# -*- coding: utf-8 -*-
# ProDy: A Python Package for Protein Dynamics Analysis
# 
# Copyright (C) 2010-2012 Ahmet Bakan
# 
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# 
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#  
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>

"""This module defines a class and a function for anisotropic network model
(ANM) calculations.""" 

__author__ = 'Ahmet Bakan'
__copyright__ = 'Copyright (C) 2010-2012 Ahmet Bakan'

import time
from types import FunctionType 

import numpy as np

from prody import LOGGER
from prody.atomic import Atomic, AtomGroup
from prody.proteins import parsePDB
from prody.utilities import importLA, checkCoords
from prody.kdtree import KDTree

from .gnm import GNMBase, ZERO, checkENMParameters

__all__ = ['ANM', 'calcANM']

class ANM(GNMBase):

    """Class for Anisotropic Network Model (ANM) analysis of proteins 
    ([PD00]_, [ARA01]_)
    
    |example| See example :ref:`anm`.
    
    """

    def __init__(self, name='Unknown'):
        
        GNMBase.__init__(self, name)
        self._is3d = True
        self._cutoff = None
        self._kirchhoff = None
        self._gamma = None
        self._hessian = None

    def _reset(self):
        
        GNMBase._reset(self)
        self._hessian = None
        self._is3d = True
        
    def getHessian(self):
        """Return a copy of the Hessian matrix."""
        
        if self._hessian is None: return None
        return self._hessian.copy()
    
    def _getHessian(self):
        """Return the Hessian matrix."""
        
        return self._hessian
    
    def setHessian(self, hessian):
        """Set Hessian matrix.  A symmetric matrix is expected, i.e. not a 
        lower- or upper-triangular matrix."""
        
        if not isinstance(hessian, np.ndarray):
            raise TypeError('hessian must be a Numpy array')
        elif hessian.ndim != 2 or hessian.shape[0] != hessian.shape[1]:
            raise ValueError('hessian must be square matrix')
        elif hessian.shape[0] % 3:
            raise ValueError('hessian.shape must be (3*n_atoms,3*n_atoms)')
        elif hessian.dtype != float:
            try:
                hessian = hessian.astype(float)
            except:
                raise ValueError('hessian.dtype must be float')
        self._reset()
        self._hessian = hessian
        self._dof = hessian.shape[0]
        self._n_atoms = self._dof / 3 

    def buildHessian(self, coords, cutoff=15., gamma=1., **kwargs):
        """Build Hessian matrix for given coordinate set.
        
        :arg coords: a coordinate set or an object with ``getCoords`` method
        :type coords: :class:`numpy.ndarray`
        
        :arg cutoff: cutoff distance (Å) for pairwise interactions,
            default is 15.0 Å, minimum is 4.0 Å 
        :type cutoff: float
        
        :arg gamma: spring constant, default is 1.0 
        :type gamma: float, :class:`Gamma`
        
        :arg sparse: elect to use sparse matrices, default is **False**. If 
            Scipy is not found, :class:`ImportError` is raised.
        :type sparse: bool
        
        :arg kdtree: elect to use KDTree for building Hessian matrix, 
            default is **False** since KDTree method is slower
        :type kdtree: bool

        
        Instances of :class:`Gamma` classes and custom functions are
        accepted as *gamma* argument.        
    
        When Scipy is available, user can select to use sparse matrices for
        efficient usage of memory at the cost of computation speed."""
        
        try:
            coords = (coords._getCoords() if hasattr(coords, '_getCoords') else
                      coords.getCoords()) 
        except AttributeError:
            try:
                checkCoords(coords)
            except TypeError:
                raise TypeError('coords must be a Numpy array or an object '
                                'with `getCoords` method')
        
        cutoff, g, gamma = checkENMParameters(cutoff, gamma)
        self._reset()
        self._cutoff = cutoff
        self._gamma = g
        n_atoms = coords.shape[0]
        dof = n_atoms * 3
        start = time.time()
        
        if kwargs.get('sparse', False):
            try:
                from scipy import sparse as scipy_sparse
            except ImportError:    
                raise ImportError('failed to import scipy.sparse, which  is '
                                  'required for sparse matrix calculations')
            kirchhoff = scipy_sparse.lil_matrix((n_atoms, n_atoms))
            hessian = scipy_sparse.lil_matrix((dof, dof))
        else:
            kirchhoff = np.zeros((n_atoms, n_atoms), 'd')
            hessian = np.zeros((dof, dof), float)
            
        if kwargs.get('kdtree', False):
            LOGGER.info('Using KDTree for building the Hessian.')
            kdtree = KDTree(coords) 
            kdtree.search(cutoff)
            for i, j in kdtree.getIndices():
                i2j = coords[j] - coords[i]
                dist2 = np.dot(i2j, i2j)
                g = gamma(dist2, i, j)
                super_element = np.outer(i2j, i2j) * (- g / dist2)  
                res_i3 = i*3
                res_i33 = res_i3+3
                res_j3 = j*3
                res_j33 = res_j3+3
                hessian[res_i3:res_i33, res_j3:res_j33] = super_element
                hessian[res_j3:res_j33, res_i3:res_i33] = super_element
                hessian[res_i3:res_i33, res_i3:res_i33] = \
                    hessian[res_i3:res_i33, res_i3:res_i33] - super_element
                hessian[res_j3:res_j33, res_j3:res_j33] = \
                    hessian[res_j3:res_j33, res_j3:res_j33] - super_element
                kirchhoff[i, j] = -g
                kirchhoff[j, i] = -g
                kirchhoff[i, i] = kirchhoff[i, i] - g
                kirchhoff[j, j] = kirchhoff[j, j] - g
        else:
            cutoff2 = cutoff * cutoff 
            for i in range(n_atoms):
                res_i3 = i*3
                res_i33 = res_i3+3
                i_p1 = i+1
                i2j_all = coords[i_p1:, :] - coords[i]
                for j, dist2 in enumerate((i2j_all ** 2).sum(1)):
                    if dist2 > cutoff2:
                        continue             
                    i2j = i2j_all[j]
                    j += i_p1
                    g = gamma(dist2, i, j)
                    res_j3 = j*3
                    res_j33 = res_j3+3
                    super_element = np.outer(i2j, i2j) * (- g / dist2) 
                    hessian[res_i3:res_i33, res_j3:res_j33] = super_element 
                    hessian[res_j3:res_j33, res_i3:res_i33] = super_element
                    hessian[res_i3:res_i33, res_i3:res_i33] = \
                        hessian[res_i3:res_i33, res_i3:res_i33] - super_element
                    hessian[res_j3:res_j33, res_j3:res_j33] = \
                        hessian[res_j3:res_j33, res_j3:res_j33] - super_element
                    kirchhoff[i, j] = -g
                    kirchhoff[j, i] = -g
                    kirchhoff[i, i] = kirchhoff[i, i] - g
                    kirchhoff[j, j] = kirchhoff[j, j] - g
        LOGGER.info('Hessian was built in {0:.2f}s.'.format(time.time()-start))
        self._kirchhoff = kirchhoff
        self._hessian = hessian
        self._n_atoms = n_atoms
        self._dof = dof

    def calcModes(self, n_modes=20, zeros=False, turbo=True):
        """Calculate normal modes.  This method uses :func:`scipy.linalg.eigh` 
        function to diagonalize the Hessian matrix. When Scipy is not found, 
        :func:`numpy.linalg.eigh` is used.

        :arg n_modes: number of non-zero eigenvalues/vectors to calculate. 
            If ``None`` is given, all modes will be calculated. 
        :type n_modes: int or None, default is 20
        
        :arg zeros: If ``True``, modes with zero eigenvalues will be kept.
        :type zeros: bool, default is ``False``
        
        :arg turbo: Use a memory intensive, but faster way to calculate modes.
        :type turbo: bool, default is ``True``
        """
        
        if self._hessian is None:
            raise ValueError('Hessian matrix is not built or set')
        assert n_modes is None or isinstance(n_modes, int) and n_modes > 0, \
            'n_modes must be a positive integer'
        assert isinstance(zeros, bool), 'zeros must be a boolean' 
        assert isinstance(turbo, bool), 'turbo must be a boolean'
        linalg = importLA()
        start = time.time()
        shift = 5
        if linalg.__package__.startswith('scipy'):
            if n_modes is None:
                eigvals = None
                n_modes = self._dof 
            else: 
                if n_modes >= self._dof:
                    eigvals = None
                    n_modes = self._dof 
                else:
                    eigvals = (0, n_modes + shift)
            if eigvals: 
                turbo = False
            if isinstance(self._hessian, np.ndarray):            
                values, vectors = linalg.eigh(self._hessian, turbo=turbo, 
                                              eigvals=eigvals)
            else:
                try:
                    from scipy.sparse import linalg as scipy_sparse_la
                except ImportError:    
                    raise ImportError('failed to import scipy.sparse.linalg, '
                                      'which is required for sparse matrix '
                                      'decomposition')
                try:
                    values, vectors = scipy_sparse_la.eigsh(
                            self._hessian, k=n_modes+6, which='SA')
                except:                
                    values, vectors = scipy_sparse_la.eigen_symmetric(
                            self._hessian, k=n_modes+6, which='SA')
        
        else:
            if n_modes is not None:
                LOGGER.info('Scipy is not found, all modes are calculated.')
            values, vectors = linalg.eigh(self._hessian)
        n_zeros = sum(values < ZERO)
        if n_zeros < 6: 
            LOGGER.warning('Less than 6 zero eigenvalues are calculated.')
            shift = n_zeros - 1
        elif n_zeros > 6: 
            LOGGER.warning('More than 6 zero eigenvalues are calculated.')
            shift = n_zeros - 1
        if zeros:
            shift = -1
        self._eigvals = values[1+shift:]
        self._vars = 1 / self._eigvals
        self._trace = self._vars.sum()
        self._array = vectors[:, 1+shift:]
        self._n_modes = len(self._eigvals)
        LOGGER.debug('{0} modes were calculated in {1:.2f}s.'
                          ''.format(self._n_modes, time.time()-start))


def calcANM(pdb, selstr='calpha', cutoff=15., gamma=1., n_modes=20, 
            zeros=False):
    """Return an :class:`ANM` instance and atoms used for the calculations.
    By default only alpha carbons are considered, but selection string helps 
    selecting a subset of it.  *pdb* can be :class:`.Atomic` instance."""
    
    if isinstance(pdb, str):
        ag = parsePDB(pdb)
        title = ag.getTitle()
    elif isinstance(pdb, Atomic):
        ag = pdb
        if isinstance(pdb, AtomGroup):
            title = ag.getTitle()
        else: 
            title = ag.getAtomGroup().getTitle()
    else:
        raise TypeError('pdb must be an atomic class, not {0}'
                        .format(type(pdb)))
    anm = ANM(title)
    sel = ag.select(selstr)
    anm.buildHessian(sel, cutoff, gamma)
    anm.calcModes(n_modes)
    return anm, sel 
