Numpy split cube into cubes

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南方客
南方客 2021-02-09 04:01

There is a function np.split() which can split an array along 1 axis. I was wondering if there was a multi axis version where you can split along axes (0,1,2) for e

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  • 2021-02-09 04:19

    I don't think there is a multi axis version where you can split along some given axes. But you can split it up one dimension at a time. For example like this:

    def split2(arys, sections, axis=[0, 1]):
        if not isinstance(arys, list):
             arys = [arys]
        for ax in axis:
            arys = [np.split(ary, sections, axis=ax) for ary in arys]
            arys = [ary for aa in arys for ary in aa]  # Flatten
        return arys
    

    It can be used like this:

    In [1]: a = np.array(range(100)).reshape(10, 10)
    In [2]: split2(a, 2, axis=[0, 1])
    Out[2]:
    [array([[ 0,  1,  2,  3,  4],
           [10, 11, 12, 13, 14],
           [20, 21, 22, 23, 24],
           [30, 31, 32, 33, 34],
           [40, 41, 42, 43, 44]]),
     array([[ 5,  6,  7,  8,  9],
           [15, 16, 17, 18, 19],
           [25, 26, 27, 28, 29],
           [35, 36, 37, 38, 39],
           [45, 46, 47, 48, 49]]),
     array([[50, 51, 52, 53, 54],
           [60, 61, 62, 63, 64],
           [70, 71, 72, 73, 74],
           [80, 81, 82, 83, 84],
           [90, 91, 92, 93, 94]]),
     array([[55, 56, 57, 58, 59],
           [65, 66, 67, 68, 69],
           [75, 76, 77, 78, 79],
           [85, 86, 87, 88, 89],
           [95, 96, 97, 98, 99]])]
    
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  • 2021-02-09 04:34

    Suppose the cube has shape (W, H, D) and you wish to break it up into N little cubes of shape (w, h, d). Since NumPy arrays have axes of fixed length, w must evenly divide W, and similarly for h and d.

    Then there is a way to reshape the cube of shape (W, H, D) into a new array of shape (N, w, h, d).

    For example, if arr = np.arange(4*4*4).reshape(4,4,4) (so (W,H,D) = (4,4,4)) and we wish to break it up into cubes of shape (2,2,2), then we could use

    In [283]: arr.reshape(2,2,2,2,2,2).transpose(0,2,4,1,3,5).reshape(-1,2,2,2)
    Out[283]: 
    array([[[[ 0,  1],
             [ 4,  5]],
    
            [[16, 17],
             [20, 21]]],
    
    ...
           [[[42, 43],
             [46, 47]],
    
            [[58, 59],
             [62, 63]]]])
    

    The idea here is to add extra axes to the array which sort of act as place markers:

     number of repeats act as placemarkers
     o---o---o
     |   |   |
     v   v   v
    (2,2,2,2,2,2)
       ^   ^   ^
       |   |   |
       o---o---o
       newshape
    

    We can then reorder the axes (using transpose) so that the number of repeats comes first, and the newshape comes at the end:

    arr.reshape(2,2,2,2,2,2).transpose(0,2,4,1,3,5)
    

    And finally, call reshape(-1, w, h, d) to squash all the placemarking axes into a single axis. This produces an array of shape (N, w, h, d) where N is the number of little cubes.


    The idea used above is a generalization of this idea to 3 dimensions. It can be further generalized to ndarrays of any dimension:

    import numpy as np
    def cubify(arr, newshape):
        oldshape = np.array(arr.shape)
        repeats = (oldshape / newshape).astype(int)
        tmpshape = np.column_stack([repeats, newshape]).ravel()
        order = np.arange(len(tmpshape))
        order = np.concatenate([order[::2], order[1::2]])
        # newshape must divide oldshape evenly or else ValueError will be raised
        return arr.reshape(tmpshape).transpose(order).reshape(-1, *newshape)
    
    print(cubify(np.arange(4*6*16).reshape(4,6,16), (2,3,4)).shape)
    print(cubify(np.arange(8*8*8*8).reshape(8,8,8,8), (2,2,2,2)).shape)
    

    yields new arrays of shapes

    (16, 2, 3, 4)
    (256, 2, 2, 2, 2)
    

    To "uncubify" the arrays:

    def uncubify(arr, oldshape):
        N, newshape = arr.shape[0], arr.shape[1:]
        oldshape = np.array(oldshape)    
        repeats = (oldshape / newshape).astype(int)
        tmpshape = np.concatenate([repeats, newshape])
        order = np.arange(len(tmpshape)).reshape(2, -1).ravel(order='F')
        return arr.reshape(tmpshape).transpose(order).reshape(oldshape)
    

    Here is some test code to check that cubify and uncubify are inverses.

    import numpy as np
    def cubify(arr, newshape):
        oldshape = np.array(arr.shape)
        repeats = (oldshape / newshape).astype(int)
        tmpshape = np.column_stack([repeats, newshape]).ravel()
        order = np.arange(len(tmpshape))
        order = np.concatenate([order[::2], order[1::2]])
        # newshape must divide oldshape evenly or else ValueError will be raised
        return arr.reshape(tmpshape).transpose(order).reshape(-1, *newshape)
    
    def uncubify(arr, oldshape):
        N, newshape = arr.shape[0], arr.shape[1:]
        oldshape = np.array(oldshape)    
        repeats = (oldshape / newshape).astype(int)
        tmpshape = np.concatenate([repeats, newshape])
        order = np.arange(len(tmpshape)).reshape(2, -1).ravel(order='F')
        return arr.reshape(tmpshape).transpose(order).reshape(oldshape)
    
    tests = [[np.arange(4*6*16), (4,6,16), (2,3,4)],
             [np.arange(8*8*8*8), (8,8,8,8), (2,2,2,2)]]
    
    for arr, oldshape, newshape in tests:
        arr = arr.reshape(oldshape)
        assert np.allclose(uncubify(cubify(arr, newshape), oldshape), arr)
        # cuber = Cubify(oldshape,newshape)
        # assert np.allclose(cuber.uncubify(cuber.cubify(arr)), arr)
    
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  • 2021-02-09 04:35

    In addition to my extra question to @unutbu's answer I think I have got the reverse to work (in case you want to split a cube into cubes, apply a function to each one and then combine them back).

    import numpy as np
    import pdb
    np.set_printoptions(precision=3,linewidth=300)
    
    class Cubify():
        def __init__(self,oldshape,newshape):
            self.newshape = np.array(newshape)
            self.oldshape = np.array(oldshape)
            self.repeats = (oldshape / newshape).astype(int)
            self.tmpshape = np.column_stack([self.repeats, newshape]).ravel()
            order = np.arange(len(self.tmpshape))
            self.order = np.concatenate([order[::2], order[1::2]])
            self.reverseOrder = self.order.copy()
            self.reverseOrder = np.arange(len(self.tmpshape)).reshape(2, -1).ravel(order='F')
            self.reverseReshape = np.concatenate([self.repeats,self.newshape])
    
        def cubify(self,arr):
            # newshape must divide oldshape evenly or else ValueError will be raised
            return arr.reshape(self.tmpshape).transpose(self.order).reshape(-1, *self.newshape)
    
        def uncubify(self,arr):
            return arr.reshape(self.reverseReshape).transpose(self.reverseOrder).reshape(self.oldshape)
    
    if __name__ == "__main__":
        N = 9
        x = np.arange(N**3).reshape(N,N,N)
        oldshape = x.shape
        newshape = np.array([3,3,3])
        cuber = Cubify(oldshape,newshape)
        out = cuber.cubify(x)
        back = cuber.uncubify(out)
    
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