ResidueTheorem_Handwriting.py

import numpy as np 
import matplotlib.pyplot as plt 
import sympy as sb
from scipy import integrate

plt.rcParams["font.size"] = 10

# 複素変数
z = sb.Symbol('z')

# 複素関数
F = 1/(z**4 + 1)

# sympy to lambda 
f = sb.lambdify(z,F)

# 特異点
SP = list(sb.singularities(F,z))

# 留数
Res = []
for sp in SP:
    res = sb.residue(F,z,sp)
    Res.append(res)
    
# 押した時
def Press(e):
    global x,y,C,DragFlag

    # 値がNoneなら終了
    if (e.xdata is None) or (e.ydata is None):
        return 

    # フラグをたてる
    DragFlag = True

# ドラッグした時
def Drag(e):
    global x,y,C,DragFlag

    # 値がNoneなら終了
    if (e.xdata is None) or (e.ydata is None):
        return 

    x0 = e.xdata
    y0 = e.ydata
    z0 = x0+1j*y0
    
    x = np.append(x, x0)
    y = np.append(y, y0)
    C = np.append(C, z0)

    w0 = f(z0)

    w  = f(C)
    
    I = integrate.cumtrapz(w,C)
    
    ln_z0.set_data(x0,y0)
    ln_C.set_data(C.real,C.imag)
    ln_C0.set_data(C[0].real,C[0].imag)

    if len(I) is not 0:
        ln_I.set_data(I.real,I.imag)
        ln_i.set_data(I[-1].real,I[-1].imag)
    
    plt.draw()

# 離した時
def Release(e):
    global x,y,C,DragFlag
    # フラグをたおす
    DragFlag = False

    x = np.array([]) 
    y = np.array([])
    C = np.array([])

x = np.array([]) 
y = np.array([])
C = np.array([])

DragFlag = False

plt.close('all')

fig = plt.figure(figsize=(8,4))

plt.subplot(1,2,1)
ln_z0, = plt.plot([],[],'ko',zorder=2)
ln_C0, = plt.plot([],[],'ko',zorder=2)
ln_C, = plt.plot([],[],zorder=1)

xlm=[-3,3]
ylm=[-3,3]
plt.xlim(xlm)
plt.ylim(ylm)
plt.xlabel('$\\rm{Re}(z)$')
plt.ylabel('$\\rm{Im}(z)$')
plt.title('$f(z)='+sb.latex(F)+'$')

for sp in SP:
    plt.plot(sb.re(sp), sb.im(sp),'kx')

plt.subplot(1,2,2)
ln_I, = plt.plot([],[])
ln_i, = plt.plot([],[],'ko')
plt.title('$\int_C f(z)dz$')

for res in Res:
    plt.plot(sb.re(2*np.pi*sb.I*res), sb.im(2*np.pi*sb.I*res),'kx')

plt.xlim(xlm)
plt.ylim(ylm)
plt.xlabel('$\\rm{Re}$')
plt.ylabel('$\\rm{Im}$')

axes = plt.gcf().get_axes()
for i,axis in enumerate(axes):
    plt.axes(axis)
    plt.grid()

plt.tight_layout()

plt.connect('button_press_event', Press)
plt.connect('motion_notify_event', Drag)
plt.connect('button_release_event', Release)

plt.show()