In [11]:

    

%matplotlib qt
exec(open("Simpson's_vector_free_iterative.py").read())


    

    




It took 515.92 seconds for this script to perform the integration.

In [19]:

    

from numpy import array, matmul
from numpy.linalg import inv, eig, det
a=array([[7,3,-1],[6,5,2],[2,7,8]])
det(a)*inv(a)


    

    
Out[19]:





array([[ 26., -31.,  11.],
       [-44.,  58., -20.],
       [ 32., -43.,  17.]])

In [ ]:

    

# With N=100000000
1.505263e-04 # 1/100N tol
4.357402e-05 # 1/30N tol
3.231596e-05 # 1/25N tol
2.750370e-05 # 1/23N tol
2.626899e-05 # 1/22.5N tol
2.602042e-05 # 1/22.4N tol
2.589594e-05 # 1/22.35N tol
2.577133e-05 # 1/22.3N tol
2.554667e-05 # 1/22.21N tol
4.207666e-06 # 1/22.201N tol
4.210182e-06 # 1/22.2N tol
4.212699e-06 # 1/22.199N tol
4.222765e-06 # 1/22.195N tol
4.235348e-06 # 1/22.19N tol
4.336069e-06 # 1/22.15N tol
4.462099e-06 # 1/22.1N tol
4.714593e-06 # 1/22N tol
7.272229e-06 # 1/21N tol
9.892468e-06 # 1/20N tol
1.306198e-05 # 1/18.823N tol
4.109402e-05 # 1/10N tol
8.936810e-05 # 1/1.8823N tol


    

In [39]:

    

# With N=10000000
0.002046    # 1e-10
0.000050426 # 1/25N tol
0.000018455 # 1/21N tol
0.000010170 # 1/20N tol
0.000001551 # 1/19N tol
0.000000689 # 1/18.9N tol
0.000000061 # 1/18.83N tol
0.000000018 # 1/18.825N tol
0.000000009 # 1/18.824N tol
0.000000000615 # 1/18.823N tol
0.000000025 # 1/18.82N tol
0.000000198 # 1/18.8N tol
0.000000630 # 1/18.75N tol
0.000002806 # 1/18.5N tol
0.000007600 # 1/18N tol
0.000036971 # 1/15N tol
0.000093439 # 1/10N tol
0.000154190 # 1/6N tol
0.000174266 # 1/5N tol
0.000196957 # 1/4N tol
0.000226335 # 1/3N tol
0.000267056 # 1/2N tol
0.000346898 # 1/N  tol
0.00045358  # 2/N  tol
0.000608279 # 4/N  tol


    

    
Out[39]:





0.000608279

In [47]:

    

1/(100*N)


    

    
Out[47]:





6.666666666666667e-09

In [2]:

    

from numpy import sqrt
(240-250)/(12/sqrt(3))


    

    
Out[2]:





-1.4433756729740643

In [ ]:

    

exec(open("Simpson's_vector_free_iterative.py").read())


    

In [ ]: