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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 _compute_B_statistics(self, K, W, log_concave, *args, **kwargs):
 """ Rasmussen suggests the use of a numerically stable positive definite matrix B Which has a positive diagonal elements and can be easily inverted :param K: Prior Covariance matrix evaluated at locations X :type K: NxN matrix :param W: Negative hessian at a point (diagonal matrix) :type W: Vector of diagonal values of Hessian (1xN) :returns: (W12BiW12, L_B, Li_W12) """

        if not log_concave:
            #print "Under 1e-10: {}".format(np.sum(W < 1e-6))
            W = np.clip(W, 1e-6, 1e+30)
            # For student-T we can clip this more intelligently. If the
            # objective has hardly changed, we can increase the clipping limit
            # by ((v+1)/v)/sigma2
            # NOTE: when setting a parameter inside parameters_changed it will allways come to closed update circles!!!
            #W.__setitem__(W < 1e-6, 1e-6, update=False)  # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
                                # If the likelihood is non-log-concave. We wan't to say that there is a negative variance
                                # To cause the posterior to become less certain than the prior and likelihood,
                                # This is a property only held by non-log-concave likelihoods
        if np.any(np.isnan(W)):
            raise ValueError('One or more element(s) of W is NaN')
        #W is diagonal so its sqrt is just the sqrt of the diagonal elements
        W_12 = np.sqrt(W)
        B = np.eye(K.shape[0]) + W_12*K*W_12.T
        L = jitchol(B)

        LiW12, _ = dtrtrs(L, np.diagflat(W_12), lower=1, trans=0)
        K_Wi_i = np.dot(LiW12.T, LiW12) # R = W12BiW12, in R&W p 126, eq 5.25

        #here's a better way to compute the required matrix.
        # you could do the model finding witha backsub, instead of a dot...
        #L2 = L/W_12
        #K_Wi_i_2 , _= dpotri(L2)
        #symmetrify(K_Wi_i_2)

        #compute vital matrices
        C = np.dot(LiW12, K)
        Ki_W_i = K - C.T.dot(C)

        I_KW_i = np.eye(K.shape[0]) - np.dot(K, K_Wi_i)
        logdet_I_KW = 2*np.sum(np.log(np.diag(L)))

        return K_Wi_i, logdet_I_KW, I_KW_i, Ki_W_i