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 | //
// Fits nbar(z)
//
#include <iostream>
#include <vector>
#include <cmath>
#include <cassert>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_multimin.h>
#include "msg.h"
#include "cosmology.h"
#include "nbar.h"
#include "nbar_fitting.h"
using namespace std;
static double nbar_multimin_f (const gsl_vector *v, void *params);
static double compute_cost_function(vector<Nbar> const * const vobs,
vector<Nbar> const * const vhod);
NbarFitting* nbar_fitting_alloc(PowerSpectrum const * const ps,
Hod* const hod,
const vector<Nbar>* const vnbar_obs,
const double z_min, const double z_max)
{
// Setup nbar fitting
// z_min, z_max: fitting redshift range
NbarFitting* fitting= new NbarFitting();
NbarIntegration* ni0= nbar_integration_alloc(ps, hod);
const int n= vnbar_obs->size(); assert(n > 0);
fitting->vni.reserve(n);
for(int i=0; i<n; ++i) {
fitting->vni.push_back(new NbarIntegration(ni0));
}
assert(fitting->vni.size() == n);
fitting->hod= hod;
fitting->z_min= z_min;
fitting->z_max= z_max;
fitting->vobs= vnbar_obs;
fitting->vhod= new vector<Nbar>(*vnbar_obs);
fitting->iter= 0;
fitting->chi2= 0.0;
msg_printf(msg_debug, "Allocated nbar_fitting\n");
return fitting;
}
void nbar_fitting_free(NbarFitting* const fitting)
{
const int n= fitting->vni.size();
if(n > 0) {
NbarIntegration* const ni= fitting->vni.front();
nbar_integration_free(ni);
}
for(int i=1; i<n; ++i) {
// i=0 is already freed above
delete fitting->vni[i];
}
delete fitting->vhod;
delete fitting;
}
void nbar_fitting_compute(NbarFitting* fitting)
{
// Compute best fitting logMmin function
// logMmin = c[0] + c[1]*x + c[2]*x^2 + c[3]*x^3
// for given c[4-9] coefficients in fitting->hod->c,
// where x = z - hod::z0
// This function updates fitting->hod->c[0-3]
const int n= fitting->vni.size();
assert(fitting->vhod->size() == n);
assert(fitting->vobs->size() == n);
const int nparam= 4;
// Starting point
gsl_vector* const x = gsl_vector_alloc(nparam);
gsl_vector_set(x, 0, fitting->hod->c[0]);
gsl_vector_set(x, 1, fitting->hod->c[1]);
gsl_vector_set(x, 2, fitting->hod->c[2]);
gsl_vector_set(x, 3, fitting->hod->c[3]);
// initial stepsize
gsl_vector* const ss = gsl_vector_alloc(nparam);
gsl_vector_set(ss, 0, 1.0);
gsl_vector_set(ss, 1, 0.05);
gsl_vector_set(ss, 2, 0.05);
gsl_vector_set(ss, 3, 0.01);
//gsl_vector_set_all(ss, 0.01);
// Initialize method and iterate
gsl_multimin_function minex_func;
minex_func.n = nparam;
minex_func.f = nbar_multimin_f;
minex_func.params = fitting;
gsl_multimin_fminimizer *s=
gsl_multimin_fminimizer_alloc(gsl_multimin_fminimizer_nmsimplex2, nparam);
gsl_multimin_fminimizer_set(s, &minex_func, x, ss);
int iter = 0; int status;
const int max_iter= 1000;
do {
iter++;
status = gsl_multimin_fminimizer_iterate(s);
if(status)
break;
double size= gsl_multimin_fminimizer_size(s);
status = gsl_multimin_test_size(size, 1e-3);
if (status == GSL_SUCCESS) {
msg_printf(msg_verbose, "nbar converged to minimum with %d steps.\n", iter);
}
msg_printf(msg_verbose, "nbar_fitting %3d %e | %.4f %.5f %.5f %.5f %.3f\n",
iter,
s->fval,
gsl_vector_get(s->x, 0),
gsl_vector_get(s->x, 1),
gsl_vector_get(s->x, 2),
gsl_vector_get(s->x, 3),
size);
} while (status == GSL_CONTINUE && iter < max_iter);
if(iter == max_iter) {
msg_printf(msg_warn, "Reached maximum iteration for nbar fitting\n");
}
fitting->hod->c[0]= gsl_vector_get(s->x, 0);
fitting->hod->c[1]= gsl_vector_get(s->x, 1);
fitting->hod->c[2]= gsl_vector_get(s->x, 2);
fitting->hod->c[3]= gsl_vector_get(s->x, 3);
fitting->iter= iter;
msg_printf(msg_verbose, "final c[0-3] %e %e %e %e\n",
gsl_vector_get(s->x, 0),
gsl_vector_get(s->x, 1),
gsl_vector_get(s->x, 2),
gsl_vector_get(s->x, 3));
fitting->chi2= nbar_multimin_f(s->x, fitting);
//printf("final %e\n", chi2_final);
gsl_vector_free(x);
gsl_vector_free(ss);
gsl_multimin_fminimizer_free(s);
}
double nbar_multimin_f(const gsl_vector *v, void *params)
{
// The minimiser library minimise this function
NbarFitting* const fitting= (NbarFitting*) params;
// The minisation algorithm gives the c to evaluate
fitting->hod->c[0]= gsl_vector_get(v, 0);
fitting->hod->c[1]= gsl_vector_get(v, 1);
fitting->hod->c[2]= gsl_vector_get(v, 2);
fitting->hod->c[3]= gsl_vector_get(v, 3);
//printf("hod->c %e\n", fitting->hod->c[0]);
// compute n(z) from parameter hod->c[]
const int n= fitting->vni.size();
for(int i=0; i<n; ++i) {
NbarIntegration* const ni= fitting->vni[i];
const double z= (*fitting->vobs)[i].z;
(*fitting->vhod)[i].nbar= nbar_compute(ni, z);
}
// evaluate the cost function between vobs and vhod
return compute_cost_function(fitting->vobs, fitting->vhod);
}
double compute_cost_function(vector<Nbar> const * const vobs,
vector<Nbar> const * const vhod)
{
// cost function is a measure how close vobs and vhod are.
double chi2= 0.0;
const int m= vobs->size();
for(int i=0; i<m; ++i) {
double diff= ((*vobs)[i].nbar - (*vhod)[i].nbar)/ (*vobs)[i].dnbar;
chi2 += diff*diff;
//printf("%e %e %e %e\n", (*vobs)[i].z, (*vobs)[i].nbar, (*vhod)[i].nbar, diff);
}
return chi2;
}
|