vl_bfgs.py 6.97 KB
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# -*- coding: utf-8 -*-

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import numpy as np

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from .quasi_newton_minimizer import QuasiNewtonMinimizer
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from .line_searching import LineSearchStrongWolfe
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from .bare_dot import bare_dot

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class VL_BFGS(QuasiNewtonMinimizer):
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    def __init__(self, line_searcher=LineSearchStrongWolfe(), callback=None,
                 convergence_tolerance=1E-4, convergence_level=3,
                 iteration_limit=None, max_history_length=10):

        super(VL_BFGS, self).__init__(
                                line_searcher=line_searcher,
                                callback=callback,
                                convergence_tolerance=convergence_tolerance,
                                convergence_level=convergence_level,
                                iteration_limit=iteration_limit)

        self.max_history_length = max_history_length

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    def __call__(self, x0, f, fprime, f_args=()):
        self._information_store = None
        return super(VL_BFGS, self).__call__(x0, f, fprime, f_args=())

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    def _get_descend_direction(self, x, gradient):
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        # initialize the information store if it doesn't already exist
        try:
            self._information_store.add_new_point(x, gradient)
        except AttributeError:
            self._information_store = InformationStore(self.max_history_length,
                                                       x0=x,
                                                       gradient=gradient)

        b = self._information_store.b
        delta = self._information_store.delta

        descend_direction = delta[0] * b[0]
        for i in xrange(1, len(delta)):
            descend_direction += delta[i] * b[i]

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        norm = np.sqrt(bare_dot(descend_direction, descend_direction))
        if norm != 1:
            descend_direction /= norm
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        return descend_direction
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class InformationStore(object):
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    def __init__(self, max_history_length, x0, gradient):
        self.max_history_length = max_history_length
        self.s = LimitedList(max_history_length)
        self.y = LimitedList(max_history_length)
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        self.last_x = x0.copy()
        self.last_gradient = gradient.copy()
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        self.k = 0
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        self._ss_store = {}
        self._sy_store = {}
        self._yy_store = {}
        self._sgrad_store = {}
        self._ygrad_store = {}
        self._gradgrad_store = None

#        self.dot_matrix = {}

    @property
    def history_length(self):
        return min(self.k, self.max_history_length)

    @property
    def b(self):
        result = []
        m = self.history_length
        k = self.k

        s = self.s
        for i in xrange(m):
            result.append(s[k-m+i])

        y = self.y
        for i in xrange(m):
            result.append(y[k-m+i])

        result.append(self.last_gradient)

        return result

    @property
    def b_dot_b(self):
        m = self.history_length
        k = self.k
        result = np.empty((2*m+1, 2*m+1), dtype=np.float)

        for i in xrange(m):
            for j in xrange(m):
                result[i, j] = self.ss_store(k-m+i, k-m+j)

                sy_ij = self.sy_store(k-m+i, k-m+j)
                result[i, m+j] = sy_ij
                result[m+j, i] = sy_ij

                result[m+i, m+j] = self.yy_store(k-m+i, k-m+j)

            sgrad_i = self.sgrad_store(k-m+i)
            result[2*m, i] = sgrad_i
            result[i, 2*m] = sgrad_i

            ygrad_i = self.ygrad_store(k-m+i)
            result[2*m, m+i] = ygrad_i
            result[m+i, 2*m] = ygrad_i

        result[2*m, 2*m] = self.gradgrad_store()

        return result
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    @property
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    def delta(self):
        m = self.history_length
        b_dot_b = self.b_dot_b

        delta = np.zeros(2*m+1, dtype=np.float)
        delta[2*m] = -1

        alpha = np.empty(m, dtype=np.float)

        for j in xrange(m-1, -1, -1):
            delta_b_b = sum([delta[l] * b_dot_b[l, j] for l in xrange(2*m+1)])
            alpha[j] = delta_b_b/b_dot_b[j, m+j]
            delta[m+j] -= alpha[j]

        for i in xrange(2*m+1):
            delta[i] *= b_dot_b[m-1, 2*m-1]/b_dot_b[2*m-1, 2*m-1]

        for j in xrange(m-1, -1, -1):
            delta_b_b = sum([delta[l]*b_dot_b[m+j, l] for l in xrange(2*m+1)])
            beta = delta_b_b/b_dot_b[j, m+j]
            delta[j] += (alpha[j] - beta)

        return delta

    def ss_store(self, i, j):
        key = tuple(sorted((i, j)))
        if key not in self._ss_store:
            self._ss_store[key] = self.s[i].dot(self.s[j])
        return self._ss_store[key]

    def sy_store(self, i, j):
        key = (i, j)
        if key not in self._sy_store:
            self._sy_store[key] = self.s[i].dot(self.y[j])
        return self._sy_store[key]

    def yy_store(self, i, j):
        key = tuple(sorted((i, j)))
        if key not in self._yy_store:
            self._yy_store[key] = self.y[i].dot(self.y[j])
        return self._yy_store[key]

    def sgrad_store(self, i):
        return self.s[i].dot(self.last_gradient)

    def ygrad_store(self, i):
        return self.y[i].dot(self.last_gradient)

    def gradgrad_store(self):
        return self.last_gradient.dot(self.last_gradient)
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    def add_new_point(self, x, gradient):
        self.k += 1

        new_s = x - self.last_x
        self.s.add(new_s)

        new_y = gradient - self.last_gradient
        self.y.add(new_y)

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        self.last_x = x.copy()
        self.last_gradient = gradient.copy()
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#
#        k = self.k
#        m = self.actual_history_length
#        big_m = self.history_length
#
#        # compute dot products
#        for i in xrange(k-1, k-m-1, -1):
#            # new_s with s
#            key = (big_m+m, big_m+1+i)
#            self.dot_matrix[key] = new_s.dot(self.s[i])
#
#            # new_s with y
#            key = (big_m+m, i+1)
#            self.dot_matrix[key] = new_s.dot(self.y[i])
#
#            # new_y with s
#            if i != k-1:
#                key = (big_m+1+i, k)
#                self.dot_matrix[key] = new_y.dot(self.s[i])
#
#            # new_y with y
#            # actually key = (i+1, k) but the convention is that the first
#            # index is larger than the second one
#            key = (k, i+1)
#            self.dot_matrix[key] = new_y.dot(self.y[i])
#
#            # gradient with s
#            key = (big_m+1+i, 0)
#            self.dot_matrix[key] = gradient.dot(self.s[i])
#
#            # gradient with y
#            key = (i+1, 0)
#            self.dot_matrix[key] = gradient.dot(self.y[i])
#
#        # gradient with gradient
#        key = (0, 0)
#        self.dot_matrix[key] = gradient.dot(gradient)
#
#        self.last_x = x
#        self.last_gradient = gradient
#
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class LimitedList(object):
    def __init__(self, history_length):
        self.history_length = int(history_length)
        self._offset = 0
        self._storage = []

    def __getitem__(self, index):
        return self._storage[index-self._offset]

    def add(self, value):
        if len(self._storage) == self.history_length:
            self._storage.pop(0)
            self._offset += 1
        self._storage.append(value)