def test_eigh1_pullback(self):
(D,P,N) = 2,1,2
A = UTPM(numpy.zeros((D,P,N,N)))
A.data[0,0] = numpy.eye(N)
A.data[1,0] = numpy.diag([3,4])
cg = CGraph()
FA = Function(A)
# print A
FL,FQ,Fb = Function.eigh1(FA)
cg.trace_off()
cg.independentFunctionList = [FA]
cg.dependentFunctionList = [FL]
Lbar = UTPM.diag(UTPM(numpy.zeros((D,P,N))))
Lbar.data[0,0] = [0.5,0.5]
# print cg
cg.pullback([Lbar])
L = FL.x; Q = FQ.x; b = Fb.x
assert_array_almost_equal(dot(Q, dot(L,Q.T)).data, A.data, decimal = 13)
Qbar = UTPM(numpy.zeros((D,P,N,N)))
Abar = UTPM.pb_eigh1( Lbar, Qbar, None, A, L, Q, b)
assert_array_almost_equal(Abar.data, FA.xbar.data)
Abar = Abar.data[0,0]
Adot = A.data[1,0]
Lbar = Lbar.data[0,0]
Ldot = L.data[1,0]
Qbar = Qbar.data[0,0]
Qdot = Q.data[1,0]
assert_almost_equal(numpy.trace(numpy.dot(Abar.T, Adot)), numpy.trace( numpy.dot(Lbar.T, Ldot) + numpy.dot(Qbar.T, Qdot)))
