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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 smooth_knn_dist(distances, k, n_iter=64, local_connectivity=1.0, bandwidth=1.0):
 """Compute a continuous version of the distance to the kth nearest neighbor. That is, this is similar to knn-distance but allows continuous k values rather than requiring an integral k. In esscence we are simply computing the distance such that the cardinality of fuzzy set we generate is k. Parameters distances: array of shape (n_samples, n_neighbors) Distances to nearest neighbors for each samples. Each row should be a sorted list of distances to a given samples nearest neighbors. k: float The number of nearest neighbors to approximate for. n_iter: int (optional, default 64) We need to binary search for the correct distance value. This is the max number of iterations to use in such a search. local_connectivity: int (optional, default 1) The local connectivity required -- i.e. the number of nearest neighbors that should be assumed to be connected at a local level. The higher this value the more connected the manifold becomes locally. In practice this should be not more than the local intrinsic dimension of the manifold. bandwidth: float (optional, default 1) The target bandwidth of the kernel, larger values will produce larger return values. Returns ------- knn_dist: array of shape (n_samples,) The distance to kth nearest neighbor, as suitably approximated. nn_dist: array of shape (n_samples,) The distance to the 1st nearest neighbor for each point. """

    target = np.log2(k) * bandwidth
    rho = np.zeros(distances.shape[0])
    result = np.zeros(distances.shape[0])

    for i in range(distances.shape[0]):
        lo = 0.0
        hi = NPY_INFINITY
        mid = 1.0

        # TODO: This is very inefficient, but will do for now. FIXME
        ith_distances = distances[i]
        non_zero_dists = ith_distances[ith_distances > 0.0]
        if non_zero_dists.shape[0] >= local_connectivity:
            index = int(np.floor(local_connectivity))
            interpolation = local_connectivity - index
            if index > 0:
                rho[i] = non_zero_dists[index - 1]
                if interpolation > SMOOTH_K_TOLERANCE:
                    rho[i] += interpolation * (non_zero_dists[index] - non_zero_dists[index - 1])
            else:
                rho[i] = interpolation * non_zero_dists[0]
        elif non_zero_dists.shape[0] > 0:
            rho[i] = np.max(non_zero_dists)

        for n in range(n_iter):

            psum = 0.0
            for j in range(1, distances.shape[1]):
                d = distances[i, j] - rho[i]
                if d > 0:
                    psum += np.exp(-(d / mid))
                else:
                    psum += 1.0


            if np.fabs(psum - target) < SMOOTH_K_TOLERANCE:
                break

            if psum > target:
                hi = mid
                mid = (lo + hi) / 2.0
            else:
                lo = mid
                if hi == NPY_INFINITY:
                    mid *= 2
                else:
                    mid = (lo + hi) / 2.0

        result[i] = mid

        # TODO: This is very inefficient, but will do for now. FIXME
        if rho[i] > 0.0:
            if result[i] < MIN_K_DIST_SCALE * np.mean(ith_distances):
                result[i] = MIN_K_DIST_SCALE * np.mean(ith_distances)
        else:
            if result[i] < MIN_K_DIST_SCALE * np.mean(distances):
                result[i] = MIN_K_DIST_SCALE * np.mean(distances)

    return result, rho