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lab2015larc.cpp
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lab2015larc.cpp
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/*============================================================================
* Daniel J. Greenhoe
*============================================================================*/
/*=====================================
* headers
*=====================================*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include "main.h"
#include "symseq.h"
#include "r1.h"
#include "r2.h"
#include "r3.h"
#include "r4.h"
#include "r6.h"
#include "c1.h"
#include "c4.h"
#include "c6.h"
#include "r1op.h"
#include "r2op.h"
#include "r3op.h"
#include "r4op.h"
#include "r6op.h"
#include "elliptic.h"
#include "larc.h"
#include "mca.h"
#include "euclid.h"
#include "fileplot.h"
#include "lab2015larc.h"
#include "gtest/gtest.h" // https://github.com/google/googletest/blob/master/googletest/docs/primer.md
/*-------------------------------------------------------------------------
* generate larc distance data in R^2
*-------------------------------------------------------------------------*/
int lab_larc_distances_R2(const char *basefilename){
time_t time1; time(&time1); //starting time stamp (passed to plotting routine)
vectR2 p,q;
double d,dN;
int fails=0;
char comment[1024]; //comment to be passed to plotting function
char buf[1024]; //general purpose buffer
char filename[1024];
FILE *lptr; // pointer to log file
//----------------------------------------------
//open log file
//----------------------------------------------
printf( "----------------------------------------------------------------\n");
sprintf(comment,"Experiment: calculate distances in R^2 using Lagrange arc distance function"); printf("%s\n",comment);
printf( "----------------------------------------------------------------\n");
sprintf(filename,"%s",basefilename);
lptr=log_open (filename,time1,comment);
//----------------------------------------------
//sprintf(buf,"Generate fair die sequence...");printofe(lptr,buf,time1);
//----------------------------------------------
printof(lptr,"Theorem 3.9 (1): triangle inequality fails\n");
p.put(1,0); q.put(-0.5,0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(1,0); q.put(-0.5,0.2); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(-0.5,0.2); q.put(-0.5,0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
printof(lptr,"Theorem 3.9 (2): translation invariance fails\n");
p.put(1,0.5); q.put(0.5,1); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(0.5,0); q.put(0,0.5); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
printof(lptr,"Theorem 3.9 (5): balls are not convex\n");
p.put(0,1); q.put(-0.70,-1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
q.put(0,1); p.put(-0.70,-1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(0,1); q.put( 0.70,-1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
q.put(0,1); p.put( 0.70,-1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(0,1); q.put( 0, -1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
q.put(0,1); p.put( 0, -1.12); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
printof(lptr,"Theorem 3.10: Lagrange arc distance versus Euclidean metric\n");
p.put(1,0); q.put(-0.50,0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
q.put(1,0); p.put(-0.50,0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(1,0); q.put(-0.50,0.75); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
q.put(1,0); p.put(-0.50,0.75); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
printof(lptr,"Example 3.12: Lagrange arc distance in R^2\n");
p.put( 0,1); q.put( 1, 0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 0,1); q.put(-1, 0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 0,1); q.put( 0,-1); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 1,0); q.put( 0,-1); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 1,0); q.put(-1, 0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put(-1,0); q.put( 0,-1); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 0,1); q.put( 2, 0); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 0,1); q.put( 0,-2); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
p.put( 0,1); q.put(-2, 1); d=larc_metric(p,q); dN=larc_metric(p,q,1000); sprintf(buf,"d((%6.3lf,%6.3lf),(%6.3lf,%6.3lf))=%13.10lf ~= %13.10lf ",p.getx(),p.gety(),q.getx(),q.gety(),d,dN);printof(lptr,buf); if(dN<d*0.999||dN>d*1.001){printof(lptr,"FAIL\n");fails++;}else printof(lptr,"ok\n");
sprintf(buf,"number of fails = %d\n",fails); printof(lptr,buf);
//----------------------------------------------
// close log file
//----------------------------------------------
sprintf(buf,"lab_larc_distances_R2 experiment complete"); printofe(lptr,buf,time1);
plot_close(lptr,time1);
return 0;
}
/*-------------------------------------------------------------------------
* generate larc R^3 distance data
*-------------------------------------------------------------------------*/
int lab_larc_distances_R3(const char *basefilename){
time_t time1; time(&time1); //starting time stamp (passed to plotting routine)
vectR3 p,q;
double d,de,s=1.0/PI;
char comment[1024]; //comment to be passed to plotting function
char buf[1024]; //general purpose buffer
char filename[1024];
FILE *lptr; // pointer to log file
//----------------------------------------------
//open log file
//----------------------------------------------
printf( "----------------------------------------------------------------\n");
sprintf(comment,"Experiment: calculate distances in R^3 using Lagrange arc distance function"); printf("%s\n",comment);
printf( "----------------------------------------------------------------\n");
sprintf(filename,"%s",basefilename);
lptr=log_open (filename,time1,comment);
//----------------------------------------------
printof(lptr,"Example 3.13: Lagrange arc distance in R^3\n");
//----------------------------------------------
p.put( 0, 1, 0); q.put( 2, 0, 0); d=larc_metric(p,q); de=ae_metric(s,p,q); sprintf(buf,"d((%6.3lf,%6.3lf,%6.3lf),(%6.3lf,%6.3lf,%6.3lf))=%12.9lf ae=%12.9lf\n",p.getx(),p.gety(),p.getz(),q.getx(),q.gety(),q.getz(),d,de); printof(lptr,buf);
p.put( 0, 1, 0); q.put( 0,-2, 0); d=larc_metric(p,q); de=ae_metric(s,p,q); sprintf(buf,"d((%6.3lf,%6.3lf,%6.3lf),(%6.3lf,%6.3lf,%6.3lf))=%12.9lf ae=%12.9lf\n",p.getx(),p.gety(),p.getz(),q.getx(),q.gety(),q.getz(),d,de); printof(lptr,buf);
p.put( 0, 1, 0); q.put(-2, 1, 0); d=larc_metric(p,q); de=ae_metric(s,p,q); sprintf(buf,"d((%6.3lf,%6.3lf,%6.3lf),(%6.3lf,%6.3lf,%6.3lf))=%12.9lf ae=%12.9lf\n",p.getx(),p.gety(),p.getz(),q.getx(),q.gety(),q.getz(),d,de); printof(lptr,buf);
p.put( 0, 1, 0); q.put(-1, 0,-1); d=larc_metric(p,q); de=ae_metric(s,p,q); sprintf(buf,"d((%6.3lf,%6.3lf,%6.3lf),(%6.3lf,%6.3lf,%6.3lf))=%12.9lf ae=%12.9lf\n",p.getx(),p.gety(),p.getz(),q.getx(),q.gety(),q.getz(),d,de); printof(lptr,buf);
p.put( 1, 1, 1); q.put(-0.5,0.25,-2); d=larc_metric(p,q); de=ae_metric(s,p,q); sprintf(buf,"d((%6.3lf,%6.3lf,%6.3lf),(%6.3lf,%6.3lf,%6.3lf))=%12.9lf ae=%12.9lf\n",p.getx(),p.gety(),p.getz(),q.getx(),q.gety(),q.getz(),d,de); printof(lptr,buf);
//----------------------------------------------
// close log file
//----------------------------------------------
sprintf(buf,"lab_larc_distances_R3 experiment complete"); printofe(lptr,buf,time1);
plot_close(lptr,time1);
return 0;
}
/*-------------------------------------------------------------------------
* compute Lebesgue arc metric ball in R^2 with center <p> and radius <r>
* using Lebesgue arc metric
*-------------------------------------------------------------------------*/
int lab_larc_ball_R2(const double px, const double py, const double r, const double rmin, const double rmax, const double maxerror, const long Nsearch, const long Nplot, const char *basefilename){
time_t time1,time2; time(&time1); //starting time stamp (passed to plotting routine)
struct tm *gmt;
double seconds;
double theta;
double d=0;
vectR2 p(px,py);
vectR2 q;
char comment[2*1024]; //comment to be passed to plotting function
char buf[1024]; //general purpose buffer
char filename[1024];
FILE *lptr; // pointer to log file
FILE *fptr; // pointer to data file
gmt = gmtime(&time1);
//----------------------------------------------
//open log file
//----------------------------------------------
printf( "----------------------------------------------------------------\n");
sprintf(comment,"Experiment: plot ball centered at (%lf,%lf) in R^2 using Lagrange arc distance function",p.getx(),p.gety()); printf("%s\n",comment);
printf( "----------------------------------------------------------------\n");
sprintf(filename,"%s",basefilename);
lptr=log_open (filename,time1,comment);
//----------------------------------------------
//open data file
//----------------------------------------------
sprintf(filename,"%s.dat",basefilename);
sprintf(comment,"open \"%s\" to plot ball centered at (%lf,%lf) in R^2 using Lagrange arc distance function...",filename,p.getx(),p.gety());
printof(lptr,comment);
fptr=fopen(filename,"w");
if(fptr==NULL){
fprintf(stderr,"ERROR attempting to open experiment log file %s\n",filename);
exit(EXIT_FAILURE);
}
printof(lptr,"success.\n");
fprintf(fptr,"%%========================================================================\n");
fprintf(fptr,"%% Daniel J. Greenhoe \n");
fprintf(fptr,"%% data file for plotting Lebesgue Arc metric ball\n");
fprintf(fptr,"%% The command \\fileplot{<filename>} may be used in a LaTeX environment\n");
fprintf(fptr,"%% for plotting data.\n");
fprintf(fptr,"%% \\fileplot is available in the LaTeX PSTricks package.\n");
fprintf(fptr,"%% Reference: http://www.ctan.org/pkg/pstricks-base\n");
fprintf(fptr,"%% GMT %s",asctime(gmt));
fprintf(fptr,"%%========================================================================\n");
fprintf(fptr,"[\n");
printf("\ntheta = 0 PI");
for(theta=0;theta<(2*PI);theta+=(2*PI/Nplot)){
//q.put(x,y);
if(larc_findq(p, theta, r, rmin, rmax, maxerror, Nsearch, &q))
fprintf(fptr,"(%9.6lf,%9.6lf) %%=(x,y); p=(%9.6lf,%9.6lf) d(p,q)=%9.6lf\n",q.getx(),q.gety(),p.getx(),p.gety(),d);
printf("\b\b\b\b\b\b\b%4.2lf PI",theta/PI);
}
printf("\ndone.\n");
fprintf(fptr,"]\n");
time(&time2);
gmt = gmtime(&time2);
seconds = difftime(time2,time1);
fprintf(fptr,"%%========================================================================\n");
fprintf(fptr,"%% end data \n");
fprintf(fptr,"%% GMT %s",asctime(gmt));
fprintf(fptr,"%% (%.0lf seconds ellapsed)\n",seconds);
fprintf(fptr,"%%========================================================================\n");
//----------------------------------------------
// close log file
//----------------------------------------------
fclose(fptr);
sprintf(buf,"lab_larc_ball_R2 experiment complete"); printofe(lptr,buf,time1);
plot_close(lptr,time1);
return 0;
}
/*-------------------------------------------------------------------------
* compute Lebesgue arc metric ball in R^3 with center <p> and radius <r>
* using Lebesgue arc metric
*-------------------------------------------------------------------------*/
int lab_larc_ball_R3(const double px, const double py, const double pz, const double r, const char *basefilename){
time_t time1,time2; time(&time1); //starting time stamp (passed to plotting routine)
struct tm *gmt;
double seconds;
double theta,phi;
vectR3 p(px,py,pz);
vectR3 q;
char comment[2*1024]; //comment to be passed to plotting function
int row,col;
char filename[1024];
FILE *lptr; // pointer to log file
FILE *fptr; // pointer to data file
gmt = gmtime(&time1);
//----------------------------------------------
//open log file
//----------------------------------------------
printf( "----------------------------------------------------------------\n");
sprintf(comment,"Experiment: plot ball centered at (%lf,%lf,%lf) in R^3 using Lagrange arc distance function",p.getx(),p.gety(),p.getz());
printf("%s\n",comment);
printf( "----------------------------------------------------------------\n");
sprintf(filename,"%s",basefilename);
lptr=log_open (filename,time1,comment);
//----------------------------------------------
//open data file
//----------------------------------------------
sprintf(filename,"%s.dat",basefilename);
sprintf(comment,"open \"%s\" to plot ball centered at (%lf,%lf,%lf) in R^3 using Lagrange arc distance function...",filename,p.getx(),p.gety(),p.getz());
printof(lptr,comment);
fptr=fopen(filename,"w");
if(fptr==NULL){
fprintf(stderr,"ERROR attempting to open experiment log file %s\n",filename);
exit(EXIT_FAILURE);
}
printof(lptr,"success.\n");
fprintf(fptr,"%%========================================================================\n");
fprintf(fptr,"%% Daniel J. Greenhoe \n");
fprintf(fptr,"%% data file for plotting Lebesgue arc distance ball in R^3\n");
fprintf(fptr,"%% with radius %lf and centered at p=(%lf,%lf,%lf).\n",r,px,py,pz);
fprintf(fptr,"%% The tikzpicture environment may be used in LaTeX\n");
fprintf(fptr,"%% for plotting data.\n");
fprintf(fptr,"%% tikzpicture is available in the LaTeX pgfplots package.\n");
fprintf(fptr,"%% Reference:\n");
fprintf(fptr,"%% ftp://ftp.ccu.edu.tw/pub/tex/graphics/pgf/contrib/pgfplots/doc/pgfplots.pdf\n");
fprintf(fptr,"%% GMT %s",asctime(gmt));
fprintf(fptr,"%%========================================================================\n");
//fprintf(fptr,"[\n");
// for(phi=PI/2; phi>=-PI/2; phi-=PI/18){
for(phi=-PI/2+PI/64,row=1; phi<=(PI/2-PI/64); phi+=PI/32,row++){
for(theta=0,col=1; theta<=2*PI; theta+=2*PI/32,col++){
q=larc_findq(p,theta,phi,r, 0.1, 10, 0.001, 10000);
fprintf(fptr,"%9.6lf %9.6lf %9.6lf %%=q; row=%3d col=%3d phi=%.3lf PI theta=%.3lf PI\n",q.getx(),q.gety(),q.getz(),row,col,phi/PI,theta/PI);
}
q=larc_findq(p,0,phi,r, 0.1, 10, 0.001, 10000);
fprintf(fptr,"%9.6lf %9.6lf %9.6lf %%=q; row=%3d col=%3d phi=%.3lf PI theta=%.3lf PI\n",q.getx(),q.gety(),q.getz(),row,col,phi/PI,theta/PI);
fprintf(fptr,"\n");
printf(":");
}
phi=PI/2-PI/64;
for(theta=0,col=1; theta<=2*PI; theta+=2*PI/32,col++){
q=larc_findq(p,theta,phi,r, 0.1, 10, 0.001, 10000);
fprintf(fptr,"%9.6lf %9.6lf %9.6lf %%=q; row=%3d col=%3d phi=%.3lf PI theta=%.3lf PI\n",q.getx(),q.gety(),q.getz(),row,col,phi/PI,theta/PI);
}
row++;
q=larc_findq(p,0,phi,r, 0.1, 10, 0.001, 10000);
fprintf(fptr,"%9.6lf %9.6lf %9.6lf %%=q; row=%3d col=%3d phi=%.3lf PI theta=%.3lf PI\n",q.getx(),q.gety(),q.getz(), row,col,phi/PI,theta/PI);
fprintf(fptr,"\n");
printf(":");
time(&time2);
gmt = gmtime(&time2);
seconds = difftime(time2,time1);
fprintf(fptr,"%%========================================================================\n");
fprintf(fptr,"%% end data \n");
fprintf(fptr,"%% GMT %s",asctime(gmt));
fprintf(fptr,"%% (%.0lf seconds ellapsed)\n",seconds);
fprintf(fptr,"%%========================================================================\n");
return 0;
}
/*-------------------------------------------------------------------------
* test if larc distance satisfies power triangle inequality
* with parameter <a>
* if sigma==0, then set sigma = 0.5*pow(2,1.0/a)
*-------------------------------------------------------------------------*/
int lab_larc_pti(const double a, const double sigma, const double min, const double max, const long N, const char *basefilename){
time_t time1; time(&time1); //starting time stamp (passed to plotting routine)
vectR2 p,q,r;
double px,py,qx,qy,rx,ry;
double dpq,dqr,dpr;
double tau;
double s;
const double delta = (max-min)/(double)(N-1);
int fails=0;
char comment[1024]; //comment to be passed to plotting function
char buf[1024]; //general purpose buffer
long count=0;
char filename[1024];
FILE *lptr; // pointer to log file
if(sigma==0.0) s=0.5*pow(2,1.0/a);
else s=sigma;
//----------------------------------------------
//open log file
//----------------------------------------------
printf( "----------------------------------------------------------------\n");
sprintf(comment,"Experiment: test if larc distance satisfies power triangle inequality for (a,sigma)=(%lf,%lf)",a,s);
printf("%s\n",comment);
printf( "----------------------------------------------------------------\n");
sprintf(filename,"%s",basefilename);
lptr=log_open (filename,time1,comment);
//----------------------------------------------
//sprintf(buf,"Generate fair die sequence...");printofe(lptr,buf,time1);
//----------------------------------------------
printof(lptr,"power triangle inequality test\n");
//p.put(1,0.75); q.put(-0.5,0.25); r.put(1,1);
p.put(1,0 ); q.put(-0.5,0.2 ); r.put(-0.5,0);
printf("%6.2lf%% complete",(double)count/(double)(N*N*N*N*N*N));
count=0;
for(px=min;px<=max;px+=delta)
for(py=min;py<=max;py+=delta){
for(qx=min;qx<=max;qx+=delta)
for(qy=min;qy<=max;qy+=delta)
for(rx=min;rx<=max;rx+=delta)
for(ry=min;ry<=max;ry+=delta){
count++;
p.put(px,py); q.put(qx,qy); r.put(rx,ry);
// p.put(1,0 ); q.put(-0.5,0.2 ); r.put(-0.5,0);
// p.put(1,1 ); q.put(0.1,0.1 ); r.put(-0.1,-0.1);
//p.put(1,1 ); q.put(0.5,0.5 ); r.put(-0.5,-0.5);
//p.put(1,1 ); q.put(0.5,0.5 ); r.put(-0.5,-0.5);
//p.put(2,0 ); q.put(1 ,0 ); r.put(-1 , 0 );
// p.put(2,0 ); q.put(1 ,0.5 ); r.put(-1 ,-0.5);
//p.put(2,0 ); q.put(1 ,0.5 ); r.put(-1 ,0.5);
p.put(1,1 ); q.put(0.05 ,0.05 ); r.put(-0.05 ,-0.05);
p.put(1,1 ); q.put(0.03 ,0.04 ); r.put(-0.05 ,-0.06);
//d(( 1.000000, 1.000000),(-0.052632,-0.052632))
// = 0.885683929273 !<= 0.857228179493
// = 2sigma[1/2( 0.426466)^a+1/2( 0.074432)^a]^(1/a)
// = 2sigma[1/2 d^a(( 1.000000, 1.000000),( 0.052632, 0.052632))
// + 1/2 d^a(( 0.052632, 0.052632),(-0.052632,-0.052632))]^(1/a)
// where (a,sigma)=(0.500000,2.000000)
dpq=larc_metric(p,q);
dqr=larc_metric(q,r);
dpr=larc_metric(p,r);
tau=larc_tau(a,s,p,r,q);
if(tau-dpr<-0.000000001){
sprintf(buf,"\nd((%12.9lf,%12.9lf),(%12.9lf,%12.9lf))\n"
" = %.12lf !<= %.12lf\n"
" = 2sigma[1/2(%12.9lf)^a+1/2(%12.9lf)^a]^(1/a)\n"
" = 2sigma[1/2 d^a((%12.9lf,%12.9lf),(%12.9lf,%12.9lf))\n"
" + 1/2 d^a((%12.9lf,%12.9lf),(%12.9lf,%12.9lf))]^(1/a)\n"
" where (a,sigma)=(%lf,%lf)\n",
p.getx(),p.gety(),r.getx(),r.gety(),
dpr,tau,dpq,dqr,
p.getx(),p.gety(),q.getx(),q.gety(),
q.getx(),q.gety(),r.getx(),r.gety(),
a,s
);
printof(lptr,buf);
fails++;
}
// printf("p=(%5.2lf,%5.2lf) q=(%5.2lf,%5.2lf) r=(%5.2lf,%5.2lf) count=%ld NNNNNN=%ld\n",px,py,qx,qy,rx,ry,count,N*N*N*N*N*N);
}
printf("\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b%6.2lf%% complete",(double)count/(double)(N*N*N*N*N*N)*100.0);
}
printf("\ncount=%ld NNNNNN=%ld\n",count,N*N*N*N*N*N);
sprintf(buf,"number of fails = %d\n",fails); printof(lptr,buf);
//----------------------------------------------
// close log file
//----------------------------------------------
sprintf(buf,"lab_larc_pti experiment complete"); printofe(lptr,buf,time1);
plot_close(lptr,time1);
return 0;
}