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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 Gram_matrix(self, F, F1, F2, F3, lower, upper):
 """ Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1. :param F: vector of functions :type F: np.array :param F1: vector of derivatives of F :type F1: np.array :param F2: vector of second derivatives of F :type F2: np.array :param F3: vector of third derivatives of F :type F3: np.array :param lower,upper: boundaries of the input domain :type lower,upper: floats """

        assert self.input_dim == 1
        def L(x,i):
            return(5*np.sqrt(5)/self.lengthscale**3*F[i](x) + 15./self.lengthscale**2*F1[i](x)+ 3*np.sqrt(5)/self.lengthscale*F2[i](x) + F3[i](x))
        n = F.shape[0]
        G = np.zeros((n,n))
        for i in range(n):
            for j in range(i,n):
                G[i,j] = G[j,i] = integrate.quad(lambda x : L(x,i)*L(x,j),lower,upper)[0]
        G_coef = 3.*self.lengthscale**5/(400*np.sqrt(5))
        Flower = np.array([f(lower) for f in F])[:,None]
        F1lower = np.array([f(lower) for f in F1])[:,None]
        F2lower = np.array([f(lower) for f in F2])[:,None]
        orig = 9./8*np.dot(Flower,Flower.T) + 9.*self.lengthscale**4/200*np.dot(F2lower,F2lower.T)
        orig2 = 3./5*self.lengthscale**2 * ( np.dot(F1lower,F1lower.T) + 1./8*np.dot(Flower,F2lower.T) + 1./8*np.dot(F2lower,Flower.T))
        return(1./self.variance* (G_coef*G + orig + orig2))