"""Effective medium theory potential."""

from math import sqrt, exp, log

import numpy as np

from ase.data import chemical_symbols
from ase.units import Bohr
from ase.calculators.neighborlist import NeighborList
from ase.calculators.calculator import Calculator, all_changes


parameters = {
    #      E0     s0    V0     eta2    kappa   lambda  n0
    #      eV     bohr  eV     bohr^-1 bohr^-1 bohr^-1 bohr^-3
    'Al': (-3.28, 3.00, 1.493, 1.240,  2.000,  1.169,  0.00700),
    'Cu': (-3.51, 2.67, 2.476, 1.652,  2.740,  1.906,  0.00910),
    'Ag': (-2.96, 3.01, 2.132, 1.652,  2.790,  1.892,  0.00547),
    'Au': (-3.80, 3.00, 2.321, 1.674,  2.873,  2.182,  0.00703),
    'Ni': (-4.44, 2.60, 3.673, 1.669,  2.757,  1.948,  0.01030),
    'Pd': (-3.90, 2.87, 2.773, 1.818,  3.107,  2.155,  0.00688),
    'Pt': (-5.85, 2.90, 4.067, 1.812,  3.145,  2.192,  0.00802),
    # extra parameters - just for fun ...
    'H':  (-3.21, 1.31, 0.132, 2.652,  2.790,  3.892,  0.00547),
    'C':  (-3.50, 1.81, 0.332, 1.652,  2.790,  1.892,  0.01322),
    'N':  (-5.10, 1.88, 0.132, 1.652,  2.790,  1.892,  0.01222),
    'O':  (-4.60, 1.95, 0.332, 1.652,  2.790,  1.892,  0.00850)}

beta = 1.809     # (16 * pi / 3)**(1.0 / 3) / 2**0.5,
                 # but preserve historical rounding


class EMT(Calculator):
    implemented_properties = ['energy', 'forces']

    nolabel = True

    def __init__(self):
        Calculator.__init__(self)

    def initialize(self, atoms):
        self.par = {}
        self.rc = 0.0
        self.numbers = atoms.get_atomic_numbers()
        maxseq = max(par[1] for par in parameters.values()) * Bohr
        rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
        rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
        self.acut = np.log(9999.0) / (rr - rc)
        for Z in self.numbers:
            if Z not in self.par:
                p = parameters[chemical_symbols[Z]]
                s0 = p[1] * Bohr
                eta2 = p[3] / Bohr
                kappa = p[4] / Bohr
                x = eta2 * beta * s0
                gamma1 = 0.0
                gamma2 = 0.0
                for i, n in enumerate([12, 6, 24]):
                    r = s0 * beta * sqrt(i + 1)
                    x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
                    gamma1 += x * exp(-eta2 * (r - beta * s0))
                    gamma2 += x * exp(-kappa / beta * (r - beta * s0))

                self.par[Z] = {'E0': p[0],
                               's0': s0,
                               'V0': p[2],
                               'eta2': eta2,
                               'kappa': kappa,
                               'lambda': p[5] / Bohr,
                               'n0': p[6] / Bohr**3,
                               'rc': rc,
                               'gamma1': gamma1,
                               'gamma2': gamma2}
                #if rc + 0.5 > self.rc:
                #    self.rc = rc + 0.5

        self.ksi = {}
        for s1, p1 in self.par.items():
            self.ksi[s1] = {}
            for s2, p2 in self.par.items():
                #self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
                #                    exp(eta1 * (p1['s0'] - p2['s0'])))
                self.ksi[s1][s2] = p2['n0'] / p1['n0']
                
        self.forces = np.empty((len(atoms), 3))
        self.sigma1 = np.empty(len(atoms))
        self.deds = np.empty(len(atoms))
                    
        self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
                               self_interaction=False)

    def calculate(self, atoms=None, properties=['energy'],
                  system_changes=all_changes):
        Calculator.calculate(self, atoms, properties, system_changes)

        if 'numbers' in system_changes:
            self.initialize(self.atoms)

        positions = self.atoms.positions
        numbers = self.atoms.numbers
        cell = self.atoms.cell
        
        self.nl.update(self.atoms)
        
        self.energy = 0.0
        self.sigma1[:] = 0.0
        self.forces[:] = 0.0

        natoms = len(self.atoms)

        for a1 in range(natoms):
            Z1 = numbers[a1]
            p1 = self.par[Z1]
            ksi = self.ksi[Z1]
            neighbors, offsets = self.nl.get_neighbors(a1)
            offsets = np.dot(offsets, cell)
            for a2, offset in zip(neighbors, offsets):
                d = positions[a2] + offset - positions[a1]
                r = sqrt(np.dot(d, d))
                if r < self.rc + 0.5:
                    Z2 = numbers[a2]
                    p2 = self.par[Z2]
                    self.interact1(a1, a2, d, r, p1, p2, ksi[Z2])
                                
        for a in range(natoms):
            Z = numbers[a]
            p = self.par[Z]
            try:
                ds = -log(self.sigma1[a] / 12) / (beta * p['eta2'])
            except (OverflowError, ValueError):
                self.deds[a] = 0.0
                self.energy -= p['E0']
                continue
            x = p['lambda'] * ds
            y = exp(-x)
            z = 6 * p['V0'] * exp(-p['kappa'] * ds)
            self.deds[a] = ((x * y * p['E0'] * p['lambda'] + p['kappa'] * z) /
                            (self.sigma1[a] * beta * p['eta2']))
            self.energy += p['E0'] * ((1 + x) * y - 1) + z

        for a1 in range(natoms):
            Z1 = numbers[a1]
            p1 = self.par[Z1]
            ksi = self.ksi[Z1]
            neighbors, offsets = self.nl.get_neighbors(a1)
            offsets = np.dot(offsets, cell)
            for a2, offset in zip(neighbors, offsets):
                d = positions[a2] + offset - positions[a1]
                r = sqrt(np.dot(d, d))
                if r < self.rc + 0.5:
                    Z2 = numbers[a2]
                    p2 = self.par[Z2]
                    self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])

        self.results['energy'] = self.energy
        self.results['forces'] = self.forces

    def interact1(self, a1, a2, d, r, p1, p2, ksi):
        x = exp(self.acut * (r - self.rc))
        theta = 1.0 / (1.0 + x)
        y1 = (0.5 * p1['V0'] * exp(-p2['kappa'] * (r / beta - p2['s0'])) *
              ksi / p1['gamma2'] * theta)
        y2 = (0.5 * p2['V0'] * exp(-p1['kappa'] * (r / beta - p1['s0'])) /
              ksi / p2['gamma2'] * theta)
        self.energy -= y1 + y2
        f = ((y1 * p2['kappa'] + y2 * p1['kappa']) / beta +
             (y1 + y2) * self.acut * theta * x) * d / r
        self.forces[a1] += f
        self.forces[a2] -= f
        self.sigma1[a1] += (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
                            ksi * theta / p1['gamma1'])
        self.sigma1[a2] += (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
                            ksi * theta / p2['gamma1'])

    def interact2(self, a1, a2, d, r, p1, p2, ksi):
        x = exp(self.acut * (r - self.rc))
        theta = 1.0 / (1.0 + x)
        y1 = (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
              ksi / p1['gamma1'] * theta * self.deds[a1])
        y2 = (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
              ksi / p2['gamma1'] * theta * self.deds[a2])
        f = ((y1 * p2['eta2'] + y2 * p1['eta2']) +
             (y1 + y2) * self.acut * theta * x) * d / r
        self.forces[a1] -= f
        self.forces[a2] += f
