#!/usr/bin/env python
# coding: utf-8

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d.axes3d import Axes3D


# In[2]:


def plot(t, r, w, dx, dy, ph):
    rx = np.arange(-r, r, w)
    ry = np.arange(-r, r, w)
    c = 1 if ph is None else 2
    fig = plt.figure(figsize=(c * 9 - 4, 5))
    fig.suptitle(t)

    if ph is not None:
        ax = fig.add_subplot(1, 2, 1, projection='3d')

        x, y, z = np.meshgrid(rx, ry, 0)
        ax.quiver(x, y, z, dx(x, y), dy(x, y), 0, length=w, color='red', normalize=True)

        x, y = np.meshgrid(rx, ry)
        ax.plot_surface(x, y, ph(x, y), cmap=plt.cm.bone)

    ax = fig.add_subplot(1, c, c)

    if ph is not None:
        r2 = np.arange(-r, r, w / 4)
        x, y = np.meshgrid(r2, r2)

        cs1 = ax.contourf(x, y, ph(x, y), 10, cmap=plt.cm.bone)
        #cs2 = ax.contour(cs1, colors='b')

        cbar = plt.colorbar(cs1)
        #cbar.add_lines(cs2)

    x, y = np.meshgrid(rx, ry)
    ax.quiver(x, y, dx(x, y), dy(x, y), color='red')


# In[3]:


dx1, dy1, ph1 = lambda x, y: x, lambda x, y: -y, lambda x, y: (x**2-y**2)/2
plot(r"$z \mapsto x\,dx-y\,dy = d(x^2-y^2)/2$", 5, 0.5, dx1, dy1, ph1)


# In[4]:


plot(r"$\bar z \mapsto x\,dx+y\,dy = d(x^2+y^2)/2$", 5, 0.5,
     lambda x, y: x, lambda x, y: y, lambda x, y: (x**2 + y**2) / 2)


# In[5]:


dx2, dy2, ph2 = lambda x, y: x**2 - y**2, lambda x, y: -2*x*y, lambda x, y: x**3/3 - x*y**2
plot(r"$z^2 \mapsto (x^2-y^2)dx-2xy\,dy = d(x^3/3-xy^2)$", 5, 0.5, dx2, dy2, ph2)


# In[6]:


plot(r"$\bar z^2 \mapsto (x^2-y^2)dx+2xy\,dy$", 5, 0.5,
     lambda x, y: x**2 - y**2, lambda x, y: 2*x*y, None)


# In[7]:


dx3, dy3, ph3 = lambda x, y: x**3 - 3*x*y**2, lambda x, y: y**3 - 3*x**2*y, lambda x, y: (x**4 - 6*x**2*y**2 + y**4) / 4
plot(r"$z^3 \mapsto (x^3-3xy^2)dx+(y^3-3x^2y)dy = d(x^4-6x^2y^2+y^4)/4$", 5, 0.5, dx3, dy3, ph3)


# In[8]:


makef = lambda a, b, c: lambda f3, f2, f1: lambda x, y: a * f3(x, y) + b * f2(x, y) + c * f1(x, y)
f = makef(1, 5, 10)
plot("$z^3+5z^2+10$", 5, 0.5, f(dx3, dx2, dx1), f(dy3, dy2, dy1), f(ph3, ph2, ph1))


# In[9]:


plot("$e^z \mapsto e^x\cos\,y\,dx-e^x\sin\,y\,dy = d(e^x\cos\,y)$", 5, 0.5,
     lambda x, y: np.exp(x) * np.cos(y), lambda x, y: -np.exp(x) * np.sin(y), lambda x, y: np.exp(x) * np.cos(y))


# In[10]:


plot("$\sin\,z \mapsto \sin\,x\,\cosh\,y\,dx-\cos\,x\,\sinh\,y\,dy = d(-\cos\,x\,\cosh\,y)$", 5, 0.5,
     lambda x, y: np.sin(x) * np.cosh(y), lambda x, y: -np.cos(x) * np.sinh(y), lambda x, y: -np.cos(x) * np.cosh(y))


# In[11]:


plot("$\cos\,z \mapsto \cos\,x\,\cosh\,y\,dx+\sin\,x\,\sinh\,y\,dy = d(\sin\,x\,\cosh\,y)$", 5, 0.5,
     lambda x, y: np.cos(x) * np.cosh(y), lambda x, y: np.sin(x) * np.sinh(y), lambda x, y: np.sin(x) * np.cosh(y))


# In[12]:


plot(r"$ω=-y\,dx+x\,dy\ ,\quad dω=2\,dx\,dy$", 5, 0.5,
     lambda x, y: -y, lambda x, y: x, None)


# In[13]:


plot(r"$ω=y\,dx\ ,\quad dω=dx\,dy$", 5, 0.5,
     lambda x, y: y, lambda x, y: 0, None)


# In[14]:


plot(r"$-iz \mapsto y\,dx+x\,dy=d(xy)$", 5, 0.5,
     lambda x, y: y, lambda x, y: x, lambda x, y: x * y)


# In[15]:


plot(r"$ω=(-y\,dx+x\,dy)/(x^2+y^2)\ ,\quad dω=0$", 5, 0.5,
     lambda x, y: -y/(x**2+y**2+.0001), lambda x, y: x/(x**2+y**2+.0001), None)


# # 参考
# 
# * [matplotlibで3Dグラフを描画する - white wheelsのメモ](http://d.hatena.ne.jp/white_wheels/20100327/p3)
# * [[Pythonによる科学・技術計算] ベクトル場の可視化例，静電磁場, matplotlib - Qiita](https://qiita.com/sci_Haru/items/21777764ae50996abd95)
# * [Matplotlib documentation](https://matplotlib.org/contents.html)
#   * [matplotlib.figure.Figure](https://matplotlib.org/api/_as_gen/matplotlib.figure.Figure.html)
#   * [Axes class](https://matplotlib.org/api/axes_api.html)
#   * [Quiver Simple Demo](https://matplotlib.org/gallery/images_contours_and_fields/quiver_simple_demo.html)
#   * [pylab_examples example code: contourf_demo.py](https://matplotlib.org/examples/pylab_examples/contourf_demo.html)
# 

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