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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 _likelihood(self, chol_sigma_s_rhos, log_det_psi, chol_sigma_s, trace_xt_invsigma2_x, inv_sigma_s_rhos, wt_invpsi_x, samples):
 """Calculate the log-likelihood function Parameters chol_sigma_s_rhos : array, shape=[features, features] Cholesky factorization of the matrix (Sigma_S + sum_i(1/rho_i^2) * I) log_det_psi : float Determinant of diagonal matrix Psi (containing the rho_i^2 value voxels_i times). chol_sigma_s : array, shape=[features, features] Cholesky factorization of the matrix Sigma_S trace_xt_invsigma2_x : float Trace of :math:`\\sum_i (||X_i||_F^2/\\rho_i^2)` inv_sigma_s_rhos : array, shape=[features, features] Inverse of :math:`(\\Sigma_S + \\sum_i(1/\\rho_i^2) * I)` wt_invpsi_x : array, shape=[features, samples] samples : int The total number of samples in the data. Returns ------- loglikehood : float The log-likelihood value. """

        log_det = (np.log(np.diag(chol_sigma_s_rhos) ** 2).sum() + log_det_psi
                   + np.log(np.diag(chol_sigma_s) ** 2).sum())
        loglikehood = -0.5 * samples * log_det - 0.5 * trace_xt_invsigma2_x
        loglikehood += 0.5 * np.trace(
            wt_invpsi_x.T.dot(inv_sigma_s_rhos).dot(wt_invpsi_x))
        # + const --> -0.5*nTR*nvoxel*subjects*math.log(2*math.pi)

        return loglikehood