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##############################################################################
#
# Copyright (c) 2003 Nexedi SARL and Contributors. All Rights Reserved.
# Yoshinori Okuji <yo@nexedi.com>
#
# WARNING: This program as such is intended to be used by professional
# programmers who take the whole responsability of assessing all potential
# consequences resulting from its eventual inadequacies and bugs
# End users who are looking for a ready-to-use solution with commercial
# garantees and support are strongly adviced to contract a Free Software
# Service Company
#
# This program 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.
#
# 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, write to the Free Software
# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
#
##############################################################################
from Numeric import *
MODEL_HEAD = """
/* The number of samples. */
param n, integer, > 0;
/* The number of resources. */
param d, integer, > 0;
/* The set of samples. */
set S := 1..n;
/* The set of resources. */
set R := 1..d;
/* The query. */
param q{i in R};
/* The samples. */
param s{j in S, i in R};
/* The normal vector of a hyperplane. */
var z{i in R};
/* The origin of a hyperplane. */
var z0;
#display q;
#display s;
/* The objective. */
maximize obj: sum {i in R} (z[i] * q[i]) - z0;
/* Constraints. */
subject to c{j in S}: sum{i in R} (z[i] * s[j,i]) - z0, <= 0;
subject to c0: sum {i in R} (z[i] * q[i]) - z0, <= 1;
data;
"""
MODEL_TAIL="""
end;
"""
def writeModelFile(file, matrix, point):
"""
Write an LP problem in MathProg.
"""
n = shape(matrix)[0]
d = shape(matrix)[1]
file.write(MODEL_HEAD)
file.write("param n := %d;\n" % n)
file.write("param d := %d;\n" % d)
file.write("param s\n:\t")
def insertTab(x,y): return str(x)+"\t"+str(y)
file.write(reduce(insertTab, range(1,d+1)))
file.write("\t:=\n")
for i in range(n):
file.write(repr(i+1))
file.write(reduce(insertTab, matrix[i], ""))
file.write("\n")
file.write(";\n")
file.write("param q := ")
def insertComma(x,y): return str(x)+','+str(y)
def flatten(x): return str(x[0])+' '+str(x[1])
file.write(reduce(insertComma,
map(flatten, map(None, range(1,d+1), point))))
file.write(";\n")
file.write(MODEL_TAIL)
def getOptimalValue(file):
"""
Solve an LP problem described in MathProg language, and return
the result of its objective function.
This version uses GNU Linear Programming Kit.
"""
import glpk
lp = glpk.glp_lpx_read_model(file, None, None)
try:
glpk.glp_lpx_set_int_parm(lp, glpk.LPX_K_PRICE, 1)
glpk.glp_lpx_set_int_parm(lp, glpk.LPX_K_PRESOL, 1)
glpk.glp_lpx_set_int_parm(lp, glpk.LPX_K_BRANCH, 2)
glpk.glp_lpx_set_int_parm(lp, glpk.LPX_K_BTRACK, 2)
glpk.glp_lpx_set_real_parm(lp, glpk.LPX_K_TMLIM, 2000) # XXX
ret = glpk.glp_lpx_simplex(lp)
if ret != glpk.LPX_E_OK:
raise RuntimeError, "The simplex method of GLPK failed"
return glpk.glp_lpx_get_obj_val(lp)
finally:
glpk.glp_lpx_delete_prob(lp)
def solve(matrix, point):
"""
Check if a point is inside a convex hull specified by a matrix.
"""
import tempfile
import os
if shape(point)[0] != shape(matrix)[1]:
raise TypeError, "The argument 'point' has a different number of dimensions from the capacity"
mod_name = tempfile.mktemp(suffix='.mod')
mod = file(mod_name, 'w')
try:
writeModelFile(mod, matrix, point)
mod.close()
obj = getOptimalValue(mod_name)
finally:
os.remove(mod_name)
return obj <= 0
# This is a test.
if __name__ == '__main__':
m = array([[ 0, 1, 2, 3, 4, 5],
[10,11,12,13,14,15],
[20,21,22,23,24,25],
[30,31,32,33,34,35],
[40,41,42,43,44,45],
[50,51,52,53,54,55],
[60,61,62,63,64,65],
[70,71,72,73,74,75]])
print m
p = ([1,2,3,4,5,6])
print p
print solve(m, p)