def test_dot(self):
""" test z = dot(x,y)"""
cg = CGraph()
D,P,N,M = 2,5,7,11
ax = UTPM(numpy.random.rand(D,P,N,M))
ay = UTPM(numpy.random.rand(D,P,M,N))
fx = Function(ax)
fy = Function(ay)
fz = Function.dot(fx,fy)
cg.independentFunctionList = [fx,fy]
cg.dependentFunctionList = [fz]
ax = UTPM(numpy.random.rand(D,P,N,M))
ay = UTPM(numpy.random.rand(D,P,M,N))
azbar = UTPM(numpy.random.rand(*fz.x.data.shape))
cg.pushforward([ax,ay])
cg.pullback([azbar])
xbar_reverse = cg.independentFunctionList[0].xbar
ybar_reverse = cg.independentFunctionList[1].xbar
xbar_symbolic = UTPM.dot(azbar,ay.T)
ybar_symbolic = UTPM.dot(ax.T,azbar)
assert_array_almost_equal(xbar_reverse.data, xbar_symbolic.data)
assert_array_almost_equal(ybar_reverse.data, ybar_symbolic.data)
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,:])
def test_pullback_solve(self):
"""
test pullback on
f = solve(A,x)
"""
(D,P,M,N,K) = 2,7,10,10,3
A_data = numpy.random.rand(D,P,M,N)
# make A_data sufficiently regular
for p in range(P):
for n in range(N):
A_data[0,p,n,n] += (N + 1)
A = UTPM(A_data)
x = UTPM(numpy.random.rand(D,P,N,K))
# STEP 1: tracing
cg = CGraph()
fA = Function(A)
fx = Function(x)
fy = Function.solve(fA,fx)
cg.independentFunctionList = [fA]
cg.dependentFunctionList = [fy]
y = fy.x
# STEP 2: pullback
ybar_data = numpy.random.rand(*y.data.shape)
ybar = UTPM(ybar_data)
cg.pullback([ybar])
Abar = fA.xbar
xbar = fx.xbar
assert_array_almost_equal(x.data, UTPM.dot(A,y).data)
for p in range(P):
Ab = Abar.data[0,p]
Ad = A.data[1,p]
xb = xbar.data[0,p]
xd = x.data[1,p]
yb = ybar.data[0,p]
yd = y.data[1,p]
assert_almost_equal(numpy.trace(numpy.dot(Ab.T,Ad)) + numpy.trace(numpy.dot(xb.T,xd)), numpy.trace(numpy.dot(yb.T,yd)))
def test_pushforward_of_qr(self):
cg = CGraph()
D,P,N,M = 1,1,3,3
x = UTPM(numpy.random.rand(D,P,N,M))
fx = Function(x)
f = Function.qr(fx)
fQ,fR = f
cg.independentFunctionList = [fx]
cg.dependentFunctionList = [fQ,fR]
x = UTPM(numpy.random.rand(D,P,N,M))
cg.pushforward([x])
Q = cg.dependentFunctionList[0].x
R = cg.dependentFunctionList[1].x
assert_array_almost_equal(x.data,UTPM.dot(Q,R).data)
def test_dot_utpm(self):
D, P, N = 3, 4, 5
x = UTPM(numpy.random.rand(D, P, N, N))
y = UTPM(numpy.random.rand(D, P, N, N))
assert_array_almost_equal(dot(x, y).data, UTPM.dot(x, y).data)
def test_binary_function_utpm(self):
D, P, N, M = 3, 4, 5, 6
x = UTPM(numpy.random.rand(*(D, P, N, M)))
y = UTPM(numpy.random.rand(*(D, P, M, N)))
assert_array_almost_equal(dot(x, y).data, UTPM.dot(x, y).data)
def test_dot_utpm(self):
D, P, N = 3, 4, 5
x = UTPM(numpy.random.rand(D, P, N, N))
y = UTPM(numpy.random.rand(D, P, N, N))
assert_array_almost_equal(dot(x, y).data, UTPM.dot(x, y).data)
def test_binary_function_utpm(self):
D, P, N, M = 3, 4, 5, 6
x = UTPM(numpy.random.rand(*(D, P, N, M)))
y = UTPM(numpy.random.rand(*(D, P, M, N)))
assert_array_almost_equal(dot(x, y).data, UTPM.dot(x, y).data)
