def main(problem_sizes=(4, 8, 16, 32, 64, 96)):
fixed_step = MinStepGenerator(num_steps=1, use_exact_steps=True, offset=0)
epsilon = MaxStepGenerator(num_steps=14,
use_exact_steps=True,
step_ratio=1.6,
offset=0)
adaptiv_txt = '_adaptive_{0:d}_{1!s}_{2:d}'.format(epsilon.num_steps,
str(epsilon.step_ratio),
epsilon.offset)
gradient_funs = OrderedDict()
hessian_funs = OrderedDict()
hessian_fun = 'Hessdiag'
hessian_fun = 'Hessian'
if nda is not None:
nda_method = 'forward'
nda_txt = 'algopy_' + nda_method
gradient_funs[nda_txt] = nda.Jacobian(1, method=nda_method)
hessian_funs[nda_txt] = getattr(nda, hessian_fun)(1, method=nda_method)
ndc_hessian = getattr(nd, hessian_fun)
order = 2
for method in ['forward', 'central', 'complex']:
method2 = method + adaptiv_txt
options = dict(method=method, order=order)
gradient_funs[method] = nd.Jacobian(1, step=fixed_step, **options)
gradient_funs[method2] = nd.Jacobian(1, step=epsilon, **options)
hessian_funs[method] = ndc_hessian(1, step=fixed_step, **options)
hessian_funs[method2] = ndc_hessian(1, step=epsilon, **options)
hessian_funs['forward_statsmodels'] = nds.Hessian(1, method='forward')
hessian_funs['central_statsmodels'] = nds.Hessian(1, method='central')
hessian_funs['complex_statsmodels'] = nds.Hessian(1, method='complex')
gradient_funs['forward_statsmodels'] = nds.Jacobian(1, method='forward')
gradient_funs['central_statsmodels'] = nds.Jacobian(1, method='central')
gradient_funs['complex_statsmodels'] = nds.Jacobian(1, method='complex')
gradient_funs['forward_scipy'] = nsc.Jacobian(1, method='forward')
gradient_funs['central_scipy'] = nsc.Jacobian(1, method='central')
gradient_funs['complex_scipy'] = nsc.Jacobian(1, method='complex')
run_gradient_and_hessian_benchmarks(gradient_funs, hessian_funs,
problem_sizes)
def test_scalar_to_vector(val):
def fun(x):
return np.array([x, x**2, x**3])
truth = np.array([[[1.]], [[2 * val]], [[3 * val**2]]])
for method in [
'multicomplex', 'complex', 'central', 'forward', 'backward'
]:
j0, info = nd.Jacobian(fun, method=method, full_output=True)(val)
if method != "multicomplex":
j00 = nds.Jacobian(fun, method=method)(val)
error = np.abs(j00 - truth)
note('statsmodel: method={}, error={}'.format(method, error))
assert_allclose(j00, truth, rtol=1e-3, atol=1e-6)
error = np.abs(j0 - truth)
note('method={}, error={}, error_est={}'.format(
method, error, info.error_estimate))
assert_allclose(j0, truth, rtol=1e-3, atol=1e-6)
hessian_funs[nda_txt] = getattr(nda, hessian_fun)(1, method=nda_method)
order = 2
for method in ['forward', 'central', 'complex']:
method2 = method + adaptiv_txt
options = dict(method=method, order=order)
gradient_funs[method] = nd.Jacobian(1, step=fixed_step, **options)
gradient_funs[method2] = nd.Jacobian(1, step=epsilon, **options)
hessian_funs[method] = ndc_hessian(1, step=fixed_step, **options)
hessian_funs[method2] = ndc_hessian(1, step=epsilon, **options)
hessian_funs['forward_statsmodels'] = nds.Hessian(1, method='forward')
hessian_funs['central_statsmodels'] = nds.Hessian(1, method='central')
hessian_funs['complex_statsmodels'] = nds.Hessian(1, method='complex')
gradient_funs['forward_statsmodels'] = nds.Jacobian(1, method='forward')
gradient_funs['central_statsmodels'] = nds.Jacobian(1, method='central')
gradient_funs['complex_statsmodels'] = nds.Jacobian(1, method='complex')
gradient_funs['forward_scipy'] = nsc.Jacobian(1, method='forward')
gradient_funs['central_scipy'] = nsc.Jacobian(1, method='central')
gradient_funs['complex_scipy'] = nsc.Jacobian(1, method='complex')
def _compute_benchmark(functions, problem_sizes):
result_list = []
for n in problem_sizes:
print('n=', n)
num_methods = len(functions)
results = np.zeros((num_methods, 3))
ref_g = None
f = BenchmarkFunction(n)
def fun_jacobian(x):
return nd.Jacobian(lambda x: to_minimize(x))(x).ravel()