Sum of elements below main diagonal of matrix: Difference between revisions
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| otherwise = Left "Not a square matrix." |
| otherwise = Left "Not a square matrix." |
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isSquare :: [[a]] -> Bool |
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isSquare [] = True |
isSquare [] = True |
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isSquare (row : rows) = all ((n ==) . length) rows |
isSquare (row : rows) = all ((n ==) . length) rows |
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Revision as of 18:16, 20 July 2021
- Task
Find and display the sum of elements that are below the main diagonal of a matrix.
The matrix should be a square matrix.
- ─── Matrix to be used: ───
[[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]]
ALGOL 68
<lang algol68>BEGIN # sum the elements below the main diagonal of a matrix #
# returns the sum of the elements below the main diagonal #
# of m, m must be a square matrix #
OP LOWERSUM = ( [,]INT m )INT:
IF 1 LWB m /= 2 LWB m OR 1 UPB m /= 2 UPB m THEN
# the matrix isn't square #
print( ( "Matrix must be suare for LOWERSUM", newline ) );
stop
ELSE
# have a square matrix #
INT sum := 0;
FOR r FROM 1 LWB m + 1 TO 1 UPB m DO
FOR c FROM 1 LWB m TO r - 1 DO
sum +:= m[ r, c ]
OD
OD;
sum
FI; # LOWERSUM #
# task test case #
print( ( whole( LOWERSUM [,]INT( ( 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 )
)
, 0
)
, newline
)
)
END</lang>
- Output:
69
ALGOL W
One of the rare occasions where the lack of lower/upper bound operators in Algol W actually simplifies things, assuming the programmer gets things right... <lang algolw>begin % sum the elements below the main diagonal of a matrix %
% returns the sum of the elements below the main diagonal %
% of m, m must have bounds lb :: ub, lb :: ub %
integer procedure lowerSum ( integer array m ( *, * )
; integer value lb, ub
) ;
begin
integer sum;
sum := 0;
for r := lb + 1 until ub do begin
for c := lb until r - 1 do sum := sum + m( r, c )
end for_r;
sum
end lowerSum ;
begin % task test case %
integer array m ( 1 :: 5, 1 :: 5 );
integer r, c;
r := 1; c := 0; for v := 1, 3, 7, 8, 10 do begin c := c + 1; m( r, c ) := v end;
r := 2; c := 0; for v := 2, 4, 16, 14, 4 do begin c := c + 1; m( r, c ) := v end;
r := 3; c := 0; for v := 3, 1, 9, 18, 11 do begin c := c + 1; m( r, c ) := v end;
r := 4; c := 0; for v := 12, 14, 17, 18, 20 do begin c := c + 1; m( r, c ) := v end;
r := 5; c := 0; for v := 7, 1, 3, 9, 5 do begin c := c + 1; m( r, c ) := v end;
write( i_w := 1, lowerSum( m, 1, 5 ) )
end
end.</lang>
- Output:
69
Go
<lang go>package main
import (
"fmt" "log"
)
func main() {
m := [][]int{
{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 len(m) != len(m[0]) {
log.Fatal("Matrix must be square.")
}
sum := 0
for i := 1; i < len(m); i++ {
for j := 0; j < i; j++ {
sum = sum + m[i][j]
}
}
fmt.Println("Sum of elements below main diagonal is", sum)
}</lang>
- Output:
Sum of elements below main diagonal is 69
Haskell
Defining the lower triangle:
<lang haskell>---------------------- LOWER TRIANGLE --------------------
lowerTriangle :: a -> Either String a lowerTriangle matrix
| isSquare matrix =
(Right . snd) $
foldr
(\xs (n, rows) -> (pred n, [take n xs] <> rows))
(pred $ length matrix, [])
matrix
| otherwise = Left "Not a square matrix."
isSquare :: a -> Bool isSquare [] = True isSquare (row : rows) = all ((n ==) . length) rows
where n = length row
TEST -------------------------
main :: IO () main =
either putStrLn (print . sum . concat) (lowerTriangle testMatrix)
testMatrix :: Integer testMatrix =
[ [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:
69
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:
69
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:
69
REXX
version 1
<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
version 2
This REXX version makes no assumption about the size of the matrix, and it determines the maximum width of any
matrix element (instead of assuming a width).
<lang rexx>/*REXX pgm finds & shows the sum of elements below the main diagonal of a square matrix.*/
$= '1 3 7 8 10 2 4 16 14 4 3 1 9 18 11 12 14 17 18 20 7 1 3 9 5'; #= words($)
do siz=1 while siz*siz<#; end /*determine the size of the matrix. */
w= 0 /*W: the maximum width any any element*/
do j=1 for #; w= max(w,length(word($,j))) /*examine each element for its width. */
end /*j*/
s= 0 /*initialize the sum; define the size.*/
do r=1 for siz; _= left(, 12) /*_: contains a row of matrix elements*/
do c=1 for siz; parse var $ x $ /*get an element of the " " */
_= _ right(x, w) /*build a row of elements for display. */
if c<r then s=s + x /*add a "lower element" to the sum. */
end /*r*/
say _ /*display a row of the matrix to term. */
end /*c*/
say 'sum of elements below main diagonal is: ' s /*stick a fork in it, we're all done. */</lang>
- output when using the internal default input:
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 of elements below main diagonal is: 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...
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.
XPL0
<lang XPL0>int Mat, X, Y, Sum; [Mat:= [[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:= 0; for Y:= 0 to 4 do
for X:= 0 to 4 do
if Y > X then
Sum:= Sum + Mat(Y,X);
IntOut(0, Sum); ]</lang>
- Output:
69