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Optimizing code for shifting content in a matrix is sought for use in a 2048 game demo. Specifically, functions are needed to move non-zero values in the matrix towards the left, right, up, or down.
The provided code offers a vectorized approach inspired by another post:
def justify(a, invalid_val=0, axis=1, side='left'): """ Justifies a 2D array Parameters ---------- A : ndarray Input array to be justified axis : int Axis along which justification is to be made side : str Direction of justification. It could be 'left', 'right', 'up', 'down' It should be 'left' or 'right' for axis=1 and 'up' or 'down' for axis=0. """ 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
In [473]: a # input array Out[473]: array([[1, 0, 2, 0], [3, 0, 4, 0], [5, 0, 6, 0], [6, 7, 0, 8]]) In [474]: justify(a, axis=0, side='up') Out[474]: array([[1, 7, 2, 8], [3, 0, 4, 0], [5, 0, 6, 0], [6, 0, 0, 0]]) In [475]: justify(a, axis=0, side='down') Out[475]: array([[1, 0, 0, 0], [3, 0, 2, 0], [5, 0, 4, 0], [6, 7, 6, 8]]) In [476]: justify(a, axis=1, side='left') Out[476]: array([[1, 2, 0, 0], [3, 4, 0, 0], [5, 6, 0, 0], [6, 7, 8, 0]]) In [477]: justify(a, axis=1, side='right') Out[477]: array([[0, 0, 1, 2], [0, 0, 3, 4], [0, 0, 5, 6], [0, 6, 7, 8]])
For a generic n-dimensional array, the code can be modified as follows:
def justify_nd(a, invalid_val, axis, side): """ Justify ndarray for the valid elements (that are not invalid_val). Parameters ---------- A : ndarray Input array to be justified invalid_val : scalar invalid value axis : int Axis along which justification is to be made side : str Direction of justification. Must be 'front' or 'end'. So, with 'front', valid elements are pushed to the front and with 'end' valid elements are pushed to the end along specified axis. """ 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
In [87]: a Out[87]: 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]]])
To 'front', along axis =0 :
In [88]: justify_nd(a, invalid_val=0, axis=0, side='front') Out[88]: array([[[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]]])
Along axis=1 :
In [89]: justify_nd(a, invalid_val=0, axis=1, side='front') Out[89]: array([[[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]]])
Along axis=2 :
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