Difference between revisions of "File:Sinftes04t300.jpg"

From TORI
Jump to navigation Jump to search
(Importing image file)
 
 
Line 1: Line 1:
  +
[[Explicit plot]] of the simplest self-[[SinFT]] function
−
Importing image file
  
  +
  +
$y=F(x)=2x \exp(-x^2/2)~$ , thin smooth curve,
  +
  +
its discrete representation at the mesh with 4 nodes (thick colored segmented line),
  +
  +
and its [[SFT]] (black segmented line). Even with so view nodes, visually, the two segmented curves practically coincide;
  +
the array is reproduced with at least 3 decimal digits.
  +
  +
==[[C++]] generator of lines==
  +
// Files [[ado.cin]] and [[scft.cin]] should be loaded in order of compile the code below
  +
<poem><nomathjax><nowiki>
  +
#include <stdio.h>
  +
#include <math.h>
  +
#include<stdlib.h>
  +
#include "scft.cin"
  +
#include "ado.cin"
  +
#define NP 4
  +
int main(){ int i; double a[NP],b[NP]; double d=sqrt(M_PI/NP); double x,y; FILE *o;
  +
for(i=0;i<NP;i++){ x=i*d; a[i]=b[i]=2.*x*exp(-.5*x*x); }
  +
sinft(b-1,NP);
  +
for(i=0;i<NP;i++) { b[i]*=sqrt(2./NP); printf("%2d %19.14lf %19.14lf %19.14lf\n",i,a[i],b[i], b[i]-a[i]);}
  +
//o=fopen("34.eps","w"); ado(o,470,140);
  +
o=fopen("sinftes04.eps","w"); ado(o,570,140);
  +
#define M(x,y) fprintf(o,"%9.4lf %9.4lf M\n",x+0.,y+0.);
  +
#define L(x,y) fprintf(o,"%9.4lf %9.4lf L\n",x+0.,y+0.);
  +
fprintf(o,"10 10 translate 100 100 scale 2 setlinecap 1 setlinejoin\n");
  +
for(i=0;i<12;i++){M(.5*i,0)L(.5*i,1)}
  +
for(i=0;i<3;i++){M(0,.5*i)L(5.5,.5*i)}
  +
fprintf(o,".007 W S\n");
  +
M(0,0); for(i=1;i<110;i++) { x=.05*i; y=2.*x*exp(-.5*x*x); L(x,y);} fprintf(o,".009 W 0 0 0 RGB S\n");
  +
M(0,0); for(i=1;i<NP;i++) { x=d*i; y=a[i]; L(x,y);} fprintf(o,".04 W 1 0 .5 RGB S\n");
  +
M(0,0); for(i=1;i<NP;i++) { x=d*i; y=b[i]; L(x,y);} fprintf(o,".015 W 0 0 0 RGB S\n");
  +
  +
fprintf(o,"showpage\n%c%cTrailer\n",'%','%');
  +
fclose(o);
  +
system("epstopdf sinftes04.eps");
  +
system( "open sinftes04.pdf");
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of curve==
  +
<poem><nomathjax><nowiki>
  +
  +
</nowiki></nomathjax></poem>
  +
  +
==References==
  +
<references/>
  +
  +
[[Category:ado.cin]]
  +
[[Category:C++]]
  +
[[Category:Explicit plot]]
  +
[[Category:Integral transform]]
  +
[[Category:Latex]]
  +
[[Category:SFT]]
  +
[[Category:scft.cin]]

Latest revision as of 08:51, 1 December 2018

Explicit plot of the simplest self-SinFT function

$y=F(x)=2x \exp(-x^2/2)~$ , thin smooth curve,

its discrete representation at the mesh with 4 nodes (thick colored segmented line),

and its SFT (black segmented line). Even with so view nodes, visually, the two segmented curves practically coincide; the array is reproduced with at least 3 decimal digits.

C++ generator of lines

// Files ado.cin and scft.cin should be loaded in order of compile the code below


#include <stdio.h>
#include <math.h>
#include<stdlib.h>
#include "scft.cin"
#include "ado.cin"
#define NP 4
int main(){ int i; double a[NP],b[NP]; double d=sqrt(M_PI/NP); double x,y; FILE *o;
for(i=0;i<NP;i++){ x=i*d; a[i]=b[i]=2.*x*exp(-.5*x*x); }
sinft(b-1,NP);
for(i=0;i<NP;i++) { b[i]*=sqrt(2./NP); printf("%2d %19.14lf %19.14lf %19.14lf\n",i,a[i],b[i], b[i]-a[i]);}
//o=fopen("34.eps","w"); ado(o,470,140);
o=fopen("sinftes04.eps","w"); ado(o,570,140);
#define M(x,y) fprintf(o,"%9.4lf %9.4lf M\n",x+0.,y+0.);
#define L(x,y) fprintf(o,"%9.4lf %9.4lf L\n",x+0.,y+0.);
fprintf(o,"10 10 translate 100 100 scale 2 setlinecap 1 setlinejoin\n");
for(i=0;i<12;i++){M(.5*i,0)L(.5*i,1)}
for(i=0;i<3;i++){M(0,.5*i)L(5.5,.5*i)}
fprintf(o,".007 W S\n");
M(0,0); for(i=1;i<110;i++) { x=.05*i; y=2.*x*exp(-.5*x*x); L(x,y);} fprintf(o,".009 W 0 0 0 RGB S\n");
M(0,0); for(i=1;i<NP;i++) { x=d*i; y=a[i]; L(x,y);} fprintf(o,".04 W 1 0 .5 RGB S\n");
M(0,0); for(i=1;i<NP;i++) { x=d*i; y=b[i]; L(x,y);} fprintf(o,".015 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer\n",'%','%');
fclose(o);
system("epstopdf sinftes04.eps");
system( "open sinftes04.pdf");
}

Latex generator of curve

References

File history

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

Date/TimeThumbnailDimensionsUserComment
current06:14, 1 December 2018Thumbnail for version as of 06:14, 1 December 20181,183 × 282 (48 KB)Maintenance script (talk | contribs)Importing image file

You cannot overwrite this file.

The following page uses 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.

Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:Sinftes04t300.jpg&oldid=21496"