Cython API for special functions#

Scalar, typed versions of many of the functions in scipy.special can be accessed directly from Cython; the complete list is given below. Functions are overloaded using Cython fused types so their names match their Python counterpart. The module follows the following conventions:

If a function’s Python counterpart returns multiple values, then the function returns its outputs via pointers in the final arguments.
If a function’s Python counterpart returns a single value, then the function’s output is returned directly.

The module is usable from Cython via:

cimport scipy.special.cython_special

Error handling#

Functions can indicate an error by returning nan; however they cannot emit warnings like their counterparts in scipy.special.

Available functions#

voigt_profile:

double voigt_profile(double, double, double)

agm:
```
double agm(double, double)
```

airy:

void airy(double, double *, double *, double *, double *)
void airy(double complex, double complex *, double complex *, double complex *, double complex *)

airye:

void airye(double complex, double complex *, double complex *, double complex *, double complex *)
void airye(double, double *, double *, double *, double *)

bdtr:

double bdtr(double, double, double)
double bdtr(double, long, double)

bdtrc:

double bdtrc(double, double, double)
double bdtrc(double, long, double)

bdtri:

double bdtri(double, double, double)
double bdtri(double, long, double)

bdtrik:
```
double bdtrik(double, double, double)
```
bdtrin:
```
double bdtrin(double, double, double)
```
bei:
```
double bei(double)
```
beip:
```
double beip(double)
```
ber:
```
double ber(double)
```
berp:
```
double berp(double)
```

besselpoly:

double besselpoly(double, double, double)

beta:
```
double beta(double, double)
```

betainc:

float betainc(float, float, float)
double betainc(double, double, double)

betaincc:

float betaincc(float, float, float)
double betaincc(double, double, double)

betaincinv:

float betaincinv(float, float, float)
double betaincinv(double, double, double)

betainccinv:

float betainccinv(float, float, float)
double betainccinv(double, double, double)

betaln:
```
double betaln(double, double)
```
binom:
```
double binom(double, double)
```
boxcox:
```
double boxcox(double, double)
```
boxcox1p:
```
double boxcox1p(double, double)
```

btdtria:

double btdtria(double, double, double)
float btdtria(float, float, float)

btdtrib:

double btdtrib(double, double, double)
float btdtrib(float, float, float)

cbrt:
```
double cbrt(double)
```
chdtr:
```
double chdtr(double, double)
```
chdtrc:
```
double chdtrc(double, double)
```
chdtri:
```
double chdtri(double, double)
```
chdtriv:
```
double chdtriv(double, double)
```
chndtr:
```
double chndtr(double, double, double)
```

chndtridf:

double chndtridf(double, double, double)

chndtrinc:

double chndtrinc(double, double, double)
float chndtrinc(float, float, float)

chndtrix:

double chndtrix(double, double, double)
float chndtrix(float, float, float)

cosdg:
```
double cosdg(double)
```
cosm1:
```
double cosm1(double)
```
cotdg:
```
double cotdg(double)
```

dawsn:

double dawsn(double)
double complex dawsn(double complex)

ellipe:
```
double ellipe(double)
```
ellipeinc:
```
double ellipeinc(double, double)
```

ellipj:

void ellipj(double, double, double *, double *, double *, double *)

ellipkinc:
```
double ellipkinc(double, double)
```
ellipkm1:
```
double ellipkm1(double)
```
ellipk:
```
double ellipk(double)
```

elliprc:

double elliprc(double, double)
double complex elliprc(double complex, double complex)

elliprd:

double elliprd(double, double, double)
double complex elliprd(double complex, double complex, double complex)

elliprf:

double elliprf(double, double, double)
double complex elliprf(double complex, double complex, double complex)

elliprg:

double elliprg(double, double, double)
double complex elliprg(double complex, double complex, double complex)

elliprj:

double elliprj(double, double, double, double)
double complex elliprj(double complex, double complex, double complex, double complex)

entr:
```
double entr(double)
```

erf:

double complex erf(double complex)
double erf(double)

erfc:

double complex erfc(double complex)
double erfc(double)

erfcx:

double erfcx(double)
double complex erfcx(double complex)

erfi:

double erfi(double)
double complex erfi(double complex)

erfinv:

float erfinv(float)
double erfinv(double)

erfcinv:
```
double erfcinv(double)
```

eval_chebyc:

double complex eval_chebyc(double, double complex)
double eval_chebyc(double, double)
double eval_chebyc(Py_ssize_t, double)

eval_chebys:

double complex eval_chebys(double, double complex)
double eval_chebys(double, double)
double eval_chebys(Py_ssize_t, double)

eval_chebyt:

double complex eval_chebyt(double, double complex)
double eval_chebyt(double, double)
double eval_chebyt(Py_ssize_t, double)

eval_chebyu:

double complex eval_chebyu(double, double complex)
double eval_chebyu(double, double)
double eval_chebyu(Py_ssize_t, double)

eval_gegenbauer:

double complex eval_gegenbauer(double, double, double complex)
double eval_gegenbauer(double, double, double)
double eval_gegenbauer(Py_ssize_t, double, double)

eval_genlaguerre:

double complex eval_genlaguerre(double, double, double complex)
double eval_genlaguerre(double, double, double)
double eval_genlaguerre(Py_ssize_t, double, double)

eval_hermite:

double eval_hermite(Py_ssize_t, double)

eval_hermitenorm:

double eval_hermitenorm(Py_ssize_t, double)

eval_jacobi:

double complex eval_jacobi(double, double, double, double complex)
double eval_jacobi(double, double, double, double)
double eval_jacobi(Py_ssize_t, double, double, double)

eval_laguerre:

double complex eval_laguerre(double, double complex)
double eval_laguerre(double, double)
double eval_laguerre(Py_ssize_t, double)

eval_legendre:

double complex eval_legendre(double, double complex)
double eval_legendre(double, double)
double eval_legendre(Py_ssize_t, double)

eval_sh_chebyt:

double complex eval_sh_chebyt(double, double complex)
double eval_sh_chebyt(double, double)
double eval_sh_chebyt(Py_ssize_t, double)

eval_sh_chebyu:

double complex eval_sh_chebyu(double, double complex)
double eval_sh_chebyu(double, double)
double eval_sh_chebyu(Py_ssize_t, double)

eval_sh_jacobi:

double complex eval_sh_jacobi(double, double, double, double complex)
double eval_sh_jacobi(double, double, double, double)
double eval_sh_jacobi(Py_ssize_t, double, double, double)

eval_sh_legendre:

double complex eval_sh_legendre(double, double complex)
double eval_sh_legendre(double, double)
double eval_sh_legendre(Py_size_t, double)

exp1:

double complex exp1(double complex)
double exp1(double)

exp10:
```
double exp10(double)
```
exp2:
```
double exp2(double)
```

expi:

double complex expi(double complex)
double expi(double)

expit:

double expit(double)
float expit(float)
long double expit(long double)

expm1:

double complex expm1(double complex)
double expm1(double)

expn:

double expn(double, double)
double expn(long, double)

exprel:
```
double exprel(double)
```
fdtr:
```
double fdtr(double, double, double)
```
fdtrc:
```
double fdtrc(double, double, double)
```
fdtri:
```
double fdtri(double, double, double)
```

fdtridfd:

double fdtridfd(double, double, double)

fresnel:

void fresnel(double, double *, double *)
void fresnel(double complex, double complex *, double complex *)

gamma:

double complex gamma(double complex)
double gamma(double)

gammainc:
```
double gammainc(double, double)
```
gammaincc:
```
double gammaincc(double, double)
```
gammainccinv:
```
double gammainccinv(double, double)
```
gammaincinv:
```
double gammaincinv(double, double)
```
gammaln:
```
double gammaln(double)
```
gammasgn:
```
double gammasgn(double)
```
gdtr:
```
double gdtr(double, double, double)
```
gdtrc:
```
double gdtrc(double, double, double)
```
gdtria:
```
double gdtria(double, double, double)
```
gdtrib:
```
double gdtrib(double, double, double)
```
gdtrix:
```
double gdtrix(double, double, double)
```

hankel1:

double complex hankel1(double, double complex)

hankel1e:

double complex hankel1e(double, double complex)

hankel2:

double complex hankel2(double, double complex)

hankel2e:

double complex hankel2e(double, double complex)

huber:
```
double huber(double, double)
```

hyp0f1:

double complex hyp0f1(double, double complex)
double hyp0f1(double, double)

hyp1f1:

double hyp1f1(double, double, double)
double complex hyp1f1(double, double, double complex)

hyp2f1:

double hyp2f1(double, double, double, double)
double complex hyp2f1(double, double, double, double complex)

hyperu:
```
double hyperu(double, double, double)
```
i0:
```
double i0(double)
```
i0e:
```
double i0e(double)
```
i1:
```
double i1(double)
```
i1e:
```
double i1e(double)
```
inv_boxcox:
```
double inv_boxcox(double, double)
```
inv_boxcox1p:
```
double inv_boxcox1p(double, double)
```

it2i0k0:

void it2i0k0(double, double *, double *)

it2j0y0:

void it2j0y0(double, double *, double *)

it2struve0:
```
double it2struve0(double)
```

itairy:

void itairy(double, double *, double *, double *, double *)

iti0k0:

void iti0k0(double, double *, double *)

itj0y0:

void itj0y0(double, double *, double *)

itmodstruve0:
```
double itmodstruve0(double)
```
itstruve0:
```
double itstruve0(double)
```

iv:

double complex iv(double, double complex)
double iv(double, double)

ive:

double complex ive(double, double complex)
double ive(double, double)

j0:
```
double j0(double)
```
j1:
```
double j1(double)
```

jv:

double complex jv(double, double complex)
double jv(double, double)

jve:

double complex jve(double, double complex)
double jve(double, double)

k0:
```
double k0(double)
```
k0e:
```
double k0e(double)
```
k1:
```
double k1(double)
```
k1e:
```
double k1e(double)
```
kei:
```
double kei(double)
```
keip:
```
double keip(double)
```

kelvin:

void kelvin(double, double complex *, double complex *, double complex *, double complex *)

ker:
```
double ker(double)
```
kerp:
```
double kerp(double)
```
kl_div:
```
double kl_div(double, double)
```

kn:

double kn(double, double)
double kn(long, double)

kolmogi:
```
double kolmogi(double)
```
kolmogorov:
```
double kolmogorov(double)
```

kv:

double complex kv(double, double complex)
double kv(double, double)

kve:

double complex kve(double, double complex)
double kve(double, double)

log1p:

double complex log1p(double complex)
double log1p(double)

log_expit:

double log_expit(double)
float log_expit(float)
long double log_expit(long double)

log_ndtr:

double log_ndtr(double)
double complex log_ndtr(double complex)

loggamma:

double loggamma(double)
double complex loggamma(double complex)

logit:

double logit(double)
float logit(float)
long double logit(long double)

lpmv:
```
double lpmv(double, double, double)
```
mathieu_a:
```
double mathieu_a(double, double)
```
mathieu_b:
```
double mathieu_b(double, double)
```

mathieu_cem:

void mathieu_cem(double, double, double, double *, double *)

mathieu_modcem1:

void mathieu_modcem1(double, double, double, double *, double *)

mathieu_modcem2:

void mathieu_modcem2(double, double, double, double *, double *)

mathieu_modsem1:

void mathieu_modsem1(double, double, double, double *, double *)

mathieu_modsem2:

void mathieu_modsem2(double, double, double, double *, double *)

mathieu_sem:

void mathieu_sem(double, double, double, double *, double *)

modfresnelm:

void modfresnelm(double, double complex *, double complex *)

modfresnelp:

void modfresnelp(double, double complex *, double complex *)

modstruve:
```
double modstruve(double, double)
```

nbdtr:

double nbdtr(double, double, double)
double nbdtr(long, long, double)

nbdtrc:

double nbdtrc(double, double, double)
double nbdtrc(long, long, double)

nbdtri:

double nbdtri(double, double, double)
double nbdtri(long, long, double)

nbdtrik:
```
double nbdtrik(double, double, double)
```
nbdtrin:
```
double nbdtrin(double, double, double)
```

ncfdtr:

double ncfdtr(double, double, double, double)

ncfdtri:

double ncfdtri(double, double, double, double)

ncfdtridfd:

double ncfdtridfd(double, double, double, double)

ncfdtridfn:

double ncfdtridfn(double, double, double, double)

ncfdtrinc:

double ncfdtrinc(double, double, double, double)

nctdtr:
```
double nctdtr(double, double, double)
```

nctdtridf:

double nctdtridf(double, double, double)

nctdtrinc:

double nctdtrinc(double, double, double)

nctdtrit:

double nctdtrit(double, double, double)

ndtr:

double complex ndtr(double complex)
double ndtr(double)

ndtri:
```
double ndtri(double)
```

nrdtrimn:

double nrdtrimn(double, double, double)

nrdtrisd:

double nrdtrisd(double, double, double)

obl_ang1:

void obl_ang1(double, double, double, double, double *, double *)

obl_ang1_cv:

void obl_ang1_cv(double, double, double, double, double, double *, double *)

obl_cv:
```
double obl_cv(double, double, double)
```

obl_rad1:

void obl_rad1(double, double, double, double, double *, double *)

obl_rad1_cv:

void obl_rad1_cv(double, double, double, double, double, double *, double *)

obl_rad2:

void obl_rad2(double, double, double, double, double *, double *)

obl_rad2_cv:

void obl_rad2_cv(double, double, double, double, double, double *, double *)

owens_t:
```
double owens_t(double, double)
```

pbdv:

void pbdv(double, double, double *, double *)

pbvv:

void pbvv(double, double, double *, double *)

pbwa:

void pbwa(double, double, double *, double *)

pdtr:
```
double pdtr(double, double)
```
pdtrc:
```
double pdtrc(double, double)
```

pdtri:

double pdtri(double, double)
double pdtri(long, double)

pdtrik:

double pdtrik(double, double)
float pdtrik(float, float)

poch:
```
double poch(double, double)
```

powm1:

float powm1(float, float)
double powm1(double, double)

pro_ang1:

void pro_ang1(double, double, double, double, double *, double *)

pro_ang1_cv:

void pro_ang1_cv(double, double, double, double, double, double *, double *)

pro_cv:
```
double pro_cv(double, double, double)
```

pro_rad1:

void pro_rad1(double, double, double, double, double *, double *)

pro_rad1_cv:

void pro_rad1_cv(double, double, double, double, double, double *, double *)

pro_rad2:

void pro_rad2(double, double, double, double, double *, double *)

pro_rad2_cv:

void pro_rad2_cv(double, double, double, double, double, double *, double *)

pseudo_huber:
```
double pseudo_huber(double, double)
```

psi:

double complex psi(double complex)
double psi(double)

radian:
```
double radian(double, double, double)
```
rel_entr:
```
double rel_entr(double, double)
```

rgamma:

double complex rgamma(double complex)
double rgamma(double)

round:
```
double round(double)
```

shichi:

void shichi(double complex, double complex *, double complex *)
void shichi(double, double *, double *)

sici:

void sici(double complex, double complex *, double complex *)
void sici(double, double *, double *)

sindg:
```
double sindg(double)
```

smirnov:

double smirnov(double, double)
double smirnov(long, double)

smirnovi:

double smirnovi(double, double)
double smirnovi(long, double)

spence:

double complex spence(double complex)
double spence(double)

stdtr:
```
double stdtr(double, double)
```
stdtridf:
```
double stdtridf(double, double)
```
stdtrit:
```
double stdtrit(double, double)
```
struve:
```
double struve(double, double)
```
tandg:
```
double tandg(double)
```
tklmbda:
```
double tklmbda(double, double)
```
wofz:
```
double complex wofz(double complex)
```

wrightomega:

double complex wrightomega(double complex)
double wrightomega(double)

xlog1py:

double xlog1py(double, double)
double complex xlog1py(double complex, double complex)

xlogy:

double xlogy(double, double)
double complex xlogy(double complex, double complex)

y0:
```
double y0(double)
```
y1:
```
double y1(double)
```

yn:

double yn(double, double)
double yn(long, double)

yv:

double complex yv(double, double complex)
double yv(double, double)

yve:

double complex yve(double, double complex)
double yve(double, double)

zetac:
```
double zetac(double)
```

wright_bessel:

double wright_bessel(double, double, double)

log_wright_bessel:

double log_wright_bessel(double, double, double)

ndtri_exp:
```
double ndtri_exp(double)
```

Custom functions#

Some functions in scipy.special which are not ufuncs have custom Cython wrappers.

Spherical Bessel functions#

The optional derivative boolean argument is replaced with an optional Cython bint, leading to the following signatures.

spherical_jn:

double complex spherical_jn(Py_ssize_t, double complex)
double complex spherical_jn(Py_ssize_t, double complex, bint)
double spherical_jn(Py_ssize_t, double)
double spherical_jn(Py_ssize_t, double, bint)

spherical_yn:

double complex spherical_yn(Py_ssize_t, double complex)
double complex spherical_yn(Py_ssize_t, double complex, bint)
double spherical_yn(Py_ssize_t, double)
double spherical_yn(Py_ssize_t, double, bint)

spherical_in:

double complex spherical_in(Py_ssize_t, double complex)
double complex spherical_in(Py_ssize_t, double complex, bint)
double spherical_in(Py_ssize_t, double)
double spherical_in(Py_ssize_t, double, bint)

spherical_kn:

double complex spherical_kn(Py_ssize_t, double complex)
double complex spherical_kn(Py_ssize_t, double complex, bint)
double spherical_kn(Py_ssize_t, double)
double spherical_kn(Py_ssize_t, double, bint)