Numpy Array Multiplication with Transpose-CodePudding

I have the following numpy Array

import numpy as np
A = np.array([[0.5, 0.5]])

Now I want to calculate A^t*A, for which I thought of the following

np.dot(A.T,A)

What I want to get is an Array in form of

A_new = np.array([[0.0025, 0.0025], [0.0025,0.0025]])

But what I actually get is just a number

A_new = 0.005

How can I do this kind of array multiplication? Shouldn't 2x1 shape times 1x2 shape result in 2x2 shape?

CodePudding user response：

Use matmul:

>>> np.matmul(A.transpose(), A)
array([[0.25, 0.25],
       [0.25, 0.25]])

CodePudding user response：

You can do this as:

result = A*A.T

CodePudding user response：

Your array - changed a bit to make the result a bit more interesting:

In [28]: A = np.array([[0.5, 0.25]])
In [29]: A.shape
Out[29]: (1, 2)
In [30]: A.T.shape
Out[30]: (2, 1)

Matrix multiplication

In [31]: A.T@A
Out[31]: 
array([[0.25  , 0.125 ],
       [0.125 , 0.0625]])

ELement wise, with broadcasting, does the same thing, since the @ summation is on a size 1 dimension:

In [32]: A.T*A
Out[32]: 
array([[0.25  , 0.125 ],
       [0.125 , 0.0625]])

A*A.T is the same thing, but matrix multipication produces a (1,1):

In [33]: [email protected]
Out[33]: array([[0.3125]])

If A was 1d by mistake, you could get a scalar value

In [34]: A1 = A.ravel()
In [35]: A1.shape
Out[35]: (2,)
In [36]: A1.T.shape
Out[36]: (2,)    
In [38]: A1.T@A1
Out[38]: 0.3125

dot does the same thing:

In [39]: np.dot(A.T,A)
Out[39]: 
array([[0.25  , 0.125 ],
       [0.125 , 0.0625]])
In [40]: np.dot(A1.T,A1)
Out[40]: 0.3125