"""
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 phi'(alpha)
        Objective function derivative. Returns a scalar.
    phi0 : float, optional
        Value of phi at 0
    old_phi0 : float, optional
        Value of phi at previous point
    derphi0 : float, optional
        Value derphi at 0
    c1 : float, optional
        Parameter for Armijo condition rule.
    c2 : float, optional
        Parameter for curvature condition rule.
    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=None,
                       extra_condition=None, maxiter=10):
    """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
    extra_condition : callable, optional
        A callable of the form ``extra_condition(alpha, x, f, g)``
        returning a boolean. Arguments are the proposed step ``alpha``
        and the corresponding ``x``, ``f`` and ``g`` values. The line search 
        accepts the value of ``alpha`` only if this 
        callable returns ``True``. If the callable returns ``False`` 
        for the step length, the algorithm will continue with 
        new iterates. The callable is only called for iterates 
        satisfying the strong Wolfe conditions.
    maxiter : int, optional
        Maximum number of iterations to perform

    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]
    gval_alpha = [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
            gval_alpha[0] = alpha
            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
            gval_alpha[0] = alpha
            return np.dot(gval[0], pk)

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

    if extra_condition is not None:
        # Add the current gradient as argument, to avoid needless
        # re-evaluation
        def extra_condition2(alpha, phi):
            if gval_alpha[0] != alpha:
                derphi(alpha)
            x = xk + alpha * pk
            return extra_condition(alpha, x, phi, gval[0])
    else:
        extra_condition2 = None

    alpha_star, phi_star, old_fval, derphi_star = scalar_search_wolfe2(
            phi, derphi, old_fval, old_old_fval, derphi0, c1, c2, amax,
            extra_condition2, maxiter=maxiter)

    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, phi0=None,
                         old_phi0=None, derphi0=None,
                         c1=1e-4, c2=0.9, amax=None,
                         extra_condition=None, maxiter=10):
    """Find alpha that satisfies strong Wolfe conditions.

    alpha > 0 is assumed to be a descent direction.

    Parameters
    ----------
    phi : callable phi(alpha)
        Objective scalar function.
    derphi : callable phi'(alpha)
        Objective function derivative. Returns a scalar.
    phi0 : float, optional
        Value of phi at 0
    old_phi0 : float, optional
        Value of phi at previous point
    derphi0 : float, optional
        Value of derphi at 0
    c1 : float, optional