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JFIT::JSimplex< JModel_t > Class Template Reference

Simple fit method based on Powell's algorithm, see reference: Numerical Recipes in C++, W.H. More...

#include <JSimplex.hh>

Inheritance diagram for JFIT::JSimplex< JModel_t >:
JEEP::JMessage< T > JACOUSTICS::JKatoomba< JSimplex >

Public Types

typedef double result_type
 

Public Member Functions

 JSimplex ()
 Default constructor. More...
 
template<class JFunction_t , class T >
double operator() (const JFunction_t &fit, T __begin, T __end)
 Multi-dimensional fit. More...
 
template<class JFunction_t , class T >
double operator() (const JFunction_t &fit, T __begin, T __end, const JModel_t &step)
 1D fit. More...
 

Public Attributes

JModel_t value
 
std::vector< JModel_t > step
 
int numberOfIterations
 

Static Public Attributes

static int MAXIMUM_ITERATIONS = 1000
 maximal number of iterations More...
 
static double EPSILON = 1.0e-4
 maximal distance to minimum More...
 
static int debug = 0
 debug level (default is off). More...
 

Private Member Functions

template<class JFunction_t , class T >
double evaluate (const JFunction_t &fit, T __begin, T __end) const
 Evaluate chi2 for given data set. More...
 

Private Attributes

JModel_t p0
 
JModel_t p1
 
JModel_t wall
 

Detailed Description

template<class JModel_t>
class JFIT::JSimplex< JModel_t >

Simple fit method based on Powell's algorithm, see reference: Numerical Recipes in C++, W.H.

Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press.

The template argument refers to the model that should be fitted to the data. This data structure should have arithmetic capabalities.

The data member JSimplex::value corresponds to the start, current or final value of the model of the fit procedure. The data member JSimplex::step corresponds to the step directions. Note that the step directions may change during the fit. The template fit function should return the data type JGandalf::result_type which is composed of the values of the chi2 and gradient of a hit. The function operator returns the chi2 of the fit.

Definition at line 42 of file JSimplex.hh.

Member Typedef Documentation

template<class JModel_t>
typedef double JFIT::JSimplex< JModel_t >::result_type

Definition at line 47 of file JSimplex.hh.

Constructor & Destructor Documentation

template<class JModel_t>
JFIT::JSimplex< JModel_t >::JSimplex ( )
inline

Default constructor.

Definition at line 55 of file JSimplex.hh.

56  {}

Member Function Documentation

template<class JModel_t>
template<class JFunction_t , class T >
double JFIT::JSimplex< JModel_t >::operator() ( const JFunction_t &  fit,
T  __begin,
T  __end 
)
inline

Multi-dimensional fit.

The given fit function should return the equivalent of chi2 for the current value of the given model and a given data point.

Parameters
fitfit function
__beginbegin of data
__endend of data
Returns
chi2

Definition at line 71 of file JSimplex.hh.

72  {
73  using namespace std;
74  using namespace JPP;
75 
76  double chi2_old = evaluate(fit, __begin, __end);
77 
78  const int N = step.size();
79 
80  if (N != 0) {
81 
82  p0 = value;
83  p1 = value;
84  wall = value;
85 
86  double chi2[N];
87 
88  numberOfIterations = 0;
89 
90  while (numberOfIterations != MAXIMUM_ITERATIONS) {
91 
92  DEBUG("old: " << FIXED(12,5) << chi2_old << endl);
93 
94  p0 = value;
95 
96  for (int i = 0; i != N; ++i) {
97 
98  DEBUG("step: " << i << ' ' << setw(5) << numberOfIterations << endl);
99 
100  chi2[i] = (*this)(fit, __begin, __end, step[i]);
101  }
102 
103  // overall step direction of last iteration
104 
105  wall = value;
106  wall -= p0;
107 
108  const double chi2_new = (*this)(fit, __begin, __end, wall);
109 
110  DEBUG("new: " << FIXED(12,5) << chi2_new << endl);
111 
112 
113  if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {
114  return chi2_new;
115  }
116 
117  // double overall step
118 
119  wall = value;
120  wall -= p0;
121  value += wall;
122 
123  const double fe = evaluate(fit, __begin, __end);
124 
125  value -= wall;
126 
127 
128  for (int i = N-1; i != 0; --i) {
129  chi2[i] = chi2[i-1] - chi2[i];
130  }
131 
132  chi2[0] = chi2_old - chi2[0];
133 
134 
135  double df = 0.0;
136 
137  for (int i = 0; i != N; ++i) {
138  if (chi2[i] > df) {
139  df = chi2[i];
140  }
141  }
142 
143  const double fn = chi2_new;
144  const double f0 = chi2_old;
145  const double ff = f0 - fn - df;
146 
147  // shift step directions
148 
149  if (fe < f0 && 2.0*(f0 - 2.0*fn + fe)*ff*ff < (f0-fe)*(f0-fe)*df) {
150 
151  for (int i = 0; i != N - 1; ++i) {
152  step[i] = step[i+1];
153  }
154 
155  step[N-1] = wall;
156  }
157 
158  chi2_old = chi2_new;
159  }
160  }
161 
162  return chi2_old;
163  }
FIXED
Auxiliary data structure for floating point format specification.
Definition: JManip.hh:446
JFIT::JSimplex::p1
JModel_t p1
Definition: JSimplex.hh:265
JFIT::JSimplex::numberOfIterations
int numberOfIterations
Definition: JSimplex.hh:242
JFIT::JSimplex::value
JModel_t value
Definition: JSimplex.hh:240
N
then usage $script< input file >[option[primary[working directory]]] nWhere option can be N
Definition: JMuonPostfit.sh:36
JFIT::JSimplex::p0
JModel_t p0
Definition: JSimplex.hh:264
JFIT::JSimplex::wall
JModel_t wall
Definition: JSimplex.hh:266
chi2
then if[[!-f $DETECTOR]] then JDetector sh $DETECTOR fi cat $WORKDIR trigger_parameters txt<< EOFtrigger3DMuon.enabled=1;trigger3DMuon.numberOfHits=5;trigger3DMuon.gridAngle_deg=1;ctMin=0.0;TMaxLocal_ns=15.0;EOF set_variable TRIGGEREFFICIENCY_TRIGGERED_EVENTS_ONLY INPUT_FILES=() for((i=1;$i<=$NUMBER_OF_RUNS;++i));do JSirene.sh $DETECTOR $JPP_DATA/genhen.km3net_wpd_V2_0.evt.gz $WORKDIR/sirene_ ${i}.root JTriggerEfficiency.sh $DETECTOR $DETECTOR $WORKDIR/sirene_ ${i}.root $WORKDIR/trigger_efficiency_ ${i}.root $WORKDIR/trigger_parameters.txt $JPP_DATA/PMT_parameters.txt INPUT_FILES+=($WORKDIR/trigger_efficiency_ ${i}.root) done for ANGLE_DEG in $ANGLES_DEG[*];do set_variable SIGMA_NS 3.0 set_variable OUTLIERS 3 set_variable OUTPUT_FILE $WORKDIR/matrix\[${ANGLE_DEG}\deg\].root $JPP_DIR/examples/JReconstruction-f"$INPUT_FILES[*]"-o $OUTPUT_FILE-S ${SIGMA_NS}-A ${ANGLE_DEG}-O ${OUTLIERS}-d ${DEBUG}--!fiif[[$OPTION=="plot"]];then if((0));then for H1 in h0 h1;do JPlot1D-f"$WORKDIR/matrix["${^ANGLES_DEG}" deg].root:${H1}"-y"1 2e3"-Y-L TR-T""-\^"number of events [a.u.]"-> o chi2
Definition: JMatrixNZ.sh:106
JFIT::JSimplex::evaluate
double evaluate(const JFunction_t &fit, T __begin, T __end) const
Evaluate chi2 for given data set.
Definition: JSimplex.hh:253
JFIT::JSimplex::MAXIMUM_ITERATIONS
static int MAXIMUM_ITERATIONS
maximal number of iterations
Definition: JSimplex.hh:237
JFIT::JSimplex::EPSILON
static double EPSILON
maximal distance to minimum
Definition: JSimplex.hh:238
DEBUG
#define DEBUG(A)
Message macros.
Definition: JMessage.hh:62
JFIT::JSimplex::step
std::vector< JModel_t > step
Definition: JSimplex.hh:241
template<class JModel_t>
template<class JFunction_t , class T >
double JFIT::JSimplex< JModel_t >::operator() ( const JFunction_t &  fit,
T  __begin,
T  __end,
const JModel_t &  step 
)
inline

1D fit.

The given fit function should return the equivalent of chi2 for the current value of the given model and a given data point.

Parameters
fitfit function
__beginbegin of data
__endend of data
stepstep direction

Definition at line 178 of file JSimplex.hh.

179  {
180  using namespace std;
181  using namespace JPP;
182 
183  double lambda = 0.5; // control parameter
184  double factor = 1.0; // multiplication factor
185 
186  double chi2_old = evaluate(fit, __begin, __end);
187 
188  for (int i = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations, ++i) {
189 
190  p1 = step;
191  p1 *= lambda;
192  value += p1;
193 
194  const double chi2_new = evaluate(fit, __begin, __end);
195 
196  DEBUG("step: " << setw(3) << i << ' ' << FIXED(12,5) << chi2_old << ' ' << FIXED(12,5) << chi2_new << ' ' << FIXED(5,2) << lambda << endl);
197 
198  if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {
199 
200  if (chi2_new > chi2_old) {
201 
202  p1 = step;
203  p1 *= lambda;
204  value -= p1; // undo last step
205 
206  return chi2_old;
207 
208  } else {
209 
210  return chi2_new;
211  }
212  }
213 
214  if (chi2_new < chi2_old) {
215 
216  chi2_old = chi2_new;
217 
218  } else {
219 
220  p1 = step;
221  p1 *= lambda;
222  value -= p1; // step back
223  lambda = -lambda; // change direction
224 
225  if (i != 0) {
226  factor = 0.5; // reduce step size
227  }
228  }
229 
230  lambda = factor * lambda;
231  }
232 
233  return chi2_old;
234  }
FIXED
Auxiliary data structure for floating point format specification.
Definition: JManip.hh:446
JFIT::JSimplex::p1
JModel_t p1
Definition: JSimplex.hh:265
JFIT::JSimplex::numberOfIterations
int numberOfIterations
Definition: JSimplex.hh:242
JFIT::JSimplex::value
JModel_t value
Definition: JSimplex.hh:240
JFIT::JSimplex::evaluate
double evaluate(const JFunction_t &fit, T __begin, T __end) const
Evaluate chi2 for given data set.
Definition: JSimplex.hh:253
JFIT::JSimplex::MAXIMUM_ITERATIONS
static int MAXIMUM_ITERATIONS
maximal number of iterations
Definition: JSimplex.hh:237
JFIT::JSimplex::EPSILON
static double EPSILON
maximal distance to minimum
Definition: JSimplex.hh:238
DEBUG
#define DEBUG(A)
Message macros.
Definition: JMessage.hh:62
JFIT::JSimplex::step
std::vector< JModel_t > step
Definition: JSimplex.hh:241
template<class JModel_t>
template<class JFunction_t , class T >
double JFIT::JSimplex< JModel_t >::evaluate ( const JFunction_t &  fit,
T  __begin,
T  __end 
) const
inlineprivate

Evaluate chi2 for given data set.

Parameters
fitfit function
__beginbegin of data
__endend of data

Definition at line 253 of file JSimplex.hh.

254  {
255  double chi2 = 0.0;
256 
257  for (T hit = __begin; hit != __end; ++hit) {
258  chi2 += fit(value, *hit);
259  }
260 
261  return chi2;
262  }
T
do set_variable OUTPUT_DIRECTORY $WORKDIR T
Definition: JCalibrateHeight.sh:61
JFIT::JSimplex::value
JModel_t value
Definition: JSimplex.hh:240
chi2
then if[[!-f $DETECTOR]] then JDetector sh $DETECTOR fi cat $WORKDIR trigger_parameters txt<< EOFtrigger3DMuon.enabled=1;trigger3DMuon.numberOfHits=5;trigger3DMuon.gridAngle_deg=1;ctMin=0.0;TMaxLocal_ns=15.0;EOF set_variable TRIGGEREFFICIENCY_TRIGGERED_EVENTS_ONLY INPUT_FILES=() for((i=1;$i<=$NUMBER_OF_RUNS;++i));do JSirene.sh $DETECTOR $JPP_DATA/genhen.km3net_wpd_V2_0.evt.gz $WORKDIR/sirene_ ${i}.root JTriggerEfficiency.sh $DETECTOR $DETECTOR $WORKDIR/sirene_ ${i}.root $WORKDIR/trigger_efficiency_ ${i}.root $WORKDIR/trigger_parameters.txt $JPP_DATA/PMT_parameters.txt INPUT_FILES+=($WORKDIR/trigger_efficiency_ ${i}.root) done for ANGLE_DEG in $ANGLES_DEG[*];do set_variable SIGMA_NS 3.0 set_variable OUTLIERS 3 set_variable OUTPUT_FILE $WORKDIR/matrix\[${ANGLE_DEG}\deg\].root $JPP_DIR/examples/JReconstruction-f"$INPUT_FILES[*]"-o $OUTPUT_FILE-S ${SIGMA_NS}-A ${ANGLE_DEG}-O ${OUTLIERS}-d ${DEBUG}--!fiif[[$OPTION=="plot"]];then if((0));then for H1 in h0 h1;do JPlot1D-f"$WORKDIR/matrix["${^ANGLES_DEG}" deg].root:${H1}"-y"1 2e3"-Y-L TR-T""-\^"number of events [a.u.]"-> o chi2
Definition: JMatrixNZ.sh:106

Member Data Documentation

template<class JModel_t>
int JFIT::JSimplex< JModel_t >::MAXIMUM_ITERATIONS = 1000
static

maximal number of iterations

maximal number of iterations.

Definition at line 237 of file JSimplex.hh.

template<class JModel_t>
double JFIT::JSimplex< JModel_t >::EPSILON = 1.0e-4
static

maximal distance to minimum

maximal distance to minimum.

Definition at line 238 of file JSimplex.hh.

template<class JModel_t>
JModel_t JFIT::JSimplex< JModel_t >::value

Definition at line 240 of file JSimplex.hh.

template<class JModel_t>
std::vector<JModel_t> JFIT::JSimplex< JModel_t >::step

Definition at line 241 of file JSimplex.hh.

template<class JModel_t>
int JFIT::JSimplex< JModel_t >::numberOfIterations

Definition at line 242 of file JSimplex.hh.

template<class JModel_t>
JModel_t JFIT::JSimplex< JModel_t >::p0
mutableprivate

Definition at line 264 of file JSimplex.hh.

template<class JModel_t>
JModel_t JFIT::JSimplex< JModel_t >::p1
mutableprivate

Definition at line 265 of file JSimplex.hh.

template<class JModel_t>
JModel_t JFIT::JSimplex< JModel_t >::wall
mutableprivate

Definition at line 266 of file JSimplex.hh.

template<class T>
int JEEP::JMessage< T >::debug = 0
staticinherited

debug level (default is off).

Definition at line 45 of file JMessage.hh.

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