# Help defining Functor type
**URL:** https://discourse.julialang.org/t/help-defining-functor-type/4509
**Category:** General Usage
**Tags:** question, functors
**Created:** [June 28, 2017, 3:52am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509 "2017-06-28T03:52:41Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@juliohm](https://discourse.julialang.org/u/juliohm)
#### Post date: [June 28, 2017, 3:52am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/1 "2017-06-28T03:52:41Z")
I am almost there, but this is my first time using `StaticArrays.jl` and I am not sure I got the concepts right:
```julia
using StaticArrays: SMatrix
"""
EllipsoidDistance([a₁, a₂, ...], [θ₁, θ₂, ...])
A distance defined by an ellipsoid with given semiaxes `a₁, a₂, ...`
and rotation angles `θ₁, θ₂, ...`.
The positive definite matrix A = PΛP' representing the ellipsoid is
assembled once and cached in the object as an static array. Calls to
(x-y)'*A*(x-y) are therefore very efficient.
"""
immutable EllipsoidDistance{N,T<:Real} <: AbstractDistance
# state fields
A::SMatrix{N}
function EllipsoidDistance{N,T}(as, θs) where {N,T<:Real}
@assert length(as) == length(θs) == N "number of semiaxes and rotations must match spatial dimension"
Λ = spdiagm(one(T)./as.^2)
P = eye(T, N) # TODO: define rotation matrix, probably using Rotations.jl
A = P*Λ*P'
new(A) # this is causing the error as expected since the local variable A is not static
end
end
EllipsoidDistance(as::Vector{T}, θs::Vector{T}) where {T<:Real} = EllipsoidDistance{length(as),T}(as, θs)
(d::EllipsoidDistance)(x, y) = begin
z = x - y
z'*A*z
end
```
The error is caused by the `new` operator because I am passing a non-static array to it. What would be the appropriate way of caching `A`?
---
### Author:  [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)
#### Post date: [June 28, 2017, 4:02am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/2 "2017-06-28T04:02:17Z")
Just convert `A` to a `StaticArray`? Also, you probably want to have `A` concretely typed, aka `SArray{Tuple{M, N}, T, 2, M*N}` where `M` is number of rows and `N` number of columns.
---
### Author:  [@juliohm](https://discourse.julialang.org/u/juliohm)
#### Post date: [June 28, 2017, 4:44am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/3 "2017-06-28T04:44:23Z")
Thank you @kristoffer.carlsson, I replaced `SMatrix{N}` by the concrete type `SMatrix{N,N,T}`, but how to convert `A` to this type? Also, is this a good thing to do in general? Will the functor be much faster for 2D and 3D vectors for example?
---
### Author:  [@juliohm](https://discourse.julialang.org/u/juliohm)
#### Post date: [June 28, 2017, 4:47am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/4 "2017-06-28T04:47:53Z")
Got it, just calling `SMatrix{N,N,T}(A)` will do it. I had issues with the inferred type `T`, that is why it was not working.
I am still wondering if the performance gain will be visible, starting some benchmarks.
---
### Author:  [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)
#### Post date: [June 28, 2017, 4:53am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/5 "2017-06-28T04:53:05Z")
What size is `N`? It should be significantly faster if `N` is smallish (assuming `x` and `y` are `StaticVector`s).
---
### Author:  [@juliohm](https://discourse.julialang.org/u/juliohm)
#### Post date: [June 28, 2017, 5:02am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/6 "2017-06-28T05:02:22Z")
The dimension will be usually 2D or 3D (at most 4D), but I have no guarantee on the vectors `x` and `y` multiplying the matrix, they are general heap allocated arrays. Should I forget about making `A` static in this case?
---
### Author:  [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)
#### Post date: [June 28, 2017, 5:26am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/7 "2017-06-28T05:26:16Z")
Variables ending with `s` are Static (dim = 4):
```julia
julia> f(x, A, y) = (z = x-y; z' * A * z)
f (generic function with 1 method)
julia> @btime f($x, $A, $y);
156.315 ns (2 allocations: 224 bytes)
julia> @btime f($x, $As, $y);
93.785 ns (2 allocations: 224 bytes)
julia> @btime f($xs, $As, $ys);
6.540 ns (0 allocations: 0 bytes)
```
---
### Author:  [@juliohm](https://discourse.julialang.org/u/juliohm)
#### Post date: [June 28, 2017, 5:35am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/8 "2017-06-28T05:35:06Z")
I think I will stick with heap-allocated arrays for now. If this becomes a bottleneck at some point, I will hack my way with StaticArrays.
---
### Author:  [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)
#### Post date: [June 28, 2017, 10:23am UTC](https://discourse.julialang.org/t/help-defining-functor-type/4509/9 "2017-06-28T10:23:28Z")
As a reference, for me, swapping to static arrays has lead to cleaner code with less bugs (because of array sizes in the type and immutability) as well as tremendous performance improvements. Depending on the performance characteristics of your code, the performance improvements might of course not carry over for you.