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/*
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Programme original realise en Fortran 77 en mars 1994
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pour les Travaux Pratiques de Modelisation Numerique
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DEA d'astrophysique et techniques spatiales de Meudon
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par Herve Aussel et Emmanuel Quemener
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Conversion en C par Emmanuel Quemener en aout 1997
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Modification par Emmanuel Quemener en aout 2019
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Remerciements a :
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- Herve Aussel pour sa procedure sur le spectre de corps noir
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- Didier Pelat pour l'aide lors de ce travail
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- Jean-Pierre Luminet pour son article de 1979
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- Le Numerical Recipies pour ses recettes de calcul
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- Luc Blanchet pour sa disponibilite lors de mes interrogations en RG
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Compilation sous gcc ( Compilateur GNU sous Linux ) :
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Version FP32 : gcc -O3 -ffast-math -FP32 -o trou_noir_FP32 trou_noir.c -lm
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Version FP64 : gcc -O3 -ffast-math -FP64 -o trou_noir_FP64 trou_noir.c -lm
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*/
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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <sys/time.h>
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#include <time.h>
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#define nbr 256 /* Nombre de colonnes du spectre */
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#define PI 3.14159265359
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#define TRACKPOINTS 2048
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#if TYPE == FP32
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#define MYFLOAT float
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#else
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#define MYFLOAT double
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#endif
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MYFLOAT atanp(MYFLOAT x,MYFLOAT y)
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{
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MYFLOAT angle;
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angle=atan2(y,x);
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if (angle<0)
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{
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angle+=2*PI;
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}
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return angle;
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}
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MYFLOAT f(MYFLOAT v)
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{
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return v;
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}
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MYFLOAT g(MYFLOAT u,MYFLOAT m,MYFLOAT b)
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{
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return (3.*m/b*pow(u,2)-u);
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}
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void calcul(MYFLOAT *us,MYFLOAT *vs,MYFLOAT up,MYFLOAT vp,
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MYFLOAT h,MYFLOAT m,MYFLOAT b)
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{
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MYFLOAT c[4],d[4];
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c[0]=h*f(vp);
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c[1]=h*f(vp+c[0]/2.);
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c[2]=h*f(vp+c[1]/2.);
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c[3]=h*f(vp+c[2]);
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d[0]=h*g(up,m,b);
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d[1]=h*g(up+d[0]/2.,m,b);
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d[2]=h*g(up+d[1]/2.,m,b);
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d[3]=h*g(up+d[2],m,b);
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*us=up+(c[0]+2.*c[1]+2.*c[2]+c[3])/6.;
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*vs=vp+(d[0]+2.*d[1]+2.*d[2]+d[3])/6.;
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}
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void rungekutta(MYFLOAT *ps,MYFLOAT *us,MYFLOAT *vs,
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MYFLOAT pp,MYFLOAT up,MYFLOAT vp,
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MYFLOAT h,MYFLOAT m,MYFLOAT b)
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{
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calcul(us,vs,up,vp,h,m,b);
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*ps=pp+h;
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}
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MYFLOAT decalage_spectral(MYFLOAT r,MYFLOAT b,MYFLOAT phi,
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MYFLOAT tho,MYFLOAT m)
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{
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return (sqrt(1-3*m/r)/(1+sqrt(m/pow(r,3))*b*sin(tho)*sin(phi)));
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}
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MYFLOAT spectre(MYFLOAT rf,MYFLOAT q,MYFLOAT b,MYFLOAT db,
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MYFLOAT h,MYFLOAT r,MYFLOAT m,MYFLOAT bss)
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{
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MYFLOAT flx;
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flx=exp(q*log(r/m))*pow(rf,4)*b*db*h;
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return(flx);
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}
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MYFLOAT spectre_cn(MYFLOAT rf,MYFLOAT b,MYFLOAT db,
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MYFLOAT h,MYFLOAT r,MYFLOAT m,MYFLOAT bss)
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{
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MYFLOAT flx;
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MYFLOAT nu_rec,nu_em,qu,temp_em,flux_int;
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int fi,posfreq;
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#define planck 6.62e-34
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#define k 1.38e-23
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#define c2 9.e16
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#define temp 3.e7
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#define m_point 1.
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#define lplanck (log(6.62)-34.*log(10.))
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#define lk (log(1.38)-23.*log(10.))
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#define lc2 (log(9.)+16.*log(10.))
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MYFLOAT v=1.-3./r;
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qu=1./sqrt((1.-3./r)*r)*(sqrt(r)-sqrt(6.)+sqrt(3.)/2.*log((sqrt(r)+sqrt(3.))/(sqrt(r)-sqrt(3.))* 0.17157287525380988 ));
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temp_em=temp*sqrt(m)*exp(0.25*log(m_point)-0.75*log(r)-0.125*log(v)+0.25*log(fabs(qu)));
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flux_int=0.;
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flx=0.;
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for (fi=0;fi<nbr;fi++)
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{
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nu_em=bss*(MYFLOAT)fi/(MYFLOAT)nbr;
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nu_rec=nu_em*rf;
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posfreq=(int)(nu_rec*(MYFLOAT)nbr/bss);
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if ((posfreq>0)&&(posfreq<nbr))
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{
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flux_int=2.*planck/c2*pow(nu_em,3)/(exp(planck*nu_em/(k*temp_em))-1.)*exp(3.*log(rf))*b*db*h;
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flx+=flux_int;
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}
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}
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return((MYFLOAT)flx);
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}
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void impact(MYFLOAT d,MYFLOAT phi,int dim,MYFLOAT r,MYFLOAT b,MYFLOAT tho,MYFLOAT m,
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MYFLOAT **zp,MYFLOAT **fp,
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MYFLOAT q,MYFLOAT db,
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MYFLOAT h,MYFLOAT bss,int raie)
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{
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MYFLOAT xe,ye;
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int xi,yi;
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MYFLOAT flx,rf;
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xe=d*sin(phi);
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ye=-d*cos(phi);
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xi=(int)xe+dim/2;
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yi=(int)ye+dim/2;
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rf=decalage_spectral(r,b,phi,tho,m);
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if (raie==0)
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{
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bss=1.e19;
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flx=spectre_cn(rf,b,db,h,r,m,bss);
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}
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else
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{
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bss=2.;
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flx=spectre(rf,q,b,db,h,r,m,bss);
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}
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if (zp[xi][yi]==0.)
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{
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zp[xi][yi]=1./rf;
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}
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if (fp[xi][yi]==0.)
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{
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fp[xi][yi]=flx;
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}
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}
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void sauvegarde_pgm(char nom[24],unsigned int **image,int dim)
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{
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FILE *sortie;
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unsigned long i,j;
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sortie=fopen(nom,"w");
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fprintf(sortie,"P5\n");
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fprintf(sortie,"%i %i\n",dim,dim);
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fprintf(sortie,"255\n");
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for (j=0;j<dim;j++) for (i=0;i<dim;i++)
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{
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fputc(image[i][j],sortie);
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}
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fclose(sortie);
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}
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int main(int argc,char *argv[])
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{
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MYFLOAT m,rs,ri,re,tho;
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int q;
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MYFLOAT bss,stp;
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int nmx,dim;
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MYFLOAT bmx;
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MYFLOAT **zp,**fp;
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unsigned int **izp,**ifp;
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MYFLOAT zmx,fmx;
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int zimx=0,zjmx=0,fimx=0,fjmx=0;
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int raie,fcl,zcl;
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struct timeval tv1,tv2;
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double elapsed;
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int mtv1,mtv2;
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/* Variables used inside pragma need to be placed inside loop ! */
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/* MYFLOAT d,db,b,nh,h,up,vp,pp,us,vs,ps; */
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/* MYFLOAT phi,phd,php,nr,r; */
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/* int ni,ii,imx,tst; */
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/* MYFLOAT rp[TRACKPOINTS]; */
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if (argc==2)
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{
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if (strcmp(argv[1],"-aide")==0)
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{
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printf("\nSimulation d'un disque d'accretion autour d'un trou noir\n");
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printf("\nParametres a definir :\n\n");
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printf(" 1) Dimension de l'Image\n");
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printf(" 2) Masse relative du trou noir\n");
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printf(" 3) Dimension du disque exterieur\n");
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printf(" 4) Inclinaison par rapport au disque (en degres)\n");
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printf(" 5) Rayonnement de disque MONOCHROMATIQUE ou CORPS_NOIR\n");
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printf(" 6) Impression des images NEGATIVE ou POSITIVE\n");
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printf(" 7) Nom de l'image des Flux\n");
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printf(" 8) Nom de l'image des decalages spectraux\n");
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printf("\nSi aucun parametre defini, parametres par defaut :\n\n");
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printf(" 1) Dimension de l'image : 1024 pixels de cote\n");
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printf(" 2) Masse relative du trou noir : 1\n");
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printf(" 3) Dimension du disque exterieur : 12 \n");
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printf(" 4) Inclinaison par rapport au disque (en degres) : 10\n");
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printf(" 5) Rayonnement de disque CORPS_NOIR\n");
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printf(" 6) Impression des images NEGATIVE ou POSITIVE\n");
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printf(" 7) Nom de l'image des flux : flux.pgm\n");
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printf(" 8) Nom de l'image des z : z.pgm\n");
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}
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}
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if (argc==9)
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{
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printf("# Utilisation les valeurs definies par l'utilisateur\n");
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dim=atoi(argv[1]);
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m=atof(argv[2]);
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re=atof(argv[3]);
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tho=PI/180.*(90-atof(argv[4]));
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rs=2.*m;
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ri=3.*rs;
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if (strcmp(argv[5],"CORPS_NOIR")==0)
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{
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raie=0;
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}
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else
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{
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raie=1;
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}
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}
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else
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{
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printf("# Utilisation les valeurs par defaut\n");
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dim=1024;
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m=1.;
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rs=2.*m;
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ri=3.*rs;
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re=12.;
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tho=PI/180.*80;
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// Corps noir
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raie=0;
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}
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if (raie==1)
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{
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bss=2.;
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q=-2;
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}
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else
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{
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bss=1.e19;
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q=-0.75;
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}
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printf("# Dimension de l'image : %i\n",dim);
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printf("# Masse : %f\n",m);
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printf("# Rayon singularite : %f\n",rs);
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printf("# Rayon interne : %f\n",ri);
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printf("# Rayon externe : %f\n",re);
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printf("# Inclinaison a la normale en radian : %f\n",tho);
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zp=(MYFLOAT**)calloc(dim,sizeof(MYFLOAT*));
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zp[0]=(MYFLOAT*)calloc(dim*dim,sizeof(MYFLOAT));
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fp=(MYFLOAT**)calloc(dim,sizeof(MYFLOAT*));
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fp[0]=(MYFLOAT*)calloc(dim*dim,sizeof(MYFLOAT));
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322 |
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izp=(unsigned int**)calloc(dim,sizeof(unsigned int*));
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izp[0]=(unsigned int*)calloc(dim*dim,sizeof(unsigned int));
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ifp=(unsigned int**)calloc(dim,sizeof(unsigned int*));
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ifp[0]=(unsigned int*)calloc(dim*dim,sizeof(unsigned int));
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for (int i=1;i<dim;i++)
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{
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zp[i]=zp[i-1]+dim;
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fp[i]=fp[i-1]+dim;
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izp[i]=izp[i-1]+dim;
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ifp[i]=ifp[i-1]+dim;
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}
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nmx=dim;
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stp=dim/(2.*nmx);
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bmx=1.25*re;
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340 |
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// Set start timer
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// gettimeofday(&tv1, &tz);
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gettimeofday(&tv1, NULL);
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//
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mtv1=clock()*1000/CLOCKS_PER_SEC;
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346 |
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347 |
#pragma omp parallel for
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for (int n=1;n<=nmx;n++)
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{
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350 |
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MYFLOAT d,db,b,nh,h,up,vp,pp,us,vs,ps;
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352 |
MYFLOAT phi,phd,php,nr,r;
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int ni,ii,imx,tst;
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MYFLOAT rp[TRACKPOINTS];
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355 |
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h=4.*PI/(MYFLOAT)TRACKPOINTS;
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d=stp*(MYFLOAT)n;
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358 |
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db=bmx/(MYFLOAT)nmx;
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360 |
b=db*(MYFLOAT)n;
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up=0.;
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362 |
vp=1.;
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363 |
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364 |
pp=0.;
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365 |
nh=1;
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366 |
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367 |
rungekutta(&ps,&us,&vs,pp,up,vp,h,m,b);
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368 |
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369 |
rp[(int)nh]=fabs(b/us);
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370 |
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371 |
do
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372 |
{
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373 |
nh++;
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374 |
pp=ps;
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375 |
up=us;
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376 |
vp=vs;
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377 |
rungekutta(&ps,&us,&vs,pp,up,vp,h,m,b);
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378 |
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379 |
rp[(int)nh]=b/us;
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380 |
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381 |
} while ((rp[(int)nh]>=rs)&&(rp[(int)nh]<=rp[1]));
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382 |
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383 |
for (int i=nh+1;i<TRACKPOINTS;i++)
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{
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rp[i]=0.;
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386 |
}
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387 |
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388 |
imx=(int)(8*d);
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389 |
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390 |
for (int i=0;i<=imx;i++)
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391 |
{
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392 |
phi=2.*PI/(MYFLOAT)imx*(MYFLOAT)i;
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393 |
phd=atanp(cos(phi)*sin(tho),cos(tho));
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394 |
phd=fmod(phd,PI);
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395 |
ii=0;
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396 |
tst=0;
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397 |
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398 |
do
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399 |
{
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400 |
php=phd+(MYFLOAT)ii*PI;
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401 |
nr=php/h;
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402 |
ni=(int)nr;
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403 |
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404 |
if ((MYFLOAT)ni<nh)
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405 |
{
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406 |
r=(rp[ni+1]-rp[ni])*(nr-ni*1.)+rp[ni];
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|
407 |
}
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408 |
else
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409 |
{
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410 |
r=rp[ni];
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411 |
}
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412 |
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413 |
if ((r<=re)&&(r>=ri))
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414 |
{
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415 |
tst=1;
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416 |
impact(d,phi,dim,r,b,tho,m,zp,fp,q,db,h,bss,raie);
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|
417 |
}
|
|
418 |
|
|
419 |
ii++;
|
|
420 |
} while ((ii<=2)&&(tst==0));
|
|
421 |
}
|
|
422 |
}
|
|
423 |
|
|
424 |
// Set stop timer
|
|
425 |
// gettimeofday(&tv2, &tz);
|
|
426 |
gettimeofday(&tv2, NULL);
|
|
427 |
mtv2=clock()*1000/CLOCKS_PER_SEC;
|
|
428 |
|
|
429 |
// elapsed=(double)((tv2.tv_sec-tv1.tv_sec) * 1000000L +
|
|
430 |
// (tv2.tv_usec-tv1.tv_usec))/1000000;
|
|
431 |
elapsed=(double)((mtv2-mtv1)/1000.);
|
|
432 |
|
|
433 |
fmx=fp[0][0];
|
|
434 |
zmx=zp[0][0];
|
|
435 |
|
|
436 |
for (int i=0;i<dim;i++) for (int j=0;j<dim;j++)
|
|
437 |
{
|
|
438 |
if (fmx<fp[i][j])
|
|
439 |
{
|
|
440 |
fimx=i;
|
|
441 |
fjmx=j;
|
|
442 |
fmx=fp[i][j];
|
|
443 |
}
|
|
444 |
|
|
445 |
if (zmx<zp[i][j])
|
|
446 |
{
|
|
447 |
zimx=i;
|
|
448 |
zjmx=j;
|
|
449 |
zmx=zp[i][j];
|
|
450 |
}
|
|
451 |
}
|
|
452 |
|
|
453 |
printf("\nElapsed Time : %lf",(double)elapsed);
|
|
454 |
printf("\nZ max @(%i,%i) : %f",zimx,zjmx,zmx);
|
|
455 |
printf("\nFlux max @(%i,%i) : %f\n\n",fimx,fjmx,fmx);
|
|
456 |
|
|
457 |
for (int i=0;i<dim;i++) for (int j=0;j<dim;j++)
|
|
458 |
{
|
|
459 |
zcl=(int)(255/zmx*zp[i][dim-1-j]);
|
|
460 |
fcl=(int)(255/fmx*fp[i][dim-1-j]);
|
|
461 |
|
|
462 |
if (strcmp(argv[6],"NEGATIVE")==0)
|
|
463 |
{
|
|
464 |
if (zcl>255)
|
|
465 |
{
|
|
466 |
izp[i][j]=0;
|
|
467 |
}
|
|
468 |
else
|
|
469 |
{
|
|
470 |
izp[i][j]=255-zcl;
|
|
471 |
}
|
|
472 |
|
|
473 |
if (fcl>255)
|
|
474 |
{
|
|
475 |
ifp[i][j]=0;
|
|
476 |
}
|
|
477 |
else
|
|
478 |
{
|
|
479 |
ifp[i][j]=255-fcl;
|
|
480 |
}
|
|
481 |
|
|
482 |
}
|
|
483 |
else
|
|
484 |
{
|
|
485 |
if (zcl>255)
|
|
486 |
{
|
|
487 |
izp[i][j]=255;
|
|
488 |
}
|
|
489 |
else
|
|
490 |
{
|
|
491 |
izp[i][j]=zcl;
|
|
492 |
}
|
|
493 |
|
|
494 |
if (fcl>255)
|
|
495 |
{
|
|
496 |
ifp[i][j]=255;
|
|
497 |
}
|
|
498 |
else
|
|
499 |
{
|
|
500 |
ifp[i][j]=fcl;
|
|
501 |
}
|
|
502 |
|
|
503 |
}
|
|
504 |
|
|
505 |
}
|
|
506 |
|
|
507 |
if (argc==9)
|
|
508 |
{
|
|
509 |
sauvegarde_pgm(argv[7],ifp,dim);
|
|
510 |
sauvegarde_pgm(argv[8],izp,dim);
|
|
511 |
}
|
|
512 |
else
|
|
513 |
{
|
|
514 |
sauvegarde_pgm("z.pgm",izp,dim);
|
|
515 |
sauvegarde_pgm("flux.pgm",ifp,dim);
|
|
516 |
}
|
|
517 |
|
|
518 |
free(zp[0]);
|
|
519 |
free(zp);
|
|
520 |
free(fp[0]);
|
|
521 |
free(fp);
|
|
522 |
|
|
523 |
free(izp[0]);
|
|
524 |
free(izp);
|
|
525 |
free(ifp[0]);
|
|
526 |
free(ifp);
|
|
527 |
|
|
528 |
}
|
|
529 |
|
|
530 |
|