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bibauthorid_least_squares.py
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Thu, Aug 29, 14:15

bibauthorid_least_squares.py
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# -*- coding: utf-8 -*-
##
## This file is part of Invenio.
## Copyright (C) 2011 CERN.
##
## Invenio 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; either version 2 of the
## License, or (at your option) any later version.
##
## Invenio 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 Invenio; if not, write to the Free Software Foundation, Inc.,
## 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
import operator
from itertools import izip, starmap, repeat
#python2.4 compatibility
from invenio.bibauthorid_general_utils import bai_all as all
def approximate(xs, ys, power):
assert len(xs) == len(ys)
matrix_size = power + 1
variables = 2 * power + 1
xs = map(float, xs)
ys = map(float, ys)
xs = reduce(lambda x, y: x + [list(starmap(operator.mul, izip(x[-1], y)))], repeat(xs, variables - 1), [[1] * len(xs)])
assert len(xs) == variables
s = map(sum, xs)
assert s[0] == len(ys)
b = [sum(starmap(operator.mul, izip(ys, x))) for x in xs[:matrix_size]]
a = [s[i:i + matrix_size] for i in xrange(matrix_size)]
# So, we have a*x = b and we are looking for x
matr = [ai + [bi] for ai, bi in izip(a, b)]
def unify_row(i, j):
matr[i] = [cell / matr[i][j] for cell in matr[i]]
assert matr[i][j] == 1
def subtract_row(i, j, row):
assert matr[i][j] == 1
matr[row] = [matr[row][k] - matr[i][k] * matr[row][j] for k in xrange(len(matr[i]))]
assert matr[row][j] == 0
# NOTE: Example for matrix_size = 3
# unify_row(0, 0)
# subtract_row(0, 0, 1)
# subtract_row(0, 0, 2)
# unify_row(1, 1)
# subtract_row(1, 1, 2)
# unify_row(2, 2)
# subtract_row(2, 2, 1)
# subtract_row(2, 2, 0)
# subtract_row(1, 1, 0)
for i in xrange(matrix_size):
unify_row(i, i)
for j in xrange(matrix_size - i - 1):
subtract_row(i, i, i + j + 1)
for i in xrange(matrix_size):
for j in xrange(matrix_size - i - 1):
subtract_row(matrix_size - i - 1, matrix_size - i - 1, j)
assert all(matr[i][:matrix_size] == ([0] * i) + [1] + ([0] * (matrix_size - 1 - i)) for i in xrange(matrix_size))
ret = map(operator.itemgetter(matrix_size), matr)
return ret
def to_function(poly):
power = len(poly) - 1
def func(x):
arr = [1.]
for _ in xrange(power):
arr.append(arr[-1] * x)
assert len(arr) == len(poly)
return sum(p * x for p, x in izip(poly, arr))
return func

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