eaiaiaiaoi/venv/lib/python2.7/site-packages/scipy/optimize/tests/test_linesearch.py

"""
Tests for line search routines
"""
from __future__ import division, print_function, absolute_import

from numpy.testing import assert_, assert_equal, \
     assert_array_almost_equal, assert_array_almost_equal_nulp, assert_warns
from scipy._lib._numpy_compat import suppress_warnings
import scipy.optimize.linesearch as ls
from scipy.optimize.linesearch import LineSearchWarning
import numpy as np


def assert_wolfe(s, phi, derphi, c1=1e-4, c2=0.9, err_msg=""):
    """
    Check that strong Wolfe conditions apply
    """
    phi1 = phi(s)
    phi0 = phi(0)
    derphi0 = derphi(0)
    derphi1 = derphi(s)
    msg = "s = %s; phi(0) = %s; phi(s) = %s; phi'(0) = %s; phi'(s) = %s; %s" % (
        s, phi0, phi1, derphi0, derphi1, err_msg)

    assert_(phi1 <= phi0 + c1*s*derphi0, "Wolfe 1 failed: " + msg)
    assert_(abs(derphi1) <= abs(c2*derphi0), "Wolfe 2 failed: " + msg)


def assert_armijo(s, phi, c1=1e-4, err_msg=""):
    """
    Check that Armijo condition applies
    """
    phi1 = phi(s)
    phi0 = phi(0)
    msg = "s = %s; phi(0) = %s; phi(s) = %s; %s" % (s, phi0, phi1, err_msg)
    assert_(phi1 <= (1 - c1*s)*phi0, msg)


def assert_line_wolfe(x, p, s, f, fprime, **kw):
    assert_wolfe(s, phi=lambda sp: f(x + p*sp),
                 derphi=lambda sp: np.dot(fprime(x + p*sp), p), **kw)


def assert_line_armijo(x, p, s, f, **kw):
    assert_armijo(s, phi=lambda sp: f(x + p*sp), **kw)


def assert_fp_equal(x, y, err_msg="", nulp=50):
    """Assert two arrays are equal, up to some floating-point rounding error"""
    try:
        assert_array_almost_equal_nulp(x, y, nulp)
    except AssertionError as e:
        raise AssertionError("%s\n%s" % (e, err_msg))


class TestLineSearch(object):
    # -- scalar functions; must have dphi(0.) < 0
    def _scalar_func_1(self, s):
        self.fcount += 1
        p = -s - s**3 + s**4
        dp = -1 - 3*s**2 + 4*s**3
        return p, dp

    def _scalar_func_2(self, s):
        self.fcount += 1
        p = np.exp(-4*s) + s**2
        dp = -4*np.exp(-4*s) + 2*s
        return p, dp

    def _scalar_func_3(self, s):
        self.fcount += 1
        p = -np.sin(10*s)
        dp = -10*np.cos(10*s)
        return p, dp

    # -- n-d functions

    def _line_func_1(self, x):
        self.fcount += 1
        f = np.dot(x, x)
        df = 2*x
        return f, df

    def _line_func_2(self, x):
        self.fcount += 1
        f = np.dot(x, np.dot(self.A, x)) + 1
        df = np.dot(self.A + self.A.T, x)
        return f, df

    # --

    def setup_method(self):
        self.scalar_funcs = []
        self.line_funcs = []
        self.N = 20
        self.fcount = 0

        def bind_index(func, idx):
            # Remember Python's closure semantics!
            return lambda *a, **kw: func(*a, **kw)[idx]

        for name in sorted(dir(self)):
            if name.startswith('_scalar_func_'):
                value = getattr(self, name)
                self.scalar_funcs.append(
                    (name, bind_index(value, 0), bind_index(value, 1)))
            elif name.startswith('_line_func_'):
                value = getattr(self, name)
                self.line_funcs.append(
                    (name, bind_index(value, 0), bind_index(value, 1)))

        np.random.seed(1234)
        self.A = np.random.randn(self.N, self.N)

    def scalar_iter(self):
        for name, phi, derphi in self.scalar_funcs:
            for old_phi0 in np.random.randn(3):
                yield name, phi, derphi, old_phi0

    def line_iter(self):
        for name, f, fprime in self.line_funcs:
            k = 0
            while k < 9:
                x = np.random.randn(self.N)
                p = np.random.randn(self.N)
                if np.dot(p, fprime(x)) >= 0:
                    # always pick a descent direction
                    continue
                k += 1
                old_fv = float(np.random.randn())
                yield name, f, fprime, x, p, old_fv

    # -- Generic scalar searches

    def test_scalar_search_wolfe1(self):
        c = 0
        for name, phi, derphi, old_phi0 in self.scalar_iter():
            c += 1
            s, phi1, phi0 = ls.scalar_search_wolfe1(phi, derphi, phi(0),
                                                    old_phi0, derphi(0))
            assert_fp_equal(phi0, phi(0), name)
            assert_fp_equal(phi1, phi(s), name)
            assert_wolfe(s, phi, derphi, err_msg=name)

        assert_(c > 3)  # check that the iterator really works...

    def test_scalar_search_wolfe2(self):
        for name, phi, derphi, old_phi0 in self.scalar_iter():
            s, phi1, phi0, derphi1 = ls.scalar_search_wolfe2(
                phi, derphi, phi(0), old_phi0, derphi(0))
            assert_fp_equal(phi0, phi(0), name)
            assert_fp_equal(phi1, phi(s), name)
            if derphi1 is not None:
                assert_fp_equal(derphi1, derphi(s), name)
            assert_wolfe(s, phi, derphi, err_msg="%s %g" % (name, old_phi0))

    def test_scalar_search_armijo(self):
        for name, phi, derphi, old_phi0 in self.scalar_iter():
            s, phi1 = ls.scalar_search_armijo(phi, phi(0), derphi(0))
            assert_fp_equal(phi1, phi(s), name)
            assert_armijo(s, phi, err_msg="%s %g" % (name, old_phi0))

    # -- Generic line searches

    def test_line_search_wolfe1(self):
        c = 0
        smax = 100
        for name, f, fprime, x, p, old_f in self.line_iter():
            f0 = f(x)
            g0 = fprime(x)
            self.fcount = 0
            s, fc, gc, fv, ofv, gv = ls.line_search_wolfe1(f, fprime, x, p,
                                                           g0, f0, old_f,
                                                           amax=smax)
            assert_equal(self.fcount, fc+gc)
            assert_fp_equal(ofv, f(x))
            if s is None:
                continue
            assert_fp_equal(fv, f(x + s*p))
            assert_array_almost_equal(gv, fprime(x + s*p), decimal=14)
            if s < smax:
                c += 1
                assert_line_wolfe(x, p, s, f, fprime, err_msg=name)

        assert_(c > 3)  # check that the iterator really works...

    def test_line_search_wolfe2(self):
        c = 0
        smax = 512
        for name, f, fprime, x, p, old_f in self.line_iter():
            f0 = f(x)
            g0 = fprime(x)
            self.fcount = 0
            with suppress_warnings() as sup:
                sup.filter(LineSearchWarning,
                           "The line search algorithm could not find a solution")
                sup.filter(LineSearchWarning,
                           "The line search algorithm did not converge")
                s, fc, gc, fv, ofv, gv = ls.line_search_wolfe2(f, fprime, x, p,
                                                               g0, f0, old_f,
                                                               amax=smax)
            assert_equal(self.fcount, fc+gc)
            assert_fp_equal(ofv, f(x))
            assert_fp_equal(fv, f(x + s*p))
            if gv is not None:
                assert_array_almost_equal(gv, fprime(x + s*p), decimal=14)
            if s < smax:
                c += 1
                assert_line_wolfe(x, p, s, f, fprime, err_msg=name)
        assert_(c > 3)  # check that the iterator really works...

    def test_line_search_wolfe2_bounds(self):
        # See gh-7475

        # For this f and p, starting at a point on axis 0, the strong Wolfe
        # condition 2 is met if and only if the step length s satisfies
        # |x + s| <= c2 * |x|
        f = lambda x: np.dot(x, x)
        fp = lambda x: 2 * x
        p = np.array([1, 0])

        # Smallest s satisfying strong Wolfe conditions for these arguments is 30
        x = -60 * p
        c2 = 0.5

        s, _, _, _, _, _ = ls.line_search_wolfe2(f, fp, x, p, amax=30, c2=c2)
        assert_line_wolfe(x, p, s, f, fp)

        s, _, _, _, _, _ = assert_warns(LineSearchWarning,
                                        ls.line_search_wolfe2, f, fp, x, p,
                                        amax=29, c2=c2)
        assert_(s is None)

        # s=30 will only be tried on the 6th iteration, so this won't converge
        assert_warns(LineSearchWarning, ls.line_search_wolfe2, f, fp, x, p,
                     c2=c2, maxiter=5)

    def test_line_search_armijo(self):
        c = 0
        for name, f, fprime, x, p, old_f in self.line_iter():
            f0 = f(x)
            g0 = fprime(x)
            self.fcount = 0
            s, fc, fv = ls.line_search_armijo(f, x, p, g0, f0)
            c += 1
            assert_equal(self.fcount, fc)
            assert_fp_equal(fv, f(x + s*p))
            assert_line_armijo(x, p, s, f, err_msg=name)
        assert_(c >= 9)

    # -- More specific tests

    def test_armijo_terminate_1(self):
        # Armijo should evaluate the function only once if the trial step
        # is already suitable
        count = [0]

        def phi(s):
            count[0] += 1
            return -s + 0.01*s**2
        s, phi1 = ls.scalar_search_armijo(phi, phi(0), -1, alpha0=1)
        assert_equal(s, 1)
        assert_equal(count[0], 2)
        assert_armijo(s, phi)

    def test_wolfe_terminate(self):
        # wolfe1 and wolfe2 should also evaluate the function only a few
        # times if the trial step is already suitable

        def phi(s):
            count[0] += 1
            return -s + 0.05*s**2

        def derphi(s):
            count[0] += 1
            return -1 + 0.05*2*s

        for func in [ls.scalar_search_wolfe1, ls.scalar_search_wolfe2]:
            count = [0]
            r = func(phi, derphi, phi(0), None, derphi(0))
            assert_(r[0] is not None, (r, func))
            assert_(count[0] <= 2 + 2, (count, func))
            assert_wolfe(r[0], phi, derphi, err_msg=str(func))