Refactoring a symmetric matrix into a vector and back again

General Usage
1

Hallo,

Do you know ‘good’ ways to refactor a symmetric matrix into a vector, and back again?
Ideally, something like this:

A = [1 2 3; 2 4 5; 3 5 6]
V = mat2vec(A) # V = [1 2 3 4 5 6]
A = vec2mat(V) # A = [1 2 3; 2 4 5; 3 5 6]

Many thanks,

2

See

3

Maybe it’s not a “good” way in the sense you expect, but in some cases it could work

julia> function symmat2vec(m)
           n=size(m,1)
           N=n*(n+1)÷2
           v=Vector{eltype(m)}(undef,N)
               for idx in 1: N
               j = Int(ceil(sqrt(2 * idx + 0.25) - 0.5))
               i = Int(idx - (j-1) * (j) / 2)
               v[idx] = m[i, j]
           end
           v
       end
symmat2vec (generic function with 1 method)

julia> function vec2symat(v)
           N=size(v,1)[1]
           n=Int((-1+ sqrt(1+8*N))/2)
           m=Matrix{eltype(v)}(undef,n,n)
           rngs=[Int(n*(n-1)/2+1):Int(n*(n+1)/2) for n in 1:4]
           for c in 1:4
               r=4*(c-1)+1:4*(c-1)+4
               m[r]= v[[rngs[c];getindex.(rngs[c+1:end],c)]]
           end
           m
       end
vec2symat (generic function with 1 method)

julia> m=[ 11 2 13 4; 2 3 4 25; 13 4 5 6; 4 25 6 77]  
4×4 Matrix{Int64}:
 11   2  13   4
  2   3   4  25
 13   4   5   6
  4  25   6  77

julia> v=symmat2vec(m)
10-element Vector{Int64}:
 11
  2
  3
 13
  4
  5
  4
 25
  6
 77

julia> vec2symat(v)
4×4 Matrix{Int64}:
 11   2  13   4
  2   3   4  25
 13   4   5   6
  4  25   6  77