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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _movMF( X, n_clusters, posterior_type="soft", force_weights=None, max_iter=300, verbose=False, init="random-class", random_state=None, tol=1e-6, ):
 """Mixture of von Mises Fisher clustering. Implements the algorithms (i) and (ii) from "Clustering on the Unit Hypersphere using von Mises-Fisher Distributions" by Banerjee, Dhillon, Ghosh, and Sra. TODO: Currently only supports Banerjee et al 2005 approximation of kappa, however, there are numerous other approximations see _update_params. Attribution Approximation of log-vmf distribution function from movMF R-package. movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions by Kurt Hornik, Bettina Grun, 2014 Find more at: https://cran.r-project.org/web/packages/movMF/vignettes/movMF.pdf https://cran.r-project.org/web/packages/movMF/index.html Parameters n_clusters : int, optional, default: 8 The number of clusters to form as well as the number of centroids to generate. posterior_type: 'soft' or 'hard' Type of posterior computed in exepectation step. See note about attribute: self.posterior_ force_weights : None or array [n_clusters, ] If None, the algorithm will estimate the weights. If an array of weights, algorithm will estimate concentrations and centers with given weights. max_iter : int, default: 300 Maximum number of iterations of the k-means algorithm for a single run. n_init : int, default: 10 Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia. init: (string) one of random-class [default]: random class assignment & centroid computation k-means++ : uses sklearn k-means++ initialization algorithm spherical-k-means : use centroids from one pass of spherical k-means random : random unit norm vectors random-orthonormal : random orthonormal vectors If an ndarray is passed, it should be of shape (n_clusters, n_features) and gives the initial centers. tol : float, default: 1e-6 Relative tolerance with regards to inertia to declare convergence n_jobs : int The number of jobs to use for the computation. This works by computing each of the n_init runs in parallel. If -1 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. For n_jobs below -1, (n_cpus + 1 + n_jobs) are used. Thus for n_jobs = -2, all CPUs but one are used. random_state : integer or numpy.RandomState, optional The generator used to initialize the centers. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator. verbose : int, default 0 Verbosity mode. copy_x : boolean, default True When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True, then the original data is not modified. If False, the original data is modified, and put back before the function returns, but small numerical differences may be introduced by subtracting and then adding the data mean. """

    random_state = check_random_state(random_state)
    n_examples, n_features = np.shape(X)

    # init centers (mus)
    centers = _init_unit_centers(X, n_clusters, random_state, init)

    # init weights (alphas)
    if force_weights is None:
        weights = np.ones((n_clusters,))
        weights = weights / np.sum(weights)
    else:
        weights = force_weights

    # init concentrations (kappas)
    concentrations = np.ones((n_clusters,))

    if verbose:
        print("Initialization complete")

    for iter in range(max_iter):
        centers_prev = centers.copy()

        # expectation step
        posterior = _expectation(
            X, centers, weights, concentrations, posterior_type=posterior_type
        )

        # maximization step
        centers, weights, concentrations = _maximization(
            X, posterior, force_weights=force_weights
        )

        # check convergence
        tolcheck = squared_norm(centers_prev - centers)
        if tolcheck <= tol:
            if verbose:
                print(
                    "Converged at iteration %d: "
                    "center shift %e within tolerance %e" % (iter, tolcheck, tol)
                )
            break

    # labels come for free via posterior
    labels = np.zeros((n_examples,))
    for ee in range(n_examples):
        labels[ee] = np.argmax(posterior[:, ee])

    inertia = _inertia_from_labels(X, centers, labels)

    return centers, weights, concentrations, posterior, labels, inertia