Sum of elements below main diagonal of matrix

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

Phix

constant M = {{ 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}}
atom res = 0
integer height = length(M)
for row=1 to height do
    integer width = length(M[row])
    if width!=height then crash("not square") end if
    for col=1 to row-1 do
        res += M[row][col]
    end for
end for
?res

You could of course start row from 2 and get the same result, for row==1 the col loop iterates zero times.
Without the checks for square M expect (when not square) wrong/partial answers for height<=width+1, and (still human readable) runtime crashes for height>width+1.

Output:

Python

<lang python>from numpy import array, tril, sum

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]]

print(sum(tril(A, -1))) # 69 </lang>

Raku

<lang perl6>sub lower-triangle-sum (@matrix) { sum flat (1..@matrix).map( { @matrix[^$_]»[^($_-1)] } )»[*-1] }

say lower-triangle-sum [

   [  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 ]

];</lang>

Output:

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--

Output:

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

Wren

<lang ecmascript>var m = [

   [ 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]

] if (m.count != m[0].count) Fiber.abort("Matrix must be square.") var sum = 0 for (i in 1...m.count) {

  for (j in 0...i) {
      sum = sum + m[i][j]
 }

} System.print("Sum of elements below main diagonal is %(sum).")</lang>

Output:

Sum of elements below main diagonal is 69.