import theano
import theano.tensor as T
import numpy as np


def asfloat(value):
    """ Convert variable to float type configured by theano
    floatX variable.

    Parameters
    ----------
    value : matrix, ndarray or scalar
        Value that could be converted to float type.

    Returns
    -------
    matrix, ndarray or scalar
        Output would be input value converted to float type
        configured by theano floatX variable.
    """

    if isinstance(value, (np.matrix, np.ndarray)):
        return value.astype(theano.config.floatX)

    float_x_type = np.cast[theano.config.floatX]
    return float_x_type(value)


def clone(instance):
    class_ = instance.__class__
    parameters = instance.get_params()
    return class_(**parameters)


class FuzzyCMeans(object):
    """
    Fuzzy c-means.

    Paramaters
    ----------
    n_clusters : int
        Number of clusters.
    m : float
    """
    def __init__(self, n_clusters, m=2):
        if n_clusters < 2:
            raise ValueError("Number of clusters should be greater than 2")

        if m < 1:
            raise ValueError("Parameter `m` should be greater than 1")

        self.n_clusters = n_clusters
        self.m = m

        self.centers_ = None
        self.is_initialized = False

    def init_methods(self):
        if self.is_initialized:
            raise AttributeError("Methods have already been initialized.")

        x = T.matrix('x')
        centers = self.centers_

        d = distance_to_centers = (
            x.reshape((x.shape[0], 1, x.shape[1])) -
            centers.reshape((1, centers.shape[0], centers.shape[1]))
        ).norm(L=2, axis=2)

        weights = 1 / (
            (
                distance_to_centers.reshape((d.shape[0], d.shape[1], 1)) /
                distance_to_centers.reshape((d.shape[0], 1, d.shape[1]))
            ) ** asfloat(2. / (self.m - 1))
        ).sum(axis=2)

        proba = weights / T.sum(weights, axis=1).reshape((-1, 1))
        proba_power_m = weights ** self.m
        new_centers = (
            proba_power_m.T.dot(x) /
            T.sum(proba_power_m, axis=0).reshape((-1, 1))
        )

        self.predict_proba = theano.function([x], proba)
        self.train_iteration = theano.function([x], proba, updates=[
            (centers, new_centers),
        ])

        self.is_initialized = True

    def get_params(self, deep=False):
        return dict(n_clusters=self.n_clusters, m=self.m)

    @property
    def centers(self):
        return self.centers_.get_value()

    def fit(self, data, maxiter=100, epsilon=1e-5, verbose=False):
        n_features = data.shape[1]

        if self.centers_ is None:
            data_min = data.min(axis=0)
            data_max = data.max(axis=0)

            random_centers = np.random.random((self.n_clusters, n_features))
            scaled_centers = (data_max - data_min) * random_centers + data_min
            self.centers_ = theano.shared(
                name='centers',
                value=asfloat(scaled_centers)
            )

        n_expected_features = self.centers.shape[1]
        if n_expected_features != n_features:
            raise ValueError("Input data must contain {} features, "
                             "found {}".format(n_expected_features,
                                               n_features))

        if not self.is_initialized:
            self.init_methods()

        i = 1
        proba_update = np.inf
        prev_proba = None
        while (proba_update > epsilon) and (i <= maxiter):
            proba = self.train_iteration(data)

            if prev_proba is not None:
                proba_update = np.linalg.norm(prev_proba - proba)

            prev_proba = proba
            i += 1

    def predict(self, data):
        proba = self.predict_proba(data)
        return proba.argmax(axis=1)


def select_best_clustering(algorithm, n_trials, data, **fit_kwargs):
    """ Select best clusters using SSE.

    Parameters
    ----------
    algorithm : object
    n_trials : int
    data : matrix

    Raises
    ------
    ValueError
        Exception will raise in case input parameter values
        are invalid.

    Returns
    -------
    object
        Pretrained clustering algorithm that give smallest
        SSE (sum of squared error) score.
    """

    if n_trials < 1:
        raise ValueError("Number of trials should be greater than 1")

    if not isinstance(n_trials, int):
        raise ValueError("Number of tirals should be an integer number")

    algorithms = []
    for trial in range(n_trials):
        algorithm = clone(algorithm)
        algorithm.fit(data, **fit_kwargs)

        clusters = algorithm.predict(data)
        centers = algorithm.centers[clusters, :]
        sse_score = np.sum((data - centers) ** 2)

        # We should use second variable as unique value to prevent
        # object instance comparison when we have exactly the same
        # score values.
        algorithms.append((sse_score, trial, algorithm))

    _, _, best_algorithm = min(algorithms)
    return best_algorithm


if __name__ == '__main__':
    fcm = FuzzyCMeans(n_clusters=2, m=2)
    fcm.fit(data, maxiter=100)