def test_very_simple_ODOE_objective_function(self):
"""
compute PHI = trace( (J^T,J)^-1 )
"""
D,P,N,M = 2,1,100,3
J = UTPM(numpy.random.rand(D,P,N,M))
cg = CGraph()
FJ = Function(J)
FJT = Function.transpose(FJ)
FM = Function.dot(FJT, FJ)
FC = Function.inv(FM)
FPHI = Function.trace(FC)
cg.independentFunctionList = [FJ]
cg.dependentFunctionList = [FPHI]
assert_array_equal(FPHI.shape, ())
cg.pushforward([J])
PHIbar = UTPM(numpy.random.rand(*(D,P)))
# pullback using the tracer
cg.pullback([PHIbar])
# verifying pullback by ybar.T ydot == xbar.T xdot
const1 = UTPM.dot(FPHI.xbar, UTPM.shift(FPHI.x,-1))
const2 = UTPM.trace(UTPM.dot(FJ.xbar.T, UTPM.shift(FJ.x,-1)))
# print cg
# print const1
# print const2
assert_array_almost_equal(const1.data[0,:], const2.data[0,:])
def test_more_complicated_ODOE_objective_function(self):
"""
compute PHI = trace( (J^T,J)^-1 )
"""
D,P,N,M = 2,1,100,3
MJs = [UTPM(numpy.random.rand(D,P,N,M)),UTPM(numpy.random.rand(D,P,N,M))]
cg = CGraph()
FJs= [Function(MJ) for MJ in MJs]
FM = Function(UTPM(numpy.zeros((D,P,M,M))))
for FJ in FJs:
FJT = Function.transpose(FJ)
FM += Function.dot(FJT, FJ)
FC = Function.inv(FM)
FPHI = Function.trace(FC)
cg.independentFunctionList = FJs
cg.dependentFunctionList = [FPHI]
assert_array_equal(FPHI.shape, ())
# cg.pushforward(MJs)
# pullback using the tracer
PHIbar = UTPM(numpy.ones((D,P)))
cg.pullback([PHIbar])
# # compute pullback by hand
# Cbar = UTPM.pb_trace(PHIbar, FC.x, FPHI.x)
# assert_array_almost_equal(Cbar.data, FC.xbar.data)
# Mbar = UTPM.pb_inv(Cbar, FM.x, FC.x)
# assert_array_almost_equal(Mbar.data, FM.xbar.data)
# for FJ in FJs:
# tmpbar = UTPM.pb_dot(Mbar, FJ.T.x, FJ.x, FM.x)
# assert_array_almost_equal(tmpbar[1].data , FJ.xbar.data)
# verifying pullback by ybar.T ydot == xbar.T xdot
const1 = UTPM.dot(FPHI.xbar, UTPM.shift(FPHI.x,-1))
const2 = UTPM(numpy.zeros((D,P)))
for nFJ, FJ in enumerate(FJs):
const2 += UTPM.trace(UTPM.dot(FJ.xbar.T, UTPM.shift(FJ.x,-1)))
assert_array_almost_equal(const1.data[0,:], const2.data[0,:])
