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90 lines
3.2 KiB
Python
90 lines
3.2 KiB
Python
from __future__ import annotations
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import numpy as np
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from .obs import derived_observable, Obs
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from autograd import jacobian
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from scipy.integrate import quad as squad
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from numpy import ndarray
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from typing import Callable, Union
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def quad(func: Callable, p: Union[list[Union[float, Obs]], list[float], ndarray], a: Union[Obs, float, int], b: Union[Obs, float, int], **kwargs) -> Union[tuple[Obs, float], tuple[float, float], tuple[Obs, float, dict[str, Union[int, ndarray]]]]:
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'''Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
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The integration is performed using scipy.integrate.quad().
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All parameters that can be passed to scipy.integrate.quad may also be passed to this function.
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The output is the same as for scipy.integrate.quad, the first element being an Obs.
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Parameters
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----------
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func : object
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function to integrate, has to be of the form
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```python
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import autograd.numpy as anp
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def func(p, x):
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return p[0] + p[1] * x + p[2] * anp.sinh(x)
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```
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where x is the integration variable.
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p : list of floats or Obs
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parameters of the function func.
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a: float or Obs
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Lower limit of integration (use -numpy.inf for -infinity).
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b: float or Obs
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Upper limit of integration (use -numpy.inf for -infinity).
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All parameters of scipy.integrate.quad
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Returns
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-------
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y : Obs
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The integral of func from `a` to `b`.
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abserr : float
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An estimate of the absolute error in the result.
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infodict : dict
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A dictionary containing additional information.
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Run scipy.integrate.quad_explain() for more information.
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message
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A convergence message.
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explain
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Appended only with 'cos' or 'sin' weighting and infinite
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integration limits, it contains an explanation of the codes in
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infodict['ierlst']
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'''
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Np = len(p)
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isobs = [True if isinstance(pi, Obs) else False for pi in p]
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pval = np.array([p[i].value if isobs[i] else p[i] for i in range(Np)],)
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pobs = [p[i] for i in range(Np) if isobs[i]]
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bounds = [a, b]
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isobs_b = [True if isinstance(bi, Obs) else False for bi in bounds]
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bval = np.array([bounds[i].value if isobs_b[i] else bounds[i] for i in range(2)])
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bobs = [bounds[i] for i in range(2) if isobs_b[i]]
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bsign = [-1, 1]
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ifunc = np.vectorize(lambda x: func(pval, x))
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intpars = squad.__code__.co_varnames[3:3 + len(squad.__defaults__)]
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ikwargs = {k: kwargs[k] for k in intpars if k in kwargs}
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integration_result = squad(ifunc, bval[0], bval[1], **ikwargs)
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val = integration_result[0]
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jac = jacobian(func)
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derivint = []
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for i in range(Np):
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if isobs[i]:
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ifunc = np.vectorize(lambda x: jac(pval, x)[i])
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derivint.append(squad(ifunc, bounds[0], bounds[1], **ikwargs)[0])
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for i in range(2):
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if isobs_b[i]:
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derivint.append(bsign[i] * func(pval, bval[i]))
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if len(derivint) == 0:
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return integration_result
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res = derived_observable(lambda x, **kwargs: 0 * (x[0] + np.finfo(np.float64).eps) * (pval[0] + np.finfo(np.float64).eps) + val, pobs + bobs, man_grad=derivint)
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return (res, *integration_result[1:])
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