Numpy matmul, treat each row in matrix as individual row vectors-CodePudding

I have a code below:

import numpy as np
wtsarray # shape(5000000,21)
covmat # shape(21,21)

portvol = np.zeros(shape=(wtsarray.shape[0],))
for i in range(0, wtsarray.shape[0]):
    portvol[i] = np.sqrt(np.dot(wtsarray[i].T, np.dot(covmat, wtsarray[i]))) * np.sqrt(mtx)

Nothing wrong with the above code, except that there's 5 million rows of row vector, and the for loop can be a little slow, I was wondering if you guys know of a way to vectorise it, so far I have tried with little success.

Or if there is any way to treat each individual row in a numpy matrix as a row vector and perform the above operation?

Thanks, if there are any suggestions on rephrasing my questions, please let me know as well.

CodePudding user response：

portvol = np.sqrt(np.sum(wtsarray * (wtsarray @ covmat.T), axis=1)) * np.sqrt(mtx)

should give you what you want. It replaces the first np.dot with elementwise multiplication followed by summation and it replaces the second np.dot(covmat, wtsarray[i]) with matrix multiplication, wtsarray @ covmat.T.

CodePudding user response：

For a smaller sample arrays:

In [24]: wtsarray = np.arange(15).reshape((5,3)); covmat=np.arange(9).reshape((3,3))
In [25]: portvol = np.zeros((5))
In [26]: for i in range(0, wtsarray.shape[0]):
    ...:     portvol[i] = np.sqrt(np.dot(wtsarray[i], np.dot(covmat, wtsarray[i])))
    ...: 
In [27]: portvol
Out[27]: array([ 7.74596669, 25.92296279, 43.95452195, 61.96773354, 79.97499609])

@ogdenkev's solution:

In [28]: np.sqrt(np.sum(wtsarray * (wtsarray @ covmat.T), axis=1))
Out[28]: array([ 7.74596669, 25.92296279, 43.95452195, 61.96773354, 79.97499609])
In [30]: timeit np.sqrt(np.sum(wtsarray * (wtsarray @ covmat.T), axis=1))
20.4 µs ± 891 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Same thing using einsum:

In [29]: np.sqrt(np.einsum('ij,jk,ik->i',wtsarray,covmat,wtsarray))
Out[29]: array([ 7.74596669, 25.92296279, 43.95452195, 61.96773354, 79.97499609])
In [31]: timeit np.sqrt(np.einsum('ij,jk,ik->i',wtsarray,covmat,wtsarray))
12.9 µs ± 24.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

A matmul version is in the works

In [35]: np.sqrt(np.squeeze(wtsarray[:,None,:]@covmat@wtsarray[:,:,None]))
Out[35]: array([ 7.74596669, 25.92296279, 43.95452195, 61.96773354, 79.97499609])
In [36]: timeit np.sqrt(np.squeeze(wtsarray[:,None,:]@covmat@wtsarray[:,:,None]))
13.5 µs ± 15.9 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)