#!/usr/bin/env python
################################################################################
#
#  CDDL HEADER START
#
#  The contents of this file are subject to the terms of the Common Development
#  and Distribution License Version 1.0 (the "License").
#
#  You can obtain a copy of the license at
#  http:# www.opensource.org/licenses/CDDL-1.0.  See the License for the
#  specific language governing permissions and limitations under the License.
#
#  When distributing Covered Code, include this CDDL HEADER in each file and
#  include the License file in a prominent location with the name LICENSE.CDDL.
#  If applicable, add the following below this CDDL HEADER, with the fields
#  enclosed by brackets "[]" replaced with your own identifying information:
#
#  Portions Copyright (c) [yyyy] [name of copyright owner]. All rights reserved.
#
#  CDDL HEADER END
#
#  Copyright (c) 2017, Regents of the University of Minnesota.
#  All rights reserved.
#
#  Contributor(s):
#     Ellad B. Tadmor
#
################################################################################

# The docstring below is vc_description
'''Check whether a model is invariant with respect to atom permutations that
preserve species, i.e. swapping any two atoms with the same species must
not change the energy or forces. This must be true for all models. The check
is performed for a randomly distorted non-periodic diamond cube base structure.
Separate configurations are tested for each species supported by the model,
as well as one containing a random distribution of all species.  The energy
and forces of each configuration are compared with one where each atom is
randomly swapped with another atom of the same species. The energy and
forces must remain unchanged. The verification check will pass if these
conditions are satisfied for all configurations that the model is able
to compute. Configurations used for testing are provided as auxiliary files.'''

# Python 2-3 compatible code issues
from __future__ import print_function
try:
   input = raw_input
except NameError:
   pass

from ase.lattice.cubic import Diamond
from kimcalculator import KIMCalculator, KIM_get_supported_species_list
import kimvc
import sys
import random
import numpy as np
import math

__version__ = "000"
__author__ = "Ellad Tadmor"
vc_name = "vc-permutation-symmetry"
vc_description = kimvc.vc_stripall(__doc__)
vc_category = "mandatory"
vc_grade_basis = "passfail"
vc_files = []

################################################################################
#
#   FUNCTIONS
#
################################################################################

################################################################################
def perform_permutation_symmetry_check(vc, atoms, heading, dashwidth):
    '''
    Perform perfmutation symmetry check for the ASE atoms object in 'atoms'
    '''
    # set comparison tolerance
    tole = 1e-8
    eps_prec = np.finfo(float).eps

    # compute the energy in the original location
    energy_orig = atoms.get_potential_energy()
    forces_orig = atoms.get_forces()

    # figure out which species are in the structure and create a list of
    # the indices for the occurences of each species in the structure
    species = atoms.get_chemical_symbols()
    unique_species = set(species)
    spec_indices = {}
    for spec in unique_species:
        spec_indices[spec] = [i for i, s in enumerate(species) if s == spec]

    # randomly switch each atom in the structure with another atom with the
    # same species.
    perm_map = [0]*len(atoms)
    for i in range(0,len(atoms)):
        spec = atoms[i].symbol
        # Swap this atom if it hasn't been already been swapped earlier
        if i in spec_indices[spec]:
            # choose a random atom of the same species
            if len(spec_indices[spec])>1:  # only do this if there are more than
                j = i                     # one of this atom type
                while j==i:
                    j = random.choice(spec_indices[spec])
                perm_map[i] = j
                perm_map[j] = i
                spec_indices[spec].remove(i)
                spec_indices[spec].remove(j)
                # swap atoms i and j
                posi_save = atoms[i].position.copy()
                atoms[i].position = atoms[j].position
                atoms[j].position = posi_save
            else:
                perm_map[i] = i
                spec_indices[spec].remove(i)

    # compute the energy in the permuted structure
    energy_perm = atoms.get_potential_energy()
    forces_perm = atoms.get_forces()

    # check if energy is the same up to a numerical tolerance
    den = max(0.5*(abs(energy_perm) + abs(energy_orig)), eps_prec)
    passed_energy = abs(energy_perm-energy_orig)/den < tole

    # report results and return
    vc.rwrite('')
    vc.rwrite(heading)
    vc.rwrite('-'*dashwidth)
    vc.rwrite('')
    vc.rwrite('Permutation list = {}'.format(perm_map))
    vc.rwrite('')
    vc.rwrite('Energy requirement:')
    vc.rwrite('')
    vc.rwrite( \
        'V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), '
        'where r_i is the position of atom i, V is the potential energy, ')
    vc.rwrite('and PI is the permutation operator (which randomly swaps all '
              'atoms with other atoms of the same species).')
    vc.rwrite('')
    vc.rwrite('V(r_(PI 1),...,r_(PI N)) = {0}'.format(energy_perm))
    vc.rwrite('V(r_1,...,r_N)           = {0}'.format(energy_orig))
    vc.rwrite('')

    # check forces for inversion symmetry
    vc.rwrite('Forces requirement:')
    vc.rwrite('')
    vc.rwrite( \
        'f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), '
        'where r_i is the position of atom i, f_i is the force on atom i ')
    vc.rwrite('and PI is the permutation operator (which randomly swaps all '
              'atoms with other atoms of the same species).')
    vc.rwrite('')
    hfmt = '{:>3}' + ' '*13 + '{}' + ' '*34 + '{}'
    fmt  = '{:>3}   ' + '{: .8e}   '*3 + '|   ' + '{: .8e}   '*3 + '{}'
    vc.rwrite(hfmt.format('i','f_(PI i)(r_(PI 1),...,r_(PI N))', \
                              'f_i(r_1,...,r_N)'))
    vc.rwrite('-'*dashwidth)
    passed_forces = True
    for i in range(0,len(atoms)):
        f_lhs = forces_perm[perm_map[i]]
        f_rhs = forces_orig[i]
        den=np.maximum(0.5*(np.absolute(f_lhs)+np.absolute(f_rhs)),eps_prec)
        force_ok = np.all(np.absolute(f_lhs - f_rhs)/den<tole)
        stat = ''
        if not force_ok:
            passed_forces = False
            stat = 'ERR'
        vc.rwrite(fmt.format(i, f_lhs[0], f_lhs[1], f_lhs[2], \
                                f_rhs[0], f_rhs[1], f_rhs[2], stat))
    vc.rwrite('-'*dashwidth)

    # determine overall result
    passed = passed_energy and passed_forces

    if passed:
        vc.rwrite('PASS: Energies and forces are the same to within a '
                   'relative error of {0}'.format(tole))
    else:
        vc.rwrite('FAIL: Energies and/or forces differ by more than '
                  'a relative error of {0}'.format(tole))
    vc.rwrite('-'*dashwidth)

    return passed

################################################################################
def do_vc(model, vc):
    '''
    Do Symmetry Inversion VC
    '''
    # Get supported species
    species = KIM_get_supported_species_list(model)
    species = kimvc.remove_species_not_supported_by_ASE(species)
    species.sort()

    # Basic cell parameters
    lattice_constant_orig = 5.0
    pert_amp_orig = 0.1*lattice_constant_orig
    ncells_per_side = 2
    seed = 13
    random.seed(seed)

    # Print Vc info
    dashwidth = 121
    vc.rwrite('')
    vc.rwrite('-'*dashwidth)
    vc.rwrite('Results for KIM Model      : %s' % model.strip())
    vc.rwrite('Supported species          : %s' % ' '.join(species))
    vc.rwrite('')
    vc.rwrite('random seed                = %d'    % seed)
    vc.rwrite('lattice constant (orig)    = %0.3f' % lattice_constant_orig)
    vc.rwrite('perturbation amplitude     = %0.3f' % pert_amp_orig)
    vc.rwrite('number unit cells per side = %d'    % ncells_per_side)
    vc.rwrite('-'*dashwidth + '\n')

    # Initialize variables
    got_atleast_one = False
    passed_all = True

    # Perform permutation symmetry check for monotatomic systems
    for spec in species:
        calc = KIMCalculator(model)
        lattice_constant = lattice_constant_orig
        got_initial_config = False
        while not got_initial_config:
            atoms = Diamond(
                size=(ncells_per_side, ncells_per_side, ncells_per_side),
                latticeconstant=lattice_constant, symbol=spec, pbc=False)
            atoms.set_calculator(calc)
            try:
                kimvc.rescale_to_get_nonzero_forces(atoms, 0.01)
                got_initial_config = True
            except:
                # Initial config failed. This most likely due to an evaluation
                # outside the legal model range. Increase lattice constant and
                # try again.
                lattice_constant += 0.25
                if lattice_constant > 10.0:
                    sys.exit(1)  # Cannot find a working configuration within a
                                 # a reasonable lattice constant range.
        # Randomize positions
        save_positions = atoms.get_positions()
        pert_amp = pert_amp_orig
        got_randomized_config = False
        while not got_randomized_config:
            try:
                kimvc.randomize_positions(atoms, pert_amp)
                forces = atoms.get_forces() # make sure forces can be computed
                got_randomized_config = True
            except:
                # Failed to compute forces; reset to original posns and retry
                atoms.set_positions(save_positions)
                pert_amp *= 0.5  # cut perturbation amplitude by half
        # Move atoms around until all forces are sizeable
        kimvc.perturb_until_all_forces_sizeable(atoms, pert_amp)
        aux_file = 'config-'+spec+'.xyz'
        vc_files.append(aux_file)
        vc.write_aux_ase_atoms(aux_file, atoms, 'xyz')
        heading = 'MONOATOMIC STRUCTURE -- Species = ' + spec + \
                '   (Configuration in file "' + aux_file + '")'
        try:
            passed = perform_permutation_symmetry_check(vc, atoms, \
                                                        heading, dashwidth)
            passed_all = passed_all and passed
            got_atleast_one = True
        except:
            pass

    # Perform numerical derivative check for mixed system
    if len(species)>1:
        lattice_constant = lattice_constant_orig
        while True:
            atoms = Diamond(
                    size=(ncells_per_side, ncells_per_side, ncells_per_side),
                    latticeconstant=lattice_constant, symbol="H", pbc=False)
            if len(atoms) < len(species):
                ncells_per_side += 1
            else:
                break
        kimvc.randomize_species(atoms, species)
        calc = KIMCalculator(model)
        atoms.set_calculator(calc)
        got_initial_config = False
        while not got_initial_config:
            try:
                kimvc.rescale_to_get_nonzero_forces(atoms, 0.01)
                got_initial_config = True
            except:
                # Initial config failed. This most likely due to an evaluation
                # outside the legal model range. Increase lattice constant and
                # try again.
                lattice_constant += 0.25
                if lattice_constant > 10.0:
                    sys.exit(1)  # Cannot find a working configuration within a
                                # a reasonable lattice constant range.
                acell = lattice_constant*ncells_per_side
                atoms.set_cell([acell, acell, acell],scale_atoms=True)
        # Randomize positions
        save_positions = atoms.get_positions()
        pert_amp = pert_amp_orig
        got_randomized_config = False
        while not got_randomized_config:
            try:
                kimvc.randomize_positions(atoms, pert_amp)
                forces = atoms.get_forces() # make sure forces can be computed
                got_randomized_config = True
            except:
                # Failed to compute forces; reset to original posns and retry
                atoms.set_positions(save_positions)
                pert_amp *= 0.5  # cut perturbation amplitude by half
        kimvc.perturb_until_all_forces_sizeable(atoms, pert_amp)
        aux_file = 'config-'+''.join(species)+'.xyz'
        vc_files.append(aux_file)
        vc.write_aux_ase_atoms(aux_file, atoms, 'xyz')
        heading = 'MIXED STRUCTURE -- Species = ' + ' '.join(species) + \
                  '   (Configuration in file "' + aux_file + '")'
        try:
            passed = perform_permutation_symmetry_check(vc, atoms, \
                                                        heading, dashwidth)
            passed_all = passed_all and passed
            got_atleast_one = True
        except:
            pass

    if got_atleast_one:

        # Compute grade
        vc.rwrite('')
        vc.rwrite('='*dashwidth)
        vc.rwrite( \
            'To pass this verification check the model must be invariant '
            'with respect to')
        vc.rwrite( \
            'perumutation symmetry for all configurations it was able '
            'to compute.')
        vc.rwrite('')

        if passed_all:
            vc_grade = 'P'
            vc_comment = 'Model energy has permutation symmetry for '     + \
                         'all configurations the model was able to compute.'
        else:
            vc_grade = 'F'
            vc_comment = \
                'Model energy does NOT have permutation symmetry for at ' + \
                'least one configuration that the model was able to '     + \
                'compute. This indicates an error in the implementation ' + \
                'of the model.'

        vc.rwrite('Grade: {}'.format(vc_grade))
        vc.rwrite('')
        vc.rwrite('Comment: '+vc_comment)
        vc.rwrite('')

        return vc_grade, vc_comment

    else:
        raise RuntimeError('Failed to compute all configuration for the '
                           'permutation symmetry verification check.')
        return None, None

################################################################################
#
#   MAIN PROGRAM
#
###############################################################################
if __name__ == '__main__':

    # Get the model extended KIM ID:
    model = input("Model Extended KIM ID = ")

    # Define VC object and do verification check
    vc = kimvc.vc_object(vc_name, vc_description, __author__)
    with vc:
        # Perform verification check and get grade
        try:
            vc_grade, vc_comment = do_vc(model, vc)
        except:
            vc_grade = "N/A"
            vc_comment = "Unable to perform verification check due to an error."
            sys.stderr.write('ERROR: Unable to perform verification check.\n')

        # Pack results in a dictionary and write VC property instance
        results = {"vc_name"        : vc_name,
                   "vc_description" : vc_description,
                   "vc_category"    : vc_category,
                   "vc_grade_basis" : vc_grade_basis,
                   "vc_grade"       : vc_grade,
                   "vc_comment"     : vc_comment,
                   "vc_files"       : vc_files}
        vc.write_results(results)