Function that returns two matrices in a convenient way

Question

I would like to create a function in Julia that returns two matrices. One way to do that is as follows:

function AB(n,m)
    A = rand(n,n)
    B = rand(m,m)
    return (A = A, B = B)
end

The output looks like this:

julia> AB(2,3)                                                                   
(A = [0.7001462182920173 0.5485248069467998; 0.8559801029748708 0.8023848206563642], B = [0.7970654693626167 0.08666821253389378 0.45550050243098306; 0.5436826530244554 0.9204593389763813 0.9270606176586167; 0.7055633627200892 0.3702008285594489 0.670758477684624])  

The output is not particularly convenient. What I would like to have is something similar to what the function qr() from LinearAlgebra returns. For example:

julia> qr(rand(3,3))                                                             
LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}
Q factor:
3×3 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
 -0.789051  -0.570416   -0.228089
 -0.213035  -0.0941769   0.972495
 -0.576207   0.815939   -0.0472084
R factor:
3×3 Array{Float64,2}:
 -0.929496  -0.563585  -0.787584
  0.0        0.377304  -0.505203
  0.0        0.0       -0.01765

This output is very useful to get at least some idea how these matrices look like.

How can I create a function that returns the matrices like the function qr() from LinearAlgebra?

Any help is much appreciated!

Answer 1

You will need to define your own display method. I present here an abstract approach so you can comfortably reuse it.

We start with a decorator supertype - all structs having this supertype will be nicely displayed.

abstract type Pretty end

And here is the actual implementation:

function Base.display(x::Pretty)
    for f in fieldnames(typeof(x))
         print(f," is a ")
         display(getfield(x,f))
    end
 end

Let us now see it. You just define any struct, e.g.:

struct S{T}  <: Pretty
    a::Matrix{T}
    b::Matrix{T}
end

And now you have what you need e.g.:

julia> S(rand(2,3), rand(3,2))
a is a 2×3 Matrix{Float64}:
 0.40661   0.753072   0.708016
 0.371099  0.0948791  0.538046
b is a 3×2 Matrix{Float64}:
 0.670715  0.457208
 0.353189  0.0248713
 0.455794  0.136496