Not able to plot a smooth complex mathematical function with matplotlib, why?-CodePudding

I am trying to plot a complex function with matplotlib. This function plot a normal 1D function if the imaginary part is 0 (and this works) and the whole complex function, as a 2D plot, if the imaginary part is not 0. This is the function:

import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate as sci

def plotter_complex( real_part, imaginary_part, a, b, n, coefficient ): 
        x = np.arange( a, b, ( ( b-a ) / 10 ) )

        def func( x ): #This are two functions I defined to plot the function.
            return coefficient * ut.e_parser( real_part, imaginary_part, n, x )
        
        my_label = "Normalized wave-function f(x) for n = "   str( n )
        plt.figure( figsize = ( 8, 6 ), dpi = 80 )
        plt.xlabel( "Re: f(x)" )
        plt.ylabel( "Im: f(x)" )
        plt.title( my_label )

        if imaginary_part == "0":
            X_Y_Spline = sci.make_interp_spline( x, func( x ) )
            X = np.linspace( x.min(), x.max(), 500 )
            Y = X_Y_Spline( X )
        
            plt.xlabel( "x" )
            plt.ylabel( "Re: f(x)" )
            plt.plot( X, Y, color = "green" )
        else:
            X_Y_Spline = sci.make_interp_spline( np.real( func( x ) ), np.imag( func( x ) ) )
            X = np.linspace( x.min(), x.max(), 500 )
            Y = X_Y_Spline( X )
            
            plt.plot( X, Y, color = "green" )

        plt.show()

Obviously if I try:

import numpy as np
plotter_complex( "np.cos(x)", "np.sin(x)", -1, 1, 3, 4 )

It gives me:

Traceback (most recent call last):
  File "src/main.py", line 167, in <module>
    main()
  File "src/main.py", line 20, in main
    ft.plotter_complex( "np.cos(x)", "np.sin(x)", -1, 1, 3, 4 )
  File "/home/gianluca/WaveNCC/src/functions.py", line 231, in plotter_complex
    X_Y_Spline = sci.make_interp_spline( np.real( func( x ) ), np.imag( func( x ) ) )
  File "/home/gianluca/.local/lib/python3.8/site-packages/scipy/interpolate/_bsplines.py", line 786, in make_interp_spline
    raise ValueError("Expect x to be a 1-D sorted array_like.")
ValueError: Expect x to be a 1-D sorted array_like.

And it's right, since I am trying to interpolate two functions. But I don't understand how I could smooth the complex function otherwise. Thanks.

PS: If I try to plot the normal complex function it works. The fact is that I am not able to smooth it.

CodePudding user response：

I'm not sure is this correct from the point of view of theory, but if you add sorting of the result along the X axis, then the graph is plotted:

abs, ord = np.real( func( x ) ), np.imag( func( x ) )
abs, ord = zip(*sorted(zip(abs, ord)))
X_Y_Spline = sci.make_interp_spline( abs, ord )

CodePudding user response：

A circle with 10 points:

In [131]: x = np.linspace(0,2*np.pi,10)
In [132]: c = np.cos(x); s = np.sin(x)
In [133]: plt.plot(c,s)
Out[133]: [<matplotlib.lines.Line2D at 0x7f2514b98040>]

Interpolate c and s to 100 points:

In [136]: from scipy.interpolate import make_interp_spline
In [137]: X = np.linspace(0, 2*np.pi,100)
In [138]: C = make_interp_spline(x,c)(X)
In [139]: S = make_interp_spline(x,s)(X)
In [140]: plt.plot(C,S)
Out[140]: [<matplotlib.lines.Line2D at 0x7f2508447c70>]

comparison plot with direct calculation of those 100 points:

In [141]: plt.plot(np.cos(X),np.sin(X))
Out[141]: [<matplotlib.lines.Line2D at 0x7f2508455190>]