Difference between revisions of "File:Korimap.jpg"

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[[Complex map]] of function [[kori]]
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$u+\mathrm i v=\,$[[kori]]$(x\!+\!\mathrm i y)$
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For $z\ne 1$, [[kori]] can be defined with
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[[kori]]$(z)=\displaystyle \frac{J_0\big(L_1 \sqrt{z}\big)}{1-z}$
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where $L_1=\,$[[BesselJZero]][0,1]$\approx 2.4$ is first zero of function $J_0=\,$[[BesselJ0]]
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==[[C++]] generator of map==
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Files
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[[ado.cin]],
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[[conto.cin]],
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[[besselj0.cin]]
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should be loaded in order to compile the [[C++]] code below.
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<poem><nomathjax><nowiki>
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#include <stdio.h>
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#include <stdlib.h>
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#define DB double
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#define DO(x,y) for(x=0;x<y;x++)
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#include <complex>
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typedef std::complex<double> z_type;
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#define Re(x) x.real()
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#define Im(x) x.imag()
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#define I z_type(0.,1.)
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#include "conto.cin"
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#include "besselj0.cin"
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//#include "korifit76.cin"
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DB L1=2.404825557695772768621631879326454643124;
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int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
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int M=501,M1=M+1;
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int N=551,N1=N+1;
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DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
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char v[M1*N1]; // v is working array
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//FILE *o;o=fopen("korifit76ma.eps","w");ado(o,1506,1104);
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FILE *o;o=fopen("korima.eps","w");ado(o,1506,1104);
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fprintf(o,"102 102 translate\n 10 10 scale\n");
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DO(m,M1) X[m]=-10.+.2*(m-.5)*(1+.001*m);
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DO(n,N1)Y[n]=-10+.2*(n-.5);//*(1+.001*n);
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for(m=-10;m<10;m++){if(m!=0){M(m,-10)L(m,10)}}
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for(n=-10;n<10;n++){ M( -10,n)L(10,n)}
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for(m=-10;m<160;m+=10){if(m!=0){M(m,-10)L(m,100)}}
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for(n=-10;n<110;n+=10){ M( -10,n)L(140,n)}
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fprintf(o,".01 W 0 0 0 RGB S\n");
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M(0,-10)L(0,100) fprintf(o,".03 W 0 .5 0 RGB S\n");
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DO(m,M1)DO(n,N1){g[m*N1+n]=99999; f[m*N1+n]=99999;}
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DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
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DO(n,N1){y=Y[n]; z=z_type(x,y);
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c=BesselJ0(L1*sqrt(z))/(1.-z);
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// c=korifit76(z);
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p=Re(c); q=Im(c);
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if(p>-9999. && p<9999.
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&& q>-9999. && q<9999
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)
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{g[m*N1+n]=p;
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f[m*N1+n]=q;
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}
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}}
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//#include "plodi.cin"
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fprintf(o,"1 setlinejoin 1 setlinecap\n"); q=.05;
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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");
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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");
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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");
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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");
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p=20;q=2;
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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,".01 W 0 .8 0 RGB S\n");
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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,".01 W 1 0 0 RGB S\n");
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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,".01 W 0 0 1 RGB S\n");
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for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".05 W 1 0 0 RGB S\n");
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for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 1 RGB S\n");
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conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".05 W .9 0 .9 RGB S\n");
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for(m=-8;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
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m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-2*p,2*p); fprintf(o,".03 W 0 0 0 RGB S\n");
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for(m=1;m<9;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
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//#include "plofu.cin"
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf korima.eps");
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system( "open korima.pdf");
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getchar(); system("killall Preview");//for mac
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}
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</nowiki></nomathjax></poem>
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==[[Latex]] generator of labels==
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<poem><nomathjax><nowiki>
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</nowiki></nomathjax></poem>
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==References==
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<references/>
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[[Category:Bessel function]]
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[[Category:Complex map]]
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[[Category:Kori]]
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[[Category:Morinaga function]]

Latest revision as of 08:40, 1 December 2018

Complex map of function kori

$u+\mathrm i v=\,$kori$(x\!+\!\mathrm i y)$

For $z\ne 1$, kori can be defined with

kori$(z)=\displaystyle \frac{J_0\big(L_1 \sqrt{z}\big)}{1-z}$

where $L_1=\,$BesselJZero[0,1]$\approx 2.4$ is first zero of function $J_0=\,$BesselJ0

C++ generator of map

Files ado.cin, conto.cin, besselj0.cin should be loaded in order to compile the C++ 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 "besselj0.cin"
//#include "korifit76.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=551,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("korifit76ma.eps","w");ado(o,1506,1104);
FILE *o;o=fopen("korima.eps","w");ado(o,1506,1104);
fprintf(o,"102 102 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-10.+.2*(m-.5)*(1+.001*m);
DO(n,N1)Y[n]=-10+.2*(n-.5);//*(1+.001*n);

for(m=-10;m<10;m++){if(m!=0){M(m,-10)L(m,10)}}
for(n=-10;n<10;n++){ M( -10,n)L(10,n)}

for(m=-10;m<160;m+=10){if(m!=0){M(m,-10)L(m,100)}}
for(n=-10;n<110;n+=10){ M( -10,n)L(140,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
M(0,-10)L(0,100) fprintf(o,".03 W 0 .5 0 RGB S\n");

DO(m,M1)DO(n,N1){g[m*N1+n]=99999; f[m*N1+n]=99999;}
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=korifit76(z);
     p=Re(c); q=Im(c);
     if(p>-9999. && p<9999.
      && q>-9999. && q<9999
     )
{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=20;q=2;
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,".01 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,".01 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,".01 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,".05 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,".05 W 0 0 1 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".05 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,".03 W 0 0 0 RGB S\n");
    m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-2*p,2*p); fprintf(o,".03 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,".03 W 0 0 0 RGB S\n");
//#include "plofu.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf korima.eps");
     system( "open korima.pdf");
     getchar(); system("killall Preview");//for mac
}

Latex generator of labels

References

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