In [1]:

    

%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt
plt.style.use('bmh')
from time import time


    

In [2]:

    

def tangent(x, y, f, l = 0.1):
    # Returns a line centered at x, y
    # with slope found from dy/dx = f(x, y)[1]/f(x,y)[0]
    # and length l
    dx, dy = f([x, y])
    if dx == 0:
        # if dy is also 0, then return a point
        if dy == 0:
            return np.array([x, x]), np.array([y, y])
        # Otherwise, slope is infinite, return a vertical
        else:
            return np.array([x, x]), np.array([y - l/2, y + l/2])
    else:
        # Slope is finite, return a line segment 
        # of length, and with that slope
        s  = np.sqrt((2*dx)**2 + (2*dy)**2) / l
        return np.array([x - dx/s, x + dx/s]), np.array([y - dy/s, y + dy/s])


    

In [3]:

    

def f(x):
    # Modify A to get the different types of fixed point
    A = np.array([
        [1,  -2],
        [2,  -2]
    ])
    dx = A[0,0]*x[0] + A[0,1]*x[1]
    dy = A[1,0]*x[0] + A[1,1]*x[1]
    return np.array([dx, dy])

def f(x):

    dx = x[0] + np.exp(-x[1])
    dy = -x[1]
    return np.array([dx, dy])

def f(X):
    x = X[0]
    y = X[1]
    dx = x**2*y
    dy = x**2 - y**2
    return np.array([dx, dy])

# Define grid points
Nx = 31
Ny = 31
X = np.linspace(-2, 2, Nx)
Y = np.linspace(-2, 2, Ny)

fig = plt.figure(figsize = (8, 8))
for i in range(Nx):
    for j in range(Ny):
        # For each gridpoint, plot a short straight line
        # The star in the function call below unpacks the arguments,
        # passing them one by one to the plot function.
        plt.plot(*tangent(X[i], Y[j], f, l = 0.07), lw = 1, c = '#A60628')

plt.xlim(-2, 2)
plt.ylim(-2, 2)


    

    
Out[3]:





(-2, 2)






    

In [ ]: