Special functions (cupyx.scipy.special)#

Bessel functions#

j0

Bessel function of the first kind of order 0.

j1

Bessel function of the first kind of order 1.

y0

Bessel function of the second kind of order 0.

y1

Bessel function of the second kind of order 1.

yn

Bessel function of the second kind of order n.

i0

Modified Bessel function of order 0.

i0e

Exponentially scaled modified Bessel function of order 0.

i1

Modified Bessel function of order 1.

i1e

Exponentially scaled modified Bessel function of order 1.

Raw statistical functions#

bdtr

Binomial distribution cumulative distribution function.

bdtrc

Binomial distribution survival function.

bdtri

Inverse function to bdtr with respect to p.

btdtr

Cumulative distribution function of the beta distribution.

btdtri

The p-th quantile of the beta distribution.

fdtr

F cumulative distribution function.

fdtrc

F survival function.

fdtri

The p-th quantile of the F-distribution.

gdtr

Gamma distribution cumulative distribution function.

gdtrc

Gamma distribution survival function.

nbdtr

Negative binomial distribution cumulative distribution function.

nbdtrc

Negative binomial distribution survival function.

nbdtri

Inverse function to nbdtr with respect to p.

pdtr

Poisson cumulative distribution function.

pdtrc

Binomial distribution survival function.

pdtri

Inverse function to pdtr with respect to m.

chdtr

Chi-square cumulative distribution function.

chdtrc

Chi square survival function.

chdtri

Inverse to chdtrc with respect to x.

ndtr

Cumulative distribution function of normal distribution.

log_ndtr

Logarithm of Gaussian cumulative distribution function.

ndtri

Inverse of the cumulative distribution function of the standard

logit

Logit function.

expit

Logistic sigmoid function (expit).

log_expit

Logarithm of the logistic sigmoid function.

boxcox

Compute the Box-Cox transformation.

boxcox1p

Compute the Box-Cox transformation op 1 + x.

inv_boxcox

Compute the Box-Cox transformation.

inv_boxcox1p

Compute the Box-Cox transformation op 1 + x.

Information Theory functions#

entr

Elementwise function for computing entropy.

rel_entr

Elementwise function for computing relative entropy.

kl_div

Elementwise function for computing Kullback-Leibler divergence.

huber

Elementwise function for computing the Huber loss.

pseudo_huber

Elementwise function for computing the Pseudo-Huber loss.

Error function and Fresnel integrals#

erf

Error function.

erfc

Complementary error function.

erfcx

Scaled complementary error function.

erfinv

Inverse function of error function.

erfcinv

Inverse function of complementary error function.

Legendre functions#

lpmv

Associated Legendre function of integer order and real degree.

sph_harm

Spherical Harmonic.

Other special functions#

exp1

Exponential integral E1.

expi

Exponential integral Ei.

expn

Generalized exponential integral En.

softmax(x[, axis])

Softmax function.

log_softmax(x[, axis])

Compute logarithm of softmax function

zeta

Hurwitz zeta function.

Convenience functions#

cbrt

Cube root.

exp10

Computes 10**x.

exp2

Computes 2**x.

radian

Degrees, minutes, seconds to radians:

cosdg

Cosine of x with x in degrees.

sindg

Sine of x with x in degrees.

tandg

Tangent of x with x in degrees.

cotdg

Cotangent of x with x in degrees.

log1p

Elementwise function for scipy.special.log1p

expm1

Computes exp(x) - 1.

cosm1

Computes cos(x) - 1.

round(a[, decimals, out])

xlogy

Compute x*log(y) so that the result is 0 if x = 0.

xlog1py

Compute x*log1p(y) so that the result is 0 if x = 0.

logsumexp(a[, axis, b, keepdims, return_sign])

Compute the log of the sum of exponentials of input elements.

sinc

Elementwise sinc function.