def test_jacobian(self):
print('Test Jacobian')
x = self.test_x
analytic_solution = para_est.Rosenbrock()
h = self.fd_step
# Analytic
j_analytic = analytic_solution.j(x)
# numdifftools
j_ndifftools = nd.Jacobian(analytic_solution.f_vector)(x)
j_scipy = ndscipy.Jacobian(analytic_solution.f_vector, h)(x)
# para_est
self.ps.set_objective_function(analytic_solution.f_vector, metric='e')
j_ps = self.ps.evaluate_derivatives(x, h, evaluate='jacobian')
# Log
print(' j analytic : {0}'.format(j_analytic))
print(' j_ndifftools: {0}'.format(j_ndifftools))
print(' j scipy : {0}'.format(j_scipy))
print(' j ps : {0}'.format(j_ps))
print(' ps function evaluation count: {0}'.format(
self.ps.logger.get_f_eval_count()))
self.assertEqual(
True, np.all(np.isclose(j_ps, j_analytic, rtol=1.e-14,
atol=1.e-2)))
def test_on_scalar_function():
def fun(x):
return x[0] * x[1] * x[2] + np.exp(x[0]) * x[1]
for method in ['forward', 'backward', "central", "complex"]:
j_fun = nd.Jacobian(fun, method=method)
x = j_fun([3., 5., 7.])
assert_allclose(x, [135.42768462, 41.08553692, 15.])
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_on_vector_valued_function(self):
xdata = np.arange(0, 1, 0.1)
ydata = 1 + 2 * np.exp(0.75 * xdata)
def fun(c):
return (c[0] + c[1] * np.exp(c[2] * xdata) - ydata)**2
for method in ['forward', 'backward', "central", "complex"]:
j_fun = nd.Jacobian(fun, method=method)
J = j_fun([1, 2, 0.75]) # should be numerically zero
assert_allclose(J, np.zeros((ydata.size, 3)), atol=1e-6)
def test_scalar_to_vector(val):
def fun(x):
dtype = complex if isinstance(x, complex) else float
out = np.zeros((3, ), dtype=dtype)
out[0] = x
out[1] = x**2
out[2] = x**3
return out
for method in [
'backward',
'forward',
"central",
]: # TODO: "complex" does not work
j0 = nd.Jacobian(fun, method=method)(val).T
assert_allclose(j0, [[1., 2 * val, 3 * val**2]], atol=1e-6)
def test_issue_25(self):
def g_fun(x):
out = np.zeros((2, 2), dtype=float)
out[0, 0] = x[0]
out[0, 1] = x[1]
out[1, 0] = x[0]
out[1, 1] = x[1]
return out
dg_dx = nd.Jacobian(g_fun) # TODO: method='reverse' fails
x = np.array([1, 2])
tv = [[[1., 0.], [0., 1.]], [[1., 0.], [0., 1.]]]
_EPS = np.MachAr().eps
epsilon = _EPS**(1. / 4)
assert_allclose(nd.approx_fprime(x, g_fun, epsilon), tv)
dg = dg_dx(x)
assert_allclose(dg, tv)
def test_on_matrix_valued_function(self):
def fun(x):
f0 = x[0]**2 + x[1]**2
f1 = x[0]**3 + x[1]**3
s0 = f0.size
s1 = f1.size
out = np.zeros((2, (s0 + s1) // 2), dtype=float)
out[0, :] = f0
out[1, :] = f1
return out
x = np.array([(1, 2, 3, 4), (5, 6, 7, 8)], dtype=float)
y = fun(x)
assert_allclose(y, [[26., 40., 58., 80.], [126., 224., 370., 576.]])
for method in [
'forward',
]: # TODO: 'reverse' fails
jaca = nd.Jacobian(fun, method=method)
assert_allclose(jaca([1, 2]), [[[2., 4.]], [[3., 12.]]])
assert_allclose(jaca([3, 4]), [[[6., 8.]], [[27., 48.]]])
assert_allclose(jaca([[1, 2], [3, 4]]),
[[[2., 0., 6., 0.], [0., 4., 0., 8.]],
[[3., 0., 27., 0.], [0., 12., 0., 48.]]])
val = jaca(x)
assert_allclose(val, [[[2., 0., 0., 0., 10., 0., 0., 0.],
[0., 4., 0., 0., 0., 12., 0., 0.],
[0., 0., 6., 0., 0., 0., 14., 0.],
[0., 0., 0., 8., 0., 0., 0., 16.]],
[[3., 0., 0., 0., 75., 0., 0., 0.],
[0., 12., 0., 0., 0., 108., 0., 0.],
[0., 0., 27., 0., 0., 0., 147., 0.],
[0., 0., 0., 48., 0., 0., 0., 192.]]])
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)
for i, (_key, function) in enumerate(functions.items()):
t = timeit.default_timer()
function.fun = f