#!/usr/bin/python
"""
Author: Jeremy M. Stober
Program: MDS.PY
Description: Multidimensional Scaling
"""
 
import os, sys, getopt, pdb
from numpy import *
from numpy.linalg import *
from numpy.random import *
import pylab
 
def mds(d, dimensions = 2):
    """
    Multidimensional Scaling - Given a matrix of interpoint distances,
    find a set of low dimensional points that have similar interpoint
    distances.
    """
 
    (n,n) = d.shape
    E = (-0.5 * d**2)
 
    # Use mat to get column and row means to act as column and row means.
    Er = mat(mean(E,1))
    Es = mat(mean(E,0))
 
    # From Principles of Multivariate Analysis: A User's Perspective (page 107).
    F = array(E - transpose(Er) - Es + mean(E))
 
    [U, S, V] = svd(F)
 
    Y = U * sqrt(S)
 
    return (Y[:,0:dimensions], S)
 
def norm(vec):
    return sqrt(sum(vec**2))
 
def square_points(size):
    nsensors = size ** 2
    return array([(i / size, i % size) for i in range(nsensors)])
 
def test():
 
    points = square_points(10)
 
    distance = zeros((100,100))
    for (i, pointi) in enumerate(points):
        for (j, pointj) in enumerate(points):
            distance[i,j] = norm(pointi - pointj)
 
    Y, eigs = mds(distance)
 
    pylab.figure(1)
    pylab.plot(Y[:,0],Y[:,1],'.')
 
    pylab.figure(2)
    pylab.plot(points[:,0], points[:,1], '.')
 
    pylab.show()
 
def main():
 
    def usage():
	print sys.argv[0] + "[-h] [-d]"
 
    try:
        (options, args) = getopt.getopt(sys.argv[1:], 'dh', ['help','debug'])
    except getopt.GetoptError:
        # print help information and exit:
        usage()
        sys.exit(2)
 
    for o, a in options:
        if o in ('-h', '--help'):
            usage()
            sys.exit()
	elif o in ('-d', '--debug'):
	    pdb.set_trace()
 
    test()
 
if __name__ == "__main__":
    main()