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matplotlibareacurve

How do i color the Area below the two curves?


I have the following combinations of graphs:

import pylab as pl
import numpy as np


def gauss2d(x,sigma):
    return (1/np.sqrt(2*np.pi*sigma ))*np.exp(-1/2*(x/sigma)**2 )

def markParameters(m,s,textsigma, textmean):
    p1=gauss2d(s,s)
    p2=gauss2d(0,s)

    pl.annotate("", xy=(m-s, p1), xycoords='data', xytext=(m+s, p1), textcoords='data', arrowprops=dict(arrowstyle="<->", connectionstyle="arc3"),)
    pl.text(m,p1,textsigma,horizontalalignment='center',verticalalignment='top')
    pl.annotate("", xy=(m, p2*1.1), xycoords='data', xytext=(m, p2*1.1), textcoords='data', arrowprops=dict(arrowstyle="->", connectionstyle="arc3"),)
    pl.text(m,p2*1.1,textmean,horizontalalignment='center',verticalalignment='top') # ,rotation=90
    pl.plot(m,p2)
    pl.plot(m,p2, marker="o", markeredgecolor="blue", markersize=5.0, linestyle=" ",color="blue")


def plot_gauss2d():
    x = np.mgrid[100:135:100j]

    m,s=123.24,3.56
    pl.plot(x,gauss2d(x-m,s), 'b-')
    markParameters(m,s, "$\sigma_{1}$","$\omega_{1}$")

    m,s=120.15,4.62
    pl.plot(x,gauss2d(x-m,s), 'b-')
    markParameters(m,s, "$\sigma_{2}$","$\omega_{2}$")


    m,s=109.67,3.85
    pl.plot(x,gauss2d(x-m,s), 'b-')
    markParameters(m,s,"$\sigma_{3}$","$\omega_{3}$")

def main():
    plot_gauss2d()

if __name__ == "__main__":
    main()

resulting in the following graph: example

Now what i would like to have is to color the space where the two functions overlap. Like in this picture: enter image description here

As a bonus I would like to insert two arrows somewhere in that space, but somehow cannot quite manage it.


Solution

  • This may not be the most elegant solution, but you can get the desired effect with fill_between once you solve for the intersections:

    import matplotlib.pyplot as pl
    import numpy as np
    from scipy.optimize import fsolve
    
    
    def gauss(x, mu, sig):
        return 1 / np.sqrt(2 * np.pi) / sig * np.exp(-((x - mu) / sig)**2 / 2.)
    
    
    def mark_parameters(m, s, textsigma, textmean):
        p1 = gauss(m + s, m, s)
    
        w = 0.0001
        pl.arrow(m, p1, +s, 0, fc='b', ec='b', length_includes_head=True,
                 head_width=w*30, head_length=w*3000, width=w)
        pl.arrow(m, p1, -s, 0, fc='b', ec='b', length_includes_head=True,
                 head_width=w*30, head_length=w*3000, width=w)
        
        pl.text(m, p1*0.98, textsigma, horizontalalignment='center',
                verticalalignment='top')
    
        p2 = gauss(m, m, s)
        pl.text(m, p2*1.05, textmean, horizontalalignment='center',
                verticalalignment='top')
        pl.plot(m, p2, marker="o", markeredgecolor="blue",
                markersize=5.0, linestyle=" ", color="blue")
    
    
    def plot_gauss():
        x = np.arange(100, 135, 0.01)
    
        pars = [(123.24, 3.56), (120.15, 4.62), (109.67, 3.85)]
        ipcolor = {(0, 1): 'red', (1, 2): 'green'}
    
        prev = None
        for i, (m, s) in enumerate(pars):
            pl.plot(x, gauss(x, m, s), 'b-')
            j = i + 1
            mark_parameters(m, s, "$2\sigma_{%d}$" % j, "$\omega_{%d}$" % j)
    
            if prev:
                ip, (mp, sp) = prev
    
                # look for intersection
                x0 = 0.5 * (mp + m)  # initial guess for x
                xi = fsolve(lambda x : gauss(x, mp, sp) - gauss(x, m, s), x0)
    
                # fill between gauss and y = 0, divided at intersection xi
                color = ipcolor[(ip, i)] if (ip, i) in ipcolor else 'none'
                pl.fill_between(x, gauss(x, mp, sp), where=(x <= xi),
                                color=color)
                pl.fill_between(x, gauss(x, m, s), where=(x > xi),
                                color=color)
    
            prev = (i, (m, s))
    
    
    def main():
        plot_gauss()
        pl.show()
        
    
    if __name__ == "__main__":
        main()