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# via http://numbercrunch.de/blog/2013/05/visualizing-vector-fields/


    

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%matplotlib notebook

import matplotlib 
import matplotlib.pyplot as plt
# from matplotlib.pyplot import figure, close
from numpy import *
# from pylab import *
from matplotlib.mlab import find
 
# use LaTeX, choose nice some looking fonts and tweak some settings
matplotlib.rc('font', family='serif')
matplotlib.rc('font', size=16)
matplotlib.rc('legend', fontsize=16)
matplotlib.rc('legend', numpoints=1)
matplotlib.rc('legend', handlelength=1.5)
matplotlib.rc('legend', frameon=False)
matplotlib.rc('xtick.major', pad=7)
matplotlib.rc('xtick.minor', pad=7)
matplotlib.rc('text', usetex=True)
matplotlib.rc('text.latex', 
              preamble=[r'\usepackage[T1]{fontenc}',
                        r'\usepackage{amsmath}',
                        r'\usepackage{txfonts}',
                        r'\usepackage{textcomp}'])
 
# plt.close('all')
plt.figure(figsize=(6, 4.5))
 
# generate grid
x=linspace(-2, 2, 32)
y=linspace(-1.5, 1.5, 24)
x, y=meshgrid(x, y)
 
def E(q, a, x, y):
    return q*(x-a[0])/((x-a[0])**2+(y-a[1])**2)**(1.5), \
        q*(y-a[1])/((x-a[0])**2+(y-a[1])**2)**(1.5)
 
# calculate vector field
Ex1, Ey1=E(1, [-1, 0], x, y)
Ex2, Ey2=E(-1, [1, 0], x, y)
Ex=Ex1+Ex2
Ey=Ey1+Ey2
# remove vector with length larger than E_max
E_max=10
E=sqrt(Ex**2+Ey**2)
k=where(E.flat[:]>E_max)
Ex.flat[k]=nan
Ey.flat[k]=nan
# plot vecor field
plt.quiver(x, y, Ex, Ey, pivot='middle', headwidth=4, headlength=6)
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.axis('image')
# plt.show()
# plt.savefig('visualization_vector_fields_4.png')


    

    















    












    
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(-2.0, 2.0, -1.5, 1.5)

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import matplotlib 
from numpy import *
# from pylab import *
import matplotlib.pyplot as plt

 
# use LaTeX, choose nice some looking fonts and tweak some settings
matplotlib.rc('font', family='serif')
matplotlib.rc('font', size=16)
matplotlib.rc('legend', fontsize=16)
matplotlib.rc('legend', numpoints=1)
matplotlib.rc('legend', handlelength=1.5)
matplotlib.rc('legend', frameon=False)
matplotlib.rc('xtick.major', pad=7)
matplotlib.rc('xtick.minor', pad=7)
matplotlib.rc('text', usetex=True)
matplotlib.rc('text.latex', 
              preamble=[r'\usepackage[T1]{fontenc}',
                        r'\usepackage{amsmath}',
                        r'\usepackage{txfonts}',
                        r'\usepackage{textcomp}'])
 
plt.close('all')
plt.figure(figsize=(6, 4.5))
 
# generate grid
x=linspace(-2, 2, 32)
y=linspace(-1.5, 1.5, 24)
x, y=meshgrid(x, y)
# calculate vector field
vx=-y/sqrt(x**2+y**2)*exp(-(x**2+y**2))
vy= x/sqrt(x**2+y**2)*exp(-(x**2+y**2))
# plot vecor field
quiver(x, y, vx, vy, pivot='middle', headwidth=4, headlength=6)
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.axis('image')
plt.show()


    

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