python - Autocorrelation of a multidimensional array in numpy -

i have 2 dimensional array, i.e. array of sequences arrays. each sequence calculate autocorrelation, (5,4) array, 5 results, or array of dimension (5,7).

i know loop on first dimension, that's slow , last resort. there way?

thanks!

edit:

based on chosen answer plus comment mtrw, have following function:

def xcorr(x):   """fft based autocorrelation function, faster numpy.correlate"""   # x supposed array of sequences, of shape (totalelements, length)   fftx = fft(x, n=(length*2-1), axis=1)   ret = ifft(fftx * np.conjugate(fftx), axis=1)   ret = fftshift(ret, axes=1)   return ret 

note length global variable in code, sure declare it. didn't restrict result real numbers, since need take account complex numbers well.

using fft-based autocorrelation:

import numpy numpy.fft import fft, ifft  data = numpy.arange(5*4).reshape(5, 4) print data ##[[ 0  1  2  3] ## [ 4  5  6  7] ## [ 8  9 10 11] ## [12 13 14 15] ## [16 17 18 19]] dataft = fft(data, axis=1) dataac = ifft(dataft * numpy.conjugate(dataft), axis=1).real print dataac ##[[   14.     8.     6.     8.] ## [  126.   120.   118.   120.] ## [  366.   360.   358.   360.] ## [  734.   728.   726.   728.] ## [ 1230.  1224.  1222.  1224.]] 

i'm little confused statement answer having dimension (5, 7), maybe there's important i'm not understanding.

edit: @ suggestion of mtrw, padded version doesn't wrap around:

import numpy numpy.fft import fft, ifft  data = numpy.arange(5*4).reshape(5, 4) padding = numpy.zeros((5, 3)) datapadded = numpy.concatenate((data, padding), axis=1) print datapadded ##[[  0.   1.   2.   3.   0.   0.   0.   0.] ## [  4.   5.   6.   7.   0.   0.   0.   0.] ## [  8.   9.  10.  11.   0.   0.   0.   0.] ## [ 12.  13.  14.  15.   0.   0.   0.   0.] ## [ 16.  17.  18.  19.   0.   0.   0.   0.]] dataft = fft(datapadded, axis=1) dataac = ifft(dataft * numpy.conjugate(dataft), axis=1).real print numpy.round(dataac, 10)[:, :4] ##[[   14.     8.     3.     0.     0.     3.     8.] ## [  126.    92.    59.    28.    28.    59.    92.] ## [  366.   272.   179.    88.    88.   179.   272.] ## [  734.   548.   363.   180.   180.   363.   548.] ## [ 1230.   920.   611.   304.   304.   611.   920.]] 

there must more efficient way this, because autocorrelation symmetric , don't take advantage of that.