import tensorly as tl
from ._base_decomposition import DecompositionMixin
from ..base import unfold
from ..tenalg import multi_mode_dot, mode_dot
from ..tucker_tensor import tucker_to_tensor, TuckerTensor, validate_tucker_rank
import tensorly.tenalg as tlg
from math import sqrt

import warnings

# Author: Jean Kossaifi <jean.kossaifi+tensors@gmail.com>

# License: BSD 3 clause


def partial_tucker(tensor, modes, rank=None, n_iter_max=100, init='svd', tol=10e-5,
                   svd='numpy_svd', random_state=None, verbose=False, mask=None):
    """Partial tucker decomposition via Higher Order Orthogonal Iteration (HOI)

        Decomposes `tensor` into a Tucker decomposition exclusively along the provided modes.

    Parameters
    ----------
    tensor : ndarray
    modes : int list
            list of the modes on which to perform the decomposition
    rank : None, int or int list
        size of the core tensor, ``(len(ranks) == tensor.ndim)``
        if int, the same rank is used for all modes
    n_iter_max : int
                 maximum number of iteration
    init : {'svd', 'random'}, or TuckerTensor optional
        if a TuckerTensor is provided, this is used for initialization
    svd : str, default is 'numpy_svd'
        function to use to compute the SVD,
        acceptable values in tensorly.SVD_FUNS
    tol : float, optional
          tolerance: the algorithm stops when the variation in
          the reconstruction error is less than the tolerance
    random_state : {None, int, np.random.RandomState}
    verbose : int, optional
        level of verbosity
    mask : ndarray
        array of booleans with the same shape as ``tensor`` should be 0 where
        the values are missing and 1 everywhere else. Note:  if tensor is
        sparse, then mask should also be sparse with a fill value of 1 (or
        True).

    Returns
    -------
    core : ndarray
            core tensor of the Tucker decomposition
    factors : ndarray list
            list of factors of the Tucker decomposition.
            with ``core.shape[i] == (tensor.shape[i], ranks[i]) for i in modes``

    """
    if rank is None:
        message = "No value given for 'rank'. The decomposition will preserve the original size."
        warnings.warn(message, Warning)
        rank = [tl.shape(tensor)[mode] for mode in modes]
    elif isinstance(rank, int):
        message = "Given only one int for 'rank' instead of a list of {} modes. Using this rank for all modes.".format(len(modes))
        warnings.warn(message, Warning)
        rank = tuple(rank for _ in modes)
    else:
        rank = tuple(rank)

    if mask is not None and init == "svd":
        message = "Masking occurs after initialization. Therefore, random initialization is recommended."
        warnings.warn(message, Warning)

    try:
        svd_fun = tl.SVD_FUNS[svd]
    except KeyError:
        message = 'Got svd={}. However, for the current backend ({}), the possible choices are {}'.format(
                svd, tl.get_backend(), tl.SVD_FUNS)
        raise ValueError(message)

    # SVD init
    if init == 'svd':
        factors = []
        for index, mode in enumerate(modes):
            eigenvecs, _, _ = svd_fun(unfold(tensor, mode), n_eigenvecs=rank[index], random_state=random_state)
            factors.append(eigenvecs)

        # The initial core approximation is needed here for the masking step
        core = multi_mode_dot(tensor, factors, modes=modes, transpose=True)
    elif init == 'random':
        rng = tl.check_random_state(random_state)
        # len(rank) == len(modes) but we still want a core dimension for the modes not optimized
        core_shape = list(tl.shape(tensor))
        for (i, e) in enumerate(modes):
            core_shape[e] = rank[i]
        core = tl.tensor(rng.random_sample(core_shape), **tl.context(tensor))
        factors = [tl.tensor(rng.random_sample((tl.shape(tensor)[mode], rank[index])), **tl.context(tensor)) for (index, mode) in enumerate(modes)]
    else: 
        (core, factors) = init

    rec_errors = []
    norm_tensor = tl.norm(tensor, 2)

    for iteration in range(n_iter_max):
        if mask is not None:
            tensor = tensor*mask + multi_mode_dot(core, factors, modes=modes, transpose=False)*(1-mask)

        for index, mode in enumerate(modes):
            core_approximation = multi_mode_dot(tensor, factors, modes=modes, skip=index, transpose=True)
            eigenvecs, _, _ = svd_fun(unfold(core_approximation, mode), n_eigenvecs=rank[index], random_state=random_state)
            factors[index] = eigenvecs

        core = multi_mode_dot(tensor, factors, modes=modes, transpose=True)

        # The factors are orthonormal and therefore do not affect the reconstructed tensor's norm
        rec_error = sqrt(abs(norm_tensor**2 - tl.norm(core, 2)**2)) / norm_tensor
        rec_errors.append(rec_error)

        if iteration > 1:
            if verbose:
                print('reconstruction error={}, variation={}.'.format(
                    rec_errors[-1], rec_errors[-2] - rec_errors[-1]))

            if tol and abs(rec_errors[-2] - rec_errors[-1]) < tol:
                if verbose:
                    print('converged in {} iterations.'.format(iteration))
                break

    return (core, factors)


def tucker(tensor, rank, fixed_factors=None, n_iter_max=100, init='svd',
           svd='numpy_svd', tol=10e-5, random_state=None, mask=None, verbose=False):
    """Tucker decomposition via Higher Order Orthogonal Iteration (HOI)

        Decomposes `tensor` into a Tucker decomposition:
        ``tensor = [| core; factors[0], ...factors[-1] |]`` [1]_

    Parameters
    ----------
    tensor : ndarray
    rank : None, int or int list
        size of the core tensor, ``(len(ranks) == tensor.ndim)``
        if int, the same rank is used for all modes
    fixed_factors : int list or None, default is None
        if not None, list of modes for which to keep the factors fixed.
        Only valid if a Tucker tensor is provided as init.
    n_iter_max : int
                 maximum number of iteration
    init : {'svd', 'random'}, optional
    svd : str, default is 'numpy_svd'
        function to use to compute the SVD,
        acceptable values in tensorly.SVD_FUNS
    tol : float, optional
          tolerance: the algorithm stops when the variation in
          the reconstruction error is less than the tolerance
    random_state : {None, int, np.random.RandomState}
    mask : ndarray
        array of booleans with the same shape as ``tensor`` should be 0 where
        the values are missing and 1 everywhere else. Note:  if tensor is
        sparse, then mask should also be sparse with a fill value of 1 (or
        True).
    verbose : int, optional
        level of verbosity

    Returns
    -------
    core : ndarray of size `ranks`
            core tensor of the Tucker decomposition
    factors : ndarray list
            list of factors of the Tucker decomposition.
            Its ``i``-th element is of shape ``(tensor.shape[i], ranks[i])``

    References
    ----------
    .. [1] tl.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications",
       SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.
    """    
    if fixed_factors:
        try:
            (core, factors) = init
        except:
            raise ValueError(f'Got fixed_factor={fixed_factors} but no appropriate Tucker tensor was passed for "init".')
        
        fixed_factors = sorted(fixed_factors)
        modes_fixed, factors_fixed = zip(*[(i, f) for (i, f) in enumerate(factors) if i in fixed_factors])
        core = multi_mode_dot(core, factors_fixed, modes=modes_fixed)
        modes, factors = zip(*[(i, f) for (i, f) in enumerate(factors) if i not in fixed_factors])
        init = (core, list(factors))

        core, new_factors = partial_tucker(tensor, modes, rank=rank, n_iter_max=n_iter_max, init=init,
                             svd=svd, tol=tol, random_state=random_state, mask=mask, verbose=verbose)

        factors = list(new_factors)
        for i, e in enumerate(fixed_factors):
            factors.insert(e, factors_fixed[i])
        core = multi_mode_dot(core, factors_fixed, modes=modes_fixed, transpose=True)

        return TuckerTensor((core, factors))

    else:
        modes = list(range(tl.ndim(tensor)))
        # TO-DO validate rank for partial tucker as well
        rank = validate_tucker_rank(tl.shape(tensor), rank=rank)

        core, factors = partial_tucker(tensor, modes, rank=rank, n_iter_max=n_iter_max, init=init,
                            svd=svd, tol=tol, random_state=random_state, mask=mask, verbose=verbose)
        return TuckerTensor((core, factors))

def non_negative_tucker(tensor, rank, n_iter_max=10, init='svd', tol=10e-5,
                        random_state=None, verbose=False):
    """Non-negative Tucker decomposition

        Iterative multiplicative update, see [2]_

    Parameters
    ----------
    tensor : ``ndarray``
    rank : None, int or int list
        size of the core tensor, ``(len(ranks) == tensor.ndim)``
        if int, the same rank is used for all modes
    n_iter_max : int
        maximum number of iteration
    init : {'svd', 'random'}
    random_state : {None, int, np.random.RandomState}
    verbose : int , optional
        level of verbosity
    ranks : None or int list
    size of the core tensor

    Returns
    -------
    core : ndarray
            positive core of the Tucker decomposition
            has shape `ranks`
    factors : ndarray list
            list of factors of the CP decomposition
            element `i` is of shape ``(tensor.shape[i], rank)``

    References
    ----------
    .. [2] Yong-Deok Kim and Seungjin Choi,
       "Non-negative tucker decomposition",
       IEEE Conference on Computer Vision and Pattern Recognition s(CVPR),
       pp 1-8, 2007
    """
    rank = validate_tucker_rank(tl.shape(tensor), rank=rank)

    epsilon = 10e-12

    # Initialisation
    if init == 'svd':
        core, factors = tucker(tensor, rank)
        nn_factors = [tl.abs(f) for f in factors]
        nn_core = tl.abs(core)
    else:
        rng = tl.check_random_state(random_state)
        core = tl.tensor(rng.random_sample(rank) + 0.01, **tl.context(tensor))  # Check this
        factors = [tl.tensor(rng.random_sample(s), **tl.context(tensor)) for s in zip(tl.shape(tensor), rank)]
        nn_factors = [tl.abs(f) for f in factors]
        nn_core = tl.abs(core)

    norm_tensor = tl.norm(tensor, 2)
    rec_errors = []

    for iteration in range(n_iter_max):
        for mode in range(tl.ndim(tensor)):
            B = tucker_to_tensor((nn_core, nn_factors), skip_factor=mode)
            B = tl.transpose(unfold(B, mode))

            numerator = tl.dot(unfold(tensor, mode), B)
            numerator = tl.clip(numerator, a_min=epsilon, a_max=None)
            denominator = tl.dot(nn_factors[mode], tl.dot(tl.transpose(B), B))
            denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
            nn_factors[mode] *= numerator / denominator

        numerator = tucker_to_tensor((tensor, nn_factors), transpose_factors=True)
        numerator = tl.clip(numerator, a_min=epsilon, a_max=None)
        for i, f in enumerate(nn_factors):
            if i:
                denominator = mode_dot(denominator, tl.dot(tl.transpose(f), f), i)
            else:
                denominator = mode_dot(nn_core, tl.dot(tl.transpose(f), f), i)
        denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
        nn_core *= numerator / denominator

        rec_error = tl.norm(tensor - tucker_to_tensor((nn_core, nn_factors)), 2) / norm_tensor
        rec_errors.append(rec_error)
        if iteration > 1 and verbose:
            print('reconstruction error={}, variation={}.'.format(
                rec_errors[-1], rec_errors[-2] - rec_errors[-1]))

        if iteration > 1 and abs(rec_errors[-2] - rec_errors[-1]) < tol:
            if verbose:
                print('converged in {} iterations.'.format(iteration))
            break

    return TuckerTensor((nn_core, nn_factors))


class Tucker(DecompositionMixin):
    """Tucker decomposition via Higher Order Orthogonal Iteration (HOI).

            Decomposes `tensor` into a Tucker decomposition:
            ``tensor = [| core; factors[0], ...factors[-1] |]`` [1]_

        Parameters
        ----------
        tensor : ndarray
        rank : None, int or int list
            size of the core tensor, ``(len(ranks) == tensor.ndim)``
            if int, the same rank is used for all modes
        non_negative : bool, default is False
            if True, uses a non-negative Tucker via iterative multiplicative updates
            otherwise, uses a Higher-Order Orthogonal Iteration.
        fixed_factors : int list or None, default is None
            if not None, list of modes for which to keep the factors fixed.
            Only valid if a Tucker tensor is provided as init.
        n_iter_max : int
                    maximum number of iteration
        init : {'svd', 'random'}, optional
        svd : str, default is 'numpy_svd'
            ignore if non_negative is True
            function to use to compute the SVD,
            acceptable values in tensorly.SVD_FUNS
        tol : float, optional
            tolerance: the algorithm stops when the variation in
            the reconstruction error is less than the tolerance
        random_state : {None, int, np.random.RandomState}
        verbose : int, optional
            level of verbosity

        Returns
        -------
        core : ndarray of size `ranks`
                core tensor of the Tucker decomposition
        factors : ndarray list
                list of factors of the Tucker decomposition.
                Its ``i``-th element is of shape ``(tensor.shape[i], ranks[i])``

        References
        ----------
        .. [1] tl.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications",
        SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.
        """
    def __init__(self, rank=None, n_iter_max=100,
                 init='svd', svd='numpy_svd', tol=10e-5, fixed_factors=None,
                 random_state=None, mask=None, verbose=False):
        self.rank = rank
        self.n_iter_max = n_iter_max
        self.init = init
        self.svd = svd
        self.tol = tol
        self.random_state = random_state
        self.mask = mask
        self.verbose = verbose

    def fit_transform(self, tensor):
        tucker_tensor = tucker(tensor, rank=self.rank,
                            n_iter_max=self.n_iter_max,
                            init=self.init,
                            svd=self.svd,
                            tol=self.tol,
                            random_state=self.random_state,
                            mask=self.mask,
                            verbose=self.verbose)        
        self.decomposition_ = tucker_tensor
        return tucker_tensor

    # def transform(self, tensor):
    #     _, factors = self.decomposition_
    #     return tlg.multi_mode_dot(tensor, factors, transpose=True)

    # def inverse_transform(self, tensor):
    #     _, factors = self.decomposition_
    #     return tlg.multi_mode_dot(tensor, factors)

    def __repr__(self):
        return f'Rank-{self.rank} Tucker decomposition via HOOI.'


class TuckerNN(DecompositionMixin):
    """Non-Negative Tucker decomposition via iterative multiplicative update.

        Decomposes `tensor` into a Tucker decomposition:
        ``tensor = [| core; factors[0], ...factors[-1] |]`` [1]_

    Parameters
    ----------
    tensor : ndarray
    rank : None, int or int list
        size of the core tensor, ``(len(ranks) == tensor.ndim)``
        if int, the same rank is used for all modes
    non_negative : bool, default is False
        if True, uses a non-negative Tucker via iterative multiplicative updates
        otherwise, uses a Higher-Order Orthogonal Iteration.
    n_iter_max : int
                maximum number of iteration
    init : {'svd', 'random'}, optional
    svd : str, default is 'numpy_svd'
        ignore if non_negative is True
        function to use to compute the SVD,
        acceptable values in tensorly.SVD_FUNS
    tol : float, optional
        tolerance: the algorithm stops when the variation in
        the reconstruction error is less than the tolerance
    random_state : {None, int, np.random.RandomState}
    verbose : int, optional
        level of verbosity

    Returns
    -------
    core : ndarray of size `ranks`
            core tensor of the Tucker decomposition
    factors : ndarray list
            list of factors of the Tucker decomposition.
            Its ``i``-th element is of shape ``(tensor.shape[i], ranks[i])``

    References
    ----------
    .. [1] tl.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications",
    SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.
    """
    def __init__(self, rank=None, n_iter_max=100,
                 init='svd', svd='numpy_svd', tol=10e-5, 
                 random_state=None, verbose=False):
        self.rank = rank
        self.n_iter_max = n_iter_max
        self.init = init
        self.svd = svd
        self.tol = tol
        self.random_state = random_state
        self.verbose = verbose

    def fit_transform(self, tensor):
        tucker_tensor = non_negative_tucker(tensor, rank=self.rank,
                            n_iter_max=self.n_iter_max,
                            init=self.init,
                            tol=self.tol,
                            random_state=self.random_state,
                            verbose=self.verbose)
        self.decomposition_ = tucker_tensor
        return tucker_tensor

    # def transform(self, tensor):
    #     _, factors = self.decomposition_
    #     return tlg.multi_mode_dot(tensor, factors, transpose=True)

    # def inverse_transform(self, tensor):
    #     _, factors = self.decomposition_
    #     return tlg.multi_mode_dot(tensor, factors)

    def __repr__(self):
        return f'Rank-{self.rank} Non-Negative Tucker decomposition via multiplicative updates.'