Blockwise operations in Numpy

Question

Are there any convenience utilities for doing blockwise operations on Numpy arrays?

I am thinking of operations like Ising spin renormalization where you divide a ma

Answer 1

For sliding blockwise operations, you can borrow an implementation from Implement Matlab's im2col_sliding 'sliding' in python that groups each block into a column, thereby blockwise operation would become as easy as operating along the axis = 0 and as such would accept all NumPy ufuncs for vectorized solutions. Here's a formal way to define such a sliding blocks creating function -

def im2col_sliding(A,BLKSZ):   

    # Parameters
    M,N = A.shape
    col_extent = N - BLKSZ[1] + 1
    row_extent = M - BLKSZ[0] + 1

    # Get Starting block indices
    start_idx = np.arange(BLKSZ[0])[:,None]*N + np.arange(BLKSZ[1])

    # Get offsetted indices across the height and width of input array
    offset_idx = np.arange(row_extent)[:,None]*N + np.arange(col_extent)

    # Get all actual indices & index into input array for final output
    return np.take (A,start_idx.ravel()[:,None] + offset_idx.ravel())

---

Sample run to calculate blockwise sum, average, std, etc. -

In [6]: arr                 # Sample array
Out[6]: 
array([[6, 5, 0, 6, 0],
       [7, 4, 2, 3, 6],
       [6, 3, 3, 8, 1],
       [5, 5, 1, 1, 8]])

In [7]: im2col_sliding(arr,[2,3])   # Blockwise array with blocksize : (2,3)
Out[7]: 
array([[6, 5, 0, 7, 4, 2, 6, 3, 3],
       [5, 0, 6, 4, 2, 3, 3, 3, 8],
       [0, 6, 0, 2, 3, 6, 3, 8, 1],
       [7, 4, 2, 6, 3, 3, 5, 5, 1],
       [4, 2, 3, 3, 3, 8, 5, 1, 1],
       [2, 3, 6, 3, 8, 1, 1, 1, 8]])

In [8]: np.sum(im2col_sliding(arr,[2,3]),axis=0) # Perform blockwise summation
Out[8]: array([24, 20, 17, 25, 23, 23, 23, 21, 22])

In [9]: np.mean(im2col_sliding(arr,[2,3]),axis=0) # Perform blockwise averaging
Out[9]: 
array([ 4.        ,  3.33333333,  2.83333333,  4.16666667,  3.83333333,
        3.83333333,  3.83333333,  3.5       ,  3.66666667])

In [10]: np.std(im2col_sliding(arr,[2,3]),axis=0) # Blockwise std. deviation
Out[10]: 
array([ 2.38047614,  1.97202659,  2.47767812,  1.77169097,  1.95078332,
        2.40947205,  1.67497927,  2.43241992,  3.14466038])