Dot product

Dot product
You are encouraged to solve this task according to the task description, using any language you may know.

Create a function/use an in-built function, to compute the dot product, also known as the scalar product of two vectors. If possible, make the vectors of arbitrary length.

As an example, compute the dot product of the vectors `[1, 3, -5]` and `[4, -2, -1]`.

If implementing the dot product of two vectors directly, each vector must be the same length; multiply corresponding terms from each vector then sum the results to produce the answer.

Reference

ABAP

<lang ABAP>report zdot_product data: lv_n type i,

```     lv_sum type i,
lt_a type standard table of i,
lt_b type standard table of i.
```

append: '1' to lt_a, '3' to lt_a, '-5' to lt_a. append: '4' to lt_b, '-2' to lt_b, '-1' to lt_b. describe table lt_a lines lv_n.

perform dot_product using lt_a lt_b lv_n changing lv_sum.

write lv_sum left-justified.

form dot_product using it_a like lt_a

```                      it_b like lt_b
iv_n type i
changing
ev_sum type i.
field-symbols: <wa_a> type i, <wa_b> type i.
```
``` do iv_n times.
read table: it_a assigning <wa_a> index sy-index, it_b assigning <wa_b> index sy-index.
lv_sum = lv_sum + ( <wa_a> * <wa_b> ).
enddo.
```

endform.</lang> Output:

```3
```

ACL2

<lang Lisp>(defun dotp (v u)

```  (if (or (endp v) (endp u))
0
(+ (* (first v) (first u))
(dotp (rest v) (rest u)))))</lang>
```
```> (dotp '(1 3 -5) '(4 -2 -1))
3```

ActionScript

<lang ActionScript>function dotProduct(v1:Vector.<Number>, v2:Vector.<Number>):Number { if(v1.length != v2.length) return NaN; var sum:Number = 0; for(var i:uint = 0; i < v1.length; i++) sum += v1[i]*v2[i]; return sum; } trace(dotProduct(Vector.<Number>([1,3,-5]),Vector.<Number>([4,-2,-1])));</lang>

<lang Ada>with Ada.Text_IO; use Ada.Text_IO; procedure dot_product is type vect is array(Positive range <>) of Integer; v1 : vect := (1,3,-5); v2 : vect := (4,-2,-1);

function dotprod(a: vect; b: vect) return Integer is sum : Integer := 0; begin if not (a'Length=b'Length) then raise Constraint_Error; end if; for p in a'Range loop sum := sum + a(p)*b(p); end loop; return sum; end dotprod;

begin put_line(Integer'Image(dotprod(v1,v2))); end dot_product;</lang> Output:

```3
```

ALGOL 68

Translation of: C++
Works with: ALGOL 68 version Standard - with prelude inserted manually
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

<lang algol68>MODE DOTFIELD = REAL; MODE DOTVEC = [1:0]DOTFIELD;

1. The "Spread Sheet" way of doing a dot product:
``` o Assume bounds are equal, and start at 1
o Ignore round off error
```

PRIO SSDOT = 7; OP SSDOT = (DOTVEC a,b)DOTFIELD: (

``` DOTFIELD sum := 0;
FOR i TO UPB a DO sum +:= a[i]*b[i] OD;
sum
```

);

1. An improved dot-product version:
``` o Handles sparse vectors
o Improves summation by gathering round off error
with no additional multiplication - or LONG - operations.
```

OP * = (DOTVEC a,b)DOTFIELD: (

``` DOTFIELD sum := 0, round off error:= 0;
FOR i
```
1. Assume bounds may not be equal, empty members are zero (sparse) #
```   FROM LWB (LWB a > LWB b | a | b )
TO UPB (UPB a < UPB b | a | b )
DO
DOTFIELD org = sum, prod = a[i]*b[i];
sum +:= prod;
round off error +:= sum - org - prod
OD;
sum - round off error
```

);

1. Test: #

DOTVEC a=(1,3,-5), b=(4,-2,-1);

print(("a SSDOT b = ",fixed(a SSDOT b,0,real width), new line)); print(("a * b = ",fixed(a * b,0,real width), new line))</lang> Output:

```a SSDOT b = 3.000000000000000
a   *   b = 3.000000000000000
```

AutoHotkey

<lang AutoHotkey>Vet1 := "1,3,-5" Vet2 := "4 , -2 , -1" MsgBox % DotProduct( Vet1 , Vet2 )

---------------------------

DotProduct( VectorA , VectorB ) {

``` Sum := 0
StringSplit, ArrayA, VectorA, `,, %A_Space%
StringSplit, ArrayB, VectorB, `,, %A_Space%
If ( ArrayA0 <> ArrayB0 )
Return ERROR
While ( A_Index <= ArrayA0 )
Sum += ArrayA%A_Index% * ArrayB%A_Index%
Return Sum
```

}</lang>

AWK

<lang AWK>

1. syntax: GAWK -f DOT_PRODUCT.AWK

BEGIN {

```   v1 = "1,3,-5"
v2 = "4,-2,-1"
if (split(v1,v1arr,",") != split(v2,v2arr,",")) {
print("error: vectors are of unequal lengths")
exit(1)
}
printf("%g\n",dot_product(v1arr,v2arr))
exit(0)
```

} function dot_product(v1,v2, i,sum) {

```   for (i in v1) {
sum += v1[i] * v2[i]
}
return(sum)
```

} </lang>

output:

```3
```

BBC BASIC

BBC BASIC has a built-in dot-product operator: <lang bbcbasic> DIM vec1(2), vec2(2), dot(0)

```     vec1() = 1, 3, -5
vec2() = 4, -2, -1

dot() = vec1() . vec2()
PRINT "Result is "; dot(0)</lang>
```

Output:

`Result is 3`

Befunge 93

<lang befunge> v Space for variables v Space for vector1 v Space for vector2 v http://rosettacode.org/wiki/Dot_product

```                                           >00pv
```

>>55+":htgneL",,,,,,,,&:0` | v,,,,,,,"Length can't be negative."+55< >,,,,,,,,,,,,,,,,,,,@ |!`-10<

```                                     >0.@
```

v,")".g00,,,,,,,,,,,,,,"Vector a(size " < 0v01g00,")".g00,,,,,,,,,,,,,,"Vector b"< 0pvp2g01&p01-1g01< " g>> 10g0`| @.g30<( 1 >03g:-03p>00g1-` |s 0 vp00-1g00p30+g30*g2-1g00g1-1g00 v # z vp1g01&p01-1g01<> ^ e > 10g0` | vp01-1g01.g1<

```              >00g1-10p>10g:01-`   |  "
>  ^
```

</lang> Output: Length: 3 Vector a(size 3 )1 3 -5 1 3 -5 Vector b(size 3 )4 -2 -1 3

Bracmat

<lang bracmat> ( dot

``` =   a A z Z
.     !arg:(%?a ?z.%?A ?Z)
& !a*!A+dot\$(!z.!Z)
| 0
)
```

& out\$(dot\$(1 3 -5.4 -2 -1));</lang> Output:

`3`

C

<lang c>#include <stdio.h>

1. include <stdlib.h>

int dot_product(int *, int *, size_t);

int main(void) {

```       int a[3] = {1, 3, -5};
int b[3] = {4, -2, -1};
```
```       printf("%d\n", dot_product(a, b, sizeof(a) / sizeof(a[0])));
```
```       return EXIT_SUCCESS;
```

}

int dot_product(int *a, int *b, size_t n) {

```       int sum = 0;
size_t i;
```
```       for (i = 0; i < n; i++) {
sum += a[i] * b[i];
}
```
```       return sum;
```

}</lang> Output:

`3`

C#

<lang csharp>static void Main(string[] args) { Console.WriteLine(DotProduct(new decimal[] { 1, 3, -5 }, new decimal[] { 4, -2, -1 })); Console.Read(); }

private static decimal DotProduct(decimal[] vec1, decimal[] vec2) { if (vec1 == null) return 0;

if (vec2 == null) return 0;

if (vec1.Length != vec2.Length) return 0;

decimal tVal = 0; for (int x = 0; x < vec1.Length; x++) { tVal += vec1[x] * vec2[x]; }

return tVal; }</lang> Output:

`3`

Alternative using Linq (C# 4)

Works with: C# version 4

<lang csharp>public static decimal DotProduct(decimal[] a, decimal[] b) {

```   return a.Zip(b, (x, y) => x * y).Sum();
```

}</lang>

C++

<lang cpp>#include <iostream>

1. include <numeric>

int main() {

```   int a[] = { 1, 3, -5 };
int b[] = { 4, -2, -1 };
```
```   std::cout << std::inner_product(a, a + sizeof(a) / sizeof(a[0]), b, 0) << std::endl;
```
```   return 0;
```

}</lang> Output:

`3`

Clojure

Works with: Clojure version 1.1

Preconditions are new in 1.1. The actual code also works in older Clojure versions. <lang clojure>(defn dot-product [& matrix]

``` {:pre [(apply == (map count matrix))]}
(apply + (apply map * matrix)))
```
Example Usage

(println (dot-product [1 3 -5] [4 -2 -1]))</lang>

CoffeeScript

<lang coffeescript>dot_product = (ary1, ary2) ->

``` if ary1.length != ary2.length
throw "can't find dot product: arrays have different lengths"
dotprod = 0
for v, i in ary1
dotprod += v * ary2[i]
dotprod
```

console.log dot_product([ 1, 3, -5 ], [ 4, -2, -1 ]) # 3 try

``` console.log dot_product([ 1, 3, -5 ], [ 4, -2, -1, 0 ]) # exception
```

catch e

``` console.log e</lang>
```

output

```> coffee foo.coffee
3
can't find dot product: arrays have different lengths
```

Common Lisp

<lang lisp>(defun dot-product (a b)

``` (apply #'+ (mapcar #'* (coerce a 'list) (coerce b 'list))))</lang>
```

This works with any size vector, and (as usual for Common Lisp) all numeric types (rationals, bignums, complex numbers, etc.).

Maybe it is better to do it without coercing. Then we got a cleaner code. <lang lisp>(defun dot-prod (a b)

``` (reduce #'+ (map 'simple-vector #'* a b)))</lang>
```

D

<lang d>void main() {

```   import std.stdio, std.numeric;
```
```   [1.0, 3.0, -5.0].dotProduct([4.0, -2.0, -1.0]).writeln;
```

}</lang> Output:

`3`

Using an array operation: <lang d>void main() {

```   import std.stdio, std.range, std.algorithm;
```
```   double[3] a = [1.0, 3.0, -5.0];
double[3] b = [4.0, -2.0, -1.0];
double[3] c;
c[] = a[] * b[];
c.reduce!q{a + b}.writeln;
```

}</lang>

Delphi

Works with: Lazarus

<lang delphi>program Project1;

{\$APPTYPE CONSOLE}

type

``` doublearray = array of Double;
```

function DotProduct(const A, B : doublearray): Double; var I: integer; begin

``` assert (Length(A) = Length(B), 'Input arrays must be the same length');
Result := 0;
for I := 0 to Length(A) - 1 do
Result := Result + (A[I] * B[I]);
```

end;

var

``` x,y: doublearray;
```

begin

``` SetLength(x, 3);
SetLength(y, 3);
x[0] := 1; x[1] := 3; x[2] := -5;
y[0] := 4; y[1] :=-2; y[2] := -1;
WriteLn(DotProduct(x,y));
```

end.</lang> Output:

```3.00000000000000E+0000
```

Note: Delphi does not like arrays being declared in procedure headings, so it is necessary to declare it beforehand. To use integers, modify doublearray to be an array of integer.

DWScript

For arbitrary length vectors, using a precondition to check vector length: <lang delphi>function DotProduct(a, b : array of Float) : Float; require

```  a.Length = b.Length;
```

var

```  i : Integer;
```

begin

```  Result := 0;
for i := 0 to a.High do
Result += a[i]*b[i];
```

end;

PrintLn(DotProduct([1,3,-5], [4,-2,-1]));</lang> Using built-in 4D Vector type: <lang delphi>var a := Vector(1, 3, -5, 0); var b := Vector(4, -2, -1, 0);

PrintLn(a * b);</lang>

Ouput in both cases:
`3`

Ela

<lang ela>open list

dotp a b | length a == length b = sum (zipWith (*) a b)

```        | else = fail "Vector sizes must match."
```

dotp [1,3,-5] [4,-2,-1]</lang>

Output:

`3`

Erlang

<lang erlang>dotProduct(A,B) when length(A) == length(B) -> dotProduct(A,B,0); dotProduct(_,_) -> erlang:error('Vectors must have the same length.').

dotProduct([H1|T1],[H2|T2],P) -> dotProduct(T1,T2,P+H1*H2); dotProduct([],[],P) -> P.

dotProduct([1,3,-5],[4,-2,-1]).</lang> Output:

`3`

Euphoria

<lang Euphoria>function dotprod(sequence a, sequence b)

```   atom sum
a *= b
sum = 0
for n = 1 to length(a) do
sum += a[n]
end for
return sum
```

end function

? dotprod({1,3,-5},{4,-2,-1})</lang>

```Sample Output:
3
```

<lang Euphoria>-- Here is an alternative method, -- using the standard Euphoria Version 4+ Math Library include std/math.e sequence a = {1,3,-5}, b = {4,-2,-1} -- Make them any length you want ? sum(a * b)</lang>

```Sample Output:
3
```

F#

<lang fsharp>let dot_product (a:array<'a>) (b:array<'a>) =

```   if Array.length a <> Array.length b then failwith "invalid argument: vectors must have the same lengths"
Array.fold2 (fun acc i j -> acc + (i * j)) 0 a b</lang>
```
```> dot_product [| 1; 3; -5 |] [| 4; -2; -1 |] ;;
val it : int = 3```

Factor

The built-in word `v.` is used to compute the dot product. It doesn't enforce that the vectors are of the same length, so here's a wrapper. <lang factor>USING: kernel math.vectors sequences ;

dot-product ( u v -- w )
```   2dup [ length ] bi@ =
[ v. ] [ "Vector lengths must be equal" throw ] if ;</lang>
```
```( scratchpad ) { 1 3 -5 } { 4 -2 -1 } dot-product .
3
```

FALSE

<lang false>[[\1-\$0=~][\$d;2*1+\-ø\\$d;2+\-ø@*@+]#]p: 3d: {Vectors' length} 1 3 5_ 4 2_ 1_ d;\$1+ø@*p;!%. {Output: 3}</lang>

Fantom

Dot product of lists of Int: <lang fantom>class DotProduct {

``` static Int dotProduct (Int[] a, Int[] b)
{
Int result := 0
[a.size,b.size].min.times |i|
{
result += a[i] * b[i]
}
return result
}
```
``` public static Void main ()
{
Int[] x := [1,2,3,4]
Int[] y := [2,3,4]
```
```   echo ("Dot product of \$x and \$y is \${dotProduct(x, y)}")
}
```

}</lang>

Forth

<lang forth>: vector create cells allot ;

th cells + ;

3 constant /vector /vector vector a /vector vector b

dotproduct ( a1 a2 -- n)
``` 0 tuck ?do -rot over i th @ over i th @ * >r rot r> + loop nip nip
```
vector! cells over + swap ?do i ! 1 cells +loop ;

-5 3 1 a /vector vector! -1 -2 4 b /vector vector!

a b /vector dotproduct . 3 ok</lang>

Fortran

Works with: Fortran version 90 and later

<lang fortran>program test_dot_product

``` write (*, '(i0)') dot_product ((/1, 3, -5/), (/4, -2, -1/))
```

end program test_dot_product</lang> Output:

`3`

GAP

<lang gap># Built-in

[1, 3, -5]*[4, -2, -1];

1. 3</lang>

Go

<lang go>package main

import (

```   "errors"
"fmt"
```

)

func dot(x, y []int) (r int, err error) {

```   if len(x) != len(y) {
return 0, errors.New("incompatible lengths")
}
for i := range x {
r += x[i] * y[i]
}
return
```

}

func main() {

```   d, err := dot([]int{1, 3, -5}, []int{4, -2, -1})
if err != nil {
fmt.Println(err)
return
}
fmt.Println(d)
```

}</lang> Output:

```3
```

Groovy

Solution: <lang groovy>def dotProduct = { x, y ->

```   assert x && y && x.size() == y.size()
[x, y].transpose().collect{ it[0] * it[1] }.sum()
```

}</lang> Test: <lang groovy>println dotProduct([1, 3, -5], [4, -2, -1])</lang> Output:

`3`

<lang haskell>dotp a b | length a == length b = sum (zipWith (*) a b)

```        | otherwise = error "Vector sizes must match"
```

main = print \$ dotp [1, 3, -5] [4, -2, -1] -- prints 3</lang>

Icon and Unicon

The procedure below computes the dot product of two vectors of arbitrary length or generates a run time error if its arguments are the wrong type or shape. <lang Icon>procedure main() write("a dot b := ",dotproduct([1, 3, -5],[4, -2, -1])) end

procedure dotproduct(a,b) #: return dot product of vectors a & b or error if *a ~= *b & type(a) == type(b) == "list" then runerr(205,a) # invalid value every (dp := 0) +:= a[i := 1 to *a] * b[i] return dp end</lang>

J

<lang j> 1 3 _5 +/ . * 4 _2 _1 3

```  dotp=: +/ . *                  NB. Or defined as a verb (function)
1 3 _5  dotp 4 _2 _1
```

3</lang> Note also: The verbs built using the conjunction `.` generally apply to matricies and arrays of higher dimensions and can be built with verbs (functions) other than sum ( `+/` ) and product ( `*` ).

Java

<lang java>public class DotProduct {

public static void main(String[] args) { double[] a = {1, 3, -5}; double[] b = {4, -2, -1};

System.out.println(dotProd(a,b)); }

public static double dotProd(double[] a, double[] b){ if(a.length != b.length){ throw new IllegalArgumentException("The dimensions have to be equal!"); } double sum = 0; for(int i = 0; i < a.length; i++){ sum += a[i] * b[i]; } return sum; } }</lang> Output:

`3.0`

JavaScript

<lang javascript>function dot_product(ary1, ary2) {

```   if (ary1.length != ary2.length)
throw "can't find dot product: arrays have different lengths";
var dotprod = 0;
for (var i = 0; i < ary1.length; i++)
dotprod += ary1[i] * ary2[i];
return dotprod;
```

}

print(dot_product([1,3,-5],[4,-2,-1])); // ==> 3 print(dot_product([1,3,-5],[4,-2,-1,0])); // ==> exception</lang>

Julia

Linear algebra functions in Julia are largely implemented by calling functions from LAPACK. <lang julia> x = [1, 3, -5] y = [4, -2, -1] z = dot(x, y) </lang>

K

<lang K> +/1 3 -5 * 4 -2 -1 3

```  1 3 -5 _dot 4 -2 -1
```

3</lang>

LFE

<lang lisp>(defun dot-product (a b)

``` (: lists foldl #'+/2 0
(: lists zipwith #'*/2 a b)))
```

</lang>

Liberty BASIC

<lang lb>vectorA\$ = "1, 3, -5" vectorB\$ = "4, -2, -1" print "DotProduct of ";vectorA\$;" and "; vectorB\$;" is "; print DotProduct(vectorA\$, vectorB\$)

'arbitrary length vectorA\$ = "3, 14, 15, 9, 26" vectorB\$ = "2, 71, 18, 28, 1" print "DotProduct of ";vectorA\$;" and "; vectorB\$;" is "; print DotProduct(vectorA\$, vectorB\$)

end

function DotProduct(a\$, b\$)

```   DotProduct = 0
i = 1
while 1
x\$=word\$( a\$, i, ",")
y\$=word\$( b\$, i, ",")
if x\$="" or y\$="" then exit function
DotProduct = DotProduct + val(x\$)*val(y\$)
i = i+1
wend
```

end function </lang>

Logo

<lang logo>to dotprod :a :b

``` output apply "sum (map "product :a :b)
```

end

show dotprod [1 3 -5] [4 -2 -1]  ; 3</lang>

Logtalk

<lang logtalk>dot_product(A, B, Sum) :-

```   dot_product(A, B, 0, Sum).
```

dot_product([], [], Sum, Sum). dot_product([A| As], [B| Bs], Acc, Sum) :-

```   Acc2 is Acc + A*B,
dot_product(As, Bs, Acc2, Sum).</lang>
```

Lua

<lang lua>function dotprod(a, b)

``` local ret = 0
for i = 1, #a do
ret = ret + a[i] * b[i]
end
return ret
```

end

print(dotprod({1, 3, -5}, {4, -2, 1}))</lang>

Mathematica

<lang Mathematica>{1,3,-5}.{4,-2,-1}</lang>

MATLAB

The dot product operation is a built-in function that operates on vectors of arbitrary length. <lang matlab>A = [1 3 -5] B = [4 -2 -1] C = dot(A,B)</lang> For the Octave implimentation: <lang matlab>function C = DotPro(A,B)

``` C = sum( A.*B );
```

end</lang>

Maxima

<lang maxima>[1, 3, -5] . [4, -2, -1]; /* 3 */</lang>

Mercury

This will cause a software_error/1 exception if the lists are of different lengths. <lang mercury>:- module dot_product.

- interface.
- import_module io.
- pred main(io::di, io::uo) is det.
- implementation.
- import_module int, list.

main(!IO) :-

```   io.write_int([1, 3, -5] `dot_product` [4, -2, -1], !IO),
io.nl(!IO).
```
- func dot_product(list(int), list(int)) = int.

dot_product(As, Bs) =

```   list.foldl_corresponding((func(A, B, Acc) = Acc + A * B), As, Bs, 0).</lang>
```

MUMPS

<lang MUMPS>DOTPROD(A,B)

```;Returns the dot product of two vectors. Vectors are assumed to be stored as caret-delimited strings of numbers.
;If the vectors are not of equal length, a null string is returned.
QUIT:\$LENGTH(A,"^")'=\$LENGTH(B,"^") ""
NEW I,SUM
SET SUM=0
FOR I=1:1:\$LENGTH(A,"^") SET SUM=SUM+(\$PIECE(A,"^",I)*\$PIECE(B,"^",I))
KILL I
QUIT SUM</lang>
```

Nemerle

This will cause an exception if the arrays are different lengths. <lang Nemerle>using System; using System.Console; using Nemerle.Collections.NCollectionsExtensions;

module DotProduct {

```   DotProduct(x : array[int], y : array[int]) : int
{
\$[(a * b)|(a, b) in ZipLazy(x, y)].FoldLeft(0, _+_);
}

Main() : void
{
def arr1 = array[1, 3, -5]; def arr2 = array[4, -2, -1];
WriteLine(DotProduct(arr1, arr2));
}
```

}</lang>

NetRexx

<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary

whatsTheVectorVictor = [[double 1.0, 3.0, -5.0], [double 4.0, -2.0, -1.0]] dotProduct = Rexx dotProduct(whatsTheVectorVictor) say dotProduct.format(null, 2)

return

method dotProduct(vec1 = double[], vec2 = double[]) public constant returns double signals IllegalArgumentException

``` if vec1.length \= vec2.length then signal IllegalArgumentException('Vectors must be the same length')
```
``` scalarProduct = double 0.0
loop e_ = 0 to vec1.length - 1
scalarProduct = vec1[e_] * vec2[e_] + scalarProduct
end e_
```
``` return scalarProduct
```

method dotProduct(vecs = double[,]) public constant returns double signals IllegalArgumentException

``` return dotProduct(vecs[0], vecs[1])</lang>
```

newLISP

<lang newLISP>(define (dot-product x y)

``` (apply + (map * x y)))
```

(println (dot-product '(1 3 -5) '(4 -2 -1)))</lang>

Objective-C

<lang objc>#import <stdio.h>

1. import <stdint.h>
2. import <stdlib.h>
3. import <string.h>
4. import <objc/Object.h>

// this class exists to return a result between two // vectors: if vectors have different "size", valid // must be NO @interface VResult : Object {

```@private
double value;
BOOL valid;
```

} +(id)new: (double)v isValid: (BOOL)y; -(id)init: (double)v isValid: (BOOL)y; -(BOOL)isValid; -(double)value; @end

@implementation VResult +(id)new: (double)v isValid: (BOOL)y {

``` id s = [super new];
[s init: v isValid: y];
return s;
```

} -(id)init: (double)v isValid: (BOOL)y {

``` value = v;
valid = y;
return self;
```

} -(BOOL)isValid { return valid; } -(double)value { return value; } @end

@interface RCVector : Object {

```@private
double *vec;
uint32_t size;
```

} +(id)newWithArray: (double *)v ofLength: (uint32_t)l; -(id)initWithArray: (double *)v ofLength: (uint32_t)l; -(VResult *)dotProductWith: (RCVector *)v; -(uint32_t)size; -(double *)array; -(void)free; @end

@implementation RCVector +(id)newWithArray: (double *)v ofLength: (uint32_t)l {

``` id s = [super new];
[s initWithArray: v ofLength: l];
return s;
```

} -(id)initWithArray: (double *)v ofLength: (uint32_t)l {

``` size = l;
vec = malloc(sizeof(double) * l);
if ( vec != NULL ) {
memcpy(vec, v, sizeof(double)*l);
return self;
}
[super free];
return nil;
```

} -(void)free {

``` free(vec);
[super free];
```

} -(uint32_t)size { return size; } -(double *)array { return vec; } -(VResult *)dotProductWith: (RCVector *)v {

``` double r = 0.0;
uint32_t i, s;
double *v1;
if ( [self size] != [v size] ) return [VResult new: r isValid: NO];
s = [self size];
v1 = [v array];
for(i = 0; i < s; i++) {
r += vec[i] * v1[i];
}
return [VResult new: r isValid: YES];
```

} @end

double val1[] = { 1, 3, -5 }; double val2[] = { 4,-2, -1 };

int main() {

``` RCVector *v1 = [RCVector newWithArray: val1 ofLength: sizeof(val1)/sizeof(double)];
RCVector *v2 = [RCVector newWithArray: val2 ofLength: sizeof(val1)/sizeof(double)];
VResult *r = [v1 dotProductWith: v2];
if ( [r isValid] ) {
printf("%lf\n", [r value]);
} else {
fprintf(stderr, "length of vectors differ\n");
}
return 0;
```

}</lang>

Objeck

<lang objeck>bundle Default {

``` class DotProduct {
function : Main(args : String[]) ~ Nil {
DotProduct([1, 3, -5], [4, -2, -1])->PrintLine();
}

function : DotProduct(array_a : Int[], array_b : Int[]) ~ Int {
if(array_a = Nil) {
return 0;
};

if(array_b = Nil) {
return 0;
};

if(array_a->Size() <> array_b->Size()) {
return 0;
};

val := 0;
for(x := 0; x < array_a->Size(); x += 1;) {
val += (array_a[x] * array_b[x]);
};

return val;
}
}
```

}</lang>

OCaml

With lists: <lang ocaml>let dot = List.fold_left2 (fun z x y -> z +. x *. y) 0.

(*

1. dot [1.0; 3.0; -5.0] [4.0; -2.0; -1.0];;

- : float = 3.

• )</lang>

With arrays: <lang ocaml>let dot v u =

``` if Array.length v <> Array.length u
then invalid_arg "Different array lengths";
let times v u =
Array.mapi (fun i v_i -> v_i *. u.(i)) v
in Array.fold_left (+.) 0. (times v u)
```

(*

1. dot [| 1.0; 3.0; -5.0 |] [| 4.0; -2.0; -1.0 |];;

- : float = 3.

• )</lang>

Octave

See Dot product#MATLAB for an implementation. If we have a row-vector and a column-vector, we can use simply *. <lang octave>a = [1, 3, -5] b = [4, -2, -1] % or [4; -2; -1] and avoid transposition with ' disp( a * b' )  % ' means transpose</lang>

Oz

Vectors are represented as lists in this example. <lang oz>declare

``` fun {DotProduct Xs Ys}
{Length Xs} = {Length Ys} %% assert
{List.foldL {List.zip Xs Ys Number.'*'} Number.'+' 0}
end
```

in

``` {Show {DotProduct [1 3 ~5] [4 ~2 ~1]}}</lang>
```

PARI/GP

<lang parigp>dot(u,v)={

``` sum(i=1,#u,u[i]*v[i])
```

};</lang>

See Delphi

Perl

<lang perl>sub dotprod {

```       my(\$vec_a, \$vec_b) = @_;
die "they must have the same size\n" unless @\$vec_a == @\$vec_b;
my \$sum = 0;
\$sum += \$vec_a->[\$_] * \$vec_b->[\$_] for 0..\$#\$vec_a;
return \$sum;
```

}

my @vec_a = (1,3,-5); my @vec_b = (4,-2,-1);

print dotprod(\@vec_a,\@vec_b), "\n"; # 3</lang>

Perl 6

Works with: Rakudo version 2010.07

We use the square-bracket meta-operator to turn the infix operator `+` into a reducing list operator, and the guillemet meta-operator to vectorize the infix operator `*`. Length validation is automatic in this form. <lang perl6>say [+] (1, 3, -5) »*« (4, -2, -1);</lang>

PHP

<lang php><?php function dot_product(\$v1, \$v2) {

``` if (count(\$v1) != count(\$v2))
throw new Exception('Arrays have different lengths');
return array_sum(array_map('bcmul', \$v1, \$v2));
```

}

echo dot_product(array(1, 3, -5), array(4, -2, -1)), "\n"; ?></lang>

PicoLisp

<lang PicoLisp>(de dotProduct (A B)

```  (sum * A B) )
```

(dotProduct (1 3 -5) (4 -2 -1))</lang> Output:

`-> 3`

PL/I

<lang PL/I>get (n); begin;

```  declare (A(n), B(n)) float;
declare dot_product float;
```
```  get list (A);
get list (B);
dot_product = sum(a*b);
put (dot_product);
```

end;</lang>

PostScript

<lang postscript>/dotproduct{ /x exch def /y exch def /sum 0 def /i 0 def x length y length eq %Check if both arrays have the same length { x length{ /sum x i get y i get mul sum add def /i i 1 add def }repeat sum == } { -1 == }ifelse }def</lang>

Prolog

Works with SWI-Prolog. <lang Prolog>dot_product(L1, L2, N) :- maplist(mult, L1, L2, P), sumlist(P, N).

mult(A,B,C) :- C is A*B.</lang> Example :

``` ?- dot_product([1,3,-5], [4,-2,-1], N).
N = 3.```

PureBasic

<lang PureBasic>Procedure dotProduct(Array a(1),Array b(1))

``` Protected i, sum, length = ArraySize(a())
```
``` If ArraySize(a()) = ArraySize(b())
For i = 0 To length
sum + a(i) * b(i)
Next
EndIf
```
``` ProcedureReturn sum
```

EndProcedure

If OpenConsole()

``` Dim a(2)
Dim b(2)

a(0) = 1 : a(1) = 3 : a(2) = -5
b(0) = 4 : b(1) = -2 : b(2) = -1

PrintN(Str(dotProduct(a(),b())))

Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit"): Input()
CloseConsole()
```

EndIf</lang>

Python

<lang python>def dotp(a,b):

```   assert len(a) == len(b), 'Vector sizes must match'
return sum(aterm * bterm for aterm,bterm in zip(a, b))
```

if __name__ == '__main__':

```   a, b = [1, 3, -5], [4, -2, -1]
assert dotp(a,b) == 3</lang>
```

R

Here are several ways to do the task. <lang R>x <- c(1, 3, -5) y <- c(4, -2, -1)

sum(x*y) # compute products, then do the sum x %*% y # inner product

1. loop implementation

dotp <- function(x, y) { n <- length(x) if(length(y) != n) stop("invalid argument") s <- 0 for(i in 1:n) s <- s + x[i]*y[i] s }

dotp(x, y)</lang>

Racket

<lang Racket>

1. lang racket

(define (dot-product l r) (for/sum ([x l] [y r]) (* x y)))

(dot-product '(1 3 -5) '(4 -2 -1))

dot-product works on sequences such as vectors

(dot-product #(1 2 3) #(4 5 6)) </lang>

Rascal

<lang Rascal>import List;

public int dotProduct(list[int] L, list[int] M){ result = 0; if(size(L) == size(M)) { while(size(L) >= 1) { result += (head(L) * head(M)); L = tail(L); M = tail(M); } return result; } else { throw "vector sizes must match"; } }</lang>

Alternative solution

If a matrix is represented by a relation of <x-coordinate, y-coordinate, value>, then function below can be used to find the Dot product. <lang Rascal>import Prelude;

public real matrixDotproduct(rel[real x, real y, real v] column1, rel[real x, real y, real v] column2){ return (0.0 | it + v1*v2 | <x1,y1,v1> <- column1, <x2,y2,v2> <- column2, y1==y2); }

//a matrix, given by a relation of x-coordinate, y-coordinate, value. public rel[real x, real y, real v] matrixA = { <0.0,0.0,12.0>, <0.0,1.0, 6.0>, <0.0,2.0,-4.0>, <1.0,0.0,-51.0>, <1.0,1.0,167.0>, <1.0,2.0,24.0>, <2.0,0.0,4.0>, <2.0,1.0,-68.0>, <2.0,2.0,-41.0> };</lang>

REXX

Checks could've been added to the REXX code to insure that the vector elements are numeric. <lang rexx>/*REXX program computes the dot product of two equal size vectors. */ vectorA = ' 1 3 -5 ' /*populate vectorA with numbers, */ vectorB = ' 4 -2 -1 ' /* ∙∙∙ and the same for vectorB. */ say /*display a blank line. */ say 'vector A='vectorA /*echo the vectorA's values. */ say 'vector B='vectorB /*echo the vectorB's values. */ say /*display another blank line. */ p = dotProd(vectorA, vectorB) /*go and compute the dot product.*/ say 'dot product = ' p /*show and tell the dot product. */ say /*display another a blank line. */ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────DOTPROD subroutine──────────────────*/ dotProd: procedure; parse arg A,B /*compute the dot product. */ sum = 0 /*initilize the sum to 0 (zero). */ lenA = words(A) /*length of vector A in words. */ lenB = words(B) /*length of vector B in words. */

if lenA\==lenB then do

```                    say
say '*** error! ***'
say "vectors aren't the same size:"
say 'vectorA length='lenA
say 'vectorB length='lenB
say
exit 13           /*exit with  return code 13.     */
end
```
``` do j=1  for lenA                     /*multiply each number in vectors*/
sum = sum +   word(A,j) * word(B,j)  /*∙∙∙ and add the product to SUM.*/
end   /*j*/
```

return sum /*return the SUM to the invoker. */</lang> output

```vector A=  1   3  -5
vector B=  4  -2  -1

dot product =  3
```

RLaB

In its simplest form dot product is a composition of two functions: element-by-element multiplication '.*' followed by sumation of an array. Consider an example: <lang RLaB>x = rand(1,10); y = rand(1,10); s = sum( x .* y );</lang> Warning: element-by-element multiplication is matrix optimized. As the interpretation of the matrix optimization is quite general, and unique to RLaB, any two matrices can be so multiplied irrespective of their dimensions. It is up to user to check whether in his/her case the matrix optimization needs to be restricted, and then to implement restrictions in his/her code.

Ruby

With the standard library, require 'matrix' and call Vector#inner_product. <lang ruby>irb(main):001:0> require 'matrix' => true irb(main):002:0> Vector[1, 3, -5].inner_product Vector[4, -2, -1] => 3</lang> Or implement dot product. <lang ruby>class Array

``` def dot_product(other)
raise "not the same size!" if self.length != other.length
self.zip(other).inject(0) {|dp, (a, b)| dp += a*b}
end
```

end

p [1, 3, -5].dot_product [4, -2, -1] # => 3</lang>

Run BASIC

<lang runbasic>v1\$ = "1, 3, -5" v2\$ = "4, -2, -1"

print "DotProduct of ";v1\$;" and "; v2\$;" is ";dotProduct(v1\$,v2\$) end

function dotProduct(a\$, b\$)

```   while word\$(a\$,i + 1,",") <> ""
i = i + 1
v1\$=word\$(a\$,i,",")
v2\$=word\$(b\$,i,",")
dotProduct = dotProduct + val(v1\$) * val(v2\$)
wend
```

end function</lang>

Sather

Built-in class VEC "implements" euclidean (geometric) vectors. <lang sather>class MAIN is

``` main is
x ::= #VEC(|1.0, 3.0, -5.0|);
y ::= #VEC(|4.0, -2.0, -1.0|);
#OUT + x.dot(y) + "\n";
end;
```

end;</lang>

Scala

Works with: Scala version 2.8

<lang scala>class Dot[T](v1: Seq[T])(implicit n: Numeric[T]) {

``` import n._
def dot(v2: Seq[T]) = {
require(v1.length == v2.length)
v1 zip v2 map Function.tupled(_*_) sum
}
```

}

implicit def toDot[T : Numeric](v1: Seq[T]) = new Dot(v1) val v1 = List(1, 3, -5) val v2 = List(4, -2, -1) println(v1 dot v2)</lang>

Seed7

<lang seed7>\$ include "seed7_05.s7i";

\$ syntax expr: .().dot.() is -> 6; # priority of dot operator

const func integer: (in array integer: a) dot (in array integer: b) is func

``` result
var integer: sum is 0;
local
var integer: index is 0;
begin
if length(a) <> length(b) then
raise RANGE_ERROR;
else
for index range 1 to length(a) do
sum +:= a[index] * b[index];
end for;
end if;
end func;

```

const proc: main is func

``` begin
writeln([](1, 3, -5) dot [](4, -2, -1));
end func;</lang>
```

Scheme

Works with: Scheme version R${\displaystyle ^{5}}$RS

<lang scheme>(define (dot-product a b)

``` (apply + (map * a b)))
```

(display (dot-product '(1 3 -5) '(4 -2 -1))) (newline)</lang> Output:

`3`

Slate

<lang slate>v@(Vector traits) <dot> w@(Vector traits) "Dot-product." [

``` (0 below: (v size min: w size)) inject: 0 into:
[| :sum :index | sum + ((v at: index) * (w at: index))]
```

].</lang>

Smalltalk

Works with: GNU Smalltalk

<lang smalltalk>Array extend [

``` * anotherArray [
|acc| acc := 0.
self with: anotherArray collect: [ :a :b |
acc := acc + ( a * b )
].
^acc
]
```

]

( #(1 3 -5) * #(4 -2 -1 ) ) printNl.</lang>

SNOBOL4

<lang snobol4> define("dotp(a,b)sum,i")  :(dotp_end) dotp i = 1; sum = 0 loop sum = sum + (a * b)

```       i = i + 1 ?a :s(loop)
dotp = sum      :(return)
```

dotp_end

```       a = array(3); a<1> = 1; a<2> = 3; a<3> = -5;
b = array(3); b<1> = 4; b<2> = -2; b<3> = -1;
output = dotp(a,b)
```

end</lang>

SPARK

Works with SPARK GPL 2010 and GPS GPL 2010.

By defining numeric subtypes with suitable ranges we can prove statically that there will be no run-time errors. (The Simplifier leaves 2 VCs unproven, but these are clearly provable by inspection.)

The precondition enforces equality of the ranges of the two vectors. <lang ada>with Spark_IO; --# inherit Spark_IO; --# main_program; procedure Dot_Product_Main --# global in out Spark_IO.Outputs; --# derives Spark_IO.Outputs from *; is

```  Limit : constant := 1000;
type V_Elem is range -Limit .. Limit;
V_Size : constant := 100;
type V_Index is range 1 .. V_Size;
type Vector is array(V_Index range <>) of V_Elem;
```
```  type V_Prod is range -(Limit**2)*V_Size .. (Limit**2)*V_Size;
--# assert V_Prod'Base is Integer;
```
```  subtype Index3 is V_Index range 1 .. 3;
subtype Vector3 is Vector(Index3);
Vect1 : constant Vector3 := Vector3'(1, 3, -5);
Vect2 : constant Vector3 := Vector3'(4, -2, -1);
```
```  function Dot_Product(V1, V2 : Vector) return V_Prod
--# pre  V1'First = V2'First
--#  and V1'Last  = V2'Last;
is
Sum : V_Prod := 0;
begin
for I in V_Index range V1'Range
--# assert Sum in -(Limit**2)*V_Prod(I-1) .. (Limit**2)*V_Prod(I-1);
loop
Sum := Sum + V_Prod(V1(I)) * V_Prod(V2(I));
end loop;
return Sum;
end Dot_Product;
```

begin

```  Spark_IO.Put_Integer(File  => Spark_IO.Standard_Output,
Item  => Integer(Dot_Product(Vect1, Vect2)),
Width => 6,
Base  => 10);
```

end Dot_Product_Main;</lang> The output:

`     3`

SQL

ANSI sql does not support functions and is missing some other concepts that would be needed for a general case implementation of inner product (column names and tables would need to be first class in SQL -- capable of being passed to functions).

However, inner product is fairly simple to specify in SQL.

Given two tables `A` and `B` where A has key columns `i` and `j` and B has key columns `j` and `k` and both have value columns `N`, the inner product of A and B would be: <lang sql>select i, k, sum(A.N*B.N) as N

```       from A inner join B on A.j=B.j
group by i, k</lang>
```

Standard ML

With lists: <lang sml>val dot = ListPair.foldlEq Real.*+ 0.0

(* - dot ([1.0, 3.0, ~5.0], [4.0, ~2.0, ~1.0]); val it = 3.0 : real

• )</lang>

With vectors: <lang sml>fun dot (v, u) = (

``` if Vector.length v <> Vector.length u then
raise ListPair.UnequalLengths
else ();
Vector.foldli (fn (i, v_i, z) => v_i * Vector.sub (u, i) + z) 0.0 v
)
```

(* - dot (#[1.0, 3.0, ~5.0], #[4.0, ~2.0, ~1.0]); val it = 3.0 : real

• )</lang>

Tcl

Library: Tcllib (Package: math::linearalgebra)

<lang tcl>package require math::linearalgebra

set a {1 3 -5} set b {4 -2 -1} set dotp [::math::linearalgebra::dotproduct \$a \$b] proc pp vec {return \[[join \$vec ,]\]} puts "[pp \$a] \u2219 [pp \$b] = \$dotp"</lang> Output:

```[1,3,-5] ∙ [4,-2,-1] = 3.0
```

TI-89 BASIC

```dotP([1, 3, –5], [4, –2, –1])
3```

Ursala

A standard library function for dot products of floating point numbers exists, but a new one can be defined for integers as shown using the map operator (`*`) with the zip suffix (`p`) to construct a "zipwith" operator (`*p`), which operates on the integer `product` function. A catchable exception is thrown if the list lengths are unequal. This function is then composed (`+`) with a cumulative summation function, which is constructed from the binary `sum` function, and the reduction operator (`:-`) with `0` specified for the vacuous sum. <lang Ursala>#import int

dot = sum:-0+ product*p

1. cast %z

test = dot(<1,3,-5>,<4,-2,-1>)</lang> output:

```3
```

XPL0

<lang XPL0>include c:\cxpl\codes;

func DotProd(U, V, L); int U, V, L; int S, I; [S:= 0; for I:= 0 to L-1 do S:= S + U(I)*V(I); return S; ];

[IntOut(0, DotProd([1, 3, -5], [4, -2, -1], 3)); CrLf(0); ]</lang>

Output:

```3
```