ApproxFun.jl multiplying fourier series and cosine/sine series issue

General Usage
1

Hi @dlfivefifty
I am using ApproxFun.jl along with Num type from SYmbolics to work with sin/cosine/Fourier series as follows:

julia> myg =Fun(CosSpace(), rand(10));

myf = Fun(SinSpace(), rand(10));

using Symbolics

a=Symbolics.variables(:a, 0:9);   # create a Num vector

myh = Fun(Fourier(), a);

myg*myf;  # this works

myg*myh   # this doesnt work

myf*myh  # this also doesnt work

Both cases that dont work throw following error, If someone can help me here ?

ERROR: TypeError: non-boolean (Num) used in boolean context
Stacktrace:
  [1] standardchoplength(coeffs::Vector{Num}, tol::Num)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/LinearAlgebra/standardchop.jl:46
  [2] chop!
    @ ~/.julia/packages/ApproxFunBase/OfsLT/src/Fun.jl:494 [inlined]
  [3] chop!
    @ ~/.julia/packages/ApproxFunBase/OfsLT/src/Fun.jl:503 [inlined]
  [4] chop(f::Fun{CosSpace{PeriodicSegment{Float64}, Float64}, Num, SubArray{Num, 1, Vector{Num}, Tuple{StepRange{Int64, Int64}}, true}}, tol::Num)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Fun.jl:521
  [5] ConcreteMultiplication
    @ ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:16 [inlined]
  [6] ConcreteMultiplication
    @ ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:26 [inlined]
  [7] Multiplication(f::Fun{SS}, sp::CosSpace) where SS<:SinSpace
    @ ApproxFunFourier ~/.julia/packages/ApproxFunFourier/a7eyk/src/FourierOperators.jl:218 [inlined]
  [8] coefficienttimes(f::Fun{CosSpace{…}, Num, SubArray{…}}, g::Fun{CosSpace{…}, Float64, Vector{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:166
  [9] default_mult_compatible(f::Fun{CosSpace{…}, Float64, Vector{…}}, g::Fun{CosSpace{…}, Num, SubArray{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:148
 [10] default_mult(f::Fun{CosSpace{…}, Float64, Vector{…}}, g::Fun{CosSpace{…}, Num, SubArray{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:155
 [11] *(f::Fun{CosSpace{…}, Float64, Vector{…}}, g::Fun{CosSpace{…}, Num, SubArray{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:164
 [12] (::ApproxFunBase.var"#527#528"{Fun{CosSpace{PeriodicSegment{Float64}, Float64}, Float64, Vector{Float64}}})(gg::Function)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Spaces/ProductSpaceOperators.jl:323
 [13] _mapreduce(f::ApproxFunBase.var"#527#528"{Fun{CosSpace{…}, Float64, Vector{…}}}, op::typeof(+), ::IndexLinear, A::Vector{Fun{S, Num, SubArray{…}} where S})
    @ Base ./reduce.jl:440
 [14] _mapreduce_dim
    @ ./reducedim.jl:365 [inlined]
 [15] mapreduce(f::Any, op::Any, A::Union{Base.AbstractBroadcasted, AbstractArray})
    @ Base ./reducedim.jl:357 [inlined]
 [16] coefficienttimes
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Spaces/ProductSpaceOperators.jl:323 [inlined]
 [17] default_mult_compatible(f::Fun{CosSpace{…}, Float64, Vector{…}}, g::Fun{ApproxFunBase.SumSpace{…}, Num, Vector{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:146
 [18] default_mult(f::Fun{CosSpace{…}, Float64, Vector{…}}, g::Fun{ApproxFunBase.SumSpace{…}, Num, Vector{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:155
 [19] *(f::Fun{CosSpace{PeriodicSegment{…}, Float64}, Float64, Vector{Float64}}, g::Fun{ApproxFunBase.SumSpace{Tuple{…}, PeriodicSegment{…}, Float64}, Num, Vector{Num}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/OfsLT/src/Operators/banded/Multiplication.jl:164
 [20] top-level scope
    @ REPL[55]:1
Some type information was truncated. Use `show(err)` to see complete types.
2

Create the constant length operator for myg first instead of trying to have it be adaptive.

1 Like
3

Thanks ! that was helpful. Any idea how do i multiply cosine series of many coeffs having different periods ? Requesting @dlfivefifty to take a look if possible


 julia> G = Fun(CosSpace(), rand(3)) 
Fun(CosSpace(【0.0,6.283185307179586❫), [0.587619, 0.499599, 0.616276]) 
 
 
julia> F = Fun(SinSpace(PeriodicSegment(0, pi)), rand(3)); 
 
julia> Multiplication(F, CosSpace())*G 
ERROR: AssertionError: domain(f) == domain(sp) 
Stacktrace: 
 [1] Multiplication(f::Fun{SinSpace{PeriodicSegment{Float64}, Float64}, Float64, Vector{Float64}}, sp::CosSpace{PeriodicSegment{Float64}, Float64}) 
  @ ApproxFunFourier ~/.julia/packages/ApproxFunFourier/lFQDK/src/FourierOperators.jl:222 
 [2] top-level scope 
  @ REPL[11]:1
4

I’m not sure what you expect it to do? Create a series with all possible combinations?

5

@dlfivefifty Thanks for reply.
Yes I wished to create series in following way

a= rand(3);  b= rand(3);  # typically arrays of of n elements

# simplify following multiplication into another cosine series of period 2pi
(a[1] + a[2]*cos(θ) + a[3]*cos)(2θ) + ...)*(b[1] + b[2]*cos(2θ) + b[3]*cos(4θ) + ...)