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File Content: `linesearch.py`

"""
Functions
---------
.. autosummary::
   :toctree: generated/

    line_search_armijo
    line_search_wolfe1
    line_search_wolfe2
    scalar_search_wolfe1
    scalar_search_wolfe2

"""
from __future__ import division, print_function, absolute_import

from warnings import warn

from scipy.optimize import minpack2
import numpy as np
from scipy._lib.six import xrange

__all__ = ['LineSearchWarning', 'line_search_wolfe1', 'line_search_wolfe2',
           'scalar_search_wolfe1', 'scalar_search_wolfe2',
           'line_search_armijo']

class LineSearchWarning(RuntimeWarning):
    pass


#------------------------------------------------------------------------------
# Minpack's Wolfe line and scalar searches
#------------------------------------------------------------------------------

def line_search_wolfe1(f, fprime, xk, pk, gfk=None,
                       old_fval=None, old_old_fval=None,
                       args=(), c1=1e-4, c2=0.9, amax=50, amin=1e-8,
                       xtol=1e-14):
    """
    As `scalar_search_wolfe1` but do a line search to direction `pk`

    Parameters
    ----------
    f : callable
        Function `f(x)`
    fprime : callable
        Gradient of `f`
    xk : array_like
        Current point
    pk : array_like
        Search direction

    gfk : array_like, optional
        Gradient of `f` at point `xk`
    old_fval : float, optional
        Value of `f` at point `xk`
    old_old_fval : float, optional
        Value of `f` at point preceding `xk`

    The rest of the parameters are the same as for `scalar_search_wolfe1`.

    Returns
    -------
    stp, f_count, g_count, fval, old_fval
        As in `line_search_wolfe1`
    gval : array
        Gradient of `f` at the final point

    """
    if gfk is None:
        gfk = fprime(xk)

    if isinstance(fprime, tuple):
        eps = fprime[1]
        fprime = fprime[0]
        newargs = (f, eps) + args
        gradient = False
    else:
        newargs = args
        gradient = True

    gval = [gfk]
    gc = [0]
    fc = [0]

    def phi(s):
        fc[0] += 1
        return f(xk + s*pk, *args)

    def derphi(s):
        gval[0] = fprime(xk + s*pk, *newargs)
        if gradient:
            gc[0] += 1
        else:
            fc[0] += len(xk) + 1
        return np.dot(gval[0], pk)

    derphi0 = np.dot(gfk, pk)

    stp, fval, old_fval = scalar_search_wolfe1(
            phi, derphi, old_fval, old_old_fval, derphi0,
            c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol)

    return stp, fc[0], gc[0], fval, old_fval, gval[0]


def scalar_search_wolfe1(phi, derphi, phi0=None, old_phi0=None, derphi0=None,
                         c1=1e-4, c2=0.9,
                         amax=50, amin=1e-8, xtol=1e-14):
    """
    Scalar function search for alpha that satisfies strong Wolfe conditions

    alpha > 0 is assumed to be a descent direction.

    Parameters
    ----------
    phi : callable phi(alpha)
        Function at point `alpha`
    derphi : callable dphi(alpha)
        Derivative `d phi(alpha)/ds`. Returns a scalar.

    phi0 : float, optional
        Value of `f` at 0
    old_phi0 : float, optional
        Value of `f` at the previous point
    derphi0 : float, optional
        Value `derphi` at 0
    c1, c2 : float, optional
        Wolfe parameters
    amax, amin : float, optional
        Maximum and minimum step size
    xtol : float, optional
        Relative tolerance for an acceptable step.

    Returns
    -------
    alpha : float
        Step size, or None if no suitable step was found
    phi : float
        Value of `phi` at the new point `alpha`
    phi0 : float
        Value of `phi` at `alpha=0`

    Notes
    -----
    Uses routine DCSRCH from MINPACK.

    """

    if phi0 is None:
        phi0 = phi(0.)
    if derphi0 is None:
        derphi0 = derphi(0.)

    if old_phi0 is not None and derphi0 != 0:
        alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0)
        if alpha1 < 0:
            alpha1 = 1.0
    else:
        alpha1 = 1.0

    phi1 = phi0
    derphi1 = derphi0
    isave = np.zeros((2,), np.intc)
    dsave = np.zeros((13,), float)
    task = b'START'

    maxiter = 100
    for i in xrange(maxiter):
        stp, phi1, derphi1, task = minpack2.dcsrch(alpha1, phi1, derphi1,
                                                   c1, c2, xtol, task,
                                                   amin, amax, isave, dsave)
        if task[:2] == b'FG':
            alpha1 = stp
            phi1 = phi(stp)
            derphi1 = derphi(stp)
        else:
            break
    else:
        # maxiter reached, the line search did not converge
        stp = None

    if task[:5] == b'ERROR' or task[:4] == b'WARN':
        stp = None  # failed

    return stp, phi1, phi0

line_search = line_search_wolfe1


#------------------------------------------------------------------------------
# Pure-Python Wolfe line and scalar searches
#------------------------------------------------------------------------------

def line_search_wolfe2(f, myfprime, xk, pk, gfk=None, old_fval=None,
                       old_old_fval=None, args=(), c1=1e-4, c2=0.9, amax=50):
    """Find alpha that satisfies strong Wolfe conditions.

    Parameters
    ----------
    f : callable f(x,*args)
        Objective function.
    myfprime : callable f'(x,*args)
        Objective function gradient.
    xk : ndarray
        Starting point.
    pk : ndarray
        Search direction.
    gfk : ndarray, optional
        Gradient value for x=xk (xk being the current parameter
        estimate). Will be recomputed if omitted.
    old_fval : float, optional
        Function value for x=xk. Will be recomputed if omitted.
    old_old_fval : float, optional
        Function value for the point preceding x=xk
    args : tuple, optional
        Additional arguments passed to objective function.
    c1 : float, optional
        Parameter for Armijo condition rule.
    c2 : float, optional
        Parameter for curvature condition rule.
    amax : float, optional
        Maximum step size

    Returns
    -------
    alpha : float or None
        Alpha for which ``x_new = x0 + alpha * pk``,
        or None if the line search algorithm did not converge.
    fc : int
        Number of function evaluations made.
    gc : int
        Number of gradient evaluations made.
    new_fval : float or None
        New function value ``f(x_new)=f(x0+alpha*pk)``,
        or None if the line search algorithm did not converge.
    old_fval : float
        Old function value ``f(x0)``.
    new_slope : float or None
        The local slope along the search direction at the
        new value ``<myfprime(x_new), pk>``,
        or None if the line search algorithm did not converge.


    Notes
    -----
    Uses the line search algorithm to enforce strong Wolfe
    conditions.  See Wright and Nocedal, 'Numerical Optimization',
    1999, pg. 59-60.

    For the zoom phase it uses an algorithm by [...].

    """
    fc = [0]
    gc = [0]
    gval = [None]

    def phi(alpha):
        fc[0] += 1
        return f(xk + alpha * pk, *args)

    if isinstance(myfprime, tuple):
        def derphi(alpha):
            fc[0] += len(xk) + 1
            eps = myfprime[1]
            fprime = myfprime[0]
            newargs = (f, eps) + args
            gval[0] = fprime(xk + alpha * pk, *newargs)  # store for later use
            return np.dot(gval[0], pk)
    else:
        fprime = myfprime

        def derphi(alpha):
            gc[0] += 1
            gval[0] = fprime(xk + alpha * pk, *args)  # store for later use
            return np.dot(gval[0], pk)

    if gfk is None:
        gfk = fprime(xk, *args)
    derphi0 = np.dot(gfk, pk)

    alpha_star, phi_star, old_fval, derphi_star = scalar_search_wolfe2(
            phi, derphi, old_fval, old_old_fval, derphi0, c1, c2, amax)

    if derphi_star is None:
        warn('The line search algorithm did not converge', LineSearchWarning)
    else:
        # derphi_star is a number (derphi) -- so use the most recently
        # calculated gradient used in computing it derphi = gfk*pk
        # this is the gradient at the next step no need to compute it
        # again in the outer loop.
        derphi_star = gval[0]

    return alpha_star, fc[0], gc[0], phi_star, old_fval, derphi_star


def scalar_search_wolfe2(phi, derphi=None, phi0=None,
                         old_phi0=None, derphi0=None,
                         c1=1e-4, c2=0.9, amax=50):
    """Find alpha that satisfies strong Wolfe conditions.

    alpha > 0 is assumed to be a descent direction.

    Parameters
    ----------
    phi : callable f(x)
        Objective scalar function.
    derphi : callable f'(x), optional
        Objective function derivative (can be None)
    phi0 : float, optional
        Value of phi at s=0
    old_phi0 : float, optional
        Value of phi at previous point
    derphi0 : float, optional
        Value of derphi at s=0
    c1 : float, optional
        Parameter for Armijo condition rule.
    c2 : float, optional
        Parameter for curvature condition rule.
    amax : float, optional
        Maximum step size

    Returns
    -------
    alpha_star : float or None
        Best alpha, or None if the line search algorithm did not converge.
    phi_star : float
        phi at alpha_star
    phi0 : float
        phi at 0
    derphi_star : float or None
        derphi at alpha_star, or None if the line search algorithm
        did not converge.

    Notes
    -----
    Uses the line search algorithm to enforce strong Wolfe
    conditions.  See Wright and Nocedal, 'Numerical Optimization',
    1999, pg. 59-60.

    For the zoom phase it uses an algorithm by [...].

    """

    if phi0 is None:
        phi0 = phi(0.)

    if derphi0 is None and derphi is not None:
        derphi0 = derphi(0.)

    alpha0 = 0
    if old_phi0 is not None and derphi0 != 0:
        alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0)
    else:
        alpha1 = 1.0

    if alpha1 < 0:
        alpha1 = 1.0

    if alpha1 == 0:
        # This shouldn't happen. Perhaps the increment has slipped below
        # machine precision?  For now, set the return variables skip the
        # useless while loop, and raise warnflag=2 due to possible imprecision.
        alpha_star = None
        phi_star = phi0
        phi0 = old_phi0
        derphi_star = None

    phi_a1 = phi(alpha1)
    #derphi_a1 = derphi(alpha1)  evaluated below

    phi_a0 = phi0
    derphi_a0 = derphi0

    i = 1
    maxiter = 10
    for i in xrange(maxiter):
        if alpha1 == 0:
            break
        if (phi_a1 > phi0 + c1 * alpha1 * derphi0) or \
           ((phi_a1 >= phi_a0) and (i > 1)):
            alpha_star, phi_star, derphi_star = \
                        _zoom(alpha0, alpha1, phi_a0,
                              phi_a1, derphi_a0, phi, derphi,
                              phi0, derphi0, c1, c2)
            break

        derphi_a1 = derphi(alpha1)
        if (abs(derphi_a1) <= -c2*derphi0):
            alpha_star = alpha1
            phi_star = phi_a1
            derphi_star = derphi_a1
            break

        if (derphi_a1 >= 0):
            alpha_star, phi_star, derphi_star = \
                        _zoom(alpha1, alpha0, phi_a1,
                              phi_a0, derphi_a1, phi, derphi,
                              phi0, derphi0, c1, c2)
            break

        alpha2 = 2 * alpha1   # increase by factor of two on each iteration
        i = i + 1
        alpha0 = alpha1
        alpha1 = alpha2
        phi_a0 = phi_a1
        phi_a1 = phi(alpha1)
        derphi_a0 = derphi_a1

    else:
        # stopping test maxiter reached
        alpha_star = alpha1
        phi_star = phi_a1
        derphi_star = None
        warn('The line search algorithm did not converge', LineSearchWarning)

    return alpha_star, phi_star, phi0, derphi_star


def _cubicmin(a, fa, fpa, b, fb, c, fc):
    """
    Finds the minimizer for a cubic polynomial that goes through the
    points (a,fa), (b,fb), and (c,fc) with derivative at a of fpa.

    If no minimizer can be found return None

    """
    # f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D

    with np.errstate(divide='raise', over='raise', invalid='raise'):
        try:
            C = fpa
            db = b - a
            dc = c - a
            denom = (db * dc) ** 2 * (db - dc)
            d1 = np.empty((2, 2))
            d1[0, 0] = dc ** 2
            d1[0, 1] = -db ** 2
            d1[1, 0] = -dc ** 3
            d1[1, 1] = db ** 3
            [A, B] = np.dot(d1, np.asarray([fb - fa - C * db,
                                            fc - fa - C * dc]).flatten())
            A /= denom
            B /= denom
            radical = B * B - 3 * A * C
            xmin = a + (-B + np.sqrt(radical)) / (3 * A)
        except ArithmeticError:
            return None
    if not np.isfinite(xmin):
        return None
    return xmin


def _quadmin(a, fa, fpa, b, fb):
    """
    Finds the minimizer for a quadratic polynomial that goes through
    the points (a,fa), (b,fb) with derivative at a of fpa,

    """
    # f(x) = B*(x-a)^2 + C*(x-a) + D
    with np.errstate(divide='raise', over='raise', invalid='raise'):
        try:
            D = fa
            C = fpa
            db = b - a * 1.0
            B = (fb - D - C * db) / (db * db)
            xmin = a - C / (2.0 * B)
        except ArithmeticError:
            return None
    if not np.isfinite(xmin):
        return None
    return xmin


def _zoom(a_lo, a_hi, phi_lo, phi_hi, derphi_lo,
          phi, derphi, phi0, derphi0, c1, c2):
    """
    Part of the optimization algorithm in `scalar_search_wolfe2`.
    """

    maxiter = 10
    i = 0
    delta1 = 0.2  # cubic interpolant check
    delta2 = 0.1  # quadratic interpolant check
    phi_rec = phi0
    a_rec = 0
    while True:
        # interpolate to find a trial step length between a_lo and
        # a_hi Need to choose interpolation here.  Use cubic
        # interpolation and then if the result is within delta *
        # dalpha or outside of the interval bounded by a_lo or a_hi
        # then use quadratic interpolation, if the result is still too
        # close, then use bisection

        dalpha = a_hi - a_lo
        if dalpha < 0:
            a, b = a_hi, a_lo
        else:
            a, b = a_lo, a_hi

        # minimizer of cubic interpolant
        # (uses phi_lo, derphi_lo, phi_hi, and the most recent value of phi)
        #
        # if the result is too close to the end points (or out of the
        # interval) then use quadratic interpolation with phi_lo,
        # derphi_lo and phi_hi if the result is stil too close to the
        # end points (or out of the interval) then use bisection

        if (i > 0):
            cchk = delta1 * dalpha
            a_j = _cubicmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi,
                            a_rec, phi_rec)
        if (i == 0) or (a_j is None) or (a_j > b - cchk) or (a_j < a + cchk):
            qchk = delta2 * dalpha
            a_j = _quadmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi)
            if (a_j is None) or (a_j > b-qchk) or (a_j < a+qchk):
                a_j = a_lo + 0.5*dalpha

        # Check new value of a_j

        phi_aj = phi(a_j)
        if (phi_aj > phi0 + c1*a_j*derphi0) or (phi_aj >= phi_lo):
            phi_rec = phi_hi
            a_rec = a_hi
            a_hi = a_j
            phi_hi = phi_aj
        else:
            derphi_aj = derphi(a_j)
            if abs(derphi_aj) <= -c2*derphi0:
                a_star = a_j
                val_star = phi_aj
                valprime_star = derphi_aj
                break
            if derphi_aj*(a_hi - a_lo) >= 0:
                phi_rec = phi_hi
                a_rec = a_hi
                a_hi = a_lo
                phi_hi = phi_lo
            else:
                phi_rec = phi_lo
                a_rec = a_lo
            a_lo = a_j
            phi_lo = phi_aj
            derphi_lo = derphi_aj
        i += 1
        if (i > maxiter):
            # Failed to find a conforming step size
            a_star = None
            val_star = None
            valprime_star = None
            break
    return a_star, val_star, valprime_star


#------------------------------------------------------------------------------
# Armijo line and scalar searches
#------------------------------------------------------------------------------

def line_search_armijo(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1):
    """Minimize over alpha, the function ``f(xk+alpha pk)``.

    Parameters
    ----------
    f : callable
        Function to be minimized.
    xk : array_like
        Current point.
    pk : array_like
        Search direction.
    gfk : array_like
        Gradient of `f` at point `xk`.
    old_fval : float
        Value of `f` at point `xk`.
    args : tuple, optional
        Optional arguments.
    c1 : float, optional
        Value to control stopping criterion.
    alpha0 : scalar, optional
        Value of `alpha` at start of the optimization.

    Returns
    -------
    alpha
    f_count
    f_val_at_alpha

    Notes
    -----
    Uses the interpolation algorithm (Armijo backtracking) as suggested by
    Wright and Nocedal in 'Numerical Optimization', 1999, pg. 56-57

    """
    xk = np.atleast_1d(xk)
    fc = [0]

    def phi(alpha1):
        fc[0] += 1
        return f(xk + alpha1*pk, *args)

    if old_fval is None:
        phi0 = phi(0.)
    else:
        phi0 = old_fval  # compute f(xk) -- done in past loop

    derphi0 = np.dot(gfk, pk)
    alpha, phi1 = scalar_search_armijo(phi, phi0, derphi0, c1=c1,
                                       alpha0=alpha0)
    return alpha, fc[0], phi1


def line_search_BFGS(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1):
    """
    Compatibility wrapper for `line_search_armijo`
    """
    r = line_search_armijo(f, xk, pk, gfk, old_fval, args=args, c1=c1,
                           alpha0=alpha0)
    return r[0], r[1], 0, r[2]


def scalar_search_armijo(phi, phi0, derphi0, c1=1e-4, alpha0=1, amin=0):
    """Minimize over alpha, the function ``phi(alpha)``.

    Uses the interpolation algorithm (Armijo backtracking) as suggested by
    Wright and Nocedal in 'Numerical Optimization', 1999, pg. 56-57

    alpha > 0 is assumed to be a descent direction.

    Returns
    -------
    alpha
    phi1

    """
    phi_a0 = phi(alpha0)
    if phi_a0 <= phi0 + c1*alpha0*derphi0:
        return alpha0, phi_a0

    # Otherwise compute the minimizer of a quadratic interpolant:

    alpha1 = -(derphi0) * alpha0**2 / 2.0 / (phi_a0 - phi0 - derphi0 * alpha0)
    phi_a1 = phi(alpha1)

    if (phi_a1 <= phi0 + c1*alpha1*derphi0):
        return alpha1, phi_a1

    # Otherwise loop with cubic interpolation until we find an alpha which
    # satifies the first Wolfe condition (since we are backtracking, we will
    # assume that the value of alpha is not too small and satisfies the second
    # condition.

    while alpha1 > amin:       # we are assuming alpha>0 is a descent direction
        factor = alpha0**2 * alpha1**2 * (alpha1-alpha0)
        a = alpha0**2 * (phi_a1 - phi0 - derphi0*alpha1) - \
            alpha1**2 * (phi_a0 - phi0 - derphi0*alpha0)
        a = a / factor
        b = -alpha0**3 * (phi_a1 - phi0 - derphi0*alpha1) + \
            alpha1**3 * (phi_a0 - phi0 - derphi0*alpha0)
        b = b / factor

        alpha2 = (-b + np.sqrt(abs(b**2 - 3 * a * derphi0))) / (3.0*a)
        phi_a2 = phi(alpha2)

        if (phi_a2 <= phi0 + c1*alpha2*derphi0):
            return alpha2, phi_a2

        if (alpha1 - alpha2) > alpha1 / 2.0 or (1 - alpha2/alpha1) < 0.96:
            alpha2 = alpha1 / 2.0

        alpha0 = alpha1
        alpha1 = alpha2
        phi_a0 = phi_a1
        phi_a1 = phi_a2

    # Failed to find a suitable step length
    return None, phi_a1


#------------------------------------------------------------------------------
# Non-monotone line search for DF-SANE
#------------------------------------------------------------------------------

def _nonmonotone_line_search_cruz(f, x_k, d, prev_fs, eta,
                                  gamma=1e-4, tau_min=0.1, tau_max=0.5):
    """
    Nonmonotone backtracking line search as described in [1]_

    Parameters
    ----------
    f : callable
        Function returning a tuple ``(f, F)`` where ``f`` is the value
        of a merit function and ``F`` the residual.
    x_k : ndarray
        Initial position
    d : ndarray
        Search direction
    prev_fs : float
        List of previous merit function values. Should have ``len(prev_fs) <= M``
        where ``M`` is the nonmonotonicity window parameter.
    eta : float
        Allowed merit function increase, see [1]_
    gamma, tau_min, tau_max : float, optional
        Search parameters, see [1]_

    Returns
    -------
    alpha : float
        Step length
    xp : ndarray
        Next position
    fp : float
        Merit function value at next position
    Fp : ndarray
        Residual at next position

    References
    ----------
    [1] "Spectral residual method without gradient information for solving
        large-scale nonlinear systems of equations." W. La Cruz,
        J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006).

    """
    f_k = prev_fs[-1]
    f_bar = max(prev_fs)

    alpha_p = 1
    alpha_m = 1
    alpha = 1

    while True:
        xp = x_k + alpha_p * d
        fp, Fp = f(xp)

        if fp <= f_bar + eta - gamma * alpha_p**2 * f_k:
            alpha = alpha_p
            break

        alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k)

        xp = x_k - alpha_m * d
        fp, Fp = f(xp)

        if fp <= f_bar + eta - gamma * alpha_m**2 * f_k:
            alpha = -alpha_m
            break

        alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k)

        alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p)
        alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m)

    return alpha, xp, fp, Fp


def _nonmonotone_line_search_cheng(f, x_k, d, f_k, C, Q, eta,
                                   gamma=1e-4, tau_min=0.1, tau_max=0.5,
                                   nu=0.85):
    """
    Nonmonotone line search from [1]

    Parameters
    ----------
    f : callable
        Function returning a tuple ``(f, F)`` where ``f`` is the value
        of a merit function and ``F`` the residual.
    x_k : ndarray
        Initial position
    d : ndarray
        Search direction
    f_k : float
        Initial merit function value
    C, Q : float
        Control parameters. On the first iteration, give values
        Q=1.0, C=f_k
    eta : float
        Allowed merit function increase, see [1]_
    nu, gamma, tau_min, tau_max : float, optional
        Search parameters, see [1]_

    Returns
    -------
    alpha : float
        Step length
    xp : ndarray
        Next position
    fp : float
        Merit function value at next position
    Fp : ndarray
        Residual at next position
    C : float
        New value for the control parameter C
    Q : float
        New value for the control parameter Q

    References
    ----------
    .. [1] W. Cheng & D.-H. Li, ''A derivative-free nonmonotone line
           search and its application to the spectral residual
           method'', IMA J. Numer. Anal. 29, 814 (2009).

    """
    alpha_p = 1
    alpha_m = 1
    alpha = 1

    while True:
        xp = x_k + alpha_p * d
        fp, Fp = f(xp)

        if fp <= C + eta - gamma * alpha_p**2 * f_k:
            alpha = alpha_p
            break

        alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k)

        xp = x_k - alpha_m * d
        fp, Fp = f(xp)

        if fp <= C + eta - gamma * alpha_m**2 * f_k:
            alpha = -alpha_m
            break

        alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k)

        alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p)
        alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m)

    # Update C and Q
    Q_next = nu * Q + 1
    C = (nu * Q * (C + eta) + fp) / Q_next
    Q = Q_next

    return alpha, xp, fp, Fp, C, Q
Name	Size	Permission
__pycache__	---	0755
_lsq	---	0755
tests	---	0755
__init__.py	6526 bytes	0644
_basinhopping.py	26053 bytes	0644
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_differentialevolution.py	32558 bytes	0644
_group_columns.cpython-35m-x86_64-linux-gnu.so	141704 bytes	0755
_hungarian.py	9379 bytes	0644
_lbfgsb.cpython-35m-x86_64-linux-gnu.so	133600 bytes	0755
_linprog.py	37305 bytes	0644
_minimize.py	26435 bytes	0644
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_nnls.cpython-35m-x86_64-linux-gnu.so	46656 bytes	0755
_numdiff.py	21209 bytes	0644
_root.py	26007 bytes	0644
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_spectral.py	7986 bytes	0644
_trustregion.py	8598 bytes	0644
_trustregion_dogleg.py	4449 bytes	0644
_trustregion_ncg.py	4646 bytes	0644
_tstutils.py	1322 bytes	0644
_zeros.cpython-35m-x86_64-linux-gnu.so	15760 bytes	0755
cobyla.py	9915 bytes	0644
lbfgsb.py	18069 bytes	0644
linesearch.py	24201 bytes	0644
minpack.py	30534 bytes	0644
minpack2.cpython-35m-x86_64-linux-gnu.so	47448 bytes	0755
moduleTNC.cpython-35m-x86_64-linux-gnu.so	40336 bytes	0755
nnls.py	1423 bytes	0644
nonlin.py	46681 bytes	0644
optimize.py	101006 bytes	0644
setup.py	3267 bytes	0644
slsqp.py	17983 bytes	0644
tnc.py	16533 bytes	0644
zeros.py	19912 bytes	0644
File Content: linesearch.py

File Content: `linesearch.py`
