# -*- coding: utf-8 -*-
import sys

import numpy as np

from ase.optimize.optimize import Optimizer
from ase.utils.linesearch import LineSearch


class LBFGS(Optimizer):
    """Limited memory BFGS optimizer.
    
    A limited memory version of the bfgs algorithm. Unlike the bfgs algorithm
    used in bfgs.py, the inverse of Hessian matrix is updated.  The inverse
    Hessian is represented only as a diagonal matrix to save memory

    """
    def __init__(self, atoms, restart=None, logfile='-', trajectory=None,
                 maxstep=None, memory=100, damping=1.0, alpha=70.0,
                 use_line_search=False, master=None):
        """Parameters:

        atoms: Atoms object
            The Atoms object to relax.

        restart: string
            Pickle file used to store vectors for updating the inverse of
            Hessian matrix. If set, file with such a name will be searched
            and information stored will be used, if the file exists.

        logfile: file object or str
            If *logfile* is a string, a file with that name will be opened.
            Use '-' for stdout.

        trajectory: string
            Pickle file used to store trajectory of atomic movement.

        maxstep: float
            How far is a single atom allowed to move. This is useful for DFT
            calculations where wavefunctions can be reused if steps are small.
            Default is 0.04 Angstrom.

        memory: int
            Number of steps to be stored. Default value is 100. Three numpy
            arrays of this length containing floats are stored.

        damping: float
            The calculated step is multiplied with this number before added to
            the positions.

        alpha: float
            Initial guess for the Hessian (curvature of energy surface). A
            conservative value of 70.0 is the default, but number of needed
            steps to converge might be less if a lower value is used. However,
            a lower value also means risk of instability.

        master: boolean
            Defaults to None, which causes only rank 0 to save files.  If
            set to true,  this rank will save files.
        """
        Optimizer.__init__(self, atoms, restart, logfile, trajectory, master)

        if maxstep is not None:
            if maxstep > 1.0:
                raise ValueError('You are using a much too large value for ' +
                                 'the maximum step size: %.1f Angstrom' %
                                 maxstep)
            self.maxstep = maxstep
        else:
            self.maxstep = 0.04

        self.memory = memory
        self.H0 = 1. / alpha  # Initial approximation of inverse Hessian
                            # 1./70. is to emulate the behaviour of BFGS
                            # Note that this is never changed!
        self.damping = damping
        self.use_line_search = use_line_search
        self.p = None
        self.function_calls = 0
        self.force_calls = 0

    def initialize(self):
        """Initalize everything so no checks have to be done in step"""
        self.iteration = 0
        self.s = []
        self.y = []
        self.rho = []  # Store also rho, to avoid calculationg the dot product
                       # again and again

        self.r0 = None
        self.f0 = None
        self.e0 = None
        self.task = 'START'
        self.load_restart = False

    def read(self):
        """Load saved arrays to reconstruct the Hessian"""
        self.iteration, self.s, self.y, self.rho, \
        self.r0, self.f0, self.e0, self.task = self.load()
        self.load_restart = True

    def step(self, f):
        """Take a single step
        
        Use the given forces, update the history and calculate the next step --
        then take it"""
        r = self.atoms.get_positions()
    
        self.update(r, f, self.r0, self.f0)
        
        s = self.s
        y = self.y
        rho = self.rho
        H0 = self.H0

        loopmax = np.min([self.memory, self.iteration])
        a = np.empty((loopmax,), dtype=np.float64)

        ### The algorithm itself:
        q = -f.reshape(-1)
        for i in range(loopmax - 1, -1, -1):
            a[i] = rho[i] * np.dot(s[i], q)
            q -= a[i] * y[i]
        z = H0 * q
        
        for i in range(loopmax):
            b = rho[i] * np.dot(y[i], z)
            z += s[i] * (a[i] - b)

        self.p = - z.reshape((-1, 3))
        ###
 
        g = -f
        if self.use_line_search == True:
            e = self.func(r)
            self.line_search(r, g, e)
            dr = (self.alpha_k * self.p).reshape(len(self.atoms), -1)
        else:
            self.force_calls += 1
            self.function_calls += 1
            dr = self.determine_step(self.p) * self.damping
        self.atoms.set_positions(r + dr)
        
        self.iteration += 1
        self.r0 = r
        self.f0 = -g
        self.dump((self.iteration, self.s, self.y,
                   self.rho, self.r0, self.f0, self.e0, self.task))

    def determine_step(self, dr):
        """Determine step to take according to maxstep
        
        Normalize all steps as the largest step. This way
        we still move along the eigendirection.
        """
        steplengths = (dr**2).sum(1)**0.5
        longest_step = np.max(steplengths)
        if longest_step >= self.maxstep:
            dr *= self.maxstep / longest_step
        
        return dr

    def update(self, r, f, r0, f0):
        """Update everything that is kept in memory

        This function is mostly here to allow for replay_trajectory.
        """
        if self.iteration > 0:
            s0 = r.reshape(-1) - r0.reshape(-1)
            self.s.append(s0)

            # We use the gradient which is minus the force!
            y0 = f0.reshape(-1) - f.reshape(-1)
            self.y.append(y0)
            
            rho0 = 1.0 / np.dot(y0, s0)
            self.rho.append(rho0)

        if self.iteration > self.memory:
            self.s.pop(0)
            self.y.pop(0)
            self.rho.pop(0)

    def replay_trajectory(self, traj):
        """Initialize history from old trajectory."""
        if isinstance(traj, str):
            from ase.io.trajectory import Trajectory
            traj = Trajectory(traj, 'r')
        r0 = None
        f0 = None
        # The last element is not added, as we get that for free when taking
        # the first qn-step after the replay
        for i in range(0, len(traj) - 1):
            r = traj[i].get_positions()
            f = traj[i].get_forces()
            self.update(r, f, r0, f0)
            r0 = r.copy()
            f0 = f.copy()
            self.iteration += 1
        self.r0 = r0
        self.f0 = f0

    def func(self, x):
        """Objective function for use of the optimizers"""
        self.atoms.set_positions(x.reshape(-1, 3))
        self.function_calls += 1
        return self.atoms.get_potential_energy()

    def fprime(self, x):
        """Gradient of the objective function for use of the optimizers"""
        self.atoms.set_positions(x.reshape(-1, 3))
        self.force_calls += 1
        # Remember that forces are minus the gradient!
        return - self.atoms.get_forces().reshape(-1)

    def line_search(self, r, g, e):
        self.p = self.p.ravel()
        p_size = np.sqrt((self.p **2).sum())
        if p_size <= np.sqrt(len(self.atoms) * 1e-10):
            self.p /= (p_size / np.sqrt(len(self.atoms) * 1e-10))
        g = g.ravel()
        r = r.ravel()
        ls = LineSearch()
        self.alpha_k, e, self.e0, self.no_update = \
           ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
                           maxstep=self.maxstep, c1=.23,
                           c2=.46, stpmax=50.)
        if self.alpha_k is None:
            raise RuntimeError('LineSearch failed!')

            
class LBFGSLineSearch(LBFGS):
    """This optimizer uses the LBFGS algorithm, but does a line search that
    fulfills the Wolff conditions.
    """

    def __init__(self, *args, **kwargs):
        kwargs['use_line_search'] = True
        LBFGS.__init__(self, *args, **kwargs)

#    """Modified version of LBFGS.
#
#    This optimizer uses the LBFGS algorithm, but does a line search for the
#    minimum along the search direction. This is done by issuing an additional
#    force call for each step, thus doubling the number of calculations.
#
#    Additionally the Hessian is reset if the new guess is not sufficiently
#    better than the old one.
#    """
#    def __init__(self, *args, **kwargs):
#        self.dR = kwargs.pop('dR', 0.1)
#        LBFGS.__init__(self, *args, **kwargs)
#
#    def update(self, r, f, r0, f0):
#        """Update everything that is kept in memory
#
#        This function is mostly here to allow for replay_trajectory.
#        """
#        if self.iteration > 0:
#            a1 = abs(np.dot(f.reshape(-1), f0.reshape(-1)))
#            a2 = np.dot(f0.reshape(-1), f0.reshape(-1))
#            if not (a1 <= 0.5 * a2 and a2 != 0):
#                # Reset optimization
#                self.initialize()
#
#        # Note that the reset above will set self.iteration to 0 again
#        # which is why we should check again
#        if self.iteration > 0:
#            s0 = r.reshape(-1) - r0.reshape(-1)
#            self.s.append(s0)
#
#            # We use the gradient which is minus the force!
#            y0 = f0.reshape(-1) - f.reshape(-1)
#            self.y.append(y0)
#            
#            rho0 = 1.0 / np.dot(y0, s0)
#            self.rho.append(rho0)
#
#        if self.iteration > self.memory:
#            self.s.pop(0)
#            self.y.pop(0)
#            self.rho.pop(0)
#
#    def determine_step(self, dr):
#        f = self.atoms.get_forces()
#        
#        # Unit-vector along the search direction
#        du = dr / np.sqrt(np.dot(dr.reshape(-1), dr.reshape(-1)))
#
#        # We keep the old step determination before we figure
#        # out what is the best to do.
#        maxstep = self.maxstep * np.sqrt(3 * len(self.atoms))
#
#        # Finite difference step using temporary point
#        self.atoms.positions += (du * self.dR)
#        # Decide how much to move along the line du
#        Fp1 = np.dot(f.reshape(-1), du.reshape(-1))
#        Fp2 = np.dot(self.atoms.get_forces().reshape(-1), du.reshape(-1))
#        CR = (Fp1 - Fp2) / self.dR
#        #RdR = Fp1*0.1
#        if CR < 0.0:
#            #print "negcurve"
#            RdR = maxstep
#            #if(abs(RdR) > maxstep):
#            #    RdR = self.sign(RdR) * maxstep
#        else:
#            Fp = (Fp1 + Fp2) * 0.5
#            RdR = Fp / CR
#            if abs(RdR) > maxstep:
#                RdR = np.sign(RdR) * maxstep
#            else:
#                RdR += self.dR * 0.5
#        return du * RdR


class HessLBFGS(LBFGS):
    """Backwards compatibiliyt class"""
    def __init__(self, *args, **kwargs):
        if 'method' in kwargs:
            del kwargs['method']
        sys.stderr.write('Please use LBFGS instead of HessLBFGS!')
        LBFGS.__init__(self, *args, **kwargs)


class LineLBFGS(LBFGSLineSearch):
    """Backwards compatibiliyt class"""
    def __init__(self, *args, **kwargs):
        if 'method' in kwargs:
            del kwargs['method']
        sys.stderr.write('Please use LBFGSLineSearch instead of LineLBFGS!')
        LBFGSLineSearch.__init__(self, *args, **kwargs)
