Sum of elements below main diagonal of matrix

Sum of elements below main diagonal of matrix is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Find sum of elements below main diagonal of matrix.

The matrix should be square matrix.

Matrix =

   [[1,3,7,8,10],
    [2,4,16,14,4],
    [3,1,9,18,11],
    [12,14,17,18,20],
    [7,1,3,9,5]]

Julia

The tril function is part of Julia's built-in LinearAlgebra package. tril(A) includes the main diagonal and the components of the matrix A to the left and below the main diagonal. tril(A, -1) returns the lower triangular elements of A excluding the main diagonal. The excluded elements of the matrix are set to 0. <lang julia>using LinearAlgebra

A = [ 1 3 7 8 10;

     2  4 16 14  4;
     3  1  9 18 11;
    12 14 17 18 20;
     7  1  3  9  5 ]

@show tril(A)

@show tril(A, -1)

@show sum(tril(A, -1)) # 69

</lang>

Output:

tril(A) = [1 0 0 0 0; 2 4 0 0 0; 3 1 9 0 0; 12 14 17 18 0; 7 1 3 9 5]
tril(A, -1) = [0 0 0 0 0; 2 0 0 0 0; 3 1 0 0 0; 12 14 17 0 0; 7 1 3 9 0]
sum(tril(A, -1)) = 69

REXX

<lang rexx>/* REXX */ ml ='1 3 7 8 10 2 4 16 14 4 3 1 9 18 11 12 14 17 18 20 7 1 3 9 5' Do i=1 To 5

 Do j=1 To 5
   Parse Var ml m.i.j ml
   End
 End

l= Do i=1 To 5

 Do j=1 To 5
   l=l right(m.i.j,2)
   End
 Say l
 l=
 End

sum=0 Do i=2 To 5

 Do j=1 To i-1
   sum=sum+m.i.j
   End
 End

Say 'Sum below main diagonal:' sum</lang>

 
  1  3  7  8 10
  2  4 16 14  4
  3  1  9 18 11
 12 14 17 18 20
  7  1  3  9  5
Sum below main diagonal: 69 

Ring

<lang ring> see "working..." + nl see "Sum of elements below main diagonal of matrix:" + nl diag = [[1,3,7,8,10],

       [2,4,16,14,4],
       [3,1,9,18,11],
       [12,14,17,18,20],
       [7,1,3,9,5]]

lenDiag = len(diag) ind = lenDiag sumDiag = 0

for n=1 to lenDiag

   for m=1 to lenDiag-ind
       sumDiag += diag[n][m]
   next
   ind--

next

see "" + sumDiag + nl see "done..." + nl </lang>

Output:

working...
Sum of elements below main diagonal of matrix:
69
done...