609 lines
23 KiB
Python
609 lines
23 KiB
Python
"""
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Unit test for SLSQP optimization.
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"""
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from numpy.testing import (assert_, assert_array_almost_equal,
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assert_allclose, assert_equal)
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from pytest import raises as assert_raises
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import pytest
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import numpy as np
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from scipy.optimize import fmin_slsqp, minimize, Bounds, NonlinearConstraint
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class MyCallBack:
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"""pass a custom callback function
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This makes sure it's being used.
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"""
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def __init__(self):
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self.been_called = False
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self.ncalls = 0
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def __call__(self, x):
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self.been_called = True
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self.ncalls += 1
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class TestSLSQP:
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"""
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Test SLSQP algorithm using Example 14.4 from Numerical Methods for
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Engineers by Steven Chapra and Raymond Canale.
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This example maximizes the function f(x) = 2*x*y + 2*x - x**2 - 2*y**2,
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which has a maximum at x=2, y=1.
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"""
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def setup_method(self):
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self.opts = {'disp': False}
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def fun(self, d, sign=1.0):
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"""
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Arguments:
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d - A list of two elements, where d[0] represents x and d[1] represents y
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in the following equation.
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sign - A multiplier for f. Since we want to optimize it, and the SciPy
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optimizers can only minimize functions, we need to multiply it by
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-1 to achieve the desired solution
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Returns:
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2*x*y + 2*x - x**2 - 2*y**2
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"""
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x = d[0]
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y = d[1]
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return sign*(2*x*y + 2*x - x**2 - 2*y**2)
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def jac(self, d, sign=1.0):
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"""
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This is the derivative of fun, returning a NumPy array
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representing df/dx and df/dy.
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"""
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x = d[0]
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y = d[1]
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dfdx = sign*(-2*x + 2*y + 2)
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dfdy = sign*(2*x - 4*y)
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return np.array([dfdx, dfdy], float)
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def fun_and_jac(self, d, sign=1.0):
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return self.fun(d, sign), self.jac(d, sign)
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def f_eqcon(self, x, sign=1.0):
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""" Equality constraint """
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return np.array([x[0] - x[1]])
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def fprime_eqcon(self, x, sign=1.0):
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""" Equality constraint, derivative """
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return np.array([[1, -1]])
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def f_eqcon_scalar(self, x, sign=1.0):
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""" Scalar equality constraint """
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return self.f_eqcon(x, sign)[0]
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def fprime_eqcon_scalar(self, x, sign=1.0):
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""" Scalar equality constraint, derivative """
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return self.fprime_eqcon(x, sign)[0].tolist()
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def f_ieqcon(self, x, sign=1.0):
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""" Inequality constraint """
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return np.array([x[0] - x[1] - 1.0])
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def fprime_ieqcon(self, x, sign=1.0):
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""" Inequality constraint, derivative """
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return np.array([[1, -1]])
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def f_ieqcon2(self, x):
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""" Vector inequality constraint """
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return np.asarray(x)
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def fprime_ieqcon2(self, x):
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""" Vector inequality constraint, derivative """
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return np.identity(x.shape[0])
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# minimize
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def test_minimize_unbounded_approximated(self):
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# Minimize, method='SLSQP': unbounded, approximated jacobian.
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jacs = [None, False, '2-point', '3-point']
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for jac in jacs:
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res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
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jac=jac, method='SLSQP',
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2, 1])
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def test_minimize_unbounded_given(self):
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# Minimize, method='SLSQP': unbounded, given Jacobian.
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res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
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jac=self.jac, method='SLSQP', options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2, 1])
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def test_minimize_bounded_approximated(self):
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# Minimize, method='SLSQP': bounded, approximated jacobian.
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jacs = [None, False, '2-point', '3-point']
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for jac in jacs:
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with np.errstate(invalid='ignore'):
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res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
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jac=jac,
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bounds=((2.5, None), (None, 0.5)),
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method='SLSQP', options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2.5, 0.5])
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assert_(2.5 <= res.x[0])
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assert_(res.x[1] <= 0.5)
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def test_minimize_unbounded_combined(self):
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# Minimize, method='SLSQP': unbounded, combined function and Jacobian.
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res = minimize(self.fun_and_jac, [-1.0, 1.0], args=(-1.0, ),
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jac=True, method='SLSQP', options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2, 1])
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def test_minimize_equality_approximated(self):
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# Minimize with method='SLSQP': equality constraint, approx. jacobian.
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jacs = [None, False, '2-point', '3-point']
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for jac in jacs:
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res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
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jac=jac,
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constraints={'type': 'eq',
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'fun': self.f_eqcon,
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'args': (-1.0, )},
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method='SLSQP', options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [1, 1])
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def test_minimize_equality_given(self):
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# Minimize with method='SLSQP': equality constraint, given Jacobian.
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res = minimize(self.fun, [-1.0, 1.0], jac=self.jac,
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method='SLSQP', args=(-1.0,),
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constraints={'type': 'eq', 'fun':self.f_eqcon,
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'args': (-1.0, )},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [1, 1])
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def test_minimize_equality_given2(self):
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# Minimize with method='SLSQP': equality constraint, given Jacobian
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# for fun and const.
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res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
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jac=self.jac, args=(-1.0,),
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constraints={'type': 'eq',
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'fun': self.f_eqcon,
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'args': (-1.0, ),
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'jac': self.fprime_eqcon},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [1, 1])
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def test_minimize_equality_given_cons_scalar(self):
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# Minimize with method='SLSQP': scalar equality constraint, given
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# Jacobian for fun and const.
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res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
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jac=self.jac, args=(-1.0,),
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constraints={'type': 'eq',
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'fun': self.f_eqcon_scalar,
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'args': (-1.0, ),
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'jac': self.fprime_eqcon_scalar},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [1, 1])
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def test_minimize_inequality_given(self):
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# Minimize with method='SLSQP': inequality constraint, given Jacobian.
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res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
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jac=self.jac, args=(-1.0, ),
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constraints={'type': 'ineq',
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'fun': self.f_ieqcon,
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'args': (-1.0, )},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2, 1], atol=1e-3)
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def test_minimize_inequality_given_vector_constraints(self):
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# Minimize with method='SLSQP': vector inequality constraint, given
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# Jacobian.
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res = minimize(self.fun, [-1.0, 1.0], jac=self.jac,
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method='SLSQP', args=(-1.0,),
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constraints={'type': 'ineq',
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'fun': self.f_ieqcon2,
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'jac': self.fprime_ieqcon2},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [2, 1])
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def test_minimize_bounded_constraint(self):
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# when the constraint makes the solver go up against a parameter
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# bound make sure that the numerical differentiation of the
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# jacobian doesn't try to exceed that bound using a finite difference.
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# gh11403
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def c(x):
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assert 0 <= x[0] <= 1 and 0 <= x[1] <= 1, x
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return x[0] ** 0.5 + x[1]
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def f(x):
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assert 0 <= x[0] <= 1 and 0 <= x[1] <= 1, x
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return -x[0] ** 2 + x[1] ** 2
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cns = [NonlinearConstraint(c, 0, 1.5)]
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x0 = np.asarray([0.9, 0.5])
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bnd = Bounds([0., 0.], [1.0, 1.0])
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minimize(f, x0, method='SLSQP', bounds=bnd, constraints=cns)
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def test_minimize_bound_equality_given2(self):
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# Minimize with method='SLSQP': bounds, eq. const., given jac. for
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# fun. and const.
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res = minimize(self.fun, [-1.0, 1.0], method='SLSQP',
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jac=self.jac, args=(-1.0, ),
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bounds=[(-0.8, 1.), (-1, 0.8)],
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constraints={'type': 'eq',
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'fun': self.f_eqcon,
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'args': (-1.0, ),
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'jac': self.fprime_eqcon},
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options=self.opts)
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assert_(res['success'], res['message'])
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assert_allclose(res.x, [0.8, 0.8], atol=1e-3)
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assert_(-0.8 <= res.x[0] <= 1)
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assert_(-1 <= res.x[1] <= 0.8)
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# fmin_slsqp
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def test_unbounded_approximated(self):
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# SLSQP: unbounded, approximated Jacobian.
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res = fmin_slsqp(self.fun, [-1.0, 1.0], args=(-1.0, ),
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iprint = 0, full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [2, 1])
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def test_unbounded_given(self):
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# SLSQP: unbounded, given Jacobian.
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res = fmin_slsqp(self.fun, [-1.0, 1.0], args=(-1.0, ),
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fprime = self.jac, iprint = 0,
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full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [2, 1])
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def test_equality_approximated(self):
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# SLSQP: equality constraint, approximated Jacobian.
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res = fmin_slsqp(self.fun,[-1.0,1.0], args=(-1.0,),
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eqcons = [self.f_eqcon],
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iprint = 0, full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [1, 1])
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def test_equality_given(self):
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# SLSQP: equality constraint, given Jacobian.
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res = fmin_slsqp(self.fun, [-1.0, 1.0],
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fprime=self.jac, args=(-1.0,),
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eqcons = [self.f_eqcon], iprint = 0,
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full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [1, 1])
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def test_equality_given2(self):
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# SLSQP: equality constraint, given Jacobian for fun and const.
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res = fmin_slsqp(self.fun, [-1.0, 1.0],
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fprime=self.jac, args=(-1.0,),
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f_eqcons = self.f_eqcon,
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fprime_eqcons = self.fprime_eqcon,
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iprint = 0,
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full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [1, 1])
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def test_inequality_given(self):
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# SLSQP: inequality constraint, given Jacobian.
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res = fmin_slsqp(self.fun, [-1.0, 1.0],
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fprime=self.jac, args=(-1.0, ),
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ieqcons = [self.f_ieqcon],
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iprint = 0, full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [2, 1], decimal=3)
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def test_bound_equality_given2(self):
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# SLSQP: bounds, eq. const., given jac. for fun. and const.
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res = fmin_slsqp(self.fun, [-1.0, 1.0],
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fprime=self.jac, args=(-1.0, ),
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bounds = [(-0.8, 1.), (-1, 0.8)],
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f_eqcons = self.f_eqcon,
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fprime_eqcons = self.fprime_eqcon,
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iprint = 0, full_output = 1)
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x, fx, its, imode, smode = res
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assert_(imode == 0, imode)
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assert_array_almost_equal(x, [0.8, 0.8], decimal=3)
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assert_(-0.8 <= x[0] <= 1)
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assert_(-1 <= x[1] <= 0.8)
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def test_scalar_constraints(self):
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# Regression test for gh-2182
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x = fmin_slsqp(lambda z: z**2, [3.],
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ieqcons=[lambda z: z[0] - 1],
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iprint=0)
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assert_array_almost_equal(x, [1.])
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x = fmin_slsqp(lambda z: z**2, [3.],
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f_ieqcons=lambda z: [z[0] - 1],
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iprint=0)
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assert_array_almost_equal(x, [1.])
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def test_integer_bounds(self):
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# This should not raise an exception
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fmin_slsqp(lambda z: z**2 - 1, [0], bounds=[[0, 1]], iprint=0)
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def test_array_bounds(self):
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# NumPy used to treat n-dimensional 1-element arrays as scalars
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# in some cases. The handling of `bounds` by `fmin_slsqp` still
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# supports this behavior.
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bounds = [(-np.inf, np.inf), (np.array([2]), np.array([3]))]
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x = fmin_slsqp(lambda z: np.sum(z**2 - 1), [2.5, 2.5], bounds=bounds,
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iprint=0)
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assert_array_almost_equal(x, [0, 2])
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def test_obj_must_return_scalar(self):
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# Regression test for Github Issue #5433
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# If objective function does not return a scalar, raises ValueError
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with assert_raises(ValueError):
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fmin_slsqp(lambda x: [0, 1], [1, 2, 3])
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def test_obj_returns_scalar_in_list(self):
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# Test for Github Issue #5433 and PR #6691
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# Objective function should be able to return length-1 Python list
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# containing the scalar
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fmin_slsqp(lambda x: [0], [1, 2, 3], iprint=0)
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def test_callback(self):
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# Minimize, method='SLSQP': unbounded, approximated jacobian. Check for callback
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callback = MyCallBack()
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res = minimize(self.fun, [-1.0, 1.0], args=(-1.0, ),
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method='SLSQP', callback=callback, options=self.opts)
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assert_(res['success'], res['message'])
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assert_(callback.been_called)
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assert_equal(callback.ncalls, res['nit'])
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def test_inconsistent_linearization(self):
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# SLSQP must be able to solve this problem, even if the
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# linearized problem at the starting point is infeasible.
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# Linearized constraints are
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#
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# 2*x0[0]*x[0] >= 1
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#
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# At x0 = [0, 1], the second constraint is clearly infeasible.
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# This triggers a call with n2==1 in the LSQ subroutine.
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x = [0, 1]
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def f1(x):
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return x[0] + x[1] - 2
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def f2(x):
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return x[0] ** 2 - 1
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sol = minimize(
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lambda x: x[0]**2 + x[1]**2,
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x,
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constraints=({'type':'eq','fun': f1},
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{'type':'ineq','fun': f2}),
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bounds=((0,None), (0,None)),
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method='SLSQP')
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x = sol.x
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assert_allclose(f1(x), 0, atol=1e-8)
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assert_(f2(x) >= -1e-8)
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assert_(sol.success, sol)
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def test_regression_5743(self):
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# SLSQP must not indicate success for this problem,
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# which is infeasible.
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x = [1, 2]
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sol = minimize(
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lambda x: x[0]**2 + x[1]**2,
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x,
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constraints=({'type':'eq','fun': lambda x: x[0]+x[1]-1},
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{'type':'ineq','fun': lambda x: x[0]-2}),
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bounds=((0,None), (0,None)),
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method='SLSQP')
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assert_(not sol.success, sol)
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def test_gh_6676(self):
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def func(x):
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return (x[0] - 1)**2 + 2*(x[1] - 1)**2 + 0.5*(x[2] - 1)**2
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sol = minimize(func, [0, 0, 0], method='SLSQP')
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assert_(sol.jac.shape == (3,))
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def test_invalid_bounds(self):
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# Raise correct error when lower bound is greater than upper bound.
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# See Github issue 6875.
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bounds_list = [
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((1, 2), (2, 1)),
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((2, 1), (1, 2)),
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((2, 1), (2, 1)),
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((np.inf, 0), (np.inf, 0)),
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((1, -np.inf), (0, 1)),
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]
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for bounds in bounds_list:
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with assert_raises(ValueError):
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minimize(self.fun, [-1.0, 1.0], bounds=bounds, method='SLSQP')
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def test_bounds_clipping(self):
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#
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# SLSQP returns bogus results for initial guess out of bounds, gh-6859
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#
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def f(x):
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return (x[0] - 1)**2
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sol = minimize(f, [10], method='slsqp', bounds=[(None, 0)])
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assert_(sol.success)
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assert_allclose(sol.x, 0, atol=1e-10)
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sol = minimize(f, [-10], method='slsqp', bounds=[(2, None)])
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assert_(sol.success)
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assert_allclose(sol.x, 2, atol=1e-10)
|
|
|
|
sol = minimize(f, [-10], method='slsqp', bounds=[(None, 0)])
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
sol = minimize(f, [10], method='slsqp', bounds=[(2, None)])
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 2, atol=1e-10)
|
|
|
|
sol = minimize(f, [-0.5], method='slsqp', bounds=[(-1, 0)])
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
sol = minimize(f, [10], method='slsqp', bounds=[(-1, 0)])
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
def test_infeasible_initial(self):
|
|
# Check SLSQP behavior with infeasible initial point
|
|
def f(x):
|
|
x, = x
|
|
return x*x - 2*x + 1
|
|
|
|
cons_u = [{'type': 'ineq', 'fun': lambda x: 0 - x}]
|
|
cons_l = [{'type': 'ineq', 'fun': lambda x: x - 2}]
|
|
cons_ul = [{'type': 'ineq', 'fun': lambda x: 0 - x},
|
|
{'type': 'ineq', 'fun': lambda x: x + 1}]
|
|
|
|
sol = minimize(f, [10], method='slsqp', constraints=cons_u)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
sol = minimize(f, [-10], method='slsqp', constraints=cons_l)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 2, atol=1e-10)
|
|
|
|
sol = minimize(f, [-10], method='slsqp', constraints=cons_u)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
sol = minimize(f, [10], method='slsqp', constraints=cons_l)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 2, atol=1e-10)
|
|
|
|
sol = minimize(f, [-0.5], method='slsqp', constraints=cons_ul)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
sol = minimize(f, [10], method='slsqp', constraints=cons_ul)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, 0, atol=1e-10)
|
|
|
|
def test_inconsistent_inequalities(self):
|
|
# gh-7618
|
|
|
|
def cost(x):
|
|
return -1 * x[0] + 4 * x[1]
|
|
|
|
def ineqcons1(x):
|
|
return x[1] - x[0] - 1
|
|
|
|
def ineqcons2(x):
|
|
return x[0] - x[1]
|
|
|
|
# The inequalities are inconsistent, so no solution can exist:
|
|
#
|
|
# x1 >= x0 + 1
|
|
# x0 >= x1
|
|
|
|
x0 = (1,5)
|
|
bounds = ((-5, 5), (-5, 5))
|
|
cons = (dict(type='ineq', fun=ineqcons1), dict(type='ineq', fun=ineqcons2))
|
|
res = minimize(cost, x0, method='SLSQP', bounds=bounds, constraints=cons)
|
|
|
|
assert_(not res.success)
|
|
|
|
def test_new_bounds_type(self):
|
|
def f(x):
|
|
return x[0] ** 2 + x[1] ** 2
|
|
bounds = Bounds([1, 0], [np.inf, np.inf])
|
|
sol = minimize(f, [0, 0], method='slsqp', bounds=bounds)
|
|
assert_(sol.success)
|
|
assert_allclose(sol.x, [1, 0])
|
|
|
|
def test_nested_minimization(self):
|
|
|
|
class NestedProblem:
|
|
|
|
def __init__(self):
|
|
self.F_outer_count = 0
|
|
|
|
def F_outer(self, x):
|
|
self.F_outer_count += 1
|
|
if self.F_outer_count > 1000:
|
|
raise Exception("Nested minimization failed to terminate.")
|
|
inner_res = minimize(self.F_inner, (3, 4), method="SLSQP")
|
|
assert_(inner_res.success)
|
|
assert_allclose(inner_res.x, [1, 1])
|
|
return x[0]**2 + x[1]**2 + x[2]**2
|
|
|
|
def F_inner(self, x):
|
|
return (x[0] - 1)**2 + (x[1] - 1)**2
|
|
|
|
def solve(self):
|
|
outer_res = minimize(self.F_outer, (5, 5, 5), method="SLSQP")
|
|
assert_(outer_res.success)
|
|
assert_allclose(outer_res.x, [0, 0, 0])
|
|
|
|
problem = NestedProblem()
|
|
problem.solve()
|
|
|
|
def test_gh1758(self):
|
|
# the test suggested in gh1758
|
|
# https://nlopt.readthedocs.io/en/latest/NLopt_Tutorial/
|
|
# implement two equality constraints, in R^2.
|
|
def fun(x):
|
|
return np.sqrt(x[1])
|
|
|
|
def f_eqcon(x):
|
|
""" Equality constraint """
|
|
return x[1] - (2 * x[0]) ** 3
|
|
|
|
def f_eqcon2(x):
|
|
""" Equality constraint """
|
|
return x[1] - (-x[0] + 1) ** 3
|
|
|
|
c1 = {'type': 'eq', 'fun': f_eqcon}
|
|
c2 = {'type': 'eq', 'fun': f_eqcon2}
|
|
|
|
res = minimize(fun, [8, 0.25], method='SLSQP',
|
|
constraints=[c1, c2], bounds=[(-0.5, 1), (0, 8)])
|
|
|
|
np.testing.assert_allclose(res.fun, 0.5443310539518)
|
|
np.testing.assert_allclose(res.x, [0.33333333, 0.2962963])
|
|
assert res.success
|
|
|
|
def test_gh9640(self):
|
|
np.random.seed(10)
|
|
cons = ({'type': 'ineq', 'fun': lambda x: -x[0] - x[1] - 3},
|
|
{'type': 'ineq', 'fun': lambda x: x[1] + x[2] - 2})
|
|
bnds = ((-2, 2), (-2, 2), (-2, 2))
|
|
|
|
def target(x):
|
|
return 1
|
|
x0 = [-1.8869783504471584, -0.640096352696244, -0.8174212253407696]
|
|
res = minimize(target, x0, method='SLSQP', bounds=bnds, constraints=cons,
|
|
options={'disp':False, 'maxiter':10000})
|
|
|
|
# The problem is infeasible, so it cannot succeed
|
|
assert not res.success
|
|
|
|
def test_parameters_stay_within_bounds(self):
|
|
# gh11403. For some problems the SLSQP Fortran code suggests a step
|
|
# outside one of the lower/upper bounds. When this happens
|
|
# approx_derivative complains because it's being asked to evaluate
|
|
# a gradient outside its domain.
|
|
np.random.seed(1)
|
|
bounds = Bounds(np.array([0.1]), np.array([1.0]))
|
|
n_inputs = len(bounds.lb)
|
|
x0 = np.array(bounds.lb + (bounds.ub - bounds.lb) *
|
|
np.random.random(n_inputs))
|
|
|
|
def f(x):
|
|
assert (x >= bounds.lb).all()
|
|
return np.linalg.norm(x)
|
|
|
|
with pytest.warns(RuntimeWarning, match='x were outside bounds'):
|
|
res = minimize(f, x0, method='SLSQP', bounds=bounds)
|
|
assert res.success
|