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2212 lines
85 KiB
Python
2212 lines
85 KiB
Python
"""
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Unit tests for optimization routines from optimize.py
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Authors:
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Ed Schofield, Nov 2005
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Andrew Straw, April 2008
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To run it in its simplest form::
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nosetests test_optimize.py
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"""
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import itertools
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import numpy as np
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from numpy.testing import (assert_allclose, assert_equal,
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assert_, assert_almost_equal,
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assert_no_warnings, assert_warns,
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assert_array_less, suppress_warnings)
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import pytest
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from pytest import raises as assert_raises
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from scipy import optimize
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from scipy.optimize._minimize import MINIMIZE_METHODS, MINIMIZE_SCALAR_METHODS
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from scipy.optimize._linprog import LINPROG_METHODS
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from scipy.optimize._root import ROOT_METHODS
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from scipy.optimize._root_scalar import ROOT_SCALAR_METHODS
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from scipy.optimize._qap import QUADRATIC_ASSIGNMENT_METHODS
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from scipy.optimize._differentiable_functions import ScalarFunction
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from scipy.optimize.optimize import MemoizeJac, show_options
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def test_check_grad():
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# Verify if check_grad is able to estimate the derivative of the
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# logistic function.
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def logit(x):
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return 1 / (1 + np.exp(-x))
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def der_logit(x):
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return np.exp(-x) / (1 + np.exp(-x))**2
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x0 = np.array([1.5])
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r = optimize.check_grad(logit, der_logit, x0)
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assert_almost_equal(r, 0)
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r = optimize.check_grad(logit, der_logit, x0, epsilon=1e-6)
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assert_almost_equal(r, 0)
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# Check if the epsilon parameter is being considered.
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r = abs(optimize.check_grad(logit, der_logit, x0, epsilon=1e-1) - 0)
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assert_(r > 1e-7)
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class CheckOptimize(object):
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""" Base test case for a simple constrained entropy maximization problem
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(the machine translation example of Berger et al in
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Computational Linguistics, vol 22, num 1, pp 39--72, 1996.)
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"""
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def setup_method(self):
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self.F = np.array([[1, 1, 1],
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[1, 1, 0],
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[1, 0, 1],
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[1, 0, 0],
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[1, 0, 0]])
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self.K = np.array([1., 0.3, 0.5])
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self.startparams = np.zeros(3, np.float64)
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self.solution = np.array([0., -0.524869316, 0.487525860])
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self.maxiter = 1000
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self.funccalls = 0
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self.gradcalls = 0
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self.trace = []
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def func(self, x):
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self.funccalls += 1
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if self.funccalls > 6000:
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raise RuntimeError("too many iterations in optimization routine")
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log_pdot = np.dot(self.F, x)
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logZ = np.log(sum(np.exp(log_pdot)))
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f = logZ - np.dot(self.K, x)
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self.trace.append(np.copy(x))
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return f
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def grad(self, x):
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self.gradcalls += 1
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log_pdot = np.dot(self.F, x)
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logZ = np.log(sum(np.exp(log_pdot)))
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p = np.exp(log_pdot - logZ)
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return np.dot(self.F.transpose(), p) - self.K
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def hess(self, x):
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log_pdot = np.dot(self.F, x)
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logZ = np.log(sum(np.exp(log_pdot)))
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p = np.exp(log_pdot - logZ)
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return np.dot(self.F.T,
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np.dot(np.diag(p), self.F - np.dot(self.F.T, p)))
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def hessp(self, x, p):
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return np.dot(self.hess(x), p)
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class CheckOptimizeParameterized(CheckOptimize):
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def test_cg(self):
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# conjugate gradient optimization routine
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': self.disp,
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'return_all': False}
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res = optimize.minimize(self.func, self.startparams, args=(),
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method='CG', jac=self.grad,
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options=opts)
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params, fopt, func_calls, grad_calls, warnflag = \
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res['x'], res['fun'], res['nfev'], res['njev'], res['status']
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else:
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retval = optimize.fmin_cg(self.func, self.startparams,
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self.grad, (), maxiter=self.maxiter,
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full_output=True, disp=self.disp,
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retall=False)
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(params, fopt, func_calls, grad_calls, warnflag) = retval
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'; these are from
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# SciPy 0.7.0. Don't allow them to increase.
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assert_(self.funccalls == 9, self.funccalls)
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assert_(self.gradcalls == 7, self.gradcalls)
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# Ensure that the function behaves the same; this is from SciPy 0.7.0
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assert_allclose(self.trace[2:4],
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[[0, -0.5, 0.5],
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[0, -5.05700028e-01, 4.95985862e-01]],
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atol=1e-14, rtol=1e-7)
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def test_cg_cornercase(self):
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def f(r):
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return 2.5 * (1 - np.exp(-1.5*(r - 0.5)))**2
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# Check several initial guesses. (Too far away from the
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# minimum, the function ends up in the flat region of exp.)
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for x0 in np.linspace(-0.75, 3, 71):
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sol = optimize.minimize(f, [x0], method='CG')
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assert_(sol.success)
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assert_allclose(sol.x, [0.5], rtol=1e-5)
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def test_bfgs(self):
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# Broyden-Fletcher-Goldfarb-Shanno optimization routine
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': self.disp,
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'return_all': False}
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res = optimize.minimize(self.func, self.startparams,
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jac=self.grad, method='BFGS', args=(),
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options=opts)
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params, fopt, gopt, Hopt, func_calls, grad_calls, warnflag = (
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res['x'], res['fun'], res['jac'], res['hess_inv'],
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res['nfev'], res['njev'], res['status'])
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else:
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retval = optimize.fmin_bfgs(self.func, self.startparams, self.grad,
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args=(), maxiter=self.maxiter,
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full_output=True, disp=self.disp,
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retall=False)
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(params, fopt, gopt, Hopt,
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func_calls, grad_calls, warnflag) = retval
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'; these are from
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# SciPy 0.7.0. Don't allow them to increase.
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assert_(self.funccalls == 10, self.funccalls)
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assert_(self.gradcalls == 8, self.gradcalls)
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# Ensure that the function behaves the same; this is from SciPy 0.7.0
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assert_allclose(self.trace[6:8],
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[[0, -5.25060743e-01, 4.87748473e-01],
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[0, -5.24885582e-01, 4.87530347e-01]],
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atol=1e-14, rtol=1e-7)
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def test_bfgs_infinite(self):
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# Test corner case where -Inf is the minimum. See gh-2019.
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func = lambda x: -np.e**-x
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fprime = lambda x: -func(x)
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x0 = [0]
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with np.errstate(over='ignore'):
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if self.use_wrapper:
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opts = {'disp': self.disp}
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x = optimize.minimize(func, x0, jac=fprime, method='BFGS',
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args=(), options=opts)['x']
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else:
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x = optimize.fmin_bfgs(func, x0, fprime, disp=self.disp)
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assert_(not np.isfinite(func(x)))
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def test_powell(self):
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# Powell (direction set) optimization routine
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': self.disp,
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'return_all': False}
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res = optimize.minimize(self.func, self.startparams, args=(),
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method='Powell', options=opts)
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params, fopt, direc, numiter, func_calls, warnflag = (
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res['x'], res['fun'], res['direc'], res['nit'],
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res['nfev'], res['status'])
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else:
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retval = optimize.fmin_powell(self.func, self.startparams,
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args=(), maxiter=self.maxiter,
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full_output=True, disp=self.disp,
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retall=False)
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(params, fopt, direc, numiter, func_calls, warnflag) = retval
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'; these are from
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# SciPy 0.7.0. Don't allow them to increase.
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#
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# However, some leeway must be added: the exact evaluation
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# count is sensitive to numerical error, and floating-point
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# computations are not bit-for-bit reproducible across
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# machines, and when using e.g., MKL, data alignment
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# etc., affect the rounding error.
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#
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assert_(self.funccalls <= 116 + 20, self.funccalls)
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assert_(self.gradcalls == 0, self.gradcalls)
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# Ensure that the function behaves the same; this is from SciPy 0.7.0
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assert_allclose(self.trace[34:39],
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[[0.72949016, -0.44156936, 0.47100962],
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[0.72949016, -0.44156936, 0.48052496],
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[1.45898031, -0.88313872, 0.95153458],
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[0.72949016, -0.44156936, 0.47576729],
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[1.72949016, -0.44156936, 0.47576729]],
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atol=1e-14, rtol=1e-7)
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def test_powell_bounded(self):
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# Powell (direction set) optimization routine
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# same as test_powell above, but with bounds
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bounds = [(-np.pi, np.pi) for _ in self.startparams]
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': self.disp,
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'return_all': False}
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res = optimize.minimize(self.func, self.startparams, args=(),
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bounds=bounds,
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method='Powell', options=opts)
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params, fopt, direc, numiter, func_calls, warnflag = (
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res['x'], res['fun'], res['direc'], res['nit'],
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res['nfev'], res['status'])
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assert func_calls == self.funccalls
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'.
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# Generally, this takes 131 function calls. However, on some CI
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# checks it finds 138 funccalls. This 20 call leeway was also
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# included in the test_powell function.
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# The exact evaluation count is sensitive to numerical error, and
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# floating-point computations are not bit-for-bit reproducible
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# across machines, and when using e.g. MKL, data alignment etc.
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# affect the rounding error.
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assert self.funccalls <= 131 + 20
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assert self.gradcalls == 0
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def test_neldermead(self):
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# Nelder-Mead simplex algorithm
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': self.disp,
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'return_all': False}
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res = optimize.minimize(self.func, self.startparams, args=(),
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method='Nelder-mead', options=opts)
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params, fopt, numiter, func_calls, warnflag = (
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res['x'], res['fun'], res['nit'], res['nfev'],
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res['status'])
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else:
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retval = optimize.fmin(self.func, self.startparams,
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args=(), maxiter=self.maxiter,
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full_output=True, disp=self.disp,
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retall=False)
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(params, fopt, numiter, func_calls, warnflag) = retval
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'; these are from
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# SciPy 0.7.0. Don't allow them to increase.
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assert_(self.funccalls == 167, self.funccalls)
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assert_(self.gradcalls == 0, self.gradcalls)
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# Ensure that the function behaves the same; this is from SciPy 0.7.0
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assert_allclose(self.trace[76:78],
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[[0.1928968, -0.62780447, 0.35166118],
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[0.19572515, -0.63648426, 0.35838135]],
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atol=1e-14, rtol=1e-7)
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def test_neldermead_initial_simplex(self):
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# Nelder-Mead simplex algorithm
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simplex = np.zeros((4, 3))
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simplex[...] = self.startparams
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for j in range(3):
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simplex[j+1, j] += 0.1
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': False,
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'return_all': True, 'initial_simplex': simplex}
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res = optimize.minimize(self.func, self.startparams, args=(),
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method='Nelder-mead', options=opts)
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params, fopt, numiter, func_calls, warnflag = (res['x'],
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res['fun'],
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res['nit'],
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res['nfev'],
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res['status'])
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assert_allclose(res['allvecs'][0], simplex[0])
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else:
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retval = optimize.fmin(self.func, self.startparams,
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args=(), maxiter=self.maxiter,
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full_output=True, disp=False, retall=False,
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initial_simplex=simplex)
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(params, fopt, numiter, func_calls, warnflag) = retval
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assert_allclose(self.func(params), self.func(self.solution),
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atol=1e-6)
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# Ensure that function call counts are 'known good'; these are from
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# SciPy 0.17.0. Don't allow them to increase.
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assert_(self.funccalls == 100, self.funccalls)
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assert_(self.gradcalls == 0, self.gradcalls)
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# Ensure that the function behaves the same; this is from SciPy 0.15.0
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assert_allclose(self.trace[50:52],
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[[0.14687474, -0.5103282, 0.48252111],
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[0.14474003, -0.5282084, 0.48743951]],
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atol=1e-14, rtol=1e-7)
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def test_neldermead_initial_simplex_bad(self):
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# Check it fails with a bad simplices
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bad_simplices = []
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simplex = np.zeros((3, 2))
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simplex[...] = self.startparams[:2]
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for j in range(2):
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simplex[j+1, j] += 0.1
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bad_simplices.append(simplex)
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|
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simplex = np.zeros((3, 3))
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bad_simplices.append(simplex)
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for simplex in bad_simplices:
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if self.use_wrapper:
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opts = {'maxiter': self.maxiter, 'disp': False,
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'return_all': False, 'initial_simplex': simplex}
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assert_raises(ValueError,
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optimize.minimize,
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self.func,
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self.startparams,
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args=(),
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method='Nelder-mead',
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options=opts)
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else:
|
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assert_raises(ValueError, optimize.fmin,
|
|
self.func, self.startparams,
|
|
args=(), maxiter=self.maxiter,
|
|
full_output=True, disp=False, retall=False,
|
|
initial_simplex=simplex)
|
|
|
|
def test_ncg_negative_maxiter(self):
|
|
# Regression test for gh-8241
|
|
opts = {'maxiter': -1}
|
|
result = optimize.minimize(self.func, self.startparams,
|
|
method='Newton-CG', jac=self.grad,
|
|
args=(), options=opts)
|
|
assert_(result.status == 1)
|
|
|
|
def test_ncg(self):
|
|
# line-search Newton conjugate gradient optimization routine
|
|
if self.use_wrapper:
|
|
opts = {'maxiter': self.maxiter, 'disp': self.disp,
|
|
'return_all': False}
|
|
retval = optimize.minimize(self.func, self.startparams,
|
|
method='Newton-CG', jac=self.grad,
|
|
args=(), options=opts)['x']
|
|
else:
|
|
retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,
|
|
args=(), maxiter=self.maxiter,
|
|
full_output=False, disp=self.disp,
|
|
retall=False)
|
|
|
|
params = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
# Ensure that function call counts are 'known good'; these are from
|
|
# SciPy 0.7.0. Don't allow them to increase.
|
|
assert_(self.funccalls == 7, self.funccalls)
|
|
assert_(self.gradcalls <= 22, self.gradcalls) # 0.13.0
|
|
# assert_(self.gradcalls <= 18, self.gradcalls) # 0.9.0
|
|
# assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0
|
|
# assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0
|
|
|
|
# Ensure that the function behaves the same; this is from SciPy 0.7.0
|
|
assert_allclose(self.trace[3:5],
|
|
[[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],
|
|
[-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],
|
|
atol=1e-6, rtol=1e-7)
|
|
|
|
def test_ncg_hess(self):
|
|
# Newton conjugate gradient with Hessian
|
|
if self.use_wrapper:
|
|
opts = {'maxiter': self.maxiter, 'disp': self.disp,
|
|
'return_all': False}
|
|
retval = optimize.minimize(self.func, self.startparams,
|
|
method='Newton-CG', jac=self.grad,
|
|
hess=self.hess,
|
|
args=(), options=opts)['x']
|
|
else:
|
|
retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,
|
|
fhess=self.hess,
|
|
args=(), maxiter=self.maxiter,
|
|
full_output=False, disp=self.disp,
|
|
retall=False)
|
|
|
|
params = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
# Ensure that function call counts are 'known good'; these are from
|
|
# SciPy 0.7.0. Don't allow them to increase.
|
|
assert_(self.funccalls <= 7, self.funccalls) # gh10673
|
|
assert_(self.gradcalls <= 18, self.gradcalls) # 0.9.0
|
|
# assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0
|
|
# assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0
|
|
|
|
# Ensure that the function behaves the same; this is from SciPy 0.7.0
|
|
assert_allclose(self.trace[3:5],
|
|
[[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],
|
|
[-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],
|
|
atol=1e-6, rtol=1e-7)
|
|
|
|
def test_ncg_hessp(self):
|
|
# Newton conjugate gradient with Hessian times a vector p.
|
|
if self.use_wrapper:
|
|
opts = {'maxiter': self.maxiter, 'disp': self.disp,
|
|
'return_all': False}
|
|
retval = optimize.minimize(self.func, self.startparams,
|
|
method='Newton-CG', jac=self.grad,
|
|
hessp=self.hessp,
|
|
args=(), options=opts)['x']
|
|
else:
|
|
retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,
|
|
fhess_p=self.hessp,
|
|
args=(), maxiter=self.maxiter,
|
|
full_output=False, disp=self.disp,
|
|
retall=False)
|
|
|
|
params = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
# Ensure that function call counts are 'known good'; these are from
|
|
# SciPy 0.7.0. Don't allow them to increase.
|
|
assert_(self.funccalls <= 7, self.funccalls) # gh10673
|
|
assert_(self.gradcalls <= 18, self.gradcalls) # 0.9.0
|
|
# assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0
|
|
# assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0
|
|
|
|
# Ensure that the function behaves the same; this is from SciPy 0.7.0
|
|
assert_allclose(self.trace[3:5],
|
|
[[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],
|
|
[-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],
|
|
atol=1e-6, rtol=1e-7)
|
|
|
|
|
|
def test_obj_func_returns_scalar():
|
|
match = ("The user-provided "
|
|
"objective function must "
|
|
"return a scalar value.")
|
|
with assert_raises(ValueError, match=match):
|
|
optimize.minimize(lambda x: x, np.array([1, 1]), method='BFGS')
|
|
|
|
def test_neldermead_xatol_fatol():
|
|
# gh4484
|
|
# test we can call with fatol, xatol specified
|
|
func = lambda x: x[0]**2 + x[1]**2
|
|
|
|
optimize._minimize._minimize_neldermead(func, [1, 1], maxiter=2,
|
|
xatol=1e-3, fatol=1e-3)
|
|
assert_warns(DeprecationWarning,
|
|
optimize._minimize._minimize_neldermead,
|
|
func, [1, 1], xtol=1e-3, ftol=1e-3, maxiter=2)
|
|
|
|
|
|
def test_neldermead_adaptive():
|
|
func = lambda x: np.sum(x**2)
|
|
p0 = [0.15746215, 0.48087031, 0.44519198, 0.4223638, 0.61505159,
|
|
0.32308456, 0.9692297, 0.4471682, 0.77411992, 0.80441652,
|
|
0.35994957, 0.75487856, 0.99973421, 0.65063887, 0.09626474]
|
|
|
|
res = optimize.minimize(func, p0, method='Nelder-Mead')
|
|
assert_equal(res.success, False)
|
|
|
|
res = optimize.minimize(func, p0, method='Nelder-Mead',
|
|
options={'adaptive': True})
|
|
assert_equal(res.success, True)
|
|
|
|
|
|
def test_bounded_powell_outsidebounds():
|
|
# With the bounded Powell method if you start outside the bounds the final
|
|
# should still be within the bounds (provided that the user doesn't make a
|
|
# bad choice for the `direc` argument).
|
|
func = lambda x: np.sum(x**2)
|
|
bounds = (-1, 1), (-1, 1), (-1, 1)
|
|
x0 = [-4, .5, -.8]
|
|
|
|
# we're starting outside the bounds, so we should get a warning
|
|
with assert_warns(optimize.OptimizeWarning):
|
|
res = optimize.minimize(func, x0, bounds=bounds, method="Powell")
|
|
assert_allclose(res.x, np.array([0.] * len(x0)), atol=1e-6)
|
|
assert_equal(res.success, True)
|
|
assert_equal(res.status, 0)
|
|
|
|
# However, now if we change the `direc` argument such that the
|
|
# set of vectors does not span the parameter space, then we may
|
|
# not end up back within the bounds. Here we see that the first
|
|
# parameter cannot be updated!
|
|
direc = [[0, 0, 0], [0, 1, 0], [0, 0, 1]]
|
|
# we're starting outside the bounds, so we should get a warning
|
|
with assert_warns(optimize.OptimizeWarning):
|
|
res = optimize.minimize(func, x0,
|
|
bounds=bounds, method="Powell",
|
|
options={'direc': direc})
|
|
assert_allclose(res.x, np.array([-4., 0, 0]), atol=1e-6)
|
|
assert_equal(res.success, False)
|
|
assert_equal(res.status, 4)
|
|
|
|
|
|
def test_bounded_powell_vs_powell():
|
|
# here we test an example where the bounded Powell method
|
|
# will return a different result than the standard Powell
|
|
# method.
|
|
|
|
# first we test a simple example where the minimum is at
|
|
# the origin and the minimum that is within the bounds is
|
|
# larger than the minimum at the origin.
|
|
func = lambda x: np.sum(x**2)
|
|
bounds = (-5, -1), (-10, -0.1), (1, 9.2), (-4, 7.6), (-15.9, -2)
|
|
x0 = [-2.1, -5.2, 1.9, 0, -2]
|
|
|
|
options = {'ftol': 1e-10, 'xtol': 1e-10}
|
|
|
|
res_powell = optimize.minimize(func, x0, method="Powell", options=options)
|
|
assert_allclose(res_powell.x, 0., atol=1e-6)
|
|
assert_allclose(res_powell.fun, 0., atol=1e-6)
|
|
|
|
res_bounded_powell = optimize.minimize(func, x0, options=options,
|
|
bounds=bounds,
|
|
method="Powell")
|
|
p = np.array([-1, -0.1, 1, 0, -2])
|
|
assert_allclose(res_bounded_powell.x, p, atol=1e-6)
|
|
assert_allclose(res_bounded_powell.fun, func(p), atol=1e-6)
|
|
|
|
# now we test bounded Powell but with a mix of inf bounds.
|
|
bounds = (None, -1), (-np.inf, -.1), (1, np.inf), (-4, None), (-15.9, -2)
|
|
res_bounded_powell = optimize.minimize(func, x0, options=options,
|
|
bounds=bounds,
|
|
method="Powell")
|
|
p = np.array([-1, -0.1, 1, 0, -2])
|
|
assert_allclose(res_bounded_powell.x, p, atol=1e-6)
|
|
assert_allclose(res_bounded_powell.fun, func(p), atol=1e-6)
|
|
|
|
# next we test an example where the global minimum is within
|
|
# the bounds, but the bounded Powell method performs better
|
|
# than the standard Powell method.
|
|
def func(x):
|
|
t = np.sin(-x[0]) * np.cos(x[1]) * np.sin(-x[0] * x[1]) * np.cos(x[1])
|
|
t -= np.cos(np.sin(x[1] * x[2]) * np.cos(x[2]))
|
|
return t**2
|
|
|
|
bounds = [(-2, 5)] * 3
|
|
x0 = [-0.5, -0.5, -0.5]
|
|
|
|
res_powell = optimize.minimize(func, x0, method="Powell")
|
|
res_bounded_powell = optimize.minimize(func, x0,
|
|
bounds=bounds,
|
|
method="Powell")
|
|
assert_allclose(res_powell.fun, 0.007136253919761627, atol=1e-6)
|
|
assert_allclose(res_bounded_powell.fun, 0, atol=1e-6)
|
|
|
|
# next we test the previous example where the we provide Powell
|
|
# with (-inf, inf) bounds, and compare it to providing Powell
|
|
# with no bounds. They should end up the same.
|
|
bounds = [(-np.inf, np.inf)] * 3
|
|
|
|
res_bounded_powell = optimize.minimize(func, x0,
|
|
bounds=bounds,
|
|
method="Powell")
|
|
assert_allclose(res_powell.fun, res_bounded_powell.fun, atol=1e-6)
|
|
assert_allclose(res_powell.nfev, res_bounded_powell.nfev, atol=1e-6)
|
|
assert_allclose(res_powell.x, res_bounded_powell.x, atol=1e-6)
|
|
|
|
# now test when x0 starts outside of the bounds.
|
|
x0 = [45.46254415, -26.52351498, 31.74830248]
|
|
bounds = [(-2, 5)] * 3
|
|
# we're starting outside the bounds, so we should get a warning
|
|
with assert_warns(optimize.OptimizeWarning):
|
|
res_bounded_powell = optimize.minimize(func, x0,
|
|
bounds=bounds,
|
|
method="Powell")
|
|
assert_allclose(res_bounded_powell.fun, 0, atol=1e-6)
|
|
|
|
|
|
def test_onesided_bounded_powell_stability():
|
|
# When the Powell method is bounded on only one side, a
|
|
# np.tan transform is done in order to convert it into a
|
|
# completely bounded problem. Here we do some simple tests
|
|
# of one-sided bounded Powell where the optimal solutions
|
|
# are large to test the stability of the transformation.
|
|
kwargs = {'method': 'Powell',
|
|
'bounds': [(-np.inf, 1e6)] * 3,
|
|
'options': {'ftol': 1e-8, 'xtol': 1e-8}}
|
|
x0 = [1, 1, 1]
|
|
|
|
# df/dx is constant.
|
|
f = lambda x: -np.sum(x)
|
|
res = optimize.minimize(f, x0, **kwargs)
|
|
assert_allclose(res.fun, -3e6, atol=1e-4)
|
|
|
|
# df/dx gets smaller and smaller.
|
|
def f(x):
|
|
return -np.abs(np.sum(x)) ** (0.1) * (1 if np.all(x > 0) else -1)
|
|
|
|
res = optimize.minimize(f, x0, **kwargs)
|
|
assert_allclose(res.fun, -(3e6) ** (0.1))
|
|
|
|
# df/dx gets larger and larger.
|
|
def f(x):
|
|
return -np.abs(np.sum(x)) ** 10 * (1 if np.all(x > 0) else -1)
|
|
|
|
res = optimize.minimize(f, x0, **kwargs)
|
|
assert_allclose(res.fun, -(3e6) ** 10, rtol=1e-7)
|
|
|
|
# df/dx gets larger for some of the variables and smaller for others.
|
|
def f(x):
|
|
t = -np.abs(np.sum(x[:2])) ** 5 - np.abs(np.sum(x[2:])) ** (0.1)
|
|
t *= (1 if np.all(x > 0) else -1)
|
|
return t
|
|
|
|
kwargs['bounds'] = [(-np.inf, 1e3)] * 3
|
|
res = optimize.minimize(f, x0, **kwargs)
|
|
assert_allclose(res.fun, -(2e3) ** 5 - (1e6) ** (0.1), rtol=1e-7)
|
|
|
|
|
|
class TestOptimizeWrapperDisp(CheckOptimizeParameterized):
|
|
use_wrapper = True
|
|
disp = True
|
|
|
|
|
|
class TestOptimizeWrapperNoDisp(CheckOptimizeParameterized):
|
|
use_wrapper = True
|
|
disp = False
|
|
|
|
|
|
class TestOptimizeNoWrapperDisp(CheckOptimizeParameterized):
|
|
use_wrapper = False
|
|
disp = True
|
|
|
|
|
|
class TestOptimizeNoWrapperNoDisp(CheckOptimizeParameterized):
|
|
use_wrapper = False
|
|
disp = False
|
|
|
|
|
|
class TestOptimizeSimple(CheckOptimize):
|
|
|
|
def test_bfgs_nan(self):
|
|
# Test corner case where nan is fed to optimizer. See gh-2067.
|
|
func = lambda x: x
|
|
fprime = lambda x: np.ones_like(x)
|
|
x0 = [np.nan]
|
|
with np.errstate(over='ignore', invalid='ignore'):
|
|
x = optimize.fmin_bfgs(func, x0, fprime, disp=False)
|
|
assert_(np.isnan(func(x)))
|
|
|
|
def test_bfgs_nan_return(self):
|
|
# Test corner cases where fun returns NaN. See gh-4793.
|
|
|
|
# First case: NaN from first call.
|
|
func = lambda x: np.nan
|
|
with np.errstate(invalid='ignore'):
|
|
result = optimize.minimize(func, 0)
|
|
|
|
assert_(np.isnan(result['fun']))
|
|
assert_(result['success'] is False)
|
|
|
|
# Second case: NaN from second call.
|
|
func = lambda x: 0 if x == 0 else np.nan
|
|
fprime = lambda x: np.ones_like(x) # Steer away from zero.
|
|
with np.errstate(invalid='ignore'):
|
|
result = optimize.minimize(func, 0, jac=fprime)
|
|
|
|
assert_(np.isnan(result['fun']))
|
|
assert_(result['success'] is False)
|
|
|
|
def test_bfgs_numerical_jacobian(self):
|
|
# BFGS with numerical Jacobian and a vector epsilon parameter.
|
|
# define the epsilon parameter using a random vector
|
|
epsilon = np.sqrt(np.spacing(1.)) * np.random.rand(len(self.solution))
|
|
|
|
params = optimize.fmin_bfgs(self.func, self.startparams,
|
|
epsilon=epsilon, args=(),
|
|
maxiter=self.maxiter, disp=False)
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
def test_finite_differences(self):
|
|
methods = ['BFGS', 'CG', 'TNC']
|
|
jacs = ['2-point', '3-point', None]
|
|
for method, jac in itertools.product(methods, jacs):
|
|
result = optimize.minimize(self.func, self.startparams,
|
|
method=method, jac=jac)
|
|
assert_allclose(self.func(result.x), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
def test_bfgs_gh_2169(self):
|
|
def f(x):
|
|
if x < 0:
|
|
return 1.79769313e+308
|
|
else:
|
|
return x + 1./x
|
|
xs = optimize.fmin_bfgs(f, [10.], disp=False)
|
|
assert_allclose(xs, 1.0, rtol=1e-4, atol=1e-4)
|
|
|
|
def test_bfgs_double_evaluations(self):
|
|
# check BFGS does not evaluate twice in a row at same point
|
|
def f(x):
|
|
xp = float(x)
|
|
assert xp not in seen
|
|
seen.add(xp)
|
|
return 10*x**2, 20*x
|
|
|
|
seen = set()
|
|
optimize.minimize(f, -100, method='bfgs', jac=True, tol=1e-7)
|
|
|
|
def test_l_bfgs_b(self):
|
|
# limited-memory bound-constrained BFGS algorithm
|
|
retval = optimize.fmin_l_bfgs_b(self.func, self.startparams,
|
|
self.grad, args=(),
|
|
maxiter=self.maxiter)
|
|
|
|
(params, fopt, d) = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
# Ensure that function call counts are 'known good'; these are from
|
|
# SciPy 0.7.0. Don't allow them to increase.
|
|
assert_(self.funccalls == 7, self.funccalls)
|
|
assert_(self.gradcalls == 5, self.gradcalls)
|
|
|
|
# Ensure that the function behaves the same; this is from SciPy 0.7.0
|
|
# test fixed in gh10673
|
|
assert_allclose(self.trace[3:5],
|
|
[[8.117083e-16, -5.196198e-01, 4.897617e-01],
|
|
[0., -0.52489628, 0.48753042]],
|
|
atol=1e-14, rtol=1e-7)
|
|
|
|
def test_l_bfgs_b_numjac(self):
|
|
# L-BFGS-B with numerical Jacobian
|
|
retval = optimize.fmin_l_bfgs_b(self.func, self.startparams,
|
|
approx_grad=True,
|
|
maxiter=self.maxiter)
|
|
|
|
(params, fopt, d) = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
def test_l_bfgs_b_funjac(self):
|
|
# L-BFGS-B with combined objective function and Jacobian
|
|
def fun(x):
|
|
return self.func(x), self.grad(x)
|
|
|
|
retval = optimize.fmin_l_bfgs_b(fun, self.startparams,
|
|
maxiter=self.maxiter)
|
|
|
|
(params, fopt, d) = retval
|
|
|
|
assert_allclose(self.func(params), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
def test_l_bfgs_b_maxiter(self):
|
|
# gh7854
|
|
# Ensure that not more than maxiters are ever run.
|
|
class Callback(object):
|
|
def __init__(self):
|
|
self.nit = 0
|
|
self.fun = None
|
|
self.x = None
|
|
|
|
def __call__(self, x):
|
|
self.x = x
|
|
self.fun = optimize.rosen(x)
|
|
self.nit += 1
|
|
|
|
c = Callback()
|
|
res = optimize.minimize(optimize.rosen, [0., 0.], method='l-bfgs-b',
|
|
callback=c, options={'maxiter': 5})
|
|
|
|
assert_equal(res.nit, 5)
|
|
assert_almost_equal(res.x, c.x)
|
|
assert_almost_equal(res.fun, c.fun)
|
|
assert_equal(res.status, 1)
|
|
assert_(res.success is False)
|
|
assert_equal(res.message,
|
|
'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT')
|
|
|
|
def test_minimize_l_bfgs_b(self):
|
|
# Minimize with L-BFGS-B method
|
|
opts = {'disp': False, 'maxiter': self.maxiter}
|
|
r = optimize.minimize(self.func, self.startparams,
|
|
method='L-BFGS-B', jac=self.grad,
|
|
options=opts)
|
|
assert_allclose(self.func(r.x), self.func(self.solution),
|
|
atol=1e-6)
|
|
assert self.gradcalls == r.njev
|
|
|
|
self.funccalls = self.gradcalls = 0
|
|
# approximate jacobian
|
|
ra = optimize.minimize(self.func, self.startparams,
|
|
method='L-BFGS-B', options=opts)
|
|
# check that function evaluations in approximate jacobian are counted
|
|
# assert_(ra.nfev > r.nfev)
|
|
assert self.funccalls == ra.nfev
|
|
assert_allclose(self.func(ra.x), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
self.funccalls = self.gradcalls = 0
|
|
# approximate jacobian
|
|
ra = optimize.minimize(self.func, self.startparams, jac='3-point',
|
|
method='L-BFGS-B', options=opts)
|
|
assert self.funccalls == ra.nfev
|
|
assert_allclose(self.func(ra.x), self.func(self.solution),
|
|
atol=1e-6)
|
|
|
|
def test_minimize_l_bfgs_b_ftol(self):
|
|
# Check that the `ftol` parameter in l_bfgs_b works as expected
|
|
v0 = None
|
|
for tol in [1e-1, 1e-4, 1e-7, 1e-10]:
|
|
opts = {'disp': False, 'maxiter': self.maxiter, 'ftol': tol}
|
|
sol = optimize.minimize(self.func, self.startparams,
|
|
method='L-BFGS-B', jac=self.grad,
|
|
options=opts)
|
|
v = self.func(sol.x)
|
|
|
|
if v0 is None:
|
|
v0 = v
|
|
else:
|
|
assert_(v < v0)
|
|
|
|
assert_allclose(v, self.func(self.solution), rtol=tol)
|
|
|
|
def test_minimize_l_bfgs_maxls(self):
|
|
# check that the maxls is passed down to the Fortran routine
|
|
sol = optimize.minimize(optimize.rosen, np.array([-1.2, 1.0]),
|
|
method='L-BFGS-B', jac=optimize.rosen_der,
|
|
options={'disp': False, 'maxls': 1})
|
|
assert_(not sol.success)
|
|
|
|
def test_minimize_l_bfgs_b_maxfun_interruption(self):
|
|
# gh-6162
|
|
f = optimize.rosen
|
|
g = optimize.rosen_der
|
|
values = []
|
|
x0 = np.full(7, 1000)
|
|
|
|
def objfun(x):
|
|
value = f(x)
|
|
values.append(value)
|
|
return value
|
|
|
|
# Look for an interesting test case.
|
|
# Request a maxfun that stops at a particularly bad function
|
|
# evaluation somewhere between 100 and 300 evaluations.
|
|
low, medium, high = 30, 100, 300
|
|
optimize.fmin_l_bfgs_b(objfun, x0, fprime=g, maxfun=high)
|
|
v, k = max((y, i) for i, y in enumerate(values[medium:]))
|
|
maxfun = medium + k
|
|
# If the minimization strategy is reasonable,
|
|
# the minimize() result should not be worse than the best
|
|
# of the first 30 function evaluations.
|
|
target = min(values[:low])
|
|
xmin, fmin, d = optimize.fmin_l_bfgs_b(f, x0, fprime=g, maxfun=maxfun)
|
|
assert_array_less(fmin, target)
|
|
|
|
def test_custom(self):
|
|
# This function comes from the documentation example.
|
|
def custmin(fun, x0, args=(), maxfev=None, stepsize=0.1,
|
|
maxiter=100, callback=None, **options):
|
|
bestx = x0
|
|
besty = fun(x0)
|
|
funcalls = 1
|
|
niter = 0
|
|
improved = True
|
|
stop = False
|
|
|
|
while improved and not stop and niter < maxiter:
|
|
improved = False
|
|
niter += 1
|
|
for dim in range(np.size(x0)):
|
|
for s in [bestx[dim] - stepsize, bestx[dim] + stepsize]:
|
|
testx = np.copy(bestx)
|
|
testx[dim] = s
|
|
testy = fun(testx, *args)
|
|
funcalls += 1
|
|
if testy < besty:
|
|
besty = testy
|
|
bestx = testx
|
|
improved = True
|
|
if callback is not None:
|
|
callback(bestx)
|
|
if maxfev is not None and funcalls >= maxfev:
|
|
stop = True
|
|
break
|
|
|
|
return optimize.OptimizeResult(fun=besty, x=bestx, nit=niter,
|
|
nfev=funcalls, success=(niter > 1))
|
|
|
|
x0 = [1.35, 0.9, 0.8, 1.1, 1.2]
|
|
res = optimize.minimize(optimize.rosen, x0, method=custmin,
|
|
options=dict(stepsize=0.05))
|
|
assert_allclose(res.x, 1.0, rtol=1e-4, atol=1e-4)
|
|
|
|
def test_gh10771(self):
|
|
# check that minimize passes bounds and constraints to a custom
|
|
# minimizer without altering them.
|
|
bounds = [(-2, 2), (0, 3)]
|
|
constraints = 'constraints'
|
|
|
|
def custmin(fun, x0, **options):
|
|
assert options['bounds'] is bounds
|
|
assert options['constraints'] is constraints
|
|
return optimize.OptimizeResult()
|
|
|
|
x0 = [1, 1]
|
|
optimize.minimize(optimize.rosen, x0, method=custmin,
|
|
bounds=bounds, constraints=constraints)
|
|
|
|
def test_minimize_tol_parameter(self):
|
|
# Check that the minimize() tol= argument does something
|
|
def func(z):
|
|
x, y = z
|
|
return x**2*y**2 + x**4 + 1
|
|
|
|
def dfunc(z):
|
|
x, y = z
|
|
return np.array([2*x*y**2 + 4*x**3, 2*x**2*y])
|
|
|
|
for method in ['nelder-mead', 'powell', 'cg', 'bfgs',
|
|
'newton-cg', 'l-bfgs-b', 'tnc',
|
|
'cobyla', 'slsqp']:
|
|
if method in ('nelder-mead', 'powell', 'cobyla'):
|
|
jac = None
|
|
else:
|
|
jac = dfunc
|
|
|
|
sol1 = optimize.minimize(func, [1, 1], jac=jac, tol=1e-10,
|
|
method=method)
|
|
sol2 = optimize.minimize(func, [1, 1], jac=jac, tol=1.0,
|
|
method=method)
|
|
assert_(func(sol1.x) < func(sol2.x),
|
|
"%s: %s vs. %s" % (method, func(sol1.x), func(sol2.x)))
|
|
|
|
@pytest.mark.parametrize('method',
|
|
['fmin', 'fmin_powell', 'fmin_cg', 'fmin_bfgs',
|
|
'fmin_ncg', 'fmin_l_bfgs_b', 'fmin_tnc',
|
|
'fmin_slsqp'] + MINIMIZE_METHODS)
|
|
def test_minimize_callback_copies_array(self, method):
|
|
# Check that arrays passed to callbacks are not modified
|
|
# inplace by the optimizer afterward
|
|
|
|
# cobyla doesn't have callback
|
|
if method == 'cobyla':
|
|
return
|
|
|
|
if method in ('fmin_tnc', 'fmin_l_bfgs_b'):
|
|
func = lambda x: (optimize.rosen(x), optimize.rosen_der(x))
|
|
else:
|
|
func = optimize.rosen
|
|
jac = optimize.rosen_der
|
|
hess = optimize.rosen_hess
|
|
|
|
x0 = np.zeros(10)
|
|
|
|
# Set options
|
|
kwargs = {}
|
|
if method.startswith('fmin'):
|
|
routine = getattr(optimize, method)
|
|
if method == 'fmin_slsqp':
|
|
kwargs['iter'] = 5
|
|
elif method == 'fmin_tnc':
|
|
kwargs['maxfun'] = 100
|
|
else:
|
|
kwargs['maxiter'] = 5
|
|
else:
|
|
def routine(*a, **kw):
|
|
kw['method'] = method
|
|
return optimize.minimize(*a, **kw)
|
|
|
|
if method == 'tnc':
|
|
kwargs['options'] = dict(maxfun=100)
|
|
else:
|
|
kwargs['options'] = dict(maxiter=5)
|
|
|
|
if method in ('fmin_ncg',):
|
|
kwargs['fprime'] = jac
|
|
elif method in ('newton-cg',):
|
|
kwargs['jac'] = jac
|
|
elif method in ('trust-krylov', 'trust-exact', 'trust-ncg', 'dogleg',
|
|
'trust-constr'):
|
|
kwargs['jac'] = jac
|
|
kwargs['hess'] = hess
|
|
|
|
# Run with callback
|
|
results = []
|
|
|
|
def callback(x, *args, **kwargs):
|
|
results.append((x, np.copy(x)))
|
|
|
|
routine(func, x0, callback=callback, **kwargs)
|
|
|
|
# Check returned arrays coincide with their copies
|
|
# and have no memory overlap
|
|
assert_(len(results) > 2)
|
|
assert_(all(np.all(x == y) for x, y in results))
|
|
assert_(not any(np.may_share_memory(x[0], y[0])
|
|
for x, y in itertools.combinations(results, 2)))
|
|
|
|
@pytest.mark.parametrize('method', ['nelder-mead', 'powell', 'cg',
|
|
'bfgs', 'newton-cg', 'l-bfgs-b',
|
|
'tnc', 'cobyla', 'slsqp'])
|
|
def test_no_increase(self, method):
|
|
# Check that the solver doesn't return a value worse than the
|
|
# initial point.
|
|
|
|
def func(x):
|
|
return (x - 1)**2
|
|
|
|
def bad_grad(x):
|
|
# purposefully invalid gradient function, simulates a case
|
|
# where line searches start failing
|
|
return 2*(x - 1) * (-1) - 2
|
|
|
|
x0 = np.array([2.0])
|
|
f0 = func(x0)
|
|
jac = bad_grad
|
|
if method in ['nelder-mead', 'powell', 'cobyla']:
|
|
jac = None
|
|
sol = optimize.minimize(func, x0, jac=jac, method=method,
|
|
options=dict(maxiter=20))
|
|
assert_equal(func(sol.x), sol.fun)
|
|
|
|
if method == 'slsqp':
|
|
pytest.xfail("SLSQP returns slightly worse")
|
|
assert_(func(sol.x) <= f0)
|
|
|
|
def test_slsqp_respect_bounds(self):
|
|
# Regression test for gh-3108
|
|
def f(x):
|
|
return sum((x - np.array([1., 2., 3., 4.]))**2)
|
|
|
|
def cons(x):
|
|
a = np.array([[-1, -1, -1, -1], [-3, -3, -2, -1]])
|
|
return np.concatenate([np.dot(a, x) + np.array([5, 10]), x])
|
|
|
|
x0 = np.array([0.5, 1., 1.5, 2.])
|
|
res = optimize.minimize(f, x0, method='slsqp',
|
|
constraints={'type': 'ineq', 'fun': cons})
|
|
assert_allclose(res.x, np.array([0., 2, 5, 8])/3, atol=1e-12)
|
|
|
|
@pytest.mark.parametrize('method', ['Nelder-Mead', 'Powell', 'CG', 'BFGS',
|
|
'Newton-CG', 'L-BFGS-B', 'SLSQP',
|
|
'trust-constr', 'dogleg', 'trust-ncg',
|
|
'trust-exact', 'trust-krylov'])
|
|
def test_respect_maxiter(self, method):
|
|
# Check that the number of iterations equals max_iter, assuming
|
|
# convergence doesn't establish before
|
|
MAXITER = 4
|
|
|
|
x0 = np.zeros(10)
|
|
|
|
sf = ScalarFunction(optimize.rosen, x0, (), optimize.rosen_der,
|
|
optimize.rosen_hess, None, None)
|
|
|
|
# Set options
|
|
kwargs = {'method': method, 'options': dict(maxiter=MAXITER)}
|
|
|
|
if method in ('Newton-CG',):
|
|
kwargs['jac'] = sf.grad
|
|
elif method in ('trust-krylov', 'trust-exact', 'trust-ncg', 'dogleg',
|
|
'trust-constr'):
|
|
kwargs['jac'] = sf.grad
|
|
kwargs['hess'] = sf.hess
|
|
|
|
sol = optimize.minimize(sf.fun, x0, **kwargs)
|
|
assert sol.nit == MAXITER
|
|
assert sol.nfev >= sf.nfev
|
|
if hasattr(sol, 'njev'):
|
|
assert sol.njev >= sf.ngev
|
|
|
|
# method specific tests
|
|
if method == 'SLSQP':
|
|
assert sol.status == 9 # Iteration limit reached
|
|
|
|
def test_respect_maxiter_trust_constr_ineq_constraints(self):
|
|
# special case of minimization with trust-constr and inequality
|
|
# constraints to check maxiter limit is obeyed when using internal
|
|
# method 'tr_interior_point'
|
|
MAXITER = 4
|
|
f = optimize.rosen
|
|
jac = optimize.rosen_der
|
|
hess = optimize.rosen_hess
|
|
|
|
fun = lambda x: np.array([0.2 * x[0] - 0.4 * x[1] - 0.33 * x[2]])
|
|
cons = ({'type': 'ineq',
|
|
'fun': fun},)
|
|
|
|
x0 = np.zeros(10)
|
|
sol = optimize.minimize(f, x0, constraints=cons, jac=jac, hess=hess,
|
|
method='trust-constr',
|
|
options=dict(maxiter=MAXITER))
|
|
assert sol.nit == MAXITER
|
|
|
|
def test_minimize_automethod(self):
|
|
def f(x):
|
|
return x**2
|
|
|
|
def cons(x):
|
|
return x - 2
|
|
|
|
x0 = np.array([10.])
|
|
sol_0 = optimize.minimize(f, x0)
|
|
sol_1 = optimize.minimize(f, x0, constraints=[{'type': 'ineq',
|
|
'fun': cons}])
|
|
sol_2 = optimize.minimize(f, x0, bounds=[(5, 10)])
|
|
sol_3 = optimize.minimize(f, x0,
|
|
constraints=[{'type': 'ineq', 'fun': cons}],
|
|
bounds=[(5, 10)])
|
|
sol_4 = optimize.minimize(f, x0,
|
|
constraints=[{'type': 'ineq', 'fun': cons}],
|
|
bounds=[(1, 10)])
|
|
for sol in [sol_0, sol_1, sol_2, sol_3, sol_4]:
|
|
assert_(sol.success)
|
|
assert_allclose(sol_0.x, 0, atol=1e-7)
|
|
assert_allclose(sol_1.x, 2, atol=1e-7)
|
|
assert_allclose(sol_2.x, 5, atol=1e-7)
|
|
assert_allclose(sol_3.x, 5, atol=1e-7)
|
|
assert_allclose(sol_4.x, 2, atol=1e-7)
|
|
|
|
def test_minimize_coerce_args_param(self):
|
|
# Regression test for gh-3503
|
|
def Y(x, c):
|
|
return np.sum((x-c)**2)
|
|
|
|
def dY_dx(x, c=None):
|
|
return 2*(x-c)
|
|
|
|
c = np.array([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5])
|
|
xinit = np.random.randn(len(c))
|
|
optimize.minimize(Y, xinit, jac=dY_dx, args=(c), method="BFGS")
|
|
|
|
def test_initial_step_scaling(self):
|
|
# Check that optimizer initial step is not huge even if the
|
|
# function and gradients are
|
|
|
|
scales = [1e-50, 1, 1e50]
|
|
methods = ['CG', 'BFGS', 'L-BFGS-B', 'Newton-CG']
|
|
|
|
def f(x):
|
|
if first_step_size[0] is None and x[0] != x0[0]:
|
|
first_step_size[0] = abs(x[0] - x0[0])
|
|
if abs(x).max() > 1e4:
|
|
raise AssertionError("Optimization stepped far away!")
|
|
return scale*(x[0] - 1)**2
|
|
|
|
def g(x):
|
|
return np.array([scale*(x[0] - 1)])
|
|
|
|
for scale, method in itertools.product(scales, methods):
|
|
if method in ('CG', 'BFGS'):
|
|
options = dict(gtol=scale*1e-8)
|
|
else:
|
|
options = dict()
|
|
|
|
if scale < 1e-10 and method in ('L-BFGS-B', 'Newton-CG'):
|
|
# XXX: return initial point if they see small gradient
|
|
continue
|
|
|
|
x0 = [-1.0]
|
|
first_step_size = [None]
|
|
res = optimize.minimize(f, x0, jac=g, method=method,
|
|
options=options)
|
|
|
|
err_msg = "{0} {1}: {2}: {3}".format(method, scale,
|
|
first_step_size,
|
|
res)
|
|
|
|
assert_(res.success, err_msg)
|
|
assert_allclose(res.x, [1.0], err_msg=err_msg)
|
|
assert_(res.nit <= 3, err_msg)
|
|
|
|
if scale > 1e-10:
|
|
if method in ('CG', 'BFGS'):
|
|
assert_allclose(first_step_size[0], 1.01, err_msg=err_msg)
|
|
else:
|
|
# Newton-CG and L-BFGS-B use different logic for the first
|
|
# step, but are both scaling invariant with step sizes ~ 1
|
|
assert_(first_step_size[0] > 0.5 and
|
|
first_step_size[0] < 3, err_msg)
|
|
else:
|
|
# step size has upper bound of ||grad||, so line
|
|
# search makes many small steps
|
|
pass
|
|
|
|
@pytest.mark.parametrize('method', ['nelder-mead', 'powell', 'cg', 'bfgs',
|
|
'newton-cg', 'l-bfgs-b', 'tnc',
|
|
'cobyla', 'slsqp', 'trust-constr',
|
|
'dogleg', 'trust-ncg', 'trust-exact',
|
|
'trust-krylov'])
|
|
def test_nan_values(self, method):
|
|
# Check nan values result to failed exit status
|
|
np.random.seed(1234)
|
|
|
|
count = [0]
|
|
|
|
def func(x):
|
|
return np.nan
|
|
|
|
def func2(x):
|
|
count[0] += 1
|
|
if count[0] > 2:
|
|
return np.nan
|
|
else:
|
|
return np.random.rand()
|
|
|
|
def grad(x):
|
|
return np.array([1.0])
|
|
|
|
def hess(x):
|
|
return np.array([[1.0]])
|
|
|
|
x0 = np.array([1.0])
|
|
|
|
needs_grad = method in ('newton-cg', 'trust-krylov', 'trust-exact',
|
|
'trust-ncg', 'dogleg')
|
|
needs_hess = method in ('trust-krylov', 'trust-exact', 'trust-ncg',
|
|
'dogleg')
|
|
|
|
funcs = [func, func2]
|
|
grads = [grad] if needs_grad else [grad, None]
|
|
hesss = [hess] if needs_hess else [hess, None]
|
|
|
|
with np.errstate(invalid='ignore'), suppress_warnings() as sup:
|
|
sup.filter(UserWarning, "delta_grad == 0.*")
|
|
sup.filter(RuntimeWarning, ".*does not use Hessian.*")
|
|
sup.filter(RuntimeWarning, ".*does not use gradient.*")
|
|
|
|
for f, g, h in itertools.product(funcs, grads, hesss):
|
|
count = [0]
|
|
sol = optimize.minimize(f, x0, jac=g, hess=h, method=method,
|
|
options=dict(maxiter=20))
|
|
assert_equal(sol.success, False)
|
|
|
|
@pytest.mark.parametrize('method', ['nelder-mead', 'cg', 'bfgs',
|
|
'l-bfgs-b', 'tnc',
|
|
'cobyla', 'slsqp', 'trust-constr',
|
|
'dogleg', 'trust-ncg', 'trust-exact',
|
|
'trust-krylov'])
|
|
def test_duplicate_evaluations(self, method):
|
|
# check that there are no duplicate evaluations for any methods
|
|
jac = hess = None
|
|
if method in ('newton-cg', 'trust-krylov', 'trust-exact',
|
|
'trust-ncg', 'dogleg'):
|
|
jac = self.grad
|
|
if method in ('trust-krylov', 'trust-exact', 'trust-ncg',
|
|
'dogleg'):
|
|
hess = self.hess
|
|
|
|
with np.errstate(invalid='ignore'), suppress_warnings() as sup:
|
|
# for trust-constr
|
|
sup.filter(UserWarning, "delta_grad == 0.*")
|
|
optimize.minimize(self.func, self.startparams,
|
|
method=method, jac=jac, hess=hess)
|
|
|
|
for i in range(1, len(self.trace)):
|
|
if np.array_equal(self.trace[i - 1], self.trace[i]):
|
|
raise RuntimeError(
|
|
"Duplicate evaluations made by {}".format(method))
|
|
|
|
|
|
class TestLBFGSBBounds(object):
|
|
def setup_method(self):
|
|
self.bounds = ((1, None), (None, None))
|
|
self.solution = (1, 0)
|
|
|
|
def fun(self, x, p=2.0):
|
|
return 1.0 / p * (x[0]**p + x[1]**p)
|
|
|
|
def jac(self, x, p=2.0):
|
|
return x**(p - 1)
|
|
|
|
def fj(self, x, p=2.0):
|
|
return self.fun(x, p), self.jac(x, p)
|
|
|
|
def test_l_bfgs_b_bounds(self):
|
|
x, f, d = optimize.fmin_l_bfgs_b(self.fun, [0, -1],
|
|
fprime=self.jac,
|
|
bounds=self.bounds)
|
|
assert_(d['warnflag'] == 0, d['task'])
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
def test_l_bfgs_b_funjac(self):
|
|
# L-BFGS-B with fun and jac combined and extra arguments
|
|
x, f, d = optimize.fmin_l_bfgs_b(self.fj, [0, -1], args=(2.0, ),
|
|
bounds=self.bounds)
|
|
assert_(d['warnflag'] == 0, d['task'])
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
def test_minimize_l_bfgs_b_bounds(self):
|
|
# Minimize with method='L-BFGS-B' with bounds
|
|
res = optimize.minimize(self.fun, [0, -1], method='L-BFGS-B',
|
|
jac=self.jac, bounds=self.bounds)
|
|
assert_(res['success'], res['message'])
|
|
assert_allclose(res.x, self.solution, atol=1e-6)
|
|
|
|
@pytest.mark.parametrize('bounds', [
|
|
([(10, 1), (1, 10)]),
|
|
([(1, 10), (10, 1)]),
|
|
([(10, 1), (10, 1)])
|
|
])
|
|
def test_minimize_l_bfgs_b_incorrect_bounds(self, bounds):
|
|
with pytest.raises(ValueError, match='.*bounds.*'):
|
|
optimize.minimize(self.fun, [0, -1], method='L-BFGS-B',
|
|
jac=self.jac, bounds=bounds)
|
|
|
|
def test_minimize_l_bfgs_b_bounds_FD(self):
|
|
# test that initial starting value outside bounds doesn't raise
|
|
# an error (done with clipping).
|
|
# test all different finite differences combos, with and without args
|
|
|
|
jacs = ['2-point', '3-point', None]
|
|
argss = [(2.,), ()]
|
|
for jac, args in itertools.product(jacs, argss):
|
|
res = optimize.minimize(self.fun, [0, -1], args=args,
|
|
method='L-BFGS-B',
|
|
jac=jac, bounds=self.bounds,
|
|
options={'finite_diff_rel_step': None})
|
|
assert_(res['success'], res['message'])
|
|
assert_allclose(res.x, self.solution, atol=1e-6)
|
|
|
|
|
|
class TestOptimizeScalar(object):
|
|
def setup_method(self):
|
|
self.solution = 1.5
|
|
|
|
def fun(self, x, a=1.5):
|
|
"""Objective function"""
|
|
return (x - a)**2 - 0.8
|
|
|
|
def test_brent(self):
|
|
x = optimize.brent(self.fun)
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.brent(self.fun, brack=(-3, -2))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.brent(self.fun, full_output=True)
|
|
assert_allclose(x[0], self.solution, atol=1e-6)
|
|
|
|
x = optimize.brent(self.fun, brack=(-15, -1, 15))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
def test_golden(self):
|
|
x = optimize.golden(self.fun)
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.golden(self.fun, brack=(-3, -2))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.golden(self.fun, full_output=True)
|
|
assert_allclose(x[0], self.solution, atol=1e-6)
|
|
|
|
x = optimize.golden(self.fun, brack=(-15, -1, 15))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.golden(self.fun, tol=0)
|
|
assert_allclose(x, self.solution)
|
|
|
|
maxiter_test_cases = [0, 1, 5]
|
|
for maxiter in maxiter_test_cases:
|
|
x0 = optimize.golden(self.fun, maxiter=0, full_output=True)
|
|
x = optimize.golden(self.fun, maxiter=maxiter, full_output=True)
|
|
nfev0, nfev = x0[2], x[2]
|
|
assert_equal(nfev - nfev0, maxiter)
|
|
|
|
def test_fminbound(self):
|
|
x = optimize.fminbound(self.fun, 0, 1)
|
|
assert_allclose(x, 1, atol=1e-4)
|
|
|
|
x = optimize.fminbound(self.fun, 1, 5)
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.fminbound(self.fun, np.array([1]), np.array([5]))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
assert_raises(ValueError, optimize.fminbound, self.fun, 5, 1)
|
|
|
|
def test_fminbound_scalar(self):
|
|
with pytest.raises(ValueError, match='.*must be scalar.*'):
|
|
optimize.fminbound(self.fun, np.zeros((1, 2)), 1)
|
|
|
|
x = optimize.fminbound(self.fun, 1, np.array(5))
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
def test_gh11207(self):
|
|
def fun(x):
|
|
return x**2
|
|
optimize.fminbound(fun, 0, 0)
|
|
|
|
def test_minimize_scalar(self):
|
|
# combine all tests above for the minimize_scalar wrapper
|
|
x = optimize.minimize_scalar(self.fun).x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, method='Brent')
|
|
assert_(x.success)
|
|
|
|
x = optimize.minimize_scalar(self.fun, method='Brent',
|
|
options=dict(maxiter=3))
|
|
assert_(not x.success)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bracket=(-3, -2),
|
|
args=(1.5, ), method='Brent').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, method='Brent',
|
|
args=(1.5,)).x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bracket=(-15, -1, 15),
|
|
args=(1.5, ), method='Brent').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bracket=(-3, -2),
|
|
args=(1.5, ), method='golden').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, method='golden',
|
|
args=(1.5,)).x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bracket=(-15, -1, 15),
|
|
args=(1.5, ), method='golden').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bounds=(0, 1), args=(1.5,),
|
|
method='Bounded').x
|
|
assert_allclose(x, 1, atol=1e-4)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bounds=(1, 5), args=(1.5, ),
|
|
method='bounded').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
x = optimize.minimize_scalar(self.fun, bounds=(np.array([1]),
|
|
np.array([5])),
|
|
args=(np.array([1.5]), ),
|
|
method='bounded').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
assert_raises(ValueError, optimize.minimize_scalar, self.fun,
|
|
bounds=(5, 1), method='bounded', args=(1.5, ))
|
|
|
|
assert_raises(ValueError, optimize.minimize_scalar, self.fun,
|
|
bounds=(np.zeros(2), 1), method='bounded', args=(1.5, ))
|
|
|
|
x = optimize.minimize_scalar(self.fun, bounds=(1, np.array(5)),
|
|
method='bounded').x
|
|
assert_allclose(x, self.solution, atol=1e-6)
|
|
|
|
def test_minimize_scalar_custom(self):
|
|
# This function comes from the documentation example.
|
|
def custmin(fun, bracket, args=(), maxfev=None, stepsize=0.1,
|
|
maxiter=100, callback=None, **options):
|
|
bestx = (bracket[1] + bracket[0]) / 2.0
|
|
besty = fun(bestx)
|
|
funcalls = 1
|
|
niter = 0
|
|
improved = True
|
|
stop = False
|
|
|
|
while improved and not stop and niter < maxiter:
|
|
improved = False
|
|
niter += 1
|
|
for testx in [bestx - stepsize, bestx + stepsize]:
|
|
testy = fun(testx, *args)
|
|
funcalls += 1
|
|
if testy < besty:
|
|
besty = testy
|
|
bestx = testx
|
|
improved = True
|
|
if callback is not None:
|
|
callback(bestx)
|
|
if maxfev is not None and funcalls >= maxfev:
|
|
stop = True
|
|
break
|
|
|
|
return optimize.OptimizeResult(fun=besty, x=bestx, nit=niter,
|
|
nfev=funcalls, success=(niter > 1))
|
|
|
|
res = optimize.minimize_scalar(self.fun, bracket=(0, 4),
|
|
method=custmin,
|
|
options=dict(stepsize=0.05))
|
|
assert_allclose(res.x, self.solution, atol=1e-6)
|
|
|
|
def test_minimize_scalar_coerce_args_param(self):
|
|
# Regression test for gh-3503
|
|
optimize.minimize_scalar(self.fun, args=1.5)
|
|
|
|
@pytest.mark.parametrize('method', ['brent', 'bounded', 'golden'])
|
|
def test_nan_values(self, method):
|
|
# Check nan values result to failed exit status
|
|
np.random.seed(1234)
|
|
|
|
count = [0]
|
|
|
|
def func(x):
|
|
count[0] += 1
|
|
if count[0] > 4:
|
|
return np.nan
|
|
else:
|
|
return x**2 + 0.1 * np.sin(x)
|
|
|
|
bracket = (-1, 0, 1)
|
|
bounds = (-1, 1)
|
|
|
|
with np.errstate(invalid='ignore'), suppress_warnings() as sup:
|
|
sup.filter(UserWarning, "delta_grad == 0.*")
|
|
sup.filter(RuntimeWarning, ".*does not use Hessian.*")
|
|
sup.filter(RuntimeWarning, ".*does not use gradient.*")
|
|
|
|
count = [0]
|
|
sol = optimize.minimize_scalar(func, bracket=bracket,
|
|
bounds=bounds, method=method,
|
|
options=dict(maxiter=20))
|
|
assert_equal(sol.success, False)
|
|
|
|
|
|
def test_brent_negative_tolerance():
|
|
assert_raises(ValueError, optimize.brent, np.cos, tol=-.01)
|
|
|
|
|
|
class TestNewtonCg(object):
|
|
def test_rosenbrock(self):
|
|
x0 = np.array([-1.2, 1.0])
|
|
sol = optimize.minimize(optimize.rosen, x0,
|
|
jac=optimize.rosen_der,
|
|
hess=optimize.rosen_hess,
|
|
tol=1e-5,
|
|
method='Newton-CG')
|
|
assert_(sol.success, sol.message)
|
|
assert_allclose(sol.x, np.array([1, 1]), rtol=1e-4)
|
|
|
|
def test_himmelblau(self):
|
|
x0 = np.array(himmelblau_x0)
|
|
sol = optimize.minimize(himmelblau,
|
|
x0,
|
|
jac=himmelblau_grad,
|
|
hess=himmelblau_hess,
|
|
method='Newton-CG',
|
|
tol=1e-6)
|
|
assert_(sol.success, sol.message)
|
|
assert_allclose(sol.x, himmelblau_xopt, rtol=1e-4)
|
|
assert_allclose(sol.fun, himmelblau_min, atol=1e-4)
|
|
|
|
|
|
def test_line_for_search():
|
|
# _line_for_search is only used in _linesearch_powell, which is also
|
|
# tested below. Thus there are more tests of _line_for_search in the
|
|
# test_linesearch_powell_bounded function.
|
|
|
|
line_for_search = optimize.optimize._line_for_search
|
|
# args are x0, alpha, lower_bound, upper_bound
|
|
# returns lmin, lmax
|
|
|
|
lower_bound = np.array([-5.3, -1, -1.5, -3])
|
|
upper_bound = np.array([1.9, 1, 2.8, 3])
|
|
|
|
# test when starting in the bounds
|
|
x0 = np.array([0., 0, 0, 0])
|
|
# and when starting outside of the bounds
|
|
x1 = np.array([0., 2, -3, 0])
|
|
|
|
all_tests = (
|
|
(x0, np.array([1., 0, 0, 0]), -5.3, 1.9),
|
|
(x0, np.array([0., 1, 0, 0]), -1, 1),
|
|
(x0, np.array([0., 0, 1, 0]), -1.5, 2.8),
|
|
(x0, np.array([0., 0, 0, 1]), -3, 3),
|
|
(x0, np.array([1., 1, 0, 0]), -1, 1),
|
|
(x0, np.array([1., 0, -1, 2]), -1.5, 1.5),
|
|
(x0, np.array([2., 0, -1, 2]), -1.5, 0.95),
|
|
(x1, np.array([1., 0, 0, 0]), -5.3, 1.9),
|
|
(x1, np.array([0., 1, 0, 0]), -3, -1),
|
|
(x1, np.array([0., 0, 1, 0]), 1.5, 5.8),
|
|
(x1, np.array([0., 0, 0, 1]), -3, 3),
|
|
(x1, np.array([1., 1, 0, 0]), -3, -1),
|
|
(x1, np.array([1., 0, -1, 0]), -5.3, -1.5),
|
|
)
|
|
|
|
for x, alpha, lmin, lmax in all_tests:
|
|
mi, ma = line_for_search(x, alpha, lower_bound, upper_bound)
|
|
assert_allclose(mi, lmin, atol=1e-6)
|
|
assert_allclose(ma, lmax, atol=1e-6)
|
|
|
|
# now with infinite bounds
|
|
lower_bound = np.array([-np.inf, -1, -np.inf, -3])
|
|
upper_bound = np.array([np.inf, 1, 2.8, np.inf])
|
|
|
|
all_tests = (
|
|
(x0, np.array([1., 0, 0, 0]), -np.inf, np.inf),
|
|
(x0, np.array([0., 1, 0, 0]), -1, 1),
|
|
(x0, np.array([0., 0, 1, 0]), -np.inf, 2.8),
|
|
(x0, np.array([0., 0, 0, 1]), -3, np.inf),
|
|
(x0, np.array([1., 1, 0, 0]), -1, 1),
|
|
(x0, np.array([1., 0, -1, 2]), -1.5, np.inf),
|
|
(x1, np.array([1., 0, 0, 0]), -np.inf, np.inf),
|
|
(x1, np.array([0., 1, 0, 0]), -3, -1),
|
|
(x1, np.array([0., 0, 1, 0]), -np.inf, 5.8),
|
|
(x1, np.array([0., 0, 0, 1]), -3, np.inf),
|
|
(x1, np.array([1., 1, 0, 0]), -3, -1),
|
|
(x1, np.array([1., 0, -1, 0]), -5.8, np.inf),
|
|
)
|
|
|
|
for x, alpha, lmin, lmax in all_tests:
|
|
mi, ma = line_for_search(x, alpha, lower_bound, upper_bound)
|
|
assert_allclose(mi, lmin, atol=1e-6)
|
|
assert_allclose(ma, lmax, atol=1e-6)
|
|
|
|
|
|
def test_linesearch_powell():
|
|
# helper function in optimize.py, not a public function.
|
|
linesearch_powell = optimize.optimize._linesearch_powell
|
|
# args are func, p, xi, fval, lower_bound=None, upper_bound=None, tol=1e-3
|
|
# returns new_fval, p + direction, direction
|
|
func = lambda x: np.sum((x - np.array([-1., 2., 1.5, -.4]))**2)
|
|
p0 = np.array([0., 0, 0, 0])
|
|
fval = func(p0)
|
|
lower_bound = np.array([-np.inf] * 4)
|
|
upper_bound = np.array([np.inf] * 4)
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), -1),
|
|
(np.array([0., 1, 0, 0]), 2),
|
|
(np.array([0., 0, 1, 0]), 1.5),
|
|
(np.array([0., 0, 0, 1]), -.4),
|
|
(np.array([-1., 0, 1, 0]), 1.25),
|
|
(np.array([0., 0, 1, 1]), .55),
|
|
(np.array([2., 0, -1, 1]), -.65),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi,
|
|
fval=fval, tol=1e-5)
|
|
assert_allclose(f, func(l * xi), atol=1e-6)
|
|
assert_allclose(p, l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(l * xi), atol=1e-6)
|
|
assert_allclose(p, l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
|
|
def test_linesearch_powell_bounded():
|
|
# helper function in optimize.py, not a public function.
|
|
linesearch_powell = optimize.optimize._linesearch_powell
|
|
# args are func, p, xi, fval, lower_bound=None, upper_bound=None, tol=1e-3
|
|
# returns new_fval, p+direction, direction
|
|
func = lambda x: np.sum((x-np.array([-1., 2., 1.5, -.4]))**2)
|
|
p0 = np.array([0., 0, 0, 0])
|
|
fval = func(p0)
|
|
|
|
# first choose bounds such that the same tests from
|
|
# test_linesearch_powell should pass.
|
|
lower_bound = np.array([-2.]*4)
|
|
upper_bound = np.array([2.]*4)
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), -1),
|
|
(np.array([0., 1, 0, 0]), 2),
|
|
(np.array([0., 0, 1, 0]), 1.5),
|
|
(np.array([0., 0, 0, 1]), -.4),
|
|
(np.array([-1., 0, 1, 0]), 1.25),
|
|
(np.array([0., 0, 1, 1]), .55),
|
|
(np.array([2., 0, -1, 1]), -.65),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(l * xi), atol=1e-6)
|
|
assert_allclose(p, l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
# now choose bounds such that unbounded vs bounded gives different results
|
|
lower_bound = np.array([-.3]*3 + [-1])
|
|
upper_bound = np.array([.45]*3 + [.9])
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), -.3),
|
|
(np.array([0., 1, 0, 0]), .45),
|
|
(np.array([0., 0, 1, 0]), .45),
|
|
(np.array([0., 0, 0, 1]), -.4),
|
|
(np.array([-1., 0, 1, 0]), .3),
|
|
(np.array([0., 0, 1, 1]), .45),
|
|
(np.array([2., 0, -1, 1]), -.15),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(l * xi), atol=1e-6)
|
|
assert_allclose(p, l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
# now choose as above but start outside the bounds
|
|
p0 = np.array([-1., 0, 0, 2])
|
|
fval = func(p0)
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), .7),
|
|
(np.array([0., 1, 0, 0]), .45),
|
|
(np.array([0., 0, 1, 0]), .45),
|
|
(np.array([0., 0, 0, 1]), -2.4),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(p0 + l * xi), atol=1e-6)
|
|
assert_allclose(p, p0 + l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
# now mix in inf
|
|
p0 = np.array([0., 0, 0, 0])
|
|
fval = func(p0)
|
|
|
|
# now choose bounds that mix inf
|
|
lower_bound = np.array([-.3, -np.inf, -np.inf, -1])
|
|
upper_bound = np.array([np.inf, .45, np.inf, .9])
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), -.3),
|
|
(np.array([0., 1, 0, 0]), .45),
|
|
(np.array([0., 0, 1, 0]), 1.5),
|
|
(np.array([0., 0, 0, 1]), -.4),
|
|
(np.array([-1., 0, 1, 0]), .3),
|
|
(np.array([0., 0, 1, 1]), .55),
|
|
(np.array([2., 0, -1, 1]), -.15),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(l * xi), atol=1e-6)
|
|
assert_allclose(p, l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
# now choose as above but start outside the bounds
|
|
p0 = np.array([-1., 0, 0, 2])
|
|
fval = func(p0)
|
|
|
|
all_tests = (
|
|
(np.array([1., 0, 0, 0]), .7),
|
|
(np.array([0., 1, 0, 0]), .45),
|
|
(np.array([0., 0, 1, 0]), 1.5),
|
|
(np.array([0., 0, 0, 1]), -2.4),
|
|
)
|
|
|
|
for xi, l in all_tests:
|
|
f, p, direction = linesearch_powell(func, p0, xi, tol=1e-5,
|
|
lower_bound=lower_bound,
|
|
upper_bound=upper_bound,
|
|
fval=fval)
|
|
assert_allclose(f, func(p0 + l * xi), atol=1e-6)
|
|
assert_allclose(p, p0 + l * xi, atol=1e-6)
|
|
assert_allclose(direction, l * xi, atol=1e-6)
|
|
|
|
|
|
class TestRosen(object):
|
|
|
|
def test_hess(self):
|
|
# Compare rosen_hess(x) times p with rosen_hess_prod(x,p). See gh-1775.
|
|
x = np.array([3, 4, 5])
|
|
p = np.array([2, 2, 2])
|
|
hp = optimize.rosen_hess_prod(x, p)
|
|
dothp = np.dot(optimize.rosen_hess(x), p)
|
|
assert_equal(hp, dothp)
|
|
|
|
|
|
def himmelblau(p):
|
|
"""
|
|
R^2 -> R^1 test function for optimization. The function has four local
|
|
minima where himmelblau(xopt) == 0.
|
|
"""
|
|
x, y = p
|
|
a = x*x + y - 11
|
|
b = x + y*y - 7
|
|
return a*a + b*b
|
|
|
|
|
|
def himmelblau_grad(p):
|
|
x, y = p
|
|
return np.array([4*x**3 + 4*x*y - 42*x + 2*y**2 - 14,
|
|
2*x**2 + 4*x*y + 4*y**3 - 26*y - 22])
|
|
|
|
|
|
def himmelblau_hess(p):
|
|
x, y = p
|
|
return np.array([[12*x**2 + 4*y - 42, 4*x + 4*y],
|
|
[4*x + 4*y, 4*x + 12*y**2 - 26]])
|
|
|
|
|
|
himmelblau_x0 = [-0.27, -0.9]
|
|
himmelblau_xopt = [3, 2]
|
|
himmelblau_min = 0.0
|
|
|
|
|
|
def test_minimize_multiple_constraints():
|
|
# Regression test for gh-4240.
|
|
def func(x):
|
|
return np.array([25 - 0.2 * x[0] - 0.4 * x[1] - 0.33 * x[2]])
|
|
|
|
def func1(x):
|
|
return np.array([x[1]])
|
|
|
|
def func2(x):
|
|
return np.array([x[2]])
|
|
|
|
cons = ({'type': 'ineq', 'fun': func},
|
|
{'type': 'ineq', 'fun': func1},
|
|
{'type': 'ineq', 'fun': func2})
|
|
|
|
f = lambda x: -1 * (x[0] + x[1] + x[2])
|
|
|
|
res = optimize.minimize(f, [0, 0, 0], method='SLSQP', constraints=cons)
|
|
assert_allclose(res.x, [125, 0, 0], atol=1e-10)
|
|
|
|
|
|
class TestOptimizeResultAttributes(object):
|
|
# Test that all minimizers return an OptimizeResult containing
|
|
# all the OptimizeResult attributes
|
|
def setup_method(self):
|
|
self.x0 = [5, 5]
|
|
self.func = optimize.rosen
|
|
self.jac = optimize.rosen_der
|
|
self.hess = optimize.rosen_hess
|
|
self.hessp = optimize.rosen_hess_prod
|
|
self.bounds = [(0., 10.), (0., 10.)]
|
|
|
|
def test_attributes_present(self):
|
|
attributes = ['nit', 'nfev', 'x', 'success', 'status', 'fun',
|
|
'message']
|
|
skip = {'cobyla': ['nit']}
|
|
for method in MINIMIZE_METHODS:
|
|
with suppress_warnings() as sup:
|
|
sup.filter(RuntimeWarning,
|
|
("Method .+ does not use (gradient|Hessian.*)"
|
|
" information"))
|
|
res = optimize.minimize(self.func, self.x0, method=method,
|
|
jac=self.jac, hess=self.hess,
|
|
hessp=self.hessp)
|
|
for attribute in attributes:
|
|
if method in skip and attribute in skip[method]:
|
|
continue
|
|
|
|
assert hasattr(res, attribute)
|
|
assert_(attribute in dir(res))
|
|
|
|
# gh13001, OptimizeResult.message should be a str
|
|
assert isinstance(res.message, str)
|
|
|
|
|
|
def f1(z, *params):
|
|
x, y = z
|
|
a, b, c, d, e, f, g, h, i, j, k, l, scale = params
|
|
return (a * x**2 + b * x * y + c * y**2 + d*x + e*y + f)
|
|
|
|
|
|
def f2(z, *params):
|
|
x, y = z
|
|
a, b, c, d, e, f, g, h, i, j, k, l, scale = params
|
|
return (-g*np.exp(-((x-h)**2 + (y-i)**2) / scale))
|
|
|
|
|
|
def f3(z, *params):
|
|
x, y = z
|
|
a, b, c, d, e, f, g, h, i, j, k, l, scale = params
|
|
return (-j*np.exp(-((x-k)**2 + (y-l)**2) / scale))
|
|
|
|
|
|
def brute_func(z, *params):
|
|
return f1(z, *params) + f2(z, *params) + f3(z, *params)
|
|
|
|
|
|
class TestBrute:
|
|
# Test the "brute force" method
|
|
def setup_method(self):
|
|
self.params = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5)
|
|
self.rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))
|
|
self.solution = np.array([-1.05665192, 1.80834843])
|
|
|
|
def brute_func(self, z, *params):
|
|
# an instance method optimizing
|
|
return brute_func(z, *params)
|
|
|
|
def test_brute(self):
|
|
# test fmin
|
|
resbrute = optimize.brute(brute_func, self.rranges, args=self.params,
|
|
full_output=True, finish=optimize.fmin)
|
|
assert_allclose(resbrute[0], self.solution, atol=1e-3)
|
|
assert_allclose(resbrute[1], brute_func(self.solution, *self.params),
|
|
atol=1e-3)
|
|
|
|
# test minimize
|
|
resbrute = optimize.brute(brute_func, self.rranges, args=self.params,
|
|
full_output=True,
|
|
finish=optimize.minimize)
|
|
assert_allclose(resbrute[0], self.solution, atol=1e-3)
|
|
assert_allclose(resbrute[1], brute_func(self.solution, *self.params),
|
|
atol=1e-3)
|
|
|
|
# test that brute can optimize an instance method (the other tests use
|
|
# a non-class based function
|
|
resbrute = optimize.brute(self.brute_func, self.rranges,
|
|
args=self.params, full_output=True,
|
|
finish=optimize.minimize)
|
|
assert_allclose(resbrute[0], self.solution, atol=1e-3)
|
|
|
|
def test_1D(self):
|
|
# test that for a 1-D problem the test function is passed an array,
|
|
# not a scalar.
|
|
def f(x):
|
|
assert_(len(x.shape) == 1)
|
|
assert_(x.shape[0] == 1)
|
|
return x ** 2
|
|
|
|
optimize.brute(f, [(-1, 1)], Ns=3, finish=None)
|
|
|
|
def test_workers(self):
|
|
# check that parallel evaluation works
|
|
resbrute = optimize.brute(brute_func, self.rranges, args=self.params,
|
|
full_output=True, finish=None)
|
|
|
|
resbrute1 = optimize.brute(brute_func, self.rranges, args=self.params,
|
|
full_output=True, finish=None, workers=2)
|
|
|
|
assert_allclose(resbrute1[-1], resbrute[-1])
|
|
assert_allclose(resbrute1[0], resbrute[0])
|
|
|
|
|
|
def test_cobyla_threadsafe():
|
|
|
|
# Verify that cobyla is threadsafe. Will segfault if it is not.
|
|
|
|
import concurrent.futures
|
|
import time
|
|
|
|
def objective1(x):
|
|
time.sleep(0.1)
|
|
return x[0]**2
|
|
|
|
def objective2(x):
|
|
time.sleep(0.1)
|
|
return (x[0]-1)**2
|
|
|
|
min_method = "COBYLA"
|
|
|
|
def minimizer1():
|
|
return optimize.minimize(objective1,
|
|
[0.0],
|
|
method=min_method)
|
|
|
|
def minimizer2():
|
|
return optimize.minimize(objective2,
|
|
[0.0],
|
|
method=min_method)
|
|
|
|
with concurrent.futures.ThreadPoolExecutor() as pool:
|
|
tasks = []
|
|
tasks.append(pool.submit(minimizer1))
|
|
tasks.append(pool.submit(minimizer2))
|
|
for t in tasks:
|
|
res = t.result()
|
|
|
|
|
|
class TestIterationLimits(object):
|
|
# Tests that optimisation does not give up before trying requested
|
|
# number of iterations or evaluations. And that it does not succeed
|
|
# by exceeding the limits.
|
|
def setup_method(self):
|
|
self.funcalls = 0
|
|
|
|
def slow_func(self, v):
|
|
self.funcalls += 1
|
|
r, t = np.sqrt(v[0]**2+v[1]**2), np.arctan2(v[0], v[1])
|
|
return np.sin(r*20 + t)+r*0.5
|
|
|
|
def test_neldermead_limit(self):
|
|
self.check_limits("Nelder-Mead", 200)
|
|
|
|
def test_powell_limit(self):
|
|
self.check_limits("powell", 1000)
|
|
|
|
def check_limits(self, method, default_iters):
|
|
for start_v in [[0.1, 0.1], [1, 1], [2, 2]]:
|
|
for mfev in [50, 500, 5000]:
|
|
self.funcalls = 0
|
|
res = optimize.minimize(self.slow_func, start_v,
|
|
method=method,
|
|
options={"maxfev": mfev})
|
|
assert_(self.funcalls == res["nfev"])
|
|
if res["success"]:
|
|
assert_(res["nfev"] < mfev)
|
|
else:
|
|
assert_(res["nfev"] >= mfev)
|
|
for mit in [50, 500, 5000]:
|
|
res = optimize.minimize(self.slow_func, start_v,
|
|
method=method,
|
|
options={"maxiter": mit})
|
|
if res["success"]:
|
|
assert_(res["nit"] <= mit)
|
|
else:
|
|
assert_(res["nit"] >= mit)
|
|
for mfev, mit in [[50, 50], [5000, 5000], [5000, np.inf]]:
|
|
self.funcalls = 0
|
|
res = optimize.minimize(self.slow_func, start_v,
|
|
method=method,
|
|
options={"maxiter": mit,
|
|
"maxfev": mfev})
|
|
assert_(self.funcalls == res["nfev"])
|
|
if res["success"]:
|
|
assert_(res["nfev"] < mfev and res["nit"] <= mit)
|
|
else:
|
|
assert_(res["nfev"] >= mfev or res["nit"] >= mit)
|
|
for mfev, mit in [[np.inf, None], [None, np.inf]]:
|
|
self.funcalls = 0
|
|
res = optimize.minimize(self.slow_func, start_v,
|
|
method=method,
|
|
options={"maxiter": mit,
|
|
"maxfev": mfev})
|
|
assert_(self.funcalls == res["nfev"])
|
|
if res["success"]:
|
|
if mfev is None:
|
|
assert_(res["nfev"] < default_iters*2)
|
|
else:
|
|
assert_(res["nit"] <= default_iters*2)
|
|
else:
|
|
assert_(res["nfev"] >= default_iters*2 or
|
|
res["nit"] >= default_iters*2)
|
|
|
|
|
|
def test_result_x_shape_when_len_x_is_one():
|
|
def fun(x):
|
|
return x * x
|
|
|
|
def jac(x):
|
|
return 2. * x
|
|
|
|
def hess(x):
|
|
return np.array([[2.]])
|
|
|
|
methods = ['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'L-BFGS-B', 'TNC',
|
|
'COBYLA', 'SLSQP']
|
|
for method in methods:
|
|
res = optimize.minimize(fun, np.array([0.1]), method=method)
|
|
assert res.x.shape == (1,)
|
|
|
|
# use jac + hess
|
|
methods = ['trust-constr', 'dogleg', 'trust-ncg', 'trust-exact',
|
|
'trust-krylov', 'Newton-CG']
|
|
for method in methods:
|
|
res = optimize.minimize(fun, np.array([0.1]), method=method, jac=jac,
|
|
hess=hess)
|
|
assert res.x.shape == (1,)
|
|
|
|
|
|
class FunctionWithGradient(object):
|
|
def __init__(self):
|
|
self.number_of_calls = 0
|
|
|
|
def __call__(self, x):
|
|
self.number_of_calls += 1
|
|
return np.sum(x**2), 2 * x
|
|
|
|
|
|
@pytest.fixture
|
|
def function_with_gradient():
|
|
return FunctionWithGradient()
|
|
|
|
|
|
def test_memoize_jac_function_before_gradient(function_with_gradient):
|
|
memoized_function = MemoizeJac(function_with_gradient)
|
|
|
|
x0 = np.array([1.0, 2.0])
|
|
assert_allclose(memoized_function(x0), 5.0)
|
|
assert function_with_gradient.number_of_calls == 1
|
|
|
|
assert_allclose(memoized_function.derivative(x0), 2 * x0)
|
|
assert function_with_gradient.number_of_calls == 1, \
|
|
"function is not recomputed " \
|
|
"if gradient is requested after function value"
|
|
|
|
assert_allclose(
|
|
memoized_function(2 * x0), 20.0,
|
|
err_msg="different input triggers new computation")
|
|
assert function_with_gradient.number_of_calls == 2, \
|
|
"different input triggers new computation"
|
|
|
|
|
|
def test_memoize_jac_gradient_before_function(function_with_gradient):
|
|
memoized_function = MemoizeJac(function_with_gradient)
|
|
|
|
x0 = np.array([1.0, 2.0])
|
|
assert_allclose(memoized_function.derivative(x0), 2 * x0)
|
|
assert function_with_gradient.number_of_calls == 1
|
|
|
|
assert_allclose(memoized_function(x0), 5.0)
|
|
assert function_with_gradient.number_of_calls == 1, \
|
|
"function is not recomputed " \
|
|
"if function value is requested after gradient"
|
|
|
|
assert_allclose(
|
|
memoized_function.derivative(2 * x0), 4 * x0,
|
|
err_msg="different input triggers new computation")
|
|
assert function_with_gradient.number_of_calls == 2, \
|
|
"different input triggers new computation"
|
|
|
|
|
|
def test_memoize_jac_with_bfgs(function_with_gradient):
|
|
""" Tests that using MemoizedJac in combination with ScalarFunction
|
|
and BFGS does not lead to repeated function evaluations.
|
|
Tests changes made in response to GH11868.
|
|
"""
|
|
memoized_function = MemoizeJac(function_with_gradient)
|
|
jac = memoized_function.derivative
|
|
hess = optimize.BFGS()
|
|
|
|
x0 = np.array([1.0, 0.5])
|
|
scalar_function = ScalarFunction(
|
|
memoized_function, x0, (), jac, hess, None, None)
|
|
assert function_with_gradient.number_of_calls == 1
|
|
|
|
scalar_function.fun(x0 + 0.1)
|
|
assert function_with_gradient.number_of_calls == 2
|
|
|
|
scalar_function.fun(x0 + 0.2)
|
|
assert function_with_gradient.number_of_calls == 3
|
|
|
|
|
|
def test_gh12696():
|
|
# Test that optimize doesn't throw warning gh-12696
|
|
with assert_no_warnings():
|
|
optimize.fminbound(
|
|
lambda x: np.array([x**2]), -np.pi, np.pi, disp=False)
|
|
|
|
|
|
def test_show_options():
|
|
solver_methods = {
|
|
'minimize': MINIMIZE_METHODS,
|
|
'minimize_scalar': MINIMIZE_SCALAR_METHODS,
|
|
'root': ROOT_METHODS,
|
|
'root_scalar': ROOT_SCALAR_METHODS,
|
|
'linprog': LINPROG_METHODS,
|
|
'quadratic_assignment': QUADRATIC_ASSIGNMENT_METHODS,
|
|
}
|
|
for solver, methods in solver_methods.items():
|
|
for method in methods:
|
|
# testing that `show_options` works without error
|
|
show_options(solver, method)
|
|
|
|
unknown_solver_method = {
|
|
'minimize': "ekki", # unknown method
|
|
'maximize': "cg", # unknown solver
|
|
'maximize_scalar': "ekki", # unknown solver and method
|
|
}
|
|
for solver, method in unknown_solver_method.items():
|
|
# testing that `show_options` raises ValueError
|
|
assert_raises(ValueError, show_options, solver, method)
|
|
|