def test_sum_squared(self):
x0 = np.array([0.5, -np.pi, np.pi])
sol = np.zeros(3)
fun = 0.
results = nelder_mead(sum_squared, x0, tol_f=1e-50, tol_x=1e-50)
assert_allclose(results.x, sol, atol=1e-5)
assert_allclose(results.fun, fun, atol=1e-5)
def test_sum_squared(self):
x0 = np.array([0.5, -np.pi, np.pi])
sol = np.zeros(3)
fun = 0.
results = nelder_mead(sum_squared, x0, tol_f=1e-50, tol_x=1e-50)
assert_allclose(results.x, sol, atol=1e-5)
assert_allclose(results.fun, fun, atol=1e-5)
def test_powell(self):
sol = np.zeros(4)
fun = 0.
x0 = np.array([3., -1., 0., 1.])
results = nelder_mead(powell, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_discontinuous(self):
sol = np.array([1.])
fun = -0.5
x0 = np.array([-10.])
results = nelder_mead(g, x0)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun)
def test_easom(self):
sol = np.array([np.pi, np.pi])
fun = 1.
x0 = np.array([5, -1])
results = nelder_mead(easom, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_rosenbrock(self):
sol = np.array([1., 1.])
fun = 0.
x0 = np.array([-2, 1])
results = nelder_mead(rosenbrock, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_goldstein_price(self):
x0 = np.array([-1.5, 0.5])
results = nelder_mead(goldstein_price, x0)
sol = np.array([0., -1.])
fun = -3.
assert_allclose(results.x, sol, atol=1e-5)
assert_allclose(results.fun, fun)
def test_easom(self):
sol = np.array([np.pi, np.pi])
fun = 1.
x0 = np.array([5, -1])
results = nelder_mead(easom, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_powell(self):
sol = np.zeros(4)
fun = 0.
x0 = np.array([3., -1., 0., 1.])
results = nelder_mead(powell, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_booth(self):
x0 = np.array([0., 0.])
sol = np.array([1., 3.])
fun = 0.
results = nelder_mead(booth, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_booth(self):
x0 = np.array([0., 0.])
sol = np.array([1., 3.])
fun = 0.
results = nelder_mead(booth, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_goldstein_price(self):
x0 = np.array([-1.5, 0.5])
results = nelder_mead(goldstein_price, x0)
sol = np.array([0., -1.])
fun = -3.
assert_allclose(results.x, sol, atol=1e-5)
assert_allclose(results.fun, fun)
def test_rosenbrock(self):
sol = np.array([1., 1.])
fun = 0.
x0 = np.array([-2, 1])
results = nelder_mead(rosenbrock, x0, tol_x=1e-20, tol_f=1e-20)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_discontinuous(self):
sol = np.array([1.])
fun = -0.5
x0 = np.array([-10.])
results = nelder_mead(g, x0)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun)
def test_corner_sol(self):
sol = np.array([0.])
fun = 0.
x0 = np.array([10.])
bounds = np.array([[0., np.inf]])
results = nelder_mead(f, x0, bounds=bounds, tol_f=1e-20)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun)
def test_corner_sol(self):
sol = np.array([0.])
fun = 0.
x0 = np.array([10.])
bounds = np.array([[0., np.inf]])
results = nelder_mead(f, x0, bounds=bounds, tol_f=1e-20)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun)
def test_bohachevsky(self):
sol = np.array([0., 0.])
fun = 0.
# Starting point makes significant difference
x0 = np.array([np.pi, -np.pi])
results = nelder_mead(bohachevsky, x0)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_bohachevsky(self):
sol = np.array([0., 0.])
fun = 0.
# Starting point makes significant difference
x0 = np.array([np.pi, -np.pi])
results = nelder_mead(bohachevsky, x0)
assert_allclose(results.x, sol, atol=1e-4)
assert_allclose(results.fun, fun, atol=1e-4)
def test_mccormick(self):
sol = np.array([-0.54719, -1.54719])
fun = 1.9133
x0 = np.array([-1., -1.5])
bounds = np.array([[-1.5, 4.], [-3., 4.]])
results = nelder_mead(mccormick, x0, bounds=bounds)
assert_allclose(results.x, sol, rtol=1e-3)
assert_allclose(results.fun, fun, rtol=1e-3)
def test_zakharov(self):
x0 = np.array([-3., 8., 1., 3., -0.5])
bounds = np.array([[-5., 10.]] * 5)
sol = np.zeros(5)
fun = 0.
results = nelder_mead(zakharov, x0, bounds=bounds, tol_f=1e-30,
tol_x=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_colville(self):
x0 = np.array([-3.5, 9., 0.25, -1.])
bounds = np.array([[-10., 10.]] * 4)
sol = np.ones(4)
fun = 0.
results = nelder_mead(colville, x0, bounds=bounds, tol_f=1e-35,
tol_x=1e-35)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun, atol=1e-7)
def test_mccormick(self):
sol = np.array([-0.54719, -1.54719])
fun = 1.9133
x0 = np.array([-1., -1.5])
bounds = np.array([[-1.5, 4.],
[-3., 4.]])
results = nelder_mead(mccormick, x0, bounds=bounds)
assert_allclose(results.x, sol, rtol=1e-3)
assert_allclose(results.fun, fun, rtol=1e-3)
def test_perm_function(self):
d = 4.
x0 = np.ones(int(d))
bounds = np.array([[-d, d]] * int(d))
sol = np.array([1 / d for d in range(1, int(d)+1)])
fun = 0.
results = nelder_mead(perm_function, x0, bounds=bounds, args=(1., ),
tol_x=1e-30, tol_f=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_rotated_hyper_ellipsoid(self):
d = 5
x0 = np.random.normal(size=d)
bounds = np.array([[-65.536, 65.536]] * d)
sol = np.zeros(d)
fun = 0.
results = nelder_mead(rotated_hyper_ellipsoid, x0, bounds=bounds,
tol_x=1e-30, tol_f=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_styblinski_tang(self):
d = 8
x0 = -np.ones(d)
bounds = np.array([[-5., 5.]] * d)
sol = np.array([-2.903534] * d)
fun = 39.16599 * d
results = nelder_mead(styblinski_tang, x0, bounds=bounds, tol_f=1e-35,
tol_x=1e-35)
assert_allclose(results.x, sol, rtol=1e-4)
assert_allclose(results.fun, fun, rtol=1e-5)
def test_colville(self):
x0 = np.array([-3.5, 9., 0.25, -1.])
bounds = np.array([[-10., 10.]] * 4)
sol = np.ones(4)
fun = 0.
results = nelder_mead(colville,
x0,
bounds=bounds,
tol_f=1e-35,
tol_x=1e-35)
assert_allclose(results.x, sol)
assert_allclose(results.fun, fun, atol=1e-7)
def test_zakharov(self):
x0 = np.array([-3., 8., 1., 3., -0.5])
bounds = np.array([[-5., 10.]] * 5)
sol = np.zeros(5)
fun = 0.
results = nelder_mead(zakharov,
x0,
bounds=bounds,
tol_f=1e-30,
tol_x=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_styblinski_tang(self):
d = 8
x0 = -np.ones(d)
bounds = np.array([[-5., 5.]] * d)
sol = np.array([-2.903534] * d)
fun = 39.16599 * d
results = nelder_mead(styblinski_tang,
x0,
bounds=bounds,
tol_f=1e-35,
tol_x=1e-35)
assert_allclose(results.x, sol, rtol=1e-4)
assert_allclose(results.fun, fun, rtol=1e-5)
def test_rotated_hyper_ellipsoid(self):
d = 5
x0 = np.random.normal(size=d)
bounds = np.array([[-65.536, 65.536]] * d)
sol = np.zeros(d)
fun = 0.
results = nelder_mead(rotated_hyper_ellipsoid,
x0,
bounds=bounds,
tol_x=1e-30,
tol_f=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_perm_function(self):
d = 4.
x0 = np.ones(int(d))
bounds = np.array([[-d, d]] * int(d))
sol = np.array([1 / d for d in range(1, int(d) + 1)])
fun = 0.
results = nelder_mead(perm_function,
x0,
bounds=bounds,
args=(1., ),
tol_x=1e-30,
tol_f=1e-30)
assert_allclose(results.x, sol, atol=1e-7)
assert_allclose(results.fun, fun, atol=1e-7)
def test_invalid_bounds_2():
vertices = np.array([[-2., 1.], [1.05 * -2., 1.], [-2., 1.05 * 1.]])
x0 = np.array([-2., 1.])
bounds = np.array([[10., -10., 10., -10.]])
nelder_mead(rosenbrock, x0, bounds=bounds)
def test_invalid_bounds_2():
x0 = np.array([-2., 1.])
bounds = np.array([[10., -10., 10., -10.]])
nelder_mead(rosenbrock, x0, bounds=bounds)
def test_invalid_bounds_2():
x0 = np.array([-2., 1.])
bounds = np.array([[10., -10., 10., -10.]])
nelder_mead(rosenbrock, x0, bounds=bounds)
