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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 marginalize(self, variables, inplace=True):
 u""" Modifies the factor with marginalized values. Let C(X,Y ; K, h, g) be some canonical form over X,Y where, k = [[K_XX, K_XY], ; h = [[h_X], [K_YX, K_YY]] [h_Y]] In this case, the result of the integration operation is a canonical from C (K', h', g') given by, .. math:: K' = K_{XX} - K_{XY} * {K^{-1}}_{YY} * K_YX .. math:: h' = h_X - K_{XY} * {K^{-1}}_{YY} * h_Y .. math:: g' = g + 0.5 * (|Y| * log(2*pi) - log(|K_{YY}|) + {h^T}_Y * K_{YY} * h_Y) Parameters variables: list or array-like List of variables over which to marginalize. inplace: boolean If inplace=True it will modify the distribution itself, else would return a new distribution. Returns ------- CanonicalDistribution or None : if inplace=True (default) returns None if inplace=False return a new CanonicalDistribution instance Examples -------- array([[ 1, -1, 0], [-1, 4, -2], [ 0, -2, 4]]) array([[ 1], [ 4], [-1]]) -2 array([[ 1., -1.], [-1., 3.]]) array([[ 1. ], [ 3.5]]) 0.22579135 """

        if not isinstance(variables, (list, tuple, np.ndarray)):
            raise TypeError("variables: Expected type list or array-like, "
                            "got type {var_type}".format(var_type=type(variables)))

        if not all([var in self.variables for var in variables]):
            raise ValueError("Variable not in scope.")

        phi = self if inplace else self.copy()

        # index_to_keep -> i vector
        index_to_keep = [self.variables.index(var) for var in self.variables
                         if var not in variables]
        # index_to_marginalize -> j vector
        index_to_marginalize = [self.variables.index(var) for var in variables]

        K_i_i = self.K[np.ix_(index_to_keep, index_to_keep)]
        K_i_j = self.K[np.ix_(index_to_keep, index_to_marginalize)]
        K_j_i = self.K[np.ix_(index_to_marginalize, index_to_keep)]
        K_j_j = self.K[np.ix_(index_to_marginalize, index_to_marginalize)]
        K_j_j_inv = np.linalg.inv(K_j_j)
        h_i = self.h[index_to_keep]
        h_j = self.h[index_to_marginalize]

        phi.variables = [self.variables[index] for index in index_to_keep]

        phi.K = K_i_i - np.dot(np.dot(K_i_j, K_j_j_inv), K_j_i)
        phi.h = h_i - np.dot(np.dot(K_i_j, K_j_j_inv), h_j)
        phi.g = self.g + 0.5 * (len(variables) * np.log(2 * np.pi) -
                                np.log(abs(np.linalg.det(K_j_j))) + np.dot(np.dot(h_j.T, K_j_j), h_j))[0][0]

        if not inplace:
            return phi