Gram-Schmidt orthonormalization with itertools.

gistfile1.py

# -*- coding: utf-8 -*-
# Gram-Schmidt orthonormalization with itertools.
# Copyright (C) 2012 Danilo de Jesus da Silva Bellini
#
# This is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, version 3 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Created on Fri Feb 22 04:36:17 2013
# danilo [dot] bellini [at] gmail [dot] com
"""
Gram-Schmidt orthonormalization with itertools.
"""

import itertools as it

def gram_schmidt(vects):
  """
  Apply the Gram-Schmidt orthonormalization procedure to the given list of
  lists (or a NumPy 2D array).

  """
  result = []
  for vect in vects:
    coeffs = [sum(d * r for d, r in it.izip(vect, res)) for res in result]
    data = [d - sum(r * c for r, c in it.izip(rs, coeffs))
                   for rs, d in it.izip_longest(it.izip(*result),
                                                vect,
                                                fillvalue=[])]
    sqrt_norm = sum(abs(d) ** 2 for d in data) ** .5
    result.append([d/sqrt_norm for d in data])
  return result

if __name__ == "__main__":
  # The example given in the material
  data = gram_schmidt([[.866, .5, 0.],
                       [0., .5, .866],
                       [.7071, 0., .7071]])
  # Below is just a nice way of printing the matrix
  for row in data:
    for el in row:
      print "{0:>10f}".format(el),
    print