Sum of elements below main diagonal of matrix: Difference between revisions
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T sum = 0; |
T sum = 0; |
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for (std::size_t y = 0; y < matrix.size(); y++) |
for (std::size_t y = 0; y < matrix.size(); y++) |
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for (std::size_t x = 0; x < |
for (std::size_t x = 0; x < matrix[y].size() && x < y; x++) |
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sum += matrix[y][x]; |
sum += matrix[y][x]; |
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return sum; |
return sum; |
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Revision as of 23:27, 23 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
APL
<lang apl>sum_below_diagonal ← +/(∊⊢×(>/¨⍳∘⍴))</lang>
- Output:
matrix ← 5 5⍴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_diagonal matrix
69
C++
<lang cpp>#include <iostream>
- include <vector>
template<typename T> T sum_below_diagonal(const std::vector<std::vector<T>>& matrix) {
T sum = 0;
for (std::size_t y = 0; y < matrix.size(); y++)
for (std::size_t x = 0; x < matrix[y].size() && x < y; x++)
sum += matrix[y][x];
return sum;
}
int main() {
std::vector<std::vector<int>> 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}
};
std::cout << sum_below_diagonal(matrix) << std::endl;
return 0;
}</lang>
- Output:
69
F#
<lang fsharp> // Sum below leading diagnal. Nigel Galloway: July 21st., 2021 let _,n=[[ 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]]|>List.fold(fun(n,g) i->let i,_=i|>List.splitAt n in (n+1,g+(i|>List.sum)))(0,0) in printfn "%d" n
</lang>
- Output:
69
Factor
<lang factor>USING: kernel math math.matrices prettyprint sequences ;
- sum-below-diagonal ( matrix -- sum )
dup square-matrix? [ "Matrix must be square." throw ] unless 0 swap [ head sum + ] each-index ;
{
{ 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-diagonal .</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 rows = all ((n ==) . length) rows
where n = length rows
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
J
<lang j>sum_below_diagonal =: [:+/@,[*>/~@i.@#</lang>
- Output:
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_below_diagonal mat 69
JavaScript
Defining the lower triangle of a square matrix.
<lang javascript>(() => {
"use strict";
// -------- LOWER TRIANGLE OF A SQUARE MATRIX --------
// lowerTriangle :: a -> Either String a const lowerTriangle = matrix => // Either a message, if the matrix is not square, // or the lower triangle of the matrix. isSquare(matrix) ? ( Right( matrix.reduce( ([n, rows], xs) => [ 1 + n, rows.concat([xs.slice(0, n)]) ], [0, []] )[1] ) ) : Left("Not a square matrix");
// isSquare :: a -> Bool const isSquare = rows => { // True if the length of every row in the matrix // matches the number of rows in the matrix. const n = rows.length;
return rows.every(x => n === x.length); };
// ---------------------- TEST -----------------------
const main = () =>
either(
msg => `Lower triangle undefined :: ${msg}`
)(
rows => sum([].concat(...rows))
)(
lowerTriangle([
[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]
])
);
// --------------------- GENERIC ---------------------
// Left :: a -> Either a b
const Left = x => ({
type: "Either",
Left: x
});
// Right :: b -> Either a b
const Right = x => ({
type: "Either",
Right: x
});
// either :: (a -> c) -> (b -> c) -> Either a b -> c
const either = fl =>
// Application of the function fl to the
// contents of any Left value in e, or
// the application of fr to its Right value.
fr => e => e.Left ? (
fl(e.Left)
) : fr(e.Right);
// sum :: [Num] -> Num
const sum = xs =>
// The numeric sum of all values in xs.
xs.reduce((a, x) => a + x, 0);
// MAIN --- return main();
})();</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
MiniZinc
<lang MiniZinc> % Sum below leading diagnal. Nigel Galloway: July 22nd., 2021 array [1..5,1..5] of int: N=[|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|]; int: res=sum(n,g in 1..5 where n>g)(N[n,g]); output([show(res)]) </lang>
- Output:
69 ----------
Nim
We use a generic definition for the square matrix type. The compiler insures that the matrix we provide is actually square.
<lang Nim>type SquareMatrix[T: SomeNumber; N: static Positive] = array[N, array[N, T]]
func sumBelowDiagonal[T, N](m: SquareMatrix[T, N]): T =
for i in 1..<N:
for j in 0..<i:
result += m[i][j]
const 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]]
echo sumBelowDiagonal(M)</lang>
- Output:
69
Perl
<lang perl>#!/usr/bin/perl
use strict; use warnings; use List::Util qw( sum );
my $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]];
my $lowersum = sum map @{ $matrix->[$_] }[0 .. $_ - 1], 1 .. $#$matrix; print "lower sum = $lowersum\n";</lang>
- Output:
lower sum = 69
Phix
constant M = {{ 1, 3, 7, 8, 10}, { 2, 4, 16, 14, 4}, { 3, 1, 9, 18, 11}, {12, 14, 17, 18, 20}, { 7, 1, 3, 9, 5}} atom res = 0 integer height = length(M) for row=1 to height do integer width = length(M[row]) if width!=height then crash("not square") end if for col=1 to row-1 do res += M[row][col] end for end for ?res
You could of course start row from 2 and get the same result, for row==1 the col loop iterates zero times.
Without the checks for square M expect (when not square) wrong/partial answers for height<=width+1, and (still human readable) runtime crashes for height>width+1.
- Output:
69
PL/M
This can be compiled with the original 8080 PL/M compiler and run under CP/M or an emulator/clone. <lang pli>100H: /* SUM THE ELEMENTS BELOW THE MAIN DIAGONAL OF A MATRIX */
/* CP/M BDOS SYSTEM CALL, IGNORE THE RETURN VALUE */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* RETURNS THE SUM OF THE ELEMENTS BELOW THE MAIN DIAGONAL OF MX */
/* MX WOULD BE DECLARED AS ( UB, UB )ADDRESS IF PL/M SUPPORTED */
/* 2-DIMENSIONAL ARRAYS, IT DOESN'T SO MX MUST ACTULLY BE DECLARED */
/* ( UB * UB )ADDRESS - EXCEPT THE BOUND MUST BE A CONSTANT, NOT AN */
/* EXPRESSION */
/* NOTE ADDRESS MEANS UNSIGNED 16-BIT QUANTITY, WHICH CAN BE USED FOR */
/* OTHER PURPOSES THAN JUST POINTERS */
LOWER$SUM: PROCEDURE( MX, UB )ADDRESS;
DECLARE ( MX, UB ) ADDRESS;
DECLARE ( SUM, R, C, STRIDE, R$PTR ) ADDRESS;
DECLARE M$PTR ADDRESS, M$VALUE BASED M$PTR ADDRESS;
SUM = 0;
STRIDE = UB + UB;
R$PTR = MX + STRIDE; /* ADDRESS OF ROW 1 ( THE FIRST ROW IS 0 ) */
DO R = 1 TO UB - 1;
M$PTR = R$PTR;
DO C = 0 TO R - 1;
SUM = SUM + M$VALUE;
M$PTR = M$PTR + 2;
END;
R$PTR = R$PTR + STRIDE; /* ADDRESS OF THE NEXT ROW */
END;
RETURN SUM;
END LOWER$SUM ;
/* TASK TEST CASE */
DECLARE T ( 25 )ADDRESS
INITIAL( 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
);
CALL PR$NUMBER( LOWER$SUM( .T, 5 ) );
EOF</lang>
- 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>
Or, defining the lower triangle for ourselves:
<lang python>Lower triangle of a matrix
from itertools import chain, islice from functools import reduce
def lowerTriangle(matrix):
Either None, if the matrix is not square, or
the rows of the matrix, each containing only
those values that form part of the lower triangle.
def go(n_rows, xs):
n, rows = n_rows
return 1 + n, rows + [list(islice(xs, n))]
return reduce(
go,
matrix,
(0, [])
)[1] if isSquare(matrix) else None
- isSquare :: a -> Bool
def isSquare(matrix):
True if all rows of the matrix share
the length of the matrix itself.
n = len(matrix)
return all([n == len(x) for x in matrix])
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
Sum of integers in the lower triangle of a matrix.
rows = lowerTriangle([
[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(
"Not a square matrix." if None is rows else (
sum(chain(*rows))
)
)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
69
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 that might not properly show the true value of an element).
<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 #; parse var $ @..j $ /*obtain a number of the array (list). */
w= max(w, length(@..j)) /*examine each element for its width. */
end /*j*/ /* [↑] this is aligning matrix elements*/
s= 0; z= 0 /*initialize the sum [S] to zero. */
do r=1 for siz; _= left(, 12) /*_: contains a row of matrix elements*/
do c=1 for siz; z= z + 1; @.z= @..z /*get a number of the " " */
_= _ right(@.z, w) /*build a row of elements for display. */
if c<r then s= s + @.z /*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