Requesting NumPy/SciPy vectorization replacements of for loops and list comprehensions

Question

I have two different array processing problems that I'd like to solve AQAP (Q=quickly) to ensure that the solutions aren't rate-limiting in my process (using NEAT to train a video game bot). In one case, I want to build a penalty function for making larger column heights, and in the other I want to reward building "islands of a common value.

Operations begin on a 26 row x 6 column numpy array of grayscale values with a black/0 background.

I have working solutions for each problem that already implement some numpy, but I'd like to push for a fully vectorized approach to both.

    import numpy as np,
    from scipy.ndimage.measurements import label as sp_label
    from math import ceil

Both problems start from an array like this:

    img= np.array([[ 0.,  0.,  0., 12.,  0.,  0.],
                   [ 0.,  0.,  0., 14.,  0.,  0.],               
                   [ 0.,  0.,  0., 14.,  0.,  0.],
                   [ 0.,  0.,  0., 14.,  0.,  0.],               
                   [16.,  0.,  0., 14.,  0.,  0.],
                   [16.,  0.,  0., 12.,  0.,  0.],               
                   [12.,  0., 11.,  0.,  0.,  0.],
                   [12.,  0., 11.,  0.,  0.,  0.],               
                   [16.,  0., 15.,  0., 15.,  0.],
                   [16.,  0., 15.,  0., 15.,  0.],               
                   [14.,  0., 12.,  0., 11.,  0.],
                   [14.,  0., 12.,  0., 11.,  0.],               
                   [14., 15., 11.,  0., 11.,  0.],
                   [14., 15., 11.,  0., 11.,  0.],               
                   [13., 16., 12.,  0., 13.,  0.],
                   [13., 16., 12.,  0., 13.,  0.],               
                   [13., 14., 16.,  0., 16.,  0.],
                   [13., 14., 16.,  0., 16.,  0.],               
                   [16., 14., 15.,  0., 14.,  0.],
                   [16., 14., 15.,  0., 14.,  0.],               
                   [14., 16., 14.,  0., 11.,  0.],
                   [14., 16., 14.,  0., 11.,  0.],               
                   [11., 13., 14., 16., 12., 13.],
                   [11., 13., 14., 16., 12., 13.],               
                   [12., 12., 15., 14., 15., 11.], 
                   [12., 12., 15., 14., 15., 11.]])

The first (column height) problem is currently being solved with:

    # define valid connection directions for sp_label
    c_valid_conns = np.array((0,1,0,0,1,0,0,1,0,), dtype=np.int).reshape((3,3))

    # run the island labeling function sp_label    
    # c_ncomponents is a simple count of the conected columns in labeled
    columns, c_ncomponents = sp_label(img, c_valid_conns)

    # calculate out the column lengths
    col_lengths = np.array([(columns[columns == n]/n).sum() for n in range(1, c_ncomponents+1)])
    col_lengths

to give me this array: [ 6. 22. 20. 18. 14. 4. 4.]

(bonus if the code consistently ignores the labeled region that does not "contain" the bottom of the array (row index 25/-1))

The second problem involves masking for each unique value and calculating the contiguous bodies in each masked array to get me the size of the contiguous bodies:

    # initial values to start the ball rolling
    values = [11, 12, 13, 14, 15, 16]
    isle_avgs_i = [1.25, 2, 0, 1,5, 2.25, 1]

    # apply filter masks to img to isolate each value 
    # Could these masks be pushed out into a third array dimension instead?
    masks = [(img == g) for g in np.unique(values)]

    # define the valid connectivities (8-way) for the sp_label function
    m_valid_conns = np.ones((3,3), dtype=np.int)

    # initialize islanding lists 
    # I'd love to do away with these when I no longer need the .append() method)
    mask_isle_avgs, isle_avgs = [],[]

    # for each mask in the image:         
    for i, mask in enumerate(masks):

        # run the island labeling function sp_label
        # m_labeled is the array containing the sequentially labeled islands
        # m_ncomponents is a simple count of the islands in m_labeled
        m_labeled, m_ncomponents = sp_label(mask, m_valid_conns)

        # collect the average (island size-1)s (halving to account for... 
        # ... y resolution) for each island into mask_isle_avgs list 
        # I'd like to vectorize this step
        mask_isle_avgs.append((sum([ceil((m_labeled[m_labeled == n]/n).sum()/2)-1 
                                    for n in range(1, m_ncomponents+1)]))/(m_ncomponents+1))

        # add up the mask isle averages for all the islands... 
        # ... and collect into isle_avgs list
        # I'd like to vectorize this step
        isle_avgs.append(sum(mask_isle_avgs))

    # initialize a difference list for the isle averages (I also want to do away with this step)
    d_avgs = []

    # evaluate whether isle_avgs is greater for the current frame or the...
    # ... previous frame (isle_avgs_i) and append either the current...
    # ... element or 0, depending on whether the delta is non-negative
    # I want this command vectorized
    [d_avgs.append(isle_avgs[j]) 
     if (isle_avgs[j]-isle_avgs_i[j])>=0 
     else d_avgs.append(0) for j in range(len(isle_avgs))]
    d_avgs

to give me this d_avgs array: [0, 0, 0.46785714285714286, 1.8678571428571429, 0, 0]

(bonus again if the code consistently ignores the labeled region that does not "contain" the bottom of the array (row index 25/-1) to instead give this array:

[0, 0, 0.43452380952380953, 1.6345238095238095, 0, 0] )

I'm looking to remove any list operations and comprehensions and move them into fully vectorized numpy/scipy implementation with the same results.

Any help removing any of these steps would be greatly appreciated.

Answer 1

Here's how I ultimately solved this issue:

######## column height penalty calculation ########
            # c_ncomponents is a simple count of the conected columns in labeled
            columns, c_ncomponents = sp_label(unit_img, c_valid_conns)
#                 print(columns)
            # throw out the falling block with .isin(x,x[-1]) combined with... 
            # the mask nonzero(x) 
            drop_falling = np.isin(columns, columns[-1][np.nonzero(columns[-1])])
            col_hts = drop_falling.sum(axis=0)
#                 print(f'col_hts {col_hts}')
            # calculate differentials for the (grounded) column heights
            d_col_hts = np.sum(col_hts - col_hts_i)
#                 print(f'col_hts {col_hts} - col_hts_i {col_hts_i} ===> d_col_hts {d_col_hts}')
            # set col_hts_i to current col_hts for next evaluation
            col_hts_i = col_hts
            # calculate penalty/bonus function
#                 col_pen = (col_hts**4 - 3**4).sum()
            col_pen = np.where(d_col_hts > 0, (col_hts**4 - 3**4), 0).sum()
#                 
#             if col_pen !=0:
#                 print(f'col_pen: {col_pen}')
######## end column height penalty calculation ########

######## color island bonus calculation ########
            # mask the unit_img to remove the falling block
            isle_img = drop_falling * unit_img
#             print(isle_img)
            # broadcast the game board to add a layer for each color
            isle_imgs = np.broadcast_to(isle_img,(7,*isle_img.shape))
            # define a mask to discriminate on color in each layer
            isle_masked = isle_imgs*[isle_imgs==ind_grid[0]]
            # reshape the array to return to 3 dimensions
            isle_masked = isle_masked.reshape(isle_imgs.shape)
            # generate the isle labels
            isle_labels, isle_ncomps = sp_label(isle_masked, i_valid_conns)
            # determine the island sizes (via return_counts) for all the unique labels
            isle_inds, isle_sizes = np.unique(isle_labels, return_counts=True)
            # zero out isle_sizes[0] to remove spike for background (500+ for near empty board)
            isle_sizes[0] = 0
            # evaluate difference to determine whether bonus applies
            if isle_sizes_i.sum() != isle_sizes.sum():
            # calculate bonus for all island sizes ater throwing away the 0 count
                isle_bonus = (isle_sizes**3).sum()
            else:
                isle_bonus = 0