#!/bin/env python
from __future__ import print_function
import xpress as xp
#
# Construct a problem using addVariable and addConstraint, then use
# the Xpress API routines to amend the problem with rows and quadratic
# terms.
#
p = xp.problem ()
N = 5
S = range (N)
x = [xp.var (vartype = xp.binary) for i in S]
p.addVariable (x)
# vectors can be used whole or addressed with their index
c0 = xp.Sum (x) <= 10
cc = [x[i]/1.1 <= x[i+1]*2 for i in range (N-1)]
p.addConstraint (c0, cc)
p.setObjective (3 - x[0])
mysol = [0, 0, 1, 1, 1, 1.4]
# add a variable with its coefficients
p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 1.4], [0], [2], ['YY'], ['B'])
p.write ("problem1", "lp")
# load a MIP solution
p.loadmipsol ([0,0,1,1,1,1.4])
# Add quadratic term x[0]^2 - 2 x[0] x[1] + x[1]^2 to the second
# constraint. Note that the -2 coefficient for an off-diagonal element
# must be passed divided by two.
#
# The same effect would be obtained with p.addqmatrix (cc[0],
# [x[0],x[3],x[3]], [x[0],x[0],x[3]], [1,-1,1])
#
# As constraint vector 'cc' was added after c0
p.addqmatrix (1, [x[0],x[3],x[3]], [x[0],x[0],x[3]], [1,-1,1])
# add seventh and eighth constraints:
#
# x[0] + 2 x[1] + 3 x[2] >= 4
# 4 x[0] + 5 x[1] + 6 x[2] + 7 x[3] + 8 x[4] - 3 YY <= 4.4
#
# Note the new column named 'YY' added with its index 5 (variables'
# indices begin at 0). The same would happen if 5 were substituted by
# YY.
p.addrows (qrtype = ['G', 'L'],
rhs = [4, 4.4],
mstart = [0, 3, 9],
mclind = [x[0],x[1],x[2], x[0],x[1],x[2],x[3],x[4], 5],
dmatval = [1,2,3,4,5,6,7,8,-3],
names = ['newcon1', 'newcon2'])
p.solve ()
p.write ("amended", "lp")
slacks = []
p.calcslacks (solution = mysol, calculatedslacks = slacks)
print ("slacks:", slacks)
# The five commands below are equivalent to the following:
#
# p.addcols ([4,4,4,4,4],
# [0,3,6,9,12,15],
# [c0,4,2,c0,4,2,c0,4,2,c0,4,2,c0,4,2],
# [3, -2, 1, -3, 2.4, 1.4, 3, 2, 1, -3, 2.4, 4, 3, 2, 1],
# [0,0,0,0,0],
# [2,10,1,2,2],
# ['p1','p2','p3','p4','p5'],
# ['I','C','S','P','R'])
p.addcols ([4], [0,3], [c0,4,2], [-3, -2, 1], [0], [2], ['p1'], ['I'])
p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 1.4], [0], [10], ['p2'], ['C'])
p.addcols ([4], [0,3], [c0,4,2], [-3, 2, 1], [0], [1], ['p3'], ['S'])
p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 4], [0], [2], ['p4'], ['P'])
p.addcols ([4], [0,3], [c0,4,2], [-3, 2, 1], [0], [2], ['p5'], ['R'])
p.solve ()
try:
print ("new solution:", p.getSolution ())
except:
print ("could not get solution, perhaps problem is infeasible")
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