Plotting exercises for C and GNUPlot

Gnuplot is a portable command-line driven graphing utility for Linux and other OS.
C and Gnuplot can be used to plot complex functions.

One can write the function in C and then write the values of the function at various values in a txt file, which can then be plotted using Gnuplot.
The txt file should have numerical values in at least two columns. The first column is for x values. The rest of the columns are for y-axis values.

Following are some of the exercises to help you understand the process in a better way.

Plot a circle of a given radius and center using C and Gnuplot.

A. We can do this by writing a C program that calculates the x and y-values of the required circle and then write those values in a txt file. Then we can plot the file using Gnuplot.

Program:

/*************************************
 ***********PLOT A CIRCLE ************
 ************************************/
#include<stdio.h>
#include<math.h>
main(){
  FILE *fp=NULL;
  fp=fopen("circle.txt","w");
  double r;
  double x,y,x0,y0;
  printf("Enter the radius of the circle to be plotted: ");
  scanf("%lf",&r);
  printf("Enter the x and y-coordinates of the center: ");
  scanf("%lf%lf",&x0,&y0);
  for(y=y0-r;y<=y0+r;y=y+0.1){
    x=sqrt(r*r-(y-y0)*(y-y0))+x0; 
    fprintf(fp,"%lf\t %lf\n",x,y);
  }
  for(y=y0+r;y>=y0-r;y=y-0.1){
    x=-sqrt(r*r-(y-y0)*(y-y0))+x0; 
    fprintf(fp,"%lf\t %lf\n",x,y);
  
  }
}

The above program will generate a txt file(circle.txt) with the x and y-values for the circle of required radius and center coordinates.
Then the plotting can be done using Gnuplot by using the following command:
plot 'circle.txt' w l

OUTPUT:

Plot $|\Theta_{lm}(\theta)|^2$ , the square modulus of the orbital wave function for $l = 3;m = 0,\pm1,\pm2,\pm3$ . The values of $|\Theta_{lm}(\theta)|^2$ are given by

$\Theta_{3,0}(\theta)=\frac{3\sqrt{14}}{4}\left(\frac{5}{3}\cos^3\theta-\cos\theta\right)$
$\Theta_{3,\pm1}(\theta)=\frac{\sqrt{42}}{8}\sin\theta\left(5\cos^2\theta-1\right)$
$\Theta_{3,\pm2}(\theta)=\frac{\sqrt{105}}{4}\sin^2\theta\cos\theta$
$\Theta_{3,\pm3}(\theta)=\frac{\sqrt{70}}{8}\sin^3\theta$

Solution:

PROGRAM:

/**************************************
 ******PLOT ORBITAL WAVEFUNCTIONS******
 *************************************/
#include<stdio.h>
#include<math.h>
double theta30(double x){
  double out=3.0*sqrt(14.0)/4.0*(5.0/3.0*pow(cos(x),3)-cos(x));
  return out;
}
double theta31(double x){
  double out=(sqrt(42))/(8)*sin(x)*(5*pow(cos(x),2)-1);
  return out;
}
double theta32(double x){
  double out=sqrt(105)/4*pow(sin(x),2)*cos(x);
  return out;
}
double theta33(double x){
  double out=(sqrt(70))/(8)*(pow(sin(x),3));
  return out;
}
main(){
  double theta;
  double x1,x2,x3,x4,y1,y2,y3,y4;
  FILE *fp1=NULL;
  FILE *fp2=NULL;
  FILE *fp3=NULL;
  FILE *fp4=NULL;
  fp1=fopen("orbital1.txt","w");
  fp2=fopen("orbital2.txt","w");
  fp3=fopen("orbital3.txt","w");
  fp4=fopen("orbital4.txt","w");
  for(theta=0;theta<=2*M_PI;theta=theta+0.01){
    x1=theta30(theta)*theta30(theta)*cos(theta);
    x2=theta31(theta)*theta31(theta)*cos(theta);
    x3=theta32(theta)*theta32(theta)*cos(theta);
    x4=theta33(theta)*theta33(theta)*cos(theta);
    y1=theta30(theta)*theta30(theta)*sin(theta);
    y2=theta31(theta)*theta31(theta)*sin(theta);
    y3=theta32(theta)*theta32(theta)*sin(theta);
    y4=theta33(theta)*theta33(theta)*sin(theta);
    fprintf(fp1,"%lf\t%lf\n",x1,y1);
    fprintf(fp2,"%lf\t%lf\n",x2,y2);
    fprintf(fp3,"%lf\t%lf\n",x3,y3);
    fprintf(fp4,"%lf\t%lf\n",x4,y4);
  }
}

The above program would generate for txt files containing the data-points for the four orbital equations(orbital1.txt,orbital2.tx,….). These can then be plotted using Gnuplot by using the following command:
plot 'orbital1.txt' w l

OUTPUT:

$\Theta_{3,0}(\theta)=\frac{3\sqrt{14}}{4}\left(\frac{5}{3}\cos^3\theta-\cos\theta\right)$

$\Theta_{3,\pm1}(\theta)=\frac{\sqrt{42}}{8}\sin\theta\left(5\cos^2\theta-1\right)$

$\Theta_{3,\pm2}(\theta)=\frac{\sqrt{105}}{4}\sin^2\theta\cos\theta$

$\Theta_{3,\pm3}(\theta)=\frac{\sqrt{70}}{8}\sin^3\theta$

REFERENCES:

The above problems have been taken from the Computer Programming & Numerical Analysis Manual by Dr. Shobhit Mahajan.

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Manas Sharma

I’m a physicist specializing in computational material science with a PhD in Physics from Friedrich-Schiller University Jena, Germany. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

manas.bragitoff.com/