Multiplication of submatrices problem

@ea42gh wrote:

I was trying to transcribe the algorithm in the appendix of geninv

function pseudoinverse(G) # need to restrict types here
    m,n = size(G)
    if m < n
        transpose=true
        A=G*G'
        n=m
    else
        transpose=false
        A=G'G
    end
    
    dA  = diag(A)
    tol = 1e-9*minimum( dA[dA .> 0.] )   # catch dA=zeros()
    L   = fill( zero(A[1,1]), size(A) )

    r = 0 
    for k = 1:n
        if r > 0
println("indices: L[$k:$n,$r+1] = A[$k:$n,$k] - ( L[$k:$n,1:$r] * L[$k,1:$r]')")
println(". shape  L[ $(size(L[k:n,1:r])) ]:   coded as  L[$k:$n,1:$r]")
println(". shape  L[ $(size(L[k,1:r]')) ]:    coded as  L[$k,1:$r]'")
println(".  .  $( L[k:n,1:r] * L[k,1:r]')")

            L[k:n,r+1] = A[k:n,k] - ( L[k:n,1:r] * L[k,1:r]')
        else
            L[k:n,r+1] = A[k:n,k]
        end
        r += 1
        if L[k,r] > tol
            L[k,r] = sqrt( L[k,r] )
            if k < n
                L[(k+1):n,r] = L[(k+1):n,r] ./ L[k,r]
            end
        else
            r -= 1
        end
    end
    L = L[:,1:r]
    M = inv(L'L)
    if transpose
        G'*L*M*M*L'
    else
        L*M*M*L'*G'
    end
end
pseudoinverse([1. 2 1; 2 2 1; 0 0 0])

It fails in the loop with

indices: L[3:3,2+1] = A[3:3,3] - ( L[3:3,1:2] * L[3,1:2]')
. shape  L[ (1, 2) ]:   coded as  L[3:3,1:2]
. shape  L[ (1, 2) ]:    coded as  L[3,1:2]'

which leaves me puzzled: the matrix sizes are consistent,
but somehow the transpose appears to be lost?!

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