How to calculate this equation in Python or NumPy loop?

Question

What is the best way to calculate this in a loop in Python (or NumPy, if you think it is preferred for this kind of operation)?

KT = K0[1]*Var0 + K1[1]*Var1 + K2[1]*Var2 + K3[1]*Var3 +
     K0[2]*Var0 + K1[2]*Var1 + K2[2]*Var2 + K3[2]*Var3 +
     ...
     K0[51]*Var0 + K1[51]*Var1 + K2[51]*Var2 + K3[51]*Var3

where K0 is an array, containing 51 coefficients (floats). The same for K1, K2 and K3.
Var0, Var1, Var2 and Var3 are constants.

KT is the result, depending on Var0, ... Var3. The coefficient arrays are always the same. They do not change.

I'm coming from Fortran, and am currently learning/experimenting with Python, so forgive maybe the novice question. Python loops sometimes behave un-intuitively to me.

blue note · Accepted Answer · 2019-04-14 10:41:54Z

1

Make a 51 X 4 array with your Ks and a 4 X 1 array with you X and multiply. Numpy has something called broadcasting that will expand X to be multiplied with every row of K.

import numpy as np
K = np.column_stack([k0, k1, k2, k3])
X = np.array([x0, x1, x2, x3])
result = K * X

answered Apr 14, 2019 at 10:41

blue note

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Umesh · Accepted Answer · 2019-04-14 11:20:21Z

1

num1 = np.multiply(K0, var0) # type: numpy array
num2 = np.multiply(K1, var1)
num3 = np.multiply(K2, var2)
num4 = np.multiply(K3, var3)
# (num1 + num2 + num3 + num4) will give a single numpy array and then sum() operation will give you summation of all elemnts
KT = (num1 + num2 + num3 + num4).sum()

edited Apr 14, 2019 at 11:20

answered Apr 14, 2019 at 11:03

Umesh

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Pavel Kovtun · Accepted Answer · 2019-04-14 11:59:13Z

1

Fix Vars as a numpy array[Var0, Var1,..,VarN]
Fix K is a numpy array of arrays [[K11, K12,..,K1N][K21, K22,..,K2N],...]
Write a lambda function for multiplying Var_row * K_row
Vectorize this function using numpy (np.vectorize)
Apply vectorized function over data massive (2)
Be happy =)

a draft:

V_arr = np.array([2, 2, 2, 2])
K_arr = np.array([[1, 2, 3, 4],[4, 3, 2, 1],[5, 4, 4, 4]])

def mult_arr(a, b):
   return a * b

mult_vector = np.vectorize(mult_arr)

res = mult_vector(K_arr, V_arr)

edited Apr 14, 2019 at 11:59

answered Apr 14, 2019 at 10:43

Pavel Kovtun

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2 Comments

Rook Over a year ago

Paul, thanks for answering. I'm trying to code this at the moment, but frankly, to me that looks like a terribly overcomplex way of calculating this thing. Setting constants as arrays, setting arrays as arrays-of-arrays, ... Is there a more intuitive way of doing this thing (something, that will enable someone not familiar with what I'm trying to do, to figure out what way being done, by reading the code afterwards?)

Pavel Kovtun Over a year ago

it's the most numpy-kind approach. with most internal optimisations. it's not very complex in the code, tho. I'll update an answer with a draft

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