def test_run_hamiltonian(self):
# Important to restrict the step in order to avoid the
# discontinutiy at x=[0,0] of the hamiltonian
for method in ['central', 'complex']:
step = nd.MaxStepGenerator(base_step=1e-4)
hessian = nd.Hessian(None, step=step, method=method)
h, _error_estimate, true_h = run_hamiltonian(hessian,
verbose=False)
assert (np.abs((h - true_h) / true_h) < 1e-4).all()
def test_hessian_cos_x_y_at_0_0():
# cos(x-y), at (0,0)
def fun(xy):
return np.cos(xy[0] - xy[1])
htrue = [[-1., 1.], [1., -1.]]
methods = [
'multicomplex', 'complex', 'central', 'central2', 'forward',
'backward'
]
for num_steps in [10, 1]:
step = nd.MinStepGenerator(num_steps=num_steps)
for method in methods:
h_fun = nd.Hessian(fun,
method=method,
step=step,
full_output=True)
h_val, _info = h_fun([0, 0])
# print(method, (h_val-np.array(htrue)))
assert_allclose(h_val, htrue)
def test_complex_hessian_issue_35(self):
""" """
def foo(x):
return 1j * np.inner(x, x)
for method in [
'multicomplex', 'complex', 'central', 'central2', 'forward',
'backward'
]:
for offset in [0, 1j]: # testing real and complex argument
print(method)
x = np.random.randn(3) + offset
hessn = nd.Hessian(foo, method=method)
if method.endswith('complex'):
self.assertRaises(ValueError, hessn, x)
else:
val = hessn(x)
assert_allclose(val,
[[2j, 0j, 0j], [0j, 2j, 0j], [0j, 0j, 2j]],
atol=1e-13)
def test_hessian_cosIx_yI_at_I0_0I():
# cos(x-y), at (0,0)
def fun(xy):
return np.cos(xy[0] - xy[1])
htrue = [[-1., 1.], [1., -1.]]
methods = [
'multicomplex', 'complex', 'central', 'central2', 'forward',
'backward'
]
for num_steps in [10, 1]:
step = nd.MinStepGenerator(num_steps=num_steps)
for method in methods:
Hfun2 = nd.Hessian(fun,
method=method,
step=step,
full_output=True)
h2, _info = Hfun2([0, 0])
# print(method, (h2-np.array(htrue)))
assert_array_almost_equal(h2, htrue)