def test_points(a, b):
# Check that initial interval splitting is done according to
# `points`, by checking that consecutive sets of 15 point (for
# gk15) function evaluations lie between `points`
points = (0, 0.25, 0.5, 0.75, 1.0)
points += tuple(-x for x in points)
quadrature_points = 15
interval_sets = []
count = 0
def f(x):
nonlocal count
if count % quadrature_points == 0:
interval_sets.append(set())
count += 1
interval_sets[-1].add(float(x))
return 0.0
quad_vec(f, a, b, points=points, quadrature='gk15', limit=0)
# Check that all point sets lie in a single `points` interval
for p in interval_sets:
j = np.searchsorted(sorted(points), tuple(p))
assert np.all(j == j[0])
def test_quad_vec_simple(quadrature):
n = np.arange(10)
f = lambda x: x**n
for epsabs in [0.1, 1e-3, 1e-6]:
if quadrature == 'trapz' and epsabs < 1e-4:
# slow: skip
continue
kwargs = dict(epsabs=epsabs, quadrature=quadrature)
exact = 2**(n+1)/(n + 1)
res, err = quad_vec(f, 0, 2, norm='max', **kwargs)
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err = quad_vec(f, 0, 2, norm='2', **kwargs)
assert np.linalg.norm(res - exact) < epsabs
res, err = quad_vec(f, 0, 2, norm='max', points=(0.5, 1.0), **kwargs)
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err, *rest = quad_vec(f, 0, 2, norm='max',
epsrel=1e-8,
full_output=True,
limit=10000,
**kwargs)
assert_allclose(res, exact, rtol=0, atol=epsabs)
def test_quad_vec_simple():
n = np.arange(10)
f = lambda x: x**n
for epsabs in [0.1, 1e-3, 1e-6]:
exact = 2**(n + 1) / (n + 1)
res, err = quad_vec(f, 0, 2, norm='max', epsabs=epsabs)
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err = quad_vec(f, 0, 2, norm='2', epsabs=epsabs)
assert np.linalg.norm(res - exact) < epsabs
res, err = quad_vec(f,
0,
2,
norm='max',
epsabs=epsabs,
points=(0.5, 1.0))
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err, *rest = quad_vec(f,
0,
2,
norm='max',
epsrel=1e-8,
epsabs=epsabs,
full_output=True,
limit=10000,
quadrature='trapz')
assert_allclose(res, exact, rtol=0, atol=epsabs)
def test_quad_vec_pool():
f = _lorenzian
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=1e-4, workers=4)
assert_allclose(res, np.pi, rtol=0, atol=1e-4)
with Pool(10) as pool:
f = lambda x: 1 / (1 + x**2)
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=1e-4, workers=pool.map)
assert_allclose(res, np.pi, rtol=0, atol=1e-4)
def test_quad_vec_pool_args(extra_args, workers):
f = _func_with_args
exact = np.array([0, 4/3, 8/3])
res, err = quad_vec(f, 0, 1, args=extra_args, workers=workers)
assert_allclose(res, exact, rtol=0, atol=1e-4)
with Pool(workers) as pool:
res, err = quad_vec(f, 0, 1, args=extra_args, workers=pool.map)
assert_allclose(res, exact, rtol=0, atol=1e-4)
def test_quad_vec_pool():
from multiprocessing.dummy import Pool
f = _lorenzian
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=1e-4, workers=4)
assert_allclose(res, np.pi, rtol=0, atol=1e-4)
with Pool(10) as pool:
f = lambda x: 1 / (1 + x**2)
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=1e-4, workers=pool.map)
assert_allclose(res, np.pi, rtol=0, atol=1e-4)
def LF2_2d(mu_x, mu_y, sigma, f):
Print("Called")
loss = -np.sum(
np.log(
quad_vec(
lambda y: quad_vec(
lambda x: P_2d(x, y, mu_x, mu_y, sigma, f) *
(gauss2d(x, y, xy_reco, xy_sigma)), -lim, lim)[0],
-lim, lim)[0]))
Print("Returning Loss")
return loss
def test_nan_inf():
def f_nan(x):
return np.nan
def f_inf(x):
return np.inf if x < 0.1 else 1/x
res, err, info = quad_vec(f_nan, 0, 1, full_output=True)
assert info.status == 3
res, err, info = quad_vec(f_inf, 0, 1, full_output=True)
assert info.status == 3
def test_nan_inf():
def f_nan(x):
return np.nan
def f_inf(x):
return np.inf if x < 0.1 else 1 / x
res, err, info = quad_vec(f_nan, 0, 1, full_output=True)
assert info.status == 3
res, err, info = quad_vec(f_inf, 0, 1, full_output=True)
assert info.status == 3
def test_quad_vec_simple_inf(quadrature):
f = lambda x: 1 / (1 + np.float64(x)**2)
for epsabs in [0.1, 1e-3, 1e-6]:
if quadrature == 'trapz' and epsabs < 1e-4:
# slow: skip
continue
kwargs = dict(norm='max', epsabs=epsabs, quadrature=quadrature)
res, err = quad_vec(f, 0, np.inf, **kwargs)
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, 0, -np.inf, **kwargs)
assert_allclose(res, -np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, 0, **kwargs)
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, 0, **kwargs)
assert_allclose(res, -np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, np.inf, **kwargs)
assert_allclose(res, np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, -np.inf, **kwargs)
assert_allclose(res, -np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, np.inf, **kwargs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, -np.inf, **kwargs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, 0, np.inf, points=(1.0, 2.0), **kwargs)
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
f = lambda x: np.sin(x + 2) / (1 + x**2)
exact = np.pi / np.e * np.sin(2)
epsabs = 1e-5
res, err, info = quad_vec(f,
-np.inf,
np.inf,
limit=1000,
norm='max',
epsabs=epsabs,
quadrature=quadrature,
full_output=True)
assert info.status == 1
assert_allclose(res, exact, rtol=0, atol=max(epsabs, 1.5 * err))
def test_quad_vec_simple_inf():
f = lambda x: 1 / (1 + np.float64(x)**2)
for epsabs in [0.1, 1e-3, 1e-6]:
res, err = quad_vec(f, 0, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, 0, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, 0, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, 0, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi / 2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f,
0,
np.inf,
norm='max',
epsabs=epsabs,
points=(1.0, 2.0))
assert_allclose(res, np.pi / 2, rtol=0, atol=max(epsabs, err))
f = lambda x: np.sin(x + 2) / (1 + x**2)
exact = np.pi / np.e * np.sin(2)
epsabs = 1e-5
res, err, info = quad_vec(f,
-np.inf,
np.inf,
limit=1000,
norm='max',
epsabs=epsabs,
full_output=True)
assert_allclose(res, exact, rtol=0, atol=max(epsabs, err))
def test_quad_vec_args():
f = lambda x, a: x * (x + a) * np.arange(3)
a = 2
exact = np.array([0, 4/3, 8/3])
res, err = quad_vec(f, 0, 1, args=(a,))
assert_allclose(res, exact, rtol=0, atol=1e-4)
def voigt_nobg(x, a, b, s, g, clib=True):
"""Voigt function with no background (Base Voigt function).
This is the base of all the other Voigt functions.
Parameters
----------
${SINGLE_VOIGT}
${CLIB}
${EXTRA_STD}
"""
warnings.filterwarnings("ignore", category=IntegrationWarning)
u = x - b
if clib and not_on_rtd:
i = [
quad(cvoigt,
-np.inf,
np.inf,
args=(v, s, g),
epsabs=1.49e-1,
epsrel=1.49e-4)[0] for v in u
]
else:
i = quad_vec(
lambda y: np.exp(-y**2 / (2 * s**2)) / (g**2 + (u - y)**2),
-np.inf, np.inf, **rtd)[0]
const = g / (s * np.sqrt(2 * np.pi**3))
return a * const * np.array(i)
def test_univar_cond(self): # ================= Univarite unconditional density with Boston dataset ==================
for estimator_cls in ESTIMATOR_CLS:
X, y = load_boston(return_X_y=True)
# Train/test splits
y_train, y_test, X_train, X_test = train_test_split(y, X, random_state=11)
estimator = estimator_cls(context_size=X_train.shape[1], n_epochs=1000, input_noise_std=0.3, context_noise_std=0.1,
n_components=5, lr=0.001, transform_classes=DEFAULT_TRANSFORMS)
estimator.fit(train_inputs=y_train, train_context=X_train, verbose=True, val_inputs=y_test, val_context=X_test,
log_frequency=1000)
# Density check
with torch.no_grad():
int_res = integrate.quad_vec(lambda x: np.exp(estimator.log_prob(np.repeat(x, len(X_test)), context=X_test)),
-np.inf, np.inf, epsabs=EPSABS)[0]
logging.info(f'Mean integral of cond density: {int_res.mean()}')
np.testing.assert_array_almost_equal(int_res, np.ones(len(X_test)), ASSERT_DECIMAL)
# Sampling
with torch.no_grad():
y_sampled = estimator.sample(num_samples=1, context=X_test).reshape(-1)
g = self._plot_univariate(y_test, y_sampled)
g.fig.suptitle(f'Uni-variate conditional sampling ({estimator_cls.__name__})')
plt.show()
def quad_fn(interp3d, ray_axes, near, far):
points = None #np.linspace(near, far, nx/2)
res = integrate.quad_vec(lambda r: interp3d(ray_axes * r - dv),
near,
far,
points=points,
limit=quad_lim)
return res[0]
def SolveStokes(force, pos, args):
mu = args[0]
if args[1] == "stokeslet":
res = si.quad_vec(
lambda x: nm.einsum("ij,j",
OseenTensor([pos[0] - x, pos[1], pos[2]], mu),
f(x, 0, 0)), -np.inf, np.inf)[0]
return res
def test_num_eval(quadrature):
def f(x):
count[0] += 1
return x**5
count = [0]
res = quad_vec(f, 0, 1, norm='max', full_output=True, quadrature=quadrature)
assert res[2].neval == count[0]
def test_num_eval():
def f(x):
count[0] += 1
return x**5
for q in ['gk21', 'trapz']:
count = [0]
res = quad_vec(f, 0, 1, norm='max', full_output=True, quadrature=q)
assert res[2].neval == count[0]
def test_num_eval():
def f(x):
count[0] += 1
return x**5
for q in ['gk21', 'trapz']:
count = [0]
res = quad_vec(f, 0, 1, norm='max', full_output=True, quadrature=q)
assert res[2].neval == count[0]
def _integrate_esd_second_term_quad(self):
second_term, second_term_errors = integrate.quad_vec(
lambda theta: self._esd_second_term_integrand_func(
np.array([theta])),
0,
np.pi / 2,
)
_check_errors_ok(second_term_errors)
return second_term
def Q_day(t, beta, rho, eps, phi=phis):
# Takes either single or list of days to calculate insol for
r, theta = polar_pos(eps, t)
mag, phase, c = trig_coefs(beta, rho, theta.reshape(-1, 1), phi)
I_day = quad_vec(lambda gamma: I_fast(gamma, mag, phase, c),
0,
2 * np.pi,
epsrel=1)[0]
Q_day = K / (8 * np.pi**2 * r**2) * I_day.T
return Q_day
def integrated_vortex_c_2d(start_pt, end_pt, col_pt):
"""Integrates vortex_2d to obtain vortex_c_2d output."""
panel_length = np.linalg.norm(end_pt - start_pt)
panel_tangent = (end_pt - start_pt) / panel_length
def integrand(s):
vortex_pt = start_pt + panel_tangent * s
return vortex_2d(1, vortex_pt, col_pt)
return integrate.quad_vec(integrand, 0, panel_length, epsabs=1e-9)[0]
def test_quad_vec_simple():
n = np.arange(10)
f = lambda x: x**n
for epsabs in [0.1, 1e-3, 1e-6]:
exact = 2**(n+1)/(n + 1)
res, err = quad_vec(f, 0, 2, norm='max', epsabs=epsabs)
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err = quad_vec(f, 0, 2, norm='2', epsabs=epsabs)
assert np.linalg.norm(res - exact) < epsabs
res, err = quad_vec(f, 0, 2, norm='max', epsabs=epsabs, points=(0.5, 1.0))
assert_allclose(res, exact, rtol=0, atol=epsabs)
res, err, *rest = quad_vec(f, 0, 2, norm='max',
epsrel=1e-8, epsabs=epsabs,
full_output=True,
limit=10000, quadrature='trapz')
assert_allclose(res, exact, rtol=0, atol=epsabs)
def test_info():
def f(x):
return np.ones((3, 2, 1))
res, err, info = quad_vec(f, 0, 1, norm='max', full_output=True)
assert info.success == True
assert info.status == 0
assert info.message == 'Target precision reached.'
assert info.neval > 0
assert info.intervals.shape[1] == 2
assert info.integrals.shape == (info.intervals.shape[0], 3, 2, 1)
assert info.errors.shape == (info.intervals.shape[0],)
def test_info():
def f(x):
return np.ones((3, 2, 1))
res, err, info = quad_vec(f, 0, 1, norm='max', full_output=True)
assert info.success == True
assert info.status == 0
assert info.message == 'Target precision reached.'
assert info.neval > 0
assert info.intervals.shape[1] == 2
assert info.integrals.shape == (info.intervals.shape[0], 3, 2, 1)
assert info.errors.shape == (info.intervals.shape[0], )
def test_quad_vec_simple_inf():
f = lambda x: 1 / (1 + np.float64(x)**2)
for epsabs in [0.1, 1e-3, 1e-6]:
res, err = quad_vec(f, 0, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi/2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, 0, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi/2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, 0, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi/2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, 0, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi/2, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, -np.pi, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, np.inf, np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, -np.inf, -np.inf, norm='max', epsabs=epsabs)
assert_allclose(res, 0, rtol=0, atol=max(epsabs, err))
res, err = quad_vec(f, 0, np.inf, norm='max', epsabs=epsabs, points=(1.0, 2.0))
assert_allclose(res, np.pi/2, rtol=0, atol=max(epsabs, err))
f = lambda x: np.sin(x + 2) / (1 + x**2)
exact = np.pi / np.e * np.sin(2)
epsabs = 1e-5
res, err, info = quad_vec(f, -np.inf, np.inf, limit=1000, norm='max', epsabs=epsabs,
full_output=True)
assert_allclose(res, exact, rtol=0, atol=max(epsabs, err))
def computeMagFieldResponse(coiloffset, reflection_coefficient, wavenumber):
"""
.
"""
from scipy.special import jv
from scipy.integrate import quad_vec
def integrand(wavenumber):
return np.imag(reflection_coefficient) * jv(
0, wavenumber * coiloffset) * wavenumber**2
integrated, error = quad_vec(integrand, 0, np.inf)
return 1 - coiloffset**3 * integrated
def _integrate_esd_first_term_quad(self):
rflats = self.radii.flatten()
first_term_integral = np.array(
[
integrate.quad_vec(
lambda x: self._esd_first_term_integrand_func(
np.array([x]), rflats[i:i + 1]),
MIN_INTEGRATION_RADIUS,
rflats[i],
) for i in range(self.radii.size)
],
dtype=object,
)
_check_errors_ok(first_term_integral[:, 1].astype(float))
return np.concatenate(first_term_integral[:, 0]).astype(float)
def _plot_and_test_mb_cond_dist(synt_ex: SyntheticExample, var_ind,
method):
logging.info(
f'Calculating MB conditional distribution, using method {method}')
var = synt_ex.var_names[var_ind]
sample = synt_ex.sem.sample(SAMPLE_SIZE, seed=SEED)
global_context = {
node: sample[:, node_ind]
for (node_ind, node) in enumerate(synt_ex.var_names) if node != var
}
mc_prob = synt_ex.sem.mb_conditional_log_prob(
var,
global_context=global_context,
method=method,
quad_epsabs=EPSABS,
mc_size=MC_SIZE)
# Checking integration to zero
integrand = lambda val: mc_prob(
torch.tensor(val).repeat(1, len(sample))).exp().numpy()
int_res = quad_vec(integrand,
*synt_ex.sem.support_bounds,
epsabs=EPSABS)[0]
logging.info(f'Mean integral of cond density: {int_res.mean()}')
if method == 'quad':
np.testing.assert_array_almost_equal(int_res.flatten(),
np.ones(len(sample)),
ASSERT_DECIMAL)
# Plotting conditional distributions
values = torch.linspace(sample[:, var_ind].min() - 1.0,
sample[:, var_ind].max() + 1.0, 200)
mc_prob_vals = mc_prob(values.unsqueeze(-1).repeat(
1, len(sample))).exp().T
fig, ax = plt.subplots()
for i, mc_prob_val in enumerate(mc_prob_vals):
ax.plot(values, mc_prob_val, alpha=0.1, c='blue')
plt.title(
f'Density of {var} / {[node for node in synt_ex.var_names if node != var]}'
)
plt.show(block=False)
no_time_steps = 10
f0 = 100
seed = 123456789
no_paths = 1000000
delta_vix = 1.0 / 12.0
T = 0.1
# random number generator
rnd_generator = RNG.RndGenerator(seed)
option_vix_price = []
implied_vol_vix = []
value = quad_vec(lambda x: np.exp(nu * nu * np.power(x, 2.0 * h)), 0.0, 1.0 / 12.0)
beta_vix_0 = np.sqrt(value[0] / delta_vix)
vix_t0 = sigma_0 * beta_vix_0
vix_t_0_aux = ExpansionTools.get_vix_rbergomi_t(0.000001, delta_vix + 0.000001, delta_vix, nu, h,
np.asfortranarray(v0),
v0, 200)
no_strikes = 30
strikes = np.linspace(0.95, 1.05, no_strikes) * vix_t0
map_output = RBergomi_Engine.get_path_multi_step(0.0, T, parameters, f0, sigma_0, no_paths, no_time_steps,
Types.TYPE_STANDARD_NORMAL_SAMPLING.ANTITHETIC, rnd_generator)
for i in range(0, no_strikes):
t_i_vix = T + delta_vix
def mb_conditional_log_prob(self,
node: str,
global_context: Dict[str, Tensor] = None,
method='mc',
mc_size=500,
quad_epsabs=1e-2,
mc_seed=None) -> callable:
"""
Conditional log-probability function (density) of node, conditioning on Markov-Blanket of node
Args:
node: Node
global_context: Conditioning global_context, as dict of all the other variables,
each value should be torch.Tensor of shape (n, )
method: 'mc' or 'quad', method to compute normalisation constant (Monte-Carlo integration or quadrature integration)
mc_size: if method == 'mc', MC samples for integration
mc_seed: mc_seed for MC sampling
quad_epsabs: epsabs for scipy.integrate.quad
Returns:
"""
global_context = {} if global_context is None else global_context
# Checking, if all vars from MarkovBlanket(node) are present
assert all([
mb_var in global_context.keys()
for mb_var in self.get_markov_blanket(node)
])
parents_context = {
par: global_context[par]
for par in self.model[node]['parents']
}
context_size = len(list(global_context.values())[0])
if method == 'mc':
torch.manual_seed(mc_seed) if mc_seed is not None else None
sample_shape = (
mc_size,
1) if len(parents_context) != 0 and self.is_batched else (
mc_size, context_size)
sampled_value = self.parents_conditional_sample(
node, parents_context, sample_shape)
normalisation_constant = self.children_log_prob(
node, sampled_value, global_context).exp().mean(0)
elif method == 'quad':
normalisation_constant = []
for cont_ind in tqdm(range(context_size)):
global_context_slice = {
node: value[cont_ind:cont_ind + 1]
for (node, value) in global_context.items()
}
parents_context_slice = {
par: global_context_slice[par]
for par in self.model[node]['parents']
}
def integrand(value):
value = torch.tensor([value])
parents_cond_dist = self.parents_conditional_distribution(
node, parents_context_slice)
unnorm_log_prob = parents_cond_dist.log_prob(value) + \
self.children_log_prob(node, value, global_context_slice)
return unnorm_log_prob.exp().item()
normalisation_constant.append(
quad_vec(integrand,
*self.support_bounds,
epsabs=quad_epsabs)[0])
normalisation_constant = torch.tensor(normalisation_constant)
else:
raise NotImplementedError()
def cond_log_prob(value):
value = value.reshape(-1, context_size)
result = self.parents_conditional_distribution(
node, parents_context).log_prob(value)
# Considering only inside-support values for conditional distributions of children_nodes
in_support = (~torch.isinf(result))
for val_ind, val in enumerate(value):
global_context_tile = {
n: v[in_support[val_ind]]
for (n, v) in global_context.items()
}
children_lob_prob = self.children_log_prob(
node, val[in_support[val_ind]].unsqueeze(0),
global_context_tile)
result[val_ind,
in_support[val_ind]] += children_lob_prob.squeeze()
return result - normalisation_constant.log()
return cond_log_prob
def LF2_1d(mu, sigma):
return -np.sum(
np.log(
quad_vec(lambda x: gauss(x, mu, sigma) * gauss(x, mus, sigmas),
*lims)[0]))
def gamma_n_to_p(z_gamma,xi_nu):
integral=quad_vec(lambda epsilon: n_to_p_int(epsilon,z_gamma,sign=1,xi_nu=xi_nu),1,np.inf)
return integral[0]
# ..., c-3, c-2, c-1, c0, c1, c2, c3, ...
order = 100 # -order to order i.e -100 to 100
# you can change the order to get proper figure
# too much is also not good, and too less will not produce good result
print("generating coefficients ...")
# lets compute fourier coefficients from -order to order
c = []
pbar = tqdm(total=(order * 2 + 1))
# we need to calculate the coefficients from -order to order
for n in range(-order, order + 1):
# calculate definite integration from 0 to 2*PI
# formula is given in readme
coef = 1 / tau * quad_vec(
lambda t: f(t, t_list, x_list, y_list) * np.exp(-n * t * 1j),
0,
tau,
limit=100,
full_output=1)[0]
c.append(coef)
pbar.update(1)
pbar.close()
print("completed generating coefficients.")
# converting list into numpy array
c = np.array(c)
# save the coefficients for later use
np.save("coeff.npy", c)
## -- now to make animation with epicycle -- ##
def __call__(self,
estimator: ConditionalDistributionEstimator,
sem: StructuralEquationModel,
target_var: str,
context_vars: Tuple[str],
exp_args: Union[DictConfig, dict],
conditioning_mode: str = 'all',
test_df: pd.DataFrame = None,
sort_estimator_context=True):
logger.info(
f"Calculating {self.name} for {target_var} / {context_vars}")
assert target_var not in context_vars
context = {
node: torch.tensor(test_df.loc[:, node])
for node in context_vars
}
context_size = len(test_df)
logger.info("Initializing SEM conditional distributions")
if conditioning_mode == 'true_parents':
data_log_prob = sem.parents_conditional_distribution(
target_var, parents_context=context).log_prob
elif conditioning_mode == 'true_markov_blanket' or conditioning_mode == 'all':
data_log_prob = sem.mb_conditional_log_prob(target_var,
global_context=context,
**exp_args['mb_dist'])
elif conditioning_mode == 'arbitrary' and isinstance(
sem, LinearGaussianNoiseSEM):
data_log_prob = sem.conditional_distribution(
target_var, context=context).log_prob
else:
raise NotImplementedError('Unknown conditioning type!')
def log_prob_from_np(value, log_prob_func):
value = torch.tensor([[value]])
with torch.no_grad():
return log_prob_func(value.repeat(context_size, 1)).squeeze()
logger.info("Initializing estimator's conditional distributions")
if sort_estimator_context:
test_context = test_df[Sampler._order_fset(
context_vars)].to_numpy()
else:
test_context = test_df[context_vars].to_numpy()
model_log_prob = estimator.conditional_distribution(
test_context).log_prob
logger.info("Calculating integral")
if self.name == 'conditional_kl_divergence' or self.name == 'conditional_hellinger_distance':
def integrand(value):
data_log_p = log_prob_from_np(value, data_log_prob)
model_log_p = log_prob_from_np(value, model_log_prob)
if self.name == 'conditional_kl_divergence':
res = (data_log_p - model_log_p) * data_log_p.exp()
elif self.name == 'conditional_hellinger_distance':
res = (torch.sqrt(data_log_p.exp()) -
torch.sqrt(model_log_p.exp()))**2
res[torch.isnan(res)] = 0.0 # Out of support values
return res.numpy()
if self.name == 'conditional_kl_divergence':
result = integrate.quad_vec(
integrand,
*sem.support_bounds,
epsabs=exp_args['metrics']['epsabs'])[0]
else:
result = integrate.quad_vec(
integrand,
-np.inf,
np.inf,
epsabs=exp_args['metrics']['epsabs'])[0]
if self.name == 'conditional_hellinger_distance':
result = np.sqrt(0.5 * result)
elif self.name == 'conditional_js_divergence':
# functions to integrate
def integrand1(value):
data_log_p = log_prob_from_np(value, data_log_prob)
model_log_p = log_prob_from_np(value, model_log_prob)
log_mixture = np.log(0.5) + torch.logsumexp(
torch.stack([data_log_p, model_log_p]), 0)
res = (data_log_p - log_mixture) * data_log_p.exp()
res[torch.isnan(res)] = 0.0 # Out of support values
return res.numpy()
def integrand2(value):
data_log_p = log_prob_from_np(value, data_log_prob)
model_log_p = log_prob_from_np(value, model_log_prob)
log_mixture = np.log(0.5) + torch.logsumexp(
torch.stack([data_log_p, model_log_p]), 0)
res = (model_log_p - log_mixture) * model_log_p.exp()
res[torch.isnan(res)] = 0.0 # Out of support values
return res.numpy()
result = 0.5 * (
integrate.quad_vec(integrand1,
-np.inf,
np.inf,
epsabs=exp_args['metrics']['epsabs'])[0] +
integrate.quad_vec(integrand2,
-np.inf,
np.inf,
epsabs=exp_args['metrics']['epsabs'])[0])
else:
raise NotImplementedError()
# Bounds check
if not ((result + exp_args['metrics']['epsabs']) >= 0.0).all():
logger.warning(
f'{((result + exp_args["metrics"]["epsabs"]) < 0.0).sum()} contexts have negative distances, '
f'Please increase cond distribution estimation accuracy. Negative values will be ignored.'
)
result = result[(result + exp_args['metrics']['epsabs']) >= 0.0]
if self.name == 'conditional_js_divergence' and not (
result - exp_args["metrics"]["epsabs"] <= np.log(2)).all():
logger.warning(
f'{(result - exp_args["metrics"]["epsabs"] > np.log(2)).sum()} contexts have distances, '
f'larger than log(2), '
f'please increase cond distribution estimation accuracy. Larger values will be ignored.'
)
result = result[(result -
exp_args["metrics"]["epsabs"]) <= np.log(2)]
elif self.name == 'conditional_hellinger_distance' and not (
(result - exp_args["metrics"]["epsabs"]) <= 1.0).all():
logger.warning(
f'{((result - exp_args["metrics"]["epsabs"]) > 1.0).sum()} contexts have distances, larger than 1.0, '
f'please increase cond distribution estimation accuracy. Larger values will be ignored.'
)
result = result[(result - exp_args.metrics.epsabs) <= 1.0]
return result.mean()
def get_analytic_value(self, *args, model_type=None, compute_greek=False):
if model_type == ANALYTIC_MODEL.BLACK_SCHOLES_MODEL:
pass
elif model_type == ANALYTIC_MODEL.SABR_MODEL:
alpha = args[0]
rho = args[1]
nu = args[2]
pass
elif model_type == ANALYTIC_MODEL.HESTON_MODEL_ATTARI:
r = args[0]
theta = args[1]
rho = args[2]
k = args[3]
epsilon = args[4]
v0 = args[5]
risk_lambda = args[6]
b2 = k + risk_lambda
u2 = -0.5
integrator = partial(f_attari_heston,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
integral_value = quad_vec(integrator, 0.0, np.inf)
df = np.exp(-r * self._delta_time)
discrete_value = self._spot - 0.5 * self._strike * df
stochastic_adjustment = (self._strike * df /
np.pi) * integral_value[0][0]
price = discrete_value - stochastic_adjustment
if compute_greek:
delta_integrator = partial(f_delta_attari_heston,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
dual_delta_integrator = partial(f_dual_delta_attari_heston,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
gamma_integrator = partial(f_gamma_attari_heston,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
delta_integral = quad_vec(delta_integrator, 0.0, np.inf)
dual_delta = quad_vec(dual_delta_integrator, 0.0, np.inf)
gamma_integral = quad_vec(gamma_integrator, 0.0, np.inf)
aux_dual_delta = (discrete_value - price) / self._strike
greeks_map = {
TypeGreeks.DELTA:
1.0 - (self._strike * df / np.pi) * delta_integral[0],
TypeGreeks.GAMMA:
-(self._strike * df / np.pi) * gamma_integral[0],
TypeGreeks.DUAL_DELTA:
-0.5 * df - aux_dual_delta -
(df * self._strike / np.pi) * dual_delta[0]
}
return price, greeks_map
else:
return price
elif model_type == ANALYTIC_MODEL.HESTON_MODEL_LEWIS:
r = args[0]
theta = args[1]
rho = args[2]
k = args[3]
epsilon = args[4]
v0 = args[5]
integrator = partial(f_lewis_heston,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
strike=self._strike)
integral_value = quad_vec(integrator, 0.0, np.inf)
df = np.exp(-r * self._delta_time)
price = self._spot - (df * self._strike /
np.pi) * integral_value[0]
return price
elif model_type == ANALYTIC_MODEL.HESTON_MODEL_REGULAR:
r = args[0]
theta = args[1]
rho = args[2]
k = args[3]
epsilon = args[4]
v0 = args[5]
risk_lambda = args[6]
u1 = 0.5
b1 = k + risk_lambda - epsilon * rho
b2 = k + risk_lambda
u2 = -0.5
if self._option_type == TypeEuropeanOption.CALL:
phi = 1.0
else:
phi = -1.0
integrator1 = partial(f_heston,
t=self._delta_time,
x=np.log(self._spot),
v=v0,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b1,
u=u1,
strike=self._strike)
integrator2 = partial(f_heston,
t=self._delta_time,
x=np.log(self._spot),
v=v0,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
int_val_1 = quad_vec(integrator1, 0.0, np.inf)
value_1_aux = 0.5 + (1.0 / np.pi) * int_val_1[0][0]
p1 = 0.5 * (1 - phi) + phi * value_1_aux
int_val_2 = quad_vec(integrator2, 0.0, np.inf)
value_2_aux = 0.5 + (1.0 / np.pi) * int_val_2[0][0]
p2 = 0.5 * (1 - phi) + phi * value_2_aux
df = np.exp(-r * self._delta_time)
price = self._spot * p1 - df * self._strike * p2
if compute_greek:
gamma_integrator = partial(f_gamma_heston,
t=self._delta_time,
x=np.log(self._spot),
v=v0,
r_t=r,
theta=theta,
rho=rho,
k=k,
epsilon=epsilon,
b=b2,
u=u2,
strike=self._strike)
gamma_output = quad_vec(gamma_integrator, 0.0, np.inf)
gamma = gamma_output[0] / (np.pi * self._spot)
greeks_map = {
TypeGreeks.DELTA: phi * p1,
TypeGreeks.GAMMA: gamma,
TypeGreeks.DUAL_DELTA: -phi * df * p2
}
return price, greeks_map
else:
return price
elif model_type == ANALYTIC_MODEL.BATES_MODEL_LEWIS:
r = args[0]
theta = args[1]
rho = args[2]
k = args[3]
epsilon = args[4]
v0 = args[5]
muJ = args[6]
sigmaJ = args[7]
lambdaJ = args[8]
integrator = partial(f_lewis_bate,
t=self._delta_time,
v=v0,
spot=self._spot,
r_t=r,
theta=theta,
rho=rho,
k=k,
mu_jump=muJ,
sigma_jump=sigmaJ,
lambda_jump=lambdaJ,
epsilon=epsilon,
strike=self._strike)
integral_value = quad_vec(integrator, 0.0, np.inf)
df = np.exp(-r * self._delta_time)
price = self._spot - (df * self._strike /
np.pi) * integral_value[0]
return price
else:
raise Exception("The method " + str(model_type) + " is unknown.")
