Improve performance of combined for blocks with numpy

Question

I have the rather simple function func1() defined below, mainly composed of two for blocks.

It works perfectly for small N values, but being that the for blocks are combined it grows very quickly to the point of taking minutes when N>1000 .

How can I use numpy broadcasting to improve the performance of this function?

import numpy as np
import time as t


def func1(A_triang, B_triang):
    aa = []
    for i, A_tr in enumerate(A_triang):
        for j, B_tr in enumerate(B_triang):
            # Absolute value of differences.
            abs_diff = abs(np.array(A_tr) - np.array(B_tr))
            # Store the sum of the differences and the indexes
            aa.append([sum(abs_diff), i, j])
    return aa


# Generate random data with the proper format
N = 500
A_triang = np.random.uniform(0., 20., (N, 3))
A_triang[:, 0] = np.ones(N)
B_triang = np.random.uniform(0., 20., (N, 3))
B_triang[:, 0] = np.ones(N)

# Call function.
s = t.clock()
aa = func1(A_triang, B_triang)
print(t.clock() - s)

Answer 1

Here's one with NumPy broadcasting , leveraging a modified version of indices_merged_arr_generic_using_cp for index assignment part -

import functools

# Based on https://stackoverflow.com/a/46135435/ @unutbu
def indices_merged_arr_generic_using_cp(arr):
    """
    Based on cartesian_product
    http://stackoverflow.com/a/11146645/190597 (senderle)
    """
    shape = arr.shape
    arrays = [np.arange(s, dtype='int') for s in shape]
    broadcastable = np.ix_(*arrays)
    broadcasted = np.broadcast_arrays(*broadcastable)
    rows, cols = functools.reduce(np.multiply, broadcasted[0].shape),\
                                                  len(broadcasted)+1
    out = np.empty(rows * cols, dtype=arr.dtype)
    start, end = rows, 2*rows
    for a in broadcasted:
        out[start:end] = a.reshape(-1)
        start, end = end, end + rows
    out[0:rows] = arr.flatten()
    return out.reshape(cols, rows).T

def func1_numpy_broadcasting(a,b):
    val = np.abs(a[:,None,:] - b).sum(-1)
    return indices_merged_arr_generic_using_cp(val)

If the first column of the inputs are always 1s , then, we won't need to compute their differences as their sum of differences would be zero. So, alternatively to get val , we can simply use the last two columns -

val = np.abs(a[:,1,None] - b[:,1]) + np.abs(a[:,2,None] - b[:,2])

This would save memory as we are not going 3D this way.

---

Using numexpr module -

import numexpr as ne
def func1_numexpr_broadcasting(a,b):
    a3D = a[:,None,:]
    val = ne.evaluate('sum(abs(a3D - b),2)')
    return indices_merged_arr_generic_using_cp(val)

Leveraging the fact that the first columns are 1s , we would have -

def func1_numexpr_broadcasting_v2(a,b):
    a1 = a[:,1,None]
    b1 = b[:,1]
    a2 = a[:,2,None]
    b2 = b[:,2]
    val = ne.evaluate('abs(a1-b1) + abs(a2-b2)')
    return indices_merged_arr_generic_using_cp(val)