Question

A really stupid question, but I could not figure the right way..

1. A is a 2 by 2 matrix, and B is a 2 by 1 matrix.
2. In a 10 iterations loop, B_new=A*B. B_new is 2 by 1.
3. Save B_new to an output matrix B_final after each iteration. So in the end, B_final is 2 by 10.

However, I have problem of adding B to B_new in a loop. Below is my code, can anyone give me some suggestions?

import numpy as np
a=np.ones(shape=(2,2))
b=np.ones(shape=(2,1))     
c_final=np.zeros(shape=(2,10)) 

for i in range(0,10):
    c=np.dot(a,b)
    b=c
    c_final[:,i]=c

Here is the error message:

    c_final[:,i]=c
ValueError: output operand requires a reduction, but reduction is not enabled

Answer 1

The error you’re seeing is because when numpy broadcasts c_final[:,i] and np.dot(a,b) together it produces an array with shape (2,2), which then can’t be assigned to c_final[:,i] since it has a shape of (2,1). I think it’s much clearer if you just play around with it in the interpreter:

>>> import numpy as np
>>> a = np.ones((2,2))
>>> b = np.ones((2,1))
>>> c_final = np.zeros((2,10))
>>> np.dot(a,b)
array([[ 2.],
       [ 2.]])
>>> np.dot(a,b).shape
(2, 1)
>>> c_final[:,0]
array([ 0.,  0.])
>>> c_final[:,0].shape
(2,)
>>> np.broadcast(c_final[:,0],np.dot(a,b)).shape
(2, 2)

The way around this is to flatten np.dot(a,b) by using np.squeeze or something similar so that when they are broadcast together they produce a 2 element array. For example:

>>> c_final[:,0] = np.dot(a,b).squeeze()

You’re not alone in finding the error message unhelpful. Someone filed a ticket about this about a year ago.