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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 kabsch(P, Q):
 """ Using the Kabsch algorithm with two sets of paired point P and Q, centered around the centroid. Each vector set is represented as an NxD matrix, where D is the the dimension of the space. The algorithm works in three steps: - a centroid translation of P and Q (assumed done before this function call) - the computation of a covariance matrix C - computation of the optimal rotation matrix U For more info see http://en.wikipedia.org/wiki/Kabsch_algorithm Parameters P : array (N,D) matrix, where N is points and D is dimension. Q : array (N,D) matrix, where N is points and D is dimension. Returns ------- U : matrix Rotation matrix (D,D) """


    # Computation of the covariance matrix
    C = np.dot(np.transpose(P), Q)

    # Computation of the optimal rotation matrix
    # This can be done using singular value decomposition (SVD)
    # Getting the sign of the det(V)*(W) to decide
    # whether we need to correct our rotation matrix to ensure a
    # right-handed coordinate system.
    # And finally calculating the optimal rotation matrix U
    # see http://en.wikipedia.org/wiki/Kabsch_algorithm
    V, S, W = np.linalg.svd(C)
    d = (np.linalg.det(V) * np.linalg.det(W)) < 0.0

    if d:
        S[-1] = -S[-1]
        V[:, -1] = -V[:, -1]

    # Create Rotation matrix U
    U = np.dot(V, W)

    return U