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Added some rules for scaled airy and bessel functions and incomplete gamma #66

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Added some rules for scaled airy and bessel functions and incomplete gamma #66

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406d579
added rule for gamma(a, x)
amrods Aug 27, 2021
79ceb6f
added a few rules for airy and bessel functions
amrods Aug 27, 2021
af7dcfd
fixed missing $ in def of zeta
amrods Aug 27, 2021
e206f70
Fixed tests for 2-arg gamma
amrods Sep 6, 2021
b2957af
Merge branch 'JuliaDiff:master' into master
amrods Oct 19, 2021
236ad7a
Merge branch 'master' into master
devmotion Dec 11, 2021
a5ee29d
Update test/runtests.jl
devmotion Dec 11, 2021
ce09b11
Update Project.toml
devmotion Dec 11, 2021
813f4e8
Make rules consistent with ChainRules definitions in SpecialFunctions
devmotion Dec 11, 2021
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@ SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
[compat]
LogExpFunctions = "0.3.2"
NaNMath = "0.3"
SpecialFunctions = "0.10, 1.0, 2"
SpecialFunctions = "1.2, 2"
julia = "1.3"

[extras]
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23 changes: 15 additions & 8 deletions src/rules.jl
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Expand Up @@ -139,6 +139,10 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
:( SpecialFunctions.airybiprime($x) )
@define_diffrule SpecialFunctions.airybiprime(x) =
:( $x * SpecialFunctions.airybi($x) )
@define_diffrule SpecialFunctions.airyaix(x) =
:( SpecialFunctions.airyaiprimex($x) + sqrt($x) * SpecialFunctions.airyaix($x) )
@define_diffrule SpecialFunctions.airyaiprimex(x) =
:( $x * SpecialFunctions.airyaix($x) + sqrt($x) * SpecialFunctions.airyaiprimex($x) )
@define_diffrule SpecialFunctions.besselj0(x) =
:( -SpecialFunctions.besselj1($x) )
@define_diffrule SpecialFunctions.besselj1(x) =
Expand All @@ -152,8 +156,6 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
#
# eta
# zeta
# airyaix
# airyaiprimex
# airybix
# airybiprimex

Expand All @@ -168,29 +170,34 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
:NaN, :( (SpecialFunctions.bessely($ν - 1, $x) - SpecialFunctions.bessely($ν + 1, $x)) / 2 )
@define_diffrule SpecialFunctions.besselk(ν, x) =
:NaN, :( -(SpecialFunctions.besselk($ν - 1, $x) + SpecialFunctions.besselk($ν + 1, $x)) / 2 )
@define_diffrule SpecialFunctions.besselkx(ν, x) =
:NaN, :( -(SpecialFunctions.besselkx($ν - 1, $x) + SpecialFunctions.besselkx($ν + 1, $x)) / 2 + SpecialFunctions.besselkx($ν, $x) )
@define_diffrule SpecialFunctions.hankelh1(ν, x) =
:NaN, :( (SpecialFunctions.hankelh1($ν - 1, $x) - SpecialFunctions.hankelh1($ν + 1, $x)) / 2 )
@define_diffrule SpecialFunctions.hankelh1x(ν, x) =
:NaN, :( (SpecialFunctions.hankelh1x($ν - 1, $x) - SpecialFunctions.hankelh1x($ν + 1, $x)) / 2 - im * SpecialFunctions.hankelh1x($ν, $x) )
Comment on lines +177 to +178
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I always assumed that DiffRules only deals with functions with real arguments and real outputs - but hankelh1x, hankelh2x, and also hankelh1 and hankelh2 for which a rule is already defined output complex numbers. So complex numbers are supported officially? It seems based on the derivatives for conj and adjoint that you added in #54 you also thought that DiffRules only deals with real numbers @mcabbott?

@define_diffrule SpecialFunctions.hankelh2(ν, x) =
:NaN, :( (SpecialFunctions.hankelh2($ν - 1, $x) - SpecialFunctions.hankelh2($ν + 1, $x)) / 2 )
@define_diffrule SpecialFunctions.hankelh2x(ν, x) =
:NaN, :( (SpecialFunctions.hankelh2x($ν - 1, $x) - SpecialFunctions.hankelh2x($ν + 1, $x)) / 2 + im * SpecialFunctions.hankelh2x($ν, $x) )
@define_diffrule SpecialFunctions.gamma(a, x) =
:NaN, :(-exp(-$x) * $x^($a - 1))
@define_diffrule SpecialFunctions.polygamma(m, x) =
:NaN, :( SpecialFunctions.polygamma($m + 1, $x) )
@define_diffrule SpecialFunctions.beta(a, b) =
:( SpecialFunctions.beta($a, $b)*(SpecialFunctions.digamma($a) - SpecialFunctions.digamma($a + $b)) ), :( SpecialFunctions.beta($a, $b)*(SpecialFunctions.digamma($b) - SpecialFunctions.digamma($a + $b)) )
@define_diffrule SpecialFunctions.logbeta(a, b) =
@define_diffrule SpecialFunctions.logbeta(a, b) =
:( SpecialFunctions.digamma($a) - SpecialFunctions.digamma($a + $b) ), :( SpecialFunctions.digamma($b) - SpecialFunctions.digamma($a + $b) )
@define_diffrule SpecialFunctions.zeta(s, z) =
:NaN, :( -$s * SpecialFunctions.zeta(1 + $s, $z) )

# TODO:
#
# zeta
# besseljx
# besselyx
# besselix
# besselkx
# besselh
# besselhx
# hankelh1x
# hankelh2
# hankelh2x

# ternary #
#---------#
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