问测试作为PC算法一部分的python中的条件独立性

EN

(x1)---(x2)---(x3)

given n as the number of variables observed, initialize the graph as G=K(n) 
for each pair i,j of nodes:
    if exists an edge e from i to j:
        look for the neighbours of i
        if j is in neighbours of i then remove j from the set of neighbours
        call the set of neighbours k
        TEST if i and j are independent given the set k, if TRUE:
             remove the edge e from i to j

def _core_pc_algorithm(a,sigma_inverse):
l = 0
N = len(sigma_inverse[0])
n = range(N)
sep_set = [ [set() for i in n] for j in n]
act_g = complete(N)
z = lambda m,i,j : -m[i][j]/((m[i][i]*m[j][j])**0.5)
while l<N:
    for (i,j) in itertools.permutations(n,2):
        adjacents_of_i = adj(i,act_g)
        if j not in adjacents_of_i:
            continue
        else:
            adjacents_of_i.remove(j)
        if len(adjacents_of_i) >=l:
            for k in itertools.combinations(adjacents_of_i,l):
                if N-len(k)-3 < 0:
                    return (act_g,sep_set)
                if test(sigma_inverse,z,i,j,l,a,k):
                    act_g[i][j] = 0
                    act_g[j][i] = 0
                    sep_set[i][j] |= set(k)
                    sep_set[j][i] |= set(k)
    l = l + 1
return (act_g,sep_set)

def test(sigma_inverse,z,i,j,l,a,k):
    def erfinv(x): #used to approximate the inverse of a gaussian cumulative density function
        sgn = 1
        a = 0.147
        PI = numpy.pi
        if x<0:
            sgn = -1
        temp = 2/(PI*a) + numpy.log(1-x**2)/2
        add_1 = temp**2
        add_2 = numpy.log(1-x**2)/a
        add_3 = temp
        rt1 = (add_1-add_2)**0.5
        rtarg = rt1 - add_3
        return sgn*(rtarg**0.5)
    def indep_test_ijK(K): #compute partial correlation of i and j given ONE conditioning variable K
        part_corr_coeff_ij = z(sigma_inverse,i,j) #this gives the partial correlation coefficient of i and j
        part_corr_coeff_iK = z(sigma_inverse,i,K) #this gives the partial correlation coefficient of i and k
        part_corr_coeff_jK = z(sigma_inverse,j,K) #this gives the partial correlation coefficient of j and k
        part_corr_coeff_ijK = (part_corr_coeff_ij - part_corr_coeff_iK*part_corr_coeff_jK)/((((1-part_corr_coeff_iK**2))**0.5) * (((1-part_corr_coeff_jK**2))**0.5)) #this gives the partial correlation coefficient of i and j given K
        return part_corr_coeff_ijK == 0 #i independent from j given K if partial_correlation(i,k)|K == 0 (under jointly gaussian assumption) [could check if abs is < alpha?]
    def indep_test():
        n = len(sigma_inverse[0])    
        phi = lambda p : (2**0.5)*erfinv(2*p-1)
        root = (n-len(k)-3)**0.5
        return root*abs(z(sigma_inverse,i,j)) <= phi(1-a/2)
if l == 0:
    return z(sigma_inverse,i,j) == 0 #i independent from j <=> partial_correlation(i,j) == 0 (under jointly gaussian assumption) [could check if abs is < alpha?]
elif l == 1:
    return indep_test_ijK(k[0])
elif l == 2:
    return indep_test_ijK(k[0]) and indep_test_ijK(k[1]) #ASSUMING THAT IJ ARE INDEPENDENT GIVEN Y,Z <=> IJ INDEPENDENT GIVEN Y AND IJ INDEPENDENT GIVEN Z  
else: #i have to use the independent test with the z-fisher function
    return indep_test()

corr(i,j)|REST = -var^-1(i,j)/sqrt(var^-1(i,i)*var^-1(j,j))

    def indep_test():
        n = len(sigma_inverse[0])    
        phi = lambda p : (2**0.5)*erfinv(2*p-1)
        root = (n-len(k)-3)**0.5
        return root*abs(z(sigma_inverse,i,j)) <= phi(1-a/2)