logbesselk

Provide function to calculate the modified Bessel function of the second kind and its derivatives.

Reference

Takashi Takekawa, Fast parallel calculation of modified Bessel function of the second kind and its derivatives, SoftwareX, 17, 100923, 2022.

Author

TAKEKAWA Takashi takekawa@tk2lab.org

For Tensorflow

Require

• Python (>=3.10)
• Tensorflow (>=2.8)

Installation

pip install tensorflow logbesselk

Examples

import tensorflow as tf
from logbesselk.tensorflow import log_bessel_k as logk
from logbesselk.tensorflow import bessel_ke as ke
from logbesselk.tensorflow import bessel_kratio as kratio

v = 1.0
x = 1.0
a = logk(v, x)

v = tf.linspace(1, 10, 10)
x = tf.linspace(1, 10, 10)
b = logk(v, x)

# gradient
with tf.GradientTape() as g:
    g.watch(v, x)
    f = logk(v, x)
dlogkdv = g.gradient(f, v)
dlogkdx = g.gradient(f, x)

# use tf.function
logk = tf.function(logk)

# advanced version
from logbesselk.tensorflow import log_abs_deriv_bessel_k

logk = lambda v, x: log_abs_deriv_bessel_k(v, x, 0, 0)
logdkdv = lambda v, x: log_abs_deriv_bessel_k(v, x, 1, 0)
logdkdx = lambda v, x: log_abs_deriv_bessel_k(v, x, 0, 1)

For jax

Require

• Python (>=3.10)
• jax (>=0.4)

Installation

pip install jax[cuda] -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
pip install logbesselk

Examples

import jax
import jax.numpy as jnp
from logbesselk.jax import log_bessel_k as logk
from logbesselk.jax import bessel_ke as ke
from logbesselk.jax import bessel_kratio as kratio

# scalar func and grad
v = 1.0
x = 1.0
a = logk(v, x)

# dlogK/dv = (dK/dv) / K
dlogkdv = jax.grad(logk, 0)
b = dlogkdv(v, x)

# dlogK/dx = (dK/dx) / K
dlogkdx = jax.grad(logk, 1)
c = dlogkdx(v, x)

# misc
d = ke(v, x)
e = kratio(v, x, d=1)

# vectorize
logk_vec = jax.vmap(logk)

v = jnp.linspace(1, 10, 10)
x = jnp.linspace(1, 10, 10)
f = logk_vec(v)

# use jit
logk_vec_jit = jax.jit(logk_vec)

# advanced version
from logbesselk.jax import log_abs_devel_bessel_k

log_dkdv = lambda v, x: log_abs_deriv_bessel_k(v, x, 1, 0)
log_dkdx = lambda v, x: log_abs_deriv_bessel_k(v, x, 0, 1)

log_dkdv_jit = jax.jit(jax.vmap(log_dkdv))
log_dkdx_jit = jax.jit(jax.vmap(log_dkdx))