## Blockwise operations in Numpy

numpy submatrix

numpy block sum

numpy jagged array

numpy block average

numpy block reduce

numpy direct sum

numpy matrix of matrices

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 matrix into blocks and return matrix where each block is replaced by its sum, average or other function.

You might be looking for superbatfish's `blockwise_view`

. This uses `np.lib.stride_tricks.as_strided`

to create a view of the array which places "blocks" of the array in their own axes.

For example, suppose you have a 2D array such as,

In [97]: arr = np.arange(24).reshape(6, 4) In [98]: arr.shape Out[98]: (6, 4) In [99]: arr Out[99]: array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]])

and you wish to "chop it" into 4 blocks of shape (3, 2). You could use
`blockwise_view`

to convert it into a 4D array of shape (4, 3, 2):

In [34]: blocked = blockwise_view(arr, (3, 2)); blocked Out[34]: array([[[[ 0, 1], [ 4, 5], [ 8, 9]], [[ 2, 3], [ 6, 7], [10, 11]]], [[[12, 13], [16, 17], [20, 21]], [[14, 15], [18, 19], [22, 23]]]]) In [37]: blocked.shape Out[37]: (2, 2, 3, 2)

Now you could reshape it so all the values from one block are in the last axis:

In [41]: reshaped = blocked.reshape(-1, 3*2); reshaped Out[41]: array([[ 0, 1, 4, 5, 8, 9], [ 2, 3, 6, 7, 10, 11], [12, 13, 16, 17, 20, 21], [14, 15, 18, 19, 22, 23]])

Now you can sum along that axis, or take its mean or apply some other function to the elements of each block:

In [103]: reshaped.sum(axis=-1) Out[103]: array([ 27, 39, 99, 111]) In [104]: reshaped.mean(axis=-1) Out[104]: array([ 4.5, 6.5, 16.5, 18.5])

Unlike my first answer, which can only be applied to 2D arrays,
`blockwise_view`

can be applied to arbitrary N-dimensional arrays. It returns a
2N-dimensional array where the first N axes index the blocks.

**numpy.block,** numpy. block (arrays)[source]¶. Assemble an nd-array from nested lists of blocks. Blocks in the innermost lists are concatenated (see concatenate ) along the last Here is an example of Operations with NumPy arrays: The following blocks of code create new lists given input lists input_list1, input_list2, input_list3 (you can check their values in the console).

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])

**Is there an efficient way to form this block matrix with numpy or scipy ,** (exercise: compute operation count for both code fragments). whenever possible reuse previous calculations. pre-allocate output matrices, and do not store The following functions are used to perform operations on array with complex numbers. numpy.real() − returns the real part of the complex data type argument. numpy.imag() − returns the imaginary part of the complex data type argument. numpy.conj() − returns the complex conjugate, which is obtained by changing the sign of the imaginary part.

**https://docs.scipy.org/doc/numpy-1.15.1/reference/,** Are there any convenience utilities for doing blockwise operations on Numpy arrays? I am thinking of operations like Ising spin renormalization where you divide Gentle Introduction to NumPy. NumPy is the most popular Python library for high-performance array implementation: operations on arrays are a lot faster than those on lists, which in the world of big-data it can make an amplified runtime difference.

**Indexing highest value of numpy matrix - arrays - php,** Select columns in numpy - arrays. Are there any convenience utilities for doing blockwise operations on Numpy arrays? I am thinking of operations like Ising The sub-module numpy.linalg implements basic linear algebra, such as solving linear systems, singular value decomposition, etc. However, it is not guaranteed to be compiled using efficient routines, and thus we recommend the use of scipy.linalg, as detailed in section Linear algebra operations: scipy.linalg

**Select columns in numpy - arrays - php,** To deploy block operations, you can take an implementation from Implement 8, 1, 1, 1, 8]]) In [8]: np.sum(im2col_sliding(arr,[2,3]),axis=0) # Perform blockwise import numpy as np a = np.arange(0,60,5) a = a.reshape(3,4) print 'Original array is:' print a print ' ' print 'Transpose of the original array is:' b = a.T print b print ' ' print 'Sorted in C-style order:' c = b.copy(order = 'C') print c for x in np.nditer(c): print x, print ' ' print 'Sorted in F-style order:' c = b.copy(order = 'F') print c for x in np.nditer(c): print x,

**🥗 Block Operations in Numpy,** This docstring was copied from numpy.bitwise_and. Many dask.array operations are special cases of blockwise including elementwise, broadcasting, Similar to #28583, but going through BlockManager.apply. Resolved the issue with test_expressions behaving unexpectedly. Added an asv that times operations on a homogeneous-dtype DataFrame (rows=20k, cols=100) with a scalar.

##### Comments

- There's also
`view_as_windows`

in Scikit-image and`extract_patches`

in Scikit-learn.