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from __future__ import division, print_function, absolute_import
import math
import numpy as np
from numpy.testing import assert_allclose, TestCase, run_module_suite, \
assert_
from scipy.optimize import fmin_cobyla, minimize
class TestCobyla(TestCase):
def setUp(self):
self.x0 = [4.95, 0.66]
self.solution = [math.sqrt(25 - (2.0/3)**2), 2.0/3]
self.opts = {'disp': False, 'rhobeg': 1, 'tol': 1e-5,
'maxiter': 100}
def fun(self, x):
return x[0]**2 + abs(x[1])**3
def con1(self, x):
return x[0]**2 + x[1]**2 - 25
def con2(self, x):
return -self.con1(x)
def test_simple(self):
x = fmin_cobyla(self.fun, self.x0, [self.con1, self.con2], rhobeg=1,
rhoend=1e-5, iprint=0, maxfun=100)
assert_allclose(x, self.solution, atol=1e-4)
def test_minimize_simple(self):
# Minimize with method='COBYLA'
cons = ({'type': 'ineq', 'fun': self.con1},
{'type': 'ineq', 'fun': self.con2})
sol = minimize(self.fun, self.x0, method='cobyla', constraints=cons,
options=self.opts)
assert_allclose(sol.x, self.solution, atol=1e-4)
assert_(sol.success, sol.message)
assert_(sol.maxcv < 1e-5, sol)
assert_(sol.nfev < 70, sol)
assert_(sol.fun < self.fun(self.solution) + 1e-3, sol)
def test_minimize_constraint_violation(self):
np.random.seed(1234)
pb = np.random.rand(10, 10)
spread = np.random.rand(10)
def p(w):
return pb.dot(w)
def f(w):
return -(w * spread).sum()
def c1(w):
return 500 - abs(p(w)).sum()
def c2(w):
return 5 - abs(p(w).sum())
def c3(w):
return 5 - abs(p(w)).max()
cons = ({'type': 'ineq', 'fun': c1},
{'type': 'ineq', 'fun': c2},
{'type': 'ineq', 'fun': c3})
w0 = np.zeros((10, 1))
sol = minimize(f, w0, method='cobyla', constraints=cons,
options={'catol': 1e-6})
assert_(sol.maxcv > 1e-6)
assert_(not sol.success)
def test_vector_constraints():
# test that fmin_cobyla and minimize can take a combination
# of constraints, some returning a number and others an array
def fun(x):
return (x[0] - 1)**2 + (x[1] - 2.5)**2
def fmin(x):
return fun(x) - 1
def cons1(x):
a = np.array([[1, -2, 2], [-1, -2, 6], [-1, 2, 2]])
return np.array([a[i, 0] * x[0] + a[i, 1] * x[1] +
a[i, 2] for i in range(len(a))])
def cons2(x):
return x # identity, acts as bounds x > 0
x0 = np.array([2, 0])
cons_list = [fun, cons1, cons2]
xsol = [1.4, 1.7]
fsol = 0.8
# testing fmin_cobyla
sol = fmin_cobyla(fun, x0, cons_list, rhoend=1e-5, iprint=0)
assert_allclose(sol, xsol, atol=1e-4)
sol = fmin_cobyla(fun, x0, fmin, rhoend=1e-5, iprint=0)
assert_allclose(fun(sol), 1, atol=1e-4)
# testing minimize
constraints = [{'type': 'ineq', 'fun': cons} for cons in cons_list]
sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
assert_allclose(sol.x, xsol, atol=1e-4)
assert_(sol.success, sol.message)
assert_allclose(sol.fun, fsol, atol=1e-4)
constraints = {'type': 'ineq', 'fun': fmin}
sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
assert_allclose(sol.fun, 1, atol=1e-4)
if __name__ == "__main__":
run_module_suite()