Plotting complex functions. To launch run in terminal: bash start.sh

cPlot.c

// Coded by Scratchy
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <complex.h>
#include <tgmath.h>

//#define EPSILON 0.0001

void polari(long double a, long double b, long double *rho, long double *theta);
void cartesiane(long double rho, long double theta, long double *a, long double *b);

double complex funzione(long double complex z){
    return clogl(z);
}

int main(){
    long double complex z, w;
    long double az, bz, rhoz, thetaz, aw, bw, rhow, thetaw, rhozmax, thetazmax, inc;
    unsigned long long int t=0;
    
    printf("Inserisci il raggio rho massimo: ");
    int foo1 = scanf("%Lf",&rhozmax);
    
    printf("Inserisci il numero di giri dell'angolo theta: ");
    int foo2 = scanf("%Lf",&thetazmax);
    
    printf("Inserisci l'incremento per la definizione del grafico: ");
    int foo3 = scanf("%Lf",&inc);
    
    // file immagine
    FILE *pf = fopen("plot.dat","w");
    if(pf == NULL){
        perror("\n");
        exit(1);
    }
    fprintf(pf,"# i real(z) arg(z) real(w) arg(w) rhoz thetaZ rhoW thetaW abs(w)\n");
    
    /*
    Superfici di Riemann con gnuplot:
    2:3:4 <- parte reale
    2:3:5 <- parte immaginaria
    */
    
    // punto iniziale
    rhoz = 0.;
    thetaz = 0.;
    
    printf("Calcolo...\n");
    do{
        do{
            cartesiane(rhoz,thetaz,&az,&bz);
            z = az + bz * I;
            w = funzione(z);
            polari(creal(w),cimag(w),&rhow,&thetaw);
            fprintf(pf,"%llu\t%Lf\t%Lf\t%Lf\t%Lf\t%Lf\t%Lf\t%Lf\t%Lf\t%lf\n",t,creal(z),cimag(z),creal(w),cimag(w),rhoz,thetaz,rhow,thetaw,cabs(w));
            thetaz += inc;
            t++;
        }while(thetaz <= (2*M_PI)*thetazmax);
        
        thetaz = 0.; // reset dell'angolo
        rhoz += inc; // incremento il raggio
    }while(rhoz <= rhozmax);
    
    return 0;
}

void polari(long double a, long double b, long double *rho, long double *theta){
    
    *rho = sqrt((a*a)+(b*b));
    *theta = atan(b/a);
    
    return ;
}

void cartesiane(long double rho, long double theta, long double *a, long double *b){
    
    *a = rho * cos(theta);
    *b = rho * sin(theta);
    
    return ;
}

riemann_sphere.py

import cplot
import numpy as np

# funzione
def f(z):
    return np.sin(1/z**(np.sqrt(z)))

# plot
n = 5.0

#plt = cplot.plot(f,(-4.0,4.0,600),(-4.0,4.0,600))
plt = cplot.plot(
    f,
    (-n, +n, 1000),
    (-n, +n, 1000),
    #abs_scaling = lambda x: x / (x + 1), # how to scale the lightness in domain coloring
    #contours_abs = 2.0,
    #contours_arg = (-np.pi / 2, 0, np.pi / 2, np.pi),
    #emphasize_abs_contour_1 = True,
    #add_colorbars = True,
    #add_axes_labels = True,
    #saturation_adjustment = 1.28,
    #min_contour_length = None,
)
plt.show()

# sfera di riemann
plt = cplot.riemann_sphere(f)
plt.show()

script.py

import pylab
import matplotlib.pyplot as plt

# input dati
#nome_file = input("Inserisci nome file dati: ") # nel caso si usi python3
nome_file = "plot.dat"

# lettura dati
t,x,iy,w,iw,rhoz,thetaz,rhow,thetaw,absw = pylab.loadtxt(nome_file,unpack=True)

# Superficie di Riemann - parte reale
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(projection='3d')

sequence_containing_x_vals = x
sequence_containing_y_vals = iy
sequence_containing_z_vals = w

ax.scatter(sequence_containing_x_vals,sequence_containing_y_vals,sequence_containing_z_vals,c='b',marker='.',s=0.1)
ax.set_xlabel('x')
ax.set_ylabel('iy')
ax.set_zlabel('Re(w)')
plt.show()

# Superficie di Riemann - parte immaginaria
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(projection='3d')

sequence_containing_x_vals = x
sequence_containing_y_vals = iy
sequence_containing_z_vals = iw

ax.scatter(sequence_containing_x_vals,sequence_containing_y_vals,sequence_containing_z_vals,c='r',marker='.',s=0.1)
ax.set_xlabel('x')
ax.set_ylabel('iy')
ax.set_zlabel('Im(w)')
plt.show()

# Superficie modulare
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(projection='3d')

sequence_containing_x_vals = x
sequence_containing_y_vals = iy
sequence_containing_z_vals = absw
color = thetaw

punti = ax.scatter(sequence_containing_x_vals,sequence_containing_y_vals,sequence_containing_z_vals,c=color,marker='.',s=0.1,cmap="jet")
ax.set_xlabel('x')
ax.set_ylabel('iy')
ax.set_zlabel('Abs(w)')
cbar = plt.colorbar(punti)
cbar.set_label("theta")

plt.show()

start.sh

#!/bin/bash

gcc cPlot.c -lm -O3 -o cPlot.exe

./cPlot.exe

echo "Plotting..."
#gnuplot script.gp
python3 script.py

echo "Fine."

exit