Not compatible with TaylorSeries package

Question

Not compatible with TaylorSeries package

edwardcao3026 opened this issue 5 years ago · comments

I tried to use HypergeometricFunctions and TaylorSeries at the same time as follows.

using TaylorSeries, Plots
using HypergeometricFunctions

x = set_variables("x", order=100);
_₂F₁(1.0,2.0,3.0,(x-1))

However, I got the error:
ERROR: LoadError: MethodError: no method matching -(::Array{TaylorN{Float64},1}, ::Int64)
Closest candidates are:
-(::Complex{Bool}, ::Real) at complex.jl:298
-(::Missing, ::Number) at missing.jl:93
-(::Base.CoreLogging.LogLevel, ::Integer) at logging.jl:107
...
Stacktrace:
[1] top-level scope at none:0

Is there anyone to help? Thanks.

Mikael Slevinsky · Answer 1 · Thu May 23 2019 05:45:42 GMT+0800 (China Standard Time)

I don't think the code was designed with non-numeric Number types in mind. The implementation uses the group of six variable transformations (see the DLMF) to analytically continue Gauss' power series outside the disk |z| < 1, and in every case relates one evaluation to at most two further evaluations within the disk. With a symbolic-like input, it's not clear what should be expected. (Do you expect the series to terminate after some point?)

Sheehan Olver · Answer 2 · Thu May 23 2019 14:30:29 GMT+0800 (China Standard Time)

Isn’t that an error before you even get to HypergeometricFunctiobs since it’s erroring on x-1 ?

edwardcao3026 · Answer 3 · Thu May 23 2019 17:49:48 GMT+0800 (China Standard Time)

Isn’t that an error before you even get to HypergeometricFunctiobs since it’s erroring on x-1 ?

Thanks for the reply. However, x-1 works fine, and is not an error.

James Cook · Answer 4 · Fri May 24 2019 15:37:09 GMT+0800 (China Standard Time)

What versions of Julia and TalorSeries are you using? I ask because x-1 errors for me

julia> using TaylorSeries

julia> x = set_variables("x, order=100")
2-element Array{TaylorN{Float64},1}:
         1.0 x, + 𝒪(‖x‖⁷)
  1.0 order=100 + 𝒪(‖x‖⁷)

julia> x-1
ERROR: MethodError: no method matching -(::Array{TaylorN{Float64},1}, ::Int64)
Closest candidates are:
  -(::Complex{Bool}, ::Real) at complex.jl:298
  -(::Missing, ::Number) at missing.jl:97
  -(::Base.CoreLogging.LogLevel, ::Integer) at logging.jl:107
  ...
Stacktrace:
 [1] top-level scope at none:0

Failing that, did you mean x .- 1? Because that doesn't error, but unfortunately

julia> _₂F₁(1.0, 2.0, 3.0, (x .- 1))
ERROR: MethodError: no method matching isless(::TaylorN{Float64}, ::Float64)
Closest candidates are:
  isless(::Float64, ::Float64) at float.jl:459
  isless(::Missing, ::Any) at missing.jl:70
  isless(::InfiniteArrays.Infinity, ::AbstractFloat) at ~/.julia/packages/InfiniteArrays/24ELy/src/Infinity.jl:46
  ...
Stacktrace:
 [1] <(::TaylorN{Float64}, ::Float64) at ./operators.jl:260
 [2] <=(::TaylorN{Float64}, ::Float64) at ./operators.jl:309
 [3] _₂F₁general(::Float64, ::Float64, ::Float64, ::TaylorN{Float64}) at ~/.julia/packages/HypergeometricFunctions/JaGGn/src/Gauss.jl:86
 [4] _₂F₁(::Float64, ::Float64, ::Float64, ::TaylorN{Float64}) at ~/.julia/packages/HypergeometricFunctions/JaGGn/src/Gauss.jl:53
 [5] _₂F₁(::Float64, ::Float64, ::Float64, ::Array{TaylorN{Float64},1}) at ~/.julia/packages/HypergeometricFunctions/JaGGn/src/Gauss.jl:72
 [6] top-level scope at none:0

which is the same error as

julia> x .< 0.0
ERROR: MethodError: no method matching isless(::TaylorN{Float64}, ::Float64)
Closest candidates are:
  isless(::Float64, ::Float64) at float.jl:459
  isless(::Missing, ::Any) at missing.jl:70
  isless(::InfiniteArrays.Infinity, ::AbstractFloat) at ~/.julia/packages/InfiniteArrays/24ELy/src/Infinity.jl:46
  ...
Stacktrace:
 [1] <(::TaylorN{Float64}, ::Float64) at ./operators.jl:260
 [2] _broadcast_getindex_evalf at ./broadcast.jl:578 [inlined]
 [3] _broadcast_getindex at ./broadcast.jl:551 [inlined]
 [4] getindex at ./broadcast.jl:511 [inlined]
 [5] copy at ./broadcast.jl:787 [inlined]
 [6] materialize(::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1},Nothing,typeof(<),Tuple{Array{TaylorN{Float64},1},Float64}}) at ./broadcast.jl:753
 [7] top-level scope at none:0

Versions

Version 1.1.1-pre.45 (2019-05-08)
release-1.1/d9c5405702* (fork: 115 commits, 167 days)

[6aa5eb33] TaylorSeries v0.9.2

edwardcao3026 · Answer 5 · Fri May 24 2019 23:49:41 GMT+0800 (China Standard Time)

I see. I reproduced your error for the command x = set_variables("x, order=100"). I use x, y = set_variables("x y", order=100), then x-1 works fine. However, the hypergeometric error persists.

My version is v"1.0.0".

Sheehan Olver · Answer 6 · Sat May 25 2019 00:19:33 GMT+0800 (China Standard Time)

First: x above is a vector. I think you mean x = set_variables("x, order=100")[1]. We can get it working by adding the missing functionality:

julia> x = set_variables("x", order=100)[1];

julia> Base.isless(y::Number, x::TaylorN) = isless(y, x.coeffs[1].coeffs[1])

julia> Base.log1p(x::TaylorN) = log(1+x)

julia> Base.eps(::Type{TaylorN{T}}) where T = eps(T)

julia> Base.isless(x::TaylorN, y::Number) = isless(x.coeffs[1].coeffs[1], y)

julia> _₂F₁(1.0,2.0,3.0,(x-1))
 0.6137056388801087 + 0.22741127776023898 x + 0.09111691664014213 x² + 0.03815588885481866 x³ + 0.016444861063214 x⁴ + 0.007233833291493177 x⁵ + 0.003231138806309342 x⁶ + 0.0014605872604416172 x⁷ + 0.000666598108984577 x⁸ + 0.00030663682865957726 x⁹ + 0.00014198800183346362 x¹⁰ + 6.61175831375729e-5 x¹¹ + 3.0937284901315815e-5 x¹² + 1.4537030067464611e-5 x¹³ + 6.856078195624316e-6 x¹⁴ + 3.244138814946803e-6 x¹⁵ + 1.5395500556889938e-6 x¹⁶ + 7.325365567743256e-7 x¹⁷ + 3.4937741952650163e-7 x¹⁸ + 1.669918137650735e-7 x¹⁹ + 7.997399515112675e-8 x²⁰ + 3.8369378241164586e-8 x²¹ + 1.8439091439531812e-8 x²² + 8.874730907546905e-9 x²³ + 4.277408653697482e-9 x²⁴ + 2.064305243595276e-9 x²⁵ + 9.974712684076268e-10 x²⁶ + 4.825345651032184e-10 x²⁷ + 2.336803285122648e-10 x²⁸ + 1.1327664717625831e-10 x²⁹ + 5.495981038395394e-11 x³⁰ + 2.6688027662909334e-11 x³¹ + 1.2970572243188646e-11 x³² + 6.309438715257751e-12 x³³ + 3.071904695721014e-12 x³⁴ + 1.4967552080750751e-12 x³⁵ + 7.296290393609026e-13 x³⁶ + 3.557466214493406e-13 x³⁷ + 1.734781742062317e-13 x³⁸ + 8.4641167744794e-14 x³⁹ + 4.1351988664342396e-14 x⁴⁰ + 2.0245607188192277e-14 x⁴¹ + 9.933435583249127e-15 x⁴² + 4.87745577266054e-15 x⁴³ + 2.3898424070298422e-15 x⁴⁴ + 1.164730557369523e-15 x⁴⁵ + 5.638532846273414e-16 x⁴⁶ + 2.7201988011610697e-16 x⁴⁷ + 1.3204809121747408e-16 x⁴⁸ + 6.541814035827748e-17 x⁴⁹ + 3.3413699485305246e-17 x⁵⁰ + 1.750131222506521e-17 x⁵¹ + 9.158752144614354e-18 x⁵² + 4.592589955603457e-18 x⁵³ + 2.092072012797721e-18 x⁵⁴ + 8.029050207486038e-19 x⁵⁵ + 2.2317192379005413e-19 x⁵⁶ + 2.5459451555342405e-20 x⁵⁷ - 5.194425770307503e-22 x⁵⁸ + 2.508218649398269e-20 x⁵⁹ + 4.726277522731426e-20 x⁶⁰ + 5.099591855430971e-20 x⁶¹ + 4.0237927900139253e-20 x⁶² + 2.4012059810360116e-20 x⁶³ + 9.464022285185436e-21 x⁶⁴ - 8.560789937190647e-23 x⁶⁵ - 4.4530982758298455e-21 x⁶⁶ - 5.0935311392342046e-21 x⁶⁷ - 3.811703326348834e-21 x⁶⁸ - 2.0285756003983875e-21 x⁶⁹ - 5.543686046038847e-22 x⁷⁰ + 3.2889317600861456e-22 x⁷¹ + 6.678686505189806e-22 x⁷² + 6.466364352208879e-22 x⁷³ + 4.578004331394191e-22 x⁷⁴ + 2.410193593061127e-22 x⁷⁵ + 7.056801258420997e-23 x⁷⁶ - 3.118640628674264e-23 x⁷⁷ - 7.253314824525695e-23 x⁷⁸ - 7.383671851819276e-23 x⁷⁹ - 5.553094701417065e-23 x⁸⁰ - 3.2534231869591845e-23 x⁸¹ - 1.3172312889958448e-23 x⁸² - 4.6537002481632535e-25 x⁸³ + 5.852887338436875e-24 x⁸⁴ + 7.526522169523832e-24 x⁸⁵ + 6.5491773946846995e-24 x⁸⁶ + 4.527660619681191e-24 x⁸⁷ + 2.484347522530125e-24 x⁸⁸ + 9.128664351625636e-25 x⁸⁹ - 6.364263035599112e-26 x⁹⁰ - 5.26940020289893e-25 x⁹¹ - 6.36132983252991e-25 x⁹² - 5.492753722287055e-25 x⁹³ - 3.869126645659105e-25 x⁹⁴ - 2.2388952296311785e-25 x⁹⁵ - 9.622509299690597e-26 x⁹⁶ - 1.334906115815213e-26 x⁹⁷ + 3.0045944188318423e-26 x⁹⁸ + 4.508518096605067e-26 x⁹⁹ + 4.3209257579636724e-26 x¹⁰⁰ + 𝒪(‖x‖¹⁰¹)

Rather remarkably it worked!

Sheehan Olver · Answer 7 · Sat May 25 2019 00:20:36 GMT+0800 (China Standard Time)

I'm going to close this as the issue is in TaylorSeries.jl, not here.