uniform) return width;
281 0 : else plumed_merror("No valid kernel type");
282 : return 0.0;
283 : }
284 :
285 5017 : std::vector<double> KernelFunctions::getContinuousSupport( ) const {
286 : unsigned ncv=ndim();
287 5017 : std::vector<double> support( ncv );
288 5017 : if(dtype==diagonal) {
289 1946 : for(unsigned i=0; i<ncv; ++i) support[i]=getCutoff(width[i]);
290 4368 : } else if(dtype==multi) {
291 4368 : Matrix<double> mymatrix( getMatrix() ), myinv( ncv,ncv );
292 4368 : Invert(mymatrix,myinv);
293 4368 : Matrix<double> myautovec(ncv,ncv); std::vector<double> myautoval(ncv);
294 4368 : diagMat(myinv,myautoval,myautovec);
295 : double maxautoval=0.;
296 : unsigned ind_maxautoval=0;
297 13104 : for (unsigned i=0; i<ncv; i++) {
298 8736 : if(myautoval[i]>maxautoval) {maxautoval=myautoval[i]; ind_maxautoval=i;}
299 : }
300 13104 : for(unsigned i=0; i<ncv; ++i) {
301 8736 : double extent=std::fabs(std::sqrt(maxautoval)*myautovec(i,ind_maxautoval));
302 8736 : support[i]=getCutoff( extent );
303 : }
304 : } else {
305 0 : plumed_merror("cannot find support if metric is not multi or diagonal type");
306 : }
307 5017 : return support;
308 : }
309 :
310 3375 : std::vector<unsigned> KernelFunctions::getSupport( const std::vector<double>& dx ) const {
311 3375 : plumed_assert( ndim()==dx.size() );
312 3375 : std::vector<unsigned> support( dx.size() );
313 3375 : std::vector<double> vv=getContinuousSupport( );
314 10124 : for(unsigned i=0; i<dx.size(); ++i) support[i]=static_cast<unsigned>(ceil( vv[i]/dx[i] ));
315 3375 : return support;
316 : }
317 :
318 1024305 : double KernelFunctions::evaluate( const std::vector<Value*>& pos, std::vector<double>& derivatives, bool usederiv, bool doInt, double lowI_, double uppI_) const {
319 : plumed_dbg_assert( pos.size()==ndim() && derivatives.size()==ndim() );
320 : #ifndef NDEBUG
321 : if( usederiv ) plumed_massert( ktype!=uniform, "step function can not be differentiated" );
322 : #endif
323 1024305 : if(doInt) {
324 : plumed_dbg_assert(center.size()==1);
325 0 : if(pos[0]->get()<lowI_) pos[0]->set(lowI_);
326 0 : if(pos[0]->get()>uppI_) pos[0]->set(uppI_);
327 : }
328 : double r2=0;
329 1024305 : if(dtype==diagonal) {
330 161311 : for(unsigned i=0; i<ndim(); ++i) {
331 107510 : derivatives[i]=-pos[i]->difference( center[i] ) / width[i];
332 107510 : r2+=derivatives[i]*derivatives[i];
333 107510 : derivatives[i] /= width[i];
334 : }
335 970504 : } else if(dtype==multi) {
336 970504 : Matrix<double> mymatrix( getMatrix() );
337 2911512 : for(unsigned i=0; i<mymatrix.nrows(); ++i) {
338 1941008 : double dp_i, dp_j; derivatives[i]=0;
339 1941008 : dp_i=-pos[i]->difference( center[i] );
340 5823024 : for(unsigned j=0; j<mymatrix.ncols(); ++j) {
341 3882016 : if(i==j) dp_j=dp_i;
342 1941008 : else dp_j=-pos[j]->difference( center[j] );
343 :
344 3882016 : derivatives[i]+=mymatrix(i,j)*dp_j;
345 3882016 : r2+=dp_i*dp_j*mymatrix(i,j);
346 : }
347 : }
348 0 : } else if(dtype==vonmises) {
349 0 : std::vector<double> costmp( ndim() ), sintmp( ndim() ), sinout( ndim(), 0.0 );
350 0 : for(unsigned i=0; i<ndim(); ++i) {
351 0 : if( pos[i]->isPeriodic() ) {
352 0 : sintmp[i]=std::sin( 2.*pi*(pos[i]->get() - center[i])/pos[i]->getMaxMinusMin() );
353 0 : costmp[i]=std::cos( 2.*pi*(pos[i]->get() - center[i])/pos[i]->getMaxMinusMin() );
354 : } else {
355 0 : sintmp[i]=pos[i]->get() - center[i];
356 0 : costmp[i]=1.0;
357 : }
358 : }
359 :
360 0 : Matrix<double> mymatrix( getMatrix() );
361 0 : for(unsigned i=0; i<mymatrix.nrows(); ++i) {
362 0 : derivatives[i]=0;
363 0 : if( pos[i]->isPeriodic() ) {
364 0 : r2+=2*( 1 - costmp[i] )*mymatrix(i,i);
365 : } else {
366 0 : r2+=sintmp[i]*sintmp[i]*mymatrix(i,i);
367 : }
368 0 : for(unsigned j=0; j<mymatrix.ncols(); ++j) {
369 0 : if( i!=j ) sinout[i]+=mymatrix(i,j)*sintmp[j];
370 : }
371 0 : derivatives[i] = mymatrix(i,i)*sintmp[i] + sinout[i]*costmp[i];
372 0 : if( pos[i]->isPeriodic() ) derivatives[i] *= (2*pi/pos[i]->getMaxMinusMin());
373 : }
374 0 : for(unsigned i=0; i<sinout.size(); ++i) r2+=sintmp[i]*sinout[i];
375 : }
376 : double kderiv, kval;
377 1024305 : if(ktype==gaussian || ktype==truncatedgaussian) {
378 0 : kval=height*std::exp(-0.5*r2); kderiv=-kval;
379 1024305 : } else if(ktype==stretchedgaussian) {
380 1024305 : auto dp=0.5*r2;
381 1024305 : if(dp<dp2cutoff) {
382 630478 : auto ee=std::exp(-0.5*r2);
383 630478 : kval=height*(stretchA*ee+stretchB);
384 630478 : kderiv=-height*stretchA*ee;
385 : } else {
386 : kval=0.0;
387 : kderiv=0.0;
388 : }
389 : } else {
390 0 : double r=std::sqrt(r2);
391 0 : if(ktype==triangular) {
392 0 : if( r<1.0 ) {
393 : if(r==0) kderiv=0;
394 0 : kderiv=-1; kval=height*( 1. - std::fabs(r) );
395 : } else {
396 : kval=0.; kderiv=0.;
397 : }
398 0 : } else if(ktype==uniform) {
399 : kderiv=0.;
400 0 : if(r<1.0) kval=height;
401 : else kval=0;
402 : } else {
403 0 : plumed_merror("Not a valid kernel type");
404 : }
405 0 : kderiv*=height / r ;
406 : }
407 3072823 : for(unsigned i=0; i<ndim(); ++i) derivatives[i]*=kderiv;
408 1024305 : if(doInt) {
409 0 : if((pos[0]->get() <= lowI_ || pos[0]->get() >= uppI_) && usederiv ) for(unsigned i=0; i<ndim(); ++i)derivatives[i]=0;
410 : }
411 1024305 : return kval;
412 : }
413 :
414 4471 : std::unique_ptr<KernelFunctions> KernelFunctions::read( IFile* ifile, const bool& cholesky, const std::vector<std::string>& valnames ) {
415 : double h;
416 8942 : if( !ifile->scanField("height",h) ) return NULL;;
417 :
418 4471 : std::string sss; ifile->scanField("multivariate",sss);
419 12321 : std::string ktype="stretched-gaussian"; if( ifile->FieldExist("kerneltype") ) ifile->scanField("kerneltype",ktype);
420 8839 : plumed_massert( sss=="false" || sss=="true" || sss=="von-misses", "multivariate flag must be either false, true or von-misses");
421 :
422 : // Read the position of the center
423 4471 : std::vector<double> cc( valnames.size() );
424 13412 : for(unsigned i=0; i<valnames.size(); ++i) ifile->scanField(valnames[i],cc[i]);
425 :
426 : std::vector<double> sig;
427 4471 : if( sss=="false" ) {
428 103 : sig.resize( valnames.size() );
429 308 : for(unsigned i=0; i<valnames.size(); ++i) {
430 205 : ifile->scanField("sigma_"+valnames[i],sig[i]);
431 205 : if( !cholesky ) sig[i]=std::sqrt(sig[i]);
432 : }
433 : return Tools::make_unique<KernelFunctions>(cc, sig, ktype, "DIAGONAL", h);
434 : }
435 :
436 4368 : unsigned ncv=valnames.size();
437 4368 : sig.resize( (ncv*(ncv+1))/2 );
438 : Matrix<double> upper(ncv,ncv), lower(ncv,ncv), mymult( ncv, ncv ), invmatrix(ncv,ncv);
439 13104 : for(unsigned i=0; i<ncv; ++i) {
440 21840 : for(unsigned j=0; j<ncv-i; j++) {
441 26208 : ifile->scanField("sigma_" +valnames[j+i] + "_" + valnames[j], lower(j+i,j) );
442 13104 : upper(j,j+i)=lower(j+i,j); mymult(j+i,j)=mymult(j,j+i)=lower(j+i,j);
443 : }
444 : }
445 4368 : if( cholesky ) mult(lower,upper,mymult);
446 4368 : Invert( mymult, invmatrix );
447 : unsigned k=0;
448 13104 : for(unsigned i=0; i<ncv; i++) {
449 21840 : for(unsigned j=i; j<ncv; j++) { sig[k]=invmatrix(i,j); k++; }
450 : }
451 4368 : if( sss=="true" ) return Tools::make_unique<KernelFunctions>(cc, sig, ktype, "MULTIVARIATE", h);
452 : return Tools::make_unique<KernelFunctions>( cc, sig, ktype, "VON-MISSES", h );
453 : }
454 :
455 : }
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