

In [34]:

    
from __future__ import division

%matplotlib inline

import numpy as np
import assign1 as a
import math
import matplotlib.pyplot as plt

Initialization

Compute exact result with 128 points and create a fdm result array with iteration ranging from 0 to 1000 by step of 10.



In [2]:

    
x,y,exact = a.exact(128)



In [3]:

    
fdm = np.zeros([100,128])



In [73]:

    
for i in range(100):
    fdm[i] = a.get_border(a.fdm(32,32,i*10,False))

Plotting the data

Test the data by ploting them in the same graph. Blue indicates the exact result, red indicates the approximate result.



In [5]:

    
a.scatter_plot(x,y,exact,fdm[0])



In [6]:

    
a.scatter_plot(x,y,exact,fdm[1])



In [7]:

    
a.scatter_plot(x,y,exact,fdm[5])



In [8]:

    
a.scatter_plot(x,y,exact,fdm[10])



In [9]:

    
a.scatter_plot(x,y,exact,fdm[20])



In [10]:

    
a.scatter_plot(x,y,exact,fdm[50])



In [11]:

    
a.scatter_plot(x,y,exact,fdm[80])



In [12]:

    
a.scatter_plot(x,y,exact,fdm[99])

Experiencing error

Error function put in test: error with $10^{-6}$ torlerance.



In [13]:

    
a.error(exact, fdm[0])









    Out[13]:





364.63519998606785



In [14]:

    
a.error(exact, fdm[1])









    Out[14]:





138.35216937848864



In [15]:

    
a.error(exact, fdm[2])









    Out[15]:





113.32119951761369



In [16]:

    
a.error(exact, fdm[4])









    Out[16]:





83.28941465206103



In [17]:

    
a.error(exact, fdm[8])









    Out[17]:





50.88016800286405



In [18]:

    
a.error(exact, fdm[16])









    Out[18]:





14.86524516520828



In [19]:

    
a.error(exact, fdm[32])









    Out[19]:





10.414553642579925



In [20]:

    
a.error(exact, fdm[64])









    Out[20]:





10.409277174407087



In [21]:

    
a.error(exact, fdm[99])









    Out[21]:





10.40497862562813

Error function put in test: error_rel.



In [22]:

    
a.error_rel(exact, fdm[0])









    Out[22]:





0.8615030470056387



In [23]:

    
a.error_rel(exact, fdm[1])









    Out[23]:





0.6886289687473851



In [24]:

    
a.error_rel(exact, fdm[2])









    Out[24]:





0.6797471679427319



In [25]:

    
a.error_rel(exact, fdm[4])









    Out[25]:





0.665907667319058



In [26]:

    
a.error_rel(exact, fdm[8])









    Out[26]:





0.643887571348277



In [27]:

    
a.error_rel(exact, fdm[16])









    Out[27]:





0.6074968068817607



In [28]:

    
a.error_rel(exact, fdm[32])









    Out[28]:





0.5417153039151681



In [29]:

    
a.error_rel(exact, fdm[64])









    Out[29]:





0.40465507190384675



In [30]:

    
a.error_rel(exact, fdm[99])









    Out[30]:





0.2882128431039139



In [33]:

    
a.error_rel(exact, a.get_border(a.fdm(32,32,2000)))









    Out[33]:





0.17722530972332215



In [36]:

    
error_rel = [a.error_rel(exact, fdm[i]) for i in range(100)]



In [37]:

    
len(error_rel)









    Out[37]:





100



In [67]:

    
errors = [a.error(exact, fdm[i]) for i in range(100)]



In [75]:

    
fig = plt.figure(figsize=(13,4), dpi=100)
ax = fig.gca()
ax.plot(error_rel, '-o', ms=5, lw=2, alpha=1, mfc='orange')
ax.grid()
plt.ylabel('Modified Relative Error')
plt.xlabel('Iterations (x10)')

plt.show()



In [74]:

    
fig = plt.figure(figsize=(13,4), dpi=100)
ax = fig.gca()
ax.plot(errors, '-o', ms=5, lw=2, alpha=1, mfc='orange')
ax.grid()
plt.ylabel('Relative Error')
plt.xlabel('Iterations (x10)')

plt.show()



In [71]:

    
range(1,10,2)









    Out[71]:





[1, 3, 5, 7, 9]



In [76]:

    
a.scatter_plot(x,y,exact,a.get_border(a.fdm(32,32,2000)))



In [77]:

    
fdm2000 = a.get_border(a.fdm(32,32,2000))



In [78]:

    
a.error(exact,fdm2000)









    Out[78]:





10.400554663135578



In [79]:

    
a.error_rel(exact,fdm2000)









    Out[79]:





0.17722530972332215



In [80]:

    
a.error(exact,fdm[20])









    Out[80]:





10.504043780336685



In [81]:

    
a.error_rel(exact,fdm[20])









    Out[81]:





0.5907914165360616



In [ ]: