File:FacmapT500.png

File
File history
File usage
Metadata

Size of this preview: 605 × 600 pixels. Other resolutions: 242 × 240 pixels | 2,355 × 2,334 pixels.

Original file ‎(2,355 × 2,334 pixels, file size: 1.73 MB, MIME type: image/png)

C++ Generator of curves

fac.cin

z_type fracti(z_type z){ z_type s; int n;  DB a[17]=
{0.0833333333333333333, 0.0333333333333333333,  .252380952380952381, .525606469002695418, 
1.01152306812684171,   1.51747364915328740,   2.26948897420495996, 3.00991738325939817, 
4.02688719234390123,   5.00276808075403005,   6.28391137081578218, 7.49591912238403393, 
9.04066023436772670,  10.4893036545094823,   12.2971936103862059, 13.9828769539924302, 
16.0535514167049355 };
s=a[16]/(z+19./(z+25./(z)));  for(n=15;n>=0;n--) s=a[n]/(z+s);
return  s + log(2.*M_PI)/2. - z + (z+.5)*log(z);
} //  logfactorial for large values of argument except vicinity of negative part of real axis)

z_type infac0(z_type z){ z_type s; int n;  DB c[28]={ 1.,
 0.57721566490153286061,        -0.65587807152025388108,
-0.042002635034095235529,        0.16653861138229148950,
-0.042197734555544336748,       -0.0096219715278769735621,
 0.0072189432466630995424,      -0.0011651675918590651121,
-0.00021524167411495097282,      0.00012805028238811618615,
-0.000020134854780788238656,    -0.0000012504934821426706573,
 0.0000011330272319816958824,   -2.0563384169776071035e-7,
 6.1160951044814158179e-9,       5.0020076444692229301e-9,
-1.1812745704870201446e-9,       1.0434267116911005105e-10,
 7.7822634399050712540e-12,     -3.6968056186422057082e-12,
 5.1003702874544759790e-13,     -2.0583260535665067832e-14,
-5.3481225394230179824e-15,      1.2267786282382607902e-15,
-1.1812593016974587695e-16,      1.1866922547516003326e-18,
 1.4123806553180317816e-18};
 s=c[27]*z; for(n=26;n>0;n--) {s+=c[n]; s*=z;}
 s+=c[0];  return s;}

z_type fac0(z_type z){ return 1./infac0(z);}

z_type expaun(z_type z) {int n,m; DB x,y;
               x=Re(z);if(x<-.5) return expaun(z+1.)-log(z+1.);
                       if(x>.6) return expaun(z-1.)+log(z);
               y=Im(z); if(fabs(y)>1.4)return expaun(z/2.)+expaun(z/2.-.5)+z*log(2.)-log(sqrt(M_PI));
                       return -log(infac0(z)); }

z_type lof(z_type z){DB x,y; x=Re(z); y=Im(z);
        if(fabs(y)>5. ) return fracti(z);
        if(x>0 && x*x+y*y>25.) return fracti(z);
       return expaun(z);  } // lof(z) returns 16 digits of complex logfactorial.

 z_type infac1(z_type z){return infac0(z/2.)*infac0((z-1.)/2.)*sqrt(M_PI)/exp(log(2.)*z);}
 z_type infac2(z_type z){return infac1(z/2.)*infac1((z-1.)/2.)*sqrt(M_PI)/exp(log(2.)*z);}
 z_type infac3(z_type z){return infac2(z/2.)*infac2((z-1.)/2.)*sqrt(M_PI)/exp(log(2.)*z);}
 z_type inhalf(z_type z){DB x=Re(z); DB y=Im(z); DB r=x*x+y*y;
                       if(r<2.) return infac0(z); 
                       if(r<5.) return infac1(z);
                                return infac2(z); }

z_type infacmi(z_type z){ if(Re(z)> 1.) return infacmi(z-1.)/z;     return inhalf(z);}
z_type infaclu(z_type z){ if(Re(z)<-.5) return infaclu(z+1.)*(z+1.);return inhalf(z);}

z_type infac(z_type z){DB x=Re(z),y=Im(z),t=x*x+y*y; if(t<1.)return infac0(z);
       if( fabs(y)> 5. || (x>0 && t>25) )              return exp(-fracti(z));
       if( x>0 ) return infacmi(z);
                 return infaclu(z);}

z_type fac(z_type z){ DB x=Re(z),y=Im(z),t=x*x+y*y; if(t<2.)return 1./infac0(z);
               if( (x>0. && t>25.) || fabs(y)>5.)         return exp(fracti(z));
               if(x>0) return 1./infacmi(z);
                       return 1./infaclu(z);}

facmap.cc

// do not forget to load also conto.cin and ado.cin

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "fac.cin"
//#include "sinc.cin"
#include "facp.cin"
#include "afacc.cin"
//#include "superfac.cin"
#include "conto.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  int M=403,M1=M+1;
  int N=401,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
// FILE *o;o=fopen("fig2b.eps","w");ado(o,402,402);
FILE *o;o=fopen("facmap.eps","w");ado(o,402,402);
fprintf(o,"201 201 translate\n 20 20 scale\n");
DO(m,212) X[m]=-8.+.04*(m);
   X[212]=.45;
   X[213]=.46;
   X[214]=.47;
for(m=215;m<M1;m++) X[m]=-8.+.04*(m-3.); 
DO(n,200)Y[n]=-8.+.04*n;
        Y[200]=-.008;
        Y[201]= .008;
for(n=202;n<N1;n++) Y[n]=-8.+.04*(n-1.); 
for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
for(n=-8;n<9;n++){     M(  -8,n)L(8,n)}
fprintf(o,".008 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);         
//     c=afacc(z);
       c=fac(z);
//     c=superfac(z);
//     p=abs(c-d)/(abs(c)+abs(d));  p=-log(p)/log(10.)-1.;
       p=Re(c);q=Im(c);        
       if(p>-9999 && p<9999 &&
//       (fabs(y)>.034 ||x>-.9 ||fabs(x-int(x))>1.e-3) &&
          q>-9999 && q<9999 //&& fabs(q)> 1.e-19
       ) 
       {g[m*N1+n]=p;f[m*N1+n]=q;}
                       }}
//fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.8;q=.7;

fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.8;
for(m=-4;m<4;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".025 W 0 .6 0 RGB S\n");
for(m=0;m<2;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".025 W .9 0 0 RGB S\n");
for(m=0;m<2;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".025 W 0 0 .9 RGB S\n");
for(m=1;m<15;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".07 W .9 0 0 RGB S\n");
for(m=1;m<15;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".07 W 0 0 .9 RGB S\n");
                 conto(o,f,w,v,X,Y,M,N, (0.  ),-9,9); fprintf(o,".07 W .6 0 .6 RGB S\n");
for(m=-14;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".07 W 0 0 0 RGB S\n");
          m=0;     conto(o,g,w,v,X,Y,M,N, (0.+m),-9,9); fprintf(o,".07 W 0 0 0 RGB S\n");
for(m=1;m<17;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".07 W 0 0 0 RGB S\n");

//#include"plofu.cin"

x=0.8856031944;
conto(o,g,w,v,X,Y,M,N,0.8856031944,-p,p); fprintf(o,".02 W .5 .5 0 RGB S\n");
/*
M(x,-8)L(x,8) fprintf(o,"0 setlinejoin 0 setlinecap 0.004 W 0 0 0 RGB S\n");
M(x,0)L(-8.1,0) fprintf(o,"                   .05 W  1 1 1 RGB S\n");
DO(m,23){ M(x-.4*m,0)L(x-.4*(m+.5),0);} fprintf(o,".09 W  .3 .3 0 RGB S\n");
//M(x,0)L(-8.1,0) fprintf(o,"[.19 .21]0 setdash .05 W  0 0 0 RGB S\n");
// May it be, that, some printers do not interpret well the dashing ?
*/
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf facmap.eps");  
       system(    "open facmap.pdf");  //for LINUX
//     getchar(); system("killall Preview");//for mac
}

Latex generator of labels

% % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \usepackage{hyperref} % \paperwidth 339px % \paperheight 336px % \textwidth 165mm % \textheight 240mm % \topmargin -96pt % \oddsidemargin -76pt % \parindent 0pt % \begin {document} % \newcommand \sx {\scalebox} % \newcommand \rme {{e}} % \newcommand \rmi {{\rm i}} %imaginary unity is always roman font % \newcommand \ds {\displaystyle} % \newcommand \bN {\mathbb{N}} % \newcommand \bC {\mathbb{C}} % \newcommand \bR {\mathbb{R}} % \newcommand \cO {\mathcal{O}} % \newcommand \cF {\mathcal{F}} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \nS {\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!} % \newcommand \pS {{~}~{~}} % \newcommand \fac {\mathrm{Factorial}} % \newcommand \ax { % \put( 10,342){\sx{1.4}{$y$}} % \put( 10,307){\sx{1.3}{$6$}} % \put( 10,267){\sx{1.3}{$4$}} % \put( 10,227){\sx{1.3}{$2$}} % \put( 10,187){\sx{1.3}{$0$}} % \put( 0,147){\sx{1.3}{$-2$}} % \put( 0,107){\sx{1.3}{$-4$}} % \put( 0, 67){\sx{1.3}{$-6$}} % \put( 0, 27){\sx{1.3}{$-8$}} % \put( 50, 18){\sx{1.3}{$-6$}} % \put( 90, 18){\sx{1.3}{$-4$}} % \put(130, 18){\sx{1.3}{$-2$}} % \put(178, 18){\sx{1.3}{$0$}} % \put(218, 18){\sx{1.3}{$2$}} % \put(258, 18){\sx{1.3}{$4$}} % \put(298, 18){\sx{1.3}{$6$}} % \put(334, 19){\sx{1.4}{$x$}} % } % \begin{picture}(340,340) \ax % \put(-20,-10){\includegraphics{facmap}} % %\put(266,246){\rot{-14}\sx{1.6}{$u\!=\!0$}\ero} % \put(286,225){\rot{-7}\sx{1.6}{$v\!=\!0$}\ero} % \put(288,207){\rot{-5}\sx{1.6}{$u\!=\!0$}\ero} % \put(299,187){\sx{1.6}{$v\!=\!0$}} % \put(288,168){\rot{5}\sx{1.6}{$u\!=\!0$}\ero} % \put(286,150){\rot{7}\sx{1.6}{$v\!=\!0$}\ero} % % % \put(103,100){\rot{54}\sx{1.6}{$u\!=\!0$}\ero} % \put(117,100){\rot{53}\sx{1.6}{$v\!=\!0$}\ero} % \put(135,100){\rot{54}\sx{1.6}{$u\!=\!0$}\ero} % \put(152,100){\rot{54}\sx{1.6}{$v\!=\!0$}\ero} % \put(167, 99){\rot{50}\sx{1.6}{$u\!=\!0$}\ero} % \put(182, 95){\rot{41}\sx{1.6}{$v\!=\!0$}\ero} % \put(194, 85){\rot{39}\sx{1.6}{$u\!=\!0$}\ero} % \put(201, 73){\rot{35}\sx{1.6}{$v\!=\!0$}\ero} % \put(208, 61){\rot{33}\sx{1.6}{$u\!=\!0$}\ero} % \put(215, 49){\rot{28}\sx{1.6}{$v\!=\!0$}\ero} % \end{picture} % \end{document} % %

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	17:50, 20 June 2013		2,355 × 2,334 (1.73 MB)	Maintenance script (talk \| contribs)	Importing image file

You cannot overwrite this file.

File usage

There are no pages that link to this file.

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.

Horizontal resolution	196.85 dpc
Vertical resolution	196.85 dpc

File:FacmapT500.png

Contents

C++ Generator of curves

fac.cin

facmap.cc

Latex generator of labels

File history

File usage

Metadata

Navigation menu

Personal tools

Namespaces

Variants

Views

More

Search

.

Tools