Sum of squares

Write a program to find the sum of squares of a numeric vector. The program should work on a zero-length vector (with an answer of 0).

Ada

<Ada> with Ada.Text_IO; use Ada.Text_IO;

procedure Test_Sum_Of_Squares is

  type Float_Array is array (Integer range <>) of Float;

  function Sum_Of_Squares (X : Float_Array) return Float is
     Sum : Float := 0.0;
  begin
     for I in X'Range loop
        Sum := Sum + X (I) ** 2;
     end loop;
     return Sum;
  end Sum_Of_Squares;

begin

  Put_Line (Float'Image (Sum_Of_Squares ((1..0 => 1.0)))); -- Empty array
  Put_Line (Float'Image (Sum_Of_Squares ((3.0, 1.0, 4.0, 1.0, 5.0, 9.0))));

end Test_Sum_Of_Squares; </Ada> Sample output:

 0.00000E+00
 1.33000E+02

ALGOL 68

The computation can be written as a loop.

main1:(
  PROC sum of squares = ([]REAL argv)REAL:(
    REAL sum := 0;
    FOR i FROM LWB argv TO UPB argv DO
      sum +:= argv[i]**2
    OD;
    sum
  );

  printf(($xg(0)l$,sum of squares([]REAL(3, 1, 4, 1, 5, 9))));
)

Output:

Another implementation could define a procedure (PROC) or operator (OP) called map.

main2:(
  []REAL data = (3, 1, 4, 1, 5, 9);

  PROC map = ( PROC(REAL)REAL func, []REAL argv)REAL:
    ( REAL out:=0; FOR i FROM LWB argv TO UPB argv DO out:=func(argv[i]) OD; out);

  REAL sum := 0;
  printf(($xg(0)l$, map ( ((REAL argv)REAL: sum +:= argv ** 2), data) ));

  PRIO MAP = 5; # the same priority as the operators <, =<, >=, & > maybe... #
  OP MAP = ( PROC(REAL)REAL func, []REAL argv)REAL:
    ( REAL out:=0; FOR i FROM LWB argv TO UPB argv DO out:=func(argv[i]) OD; out);

  sum := 0;
  printf(($xg(0)l$, ((REAL argv)REAL: sum +:= argv ** 2) MAP data ))
)

Output:

133
133

BASIC

Works with: QuickBasic version 4.5

Assume the numbers are in a DIM called a.

sum = 0
FOR I = LBOUND(a) TO UBOUND(a)
   sum = sum + a(I) ^ 2
NEXT I
PRINT "The sum of squares is: " + sum

C++

<cpp>

include <iostream>
include <algorithm>
include <vector>

double add_square(double prev_sum, double new_val) {

 return prev_sum + new_val*new_val;

}

double vec_add_squares(std::vector<double>& v) {

 return std::accumulate(v.begin(), v.end(), 0.0, add_square);

}

int main() {

 // first, show that for empty vectors we indeed get 0
 std::vector<double> v; // empty
 std::cout << vec_add_squares(v) << std::endl;

 // now, use some values
 double data[] = { 0, 1, 3, 1.5, 42, 0.1, -4 };
 v.assign(data, data+7);
 std::cout << vec_add_squares(v) << std::endl;

} </cpp>

Common Lisp

(defun sum-of-squares (vector)
  (loop for x across vector sum (expt x 2)))

D

<d>module sumsquare ; import std.stdio ;

T sumsq(T)(T[] a) {

 T sum = 0 ;
 foreach(e ; a)
   sum += e*e ;
 return sum ;

}

void main() {

 real[] arr = [3.1L,1,4,1,5,9] ; 
 writefln(arr) ;
 writefln(arr.sumsq()) ;

}</d> Functional style

Works with: D version 2.011

See std.algorithm <d>import std.algorithm ; T sumsq(T)(inout T[] a) {

 return reduce!("a+b")(cast(T)0, map!("a*a")(a)) ;

}</d>

Forth

: fsum**2 ( addr n -- f )
  0e
  dup 0= if 2drop exit then
  floats bounds do
    i f@ fdup f* f+
  1 floats +loop ;

create test 3e f, 1e f, 4e f, 1e f, 5e f, 9e f,
test 6 fsum**2 f.     \ 133.

Fortran

In ISO Fortran 90 orlater, use SUM intrinsic and implicit element-wise array arithmetic:

 real, dimension(1000) :: a = (/ (i, i=1, 1000) /)
 real, pointer, dimension(:) :: p => a(2:1)       ! pointer to zero-length array
 real :: result, zresult
 
 result = sum(a*a)    ! Multiply array by itself to get squares
 
 result = sum(a**2)   ! Use exponentiation operator to get squares
 
 zresult = sum(p*p)   ! P is zero-length; P*P is valid zero-length array expression; SUM(P*P) == 0.0 as expected

Haskell

sumOfSquares = sum . map (^ 2)

> sumOfSquares [3,1,4,1,5,9]
133

IDL

print,total(array^2)

J

ss=: +/ @: *:

That is, sum composed with square. The verb also works on higher-ranked arrays. For example:

   ss 3 1 4 1 5 9
133
   ss $0           NB. $0 is a zero-length vector
0
   x=: 20 4 ?@$ 0  NB. a 20-by-4 table of random (0,1) numbers
   ss x
9.09516 5.19512 5.84173 6.6916

The computation can also be written as a loop. It is shown here for comparison only and is highly non-preferred compared to the version above.

ss1=: 3 : 0
 z=. 0
 for_i. i.#y do. z=. z+*:i{y end.
)

   ss1 3 1 4 1 5 9
133
   ss1 $0
0
   ss1 x
9.09516 5.19512 5.84173 6.6916

Java

Assume the numbers are in a double array called "nums".

...
double sum = 0;
for(double a : nums){
  sum+= a * a;
}
System.out.println("The sum of the squares is: " + sum);
...

JavaScript

function sumsq(array) {
  var sum = 0;
  for(var i in array)
    sum += array[i] * array[i];
  return sum;
}

alert( sumsq( [1,2,3,4,5] ) );   // 55

Library: Functional

Functional.reduce("x+y*y", 0, [1,2,3,4,5])   // 55

Logo

print apply "sum map [? * ?] [1 2 3 4 5]  ; 55

OCaml

List.fold_left (fun sum a -> sum + a * a) 0 ints

List.fold_left (fun sum a -> sum +. a *. a) 0. floats

Perl

<perl>sub sum_of_squares {

 my $sum = 0;
 $sum += $_**2 foreach @_;
 return $sum;

}

print sum_of_squares(3, 1, 4, 1, 5, 9), "\n";</perl>

Pop11

define sum_squares(v);
    lvars s = 0, j;
    for j from 1 to length(v) do
        s + v(j)*v(j) -> s;
    endfor;
    s;
enddefine;

sum_squares({1 2 3 4 5}) =>

Python

R

arr <- c(1,2,3,4,5)
result <- sum(arr^2)

Scheme

(define (sum-of-squares l)
  (apply + (map * l l)))

> (sum-of-squares (list 3 1 4 1 5 9))
133

UnixPipes

folder() {
   (read B; res=$( expr $1 \* $1 ) ; test -n "$B" && expr $res + $B || echo $res)
}

fold() {
   (while read a ; do
       fold | folder $a
   done)
}

(echo 3; echo 1; echo 4;echo 1;echo 5; echo 9) | fold

V

[sumsq [dup *] map 0 [+] fold].

[] sumsq
=0
[1 2 3] sumsq
=14