dims_bb = [
nn,
] * 11
aa = [nr.rand(_) for _ in dims_aa]
aa = [_ / sum(_) for _ in aa]
bb = [nr.rand(_) for _ in dims_bb]
bb = [_ / sum(_) for _ in bb]
cc = []
for _a in aa:
for _b in bb:
cc += [_a + _b]
emd_aa = greedy_primal_dual(aa)
emd_bb = greedy_primal_dual(bb)
emd_cc = greedy_primal_dual(cc)
print()
print(
'Does obj(A) + obj(B) == obj(A+B)?',
abs(emd_aa['primal objective'] + emd_bb['primal objective'] -
emd_cc['dual objective']) < 1e-10)
print()
print('A')
print(' |A|:', len(aa))
print(' primal obj: ', emd_aa['primal objective'])
print(' dual obj: ', emd_aa['dual objective'])
print('B')
print(' |B|:', len(bb))
print(' primal obj: ', emd_bb['primal objective'])
hh = cvxopt.matrix([cvxopt.matrix(np.zeros(cc.size)), cvxopt.matrix(beq)])
bb = cvxopt.matrix(sum(sum_aa) / len(aa) * 1.)
AA_eq = cvxopt.matrix(1., (1, cc.size))
GG = cvxopt.sparse(GG)
ret_cvx = cvx_solvers.lp(cvxopt.matrix(cc), GG, hh, A=AA_eq, b=bb)
return ret_cvx
if __name__ == '__main__':
dims = [
4,
] * 6
aa = [np.random.random(d) for d in dims]
aa = [_ / sum(_) for _ in aa]
# solve the primal and dual problems explicity
emd_aa = greedy_primal_dual(aa)
cvx_aa = cvxprimal(aa)
dul_aa = cvxdual(aa)
print('=' * 50)
print('Objectives')
print(' greedy primal obj : %6.4f' % emd_aa['primal objective'])
print(' greedy dual obj : %6.4f' % emd_aa['dual objective'])
print(' cvxopt primal obj : %6.4f' % cvx_aa['primal objective'])
print(' cvxopt dual obj : %6.4f' % cvx_aa['dual objective'])
print(' cvxopt dual primal obj : %6.4f' % -dul_aa['primal objective'])
print(' cvxopt dual dual obj : %6.4f' % -dul_aa['dual objective'])