Shear a numpy array

I'd like to 'shear' a numpy array. I'm not sure I'm using the term 'shear' correctly; by shear, I mean something like: Shift the first column by 0 places Shift the second column by 1 place Shift the third colum by 2 places etc... So this array: ``` array([[11, 12, 13], [17, 18, 19], [35, 36, 37]]) ``` would turn into either this array: ``` array([[11, 36, 19], [17, 12, 37], [35, 18, 13]]) ``` or something like this array: ``` array([[11, 0, 0], [17, 12, 0], [35, 18, 13]]) ``` depending on how we handle the edges. I'm not too particular about edge behavior. Here's my attempt at a function that does this: ``` import numpy def shear(a, strength=1, shift_axis=0, increase_axis=1, edges='clip'): strength = int(strength) shift_axis = int(shift_axis) increase_axis = int(increase_axis) if shift_axis == increase_axis: raise UserWarning("Shear can't shift in the direction it increases") temp = numpy.zeros(a.shape, dtype=int) indices = [] for d, num in enumerate(a.shape): coords = numpy.arange(num) shape = [1] * len(a.shape) shape[d] = num coords = coords.reshape(shape) + temp indices.append(coords) indices[shift_axis] -= strength * indices[increase_axis] if edges == 'clip': indices[shift_axis][indices[shift_axis] < 0] = -1 indices[shift_axis][indices[shift_axis] >= a.shape[shift_axis]] = -1 res = a[indices] res[indices[shift_axis] == -1] = 0 elif edges == 'roll': indices[shift_axis] %= a.shape[shift_axis] res = a[indices] return res if __name__ == '__main__': a = numpy.random.random((3,4)) print a print shear(a) ``` It seems to work. Please tell me if it doesn't! It also seems clunky and inelegant. Am I overlooking a builtin numpy/scipy function that does this? Is there a cleaner/better/more efficient way to do this in numpy? Am I reinventing the wheel? EDIT: Bonus points if this works on an N-dimensional array, instead of just the 2D case. This function will be at the very center of a loop I'll repeat many times in our data processing, so I suspect it's actually worth optimizing. SECOND EDIT: I finally did some benchmarking. It looks like numpy.roll is the way to go, despite the loop. Thanks, tom10 and Sven Marnach! Benchmarking code: (run on Windows, don't use time.clock on Linux I think) ``` import time, numpy def shear_1(a, strength=1, shift_axis=0, increase_axis=1, edges='roll'): strength = int(strength) shift_axis = int(shift_axis) increase_axis = int(increase_axis) if shift_axis == increase_axis: raise UserWarning("Shear can't shift in the direction it increases") temp = numpy.zeros(a.shape, dtype=int) indices = [] for d, num in enumerate(a.shape): coords = numpy.arange(num) shape = [1] * len(a.shape) shape[d] = num coords = coords.reshape(shape) + temp indices.append(coords) indices[shift_axis] -= strength * indices[increase_axis] if edges == 'clip': indices[shift_axis][indices[shift_axis] < 0] = -1 indices[shift_axis][indices[shift_axis] >= a.shape[shift_axis]] = -1 res = a[indices] res[indices[shift_axis] == -1] = 0 elif edges == 'roll': indices[shift_axis] %= a.shape[shift_axis] res = a[indices] return res def shear_2(a, strength=1, shift_axis=0, increase_axis=1, edges='roll'): indices = numpy.indices(a.shape) indices[shift_axis] -= strength * indices[increase_axis] indices[shift_axis] %= a.shape[shift_axis] res = a[tuple(indices)] if edges == 'clip': res[indices[shift_axis] < 0] = 0 res[indices[shift_axis] >= a.shape[shift_axis]] = 0 return res def shear_3(a, strength=1, shift_axis=0, increase_axis=1): if shift_axis > increase_axis: shift_axis -= 1 res = numpy.empty_like(a) index = numpy.index_exp[:] * increase_axis roll = numpy.roll for i in range(0, a.shape[increase_axis]): index_i = index + (i,) res[index_i] = roll(a[index_i], i * strength, shift_axis) return res numpy.random.seed(0) for a in ( numpy.random.random((3, 3, 3, 3)), numpy.random.random((50, 50, 50, 50)), numpy.random.random((300, 300, 10, 10)), ): print 'Array dimensions:', a.shape for sa, ia in ((0, 1), (1, 0), (2, 3), (0, 3)): print 'Shift axis:', sa print 'Increase axis:', ia ref = shear_1(a, shift_axis=sa, increase_axis=ia) for shear, label in ((shear_1, '1'), (shear_2, '2'), (shear_3, '3')): start = time.clock() b = shear(a, shift_axis=sa, increase_axis=ia) end = time.clock() print label + ': %0.6f seconds'%(end-start) if (b - ref).max() > 1e-9: print "Something's wrong." print ```