How Can NumPy's Vectorized Functions Efficiently Justify Arrays?

Justifying NumPy Arrays with Vectorized Functions

NumPy provides efficient ways to justify arrays using vectorized functions, offering improved performance and code simplicity compared to traditional Python loops.

Problem Statement

Given a NumPy array, the task is to shift its non-zero elements to the left, right, up, or down while maintaining its shape.

Numpy Solution

The following NumPy implementation performs efficient justification:

import numpy as np

def justify(a, invalid_val=0, axis=1, side='left'):    
    if invalid_val is np.nan:
        mask = ~np.isnan(a)
    else:
        mask = a!=invalid_val
    justified_mask = np.sort(mask,axis=axis)
    if (side=='up') | (side=='left'):
        justified_mask = np.flip(justified_mask,axis=axis)
    out = np.full(a.shape, invalid_val) 
    if axis==1:
        out[justified_mask] = a[mask]
    else:
        out.T[justified_mask.T] = a.T[mask.T]
    return out

This function justifies a 2D array along the specified axis and side (left, right, up, down). It works by identifying non-zero elements using mask, sorting them using sort, flipping the mask if justifying upwards or leftwards, and finally overwriting the original array with the justified values.

Example Usage

Here's a usage example that covers non-zero elements to the left:

a = np.array([[1,0,2,0], 
              [3,0,4,0], 
              [5,0,6,0], 
              [0,7,0,8]])

# Cover left
covered_left = justify(a, axis=1, side='left')

print("Original Array:")
print(a)
print("\nCovered Left:")
print(covered_left)

Output:

Original Array:
[[1 0 2 0]
 [3 0 4 0]
 [5 0 6 0]
 [0 7 0 8]]

Covered Left:
[[1 2 0 0]
 [3 4 0 0]
 [5 6 0 0]
 [7 8 0 0]]

Justifying for a Generic N-Dimensional Array

For justifying an N-dimensional array, the following function can be used:

def justify_nd(a, invalid_val, axis, side):    
    pushax = lambda a: np.moveaxis(a, axis, -1)
    if invalid_val is np.nan:
        mask = ~np.isnan(a)
    else:
        mask = a!=invalid_val
    justified_mask = np.sort(mask,axis=axis)
    
    if side=='front':
        justified_mask = np.flip(justified_mask,axis=axis)
            
    out = np.full(a.shape, invalid_val)
    if (axis==-1) or (axis==a.ndim-1):
        out[justified_mask] = a[mask]
    else:
        pushax(out)[pushax(justified_mask)] = pushax(a)[pushax(mask)]
    return out

This function supports more complex scenarios by justifying an N-dimensional array along an arbitrary axis and to either the 'front' or 'end' of the array.

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