def integral_full(limits, norm_range, params, model):
lower, upper = limits.rect_limits # for a more detailed guide, see the space.py example
param1 = params['super_param']
param2 = params['param2']
param3 = params['param3']
lower = z.convert_to_tensor(lower)
upper = z.convert_to_tensor(upper)
# calculate the integral here, dummy integral, wrong!
integral = param1 * param2 * param3 + z.reduce_sum([lower, upper])
return integral
def indefinite_integral(limits):
max_degree = model.degree + 1 # needed +1 for integral, max poly in term for n is n+1
polys = do_recurrence(x=limits,
polys=legendre_polys,
degree=max_degree,
recurrence=legendre_recurrence)
one_limit_integrals = []
for degree in range(1, max_degree):
coeff = model.params[f"c_{degree}"]
one_limit_integrals.append(
coeff * (polys[degree + 1] - polys[degree - 1]) /
(2. * (z.convert_to_tensor(degree)) + 1))
return z.reduce_sum(one_limit_integrals, axis=0)
def indefinite_integral(limits):
max_degree = model.degree + 1
polys = do_recurrence(x=limits,
polys=chebyshev_polys,
degree=max_degree,
recurrence=chebyshev_recurrence)
one_limit_integrals = []
for degree in range(2, max_degree):
coeff = model.params[f"c_{degree}"]
n_float = z.convert_to_tensor(degree)
integral = (n_float * polys[degree + 1] /
(z.square(n_float) - 1) - limits * polys[degree] /
(n_float - 1))
one_limit_integrals.append(coeff * integral)
return z.reduce_sum(one_limit_integrals, axis=0)
def _auto_ext_integrate(self, limits, norm, *, options):
try:
integral = self._ext_integrate(limits=limits, norm=norm, options=options)
except NormNotImplemented:
unnormalized_integral = self._auto_ext_integrate(
limits=limits, norm=False, options=options
)
normalization = self.ext_normalization(norm, options=options)
integral = unnormalized_integral / normalization
except MultipleLimitsNotImplemented:
integrals = [] # TODO: map?
for sub_limits in limits:
integrals.append(
self._auto_integrate(limits=sub_limits, norm=norm, options=options)
)
integral = z.reduce_sum(integrals, axis=0) # TODO: remove stack?
return integral
