Revert "Move SpecialFunctions to an extension (#564)" (#569)

This reverts commit cf27073.

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.9.10"
+version = "0.9.9"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
@@ -24,12 +24,6 @@ SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
-[weakdeps]
-SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
-
-[extensions]
-ApproxFunBaseSpecialFunctionsExt = "SpecialFunctions"
-
 [compat]
 AbstractFFTs = "0.5, 1"
 Aqua = "0.6"
@@ -56,8 +50,7 @@ julia = "1.9"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 Infinities = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "Random", "Infinities", "Test", "SpecialFunctions"]
+test = ["Aqua", "Random", "Infinities", "Test"]

ext/ApproxFunBaseSpecialFunctionsExt.jl

@@ -16,7 +16,7 @@ using IntervalSets
 using LinearAlgebra
 using LowRankMatrices
 using SparseArrays
-# using SpecialFunctions
+using SpecialFunctions
 using StaticArrays: SVector, @SArray, SArray
 import Statistics: mean
 
@@ -60,6 +60,22 @@ import LinearAlgebra: BlasInt, BlasFloat, norm, ldiv!, mul!, det, cross,
 
 import SparseArrays: blockdiag
 
+# import Arpack: eigs
+
+# we need to import all special functions to use Calculus.symbolic_derivatives_1arg
+# we can't do importall Base as we replace some Base definitions
+import SpecialFunctions: airy, besselh,
+              lfact, beta, lbeta,
+              eta, zeta, polygamma, logabsgamma, loggamma,
+              besselj, bessely, besseli, besselk, besselkx,
+              hankelh1, hankelh2, hankelh1x, hankelh2x,
+              # functions from Calculus.symbolic_derivatives_1arg
+              erf, erfinv, erfc, erfcinv, erfi, gamma, lgamma,
+              digamma, invdigamma, trigamma,
+              airyai, airybi, airyaiprime, airybiprime,
+              besselj0, besselj1, bessely0, bessely1,
+              erfcx, dawson
+
 import BandedMatrices: bandrange, inbands_setindex!, bandwidth,
               colstart, colstop, colrange, rowstart, rowstop, rowrange,
               bandwidths, _BandedMatrix, BandedMatrix, isbanded

src/ApproxFunBase.jl

@@ -164,12 +164,12 @@ end
 # ODE gives the first order ODE a special function op satisfies,
 # RHS is the right hand side
 # growth says what to use to choose a good point to impose an initial condition
-for (op, ODE, RHS, growth) in (
-                            (:(exp),    "D-f'",              "0",        :(real)),
+for (op, ODE, RHS, growth) in ((:(exp),    "D-f'",           "0",        :(real)),
                             (:(asinh),  "sqrt(f^2+1)*D",     "f'",       :(real)),
                             (:(acosh),  "sqrt(f^2-1)*D",     "f'",       :(real)),
                             (:(atanh),  "(1-f^2)*D",         "f'",       :(real)),
-                            )
+                            (:(erfcx),  "D-2f*f'",       "-2f'/sqrt(π)", :(real)),
+                            (:(dawson), "D+2f*f'",           "f'",       :(real)))
     L,R = Meta.parse(ODE), Meta.parse(RHS)
     @eval begin
         # depice before doing op
@@ -208,12 +208,16 @@ function specialfunctionnormalizationpoint2(op, growth, f, T = cfstype(f))
     xmin, xmax, opfxmin, opfxmax, opmax
 end
 
-for (op,ODE,RHS,growth) in (
+for (op,ODE,RHS,growth) in ((:(erf),"f'*D^2+(2f*f'^2-f'')*D","0",:(imag)),
+                            (:(erfi),"f'*D^2-(2f*f'^2+f'')*D","0",:(real)),
                             (:(sin),"f'*D^2-f''*D+f'^3","0",:(imag)),
                             (:(cos),"f'*D^2-f''*D+f'^3","0",:(imag)),
                             (:(sinh),"f'*D^2-f''*D-f'^3","0",:(real)),
                             (:(cosh),"f'*D^2-f''*D-f'^3","0",:(real)),
-                            )
+                            (:(airyai),"f'*D^2-f''*D-f*f'^3","0",:(imag)),
+                            (:(airybi),"f'*D^2-f''*D-f*f'^3","0",:(imag)),
+                            (:(airyaiprime),"f'*D^2-f''*D-f*f'^3","airyai(f)*f'^3",:(imag)),
+                            (:(airybiprime),"f'*D^2-f''*D-f*f'^3","airybi(f)*f'^3",:(imag)))
     L,R = Meta.parse(ODE),Meta.parse(RHS)
     @eval begin
         function $op(fin::Fun)
@@ -230,6 +234,8 @@ for (op,ODE,RHS,growth) in (
     end
 end
 
+erfc(f::Fun) = 1-erf(f)
+
 
 exp2(f::Fun) = exp(log(2)*f)
 exp10(f::Fun) = exp(log(10)*f)
@@ -271,8 +277,35 @@ end
 sinpi(f::Fun) = sin(π*f)
 cospi(f::Fun) = cos(π*f)
 
+function airy(k::Number,f::Fun)
+    if k == 0
+        airyai(f)
+    elseif k == 1
+        airyaiprime(f)
+    elseif k == 2
+        airybi(f)
+    elseif k == 3
+        airybiprime(f)
+    else
+        error("invalid argument")
+    end
+end
+
+besselh(ν,k::Integer,f::Fun) = k == 1 ? hankelh1(ν,f) : k == 2 ? hankelh2(ν,f) : throw(Base.Math.AmosException(1))
+
+for jy in (:j, :y)
+    bjy = Symbol(:bessel, jy)
+    for ν in (0,1)
+        bjynu = Symbol(bjy, ν)
+        @eval SpecialFunctions.$bjynu(f::Fun) = $bjy($ν,f)
+    end
+end
+
 ## Miscellaneous
-for op in (:(expm1),:(log1p),:(sinc),:(cosc))
+for op in (:(expm1),:(log1p),:(lfact),:(sinc),:(cosc),
+           :(erfinv),:(erfcinv),:(beta),:(lbeta),
+           :(eta),:(zeta),:(gamma),:(lgamma),
+           :(polygamma),:(invdigamma),:(digamma),:(trigamma))
     @eval begin
         $op(f::Fun) = Fun($op ∘ f,domain(f))
     end
@@ -424,18 +457,41 @@ for (funsym, exp) in Calculus.symbolic_derivatives_1arg()
     funsym == :sign && continue
     funsym == :exp && continue
     funsym == :sqrt && continue
-    if isdefined(Base, funsym)
-        @eval begin
-            $(funsym)(z::Fun{<:ConstantSpace,<:Real}) =
-                Fun($(funsym)(Number(z)),space(z))
-            $(funsym)(z::Fun{<:ConstantSpace,<:Complex}) =
-                Fun($(funsym)(Number(z)),space(z))
-            $(funsym)(z::Fun{<:ConstantSpace}) =
-                Fun($(funsym)(Number(z)),space(z))
+    @eval begin
+        $(funsym)(z::Fun{<:ConstantSpace,<:Real}) =
+            Fun($(funsym)(Number(z)),space(z))
+        $(funsym)(z::Fun{<:ConstantSpace,<:Complex}) =
+            Fun($(funsym)(Number(z)),space(z))
+        $(funsym)(z::Fun{<:ConstantSpace}) =
+            Fun($(funsym)(Number(z)),space(z))
+    end
+end
+
+# Other special functions
+for f in [:logabsgamma]
+    @eval function $f(z::Fun{<:ConstantSpace, <:Real})
+        t = $f(Number(z))
+        Fun(t[1], space(z)), t[2]
+    end
+end
+function loggamma(z::Fun{<:ConstantSpace})
+    t = loggamma(Number(z))
+    Fun(t, space(z))
+end
+for f in [:gamma, :loggamma]
+    @eval begin
+        function $f(a, z::Fun{<:ConstantSpace})
+            t = $f(a, Number(z))
+            Fun(t, space(z))
         end
     end
 end
 
+for f in [:besselj, :besselk, :besselkx, :bessely, :besseli,
+            :hankelh1x, :hankelh2x, :hankelh1, :hankelh2]
+    @eval $f(nu, x::Fun{<:ConstantSpace}) = Fun($f(nu, Number(x)), space(x))
+end
+
 # Roots
 
 for op in (:(argmax),:(argmin))