# scipy/scipy

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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()