In [1]:

    

import numpy as np


    

In [2]:

    

a = np.arange(16).reshape(4, 4)
print(a)


    

    




[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]]

In [3]:

    

print(np.tril(a))


    

    




[[ 0  0  0  0]
 [ 4  5  0  0]
 [ 8  9 10  0]
 [12 13 14 15]]

In [4]:

    

print(np.triu(a))


    

    




[[ 0  1  2  3]
 [ 0  5  6  7]
 [ 0  0 10 11]
 [ 0  0  0 15]]

In [5]:

    

print(np.tril(a).T)


    

    




[[ 0  4  8 12]
 [ 0  5  9 13]
 [ 0  0 10 14]
 [ 0  0  0 15]]

In [6]:

    

print(np.tril(a) + np.tril(a).T)


    

    




[[ 0  4  8 12]
 [ 4 10  9 13]
 [ 8  9 20 14]
 [12 13 14 30]]

In [7]:

    

print(a.diagonal())


    

    




[ 0  5 10 15]

In [8]:

    

print(np.diag(a.diagonal()))


    

    




[[ 0  0  0  0]
 [ 0  5  0  0]
 [ 0  0 10  0]
 [ 0  0  0 15]]

In [9]:

    

print(np.tril(a) + np.tril(a).T - np.diag(a.diagonal()))


    

    




[[ 0  4  8 12]
 [ 4  5  9 13]
 [ 8  9 10 14]
 [12 13 14 15]]

In [10]:

    

def get_symmetric(a, use_tril=True):
    if use_tril:
        a = np.tril(a)
    else:
        a = np.triu(a)
    return a + a.T - np.diag(a.diagonal())


    

In [11]:

    

print(get_symmetric(a))


    

    




[[ 0  4  8 12]
 [ 4  5  9 13]
 [ 8  9 10 14]
 [12 13 14 15]]

In [12]:

    

print(get_symmetric(a, False))


    

    




[[ 0  1  2  3]
 [ 1  5  6  7]
 [ 2  6 10 11]
 [ 3  7 11 15]]

In [13]:

    

def is_symmetric(a):
    return np.array_equal(a, a.T)


    

In [14]:

    

a_sym = get_symmetric(a)
print(a_sym)


    

    




[[ 0  4  8 12]
 [ 4  5  9 13]
 [ 8  9 10 14]
 [12 13 14 15]]

In [15]:

    

print(is_symmetric(a_sym))


    

    




True

In [16]:

    

print(is_symmetric(a))


    

    




False

In [17]:

    

def get_skew_symmetric(a, use_tril=True):
    if use_tril:
        a = np.tril(a)
    else:
        a = np.triu(a)
    return a - a.T


    

In [18]:

    

print(get_skew_symmetric(a))


    

    




[[  0  -4  -8 -12]
 [  4   0  -9 -13]
 [  8   9   0 -14]
 [ 12  13  14   0]]

In [19]:

    

print(get_skew_symmetric(a, False))


    

    




[[  0   1   2   3]
 [ -1   0   6   7]
 [ -2  -6   0  11]
 [ -3  -7 -11   0]]

In [20]:

    

def is_skew_symmetric(a):
    return np.array_equal(a, -a.T)


    

In [21]:

    

a_sk_sym = get_skew_symmetric(a)
print(a_sk_sym)


    

    




[[  0  -4  -8 -12]
 [  4   0  -9 -13]
 [  8   9   0 -14]
 [ 12  13  14   0]]

In [22]:

    

print(is_skew_symmetric(a_sk_sym))


    

    




True

In [23]:

    

print(is_skew_symmetric(a))


    

    




False