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"""
Unit test for SLSQP optimization.
"""
from __future__ import division, print_function, absolute_import
from numpy.testing import (assert_, assert_array_almost_equal, TestCase,
assert_allclose, assert_equal, run_module_suite)
import numpy as np
from scipy._lib._testutils import knownfailure_overridable
from scipy.optimize import fmin_slsqp, minimize
class MyCallBack(object):
"""pass a custom callback function
This makes sure it's being used.
"""
def __init__(self):
self.been_called = False
self.ncalls = 0
def __call__(self, x):
self.been_called = True
self.ncalls += 1
class TestSLSQP(TestCase):
"""
Test SLSQP algorithm using Example 14.4 from Numerical Methods for
Engineers by Steven Chapra and Raymond Canale.
This example maximizes the function f(x) = 2*x*y + 2*x - x**2 - 2*y**2,
which has a maximum at x=2, y=1.
"""
def setUp(self):
self.opts = {'disp': False}
def fun(self, d, sign=1.0):
"""
Arguments:
d - A list of two elements, where d[0] represents x and d[1] represents y
in the following equation.
sign - A multiplier for f. Since we want to optimize it, and the scipy
optimizers can only minimize functions, we need to multiply it by
-1 to achieve the desired solution
Returns:
2*x*y + 2*x - x**2 - 2*y**2
"""
x = d[0]
y = d[1]
return sign*(2*x*y + 2*x - x**2 - 2*y**2)
def jac(self, d, sign=1.0):
"""
This is the derivative of fun, returning a numpy array
representing df/dx and df/dy.
"""
x = d[0]
y = d[1]
dfdx = sign*(-2*x + 2*y + 2)
dfdy = sign*(2*x - 4*y)
return np.array([dfdx, dfdy], float)
def fun_and_jac(self, d, sign=1.0):
return self.fun(d, sign), self.jac(d, sign)
def f_eqcon(self, x, sign=1.0):
""" Equality constraint """
return np.array([x[0] - x[1]])
def fprime_eqcon(self, x, sign=1.0):
""" Equality constraint, derivative """
return np.array([[1, -1]])
def f_eqcon_scalar(self, x, sign=1.0):
""" Scalar equality constraint """
return self.f_eqcon(x, sign)[0]
def fprime_eqcon_scalar(self, x, sign=1.0):
""" Scalar equality constraint, derivative """
return self.fprime_eqcon(x, sign)[0].tolist()
def f_ieqcon(self, x, sign=1.0):
""" Inequality constraint """
return np.array([x[0] - x[1] - 1.0])
def fprime_ieqcon(self, x, sign=1.0):
""" Inequality constraint, derivative """
return np.array([[1, -1]])
def f_ieqcon2(self, x):
""" Vector inequality constraint """
return np.asarray(x)
def fprime_ieqcon2(self, x):
""" Vector inequality constraint, derivative """
return np.identity(x.shape[0])
# minimize
def test_minimize_unbounded_approximated(self):
# Minimize, method='SLSQP': unbounded, approximated jacobian.
res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
method='SLSQP', options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2, 1])
def test_minimize_unbounded_given(self):
# Minimize, method='SLSQP': unbounded, given jacobian.
res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
jac=self.jac, method='SLSQP', options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2, 1])
def test_minimize_bounded_approximated(self):
# Minimize, method='SLSQP': bounded, approximated jacobian.
with np.errstate(invalid='ignore'):
res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
bounds=((2.5, None), (None, 0.5)),
method='SLSQP', options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2.5, 0.5])
assert_(2.5 <= res.x[0])
assert_(res.x[1] <= 0.5)
def test_minimize_unbounded_combined(self):
# Minimize, method='SLSQP': unbounded, combined function and jacobian.
res = minimize(self.fun_and_jac, [-1.0, 1.0], args=(-1.0, ),
jac=True, method='SLSQP', options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2, 1])
def test_minimize_equality_approximated(self):
# Minimize with method='SLSQP': equality constraint, approx. jacobian.
res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
constraints={'type': 'eq',
'fun': self.f_eqcon,
'args': (-1.0, )},
method='SLSQP', options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [1, 1])
def test_minimize_equality_given(self):
# Minimize with method='SLSQP': equality constraint, given jacobian.
res = minimize(self.fun, [-1.0, 1.0], jac=self.jac,
method='SLSQP', args=(-1.0,),
constraints={'type': 'eq', 'fun':self.f_eqcon,
'args': (-1.0, )},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [1, 1])
def test_minimize_equality_given2(self):
# Minimize with method='SLSQP': equality constraint, given jacobian
# for fun and const.
res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
jac=self.jac, args=(-1.0,),
constraints={'type': 'eq',
'fun': self.f_eqcon,
'args': (-1.0, ),
'jac': self.fprime_eqcon},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [1, 1])
def test_minimize_equality_given_cons_scalar(self):
# Minimize with method='SLSQP': scalar equality constraint, given
# jacobian for fun and const.
res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
jac=self.jac, args=(-1.0,),
constraints={'type': 'eq',
'fun': self.f_eqcon_scalar,
'args': (-1.0, ),
'jac': self.fprime_eqcon_scalar},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [1, 1])
def test_minimize_inequality_given(self):
# Minimize with method='SLSQP': inequality constraint, given jacobian.
res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
jac=self.jac, args=(-1.0, ),
constraints={'type': 'ineq',
'fun': self.f_ieqcon,
'args': (-1.0, )},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2, 1], atol=1e-3)
def test_minimize_inequality_given_vector_constraints(self):
# Minimize with method='SLSQP': vector inequality constraint, given
# jacobian.
res = minimize(self.fun, [-1.0, 1.0], jac=self.jac,
method='SLSQP', args=(-1.0,),
constraints={'type': 'ineq',
'fun': self.f_ieqcon2,
'jac': self.fprime_ieqcon2},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [2, 1])
def test_minimize_bound_equality_given2(self):
# Minimize with method='SLSQP': bounds, eq. const., given jac. for
# fun. and const.
res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
jac=self.jac, args=(-1.0, ),
bounds=[(-0.8, 1.), (-1, 0.8)],
constraints={'type': 'eq',
'fun': self.f_eqcon,
'args': (-1.0, ),
'jac': self.fprime_eqcon},
options=self.opts)
assert_(res['success'], res['message'])
assert_allclose(res.x, [0.8, 0.8], atol=1e-3)
assert_(-0.8 <= res.x[0] <= 1)
assert_(-1 <= res.x[1] <= 0.8)
# fmin_slsqp
def test_unbounded_approximated(self):
# SLSQP: unbounded, approximated jacobian.
res = fmin_slsqp(self.fun, [-1.0, 1.0], args=(-1.0, ),
iprint = 0, full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [2, 1])
def test_unbounded_given(self):
# SLSQP: unbounded, given jacobian.
res = fmin_slsqp(self.fun, [-1.0, 1.0], args=(-1.0, ),
fprime = self.jac, iprint = 0,
full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [2, 1])
def test_equality_approximated(self):
# SLSQP: equality constraint, approximated jacobian.
res = fmin_slsqp(self.fun,[-1.0,1.0], args=(-1.0,),
eqcons = [self.f_eqcon],
iprint = 0, full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [1, 1])
def test_equality_given(self):
# SLSQP: equality constraint, given jacobian.
res = fmin_slsqp(self.fun, [-1.0, 1.0],
fprime=self.jac, args=(-1.0,),
eqcons = [self.f_eqcon], iprint = 0,
full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [1, 1])
def test_equality_given2(self):
# SLSQP: equality constraint, given jacobian for fun and const.
res = fmin_slsqp(self.fun, [-1.0, 1.0],
fprime=self.jac, args=(-1.0,),
f_eqcons = self.f_eqcon,
fprime_eqcons = self.fprime_eqcon,
iprint = 0,
full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [1, 1])
def test_inequality_given(self):
# SLSQP: inequality constraint, given jacobian.
res = fmin_slsqp(self.fun, [-1.0, 1.0],
fprime=self.jac, args=(-1.0, ),
ieqcons = [self.f_ieqcon],
iprint = 0, full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [2, 1], decimal=3)
def test_bound_equality_given2(self):
# SLSQP: bounds, eq. const., given jac. for fun. and const.
res = fmin_slsqp(self.fun, [-1.0, 1.0],
fprime=self.jac, args=(-1.0, ),
bounds = [(-0.8, 1.), (-1, 0.8)],
f_eqcons = self.f_eqcon,
fprime_eqcons = self.fprime_eqcon,
iprint = 0, full_output = 1)
x, fx, its, imode, smode = res
assert_(imode == 0, imode)
assert_array_almost_equal(x, [0.8, 0.8], decimal=3)
assert_(-0.8 <= x[0] <= 1)
assert_(-1 <= x[1] <= 0.8)
def test_scalar_constraints(self):
# Regression test for gh-2182
x = fmin_slsqp(lambda z: z**2, [3.],
ieqcons=[lambda z: z[0] - 1],
iprint=0)
assert_array_almost_equal(x, [1.])
x = fmin_slsqp(lambda z: z**2, [3.],
f_ieqcons=lambda z: [z[0] - 1],
iprint=0)
assert_array_almost_equal(x, [1.])
def test_integer_bounds(self):
# This should not raise an exception
fmin_slsqp(lambda z: z**2 - 1, [0], bounds=[[0, 1]], iprint=0)
def test_callback(self):
# Minimize, method='SLSQP': unbounded, approximated jacobian. Check for callback
callback = MyCallBack()
res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
method='SLSQP', callback=callback, options=self.opts)
assert_(res['success'], res['message'])
assert_(callback.been_called)
assert_equal(callback.ncalls, res['nit'])
def test_inconsistent_linearization(self):
# SLSQP must be able to solve this problem, even if the
# linearized problem at the starting point is infeasible.
# Linearized constraints are
#
# 2*x0[0]*x[0] >= 1
#
# At x0 = [0, 1], the second constraint is clearly infeasible.
# This triggers a call with n2==1 in the LSQ subroutine.
x = [0, 1]
f1 = lambda x: x[0] + x[1] - 2
f2 = lambda x: x[0]**2 - 1
sol = minimize(
lambda x: x[0]**2 + x[1]**2,
x,
constraints=({'type':'eq','fun': f1},
{'type':'ineq','fun': f2}),
bounds=((0,None), (0,None)),
method='SLSQP')
x = sol.x
assert_allclose(f1(x), 0, atol=1e-8)
assert_(f2(x) >= -1e-8)
assert_(sol.success, sol)
@knownfailure_overridable("This bug is not fixed")
def test_regression_5743(self):
# SLSQP must not indicate success for this problem,
# which is infeasible.
x = [1, 2]
sol = minimize(
lambda x: x[0]**2 + x[1]**2,
x,
constraints=({'type':'eq','fun': lambda x: x[0]+x[1]-1},
{'type':'ineq','fun': lambda x: x[0]-2}),
bounds=((0,None), (0,None)),
method='SLSQP')
assert_(not sol.success, sol)
if __name__ == "__main__":
run_module_suite()
|
