"""Structure optimization. """

import sys
import pickle
import time
from math import sqrt
from os.path import isfile

import numpy as np

from ase.parallel import rank, barrier
from ase.io.trajectory import Trajectory
import collections


class Dynamics:
    """Base-class for all MD and structure optimization classes."""
    def __init__(self, atoms, logfile, trajectory, master=None):
        """Dynamics object.

        Parameters:

        atoms: Atoms object
            The Atoms object to operate on.

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

        trajectory: Trajectory object or str
            Attach trajectory object.  If *trajectory* is a string a
            Trajectory will be constructed.  Use *None* for no
            trajectory.

        master: boolean
            Defaults to None, which causes only rank 0 to save files.  If
            set to true,  this rank will save files.
        """

        self.atoms = atoms
        if master is None:
            master = rank == 0
        if not master:
            logfile = None
        elif isinstance(logfile, str):
            if logfile == '-':
                logfile = sys.stdout
            else:
                logfile = open(logfile, 'a')
        self.logfile = logfile
        
        self.observers = []
        self.nsteps = 0

        if trajectory is not None:
            if isinstance(trajectory, str):
                trajectory = Trajectory(trajectory, mode='w',
                                        atoms=atoms, master=master)
            self.attach(trajectory)

    def get_number_of_steps(self):
        return self.nsteps

    def insert_observer(self, function, position=0, interval=1,
                        *args, **kwargs):
        """Insert an observer."""
        if not isinstance(function, collections.Callable):
            function = function.write
        self.observers.insert(position, (function, interval, args, kwargs))

    def attach(self, function, interval=1, *args, **kwargs):
        """Attach callback function.

        If *interval > 0*, at every *interval* steps, call *function* with
        arguments *args* and keyword arguments *kwargs*.

        If *interval <= 0*, after step *interval*, call *function* with
        arguments *args* and keyword arguments *kwargs*.  This is
        currently zero indexed."""

        if not hasattr(function, '__call__'):
            function = function.write
        self.observers.append((function, interval, args, kwargs))

    def call_observers(self):
        for function, interval, args, kwargs in self.observers:
            call = False
            # Call every interval iterations
            if interval > 0:
                if (self.nsteps % interval) == 0:
                    call = True
            # Call only on iteration interval
            elif interval <= 0:
                if self.nsteps == abs(interval):
                    call = True
            if call:
                function(*args, **kwargs)


class Optimizer(Dynamics):
    """Base-class for all structure optimization classes."""
    def __init__(self, atoms, restart, logfile, trajectory, master=None):
        """Structure optimizer object.

        Parameters:

        atoms: Atoms object
            The Atoms object to relax.
        
        restart: str
            Filename for restart file.  Default value is *None*.
        
        logfile: file object or str
            If *logfile* is a string, a file with that name will be opened.
            Use '-' for stdout.
        
        trajectory: Trajectory object or str
            Attach trajectory object.  If *trajectory* is a string a
            Trajectory will be constructed.  Use *None* for no
            trajectory.

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

        if restart is None or not isfile(restart):
            self.initialize()
        else:
            self.read()
            barrier()

    def initialize(self):
        pass

    def run(self, fmax=0.05, steps=100000000):
        """Run structure optimization algorithm.

        This method will return when the forces on all individual
        atoms are less than *fmax* or when the number of steps exceeds
        *steps*."""

        self.fmax = fmax
        step = 0
        while step < steps:
            f = self.atoms.get_forces()
            self.log(f)
            self.call_observers()
            if self.converged(f):
                return
            self.step(f)
            self.nsteps += 1
            step += 1

    def converged(self, forces=None):
        """Did the optimization converge?"""
        if forces is None:
            forces = self.atoms.get_forces()
        if hasattr(self.atoms, 'get_curvature'):
            return ((forces**2).sum(axis=1).max() < self.fmax**2 and
                    self.atoms.get_curvature() < 0.0)
        return (forces**2).sum(axis=1).max() < self.fmax**2

    def log(self, forces):
        fmax = sqrt((forces**2).sum(axis=1).max())
        e = self.atoms.get_potential_energy()
        T = time.localtime()
        if self.logfile is not None:
            name = self.__class__.__name__
            self.logfile.write('%s: %3d  %02d:%02d:%02d %15.6f %12.4f\n' %
                               (name, self.nsteps, T[3], T[4], T[5], e, fmax))
            self.logfile.flush()
        
    def dump(self, data):
        if rank == 0 and self.restart is not None:
            pickle.dump(data, open(self.restart, 'wb'), protocol=2)

    def load(self):
        return pickle.load(open(self.restart))


class NDPoly:
    def __init__(self, ndims=1, order=3):
        """Multivariate polynomium.

        ndims: int
            Number of dimensions.
        order: int
            Order of polynomium."""
        
        if ndims == 0:
            exponents = [()]
        else:
            exponents = []
            for i in range(order + 1):
                E = NDPoly(ndims - 1, order - i).exponents
                exponents += [(i,) + tuple(e) for e in E]
        self.exponents = np.array(exponents)
        self.c = None
        
    def __call__(self, *x):
        """Evaluate polynomial at x."""
        return np.dot(self.c, (x**self.exponents).prod(1))

    def fit(self, x, y):
        """Fit polynomium at points in x to values in y."""
        A = (x**self.exponents[:, np.newaxis]).prod(2)
        self.c = np.linalg.solve(np.inner(A, A), np.dot(A, y))


def polyfit(x, y, order=3):
    """Fit polynomium at points in x to values in y.

    With D dimensions and N points, x must have shape (N, D) and y
    must have length N."""
    
    p = NDPoly(len(x[0]), order)
    p.fit(x, y)
    return p
