View source for File:Doya10map4bT60.png

[[complex map]] of the [[Doya function]] at with parameter unity.

$f=\mathrm{Doya}_1(x+\mathrm i y)$ in the $x,y$ plane with 
lines $u\!=\!\Re(f)\!=\!\mathrm{const}$ and
lines $v\!=\!\Im(f)\!=\!\mathrm{const}$.

==[[C++]] generator of curves==
// Files [[conto.cin]] and [[ado.cin]] and [[doya.cin]] should be loaded to the working directory for the compilation of the code below:

 #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 "conto.cin"
 #include "doya.cin"

 main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  int M=160,M1=M+1;
  int N=161,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("doya10map4b.eps","w");ado(o,82,82);
 fprintf(o,"41 41 translate\n 10 10 scale\n");
 DO(m,M1) X[m]=-4.+.05*(m);
 DO(n,N1) Y[n]=-4.+.05*(n+.5);
 for(m=-4;m<5;m++){if(m==0){M(m,-4.2)L(m,4.2)} else{M(m,-4)L(m,4)}}
 for(n=-4;n<5;n++){     M(  -4,n)L(4,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=Doya(1.,z); 
  p=Re(c);q=Im(c);      
  if(p>-99. && p<99. &&  q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
         }}
 fprintf(o,"1 setlinejoin 2 setlinecap\n");  p=1.;q=.9;
 for(m=-6;m<5;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".016 W 0 .6 0 RGB S\n");
 for(m=0;m<6;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".016 W .9 0 0 RGB S\n");
 for(m=0;m<6;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".016 W 0 0 .9 RGB S\n");
 for(m=1;m<5;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".05 W .9 0 0 RGB S\n");
 for(m=1;m<5;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 .9 RGB S\n");
                    conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".05 W .6 0 .6 RGB S\n");
 for(m=-5;m<6;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
 DO(m,11) {x=-3.1+.287*m; M(x,0) L(x+.04,0) }
 fprintf(o,".07 W 0 .5 1 RGB S\n");
 DO(m,10) {x=-2.96+.287*m; M(x,0) L(x+.04,0) }
 fprintf(o,".07 W 1 .5 0 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf doya10map4b.eps");     
        system(    "open doya10map4b.pdf");
        getchar(); system("killall Preview");
 }
==[[Latex]] generator of the labels==
<nowiki>
% Copyleft 2011 by Dmitrii Kouznetsov <br>
\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\usepackage{graphicx} %<br>
\usepackage{rotating} %<br>
\paperwidth 860pt %<br>
\paperheight 843pt %<br>
\topmargin -94pt %<br>
\oddsidemargin -96pt %<br>
\textwidth 1200pt %<br>
\textheight 1800pt %<br>
\pagestyle {empty} %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\newcommand \ing {\includegraphics} %<br>
\begin{document} %<br>
\sx{10}{ \begin{picture}(41,81) %<br>
\put(1,1){\ing{doya10map4b}} % <br>
\put(-.5,79.6){\sx{.4}{$t$}}% <br>
\put(-1,71){\sx{.4}{$3$}}% <br>
\put(-1,61){\sx{.4}{$2$}}% <br>
\put(-1,51){\sx{.4}{$1$}}% <br>
\put(-1,41){\sx{.4}{$0$}}% <br>
\put(-4,31){\sx{.4}{$-1$}}% <br>
\put(-4,21){\sx{.4}{$-2$}}% <br>
\put(-4,11){\sx{.4}{$-3$}}% <br>
\put(9,-1.5){\sx{.4}{$-3$}}% <br>
\put(18,-1.5){\sx{.4}{$-2$}}% <br>
\put(28,-1.5){\sx{.4}{$-1$}}% <br>
\put(41,-1.5){\sx{.4}{0}}% <br>
\put(51,-1.5){\sx{.4}{1}}% <br>
\put(61,-1.5){\sx{.4}{2}}% <br>
\put(71,-1.5){\sx{.4}{3}}% <br>
\put(79.8,-1.2){\sx{.42}{$x$}}% <br>
\put(11,60){\rot{85}\sx{.6}{$u\!=\!-2$}\ero}% <br>
\put(22,59){\rot{88}\sx{.6}{$u\!=\!-1$}\ero}% <br>
\put(34,63){\rot{90}\sx{.6}{$u\!=\!0$}\ero}% <br>
\put(46,63){\rot{93}\sx{.6}{$u\!=\!1$}\ero}% <br>
\put(56,63){\rot{93}\sx{.6}{$u\!=\!2$}\ero}% <br>
\put(66,63){\rot{93}\sx{.6}{$u\!=\!3$}\ero}% <br>
\put(68,69){\rot{1}\sx{.6}{$v\!=\!3$}\ero}% <br>
\put(68,60){\rot{1}\sx{.6}{$v\!=\!2$}\ero}% <br>
\put(68,50){\rot{1}\sx{.6}{$v\!=\!1$}\ero}% <br>
\put(68,40.6){\rot{0}\sx{.6}{$v\!=\!0$}\ero}% <br>
\put(63,30.6){\rot{-1}\sx{.6}{$v\!=\!-1$}\ero}% <br>
\put(63,20.8){\rot{-1}\sx{.6}{$v\!=\!-2$}\ero}% <br>
\put(63,11.4){\rot{-2}\sx{.6}{$v\!=\!-3$}\ero}% <br>
\end{picture} %<br>
}  %<br>
\end{document}
</nowiki>

[[Category:Book]]
[[Category:BookMap]]
[[Category:Complex maps]]
[[Category:Doya function]]
[[Category:Laser science]]
[[Category:Transfer function]]