Combining Numpy Arrays in Blockwise Form

Question

I have three Numpy matrices

a = np.matrix('1 2; 3 4')

b = np.matrix('5 6 7; 8 9 10')

c = np.matrix('1 2 3; 4 5 6; 7 8 9')

and I would like to make the following block matrix:

M = [a b ; 0 c],

where 0 stands for a matrix of zeros with the relevant dimensions.

docs.scipy.org/doc/numpy/reference/generated/numpy.bmat.html — ford prefect
– ford prefect, Commented Oct 31, 2013 at 17:26

mdml · Accepted Answer · 2013-10-31 18:43:27Z

An easy way to create a block matrix is numpy.bmat (as pointed out by @inquisitiveIdiot). Judging by the block matrix you're looking to create, you need a 3x2 matrix of zeros:

>>> import numpy as np
>>> z = np.zeros( (3, 2) )

You can then create a block matrix by passing a 2x2 array of the blocks to numpy.bmat:

>>> M = np.bmat( [[a, b], [z, c]] )
>>> M
matrix([[  1.,   2.,   5.,   6.,   7.],
        [  3.,   4.,   8.,   9.,  10.],
        [  0.,   0.,   1.,   2.,   3.],
        [  0.,   0.,   4.,   5.,   6.],
        [  0.,   0.,   7.,   8.,   9.]])

Another (IMO more complicated) method is to use numpy.hstack and numpy.vstack.

>>> M = np.vstack( (np.hstack((a, b)), np.hstack((z, c))) )
>>> M
matrix([[  1.,   2.,   5.,   6.,   7.],
        [  3.,   4.,   8.,   9.,  10.],
        [  0.,   0.,   1.,   2.,   3.],
        [  0.,   0.,   4.,   5.,   6.],
        [  0.,   0.,   7.,   8.,   9.]])

Thanks, that works; will go through documentation better next time.
Watch out for the fact that this returns a np.matrix and not a np.array

LI ZEYAN · Accepted Answer · 2017-04-17 11:13:42Z

My method to generate and join block-wise matrix:

def blockwise(matrix, block=(3, 3)):
    shape = (int(matrix.shape[0] / block[0]), int(matrix.shape[1] / block[1])) + block
    strides = (matrix.strides[0] * block[0], matrix.strides[1] * block[1]) + matrix.strides
    return as_strided(matrix, shape=shape, strides=strides)

def block_join(blocks):
    return np.vstack(map(np.hstack, blocks))

arr = np.arange(36).reshape((6, 6))
blocks = blockwise(arr, (3, 3))
print(blocks)
re_join = block_join(blocks)
print(re_join)

then the output is as following:

>>>>[[[[ 0  1  2]
   [ 6  7  8]
   [12 13 14]]

  [[ 3  4  5]
   [ 9 10 11]
   [15 16 17]]]


 [[[18 19 20]
   [24 25 26]
   [30 31 32]]

  [[21 22 23]
   [27 28 29]
   [33 34 35]]]]
[[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]
 [12 13 14 15 16 17]
 [18 19 20 21 22 23]
 [24 25 26 27 28 29]
 [30 31 32 33 34 35]]

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