Difference between revisions of "File:Moriasmap1.jpg"

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[[Complex map]] of asymptotic approximation [[morias]] of function [[mori]]
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Importing image file
  
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  +
==[[C++]] generator of [[Complex map]]==
  +
// Files [[ado.cin]], [[conto.cin]], [[morias.cin]] should be loaded in order to compile the code below
  +
//<poem><nomathjax><nowiki>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
#include "conto.cin"
  +
//#include "korias.cin"
  +
//#include "besselj0.cin"
  +
//#include "korifit76.cin"
  +
#include "morias.cin"
  +
  +
//DB L1=2.404825557695772768621631879326454643124;
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
int M=501,M1=M+1;
  +
int N=301,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("moriasma1.eps","w");ado(o,1020,620);
  +
fprintf(o,"210 210 translate\n 100 100 scale\n");
  +
DO(m,M1)X[m]=-2.+.02*(m-.5);
  +
DO(n,N1)Y[n]=-2.+.02*(n-.5);;
  +
  +
for(m=-2;m<9;m+=1){M(m,-2)L(m,4)}
  +
for(n=-2;n<5;n+=1){ M(-2,n)L(8,n)}
  +
fprintf(o,".01 W 0 0 0 RGB S\n");
  +
  +
//DB po=.05;
  +
DB po=.1;
  +
//DB xo=4*L1/po;
  +
//M(xo,po); DO(m,100){ x=xo+1.+m; y=x/xo-1.; L(x,y); if(y>100) break;}
  +
//fprintf(o,".1 W 1 0 0 RGB S\n");
  +
  +
// DB x0=L1/po; M(0,0)L(x0,0)L(40.,40.-x0); fprintf(o,".2 W 0 1 0 RGB S\n");
  +
  +
DO(m,M1)DO(n,N1){g[m*N1+n]=99999999; f[m*N1+n]=999999999;}
  +
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y);
  +
// c=BesselJ0(L1*sqrt(z))/(1.-z);
  +
// c=BesselJ0(L1*z)/(1.-z*z);
  +
// c=korifit76(z);
  +
// c=korias(z);
  +
// c*=c*exp(po*I*z);
  +
// c=log(c);
  +
//c=exp(I*(-2.*L1+po*z)*z)/z ;
  +
//c=(I*(-2.*L1+po*z)*z) ;
  +
//c=(-2.*L1+po*z)*z ;
  +
c=morias(z); // c*=c*exp(I*po*z*z)*z;
  +
p=Re(c); q=Im(c);
  +
if(p>-999999. && p<999999. && q>-999999. && q<999999 ){g[m*N1+n]=p; f[m*N1+n]=q;
  +
}
  +
}}
  +
//#include "plodi.cin"
  +
/*
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n"); q=.05;
  +
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n");
  +
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n");
  +
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 0 .8 RGB S\n");
  +
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W .8 0 0 RGB S\n");
  +
*/
  +
  +
p=16;q=1;
  +
for(m=-4;m<4;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".016 W 0 .8 0 RGB S\n");
  +
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".009 W 1 0 0 RGB S\n");
  +
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".009 W 0 0 1 RGB S\n");
  +
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W 1 0 0 RGB S\n");
  +
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 1 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-4*p,4*p); fprintf(o,".03 W .9 0 .9 RGB S\n");
  +
for(m=-8;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-4*p,4*p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
for(m=1;m<9;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
//#include "plofu.cin"
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf moriasma1.eps");
  +
system( "open moriasma1.pdf");
  +
getchar(); system("killall Preview");//for mac
  +
}
  +
//</nowiki></nomathjax></poem>
  +
  +
  +
==[[Latex]] generator of labels==
  +
  +
%<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{graphicx}
  +
\usepackage{geometry}
  +
\usepackage{rotating}
  +
\paperwidth 1034px
  +
\paperheight 630px
  +
\textwidth 2000pt
  +
\textheight 900pt
  +
\newcommand \sx \scalebox
  +
\newcommand \ing \includegraphics
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\oddsidemargin -70pt
  +
\topmargin -100pt
  +
\parindent 0pt
  +
\begin{document}
  +
\begin{picture}(1020,616)
  +
%\put(20,10){\ing{moriama1}}
  +
\put(20,10){\ing{moriasma1}}
  +
\put( 8,610){\sx{2.8}{$y$}}
  +
%\put( 8,610){\sx{2.8}{$4$}}
  +
\put( 8,510){\sx{2.8}{$3$}}
  +
\put( 8,410){\sx{2.6}{$2$}}
  +
\put( 8,310){\sx{2.8}{$1$}}
  +
\put( 8,210){\sx{2.8}{$0$}}
  +
\put(-11,110){\sx{2.8}{$-1$}}
  +
\put(0,-6){\sx{2.8}{$-2$}}
  +
\put(100,-6){\sx{2.8}{$-1$}}
  +
\put(223,-6){\sx{2.8}{$0$}}
  +
\put(323,-6){\sx{2.8}{$1$}}
  +
\put(424,-6){\sx{2.8}{$2$}}
  +
\put(524,-6){\sx{2.8}{$3$}}
  +
\put(625,-6){\sx{2.8}{$4$}}
  +
\put(725,-6){\sx{2.8}{$5$}}
  +
\put(825,-6){\sx{2.8}{$6$}}
  +
\put(926,-6){\sx{2.8}{$7$}}
  +
%\put(1027,-6){\sx{2.8}{$8$}}
  +
%\put(1127,-6){\sx{2.8}{$9$}}
  +
\put(1020,-6){\sx{2.8}{$x$}}
  +
%
  +
\put(116,534){\rot{76}\sx{2.5}{$u\!=\!-8$}\ero}
  +
\put(170,544){\rot{90}\sx{2.5}{$u\!=\!8$}\ero}
  +
%
  +
\put(212,542){\rot{80}\sx{2.5}{$v\!=\!8$}\ero}
  +
\put(262,538){\rot{92}\sx{2.5}{$v\!=\!-8$}\ero}
  +
%
  +
%\put(250,230){\rot{47}\sx{2.5}{$u\!=\!1$}\ero}
  +
%
  +
\put(400,134){\rot{62}\sx{2.5}{$u\!=\!0.1$}\ero}
  +
\put(402,114){\rot{27}\sx{2.5}{$u\!=\!-0.1$}\ero}
  +
%
  +
\put(480,431){\rot{0}\sx{2.6}{$v\!=\!2$}\ero}
  +
\put(490,400){\rot{0}\sx{2.6}{$v\!=\!1$}\ero}
  +
\put(498,329){\rot{0}\sx{2.6}{$v\!=\!0.2$}\ero}
  +
\put(514,296){\rot{0}\sx{2.6}{$v\!=\!0.1$}\ero}
  +
%
  +
\put(564,419){\rot{0}\sx{2.6}{$u\!=\!1$}\ero}
  +
%
  +
\put(468,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
\put(518,213){\rot{0}\sx{2.6}{$v\!=\!0$}\ero}
  +
\put(518,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
\put(600,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
\put(656,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
\put(730,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
\put(790,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
\put(862,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
\put(922,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
\put(992,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
%\put(1054,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
%\put(1124,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
  +
%\put(1186,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
  +
\end{picture}
  +
\end{document}
  +
%</nowiki></nomathjax></poem>
  +
  +
[[Category:Asymptotic expansion]]
  +
[[Category:Bessel function]]
  +
[[Category:C++]]
  +
[[Category:Complex map]]
  +
[[Category:Latex]]
  +
[[Category:Morinaga function]]

Latest revision as of 08:43, 1 December 2018

Complex map of asymptotic approximation morias of function mori

C++ generator of Complex map

// Files ado.cin, conto.cin, morias.cin should be loaded in order to compile the code below

//


#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
//#include "korias.cin"
//#include "besselj0.cin"
//#include "korifit76.cin"
#include "morias.cin"

//DB L1=2.404825557695772768621631879326454643124;
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=501,M1=M+1;
int N=301,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("moriasma1.eps","w");ado(o,1020,620);
fprintf(o,"210 210 translate\n 100 100 scale\n");
DO(m,M1)X[m]=-2.+.02*(m-.5);
DO(n,N1)Y[n]=-2.+.02*(n-.5);;

for(m=-2;m<9;m+=1){M(m,-2)L(m,4)}
for(n=-2;n<5;n+=1){ M(-2,n)L(8,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");

//DB po=.05;
DB po=.1;
//DB xo=4*L1/po;
//M(xo,po); DO(m,100){ x=xo+1.+m; y=x/xo-1.; L(x,y); if(y>100) break;}
//fprintf(o,".1 W 1 0 0 RGB S\n");

// DB x0=L1/po; M(0,0)L(x0,0)L(40.,40.-x0); fprintf(o,".2 W 0 1 0 RGB S\n");

DO(m,M1)DO(n,N1){g[m*N1+n]=99999999; f[m*N1+n]=999999999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=BesselJ0(L1*sqrt(z))/(1.-z);
// c=BesselJ0(L1*z)/(1.-z*z);
// c=korifit76(z);
// c=korias(z);
// c*=c*exp(po*I*z);
// c=log(c);
//c=exp(I*(-2.*L1+po*z)*z)/z ;
//c=(I*(-2.*L1+po*z)*z) ;
//c=(-2.*L1+po*z)*z ;
c=morias(z); // c*=c*exp(I*po*z*z)*z;
     p=Re(c); q=Im(c);
     if(p>-999999. && p<999999. && q>-999999. && q<999999 ){g[m*N1+n]=p; f[m*N1+n]=q;
}
                     }}
//#include "plodi.cin"
/*
fprintf(o,"1 setlinejoin 1 setlinecap\n"); q=.05;
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n");
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n");
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 0 .8 RGB S\n");
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W .8 0 0 RGB S\n");
*/

p=16;q=1;
for(m=-4;m<4;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".016 W 0 .8 0 RGB S\n");
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".009 W 1 0 0 RGB S\n");
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".009 W 0 0 1 RGB S\n");
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W 1 0 0 RGB S\n");
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 1 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-4*p,4*p); fprintf(o,".03 W .9 0 .9 RGB S\n");
for(m=-8;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
    m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-4*p,4*p); fprintf(o,".02 W 0 0 0 RGB S\n");
for(m=1;m<9;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
//#include "plofu.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf moriasma1.eps");
     system( "open moriasma1.pdf");
     getchar(); system("killall Preview");//for mac
}
//


Latex generator of labels

%


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{geometry}
\usepackage{rotating}
\paperwidth 1034px
\paperheight 630px
\textwidth 2000pt
\textheight 900pt
\newcommand \sx \scalebox
\newcommand \ing \includegraphics
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\oddsidemargin -70pt
\topmargin -100pt
\parindent 0pt
\begin{document}
\begin{picture}(1020,616)
%\put(20,10){\ing{moriama1}}
\put(20,10){\ing{moriasma1}}
\put( 8,610){\sx{2.8}{$y$}}
%\put( 8,610){\sx{2.8}{$4$}}
\put( 8,510){\sx{2.8}{$3$}}
\put( 8,410){\sx{2.6}{$2$}}
\put( 8,310){\sx{2.8}{$1$}}
\put( 8,210){\sx{2.8}{$0$}}
\put(-11,110){\sx{2.8}{$-1$}}
\put(0,-6){\sx{2.8}{$-2$}}
\put(100,-6){\sx{2.8}{$-1$}}
\put(223,-6){\sx{2.8}{$0$}}
\put(323,-6){\sx{2.8}{$1$}}
\put(424,-6){\sx{2.8}{$2$}}
\put(524,-6){\sx{2.8}{$3$}}
\put(625,-6){\sx{2.8}{$4$}}
\put(725,-6){\sx{2.8}{$5$}}
\put(825,-6){\sx{2.8}{$6$}}
\put(926,-6){\sx{2.8}{$7$}}
%\put(1027,-6){\sx{2.8}{$8$}}
%\put(1127,-6){\sx{2.8}{$9$}}
\put(1020,-6){\sx{2.8}{$x$}}
%
\put(116,534){\rot{76}\sx{2.5}{$u\!=\!-8$}\ero}
\put(170,544){\rot{90}\sx{2.5}{$u\!=\!8$}\ero}
%
\put(212,542){\rot{80}\sx{2.5}{$v\!=\!8$}\ero}
\put(262,538){\rot{92}\sx{2.5}{$v\!=\!-8$}\ero}
%
%\put(250,230){\rot{47}\sx{2.5}{$u\!=\!1$}\ero}
%
\put(400,134){\rot{62}\sx{2.5}{$u\!=\!0.1$}\ero}
\put(402,114){\rot{27}\sx{2.5}{$u\!=\!-0.1$}\ero}
%
\put(480,431){\rot{0}\sx{2.6}{$v\!=\!2$}\ero}
\put(490,400){\rot{0}\sx{2.6}{$v\!=\!1$}\ero}
\put(498,329){\rot{0}\sx{2.6}{$v\!=\!0.2$}\ero}
\put(514,296){\rot{0}\sx{2.6}{$v\!=\!0.1$}\ero}
%
\put(564,419){\rot{0}\sx{2.6}{$u\!=\!1$}\ero}
%
\put(468,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
\put(518,213){\rot{0}\sx{2.6}{$v\!=\!0$}\ero}
\put(518,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
\put(600,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
\put(656,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
\put(730,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
\put(790,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
\put(862,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
\put(922,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
\put(992,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
%\put(1054,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
%\put(1124,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero}
%\put(1186,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero}
\end{picture}
\end{document}
%

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