python/Matplotlib绘制复变函数图像

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参照matlab绘制复变函数的例子，使用python实现绘制复变函数图像，网上还没搜到相关的文章，在这里分享出来供大家学习。

'''
参照matlab绘制复变函数的例子，创建函数cplxgrid,cplxmap,cplxroot
'''
# 1.导入相关库
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import *

# 2.创建函数
def cplxgrid(m):
    '''Return polar coordinate complex grid.

    Parameters
    ----------
    m: int

    Returns
    ----------
    z: ndarray,with shape (m+1)-by-(2*(m+1))
    '''
    m = m
    r = np.arange(0,m).reshape(m,1) / m
    theta = np.pi * np.arange(-m,m) / m
    z = r * np.exp(1j * theta)

    return z

def cplxroot(n=3,m=20):
    '''
    cplxroot(n): renders the Riemann surface for the n-th root
    cplxroot(): renders the Riemann surface for the cube root.
    cplxroot(n,m): uses an m-by-m grid.  Default m = 20.

    Use polar coordinates, (r,theta).
    Use polar coordinates, (r,theta).

    Parameters
    ----------
    n: n-th root
    m: int

    Returns
    ----------
    None: Plot the Riemann surface
    '''
    m = m+1
    r = np.arange(0,m).reshape(m,1) / m
    theta = np.pi * np.arange(-n * m, n * m) / m
    z = r * np.exp(1j * theta)
    s = r * (1/n) * np.exp(1j * theta / n)
    fig = plt.figure()
    ax = fig.add_subplot(111,projection='3d')
    # ax.plot_surface(np.real(z),np.imag(z),np.real(s),color = np.imag(s))
    ax.plot_surface(np.real(z),np.imag(z),np.real(s),cmap = plt.cm.hsv)
    ax.set_xlim((-1,1))
    ax.set_ylim((-1,1))
    ax.set_xlabel('Real')
    ax.set_ylabel('Imag')
    ax.set_xticks([])
    ax.set_yticks([])
    ax.set_zticks([])
    ax.set_autoscalez_on(True)#z轴自动缩放   
    ax.grid('on')
    plt.show()

def cplxmap(z,cfun):
    '''
    Plot a function of a complex variable.

    Parameters
    ----------
    z: complex plane
    cfun: complex function to plot

    Returns
    ----------
    None: Plot the surface of complex function
    '''
    blue = 0.2
    x = np.real(z)
    y = np.imag(z)
    u = np.real(cfun)
    v = np.imag(cfun)
    M = np.max(np.max(u))#复变函数实部最大值
    m = np.min(np.min(u))#复变函数实部最大值
    s = np.ones(z.shape)
    fig = plt.figure()
    ax = fig.add_subplot(111,projection='3d')
    # 投影部分用线框图
    surf1 = ax.plot_wireframe(x,y,m*s,cmap=plt.cm.hsv)
    surf2 = ax.plot_surface(x,y,u,cmap=plt.cm.hsv)

    #绘制复变函数1/z时会出错，ValueError: Axis limits cannot be NaN or Inf
    # ax.set_zlim(m, M)   
    ax.set_xlim((-1,1))
    ax.set_ylim((-1,1))
    ax.set_xlabel('Real')
    ax.set_ylabel('Imag')
    ax.set_xticks([])
    ax.set_yticks([])
    ax.set_zticks([])
    ax.set_autoscalez_on(True)#z轴自动缩放

    ax.grid('on')
    plt.show()

def _test_cplxmap():
    '''测试cplxmap函数'''
    z = cplxgrid(30)
    w1 = z
    w2 = z**3
    w3 = (z**4-1)**(1/4)
    w4 = 1/z
    w5 = np.arctan(2*z)
    w6 = np.sqrt(z)
    w = [w1,w2,w3,w4,w5,w6]
    for i in w:
        cplxmap(z,i)

def _test_cplxroot():
    '''测试cplxroot函数'''
    cplxroot(n=2)
    cplxroot(n=3)
    cplxroot(n=4)
    cplxroot(n=5)

if __name__ == '__main__':
    _test_cplxmap()
    _test_cplxroot()