Numba - How to fill 2D array in parallel

Question

I have a function that operates on a 2D matrix on float64(x,y). Basic concept: for each combination of rows (no. rows choose 2) count the number of positiv values after subtraction (row1 - row2). In a 2Dmatrix of int64(y,y) store this value in index [row1,row2] if value is above a certain threshold and [row2,row1] if below.

I've implemented that and decorated it with @njit(parallel=False), that works fine @njit(parallel=True) seems to give no speedup. Trying to speed up the whole thing I had a look at @guvectorize, that works as well. However I'm not able to figure out how to use @guvectorize with parallel true in this case either.

I had a look at numba guvectorize target='parallel' slower than target='cpu' , where the solution was to use @vecorize instead, but I can not transfer the solution to my problem, therefore I am now seeking help :)

Basic jitted and guvectorized implementation

import numpy as np
from numba import jit, guvectorize, prange
import timeit

@jit(parallel=False)
def check_pairs_sg(raw_data):
    # 2D array to be filled
    result = np.full((len(raw_data), len(raw_data)), -1)

    # Iterate over all possible gene combinations
    for r1 in range(0, len(raw_data)):
        for r2 in range(r1+1, len(raw_data)):
            diff = np.subtract(raw_data[:, r1], raw_data[:, r2])

            num_pos = len(np.where(diff > 0)[0])

            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos

    return result

@jit(parallel=True)
def check_pairs_multi(raw_data):
    # 2D array to be filled
    result = np.full((len(raw_data), len(raw_data)), -1)

    # Iterate over all possible gene combinations
    for r1 in range(0, len(raw_data)):
        for r2 in prange(r1+1, len(raw_data)):
            diff = np.subtract(raw_data[:, r1], raw_data[:, r2])

            num_pos = len(np.where(diff > 0)[0])

            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos

    return result

@guvectorize(["void(float64[:,:], int64[:,:])"],
             "(n,m)->(m,m)", target='cpu')
def check_pairs_guvec_sg(raw_data, result):
    for r1 in range(0, len(result)):
        for r2 in range(r1+1, len(result)):
            diff = np.subtract(raw_data[:, r1], raw_data[:, r2])

            num_pos = len(np.where(diff > 0)[0])

            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos

@guvectorize(["void(float64[:,:], int64[:,:])"],
             "(n,m)->(m,m)", target='parallel')
def check_pairs_guvec_multi(raw_data, result):
    for r1 in range(0, len(result)):
        for r2 in range(r1+1, len(result)):
            diff = np.subtract(raw_data[:, r1], raw_data[:, r2])

            num_pos = len(np.where(diff > 0)[0])

            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos

if __name__=="__main__":
     np.random.seed(404)
     a = np.random.random((512,512)).astype(np.float64)
     res = np.full((len(a), len(a)), -1)

and measured with

%timeit check_pairs_sg(a)
%timeit check_pairs_multi(a)
%timeit check_pairs_guvec_sg(a, res)
%timeit check_pairs_guvec_multi(a, res)

resulting in:

614 ms ± 2.54 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
507 ms ± 6.87 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
622 ms ± 3.88 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
671 ms ± 4.35 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

I cat wrap my head around on how to implement this as @vectorized or a proper parallel @guvectorize to fill the resulting 2D array truely in parallel.

I guess this is my first step before trying to taking this further to gpu.

Any help is highly appreciated.

Answer 1

Think of other compiled languages when writing Numba code

For example think of a more or less exact equivalent implementation of the lines

diff = np.subtract(raw_data[:, r1], raw_data[:, r2])
num_pos = len(np.where(diff > 0)[0])

in C++.

Pseudo Code

• Allocate an Array diff, loop over raw_data[i*size_dim_1+r1] (loop index is i)
• Allocate a Boolean Array, loop over the whole array diff and check if diff[i]>0
• Loop over the Boolean Array, get the indices where b_arr==True and save them via vector::push_back() to a vector.
• Check the size of the vector

The main problems in your code are:

• Creating temporary arrays for simple operations
• Non-contigous memory access

Optimizing the code

Removing temporary arrays and simplification

@nb.njit(parallel=False)
def check_pairs_simp(raw_data):
    # 2D array to be filled
    result = np.full((raw_data.shape[0],raw_data.shape[1]), -1)
    
    # Iterate over all possible gene combinations
    for r1 in range(0, raw_data.shape[1]):
        for r2 in range(r1+1, raw_data.shape[1]):
            num_pos=0
            for i in range(raw_data.shape[0]):
                if (raw_data[i,r1]>raw_data[i,r2]):
                    num_pos+=1
            
            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos
    
    return result

Removing temporary arrays and simplification + contigous memory access

@nb.njit(parallel=False)
def check_pairs_simp_rev(raw_data_in):
    #Create a transposed array not just a view 
    raw_data=np.ascontiguousarray(raw_data_in.T)
    
    # 2D array to be filled
    result = np.full((raw_data.shape[0],raw_data.shape[1]), -1)
    
    # Iterate over all possible gene combinations
    for r1 in range(0, raw_data.shape[0]):
        for r2 in range(r1+1, raw_data.shape[0]):
            num_pos=0
            for i in range(raw_data.shape[1]):
                if (raw_data[r1,i]>raw_data[r2,i]):
                    num_pos+=1
            
            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos
    
    return result

Removing temporary arrays and simplification + contigous memory access + Parallelization

@nb.njit(parallel=True,fastmath=True)
def check_pairs_simp_rev_p(raw_data_in):
    #Create a transposed array not just a view 
    raw_data=np.ascontiguousarray(raw_data_in.T)
    
    # 2D array to be filled
    result = np.full((raw_data.shape[0],raw_data.shape[1]), -1)
    
    # Iterate over all possible gene combinations
    for r1 in nb.prange(0, raw_data.shape[0]):
        for r2 in range(r1+1, raw_data.shape[0]):
            num_pos=0
            for i in range(raw_data.shape[1]):
                if (raw_data[r1,i]>raw_data[r2,i]):
                    num_pos+=1
            
            # Arbitrary check to illustrate
            if num_pos >= 5: 
               result[r1,r2] = num_pos
            else:
               result[r2,r1] = num_pos
    
    return result

Timings

%timeit check_pairs_sg(a)
488 ms ± 8.68 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit check_pairs_simp(a)
186 ms ± 3.83 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit check_pairs_simp_rev(a)
12.1 ms ± 226 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit check_pairs_simp_rev_p(a)
5.43 ms ± 49.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)