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24 lines
1 KiB
Python
24 lines
1 KiB
Python
from __future__ import annotations
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import scipy
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import numpy as np
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from autograd.extend import primitive, defvjp
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from autograd.scipy.special import j0, y0, j1, y1, jn, yn, i0, i1, iv, ive, beta, betainc, betaln
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from autograd.scipy.special import polygamma, psi, digamma, gamma, gammaln, gammainc, gammaincc, gammasgn, rgamma, multigammaln
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from autograd.scipy.special import erf, erfc, erfinv, erfcinv, logit, expit, logsumexp
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__all__ = ["beta", "betainc", "betaln",
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"polygamma", "psi", "digamma", "gamma", "gammaln", "gammainc", "gammaincc", "gammasgn", "rgamma", "multigammaln",
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"kn", "j0", "y0", "j1", "y1", "jn", "yn", "i0", "i1", "iv", "ive",
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"erf", "erfc", "erfinv", "erfcinv", "logit", "expit", "logsumexp"]
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@primitive
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def kn(n, x):
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"""Modified Bessel function of the second kind of integer order n"""
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if int(n) != n:
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raise TypeError("The order 'n' needs to be an integer.")
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return scipy.special.kn(n, x)
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defvjp(kn, None, lambda ans, n, x: lambda g: - g * 0.5 * (kn(np.abs(n - 1), x) + kn(n + 1, x)))
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