def test_Jacobian(self):
for n in range(1, 20):
v1 = np.random.rand() * 4 - 2
v2 = np.random.rand() * 4 - 2
o = TestObject2(v1, v2)
o.adder.set_dofs(np.random.rand(2) * 4 - 2)
o.t.set_dofs([np.random.rand() * 4 - 2])
o.t.adder1.set_dofs(np.random.rand(3) * 4 - 2)
o.t.adder2.set_dofs(np.random.rand(2) * 4 - 2)
r = Rosenbrock(b=3.0)
r.set_dofs(np.random.rand(2) * 3 - 1.5)
a = Affine(nparams=3, nvals=3)
# Randomly fix some of the degrees of freedom
o.fixed = np.random.rand(2) > 0.5
o.adder.fixed = np.random.rand(2) > 0.5
o.t.adder1.fixed = np.random.rand(3) > 0.5
o.t.adder2.fixed = np.random.rand(2) > 0.5
r.fixed = np.random.rand(2) > 0.5
a.fixed = np.random.rand(3) > 0.5
rtol = 1e-6
atol = 1e-6
for j in range(4):
# Try different sets of the objects:
if j == 0:
dofs = Dofs([o.J, r.terms, o.t.J])
nvals = 4
nvals_per_func = [1, 2, 1]
elif j == 1:
dofs = Dofs([r.term2, r.terms])
nvals = 3
nvals_per_func = [1, 2]
elif j == 2:
dofs = Dofs(
[r.term2,
Target(o.t, 'f'), r.term1,
Target(o, 'f')])
nvals = 4
nvals_per_func = [1, 1, 1, 1]
elif j == 3:
dofs = Dofs([a, o])
nvals = 4
nvals_per_func = [3, 1]
jac = dofs.jac()
dofs.diff_method = "forward"
fd_jac = dofs.fd_jac()
dofs.diff_method = "centered"
fd_jac_centered = dofs.fd_jac()
#print('j=', j, ' Diff in Jacobians:', jac - fd_jac)
#print('jac: ', jac)
#print('fd_jac: ', fd_jac)
#print('fd_jac_centered: ', fd_jac_centered)
#print('shapes: jac=', jac.shape, ' fd_jac=', fd_jac.shape, ' fd_jac_centered=', fd_jac_centered.shape)
np.testing.assert_allclose(jac, fd_jac, rtol=rtol, atol=atol)
np.testing.assert_allclose(fd_jac,
fd_jac_centered,
rtol=rtol,
atol=atol)
self.assertEqual(dofs.nvals, nvals)
self.assertEqual(list(dofs.nvals_per_func), nvals_per_func)
def test_fd_jac(self):
"""
Test the parallel finite-difference Jacobian calculation.
"""
abs_step = 1.0e-7
rel_step = 0
for ngroups in range(1, 4):
logger.debug('ngroups={}'.format(ngroups))
mpi = MpiPartition(ngroups=ngroups)
o = TestFunction1()
d = Dofs([o], diff_method="forward", abs_step=abs_step, rel_step=rel_step)
logger.debug('About to do worker loop 1')
jac, xs, evals = fd_jac_mpi(d, mpi)
jac_reference = np.array([[5.865176283537110e-01, -6.010834349701177e-01, 2.250910244305793e-01]])
if mpi.proc0_world:
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# While we're at it, also test the serial FD Jacobian:
o.set_dofs(np.array([1.2, 0.9, -0.4]))
jac = d.fd_jac()
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# Repeat with centered differences
o.set_dofs(np.array([1.2, 0.9, -0.4]))
logger.debug('About to do worker loop 2')
d.diff_method = "centered"
jac, xs, evals = fd_jac_mpi(d, mpi)
jac_reference = np.array([[5.865175337071982e-01, -6.010834789627051e-01, 2.250910093037906e-01]])
if mpi.proc0_world:
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# While we're at it, also test the serial FD Jacobian:
o.set_dofs(np.array([1.2, 0.9, -0.4]))
jac = d.fd_jac()
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# Now try a case with different nparams and nfuncs.
o = TestFunction2()
d = Dofs([o.f0, o.f1, o.f2, o.f3], diff_method="forward",
abs_step=abs_step, rel_step=rel_step)
logger.debug('About to do worker loop 3')
jac, xs, evals = fd_jac_mpi(d, mpi)
jac_reference = np.array([[8.657715439008840e-01, -8.872724499564555e-01],
[2.353411054922816e+00, -2.411856577788640e+00],
[6.397234502131255e+00, -6.556105911492693e+00],
[1.738948636642590e+01, -1.782134355643450e+01]])
if mpi.proc0_world:
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# While we're at it, also test the serial FD Jacobian:
o.set_dofs(np.array([1.2, 0.9]))
jac = d.fd_jac()
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# Repeat with centered differences
o.set_dofs(np.array([1.2, 0.9]))
d.diff_method = "centered"
logger.debug('About to do worker loop 4')
jac, xs, evals = fd_jac_mpi(d, mpi)
jac_reference = np.array([[8.657714037352271e-01, -8.872725151820582e-01],
[2.353410674116319e+00, -2.411856754314101e+00],
[6.397233469623842e+00, -6.556106388888594e+00],
[1.738948351093228e+01, -1.782134486205678e+01]])
if mpi.proc0_world:
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)
# While we're at it, also test the serial FD Jacobian:
o.set_dofs(np.array([1.2, 0.9]))
jac = d.fd_jac()
np.testing.assert_allclose(jac, jac_reference, rtol=1e-13, atol=1e-13)