# [SciPy-User] How to do symmetry detection?

iCy-fLaME icy.flame.gm@gmail....
Wed Jan 20 09:20:10 CST 2010

```Hello,

I have some signals in mirror pairs in an 1D/2D array, and I am trying
to identify the symmetry axis.

A simplified example of the signal pair can look like this:
[0, 0, 0, 0, 2, 3, 4, 0, 0, 0, 4, 3, 2, 0]

The ideal output in this case will probably be:
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]

As long as the symmetry point has the largest value, it will be fine.

There can be multiple pairs of signals in the array, and the length of
separation and duration of the signal can vary from pair to pair. The
overall length of the array is about 1k points. The output array
should reflect the level of likeness between the two sides of the
array.

I tried doing a loop as follows:

############ Begin ############
from numpy import array
from numpy import zeros
from numpy import arange

data =  array([0,0,0,0,2,3,4,0,0,0,4,3,2,0])
length = len(data)
result = zeros(length)

left = arange(length)
left[0] = 0                 # Index to be used for the end of the left portion

right = arange(length) + 1
right[-1] = length - 1      # Index to be used for the begining of the
right hand portion

for i in range(length):
l_part = zeros(length)  # Default values to be zero, so
non-overlapping region will
r_part = zeros(length)  #   return zero after the multiplication.

l_part[:left[i]] = data[:left[i]][::-1]     # Take the left hand
side and mirror it
r_part[:length-right[i]] = data[right[i]:]  # Take the right hand side
result[i] = sum(l_part*r_part)/length   # Use the product and
integral to find the similarity metric.

print l_part
print r_part
print "===============================", result[i]

print result

############ END ############

But it is rather slow for a 1000x1000 2D array, anyone got any
suggestion for a more elegant solution?