如何为两条曲线下方的区域着色？

Question

我有以下图表组合：

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()

产生以下图表：

现在我想要的是为两个函数重叠的空间着色。就像在这张图片中：

作为奖励，我想在那个空间的某处插入两个箭头，但不知何故不能完全管理它。

Answer 1

这可能不是最优雅的解决方案，但是一旦解决了交叉点，就可以通过fill_between获得所需的效果：

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()