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 , the square modulus of the orbital wave function for . The values of are given by

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:

### REFERENCES:

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

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. 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.

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