Matrix Mirroring in python

Question

I have a matrix of numbers:

[[a, b, c] 
 [d, e, f] 
 [g, h, i]]

that I would like to be mirrored accordingly:

[[g, h, i]
 [d, e, f]
 [a, b, c] 
 [d, e, f] 
 [g, h, i]]

And then again to yield:

[[i, h, g, h, i]
 [f, e, d, e, f]
 [c, b, a, b, c] 
 [f, e, d, e, f] 
 [i, h, g, h, i]]

I would like to stick to basic Python packages like numpy. Thanks in advance for any help!!

Solution 1

This can be accomplished using a simple helper function in pure python:

def mirror(seq):
    output = list(seq[::-1])
    output.extend(seq[1:])
    return output

inputs = [
   ['a', 'b', 'c'],
   ['d', 'e', 'f'],
   ['g', 'h', 'i'],
]
print(mirror([mirror(sublist) for sublist in inputs]))

Obviously, once the mirrored list is created, you can use it to create a numpy array or whatever...

Solution 2

Use numpy.lib.pad with 'reflect'

m = [['a', 'b', 'c'], 
     ['d', 'e', 'f'], 
     ['g', 'h', 'i']]

n=np.lib.pad(m,((2,0),(2,0)),'reflect')

n
Out[8]: 
array([['i', 'h', 'g', 'h', 'i'],
       ['f', 'e', 'd', 'e', 'f'],
       ['c', 'b', 'a', 'b', 'c'],
       ['f', 'e', 'd', 'e', 'f'],
       ['i', 'h', 'g', 'h', 'i']], 
      dtype='<U1')

Solution 3

import numpy as np

X= [[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]]

A = np.asanyarray(X)
B= np.flipud(A)
C= np.concatenate((B, A[1:]), axis=0)
D = C[:,1:]
F = np.fliplr(C)
E = np.concatenate((F, D), axis=1)

print(E)

I have added step by step transformation. flipud and flipud refrence

output

[[9 8 7 8 9]
 [6 5 4 5 6]
 [3 2 1 2 3]
 [6 5 4 5 6]
 [9 8 7 8 9]]

Solution 4

And here is a non-numpy solution:

a = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']]
b = list(reversed(a[1:])) + a # vertical mirror
c = list(zip(*b)) # transpose
d = list(reversed(c[1:])) + c # another vertical mirror
e = list(zip(*d)) # transpose again

Solution 5

Suppose you have

from numpy import array, concatenate
m = array([[1, 2, 3],
           [4, 5, 6],
           [7, 8, 9]])

You can invert this along the first (vertical) axis via

>>> m[::-1, ...]
array([[7, 8, 9],
       [4, 5, 6],
       [1, 2, 3]])

where ::-1 selects the rows from last to first in steps of -1.

To omit the last row, explicitly ask for the selection to stop immediately before 0:

>>> m[:0:-1, ...]
array([[7, 8, 9],
       [4, 5, 6]])

This can then be concatenated along the first axis

p = concatenate([m[:0:-1, ...], m], axis=0)

to form:

>>> p
array([[7, 8, 9],
       [4, 5, 6],
       [1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

This can be repeated along the other axis too:

q = concatenate([p[..., :0:-1], p], axis=1)

yielding

>>> q
array([[9, 8, 7, 8, 9],
       [6, 5, 4, 5, 6],
       [3, 2, 1, 2, 3],
       [6, 5, 4, 5, 6],
       [9, 8, 7, 8, 9]])

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