Operators for higher dimensional Tensorspaces

[benjione]

See #389

I modified the KroneckerOperator temporarily to allow for tuples with more than 2 entries:

struct KroneckerOperator{S, V, DS,RS,DI,RI,T} <: Operator{T}
    ops::Tuple  # used to be Tuple{S, V}
    domainspace::DS
    rangespace::RS
    domaintensorizer::DI
    rangetensorizer::RI
end

I am not sure how to change this, maybe by changing the signature to

struct KroneckerOperator{TT, DS,RS,DI,RI,T} <: Operator{T}

where TT is than the tuple type T{S,V,D,...}.

What now works is the following:

f3 = Fun(Chebyshev()^3, rand(100))
Dx = Derivative(Chebyshev()^3, [1,0,0])  # this works now
Dy = Derivative(Chebyshev()^3, [0,1,0])
Dz = Derivative(Chebyshev()^3, [0,0,1])
DD = Dx + Dy + Dz   # this works

f3dd = DD * f3
f3dd(0.0, 0.2, 0.3) # this works, since it is a polynomial of same kinds and TrivialTensorizer can be used

f3dx = Dx * f3
f3dx(0.0, 0.2, 0.3) # this does not work, since only higher dim functions of same kind are currently supported

[codecov]

Codecov Report

Attention: Patch coverage is 23.88060% with 102 lines in your changes missing coverage. Please review.

Project coverage is 60.89%. Comparing base (f1b1402) to head (40fbf7a).
Report is 203 commits behind head on master.

Files	Patch %	Lines
src/Multivariate/TensorSpace.jl	14.10%	67 Missing ⚠️
src/PDE/KroneckerOperator.jl	36.00%	32 Missing ⚠️
src/Multivariate/TrivialTensorFun.jl	0.00%	2 Missing ⚠️
src/Caching/blockbanded.jl	75.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #390      +/-   ##
==========================================
- Coverage   65.66%   60.89%   -4.77%     
==========================================
  Files          79       80       +1     
  Lines        8323     8547     +224     
==========================================
- Hits         5465     5205     -260     
- Misses       2858     3342     +484     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[jishnub]

I am not sure how to change this, maybe by changing the signature to

struct KroneckerOperator{TT, DS,RS,DI,RI,T} <: Operator{T}

where TT is than the tuple type T{S,V,D,...}.

I think this is the right approach.

Also, the CI is probably broken right now because of FFTW v1.6, but hopefully that should be fixed soon

[benjione]

The following works now:

f3 = Fun(Chebyshev()^3, rand(100))
Dx = Derivative(Chebyshev()^3, [1,0,0])
f3dx = Dx * f3
f3dx(0.0, 0.2, 0.3)

What is missing is

DefiniteIntegral(Chebyshev()^3, [0,1,0])

which is because there is no Iterator for the Tensorizer of the space ConstantSpace() ⊗ Chebyshev() ⊗ Chebyshev().
For more than 2D cases, only spaces with blocklenghts 1:infty are currently supported. I wonder if in the case of ConstantSpace one can just reduce the constant dimension and work with Chebyshev() ⊗ Chebyshev()

[benjione]

The implementation is finished, but tests are missing. I feel like most of the test are necessary in ApproxFunOrthogonalPolynomials.jl and here maybe some for the KroneckerOperator.

[jishnub]

Could you look into the test failures? The CI issue should be resolved now