void approximateSimple(std::vector<vec_t> &out, double max_flatness) const {
double f = flatness();
if (f < max_flatness) {
out.push_back(p[3]);
} else {
cubic_bezier a, b;
split(0.5, a, b);
a.approximateSimple(out, max_flatness);
b.approximateSimple(out, max_flatness);
}
}
float EffectiveLength(Triangulation::_Internal::_edge* e)
{
return e->Length();
float len = 0;
for(int i=0; i<2; ++i)
{
if(e->faces[i] != NULL)
{
float val = flatness(e->faces[i], e);
if(val > len)
{
len = val;
}
}
}
return len;
}
void approximate(std::vector<vec_t> &out, double max_flatness, unsigned n_tests = 128) const {
double f = flatness();
if (f < max_flatness) {
out.push_back(p[3]);
} else {
double best_t = .5;
double best_f = f;
cubic_bezier a, b;
for (size_t i = 1; i < n_tests; ++i) {
double t = double(i) / n_tests;
split(t, a, b);
double f = a.flatness() + b.flatness();
if (f < best_f) {
best_t = t;
best_f = f;
}
}
split(best_t, a, b);
a.approximate(out, max_flatness, n_tests);
b.approximate(out, max_flatness, n_tests);
}
}
main (int argc,char *argv[])
{
int ia,ib,ic,id,it,inow,ineigh,icont;
int in,ia2,ia3,irun,icurrent,ORTOGONALFLAG;
int RP, P,L,N,NRUNS,next,sweep,SHOWFLAG;
double u,field1,field2,field0,q,aux1,aux2;
double alfa,aux,Q1,Q2,QZ,RZQ,rho,R;
double pm,D,wmax,mQ,wx,wy,h_sigma,h_mean;
double TOL,MINLOGF,E;
double DELTA;
double E_new,Ex,DeltaE,ER;
double EW,meanhist,hvalue,wE,aratio;
double logG_old,logG_new,lf;
size_t i_old,i_new;
long seed;
double lGvR,lGv,DlG;
size_t iL,iR,i1,i2;
int I_endpoint[NBINS];
double lower,upper;
size_t i0;
FILE * wlsrange;
FILE * dos;
FILE * thermodynamics;
FILE * canonical;
FILE * logfile;
//FILE * pajek;
//***********************************
// Help
//***********************************
if (argc<15){
help();
return(1);
}
else{
DELTA = atof(argv[1]);
P = atoi(argv[2]);
RP = atoi(argv[3]);
L = atoi(argv[4]);
N = atoi(argv[5]);
TOL = atof(argv[6]);
MINLOGF = atof(argv[7]);
}
wlsrange=fopen(argv[8],"w");
dos=fopen(argv[9],"w");
thermodynamics=fopen(argv[10],"w");
canonical=fopen(argv[11],"w");
logfile=fopen(argv[12],"w");
SHOWFLAG = atoi(argv[13]);
ORTOGONALFLAG = atoi(argv[14]);
if ((ORTOGONALFLAG==1) && (P>L)) P=L;
//maximum number of orthogonal issues
if (SHOWFLAG==1){
printf("# parameters are DELTA=%1.2f P=%d ",DELTA,P);
printf("D=%d L=%d M=%d TOL=%1.2f MINLOGF=%g \n",L,N,RP,TOL,MINLOGF);
}
fprintf(logfile,"# parameters are DELTA=%1.2f P=%d D=%d",DELTA,P,L);
fprintf(logfile,"L=%d M=%d TOL=%1.2f MINLOGF=%g\n",L,RP,TOL,MINLOGF);
//**********************************************************************
// Alocate matrices
//**********************************************************************
gsl_matrix * sociedade = gsl_matrix_alloc(SIZE,L);
gsl_matrix * issue = gsl_matrix_alloc(P,L);
gsl_vector * current_issue = gsl_vector_alloc(L);
gsl_vector * v0 = gsl_vector_alloc(L);
gsl_vector * v1 = gsl_vector_alloc(L);
gsl_vector * Z = gsl_vector_alloc(L);
gsl_vector * E_borda = gsl_vector_alloc(NBINS);
//**********************************************************************
// Inicialization
//**********************************************************************
const gsl_rng_type * T;
gsl_rng * r;
gsl_rng_env_setup();
T = gsl_rng_default;
r=gsl_rng_alloc (T);
seed = time (NULL) * getpid();
//seed = 13188839657852;
gsl_rng_set(r,seed);
igraph_t graph;
igraph_vector_t neighbors;
igraph_vector_t result;
igraph_vector_t dim_vector;
igraph_real_t res;
igraph_bool_t C;
igraph_vector_init(&neighbors,1000);
igraph_vector_init(&result,0);
igraph_vector_init(&dim_vector,DIMENSION);
for(ic=0;ic<DIMENSION;ic++) VECTOR(dim_vector)[ic]=N;
gsl_histogram * HE = gsl_histogram_alloc (NBINS);
gsl_histogram * logG = gsl_histogram_alloc (NBINS);
gsl_histogram * LG = gsl_histogram_alloc (NBINS);
//********************************************************************
// Social Graph
//********************************************************************
//Barabasi-Alberts network
igraph_barabasi_game(&graph,SIZE,RP,&result,1,0);
/* for (inow=0;inow<SIZE;inow++){
igraph_neighbors(&graph,&neighbors,inow,IGRAPH_OUT);
printf("%d ",inow);
for(ic=0;ic<igraph_vector_size(&neighbors);ic++)
{
ineigh=(int)VECTOR(neighbors)[ic];
printf("%d ",ineigh);
}
printf("\n");
}*/
//pajek=fopen("graph.xml","w");
// igraph_write_graph_graphml(&graph,pajek);
//igraph_write_graph_pajek(&graph, pajek);
//fclose(pajek);
//**********************************************************************
//Quenched issues set and Zeitgeist
//**********************************************************************
gsl_vector_set_zero(Z);
gera_config(Z,issue,P,L,r,1.0);
if (ORTOGONALFLAG==1) gsl_matrix_set_identity(issue);
for (ib=0;ib<P;ib++)
{
gsl_matrix_get_row(current_issue,issue,ib);
gsl_blas_ddot(current_issue,current_issue,&Q1);
gsl_vector_scale(current_issue,1/sqrt(Q1));
gsl_vector_add(Z,current_issue);
}
gsl_blas_ddot(Z,Z,&QZ);
gsl_vector_scale(Z,1/sqrt(QZ));
//**********************************************************************
// Ground state energy
//**********************************************************************
double E0;
gera_config(Z,sociedade,SIZE,L,r,0);
E0 = hamiltoneana(sociedade,issue,SIZE,L,P,DELTA,graph);
double EMIN=E0;
double EMAX=-E0;
double E_old=E0;
gsl_histogram_set_ranges_uniform (HE,EMIN,EMAX);
gsl_histogram_set_ranges_uniform (logG,EMIN,EMAX);
if (SHOWFLAG==1) printf("# ground state: %3.0f\n",E0);
fprintf(logfile,"# ground state: %3.0f\n",E0);
//**********************************************************************
// Find sampling interval
//**********************************************************************
//printf("#finding the sampling interval...\n");
lf=1;
sweep=0;
icont=0;
int iflag=0;
int TMAX=NSWEEPS;
while(sweep<=TMAX){
if (icont==10000) {
//printf("%d sweeps\n",sweep);
icont=0;
}
for(it=0;it<SIZE;it++){
igraph_vector_init(&neighbors,SIZE);
//choose a random site
do{
inow=gsl_rng_uniform_int(r,SIZE);
}while((inow<0)||(inow>=SIZE));
gsl_matrix_get_row(v1,sociedade,inow);
igraph_neighbors(&graph,&neighbors,inow,IGRAPH_OUT);
//generates a random vector v1
gsl_vector_memcpy(v0,v1);
gera_vetor(v1,L,r);
//calculates energy change when v0->v1
// in site inow
DeltaE=variacaoE(v0,v1,inow,sociedade,
issue,N,L,P,DELTA,graph,neighbors);
E_new=E_old+DeltaE;
//WL: accepts in [EMIN,EMAX]
if ((E_new>EMIN) && (E_new<EMAX))
{
gsl_histogram_find(logG,E_old,&i_old);
logG_old=gsl_histogram_get(logG,i_old);
gsl_histogram_find(logG,E_new,&i_new);
logG_new=gsl_histogram_get(logG,i_new);
wE = GSL_MIN(exp(logG_old-logG_new),1);
if (gsl_rng_uniform(r)<wE){
E_old=E_new;
gsl_matrix_set_row(sociedade,inow,v1);
}
}
//WL: update histograms
gsl_histogram_increment(HE,E_old);
gsl_histogram_accumulate(logG,E_old,lf);
igraph_vector_destroy(&neighbors);
}
sweep++;
icont++;
}
gsl_histogram_fprintf(wlsrange,HE,"%g","%g");
double maxH=gsl_histogram_max_val(HE);
//printf("ok\n");
Ex=0;
hvalue=maxH;
while((hvalue>TOL*maxH)&&(Ex>EMIN)){
gsl_histogram_find(HE,Ex,&i0);
hvalue=gsl_histogram_get(HE,i0);
Ex-=1;
if(Ex<=EMAX)TMAX+=10000;
}
EMIN=Ex;
Ex=0;
hvalue=maxH;
while((hvalue>TOL*maxH)&&(Ex<EMAX)) {
gsl_histogram_find(HE,Ex,&i0);
hvalue=gsl_histogram_get(HE,i0);
Ex+=1;
if(Ex>=EMAX)TMAX+=10000;
}
EMAX=Ex;
EMAX=GSL_MIN(10.0,Ex);
if (SHOWFLAG==1)
printf("# the sampling interval is [%3.0f,%3.0f] found in %d sweeps \n\n"
,EMIN,EMAX,sweep);
fprintf(logfile,
"# the sampling interval is [%3.0f,%3.0f] found in %d sweeps \n\n"
,EMIN,EMAX,sweep);
gsl_histogram_set_ranges_uniform (HE,EMIN-1,EMAX+1);
gsl_histogram_set_ranges_uniform (logG,EMIN-1,EMAX+1);
gsl_histogram_set_ranges_uniform (LG,EMIN-1,EMAX+1);
//**********************************************************************
// WLS
//**********************************************************************
int iE,itera=0;
double endpoints[NBINS];
double w = WINDOW; //(EMAX-EMIN)/10.0;
//printf("W=%f\n",w);
lf=1;
//RESOLUTION ----> <------RESOLUTION*****
do{
int iverify=0,iborda=0,flat=0;
sweep=0;
Ex=EMAX;
EW=EMAX;
E_old=EMAX+1;
iE=0;
endpoints[iE]=EMAX;
iE++;
gsl_histogram_reset(LG);
//WINDOWS --> <--WINDOWS*******
while((Ex>EMIN)&&(sweep<MAXSWEEPS)){
//initial config
gera_config(Z,sociedade,SIZE,L,r,0);
E_old = hamiltoneana(sociedade,issue,SIZE,L,P,DELTA,graph);
while( (E_old<EMIN+1)||(E_old>Ex) ){
//printf("%d %3.1f\n",E_old);
do{
inow=gsl_rng_uniform_int(r,SIZE);
}while((inow<0)||(inow>=SIZE));
gsl_matrix_get_row(v0,sociedade,inow);
gera_vetor(v1,L,r);
gsl_matrix_set_row(sociedade,inow,v1);
E_old = hamiltoneana(sociedade,issue,SIZE,L,P,DELTA,graph);
if (E_old>Ex){
gsl_matrix_set_row(sociedade,inow,v0);
E_old = hamiltoneana(sociedade,issue,SIZE,L,P,DELTA,graph);
}
//printf("%3.1f %3.1f %3.1f\n",EMIN+1,E_old, Ex);
}
if (SHOWFLAG==1){
printf("# sampling [%f,%f]\n",EMIN,Ex);
printf("# walking from E=%3.0f\n",E_old);
}
fprintf(logfile,"# sampling [%f,%f]\n",EMIN,Ex);
fprintf(logfile,"# walking from E=%3.0f\n",E_old);
do{ //FLAT WINDOW------> <------FLAT WINDOW*****
//MC sweep ----> <------MC sweep********
for(it=0;it<SIZE;it++){
igraph_vector_init(&neighbors,SIZE);
//escolhe sítio aleatoriamente
do{
inow=gsl_rng_uniform_int(r,SIZE);
}while((inow<0)||(inow>=SIZE));
gsl_matrix_get_row(v1,sociedade,inow);
igraph_neighbors(&graph,&neighbors,inow,IGRAPH_OUT);
//gera vetor aleatorio v1
gsl_vector_memcpy(v0,v1);
gera_vetor(v1,L,r);
//calculates energy change when
//v0->v1 in site inow
DeltaE=variacaoE(v0,v1,inow,sociedade,issue,
N,L,P,DELTA,graph,neighbors);
E_new=E_old+DeltaE;
//WL: accepts in [EMIN,Ex]
if ((E_new>EMIN) && (E_new<Ex))
{
gsl_histogram_find(logG,E_old,&i_old);
logG_old=gsl_histogram_get(logG,i_old);
gsl_histogram_find(logG,E_new,&i_new);
logG_new=gsl_histogram_get(logG,i_new);
wE = GSL_MIN(exp(logG_old-logG_new),1);
if (gsl_rng_uniform(r)<wE){
E_old=E_new;
gsl_matrix_set_row(sociedade,inow,v1);
}
}
//WL: updates histograms
gsl_histogram_increment(HE,E_old);
gsl_histogram_accumulate(logG,E_old,lf);
itera++;
igraph_vector_destroy(&neighbors);
}
//MC sweep ----> <--------MC sweep****
sweep++; iverify++;
if( (EMAX-EMIN)<NDE*DE ) {
EW=EMIN;
}else{
EW=GSL_MAX(Ex-w,EMIN);
}
if (iverify==CHECK){//Verify flatness
if (SHOWFLAG==1)
printf(" #verificando flatness em [%f,%f]\n",EW,Ex);
fprintf(logfile," #verificando flatness em [%f,%f]\n"
,EW,Ex);
iverify=0;
flat=flatness(HE,EW,Ex,TOL,itera,meanhist,hvalue);
if (SHOWFLAG==1)
printf("#minH= %8.0f\t k<H>=%8.0f\t %d sweeps\t ",
hvalue,TOL*meanhist,sweep,flat);
fprintf(logfile,
"#minH= %8.0f\t k<H>=%8.0f\t %d sweeps\t ",
hvalue,TOL*meanhist,sweep,flat);
}
}while(flat==0);// <------FLAT WINDOW******
flat=0;
//Find ER
//printf("# EMAX=%f EMIN = %f Ex =%f\n",EMAX, EMIN, Ex);
if( (EMAX-EMIN)<NDE*DE ) {
Ex=EMIN;
endpoints[iE]=EMIN;
}
else {
if (EW>EMIN){
ER=flatwindow(HE,EW,TOL,meanhist);
if (SHOWFLAG==1)
printf("# extending flatness to[%f,%f]\n",ER,Ex);
fprintf(logfile,
"# extending flatness to [%f,%f]\n",ER,Ex);
if((ER-EMIN)<1){
ER=EMIN;
Ex=EMIN;
endpoints[iE]=EMIN;
}else{
endpoints[iE]=GSL_MIN(ER+DE,EMAX);
Ex=GSL_MIN(ER+2*DE,EMAX);
}
}
else{
endpoints[iE]=EMIN;
Ex=EMIN;
ER=EMIN;
}
}
if (SHOWFLAG==1)
printf("# window %d [%3.0f,%3.0f] is flat after %d sweeps \n",
iE,endpoints[iE],endpoints[iE-1],sweep);
fprintf(logfile,"# window %d [%3.0f,%3.0f] is flat after %d sweeps\n",
iE,endpoints[iE],endpoints[iE-1],sweep);
//saves histogram
if (iE==1){
gsl_histogram_find(logG,endpoints[iE],&i1);
gsl_histogram_find(logG,endpoints[iE-1],&i2);
for(i0=i1;i0<=i2;i0++){
lGv=gsl_histogram_get(logG,i0);
gsl_histogram_get_range(logG,i0,&lower,&upper);
E=0.5*(upper+lower);
gsl_histogram_accumulate(LG,E,lGv);
}
}else{
gsl_histogram_find(logG,endpoints[iE],&i1);
gsl_histogram_find(logG,endpoints[iE-1],&i2);
lGv=gsl_histogram_get(logG,i2);
lGvR=gsl_histogram_get(LG,i2);
DlG=lGvR-lGv;
//printf("i1=%d i2=%d lGv=%f lGvR=%f DlG=%f\n",i1,i2,lGv,lGvR,DlG);
for(i0=i1;i0<i2;i0++){
lGv=gsl_histogram_get(logG,i0);
lGv=lGv+DlG;
gsl_histogram_get_range(logG,i0,&lower,&upper);
E=(upper+lower)*0.5;
//printf("i0=%d E=%f lGv=%f\n",i0,E,lGv);
gsl_histogram_accumulate(LG,E,lGv);
}
}
//printf("#########################################\n");
//gsl_histogram_fprintf(stdout,LG,"%g","%g");
//printf("#########################################\n");
iE++;
if((Ex-EMIN)>NDE*DE) {
if (SHOWFLAG==1)
printf("# random walk is now restricted to [%3.0f,%3.0f]\n"
,EMIN,Ex);
fprintf(logfile,"# random walk is now restricted to [%3.0f,%3.0f]\n"
,EMIN,Ex);
}
gsl_histogram_reset(HE);
}
//WINDOWS -->
if(sweep<MAXSWEEPS){
if (SHOWFLAG==1)
printf("# log(f)=%f converged within %d sweeps\n\n",lf,sweep);
fprintf(logfile,"# log(f)=%f converged within %d sweeps\n\n",lf,sweep);
lf=lf/2.0;
gsl_histogram_reset(HE);
gsl_histogram_memcpy(logG,LG);
}else {
if (SHOWFLAG==1)
printf("# FAILED: no convergence has been attained.");
fprintf(logfile,
"# FAILED: no convergence has been attained. Simulation ABANDONED.");
return(1);
}
}while(lf>MINLOGF);
//RESOLUTION --> <-----RESOLUTION****
//*****************************************************************
//Density of states
//*****************************************************************
double minlogG=gsl_histogram_min_val(logG);
gsl_histogram_shift(logG,-minlogG);
gsl_histogram_fprintf(dos,logG,"%g","%g");
//*****************************************************************
//Thermodynamics
//*****************************************************************
double beta,A,wT,Zmin_beta;
double lGvalue,maxA,betaC,CTMAX=0;
double Z_beta,U,U2,CT,F,S;
for (beta=0.01;beta<=30;beta+=0.01)
{
//******************************************************************
//Energy, free-energy, entropy, specific heat and Tc
//******************************************************************
maxA=0;
for (ia2=0; ia2<NBINS;ia2++)
{
lGvalue=gsl_histogram_get(logG,ia2);
gsl_histogram_get_range(logG,ia2,&lower,&upper);
E=(lower+upper)/2;
A=lGvalue-beta*E;
if (A>maxA) maxA=A;
}
gsl_histogram_find(logG,EMIN,&i0);
Z_beta=0;U=0;U2=0;
for (ia2=0; ia2<NBINS;ia2++)
{
lGvalue=gsl_histogram_get(logG,ia2);
gsl_histogram_get_range(logG,ia2,&lower,&upper);
E=(lower+upper)/2;
A=lGvalue-beta*E-maxA;
Z_beta+=exp(A);
U+=E*exp(A);
U2+=E*E*exp(A);
if(ia2==i0) Zmin_beta=exp(A);
}
wT=Zmin_beta/Z_beta;
F=-log(Z_beta)/beta - maxA/beta;
U=U/Z_beta;
S= (U-F)*beta;
U2=U2/Z_beta;
CT=(U2-U*U)*beta*beta;
if(CT>CTMAX){
CTMAX=CT;
betaC=beta;
}
fprintf(thermodynamics,"%f %f %f %f %f %f %f \n"
,beta,1/beta,F/(double)(SIZE),S/(double)(SIZE),
U/(double)(SIZE),CT/(double)(SIZE),wT);
}
if (SHOWFLAG==1) printf("# BETAc: %f Tc:%f \n",betaC,1/betaC);
fprintf(logfile,"# BETAc: %f Tc:%f \n",betaC,1/betaC);
//******************************************************************
//canonical distribuition at Tc
//******************************************************************
beta=betaC;
double distr_canonica;
maxA=0;
for (ia2=0; ia2<NBINS;ia2++)
{
lGvalue=gsl_histogram_get(logG,ia2);
gsl_histogram_get_range(logG,ia2,&lower,&upper);
E=(lower+upper)/2;
A=lGvalue-beta*E;
if (A>maxA) maxA=A;
}
for (ia2=0; ia2<NBINS;ia2++)
{
lGvalue=gsl_histogram_get(logG,ia2);
gsl_histogram_get_range(logG,ia2,&lower,&upper);
E=(lower+upper)/2;
A=lGvalue-beta*E-maxA;
distr_canonica=exp(A);
fprintf(canonical,"%f %f %f\n",
E/(double)(SIZE),distr_canonica,A);
}
//*****************************************************************
// Finalization
//*****************************************************************
igraph_destroy(&graph);
igraph_vector_destroy(&neighbors);
igraph_vector_destroy(&result);
gsl_matrix_free(issue);
gsl_vector_free(current_issue);
gsl_vector_free(v1);
gsl_vector_free(v0);
gsl_matrix_free(sociedade);
gsl_rng_free(r);
fclose(wlsrange);
fclose(dos);
fclose(thermodynamics);
fclose(canonical);
fclose(logfile);
return(0);
}
