Efficient way to shift 2D-matrices in both directions?

Question

Given a two dimensional matrix, e.g.

l = [[1,1,1],
     [2,5,2],
     [3,3,3]])

What is the most efficient way of implementing a shift operation on columns and rows?

E.g.

shift('up', l) 

[[2, 5, 2],
 [3, 3, 3],
 [1, 1, 1]]

but

shift('left', l) 

[[1, 1, 1],
 [5, 2, 2],
 [3, 3, 3]]

I'm using collections.deque on both depths because of this answer but while a 'up' or 'down' only requires 1 shift, a 'left' or 'right' requires N shifts (my implementation is using a for cycle for each row).

In C I think this can be improved using pointer arithmetic (see e.g. this answer).

Is there a better pythonic way?

EDIT:

• By efficient I mean if there is a way of avoiding the N shifts.
• We can assume the matrix is squared.
• The shift can be in place.

Thanks to martineau for pointing out these important points of the question. I'm sorry I didn't pointed them out before.

Answer 1

Numpy provides a method called roll() to shift entries.

>>> import numpy as np
>>> x = np.arange(9)
>>> x = x.reshape(3, 3)
>>> print(x)

[[0 1 2]
 [3 4 5]
 [6 7 8]]

>>> x = np.roll(x, -1, axis=0) # up
>>> print(x)

[[3 4 5]
 [6 7 8]
 [0 1 2]]

>>> x = np.roll(x, 1, axis=0) # down
>>> print(x)

[[0 1 2]
 [3 4 5]
 [6 7 8]]

>>> x = np.roll(x, 2, axis=1) # right
>>> print(x)

[[1 2 0]
 [4 5 3]
 [7 8 6]]

>>> x = np.roll(x, -2, axis=1) # left
>>> print(x)    

[[0 1 2]
 [3 4 5]
 [6 7 8]]

I guess that Numpy will be pretty efficient compared to most solutions
in terms of matrix operations and you won't be bound to a 2 dimensional matrix.

Answer 2

Here's one fairly efficient way to do it that will work with non-square matrices:

DIRS = NONE, UP, DOWN, LEFT, RIGHT = 'unshifted', 'up', 'down', 'left', 'right'

def shift(matrix, direction, dist):
    """ Shift a 2D matrix in-place the given distance of rows or columns in the
        specified (NONE, UP, DOWN, LEFT, RIGHT) direction and return it.
    """
    if dist and direction in (UP, DOWN, LEFT, RIGHT):
        n = 0
        if direction in (UP, DOWN):
            n = (dist % len(matrix) if direction == UP else -(dist % len(matrix)))
        elif direction in (LEFT, RIGHT):
            n = (dist % len(matrix[0]) if direction == LEFT else -(dist % len(matrix[0])))
            matrix[:] = list(zip(*matrix))  # Transpose rows and columns for shifting.

        h = matrix[:n]
        del matrix[:n]
        matrix.extend(h)

        if direction in (LEFT, RIGHT):
            matrix[:] = map(list, zip(*matrix))  # Undo previous transposition.

    return matrix


if __name__ == '__main__':

    # Some non-square test matrices.
    matrix1 = [[1, 2, 3],
               [4, 5, 6],
               [7, 8, 9],
               [10, 11, 12]]

    matrix2 = [[1, 2, 3, 4],
               [5, 6, 7, 8],
               [9, 10, 11, 12]]

    def shift_and_print(matrix, direction, dist):
        GAP =  2  # Plus one for a ":" character.
        indent = max(map(len, DIRS)) + GAP
        print(direction
                + ': ' + (indent-2-len(direction))*' '
                + ('\n'+indent*' ').join(map(str, shift(matrix, direction, dist)))
                + '\n')

    for matrix in matrix1, matrix2:
        for direction in DIRS:
            shift_and_print(matrix, direction, 1)  # Printed results are cumulative.

Output (note that the results are cumulative since the operations are performed in-place and the shifting is applied to the result of the previous call):

no shift: [1, 2, 3]
          [4, 5, 6]
          [7, 8, 9]
          [10, 11, 12]

up:       [4, 5, 6]
          [7, 8, 9]
          [10, 11, 12]
          [1, 2, 3]

down:     [1, 2, 3]
          [4, 5, 6]
          [7, 8, 9]
          [10, 11, 12]

left:     [2, 3, 1]
          [5, 6, 4]
          [8, 9, 7]
          [11, 12, 10]

right:    [1, 2, 3]
          [4, 5, 6]
          [7, 8, 9]
          [10, 11, 12]

no shift: [1, 2, 3, 4]
          [5, 6, 7, 8]
          [9, 10, 11, 12]

up:       [5, 6, 7, 8]
          [9, 10, 11, 12]
          [1, 2, 3, 4]

down:     [1, 2, 3, 4]
          [5, 6, 7, 8]
          [9, 10, 11, 12]

left:     [2, 3, 4, 1]
          [6, 7, 8, 5]
          [10, 11, 12, 9]

right:    [1, 2, 3, 4]
          [5, 6, 7, 8]
          [9, 10, 11, 12]