167 lines
5.1 KiB
Python
167 lines
5.1 KiB
Python
import math
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import numpy as np
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from numpy.testing import assert_allclose, assert_, assert_array_equal
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import pytest
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from scipy.optimize import fmin_cobyla, minimize, Bounds
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class TestCobyla:
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def setup_method(self):
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self.x0 = [4.95, 0.66]
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self.solution = [math.sqrt(25 - (2.0/3)**2), 2.0/3]
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self.opts = {'disp': False, 'rhobeg': 1, 'tol': 1e-5,
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'maxiter': 100}
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def fun(self, x):
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return x[0]**2 + abs(x[1])**3
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def con1(self, x):
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return x[0]**2 + x[1]**2 - 25
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def con2(self, x):
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return -self.con1(x)
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@pytest.mark.xslow(True, reason='not slow, but noisy so only run rarely')
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def test_simple(self, capfd):
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# use disp=True as smoke test for gh-8118
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x = fmin_cobyla(self.fun, self.x0, [self.con1, self.con2], rhobeg=1,
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rhoend=1e-5, maxfun=100, disp=True)
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assert_allclose(x, self.solution, atol=1e-4)
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def test_minimize_simple(self):
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class Callback:
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def __init__(self):
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self.n_calls = 0
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self.last_x = None
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def __call__(self, x):
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self.n_calls += 1
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self.last_x = x
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callback = Callback()
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# Minimize with method='COBYLA'
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cons = ({'type': 'ineq', 'fun': self.con1},
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{'type': 'ineq', 'fun': self.con2})
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sol = minimize(self.fun, self.x0, method='cobyla', constraints=cons,
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callback=callback, options=self.opts)
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assert_allclose(sol.x, self.solution, atol=1e-4)
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assert_(sol.success, sol.message)
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assert_(sol.maxcv < 1e-5, sol)
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assert_(sol.nfev < 70, sol)
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assert_(sol.fun < self.fun(self.solution) + 1e-3, sol)
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assert_(sol.nfev == callback.n_calls,
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"Callback is not called exactly once for every function eval.")
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assert_array_equal(
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sol.x,
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callback.last_x,
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"Last design vector sent to the callback is not equal to returned value.",
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)
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def test_minimize_constraint_violation(self):
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np.random.seed(1234)
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pb = np.random.rand(10, 10)
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spread = np.random.rand(10)
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def p(w):
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return pb.dot(w)
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def f(w):
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return -(w * spread).sum()
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def c1(w):
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return 500 - abs(p(w)).sum()
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def c2(w):
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return 5 - abs(p(w).sum())
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def c3(w):
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return 5 - abs(p(w)).max()
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cons = ({'type': 'ineq', 'fun': c1},
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{'type': 'ineq', 'fun': c2},
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{'type': 'ineq', 'fun': c3})
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w0 = np.zeros((10,))
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sol = minimize(f, w0, method='cobyla', constraints=cons,
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options={'catol': 1e-6})
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assert_(sol.maxcv > 1e-6)
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assert_(not sol.success)
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def test_vector_constraints():
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# test that fmin_cobyla and minimize can take a combination
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# of constraints, some returning a number and others an array
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def fun(x):
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return (x[0] - 1)**2 + (x[1] - 2.5)**2
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def fmin(x):
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return fun(x) - 1
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def cons1(x):
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a = np.array([[1, -2, 2], [-1, -2, 6], [-1, 2, 2]])
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return np.array([a[i, 0] * x[0] + a[i, 1] * x[1] +
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a[i, 2] for i in range(len(a))])
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def cons2(x):
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return x # identity, acts as bounds x > 0
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x0 = np.array([2, 0])
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cons_list = [fun, cons1, cons2]
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xsol = [1.4, 1.7]
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fsol = 0.8
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# testing fmin_cobyla
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sol = fmin_cobyla(fun, x0, cons_list, rhoend=1e-5)
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assert_allclose(sol, xsol, atol=1e-4)
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sol = fmin_cobyla(fun, x0, fmin, rhoend=1e-5)
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assert_allclose(fun(sol), 1, atol=1e-4)
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# testing minimize
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constraints = [{'type': 'ineq', 'fun': cons} for cons in cons_list]
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sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
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assert_allclose(sol.x, xsol, atol=1e-4)
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assert_(sol.success, sol.message)
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assert_allclose(sol.fun, fsol, atol=1e-4)
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constraints = {'type': 'ineq', 'fun': fmin}
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sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
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assert_allclose(sol.fun, 1, atol=1e-4)
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class TestBounds:
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# Test cobyla support for bounds (only when used via `minimize`)
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# Invalid bounds is tested in
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# test_optimize.TestOptimizeSimple.test_minimize_invalid_bounds
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def test_basic(self):
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def f(x):
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return np.sum(x**2)
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lb = [-1, None, 1, None, -0.5]
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ub = [-0.5, -0.5, None, None, -0.5]
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bounds = [(a, b) for a, b in zip(lb, ub)]
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# these are converted to Bounds internally
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res = minimize(f, x0=[1, 2, 3, 4, 5], method='cobyla', bounds=bounds)
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ref = [-0.5, -0.5, 1, 0, -0.5]
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assert res.success
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assert_allclose(res.x, ref, atol=1e-3)
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def test_unbounded(self):
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def f(x):
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return np.sum(x**2)
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bounds = Bounds([-np.inf, -np.inf], [np.inf, np.inf])
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res = minimize(f, x0=[1, 2], method='cobyla', bounds=bounds)
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assert res.success
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assert_allclose(res.x, 0, atol=1e-3)
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bounds = Bounds([1, -np.inf], [np.inf, np.inf])
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res = minimize(f, x0=[1, 2], method='cobyla', bounds=bounds)
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assert res.success
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assert_allclose(res.x, [1, 0], atol=1e-3)
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