# tensorplay.special

Source: https://www.tensorplay.cn/docs/special.html

# tensorplay.special

## Functions

[tensorplay.functional.airy_ai](generated/tensorplay.functional.airy_ai.html#tensorplay.functional.airy_ai)

[tensorplay.functional.bessel_j0](generated/tensorplay.functional.bessel_j0.html#tensorplay.functional.bessel_j0)

[tensorplay.functional.bessel_j1](generated/tensorplay.functional.bessel_j1.html#tensorplay.functional.bessel_j1)

[tensorplay.functional.bessel_y0](generated/tensorplay.functional.bessel_y0.html#tensorplay.functional.bessel_y0)

[tensorplay.functional.bessel_y1](generated/tensorplay.functional.bessel_y1.html#tensorplay.functional.bessel_y1)

[tensorplay.functional.chebyshev_polynomial_t](generated/tensorplay.functional.chebyshev_polynomial_t.html#tensorplay.functional.chebyshev_polynomial_t)

[tensorplay.functional.chebyshev_polynomial_u](generated/tensorplay.functional.chebyshev_polynomial_u.html#tensorplay.functional.chebyshev_polynomial_u)

[tensorplay.functional.chebyshev_polynomial_v](generated/tensorplay.functional.chebyshev_polynomial_v.html#tensorplay.functional.chebyshev_polynomial_v)

[tensorplay.functional.chebyshev_polynomial_w](generated/tensorplay.functional.chebyshev_polynomial_w.html#tensorplay.functional.chebyshev_polynomial_w)

[tensorplay.functional.digamma](generated/tensorplay.functional.digamma.html#tensorplay.functional.digamma)

[tensorplay.special.entr](generated/tensorplay.special.entr.html#tensorplay.special.entr)

Entropy of a probability element: -x*log(x) (0 at x=0, NaN below).

[tensorplay.functional.erf](generated/tensorplay.functional.erf.html#tensorplay.functional.erf)

[tensorplay.functional.erfc](generated/tensorplay.functional.erfc.html#tensorplay.functional.erfc)

[tensorplay.special.erfcx](generated/tensorplay.special.erfcx.html#tensorplay.special.erfcx)

Scaled complementary error function: exp(x^2) * erfc(x).

[tensorplay.functional.erfinv](generated/tensorplay.functional.erfinv.html#tensorplay.functional.erfinv)

[tensorplay.functional.exp2](generated/tensorplay.functional.exp2.html#tensorplay.functional.exp2)

[tensorplay.special.expit](generated/tensorplay.special.expit.html#tensorplay.special.expit)

Numerically-stable sigmoid; identical to sigmoid().

[tensorplay.functional.expm1](generated/tensorplay.functional.expm1.html#tensorplay.functional.expm1)

[tensorplay.functional.gammainc](generated/tensorplay.functional.gammainc.html#tensorplay.functional.gammainc)

[tensorplay.functional.gammaincc](generated/tensorplay.functional.gammaincc.html#tensorplay.functional.gammaincc)

[tensorplay.special.gammaln](generated/tensorplay.special.gammaln.html#tensorplay.special.gammaln)

Natural log of the absolute value of the gamma function (native lgamma).

[tensorplay.functional.hermite_polynomial_h](generated/tensorplay.functional.hermite_polynomial_h.html#tensorplay.functional.hermite_polynomial_h)

[tensorplay.functional.hermite_polynomial_he](generated/tensorplay.functional.hermite_polynomial_he.html#tensorplay.functional.hermite_polynomial_he)

[tensorplay.functional.i0](generated/tensorplay.functional.i0.html#tensorplay.functional.i0)

[tensorplay.functional.i0e](generated/tensorplay.functional.i0e.html#tensorplay.functional.i0e)

[tensorplay.functional.i1](generated/tensorplay.functional.i1.html#tensorplay.functional.i1)

[tensorplay.functional.i1e](generated/tensorplay.functional.i1e.html#tensorplay.functional.i1e)

[tensorplay.functional.laguerre_polynomial_l](generated/tensorplay.functional.laguerre_polynomial_l.html#tensorplay.functional.laguerre_polynomial_l)

[tensorplay.functional.legendre_polynomial_p](generated/tensorplay.functional.legendre_polynomial_p.html#tensorplay.functional.legendre_polynomial_p)

[tensorplay.functional.log1p](generated/tensorplay.functional.log1p.html#tensorplay.functional.log1p)

[tensorplay.special.log_ndtr](generated/tensorplay.special.log_ndtr.html#tensorplay.special.log_ndtr)

log of the standard normal CDF, stable in the left tail.

[tensorplay.special.log_softmax](generated/tensorplay.special.log_softmax.html#tensorplay.special.log_softmax)

[tensorplay.functional.logit](generated/tensorplay.functional.logit.html#tensorplay.functional.logit)

[tensorplay.special.logsumexp](generated/tensorplay.special.logsumexp.html#tensorplay.special.logsumexp)

Log-sum-exp along dim, computed with the max-shift trick.

[tensorplay.special.modified_bessel_i0](generated/tensorplay.special.modified_bessel_i0.html#tensorplay.special.modified_bessel_i0)

Modified Bessel function of the first kind, order 0; alias of i0().

[tensorplay.functional.modified_bessel_i1](generated/tensorplay.functional.modified_bessel_i1.html#tensorplay.functional.modified_bessel_i1)

[tensorplay.functional.modified_bessel_k0](generated/tensorplay.functional.modified_bessel_k0.html#tensorplay.functional.modified_bessel_k0)

[tensorplay.functional.modified_bessel_k1](generated/tensorplay.functional.modified_bessel_k1.html#tensorplay.functional.modified_bessel_k1)

[tensorplay.special.multigammaln](generated/tensorplay.special.multigammaln.html#tensorplay.special.multigammaln)

Multivariate log-gamma with dimension p (p >= 2).

[tensorplay.special.ndtr](generated/tensorplay.special.ndtr.html#tensorplay.special.ndtr)

Standard normal CDF: Phi(x) = 0.5 * erfc(-x / sqrt(2)).

[tensorplay.special.ndtri](generated/tensorplay.special.ndtri.html#tensorplay.special.ndtri)

Inverse standard normal CDF: sqrt(2) * erfinv(2x - 1).

[tensorplay.special.polygamma](generated/tensorplay.special.polygamma.html#tensorplay.special.polygamma)

Polygamma of order :attr:n: \(\psi^{(n)}(x)\) (native kernel).

[tensorplay.special.psi](generated/tensorplay.special.psi.html#tensorplay.special.psi)

Digamma function; alias of digamma().

[tensorplay.special.round](generated/tensorplay.special.round.html#tensorplay.special.round)

Rounds to nearest even integer (native Tensor.round).

[tensorplay.functional.scaled_modified_bessel_k0](generated/tensorplay.functional.scaled_modified_bessel_k0.html#tensorplay.functional.scaled_modified_bessel_k0)

[tensorplay.functional.scaled_modified_bessel_k1](generated/tensorplay.functional.scaled_modified_bessel_k1.html#tensorplay.functional.scaled_modified_bessel_k1)

[tensorplay.functional.shifted_chebyshev_polynomial_t](generated/tensorplay.functional.shifted_chebyshev_polynomial_t.html#tensorplay.functional.shifted_chebyshev_polynomial_t)

[tensorplay.functional.shifted_chebyshev_polynomial_u](generated/tensorplay.functional.shifted_chebyshev_polynomial_u.html#tensorplay.functional.shifted_chebyshev_polynomial_u)

[tensorplay.functional.shifted_chebyshev_polynomial_v](generated/tensorplay.functional.shifted_chebyshev_polynomial_v.html#tensorplay.functional.shifted_chebyshev_polynomial_v)

[tensorplay.functional.shifted_chebyshev_polynomial_w](generated/tensorplay.functional.shifted_chebyshev_polynomial_w.html#tensorplay.functional.shifted_chebyshev_polynomial_w)

[tensorplay.functional.sinc](generated/tensorplay.functional.sinc.html#tensorplay.functional.sinc)

[tensorplay.special.softmax](generated/tensorplay.special.softmax.html#tensorplay.special.softmax)

[tensorplay.functional.spherical_bessel_j0](generated/tensorplay.functional.spherical_bessel_j0.html#tensorplay.functional.spherical_bessel_j0)

[tensorplay.special.xlog1py](generated/tensorplay.special.xlog1py.html#tensorplay.special.xlog1py)

x*log1p(y) with the convention x*log1p(-1) = 0 when x == 0.

[tensorplay.special.xlogy](generated/tensorplay.special.xlogy.html#tensorplay.special.xlogy)

x*log(y) with the convention 0*log(anything) = 0.

[tensorplay.functional.zeta](generated/tensorplay.functional.zeta.html#tensorplay.functional.zeta)