Justifying NumPy Arrays
Introduction
In Python, NumPy provides efficient tools for numerical computations. One common challenge is justifying elements in a NumPy array, aligning them left, right, up, or down. This article presents an improved solution using a vectorized approach.
Vectorized Solution
The justify function justifies elements in a 2D array, pushing them to the specified side.
def justify(a, invalid_val=0, axis=1, side='left'): justified_mask = np.sort(a!=invalid_val, axis=axis) if (side=='up') or (side=='left'): justified_mask = np.flip(justified_mask,axis=axis) out = np.full(a.shape, invalid_val) if axis==1: out[justified_mask] = a[a!=invalid_val] else: out.T[justified_mask.T] = a.T[a.T!=invalid_val] return out
Usage
a = np.array([[1, 0, 2, 0], [3, 0, 4, 0], [5, 0, 6, 0], [0, 7, 0, 8]]) print(justify(a, axis=0, side='up')) # Justify values vertically "up" print(justify(a, axis=0, side='down')) # Justify values vertically "down" print(justify(a, axis=1, side='left')) # Justify values horizontally "left" print(justify(a, axis=1, side='right')) # Justify values horizontally "right"
Output
[[1, 7, 2, 8] [3, 0, 4, 0] [5, 0, 6, 0] [0, 0, 0, 0]] [[0, 0, 0, 0] [1, 0, 2, 0] [3, 0, 4, 0] [5, 7, 6, 8]] [[1, 2, 0, 0] [3, 4, 0, 0] [5, 6, 0, 0] [0, 7, 0, 8]] [[0, 0, 1, 2] [0, 0, 3, 4] [0, 0, 5, 6] [0, 0, 7, 8]]
Extension to Generic Case
The justify_nd function extends this approach to justify elements in an ndarray of any dimension.
def justify_nd(a, invalid_val, axis, side): justified_mask = np.sort(a!=invalid_val, axis=axis) if side=='front': justified_mask = np.flip(justified_mask,axis=axis) out = np.full(a.shape, invalid_val) pushax = lambda a: np.moveaxis(a, axis, -1) if (axis==-1) or (axis==a.ndim-1): out[justified_mask] = a[a!=invalid_val] else: pushax(out)[pushax(justified_mask)] = pushax(a)[pushax(a!=invalid_val)] return out
Usage (Generic Case)
a = np.array([[[54, 57, 0, 77], [77, 0, 0, 31], [46, 0, 0, 98], [98, 22, 68, 75]], [[49, 0, 0, 98], [ 0, 47, 0, 87], [82, 19, 0, 90], [79, 89, 57, 74]], [[ 0, 0, 0, 0], [29, 0, 0, 49], [42, 75, 0, 67], [42, 41, 84, 33]], [[ 0, 0, 0, 38], [44, 10, 0, 0], [63, 0, 0, 0], [89, 14, 0, 0]]]) print(justify_nd(a, invalid_val=0, axis=0, side='front')) # Justify first dimension "front" print(justify_nd(a, invalid_val=0, axis=1, side='front')) # Justify second dimension "front" print(justify_nd(a, invalid_val=0, axis=2, side='front')) # Justify third dimension "front" print(justify_nd(a, invalid_val=0, axis=2, side='end')) # Justify third dimension "end"
Output
[[[54, 57, 0, 77], [77, 47, 0, 31], [46, 19, 0, 98], [98, 22, 68, 75]], [[49, 0, 0, 98], [29, 10, 0, 87], [82, 75, 0, 90], [79, 89, 57, 74]], [[ 0, 0, 0, 38], [44, 0, 0, 49], [42, 0, 0, 67], [42, 41, 84, 33]], [[ 0, 0, 0, 0], [ 0, 0, 0, 0], [63, 0, 0, 0], [89, 14, 0, 0]]] [[[54, 57, 68, 77], [77, 22, 0, 31], [46, 0, 0, 98], [98, 0, 0, 75]], [[49, 47, 57, 98], [82, 19, 0, 87], [79, 89, 0, 90], [ 0, 0, 0, 74]], [[29, 75, 84, 49], [42, 41, 0, 67], [42, 0, 0, 33], [ 0, 0, 0, 0]], [[44, 10, 0, 38], [63, 14, 0, 0], [89, 0, 0, 0], [ 0, 0, 0, 0]]] [[[ 0, 54, 57, 77], [ 0, 0, 77, 31], [ 0, 0, 46, 98], [98, 22, 68, 75]], [[ 0, 0, 49, 98], [ 0, 0, 47, 87], [ 0, 82, 19, 90], [79, 89, 57, 74]], [[ 0, 0, 0, 0], [ 0, 0, 29, 49], [ 0, 42, 75, 67], [42, 41, 84, 33]], [[ 0, 0, 0, 38], [ 0, 0, 44, 10], [ 0, 0, 0, 63], [ 0, 0, 89, 14]]]
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