python/Matplotlib绘制复变函数图像教程

Python  /  管理员 发布于 7年前   285

今天发现sympy依赖的库mpmath里也有很多数学函数，其中也有在复平面绘制二维图的函数cplot，具体例子如下

from mpmath import *def f1(z): return zdef f2(z): return z**3def f3(z): return (z**4-1)**(1/4)def f4(z): return 1/zdef f5(z): return atan(z)def f6(z): return sqrt(z)cplot(f1)cplot(f2)cplot(f3)cplot(f4)cplot(f5)cplot(f6)

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 npimport matplotlib.pyplot as pltfrom 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 zdef 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()

以上这篇python/Matplotlib绘制复变函数图像教程就是小编分享给大家的全部内容了，希望能给大家一个参考，也希望大家多多支持。