def test_solve_with_finite_differences(self):
"""
Minimize a function for which analytic derivatives are not
provided. Provides test coverage for the finite-differencing
options.
"""
#for solver in [least_squares_serial_solve]:
for solver in solvers:
if solver == serial_solve:
continue
for abs_step in [0, 1.0e-7]:
rel_steps = [0, 1.0e-7]
if abs_step == 0:
rel_steps = [1.0e-7]
for rel_step in rel_steps:
for diff_method in ["forward", "centered"]:
logger.debug(f'solver={solver} diff_method={diff_method} ' \
f'abs_step={abs_step} rel_step={rel_step}')
b = Beale()
b.set_dofs([0.1, -0.2])
prob = LeastSquaresProblem([(b, 0, 1)],
diff_method=diff_method,
abs_step=abs_step,
rel_step=rel_step)
#least_squares_serial_solve(prob, grad=True)
solver(prob, grad=True)
np.testing.assert_allclose(prob.x, [3, 0.5])
np.testing.assert_allclose(prob.f(), [0, 0, 0],
atol=1e-10)
def test_failures(self):
"""
Verify that the expected residuals are returned in cases where the
objective function evaluations fail.
"""
o1 = Failer()
r1 = Rosenbrock()
fail_val = 1.0e6
prob1 = LeastSquaresProblem([(r1.terms, 0, 1), (o1, 0, 1)],
fail=fail_val)
# First evaluation should not fail.
f = prob1.f()
print(f)
np.testing.assert_allclose(f, [-1, 0, 1, 1, 1])
# Second evaluation should fail.
f = prob1.f()
print(f)
np.testing.assert_allclose(f, np.full(5, fail_val))
# Third evaluation should not fail.
f = prob1.f()
print(f)
np.testing.assert_allclose(f, [-1, 0, 1, 1, 1])
def test_supply_tuples(self):
"""
Test basic usage
"""
# Objective function f(x) = ((x - 3) / 2) ** 2
iden1 = Identity()
term1 = (iden1.J, 3, 0.25)
prob = LeastSquaresProblem([term1])
self.assertAlmostEqual(prob.objective(), 2.25)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.dofs.f()), 1)
self.assertAlmostEqual(prob.dofs.f()[0], 0)
self.assertEqual(len(prob.f()), 1)
self.assertAlmostEqual(prob.f()[0], -1.5)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 2.25)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 2.25)
iden1.set_dofs([10])
self.assertAlmostEqual(prob.objective(), 12.25)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 12.25)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 12.25)
self.assertAlmostEqual(prob.objective([0]), 2.25)
self.assertAlmostEqual(prob.objective([10]), 12.25)
self.assertEqual(prob.dofs.all_owners, [iden1])
self.assertEqual(prob.dofs.dof_owners, [iden1])
# Objective function
# f(x,y) = ((x - 3) / 2) ** 2 + ((y + 4) / 5) ** 2
iden2 = Identity()
term2 = (iden2.J, -4, 0.04)
prob = LeastSquaresProblem([term1, term2])
self.assertAlmostEqual(prob.objective(), 12.89)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.f()), 2)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 12.89)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 12.89)
iden1.set_dofs([5])
iden2.set_dofs([-7])
self.assertAlmostEqual(prob.objective(), 1.36)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.f()), 2)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 1.36)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 1.36)
self.assertAlmostEqual(prob.objective([10, 0]), 12.89)
self.assertAlmostEqual(prob.objective([5, -7]), 1.36)
self.assertEqual(prob.dofs.dof_owners, [iden1, iden2])
self.assertEqual(prob.dofs.all_owners, [iden1, iden2])
def test_vmec_failure(self):
"""
Verify that failures of VMEC are correctly caught and represented
by large values of the objective function.
"""
for j in range(2):
filename = os.path.join(TEST_DIR, 'input.li383_low_res')
vmec = Vmec(filename)
# Use the objective function from
# stellopt_scenarios_2DOF_targetIotaAndVolume:
if j == 0:
prob = LeastSquaresProblem([(vmec.iota_axis, 0.41, 1),
(vmec.volume, 0.15, 1)])
fail_val = 1e12
else:
# Try a custom failure value
fail_val = 2.0e30
prob = LeastSquaresProblem([(vmec.iota_axis, 0.41, 1),
(vmec.volume, 0.15, 1)],
fail=fail_val)
r00 = vmec.boundary.get_rc(0, 0)
# The first evaluation should succeed.
f = prob.f()
print(f[0], f[1])
correct_f = [-0.004577338528148067, 2.8313872701632925]
# Don't worry too much about accuracy here.
np.testing.assert_allclose(f, correct_f, rtol=0.1)
# Now set a crazy boundary shape to make VMEC fail. This
# boundary causes VMEC to hit the max number of iterations
# without meeting ftol.
vmec.boundary.set_rc(0, 0, 0.2)
vmec.need_to_run_code = True
f = prob.f()
print(f)
np.testing.assert_allclose(f, np.full(2, fail_val))
# Restore a reasonable boundary shape. VMEC should work again.
vmec.boundary.set_rc(0, 0, r00)
vmec.need_to_run_code = True
f = prob.f()
print(f)
np.testing.assert_allclose(f, correct_f, rtol=0.1)
# Now set a self-intersecting boundary shape. This causes VMEC
# to fail with "ARNORM OR AZNORM EQUAL ZERO IN BCOVAR" before
# it even starts iterating.
orig_mode = vmec.boundary.get_rc(1, 3)
vmec.boundary.set_rc(1, 3, 0.5)
vmec.need_to_run_code = True
f = prob.f()
print(f)
np.testing.assert_allclose(f, np.full(2, fail_val))
# Restore a reasonable boundary shape. VMEC should work again.
vmec.boundary.set_rc(1, 3, orig_mode)
vmec.need_to_run_code = True
f = prob.f()
print(f)
np.testing.assert_allclose(f, correct_f, rtol=0.1)