

In [1]:

    
import numpy as np

Dot Product

Dot product (return a matrix/array) and vector product (return a single value)



In [28]:

    
w = np.array([1, 2, 3])
w_mat = np.expand_dims(w, axis=1)  # col vec as mat
d = 3
T = 10
X = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])


t = 0
np.dot(w.T, X[:, [t]])









    Out[28]:





array([30])



In [29]:

    
np.dot(w, X[:, t])  # all vector









    Out[29]:





30



In [31]:

    
np.dot(w, X[:, [t]])









    Out[31]:





array([30])

maintain matrix



In [32]:

    
np.dot(w_mat.T, X[:, [t]])









    Out[32]:





array([[30]])



In [33]:

    
np.dot(w_mat.T, X)









    Out[33]:





array([[30, 36, 42]])



In [35]:

    
np.dot(w_mat, X)









    



---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-35-d75f597fe870> in <module>()
----> 1 np.dot(w_mat, X)

ValueError: shapes (3,1) and (3,3) not aligned: 1 (dim 1) != 3 (dim 0)

Col vector by default



In [34]:

    
np.dot(w, X)  # more tensor-feel









    Out[34]:





array([30, 36, 42])

Stype

Suffix



In [39]:

    
X









    Out[39]:





array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])



In [40]:

    
X.mean(axis=0) # np.mean(X, axis=0)









    Out[40]:





array([ 4.,  5.,  6.])



In [41]:

    
X.sum(axis=0)









    Out[41]:





array([12, 15, 18])



In [42]:

    
X.dot(X)









    Out[42]:





array([[ 30,  36,  42],
       [ 66,  81,  96],
       [102, 126, 150]])



In [43]:

    
# However, element-wise must be np.xxx
np.divide(X, 2)









    Out[43]:





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



In [44]:

    
np.divide(X, 2.0)









    Out[44]:





array([[ 0.5,  1. ,  1.5],
       [ 2. ,  2.5,  3. ],
       [ 3.5,  4. ,  4.5]])