def __init__(self,
function: Callable,
r: np.ndarray,
max_interval,
cutoff: float = None,
cache_size: int = 4096,
cache_key_decimals: int = 2,
tolerance: float = 1e-6):
self._function = function
self._r = r
if cutoff is None:
self._cutoff = r[-1]
else:
self._cutoff = cutoff
self._cache = Cache(cache_size)
self._cache_key_decimals = cache_key_decimals
self._tolerance = tolerance
def f(z):
return self._function(
np.sqrt(self.r[0]**2 +
(z * max_interval / 2 + max_interval / 2)**2))
value, error_estimate, step_size, order = integrate(
f, -1, 1, self._tolerance)
self._xk, self._wk = tanh_sinh_nodes_and_weights(step_size, order)
def cached_integrate(self, a, b):
zm = (b - a) / 2.
zp = (a + b) / 2.
f = lambda z: self._function(np.sqrt(self.r[0]**2 + (z * zm + zp)**2))
value, error_estimate, step_size, order = integrate(
f, -1, 1, self._tolerance)
xk, wk = tanh_sinh_nodes_and_weights(step_size, order)
f = lambda z: self._function(
np.sqrt(self.r[:, None]**2 + (z * zm + zp)**2))
values = np.sum(f(xk[None]) * wk[None], axis=1) * zm
derivatives = np.diff(values) / np.diff(self.r)
return values, derivatives