sampling.py

import cplex
import numpy as np

if __name__ == "__main__":
#The histogram data, 250 histograms with 3 bins                                                                                     
    prob = cplex.Cplex()

    hists = 250
    bins = 3
    pairs = bins*(bins-1)/2
    D = np.random.randint(0,100,(bins,hists))

    varnames = ["w"+str(j) for j in range(hists)]
#The weights, one for each histogram                                                                                                
    prob.variables.add(obj=[0.0]*hists, lb=[0.0]*hists, ub=[1.0]*hists, names = varnames)
#The variable that we want to minimize                                                                                              
    prob.variables.add(obj=[1.0], lb=[0.0], ub=[cplex.infinity], names = ['z'])

#Build the constraints                                                                                                              
    rows = []
    fliprows = []
    for i in range(bins):
        for j in range(i):
            row	= np.subtract(D[i], D[j]).tolist()
            rowflip = np.subtract(D[j],	D[i]).tolist()
            prob.linear_constraints.add(lin_expr = [[varnames + ['z'], row+[-1.0]]], senses=['L'], rhs=[0.0] )
            prob.linear_constraints.add(lin_expr = [[varnames + ['z'], rowflip+[-1.0]]], senses=['L'], rhs=[0.0] )

    prob.linear_constraints.add(lin_expr=[[varnames, [1.0]*hists]], senses=['E'], rhs=[1.0]) #w sums up to 1                        

#Set objective                                                                                                                      
    prob.objective.set_sense(prob.objective.sense.minimize)
    prob.solve()

    print prob.solution.get_values()