In [5]:

    

import sympy as sym
sym.init_printing()
z = sym.Symbol("\zeta")
z


    

    
Out[5]:





$$\zeta$$

In [72]:

    

H_q = sym.Matrix([[1 -z, z]])
H_q


    

    
Out[72]:





$$\left[\begin{matrix}- \zeta + 1 & \zeta\end{matrix}\right]$$

In [73]:

    

HTH = H_q.T @ H_q


    

    
Out[73]:





$$\left[\begin{matrix}\left(- \zeta + 1\right)^{2} & \zeta \left(- \zeta + 1\right)\\\zeta \left(- \zeta + 1\right) & \zeta^{2}\end{matrix}\right]$$

In [88]:

    

(HTH.subs({z:0.5- (1/3)**(0.5) / 2}) + HTH.subs({z: 0.5+ (1/3)**(0.5) / 2})) / 2


    

    
Out[88]:





$$\left[\begin{matrix}0.333333333333333 & 0.166666666666667\\0.166666666666667 & 0.333333333333333\end{matrix}\right]$$

In [86]:

    

HTH.integrate((z, 0, 1))


    

    
Out[86]:





$$\left[\begin{matrix}\frac{1}{3} & \frac{1}{6}\\\frac{1}{6} & \frac{1}{3}\end{matrix}\right]$$

In [35]:

    

import numpy as np
a = np.array([0,1,2], dtype=int)
temp = np.array([a*2, a*2 +1], dtype=int).T.flatten()
np.array([temp] * len(temp)).T


    

    
Out[35]:





array([[0, 0, 0, 0, 0, 0],
       [1, 1, 1, 1, 1, 1],
       [2, 2, 2, 2, 2, 2],
       [3, 3, 3, 3, 3, 3],
       [4, 4, 4, 4, 4, 4],
       [5, 5, 5, 5, 5, 5]])

In [37]:

    

from scipy import sparse


    

In [47]:

    

rows = [0, 0, 1, 1]
cols = [0, 0, 1, 1]
values = [1, 1, 1, 1]
s_array = sparse.csr.csr_matrix((values, (rows, cols)))
s_array


    

    
Out[47]:





<2x2 sparse matrix of type '<class 'numpy.int64'>'
	with 2 stored elements in Compressed Sparse Row format>

In [48]:

    

s_array.toarray()


    

    
Out[48]:





array([[2, 0],
       [0, 2]], dtype=int64)

In [55]:

    

s1 = s_array sparse.csr.csr_matrix([[0], [1]])


    

In [56]:

    

s1.toarray()


    

    
Out[56]:





array([[0],
       [2]], dtype=int64)

In [58]:

    




    

    




/home/lo/.local/lib/python3.6/site-packages/scipy/sparse/compressed.py:746: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.
  SparseEfficiencyWarning)

In [59]:

    

a = set()


    

In [67]:

    

{*[1,2,3,1]}


    

    
Out[67]:





$$\left\{1, 2, 3\right\}$$

In [61]:

    

a


    

    
Out[61]:





$$\left\{0\right\}$$

In [78]:

    

sparse.dia_matrix(([1]*10, 0), shape=(10, 10)).toarray()


    

    
Out[78]:





array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

In [80]:

    

sparse.csr_matrix(([1, 2], ([0, 1], [0, 0])), shape=(2, 1)).toarray()


    

    
Out[80]:





array([[1],
       [2]], dtype=int64)

In [81]:

    

[] + [1,2,3]


    

    
Out[81]:





$$\left [ 1, \quad 2, \quad 3\right ]$$

In [89]:

    

88/5


    

    
Out[89]:





$$17.6$$

In [90]:

    

17.6*4-22*3


    

    
Out[90]:





$$4.400000000000006$$

In [ ]: