809 lines
26 KiB
Python
809 lines
26 KiB
Python
|
import numpy as np
|
||
|
|
import pytest
|
||
|
|
from scipy.linalg import block_diag
|
||
|
|
from scipy.sparse import csc_matrix
|
||
|
|
from numpy.testing import (TestCase, assert_array_almost_equal,
|
||
|
|
assert_array_less, assert_, assert_allclose,
|
||
|
|
suppress_warnings)
|
||
|
|
from scipy.optimize import (NonlinearConstraint,
|
||
|
|
LinearConstraint,
|
||
|
|
Bounds,
|
||
|
|
minimize,
|
||
|
|
BFGS,
|
||
|
|
SR1)
|
||
|
|
|
||
|
|
|
||
|
|
class Maratos:
|
||
|
|
"""Problem 15.4 from Nocedal and Wright
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize 2*(x[0]**2 + x[1]**2 - 1) - x[0]
|
||
|
|
Subject to: x[0]**2 + x[1]**2 - 1 = 0
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, degrees=60, constr_jac=None, constr_hess=None):
|
||
|
|
rads = degrees/180*np.pi
|
||
|
|
self.x0 = [np.cos(rads), np.sin(rads)]
|
||
|
|
self.x_opt = np.array([1.0, 0.0])
|
||
|
|
self.constr_jac = constr_jac
|
||
|
|
self.constr_hess = constr_hess
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
def fun(self, x):
|
||
|
|
return 2*(x[0]**2 + x[1]**2 - 1) - x[0]
|
||
|
|
|
||
|
|
def grad(self, x):
|
||
|
|
return np.array([4*x[0]-1, 4*x[1]])
|
||
|
|
|
||
|
|
def hess(self, x):
|
||
|
|
return 4*np.eye(2)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
def fun(x):
|
||
|
|
return x[0]**2 + x[1]**2
|
||
|
|
|
||
|
|
if self.constr_jac is None:
|
||
|
|
def jac(x):
|
||
|
|
return [[2*x[0], 2*x[1]]]
|
||
|
|
else:
|
||
|
|
jac = self.constr_jac
|
||
|
|
|
||
|
|
if self.constr_hess is None:
|
||
|
|
def hess(x, v):
|
||
|
|
return 2*v[0]*np.eye(2)
|
||
|
|
else:
|
||
|
|
hess = self.constr_hess
|
||
|
|
|
||
|
|
return NonlinearConstraint(fun, 1, 1, jac, hess)
|
||
|
|
|
||
|
|
|
||
|
|
class MaratosTestArgs:
|
||
|
|
"""Problem 15.4 from Nocedal and Wright
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize 2*(x[0]**2 + x[1]**2 - 1) - x[0]
|
||
|
|
Subject to: x[0]**2 + x[1]**2 - 1 = 0
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, a, b, degrees=60, constr_jac=None, constr_hess=None):
|
||
|
|
rads = degrees/180*np.pi
|
||
|
|
self.x0 = [np.cos(rads), np.sin(rads)]
|
||
|
|
self.x_opt = np.array([1.0, 0.0])
|
||
|
|
self.constr_jac = constr_jac
|
||
|
|
self.constr_hess = constr_hess
|
||
|
|
self.a = a
|
||
|
|
self.b = b
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
def _test_args(self, a, b):
|
||
|
|
if self.a != a or self.b != b:
|
||
|
|
raise ValueError()
|
||
|
|
|
||
|
|
def fun(self, x, a, b):
|
||
|
|
self._test_args(a, b)
|
||
|
|
return 2*(x[0]**2 + x[1]**2 - 1) - x[0]
|
||
|
|
|
||
|
|
def grad(self, x, a, b):
|
||
|
|
self._test_args(a, b)
|
||
|
|
return np.array([4*x[0]-1, 4*x[1]])
|
||
|
|
|
||
|
|
def hess(self, x, a, b):
|
||
|
|
self._test_args(a, b)
|
||
|
|
return 4*np.eye(2)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
def fun(x):
|
||
|
|
return x[0]**2 + x[1]**2
|
||
|
|
|
||
|
|
if self.constr_jac is None:
|
||
|
|
def jac(x):
|
||
|
|
return [[4*x[0], 4*x[1]]]
|
||
|
|
else:
|
||
|
|
jac = self.constr_jac
|
||
|
|
|
||
|
|
if self.constr_hess is None:
|
||
|
|
def hess(x, v):
|
||
|
|
return 2*v[0]*np.eye(2)
|
||
|
|
else:
|
||
|
|
hess = self.constr_hess
|
||
|
|
|
||
|
|
return NonlinearConstraint(fun, 1, 1, jac, hess)
|
||
|
|
|
||
|
|
|
||
|
|
class MaratosGradInFunc:
|
||
|
|
"""Problem 15.4 from Nocedal and Wright
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize 2*(x[0]**2 + x[1]**2 - 1) - x[0]
|
||
|
|
Subject to: x[0]**2 + x[1]**2 - 1 = 0
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, degrees=60, constr_jac=None, constr_hess=None):
|
||
|
|
rads = degrees/180*np.pi
|
||
|
|
self.x0 = [np.cos(rads), np.sin(rads)]
|
||
|
|
self.x_opt = np.array([1.0, 0.0])
|
||
|
|
self.constr_jac = constr_jac
|
||
|
|
self.constr_hess = constr_hess
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
def fun(self, x):
|
||
|
|
return (2*(x[0]**2 + x[1]**2 - 1) - x[0],
|
||
|
|
np.array([4*x[0]-1, 4*x[1]]))
|
||
|
|
|
||
|
|
@property
|
||
|
|
def grad(self):
|
||
|
|
return True
|
||
|
|
|
||
|
|
def hess(self, x):
|
||
|
|
return 4*np.eye(2)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
def fun(x):
|
||
|
|
return x[0]**2 + x[1]**2
|
||
|
|
|
||
|
|
if self.constr_jac is None:
|
||
|
|
def jac(x):
|
||
|
|
return [[4*x[0], 4*x[1]]]
|
||
|
|
else:
|
||
|
|
jac = self.constr_jac
|
||
|
|
|
||
|
|
if self.constr_hess is None:
|
||
|
|
def hess(x, v):
|
||
|
|
return 2*v[0]*np.eye(2)
|
||
|
|
else:
|
||
|
|
hess = self.constr_hess
|
||
|
|
|
||
|
|
return NonlinearConstraint(fun, 1, 1, jac, hess)
|
||
|
|
|
||
|
|
|
||
|
|
class HyperbolicIneq:
|
||
|
|
"""Problem 15.1 from Nocedal and Wright
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize 1/2*(x[0] - 2)**2 + 1/2*(x[1] - 1/2)**2
|
||
|
|
Subject to: 1/(x[0] + 1) - x[1] >= 1/4
|
||
|
|
x[0] >= 0
|
||
|
|
x[1] >= 0
|
||
|
|
"""
|
||
|
|
def __init__(self, constr_jac=None, constr_hess=None):
|
||
|
|
self.x0 = [0, 0]
|
||
|
|
self.x_opt = [1.952823, 0.088659]
|
||
|
|
self.constr_jac = constr_jac
|
||
|
|
self.constr_hess = constr_hess
|
||
|
|
self.bounds = Bounds(0, np.inf)
|
||
|
|
|
||
|
|
def fun(self, x):
|
||
|
|
return 1/2*(x[0] - 2)**2 + 1/2*(x[1] - 1/2)**2
|
||
|
|
|
||
|
|
def grad(self, x):
|
||
|
|
return [x[0] - 2, x[1] - 1/2]
|
||
|
|
|
||
|
|
def hess(self, x):
|
||
|
|
return np.eye(2)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
def fun(x):
|
||
|
|
return 1/(x[0] + 1) - x[1]
|
||
|
|
|
||
|
|
if self.constr_jac is None:
|
||
|
|
def jac(x):
|
||
|
|
return [[-1/(x[0] + 1)**2, -1]]
|
||
|
|
else:
|
||
|
|
jac = self.constr_jac
|
||
|
|
|
||
|
|
if self.constr_hess is None:
|
||
|
|
def hess(x, v):
|
||
|
|
return 2*v[0]*np.array([[1/(x[0] + 1)**3, 0],
|
||
|
|
[0, 0]])
|
||
|
|
else:
|
||
|
|
hess = self.constr_hess
|
||
|
|
|
||
|
|
return NonlinearConstraint(fun, 0.25, np.inf, jac, hess)
|
||
|
|
|
||
|
|
|
||
|
|
class Rosenbrock:
|
||
|
|
"""Rosenbrock function.
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize sum(100.0*(x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0)
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, n=2, random_state=0):
|
||
|
|
rng = np.random.RandomState(random_state)
|
||
|
|
self.x0 = rng.uniform(-1, 1, n)
|
||
|
|
self.x_opt = np.ones(n)
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
def fun(self, x):
|
||
|
|
x = np.asarray(x)
|
||
|
|
r = np.sum(100.0 * (x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0,
|
||
|
|
axis=0)
|
||
|
|
return r
|
||
|
|
|
||
|
|
def grad(self, x):
|
||
|
|
x = np.asarray(x)
|
||
|
|
xm = x[1:-1]
|
||
|
|
xm_m1 = x[:-2]
|
||
|
|
xm_p1 = x[2:]
|
||
|
|
der = np.zeros_like(x)
|
||
|
|
der[1:-1] = (200 * (xm - xm_m1**2) -
|
||
|
|
400 * (xm_p1 - xm**2) * xm - 2 * (1 - xm))
|
||
|
|
der[0] = -400 * x[0] * (x[1] - x[0]**2) - 2 * (1 - x[0])
|
||
|
|
der[-1] = 200 * (x[-1] - x[-2]**2)
|
||
|
|
return der
|
||
|
|
|
||
|
|
def hess(self, x):
|
||
|
|
x = np.atleast_1d(x)
|
||
|
|
H = np.diag(-400 * x[:-1], 1) - np.diag(400 * x[:-1], -1)
|
||
|
|
diagonal = np.zeros(len(x), dtype=x.dtype)
|
||
|
|
diagonal[0] = 1200 * x[0]**2 - 400 * x[1] + 2
|
||
|
|
diagonal[-1] = 200
|
||
|
|
diagonal[1:-1] = 202 + 1200 * x[1:-1]**2 - 400 * x[2:]
|
||
|
|
H = H + np.diag(diagonal)
|
||
|
|
return H
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
return ()
|
||
|
|
|
||
|
|
|
||
|
|
class IneqRosenbrock(Rosenbrock):
|
||
|
|
"""Rosenbrock subject to inequality constraints.
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
|
||
|
|
subject to: x[0] + 2 x[1] <= 1
|
||
|
|
|
||
|
|
Taken from matlab ``fmincon`` documentation.
|
||
|
|
"""
|
||
|
|
def __init__(self, random_state=0):
|
||
|
|
Rosenbrock.__init__(self, 2, random_state)
|
||
|
|
self.x0 = [-1, -0.5]
|
||
|
|
self.x_opt = [0.5022, 0.2489]
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
A = [[1, 2]]
|
||
|
|
b = 1
|
||
|
|
return LinearConstraint(A, -np.inf, b)
|
||
|
|
|
||
|
|
|
||
|
|
class BoundedRosenbrock(Rosenbrock):
|
||
|
|
"""Rosenbrock subject to inequality constraints.
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
|
||
|
|
subject to: -2 <= x[0] <= 0
|
||
|
|
0 <= x[1] <= 2
|
||
|
|
|
||
|
|
Taken from matlab ``fmincon`` documentation.
|
||
|
|
"""
|
||
|
|
def __init__(self, random_state=0):
|
||
|
|
Rosenbrock.__init__(self, 2, random_state)
|
||
|
|
self.x0 = [-0.2, 0.2]
|
||
|
|
self.x_opt = None
|
||
|
|
self.bounds = Bounds([-2, 0], [0, 2])
|
||
|
|
|
||
|
|
|
||
|
|
class EqIneqRosenbrock(Rosenbrock):
|
||
|
|
"""Rosenbrock subject to equality and inequality constraints.
|
||
|
|
|
||
|
|
The following optimization problem:
|
||
|
|
minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
|
||
|
|
subject to: x[0] + 2 x[1] <= 1
|
||
|
|
2 x[0] + x[1] = 1
|
||
|
|
|
||
|
|
Taken from matlab ``fimincon`` documentation.
|
||
|
|
"""
|
||
|
|
def __init__(self, random_state=0):
|
||
|
|
Rosenbrock.__init__(self, 2, random_state)
|
||
|
|
self.x0 = [-1, -0.5]
|
||
|
|
self.x_opt = [0.41494, 0.17011]
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
A_ineq = [[1, 2]]
|
||
|
|
b_ineq = 1
|
||
|
|
A_eq = [[2, 1]]
|
||
|
|
b_eq = 1
|
||
|
|
return (LinearConstraint(A_ineq, -np.inf, b_ineq),
|
||
|
|
LinearConstraint(A_eq, b_eq, b_eq))
|
||
|
|
|
||
|
|
|
||
|
|
class Elec:
|
||
|
|
"""Distribution of electrons on a sphere.
|
||
|
|
|
||
|
|
Problem no 2 from COPS collection [2]_. Find
|
||
|
|
the equilibrium state distribution (of minimal
|
||
|
|
potential) of the electrons positioned on a
|
||
|
|
conducting sphere.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] E. D. Dolan, J. J. Mor\'{e}, and T. S. Munson,
|
||
|
|
"Benchmarking optimization software with COPS 3.0.",
|
||
|
|
Argonne National Lab., Argonne, IL (US), 2004.
|
||
|
|
"""
|
||
|
|
def __init__(self, n_electrons=200, random_state=0,
|
||
|
|
constr_jac=None, constr_hess=None):
|
||
|
|
self.n_electrons = n_electrons
|
||
|
|
self.rng = np.random.RandomState(random_state)
|
||
|
|
# Initial Guess
|
||
|
|
phi = self.rng.uniform(0, 2 * np.pi, self.n_electrons)
|
||
|
|
theta = self.rng.uniform(-np.pi, np.pi, self.n_electrons)
|
||
|
|
x = np.cos(theta) * np.cos(phi)
|
||
|
|
y = np.cos(theta) * np.sin(phi)
|
||
|
|
z = np.sin(theta)
|
||
|
|
self.x0 = np.hstack((x, y, z))
|
||
|
|
self.x_opt = None
|
||
|
|
self.constr_jac = constr_jac
|
||
|
|
self.constr_hess = constr_hess
|
||
|
|
self.bounds = None
|
||
|
|
|
||
|
|
def _get_cordinates(self, x):
|
||
|
|
x_coord = x[:self.n_electrons]
|
||
|
|
y_coord = x[self.n_electrons:2 * self.n_electrons]
|
||
|
|
z_coord = x[2 * self.n_electrons:]
|
||
|
|
return x_coord, y_coord, z_coord
|
||
|
|
|
||
|
|
def _compute_coordinate_deltas(self, x):
|
||
|
|
x_coord, y_coord, z_coord = self._get_cordinates(x)
|
||
|
|
dx = x_coord[:, None] - x_coord
|
||
|
|
dy = y_coord[:, None] - y_coord
|
||
|
|
dz = z_coord[:, None] - z_coord
|
||
|
|
return dx, dy, dz
|
||
|
|
|
||
|
|
def fun(self, x):
|
||
|
|
dx, dy, dz = self._compute_coordinate_deltas(x)
|
||
|
|
with np.errstate(divide='ignore'):
|
||
|
|
dm1 = (dx**2 + dy**2 + dz**2) ** -0.5
|
||
|
|
dm1[np.diag_indices_from(dm1)] = 0
|
||
|
|
return 0.5 * np.sum(dm1)
|
||
|
|
|
||
|
|
def grad(self, x):
|
||
|
|
dx, dy, dz = self._compute_coordinate_deltas(x)
|
||
|
|
|
||
|
|
with np.errstate(divide='ignore'):
|
||
|
|
dm3 = (dx**2 + dy**2 + dz**2) ** -1.5
|
||
|
|
dm3[np.diag_indices_from(dm3)] = 0
|
||
|
|
|
||
|
|
grad_x = -np.sum(dx * dm3, axis=1)
|
||
|
|
grad_y = -np.sum(dy * dm3, axis=1)
|
||
|
|
grad_z = -np.sum(dz * dm3, axis=1)
|
||
|
|
|
||
|
|
return np.hstack((grad_x, grad_y, grad_z))
|
||
|
|
|
||
|
|
def hess(self, x):
|
||
|
|
dx, dy, dz = self._compute_coordinate_deltas(x)
|
||
|
|
d = (dx**2 + dy**2 + dz**2) ** 0.5
|
||
|
|
|
||
|
|
with np.errstate(divide='ignore'):
|
||
|
|
dm3 = d ** -3
|
||
|
|
dm5 = d ** -5
|
||
|
|
|
||
|
|
i = np.arange(self.n_electrons)
|
||
|
|
dm3[i, i] = 0
|
||
|
|
dm5[i, i] = 0
|
||
|
|
|
||
|
|
Hxx = dm3 - 3 * dx**2 * dm5
|
||
|
|
Hxx[i, i] = -np.sum(Hxx, axis=1)
|
||
|
|
|
||
|
|
Hxy = -3 * dx * dy * dm5
|
||
|
|
Hxy[i, i] = -np.sum(Hxy, axis=1)
|
||
|
|
|
||
|
|
Hxz = -3 * dx * dz * dm5
|
||
|
|
Hxz[i, i] = -np.sum(Hxz, axis=1)
|
||
|
|
|
||
|
|
Hyy = dm3 - 3 * dy**2 * dm5
|
||
|
|
Hyy[i, i] = -np.sum(Hyy, axis=1)
|
||
|
|
|
||
|
|
Hyz = -3 * dy * dz * dm5
|
||
|
|
Hyz[i, i] = -np.sum(Hyz, axis=1)
|
||
|
|
|
||
|
|
Hzz = dm3 - 3 * dz**2 * dm5
|
||
|
|
Hzz[i, i] = -np.sum(Hzz, axis=1)
|
||
|
|
|
||
|
|
H = np.vstack((
|
||
|
|
np.hstack((Hxx, Hxy, Hxz)),
|
||
|
|
np.hstack((Hxy, Hyy, Hyz)),
|
||
|
|
np.hstack((Hxz, Hyz, Hzz))
|
||
|
|
))
|
||
|
|
|
||
|
|
return H
|
||
|
|
|
||
|
|
@property
|
||
|
|
def constr(self):
|
||
|
|
def fun(x):
|
||
|
|
x_coord, y_coord, z_coord = self._get_cordinates(x)
|
||
|
|
return x_coord**2 + y_coord**2 + z_coord**2 - 1
|
||
|
|
|
||
|
|
if self.constr_jac is None:
|
||
|
|
def jac(x):
|
||
|
|
x_coord, y_coord, z_coord = self._get_cordinates(x)
|
||
|
|
Jx = 2 * np.diag(x_coord)
|
||
|
|
Jy = 2 * np.diag(y_coord)
|
||
|
|
Jz = 2 * np.diag(z_coord)
|
||
|
|
return csc_matrix(np.hstack((Jx, Jy, Jz)))
|
||
|
|
else:
|
||
|
|
jac = self.constr_jac
|
||
|
|
|
||
|
|
if self.constr_hess is None:
|
||
|
|
def hess(x, v):
|
||
|
|
D = 2 * np.diag(v)
|
||
|
|
return block_diag(D, D, D)
|
||
|
|
else:
|
||
|
|
hess = self.constr_hess
|
||
|
|
|
||
|
|
return NonlinearConstraint(fun, -np.inf, 0, jac, hess)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTrustRegionConstr(TestCase):
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
def test_list_of_problems(self):
|
||
|
|
list_of_problems = [Maratos(),
|
||
|
|
Maratos(constr_hess='2-point'),
|
||
|
|
Maratos(constr_hess=SR1()),
|
||
|
|
Maratos(constr_jac='2-point', constr_hess=SR1()),
|
||
|
|
MaratosGradInFunc(),
|
||
|
|
HyperbolicIneq(),
|
||
|
|
HyperbolicIneq(constr_hess='3-point'),
|
||
|
|
HyperbolicIneq(constr_hess=BFGS()),
|
||
|
|
HyperbolicIneq(constr_jac='3-point',
|
||
|
|
constr_hess=BFGS()),
|
||
|
|
Rosenbrock(),
|
||
|
|
IneqRosenbrock(),
|
||
|
|
EqIneqRosenbrock(),
|
||
|
|
BoundedRosenbrock(),
|
||
|
|
Elec(n_electrons=2),
|
||
|
|
Elec(n_electrons=2, constr_hess='2-point'),
|
||
|
|
Elec(n_electrons=2, constr_hess=SR1()),
|
||
|
|
Elec(n_electrons=2, constr_jac='3-point',
|
||
|
|
constr_hess=SR1())]
|
||
|
|
|
||
|
|
for prob in list_of_problems:
|
||
|
|
for grad in (prob.grad, '3-point', False):
|
||
|
|
for hess in (prob.hess,
|
||
|
|
'3-point',
|
||
|
|
SR1(),
|
||
|
|
BFGS(exception_strategy='damp_update'),
|
||
|
|
BFGS(exception_strategy='skip_update')):
|
||
|
|
|
||
|
|
# Remove exceptions
|
||
|
|
if grad in ('2-point', '3-point', 'cs', False) and \
|
||
|
|
hess in ('2-point', '3-point', 'cs'):
|
||
|
|
continue
|
||
|
|
if prob.grad is True and grad in ('3-point', False):
|
||
|
|
continue
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "delta_grad == 0.0")
|
||
|
|
result = minimize(prob.fun, prob.x0,
|
||
|
|
method='trust-constr',
|
||
|
|
jac=grad, hess=hess,
|
||
|
|
bounds=prob.bounds,
|
||
|
|
constraints=prob.constr)
|
||
|
|
|
||
|
|
if prob.x_opt is not None:
|
||
|
|
assert_array_almost_equal(result.x, prob.x_opt,
|
||
|
|
decimal=5)
|
||
|
|
# gtol
|
||
|
|
if result.status == 1:
|
||
|
|
assert_array_less(result.optimality, 1e-8)
|
||
|
|
# xtol
|
||
|
|
if result.status == 2:
|
||
|
|
assert_array_less(result.tr_radius, 1e-8)
|
||
|
|
|
||
|
|
if result.method == "tr_interior_point":
|
||
|
|
assert_array_less(result.barrier_parameter, 1e-8)
|
||
|
|
# max iter
|
||
|
|
if result.status in (0, 3):
|
||
|
|
raise RuntimeError("Invalid termination condition.")
|
||
|
|
|
||
|
|
def test_default_jac_and_hess(self):
|
||
|
|
def fun(x):
|
||
|
|
return (x - 1) ** 2
|
||
|
|
bounds = [(-2, 2)]
|
||
|
|
res = minimize(fun, x0=[-1.5], bounds=bounds, method='trust-constr')
|
||
|
|
assert_array_almost_equal(res.x, 1, decimal=5)
|
||
|
|
|
||
|
|
def test_default_hess(self):
|
||
|
|
def fun(x):
|
||
|
|
return (x - 1) ** 2
|
||
|
|
bounds = [(-2, 2)]
|
||
|
|
res = minimize(fun, x0=[-1.5], bounds=bounds, method='trust-constr',
|
||
|
|
jac='2-point')
|
||
|
|
assert_array_almost_equal(res.x, 1, decimal=5)
|
||
|
|
|
||
|
|
def test_no_constraints(self):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
result = minimize(prob.fun, prob.x0,
|
||
|
|
method='trust-constr',
|
||
|
|
jac=prob.grad, hess=prob.hess)
|
||
|
|
result1 = minimize(prob.fun, prob.x0,
|
||
|
|
method='L-BFGS-B',
|
||
|
|
jac='2-point')
|
||
|
|
|
||
|
|
result2 = minimize(prob.fun, prob.x0,
|
||
|
|
method='L-BFGS-B',
|
||
|
|
jac='3-point')
|
||
|
|
assert_array_almost_equal(result.x, prob.x_opt, decimal=5)
|
||
|
|
assert_array_almost_equal(result1.x, prob.x_opt, decimal=5)
|
||
|
|
assert_array_almost_equal(result2.x, prob.x_opt, decimal=5)
|
||
|
|
|
||
|
|
def test_hessp(self):
|
||
|
|
prob = Maratos()
|
||
|
|
|
||
|
|
def hessp(x, p):
|
||
|
|
H = prob.hess(x)
|
||
|
|
return H.dot(p)
|
||
|
|
|
||
|
|
result = minimize(prob.fun, prob.x0,
|
||
|
|
method='trust-constr',
|
||
|
|
jac=prob.grad, hessp=hessp,
|
||
|
|
bounds=prob.bounds,
|
||
|
|
constraints=prob.constr)
|
||
|
|
|
||
|
|
if prob.x_opt is not None:
|
||
|
|
assert_array_almost_equal(result.x, prob.x_opt, decimal=2)
|
||
|
|
|
||
|
|
# gtol
|
||
|
|
if result.status == 1:
|
||
|
|
assert_array_less(result.optimality, 1e-8)
|
||
|
|
# xtol
|
||
|
|
if result.status == 2:
|
||
|
|
assert_array_less(result.tr_radius, 1e-8)
|
||
|
|
|
||
|
|
if result.method == "tr_interior_point":
|
||
|
|
assert_array_less(result.barrier_parameter, 1e-8)
|
||
|
|
# max iter
|
||
|
|
if result.status in (0, 3):
|
||
|
|
raise RuntimeError("Invalid termination condition.")
|
||
|
|
|
||
|
|
def test_args(self):
|
||
|
|
prob = MaratosTestArgs("a", 234)
|
||
|
|
|
||
|
|
result = minimize(prob.fun, prob.x0, ("a", 234),
|
||
|
|
method='trust-constr',
|
||
|
|
jac=prob.grad, hess=prob.hess,
|
||
|
|
bounds=prob.bounds,
|
||
|
|
constraints=prob.constr)
|
||
|
|
|
||
|
|
if prob.x_opt is not None:
|
||
|
|
assert_array_almost_equal(result.x, prob.x_opt, decimal=2)
|
||
|
|
|
||
|
|
# gtol
|
||
|
|
if result.status == 1:
|
||
|
|
assert_array_less(result.optimality, 1e-8)
|
||
|
|
# xtol
|
||
|
|
if result.status == 2:
|
||
|
|
assert_array_less(result.tr_radius, 1e-8)
|
||
|
|
if result.method == "tr_interior_point":
|
||
|
|
assert_array_less(result.barrier_parameter, 1e-8)
|
||
|
|
# max iter
|
||
|
|
if result.status in (0, 3):
|
||
|
|
raise RuntimeError("Invalid termination condition.")
|
||
|
|
|
||
|
|
def test_raise_exception(self):
|
||
|
|
prob = Maratos()
|
||
|
|
message = "Whenever the gradient is estimated via finite-differences"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
minimize(prob.fun, prob.x0, method='trust-constr', jac='2-point',
|
||
|
|
hess='2-point', constraints=prob.constr)
|
||
|
|
|
||
|
|
def test_issue_9044(self):
|
||
|
|
# https://github.com/scipy/scipy/issues/9044
|
||
|
|
# Test the returned `OptimizeResult` contains keys consistent with
|
||
|
|
# other solvers.
|
||
|
|
|
||
|
|
def callback(x, info):
|
||
|
|
assert_('nit' in info)
|
||
|
|
assert_('niter' in info)
|
||
|
|
|
||
|
|
result = minimize(lambda x: x**2, [0], jac=lambda x: 2*x,
|
||
|
|
hess=lambda x: 2, callback=callback,
|
||
|
|
method='trust-constr')
|
||
|
|
assert_(result.get('success'))
|
||
|
|
assert_(result.get('nit', -1) == 1)
|
||
|
|
|
||
|
|
# Also check existence of the 'niter' attribute, for backward
|
||
|
|
# compatibility
|
||
|
|
assert_(result.get('niter', -1) == 1)
|
||
|
|
|
||
|
|
def test_issue_15093(self):
|
||
|
|
# scipy docs define bounds as inclusive, so it shouldn't be
|
||
|
|
# an issue to set x0 on the bounds even if keep_feasible is
|
||
|
|
# True. Previously, trust-constr would treat bounds as
|
||
|
|
# exclusive.
|
||
|
|
|
||
|
|
x0 = np.array([0., 0.5])
|
||
|
|
|
||
|
|
def obj(x):
|
||
|
|
x1 = x[0]
|
||
|
|
x2 = x[1]
|
||
|
|
return x1 ** 2 + x2 ** 2
|
||
|
|
|
||
|
|
bounds = Bounds(np.array([0., 0.]), np.array([1., 1.]),
|
||
|
|
keep_feasible=True)
|
||
|
|
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "delta_grad == 0.0")
|
||
|
|
result = minimize(
|
||
|
|
method='trust-constr',
|
||
|
|
fun=obj,
|
||
|
|
x0=x0,
|
||
|
|
bounds=bounds)
|
||
|
|
|
||
|
|
assert result['success']
|
||
|
|
|
||
|
|
class TestEmptyConstraint(TestCase):
|
||
|
|
"""
|
||
|
|
Here we minimize x^2+y^2 subject to x^2-y^2>1.
|
||
|
|
The actual minimum is at (0, 0) which fails the constraint.
|
||
|
|
Therefore we will find a minimum on the boundary at (+/-1, 0).
|
||
|
|
|
||
|
|
When minimizing on the boundary, optimize uses a set of
|
||
|
|
constraints that removes the constraint that sets that
|
||
|
|
boundary. In our case, there's only one constraint, so
|
||
|
|
the result is an empty constraint.
|
||
|
|
|
||
|
|
This tests that the empty constraint works.
|
||
|
|
"""
|
||
|
|
def test_empty_constraint(self):
|
||
|
|
|
||
|
|
def function(x):
|
||
|
|
return x[0]**2 + x[1]**2
|
||
|
|
|
||
|
|
def functionjacobian(x):
|
||
|
|
return np.array([2.*x[0], 2.*x[1]])
|
||
|
|
|
||
|
|
def functionhvp(x, v):
|
||
|
|
return 2.*v
|
||
|
|
|
||
|
|
def constraint(x):
|
||
|
|
return np.array([x[0]**2 - x[1]**2])
|
||
|
|
|
||
|
|
def constraintjacobian(x):
|
||
|
|
return np.array([[2*x[0], -2*x[1]]])
|
||
|
|
|
||
|
|
def constraintlcoh(x, v):
|
||
|
|
return np.array([[2., 0.], [0., -2.]]) * v[0]
|
||
|
|
|
||
|
|
constraint = NonlinearConstraint(constraint, 1., np.inf,
|
||
|
|
constraintjacobian, constraintlcoh)
|
||
|
|
|
||
|
|
startpoint = [1., 2.]
|
||
|
|
|
||
|
|
bounds = Bounds([-np.inf, -np.inf], [np.inf, np.inf])
|
||
|
|
|
||
|
|
result = minimize(
|
||
|
|
function,
|
||
|
|
startpoint,
|
||
|
|
method='trust-constr',
|
||
|
|
jac=functionjacobian,
|
||
|
|
hessp=functionhvp,
|
||
|
|
constraints=[constraint],
|
||
|
|
bounds=bounds,
|
||
|
|
)
|
||
|
|
|
||
|
|
assert_array_almost_equal(abs(result.x), np.array([1, 0]), decimal=4)
|
||
|
|
|
||
|
|
|
||
|
|
def test_bug_11886():
|
||
|
|
def opt(x):
|
||
|
|
return x[0]**2+x[1]**2
|
||
|
|
|
||
|
|
with np.testing.suppress_warnings() as sup:
|
||
|
|
sup.filter(PendingDeprecationWarning)
|
||
|
|
A = np.matrix(np.diag([1, 1]))
|
||
|
|
lin_cons = LinearConstraint(A, -1, np.inf)
|
||
|
|
# just checking that there are no errors
|
||
|
|
minimize(opt, 2*[1], constraints = lin_cons)
|
||
|
|
|
||
|
|
|
||
|
|
# Remove xfail when gh-11649 is resolved
|
||
|
|
@pytest.mark.xfail(reason="Known bug in trust-constr; see gh-11649.",
|
||
|
|
strict=True)
|
||
|
|
def test_gh11649():
|
||
|
|
bnds = Bounds(lb=[-1, -1], ub=[1, 1], keep_feasible=True)
|
||
|
|
|
||
|
|
def assert_inbounds(x):
|
||
|
|
assert np.all(x >= bnds.lb)
|
||
|
|
assert np.all(x <= bnds.ub)
|
||
|
|
|
||
|
|
def obj(x):
|
||
|
|
assert_inbounds(x)
|
||
|
|
return np.exp(x[0])*(4*x[0]**2 + 2*x[1]**2 + 4*x[0]*x[1] + 2*x[1] + 1)
|
||
|
|
|
||
|
|
def nce(x):
|
||
|
|
assert_inbounds(x)
|
||
|
|
return x[0]**2 + x[1]
|
||
|
|
|
||
|
|
def nci(x):
|
||
|
|
assert_inbounds(x)
|
||
|
|
return x[0]*x[1]
|
||
|
|
|
||
|
|
x0 = np.array((0.99, -0.99))
|
||
|
|
nlcs = [NonlinearConstraint(nci, -10, np.inf),
|
||
|
|
NonlinearConstraint(nce, 1, 1)]
|
||
|
|
|
||
|
|
res = minimize(fun=obj, x0=x0, method='trust-constr',
|
||
|
|
bounds=bnds, constraints=nlcs)
|
||
|
|
assert res.success
|
||
|
|
assert_inbounds(res.x)
|
||
|
|
assert nlcs[0].lb < nlcs[0].fun(res.x) < nlcs[0].ub
|
||
|
|
assert_allclose(nce(res.x), nlcs[1].ub)
|
||
|
|
|
||
|
|
ref = minimize(fun=obj, x0=x0, method='slsqp',
|
||
|
|
bounds=bnds, constraints=nlcs)
|
||
|
|
assert_allclose(res.fun, ref.fun)
|
||
|
|
|
||
|
|
|
||
|
|
class TestBoundedNelderMead:
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('bounds, x_opt',
|
||
|
|
[(Bounds(-np.inf, np.inf), Rosenbrock().x_opt),
|
||
|
|
(Bounds(-np.inf, -0.8), [-0.8, -0.8]),
|
||
|
|
(Bounds(3.0, np.inf), [3.0, 9.0]),
|
||
|
|
(Bounds([3.0, 1.0], [4.0, 5.0]), [3., 5.]),
|
||
|
|
])
|
||
|
|
def test_rosen_brock_with_bounds(self, bounds, x_opt):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "Initial guess is not within "
|
||
|
|
"the specified bounds")
|
||
|
|
result = minimize(prob.fun, [-10, -10],
|
||
|
|
method='Nelder-Mead',
|
||
|
|
bounds=bounds)
|
||
|
|
assert np.less_equal(bounds.lb, result.x).all()
|
||
|
|
assert np.less_equal(result.x, bounds.ub).all()
|
||
|
|
assert np.allclose(prob.fun(result.x), result.fun)
|
||
|
|
assert np.allclose(result.x, x_opt, atol=1.e-3)
|
||
|
|
|
||
|
|
def test_equal_all_bounds(self):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
bounds = Bounds([4.0, 5.0], [4.0, 5.0])
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "Initial guess is not within "
|
||
|
|
"the specified bounds")
|
||
|
|
result = minimize(prob.fun, [-10, 8],
|
||
|
|
method='Nelder-Mead',
|
||
|
|
bounds=bounds)
|
||
|
|
assert np.allclose(result.x, [4.0, 5.0])
|
||
|
|
|
||
|
|
def test_equal_one_bounds(self):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
bounds = Bounds([4.0, 5.0], [4.0, 20.0])
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(UserWarning, "Initial guess is not within "
|
||
|
|
"the specified bounds")
|
||
|
|
result = minimize(prob.fun, [-10, 8],
|
||
|
|
method='Nelder-Mead',
|
||
|
|
bounds=bounds)
|
||
|
|
assert np.allclose(result.x, [4.0, 16.0])
|
||
|
|
|
||
|
|
def test_invalid_bounds(self):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
message = 'An upper bound is less than the corresponding lower bound.'
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
bounds = Bounds([-np.inf, 1.0], [4.0, -5.0])
|
||
|
|
minimize(prob.fun, [-10, 3],
|
||
|
|
method='Nelder-Mead',
|
||
|
|
bounds=bounds)
|
||
|
|
|
||
|
|
@pytest.mark.xfail(reason="Failing on Azure Linux and macOS builds, "
|
||
|
|
"see gh-13846")
|
||
|
|
def test_outside_bounds_warning(self):
|
||
|
|
prob = Rosenbrock()
|
||
|
|
message = "Initial guess is not within the specified bounds"
|
||
|
|
with pytest.warns(UserWarning, match=message):
|
||
|
|
bounds = Bounds([-np.inf, 1.0], [4.0, 5.0])
|
||
|
|
minimize(prob.fun, [-10, 8],
|
||
|
|
method='Nelder-Mead',
|
||
|
|
bounds=bounds)
|