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/*
*
* gengraph - generation of random simple connected graphs with prescribed
* degree sequence
*
* Copyright (C) 2006 Fabien Viger
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
// Pascalou ...
#ifdef pascalou
#define my_random() random()
#define MY_RAND_MAX 0x7FFFFFFF
#else
#include "gengraph_definitions.h"
#endif
#include "gengraph_powerlaw.h"
#include <cstdio>
#include <cmath>
#include <cassert>
#include "igraph_error.h"
namespace gengraph {
// Destructor
powerlaw::~powerlaw() {
delete[] table;
if(dt!=NULL) delete[] dt;
}
// Constructor
powerlaw::powerlaw(double _alpha, int _mini, int _maxi) {
alpha = _alpha;
mini = _mini;
maxi = _maxi;
if(alpha<=2.0 && maxi<0)
igraph_warningf("powerlaw exponent %f should be > 2 when no "
"Maximum is specified", __FILE__, __LINE__, -1, alpha);
if(alpha<=1.0 && maxi>=0)
igraph_warningf("powerlaw exponent %f should be > 1", __FILE__, __LINE__,
-1, alpha);
if(maxi>=0 && mini>maxi)
igraph_warningf("powerlaw max %d should be greater than min %d",
__FILE__, __LINE__, -1, maxi, mini);
table = new int[POWERLAW_TABLE];
tabulated = 0;
dt = NULL;
}
// Sample
int powerlaw::sample() {
if(proba_big!=0 && test_proba(proba_big)) return int(floor(0.5+big_sample(random_float())));
int r=my_random();
// table[] contains integer from MY_RAND_MAX downto 0, in blocks. Search block...
if(r>(MY_RAND_MAX>>max_dt)) return mini;
int k=0;
while(k<max_dt) { r<<=1; r+=random_bit(); k++; };
int a=0;
int b;
while((b=dt[k++])<0 || r<table[b]) {
if(b>=0) {
a=b+1;
if(a==tabulated-1) break;
r<<=1;
r+=random_bit();
}
}
// Now that we found the good block, run a dichotomy on this block [a,b]
while(a<b) {
int c = (a+b)/2;
if(r<table[c]) a=c+1;
else b=c;
}
return mini+a;
}
// Proba
double powerlaw::proba(int k) {
if(k<mini || (maxi>=0 && k>maxi)) return 0.0;
if(k>=mini+tabulated)
return proba_big*(big_inv_sample(double(k)-0.5)-big_inv_sample(double(k)+0.5));
else {
double div = table_mul;
int prev_pos_in_table = k-mini-1;
if(prev_pos_in_table<0) return (double(MY_RAND_MAX)+1.0-double(table[0]>>max_dt))*div;
// what block are we in ?
int k=0;
while(k<max_dt) { div*=0.5; k++; };
while(dt[k]<0 || dt[k]<prev_pos_in_table) { k++; div*=0.5; };
double prob2 = double(table[prev_pos_in_table+1]);
if(dt[k]==prev_pos_in_table) do prob2*=0.5;while(dt[++k]<0);
return (double(table[prev_pos_in_table])-prob2)*div;
}
}
// Relative Error
double powerlaw::error() {
return 1.0/(double(tabulated)*double(tabulated));
}
// Mean
double powerlaw::mean() {
double sum = 0.0;
for(int i=mini+tabulated; --i>=mini; ) sum+=double(i)*proba(i);
// add proba_big * integral(big_sample(t),t=0..1)
if(proba_big!=0) sum += proba_big*((pow(_a+_b,_exp+1.0)-pow(_b,_exp+1.0))/(_a*(_exp+1.0)) +double(mini)-offset-sum);
return sum;
}
// Median. Returns integer Med such that P(X<=Med) >= 1/2
int powerlaw::median() {
if(proba_big>0.5) return int(floor(0.5+big_sample(1.0-0.5/proba_big)));
double sum = 0.0;
int i=mini;
while(sum<0.5) sum+=proba(i++);
return i-1;
}
void powerlaw::init_to_offset(double _offset, int _tabulated) {
offset = _offset;
tabulated = _tabulated;
if(maxi>=0 && tabulated > maxi-mini) tabulated=maxi-mini+1;
double sum = 0.0;
double item = double(tabulated)+offset;
// Compute sum of tabulated probabilities
for(int i=tabulated; i--; ) sum += pow(item-=1.0, -alpha);
// Compute others parameters : proba_big, table_mul, _a, _b, _exp
if(maxi>0 && maxi<=mini+tabulated-1) {
proba_big = 0;
table_mul = inv_RANDMAX;
}
else {
if(maxi<0) _b = 0.0;
else _b = pow(double(maxi-mini)+0.5+offset, 1.0-alpha);
_a = pow(double(tabulated)-0.5+offset,1.0-alpha) - _b;
_exp = 1.0 / (1.0 - alpha);
double sum_big = _a*(-_exp);
proba_big = sum_big / (sum + sum_big);
table_mul = inv_RANDMAX * sum / (sum + sum_big);
}
// How many delimiters will be necessary for the table ?
max_dt = max(0,int(floor(alpha*log(double(tabulated))/log(2.0)))-6);
if(dt!=NULL) delete[] dt;
dt = new int[max_dt+1];
// Create table as decreasing integers from MY_RAND_MAX+1 (in virtual position -1) down to 0
// Every time the index crosses a delimiter, numbers get doubled.
double ssum = 0;
double mul = (double(MY_RAND_MAX)+1.0)*pow(2.0,max_dt)/sum;
item = double(tabulated)+offset;
int k = max_dt;
dt[k--]=tabulated-1;
for(int i=tabulated; --i>0; ) {
table[i] = int(floor(0.5+ssum));
ssum += mul * pow(item-=1.0,-alpha);
if(ssum>double(MY_RAND_MAX/2) && k>=0) {
while((ssum*=0.5)>double(MY_RAND_MAX/2)) { mul*=0.5; dt[k--]=-1; };
mul*=0.5; dt[k--]=i-1;
}
}
table[0] = int(floor(0.5+ssum));
max_dt = k+1;
}
void powerlaw::adjust_offset_mean(double _mean, double err, double factor) {
// Set two bounds for offset
double ol = offset;
double oh = offset;
if(mean()<_mean) {
do {
ol = oh;
oh *= factor;
init_to_offset(oh, tabulated);
} while(mean()<_mean);
}
else {
do {
oh = ol;
ol /= factor;
init_to_offset(ol, tabulated);
} while(mean()>_mean);
}
// Now, dichotomy
while(fabs(oh-ol) > err*ol) {
double oc = sqrt(oh*ol);
init_to_offset(oc, tabulated);
if(mean()<_mean) ol = oc;
else oh = oc;
}
init_to_offset(sqrt(ol*oh), tabulated);
}
double powerlaw::init_to_mean(double _mean) {
if(maxi>=0 && _mean >= 0.5*double((mini+maxi))) {
igraph_errorf("Fatal error in powerlaw::init_to_mean(%f): "
"Mean must be in ]min, (min+max)/2[ = ]%d, %d[",
__FILE__, __LINE__, IGRAPH_EINVAL,
_mean, mini, (mini+maxi)/2);
return(-1.0);
}
init_to_offset(_mean-double(mini), 100);
adjust_offset_mean(_mean, 0.01, 2);
init_to_offset(offset, POWERLAW_TABLE);
double eps = 1.0/(double(POWERLAW_TABLE));
adjust_offset_mean(_mean, eps*eps, 1.01);
return offset;
}
} // namespace gengraph
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