def test_fixed_step(self, vals):
htrue = self._hfun(vals)
methods = [
'central2', 'central', 'multicomplex', 'complex', 'forward',
'backward'
]
for order in range(2, 7, 2):
steps = nd.MinStepGenerator(num_steps=order + 1,
use_exact_steps=True,
step_ratio=3.,
offset=0)
note('order = {}'.format(order))
for method in methods:
h_fun = nd.Hessdiag(self._fun,
step=steps,
method=method,
order=order,
full_output=True)
h_val, _info = h_fun(vals)
_error = np.abs(h_val - htrue)
note('error = {}, error_est = {}'.format(
_error, _info.error_estimate))
assert_allclose(h_val,
htrue,
rtol=1e-5,
atol=100 * max(_info.error_estimate))
def test_default_step(self):
htrue = np.array([0., 2., 18.])
methods = [
'central2', 'central', 'multicomplex', 'complex', 'forward',
'backward'
]
for order in range(2, 7, 2):
for method in methods:
Hfun = nd.Hessdiag(self._fun,
method=method,
order=order,
full_output=True)
hd, _info = Hfun([1, 2, 3])
_error = hd - htrue
assert_array_almost_equal(hd, htrue)
def test_default_step(self):
htrue = np.array([0., 2., 18.])
methods = [
'central2', 'central', 'multicomplex', 'complex', 'forward',
'backward'
]
for order in range(2, 7, 2):
for method in methods:
h_fun = nd.Hessdiag(self._fun,
method=method,
order=order,
full_output=True)
h_val, _info = h_fun([1, 2, 3])
# _error = h_val - htrue
tol = min(1e-8, _info.error_estimate.max())
assert_allclose(h_val, htrue, atol=tol)
def test_complex(self):
htrue = np.array([0., 2., 18.])
method = 'complex'
for num_steps in range(3, 7, 1):
steps = nd.MinStepGenerator(num_steps=num_steps,
use_exact_steps=True,
step_ratio=2.0,
offset=4)
h_fun = nd.Hessdiag(self._fun,
step=steps,
method=method,
full_output=True)
h_val, _info = h_fun([1, 2, 3])
assert_allclose(h_val, htrue)
def test_complex(self):
htrue = np.array([0., 2., 18.])
method = 'complex'
for num_steps in range(3, 7, 1):
steps = nd.MinStepGenerator(num_steps=num_steps,
use_exact_steps=True,
step_ratio=2.0,
offset=4)
Hfun = nd.Hessdiag(self._fun,
step=steps,
method=method,
full_output=True)
hd, _info = Hfun([1, 2, 3])
_error = hd - htrue
assert_array_almost_equal(hd, htrue)
def test_fixed_step(self):
htrue = np.array([0., 2., 18.])
methods = ['multicomplex', 'complex', 'central', 'forward', 'backward']
for order in range(2, 7, 2):
steps = nd.MinStepGenerator(num_steps=order + 1,
use_exact_steps=True,
step_ratio=3.,
offset=0)
for method in methods:
Hfun = nd.Hessdiag(self._fun,
step=steps,
method=method,
order=order,
full_output=True)
hd, _info = Hfun([1, 2, 3])
_error = hd - htrue
assert_array_almost_equal(hd, htrue)
