Element-wise operations

From Rosetta Code
Revision as of 19:18, 28 October 2016 by rosettacode>Guih.red
Task
Element-wise operations
You are encouraged to solve this task according to the task description, using any language you may know.

This task is similar to:


Task

Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.

Implement:

  •   addition
  •   subtraction
  •   multiplication
  •   division
  •   exponentiation


Extend the task if necessary to include additional basic operations, which should not require their own specialised task.

Ada

Using Generics, the task is quite trivial in Ada. Here is the main program:

<lang Ada>with Ada.Text_IO, Matrix_Scalar;

procedure Scalar_Ops is 

  subtype T is Integer range 1 .. 3;

  package M is new Matrix_Scalar(T, T, Integer);

  -- the functions to solve the task
       function "+" is new M.Func("+");
       function "-" is new M.Func("-");
       function "*" is new M.Func("*");
       function "/" is new M.Func("/");
       function "**" is new M.Func("**");
       function "mod" is new M.Func("mod");

  -- for output purposes, we need a Matrix->String conversion
       function Image is new M.Image(Integer'Image);

  A: M.Matrix := ((1,2,3),(4,5,6),(7,8,9)); -- something to begin with

begin 

  Ada.Text_IO.Put_Line("  Initial M=" & Image(A));
  Ada.Text_IO.Put_Line("        M+2=" & Image(A+2));
  Ada.Text_IO.Put_Line("        M-2=" & Image(A-2));
  Ada.Text_IO.Put_Line("        M*2=" & Image(A*2));
  Ada.Text_IO.Put_Line("        M/2=" & Image(A/2));
  Ada.Text_IO.Put_Line("  square(M)=" & Image(A ** 2));
  Ada.Text_IO.Put_Line("    M mod 2=" & Image(A mod 2));
  Ada.Text_IO.Put_Line("(M*2) mod 3=" & Image((A*2) mod 3));

end Scalar_Ops;</lang>

Output:
  Initial M=((1,2,3),(4,5,6),(7,8,9))                                                      
        M+2=((3,4,5),(6,7,8),(9,10,11))                                                    
        M-2=((-1,0,1),(2,3,4),(5,6,7))
        M*2=((2,4,6),(8,10,12),(14,16,18))                                                 
        M/2=((0,1,1),(2,2,3),(3,4,4))
  square(M)=((1,4,9),(16,25,36),(49,64,81))
    M mod 2=((1,0,1),(0,1,0),(1,0,1))
(M*2) mod 3=((2,1,0),(2,1,0),(2,1,0))


Our main program uses a generic package Matrix_Scalar. Here is the specification:

<lang Ada>generic 

  type Rows is (<>);
  type Cols is (<>);
  type Num is private;

package Matrix_Scalar is 

  type Matrix is array(Rows, Cols) of Num;

  generic
     with function F(L, R: Num) return Num;
  function Func(Left: Matrix; Right: Num) return Matrix;

  generic
     with function Image(N: Num) return String;
  function Image(M: Matrix) return String;

end Matrix_Scalar;</lang>

And here is the corresponding implementation. Note that the function Image (which we just use to output the results) takes much more lines than the function Func we need for actually solving the task:

<lang Ada>package body Matrix_Scalar is 

  function Func(Left: Matrix; Right: Num) return Matrix is
     Result: Matrix;
  begin
     for R in Rows loop
        for C in Cols loop
           Result(R,C) := F(Left(R,C), Right);
        end loop;
     end loop;
     return Result;
  end Func;

  function Image(M: Matrix) return String is

     function Img(R: Rows) return String is

        function I(C: Cols) return String is
           S: String := Image(M(R,C));
           L: Positive := S'First;
        begin
           while S(L) = ' ' loop
              L := L + 1;
           end loop;
           if C=Cols'Last then
              return S(L .. S'Last);
           else
              return S(L .. S'Last) & "," & I(Cols'Succ(C));
           end if;
        end I;

        Column: String := I(Cols'First);
     begin
        if R=Rows'Last then
           return "(" & Column & ")";
        else
           return "(" & Column & ")," & Img(Rows'Succ(R));
        end if;
     end Img;

  begin
     return("(" & Img(Rows'First) & ")");
  end Image;

end Matrix_Scalar;</lang>

ALGOL 68

Translation of: D

Note: This specimen retains the original D coding style.

Works with: ALGOL 68 version Revision 1 - no extensions to language used.
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny.

<lang algol68>#!/usr/local/bin/a68g --script #

MODE SCALAR = REAL; FORMAT scalar fmt = $g(0, 2)$;

MODE MATRIX = [3, 3]SCALAR; FORMAT vector fmt = $"("n(2 UPB LOC MATRIX - 2 LWB LOC MATRIX)(f(scalar fmt)", ")f(scalar fmt)")"$; FORMAT matrix fmt = $"("n(1 UPB LOC MATRIX - 1 LWB LOC MATRIX)(f(vector fmt)","l" ")f(vector fmt)")"$;

PROC elementwise op = (PROC(SCALAR, SCALAR)SCALAR op, MATRIX a, UNION(SCALAR, MATRIX) b)MATRIX: ( 

 [LWB a:UPB a, 2 LWB a:2 UPB a]SCALAR out;
 CASE b IN
 (SCALAR b):
   FOR i FROM LWB out TO UPB out DO
     FOR j FROM 2 LWB out TO 2 UPB out DO
       out[i, j]:=op(a[i, j], b)
     OD
   OD,
 (MATRIX b):
   FOR i FROM LWB out TO UPB out DO
     FOR j FROM 2 LWB out TO 2 UPB out DO
       out[i, j]:=op(a[i, j], b[i, j])
     OD
   OD
 ESAC;
 out

);

PROC plus = (SCALAR a, b)SCALAR: a+b, 

    minus = (SCALAR a, b)SCALAR: a-b,
    times = (SCALAR a, b)SCALAR: a*b,
    div   = (SCALAR a, b)SCALAR: a/b,
    pow   = (SCALAR a, b)SCALAR: a**b;

main:( 

   SCALAR scalar := 10;
   MATRIX matrix = (( 7, 11, 13),
                    (17, 19, 23),
                    (29, 31, 37));

   printf(($f(matrix fmt)";"l$,
     elementwise op(plus,  matrix, scalar),
     elementwise op(minus, matrix, scalar),
     elementwise op(times, matrix, scalar),
     elementwise op(div,   matrix, scalar),
     elementwise op(pow,   matrix, scalar),

     elementwise op(plus,  matrix, matrix),
     elementwise op(minus, matrix, matrix),
     elementwise op(times, matrix, matrix),
     elementwise op(div,   matrix, matrix),
     elementwise op(pow,   matrix, matrix)
 ))

)</lang>

Output:
((17.00, 21.00, 23.00),
 (27.00, 29.00, 33.00),
 (39.00, 41.00, 47.00));
((-3.00, 1.00, 3.00),
 (7.00, 9.00, 13.00),
 (19.00, 21.00, 27.00));
((70.00, 110.00, 130.00),
 (170.00, 190.00, 230.00),
 (290.00, 310.00, 370.00));
((.70, 1.10, 1.30),
 (1.70, 1.90, 2.30),
 (2.90, 3.10, 3.70));
((282475249.00, 25937424601.00, 137858491849.00),
 (2015993900449.00, 6131066257800.99, 41426511213648.90),
 (420707233300200.00, 819628286980799.00, 4808584372417840.00));
((14.00, 22.00, 26.00),
 (34.00, 38.00, 46.00),
 (58.00, 62.00, 74.00));
((.00, .00, .00),
 (.00, .00, .00),
 (.00, .00, .00));
((49.00, 121.00, 169.00),
 (289.00, 361.00, 529.00),
 (841.00, 961.00, 1369.00));
((1.00, 1.00, 1.00),
 (1.00, 1.00, 1.00),
 (1.00, 1.00, 1.00));
((823543.00, 285311670611.00, 302875106592253.00),
 (827240261886340000000.00, 1978419655660300000000000.00, 20880467999847700000000000000000.00),
 (2567686153161210000000000000000000000000000.00, 17069174130723200000000000000000000000000000000.00, 10555134955777600000000000000000000000000000000000000000000.00));

BBC BASIC

All except exponentiation (^) are native operations in BBC BASIC. <lang bbcbasic> DIM a(1,2), b(1,2), c(1,2) 

     a() = 7, 8, 7, 4, 0, 9 : b() = 4, 5, 1, 6, 2, 1
     
     REM Matrix-Matrix:
     c() = a() + b() : PRINT FNshowmm(a(), "+", b(), c())
     c() = a() - b() : PRINT FNshowmm(a(), "-", b(), c())
     c() = a() * b() : PRINT FNshowmm(a(), "*", b(), c())
     c() = a() / b() : PRINT FNshowmm(a(), "/", b(), c())
     PROCpowmm(a(), b(), c()) : PRINT FNshowmm(a(), "^", b(), c()) '
     
     REM Matrix-Scalar:
     c() = a() + 3 : PRINT FNshowms(a(), "+", 3, c())
     c() = a() - 3 : PRINT FNshowms(a(), "-", 3, c())
     c() = a() * 3 : PRINT FNshowms(a(), "*", 3, c())
     c() = a() / 3 : PRINT FNshowms(a(), "/", 3, c())
     PROCpowms(a(), 3, c()) : PRINT FNshowms(a(), "^", 3, c())
     END
     
     DEF PROCpowmm(a(), b(), c())
     LOCAL i%, j%
     FOR i% = 0 TO DIM(a(),1)
       FOR j% = 0 TO DIM(a(),2)
         c(i%,j%) = a(i%,j%) ^ b(i%,j%)
       NEXT
     NEXT
     ENDPROC
     
     DEF PROCpowms(a(), b, c())
     LOCAL i%, j%
     FOR i% = 0 TO DIM(a(),1)
       FOR j% = 0 TO DIM(a(),2)
         c(i%,j%) = a(i%,j%) ^ b
       NEXT
     NEXT
     ENDPROC
     
     DEF FNshowmm(a(), op$, b(), c())
     = FNlist(a()) + " " + op$ + " " + FNlist(b()) + " = " + FNlist(c())
     
     DEF FNshowms(a(), op$, b, c())
     = FNlist(a()) + " " + op$ + " " + STR$(b) + " = " + FNlist(c())
     
     DEF FNlist(a())
     LOCAL i%, j%, a$
     a$ = "["
     FOR i% = 0 TO DIM(a(),1)
       a$ += "["
       FOR j% = 0 TO DIM(a(),2)
         a$ += STR$(a(i%,j%)) + ", "
       NEXT
       a$ = LEFT$(LEFT$(a$)) + "]"
     NEXT
     = a$ + "]"</lang>
Output:
[[7, 8, 7][4, 0, 9]] + [[4, 5, 1][6, 2, 1]] = [[11, 13, 8][10, 2, 10]]
[[7, 8, 7][4, 0, 9]] - [[4, 5, 1][6, 2, 1]] = [[3, 3, 6][-2, -2, 8]]
[[7, 8, 7][4, 0, 9]] * [[4, 5, 1][6, 2, 1]] = [[28, 40, 7][24, 0, 9]]
[[7, 8, 7][4, 0, 9]] / [[4, 5, 1][6, 2, 1]] = [[1.75, 1.6, 7][0.666666667, 0, 9]]
[[7, 8, 7][4, 0, 9]] ^ [[4, 5, 1][6, 2, 1]] = [[2401, 32768, 7][4096, 0, 9]]

[[7, 8, 7][4, 0, 9]] + 3 = [[10, 11, 10][7, 3, 12]]
[[7, 8, 7][4, 0, 9]] - 3 = [[4, 5, 4][1, -3, 6]]
[[7, 8, 7][4, 0, 9]] * 3 = [[21, 24, 21][12, 0, 27]]
[[7, 8, 7][4, 0, 9]] / 3 = [[2.33333333, 2.66666667, 2.33333333][1.33333333, 0, 3]]
[[7, 8, 7][4, 0, 9]] ^ 3 = [[343, 512, 343][64, 0, 729]]

C

Matrices are 2D double arrays. <lang c>#include <math.h>

  1. define for_i for(i = 0; i < h; i++)
  2. define for_j for(j = 0; j < w; j++)
  3. define _M double**
  4. define OPM(name, _op_) \

void eop_##name(_M a, _M b, _M c, int w, int h){int i,j;\ for_i for_j c[i][j] = a[i][j] _op_ b[i][j];} OPM(add, +);OPM(sub, -);OPM(mul, *);OPM(div, /);

  1. define OPS(name, res) \

void eop_s_##name(_M a, double s, _M b, int w, int h) {double x;int i,j;\ for_i for_j {x = a[i][j]; b[i][j] = res;}} OPS(mul, x*s);OPS(div, x/s);OPS(add, x+s);OPS(sub, x-s);OPS(pow, pow(x, s));</lang>

Clojure

This function is for vector matrices; for list matrices, change the (vector?) function to the (list?) function and remove all the (vec) functions. <lang clojure>(defn initial-mtx [i1 i2 value] 

 (vec (repeat i1 (vec (repeat i2 value)))))

(defn operation [f mtx1 mtx2] 

 (if (vector? mtx1)
   (vec (map #(vec (map f %1 %2)) mtx1 mtx2)))
   (recur f (initial-mtx (count mtx2) (count (first mtx2)) mtx1) mtx2) 
 ))</lang>

The mtx1 argument can either be a matrix or scalar; the function will sort the difference.

Common Lisp

Element-wise matrix-matrix operations. Matrices are represented as 2D-arrays. <lang lisp>(defun element-wise-matrix (fn A B) 

 (let* ((len (array-total-size A))
        (m   (car (array-dimensions A)))
        (n   (cadr (array-dimensions A)))
        (C   (make-array `(,m ,n) :initial-element 0.0d0)))
   
   (loop for i from 0 to (1- len) do
        (setf (row-major-aref C i) 
              (funcall fn
                       (row-major-aref A i)
                       (row-major-aref B i))))
   C))
A.+B, A.-B, A.*B, A./B, A.^B.

(defun m+ (A B) (element-wise-matrix #'+ A B)) (defun m- (A B) (element-wise-matrix #'- A B)) (defun m* (A B) (element-wise-matrix #'* A B)) (defun m/ (A B) (element-wise-matrix #'/ A B)) (defun m^ (A B) (element-wise-matrix #'expt A B))</lang>

Elementwise scalar-matrix operations. <lang lisp>(defun element-wise-scalar (fn A c) 

 (let* ((len (array-total-size A))
        (m   (car (array-dimensions A)))
        (n   (cadr (array-dimensions A)))
        (B   (make-array `(,m ,n) :initial-element 0.0d0)))
   
   (loop for i from 0 to (1- len) do
        (setf (row-major-aref B i) 
              (funcall fn
                       (row-major-aref A i)
                       c)))
   B))
c.+A, A.-c, c.*A, A./c, A.^c.

(defun .+ (c A) (element-wise-scalar #'+ A c)) (defun .- (A c) (element-wise-scalar #'- A c)) (defun .* (c A) (element-wise-scalar #'* A c)) (defun ./ (A c) (element-wise-scalar #'/ A c)) (defun .^ (A c) (element-wise-scalar #'expt A c))</lang>

D

<lang d>import std.stdio, std.typetuple, std.traits;

T[][] elementwise(string op, T, U)(in T[][] A, in U B) { 

 auto R = new typeof(return)(A.length, A[0].length);
 foreach (r, row; A)
   R[r][] = mixin("row[] " ~ op ~ (isNumeric!U ? "B" : "B[r][]"));
 return R;

}

void main() { 

 const M = [[3, 5, 7], [1, 2, 3], [2, 4, 6]];
 foreach (op; TypeTuple!("+", "-", "*", "/", "^^"))
   writefln("%s:\n[%([%(%d, %)],\n %)]]\n\n[%([%(%d, %)],\n %)]]\n",
            op, elementwise!op(M, 2), elementwise!op(M, M));

}</lang>

Output:
+:
[[5, 7, 9],
 [3, 4, 5],
 [4, 6, 8]]

[[6, 10, 14],
 [2, 4, 6],
 [4, 8, 12]]

-:
[[1, 3, 5],
 [-1, 0, 1],
 [0, 2, 4]]

[[0, 0, 0],
 [0, 0, 0],
 [0, 0, 0]]

*:
[[6, 10, 14],
 [2, 4, 6],
 [4, 8, 12]]

[[9, 25, 49],
 [1, 4, 9],
 [4, 16, 36]]

/:
[[1, 2, 3],
 [0, 1, 1],
 [1, 2, 3]]

[[1, 1, 1],
 [1, 1, 1],
 [1, 1, 1]]

^^:
[[9, 25, 49],
 [1, 4, 9],
 [4, 16, 36]]

[[27, 3125, 823543],
 [1, 4, 27],
 [4, 256, 46656]]

This alternative version offers more guarantees, same output: <lang d>import std.stdio, std.typetuple, std.traits;

T[][] elementwise(string op, T, U)(in T[][] A, in U B) @safe pure nothrow if (isNumeric!U || (isArray!U && isArray!(ForeachType!U) && 

   isNumeric!(ForeachType!(ForeachType!U)))) {
   static if (!isNumeric!U)
       assert(A.length == B.length);
   if (!A.length)
       return null;
   auto R = new typeof(return)(A.length, A[0].length);

   foreach (immutable r, const row; A)
       static if (isNumeric!U) {
           R[r][] = mixin("row[] " ~ op ~ "B");
       } else {
           assert(row.length == B[r].length);
           R[r][] = mixin("row[] " ~ op ~ "B[r][]");
       }

   return R;

}

void main() { 

   enum scalar = 2;
   enum matFormat = "[%([%(%d, %)],\n %)]]\n";
   immutable matrix = [[3, 5, 7],
                       [1, 2, 3],
                       [2, 4, 6]];

   foreach (immutable op; TypeTuple!("+", "-", "*", "/", "^^")) {
       writeln(op, ":");
       writefln(matFormat, elementwise!op(matrix, scalar));
       writefln(matFormat, elementwise!op(matrix, matrix));
   }

}</lang>

Go

A package, which can be referred to in other, higher-order tasks. <lang go>package element

import ( 

   "fmt"
   "math"

)

type Matrix struct { 

   ele    []float64
   stride int

}

func MatrixFromRows(rows [][]float64) Matrix { 

   if len(rows) == 0 {
       return Matrix{nil, 0}
   }
   m := Matrix{make([]float64, len(rows)*len(rows[0])), len(rows[0])}
   for rx, row := range rows {
       copy(m.ele[rx*m.stride:(rx+1)*m.stride], row)
   }
   return m

}

func like(m Matrix) Matrix { 

   return Matrix{make([]float64, len(m.ele)), m.stride}

}

func (m Matrix) String() string { 

   s := ""
   for e := 0; e < len(m.ele); e += m.stride {
       s += fmt.Sprintf("%6.3f \n", m.ele[e:e+m.stride])
   }
   return s

}

type binaryFunc64 func(float64, float64) float64

func elementWiseMM(m1, m2 Matrix, f binaryFunc64) Matrix { 

   z := like(m1)
   for i, m1e := range m1.ele {
       z.ele[i] = f(m1e, m2.ele[i])
   }
   return z

}

func elementWiseMS(m Matrix, s float64, f binaryFunc64) Matrix { 

   z := like(m)
   for i, e := range m.ele {
       z.ele[i] = f(e, s)
   }
   return z

}

func add(a, b float64) float64 { return a + b } func sub(a, b float64) float64 { return a - b } func mul(a, b float64) float64 { return a * b } func div(a, b float64) float64 { return a / b } func exp(a, b float64) float64 { return math.Pow(a, b) }

func AddMatrix(m1, m2 Matrix) Matrix { return elementWiseMM(m1, m2, add) } func SubMatrix(m1, m2 Matrix) Matrix { return elementWiseMM(m1, m2, sub) } func MulMatrix(m1, m2 Matrix) Matrix { return elementWiseMM(m1, m2, mul) } func DivMatrix(m1, m2 Matrix) Matrix { return elementWiseMM(m1, m2, div) } func ExpMatrix(m1, m2 Matrix) Matrix { return elementWiseMM(m1, m2, exp) }

func AddScalar(m Matrix, s float64) Matrix { return elementWiseMS(m, s, add) } func SubScalar(m Matrix, s float64) Matrix { return elementWiseMS(m, s, sub) } func MulScalar(m Matrix, s float64) Matrix { return elementWiseMS(m, s, mul) } func DivScalar(m Matrix, s float64) Matrix { return elementWiseMS(m, s, div) } func ExpScalar(m Matrix, s float64) Matrix { return elementWiseMS(m, s, exp) }</lang> Package use: <lang go>package main

import ( 

   "fmt"

   "element"

)

func h(heading string, m element.Matrix) { 

   fmt.Println(heading)
   fmt.Print(m)

}

func main() { 

   m1 := element.MatrixFromRows([][]float64{{3, 1, 4}, {1, 5, 9}})
   m2 := element.MatrixFromRows([][]float64{{2, 7, 1}, {8, 2, 8}})
   h("m1:", m1)
   h("m2:", m2)
   fmt.Println()
   h("m1 + m2:", element.AddMatrix(m1, m2))
   h("m1 - m2:", element.SubMatrix(m1, m2))
   h("m1 * m2:", element.MulMatrix(m1, m2))
   h("m1 / m2:", element.DivMatrix(m1, m2))
   h("m1 ^ m2:", element.ExpMatrix(m1, m2))
   fmt.Println()
   s := .5
   fmt.Println("s:", s)
   h("m1 + s:", element.AddScalar(m1, s))
   h("m1 - s:", element.SubScalar(m1, s))
   h("m1 * s:", element.MulScalar(m1, s))
   h("m1 / s:", element.DivScalar(m1, s))
   h("m1 ^ s:", element.ExpScalar(m1, s))

}</lang>

Output:
m1:
[ 3.000  1.000  4.000] 
[ 1.000  5.000  9.000] 
m2:
[ 2.000  7.000  1.000] 
[ 8.000  2.000  8.000] 

m1 + m2:
[ 5.000  8.000  5.000] 
[ 9.000  7.000 17.000] 
m1 - m2:
[ 1.000 -6.000  3.000] 
[-7.000  3.000  1.000] 
m1 * m2:
[ 6.000  7.000  4.000] 
[ 8.000 10.000 72.000] 
m1 / m2:
[ 1.500  0.143  4.000] 
[ 0.125  2.500  1.125] 
m1 ^ m2:
[ 9.000  1.000  4.000] 
[ 1.000 25.000 43046721.000] 

s: 0.5
m1 + s:
[ 3.500  1.500  4.500] 
[ 1.500  5.500  9.500] 
m1 - s:
[ 2.500  0.500  3.500] 
[ 0.500  4.500  8.500] 
m1 * s:
[ 1.500  0.500  2.000] 
[ 0.500  2.500  4.500] 
m1 / s:
[ 6.000  2.000  8.000] 
[ 2.000 10.000 18.000] 
m1 ^ s:
[ 1.732  1.000  2.000] 
[ 1.000  2.236  3.000]

Haskell

Matrices are represented here as Immutable Arrays. <lang Haskell>{-# OPTIONS_GHC -fno-warn-duplicate-constraints #-} {-# LANGUAGE RankNTypes #-}

import Data.Array (Array, Ix) import Data.Array.Base

-- | Element-wise combine the values of two arrays 'a' and 'b' with 'f'. -- 'a' and 'b' must have the same bounds. zipWithA :: (IArray arr a, IArray arr b, IArray arr c, Ix i) => 

           (a -> b -> c) -> arr i a -> arr i b -> arr i c

zipWithA f a b = 

 case bounds a of
   ba ->
     if ba /= bounds b
     then error "elemwise: bounds mismatch"
     else
       let n = numElements a
       in unsafeArray ba [ (i, f (unsafeAt a i) (unsafeAt b i))
                         | i <- [0 .. n - 1]]

-- Convenient aliases for matrix-matrix element-wise operations. type ElemOp a b c = (IArray arr a, IArray arr b, IArray arr c, Ix i) => 

                   arr i a -> arr i b -> arr i c

type ElemOp1 a = ElemOp a a a

infixl 6 +:, -: infixl 7 *:, /:, `divE`

(+:), (-:), (*:) :: (Num a) => ElemOp1 a (+:) = zipWithA (+) (-:) = zipWithA (-) (*:) = zipWithA (*)

divE :: (Integral a) => ElemOp1 a divE = zipWithA div

(/:) :: (Fractional a) => ElemOp1 a (/:) = zipWithA (/)

infixr 8 ^:, **:, ^^:

(^:) :: (Num a, Integral b) => ElemOp a b a (^:) = zipWithA (^)

(**:) :: (Floating a) => ElemOp1 a (**:) = zipWithA (**)

(^^:) :: (Fractional a, Integral b) => ElemOp a b a (^^:) = zipWithA (^^)

-- Convenient aliases for matrix-scalar element-wise operations. type ScalarOp a b c = (IArray arr a, IArray arr c, Ix i) => 

                     arr i a -> b -> arr i c

type ScalarOp1 a = ScalarOp a a a

samap :: (IArray arr a, IArray arr c, Ix i) => 

        (a -> b -> c) -> arr i a -> b -> arr i c

samap f a s = amap (`f` s) a

infixl 6 +., -. infixl 7 *., /., `divS`

(+.), (-.), (*.) :: (Num a) => ScalarOp1 a (+.) = samap (+) (-.) = samap (-) (*.) = samap (*)

divS :: (Integral a) => ScalarOp1 a divS = samap div

(/.) :: (Fractional a) => ScalarOp1 a (/.) = samap (/)

infixr 8 ^., **., ^^.

(^.) :: (Num a, Integral b) => ScalarOp a b a (^.) = samap (^)

(**.) :: (Floating a) => ScalarOp1 a (**.) = samap (**)

(^^.) :: (Fractional a, Integral b) => ScalarOp a b a (^^.) = samap (^^)

main :: IO () main = do 

 let m1, m2 :: (forall a. (Enum a, Num a) => Array (Int, Int) a)
     m1 = listArray ((0, 0), (2, 3)) [1..]
     m2 = listArray ((0, 0), (2, 3)) [10..]
     s :: (forall a. Num a => a)
     s = 99
 putStrLn "m1"
 print m1
 putStrLn "m2"
 print m2
 putStrLn "s"
 print s
 putStrLn "m1 + m2"
 print $ m1 +: m2
 putStrLn "m1 - m2"
 print $ m1 -: m2
 putStrLn "m1 * m2"
 print $ m1 *: m2
 putStrLn "m1 `div` m2"
 print $ m1 `divE` m2
 putStrLn "m1 / m2"
 print $ m1 /: m2
 putStrLn "m1 ^ m2"
 print $ m1 ^: m2
 putStrLn "m1 ** m2"
 print $ m1 **: m2
 putStrLn "m1 ^^ m2"
 print $ m1 ^^: m2
 putStrLn "m1 + s"
 print $ m1 +. s
 putStrLn "m1 - s"
 print $ m1 -. s
 putStrLn "m1 * s"
 print $ m1 *. s
 putStrLn "m1 `div` s"
 print $ m1 `divS` s
 putStrLn "m1 / s"
 print $ m1 /. s
 putStrLn "m1 ^ s"
 print $ m1 ^. s
 putStrLn "m1 ** s"
 print $ m1 **. s
 putStrLn "m1 ^^ s"
 print $ m1 ^^. s</lang>
Output:
m1
array ((0,0),(2,3)) [((0,0),1),((0,1),2),((0,2),3),((0,3),4),((1,0),5),((1,1),6),((1,2),7),((1,3),8),((2,0),9),((2,1),10),((2,2),11),((2,3),12)]
m2
array ((0,0),(2,3)) [((0,0),10),((0,1),11),((0,2),12),((0,3),13),((1,0),14),((1,1),15),((1,2),16),((1,3),17),((2,0),18),((2,1),19),((2,2),20),((2,3),21)]
s
99
m1 + m2
array ((0,0),(2,3)) [((0,0),11),((0,1),13),((0,2),15),((0,3),17),((1,0),19),((1,1),21),((1,2),23),((1,3),25),((2,0),27),((2,1),29),((2,2),31),((2,3),33)]
m1 - m2
array ((0,0),(2,3)) [((0,0),-9),((0,1),-9),((0,2),-9),((0,3),-9),((1,0),-9),((1,1),-9),((1,2),-9),((1,3),-9),((2,0),-9),((2,1),-9),((2,2),-9),((2,3),-9)]
m1 * m2
array ((0,0),(2,3)) [((0,0),10),((0,1),22),((0,2),36),((0,3),52),((1,0),70),((1,1),90),((1,2),112),((1,3),136),((2,0),162),((2,1),190),((2,2),220),((2,3),252)]
m1 `div` m2
array ((0,0),(2,3)) [((0,0),0),((0,1),0),((0,2),0),((0,3),0),((1,0),0),((1,1),0),((1,2),0),((1,3),0),((2,0),0),((2,1),0),((2,2),0),((2,3),0)]
m1 / m2
array ((0,0),(2,3)) [((0,0),0.1),((0,1),0.18181818181818182),((0,2),0.25),((0,3),0.3076923076923077),((1,0),0.35714285714285715),((1,1),0.4),((1,2),0.4375),((1,3),0.47058823529411764),((2,0),0.5),((2,1),0.5263157894736842),((2,2),0.55),((2,3),0.5714285714285714)]
m1 ^ m2
array ((0,0),(2,3)) [((0,0),1),((0,1),2048),((0,2),531441),((0,3),67108864),((1,0),6103515625),((1,1),470184984576),((1,2),33232930569601),((1,3),2251799813685248),((2,0),150094635296999121),((2,1),10000000000000000000),((2,2),672749994932560009201),((2,3),46005119909369701466112)]
m1 ** m2
array ((0,0),(2,3)) [((0,0),1.0),((0,1),2048.0),((0,2),531441.0),((0,3),6.7108864e7),((1,0),6.103515625e9),((1,1),4.70184984576e11),((1,2),3.3232930569601e13),((1,3),2.251799813685248e15),((2,0),1.5009463529699914e17),((2,1),1.0e19),((2,2),6.727499949325601e20),((2,3),4.60051199093697e22)]
m1 ^^ m2
array ((0,0),(2,3)) [((0,0),1.0),((0,1),2048.0),((0,2),531441.0),((0,3),6.7108864e7),((1,0),6.103515625e9),((1,1),4.70184984576e11),((1,2),3.3232930569601e13),((1,3),2.251799813685248e15),((2,0),1.5009463529699914e17),((2,1),1.0e19),((2,2),6.7274999493256e20),((2,3),4.60051199093697e22)]
m1 + s
array ((0,0),(2,3)) [((0,0),100),((0,1),101),((0,2),102),((0,3),103),((1,0),104),((1,1),105),((1,2),106),((1,3),107),((2,0),108),((2,1),109),((2,2),110),((2,3),111)]
m1 - s
array ((0,0),(2,3)) [((0,0),-98),((0,1),-97),((0,2),-96),((0,3),-95),((1,0),-94),((1,1),-93),((1,2),-92),((1,3),-91),((2,0),-90),((2,1),-89),((2,2),-88),((2,3),-87)]
m1 * s
array ((0,0),(2,3)) [((0,0),99),((0,1),198),((0,2),297),((0,3),396),((1,0),495),((1,1),594),((1,2),693),((1,3),792),((2,0),891),((2,1),990),((2,2),1089),((2,3),1188)]
m1 `div` s
array ((0,0),(2,3)) [((0,0),0),((0,1),0),((0,2),0),((0,3),0),((1,0),0),((1,1),0),((1,2),0),((1,3),0),((2,0),0),((2,1),0),((2,2),0),((2,3),0)]
m1 / s
array ((0,0),(2,3)) [((0,0),1.0101010101010102e-2),((0,1),2.0202020202020204e-2),((0,2),3.0303030303030304e-2),((0,3),4.040404040404041e-2),((1,0),5.0505050505050504e-2),((1,1),6.060606060606061e-2),((1,2),7.07070707070707e-2),((1,3),8.080808080808081e-2),((2,0),9.090909090909091e-2),((2,1),0.10101010101010101),((2,2),0.1111111111111111),((2,3),0.12121212121212122)]
m1 ^ s
array ((0,0),(2,3)) [((0,0),1),((0,1),633825300114114700748351602688),((0,2),171792506910670443678820376588540424234035840667),((0,3),401734511064747568885490523085290650630550748445698208825344),((1,0),1577721810442023610823457130565572459346412870218046009540557861328125),((1,1),108886437250011817682781711193009636756190618412159145257178661061582856912896),((1,2),462068072803536855906378252728602401551029028414946485847699333055955922805275437143),((1,3),254629497041810760783555711051172270131433549208242031329517556169297662470417088272924672),((2,0),29512665430652752148753480226197736314359272517043832886063884637676943433478020332709411004889),((2,1),1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000),((2,2),12527829399838427440107579247354215251149392000034969484678615956504532008683916069945559954314411495091),((2,3),69014978768345458548673686329780708168010234321157869622016822008604576610843435253147523608071501615464448)]
m1 ** s
array ((0,0),(2,3)) [((0,0),1.0),((0,1),6.338253001141147e29),((0,2),1.7179250691067045e47),((0,3),4.017345110647476e59),((1,0),1.5777218104420236e69),((1,1),1.0888643725001182e77),((1,2),4.620680728035369e83),((1,3),2.5462949704181076e89),((2,0),2.9512665430652752e94),((2,1),1.0e99),((2,2),1.2527829399838427e103),((2,3),6.901497876834546e106)]
m1 ^^ s
array ((0,0),(2,3)) [((0,0),1.0),((0,1),6.338253001141147e29),((0,2),1.7179250691067043e47),((0,3),4.017345110647476e59),((1,0),1.5777218104420238e69),((1,1),1.0888643725001181e77),((1,2),4.620680728035369e83),((1,3),2.5462949704181076e89),((2,0),2.9512665430652752e94),((2,1),1.0000000000000001e99),((2,2),1.2527829399838425e103),((2,3),6.901497876834545e106)]

Icon and Unicon

This is a Unicon-specific solution solely because of the use of the [: ... :] operator. It would be easy to replace this with another construct to produce a version that works in both languages. The output flattens each displayed matrix onto a single line to save space here. <lang unicon>procedure main() 

  a := [[1,2,3],[4,5,6],[7,8,9]]
  b := [[9,8,7],[6,5,4],[3,2,1]]
  showMat("  a: ",a)
  showMat("  b: ",b)
  showMat("a+b: ",mmop("+",a,b))
  showMat("a-b: ",mmop("-",a,b))
  showMat("a*b: ",mmop("*",a,b))
  showMat("a/b: ",mmop("/",a,b))
  showMat("a^b: ",mmop("^",a,b))
  showMat("a+2: ",msop("+",a,2))
  showMat("a-2: ",msop("-",a,2))
  showMat("a*2: ",msop("*",a,2))
  showMat("a/2: ",msop("/",a,2))
  showMat("a^2: ",msop("^",a,2))

end

procedure mmop(op,A,B) 

   if (*A = *B) & (*A[1] = *B[1]) then {
       C := [: |list(*A[1])\*A[1] :]
       a1 := create !!A
       b1 := create !!B
       every (!!C) := op(@a1,@b1)
       return C
       }

end

procedure msop(op,A,s) 

   C := [: |list(*A[1])\*A[1] :]
   a1 := create !!A
   every (!!C) := op(@a1,s)
   return C

end

procedure showMat(label, m) 

   every writes(label | right(!!m,5) | "\n")

end</lang>

Output:
->ewo
  a:     1    2    3    4    5    6    7    8    9
  b:     9    8    7    6    5    4    3    2    1
a+b:    10   10   10   10   10   10   10   10   10
a-b:    -8   -6   -4   -2    0    2    4    6    8
a*b:     9   16   21   24   25   24   21   16    9
a/b:     0    0    0    0    1    1    2    4    9
a^b:     1  256 2187 4096 3125 1296  343   64    9
a+2:     3    4    5    6    7    8    9   10   11
a-2:    -1    0    1    2    3    4    5    6    7
a*2:     2    4    6    8   10   12   14   16   18
a/2:     0    1    1    2    2    3    3    4    4
a^2:     1    4    9   16   25   36   49   64   81
->

J

Solution: J's arithmetical primitives act elementwise by default (in J parlance, such operations are known as "scalar" or "rank zero", which means they generalize to high-order arrays transparently, operating elementwise). Thus: <lang j> scalar =: 10 

  vector =: 2 3 5
  matrix =: 3 3 $    7 11 13  17 19 23  29 31 37

  scalar * scalar

100 

  scalar * vector

20 30 50 

  scalar * matrix
70 110 130

170 190 230 290 310 370 

  vector * vector

4 9 25 

  vector * matrix
14  22  26
51  57  69

145 155 185 

  matrix * matrix
49 121  169

289 361 529 841 961 1369</lang> And similarly for +, -, % (division), and ^ .

Note that in some branches of mathematics, it has been traditional to define multiplication such that it is not performed element-wise. This can introduce some complications (wp:Einstein notation is arguably the best approach for resolving those complexities in latex, when they occur frequently enough that mentioning and using the notation is not more complicated than explicitly describing the multiply-and-sum) and makes expressing element-wise multiplication complicated. J deals with this conflict by making its multiplication primitive be elementwise (consistent with the rest of the language) and by using a different verb (typically +/ .*) to represent the traditional non-element-wise multiply and sum operation.

Java

<lang Java> import java.util.Arrays; import java.util.HashMap; import java.util.Map; import java.util.function.BiFunction; import java.util.stream.Stream;

@SuppressWarnings("serial") public class ElementWiseOp { static final Map<String, BiFunction<Double, Double, Double>> OPERATIONS = new HashMap<String, BiFunction<Double, Double, Double>>() { { put("add", (a, b) -> a + b); put("sub", (a, b) -> a - b); put("mul", (a, b) -> a * b); put("div", (a, b) -> a / b); put("pow", (a, b) -> Math.pow(a, b)); put("mod", (a, b) -> a % b); } }; public static Double[][] scalarOp(String op, Double[][] matr, Double scalar) { BiFunction<Double, Double, Double> operation = OPERATIONS.getOrDefault(op, (a, b) -> a); Double[][] result = new Double[matr.length][matr[0].length]; for (int i = 0; i < matr.length; i++) { for (int j = 0; j < matr[i].length; j++) { result[i][j] = operation.apply(matr[i][j], scalar); } } return result; } public static Double[][] matrOp(String op, Double[][] matr, Double[][] scalar) { BiFunction<Double, Double, Double> operation = OPERATIONS.getOrDefault(op, (a, b) -> a); Double[][] result = new Double[matr.length][Stream.of(matr).mapToInt(a -> a.length).max().getAsInt()]; for (int i = 0; i < matr.length; i++) { for (int j = 0; j < matr[i].length; j++) { result[i][j] = operation.apply(matr[i][j], scalar[i % scalar.length][j % scalar[i % scalar.length].length]); } } return result; } public static void printMatrix(Double[][] matr) { Stream.of(matr).map(Arrays::toString).forEach(System.out::println); } public static void main(String[] args) { printMatrix(scalarOp("mul", new Double[][] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } }, 3.0));

printMatrix(matrOp("div", new Double[][] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } }, new Double[][] { { 1.0, 2.0}, { 3.0, 4.0} })); } } </lang>

jq

The following definition of elementwise allows matrices of any type to be processed, e.g. the matrices could be string or object-valued, and they can be of mixed type.

The matrices also need not be rectangular or conformant, but the resultant matrix will be rectangular, with the same number of rows as self, and if that number is greater than 0, then the number of columns in the result will be the length of the first row of self.

In jq, it is idiomatic to specify an operation by using a jq filter. This means that composite and user-defined operations can be specified. In the following definition of "elementwise", the "operator" argument for addition, for example, would be given as (.[0] + .[1]) rather than the string "+".

In Part 2 below, a variation of "elementwise" is presented that does accept string specifications of common operators, e.g. "+" for addition. However this is done mainly for illustration and is not recommended, primarily because it introduces certain complexities.

Part 1 <lang jq># Occurrences of .[0] in "operator" will refer to an element in self,

  1. and occurrences of .[1] will refer to the corresponding element in other.

def elementwise( operator; other ): 

 length as $rows
 | if $rows == 0 then .
   else . as $self
   | other as $other
   | ($self[0]|length) as $cols
   | reduce range(0; $rows) as $i
       ([]; reduce range(0; $cols) as $j
         (.; .[$i][$j] = ([$self[$i][$j], $other[$i][$j]] | operator) ) )
   end ;</lang>

Example: <lang jq>[[3,1,4],[1,5,9]] as $m1 | [[2,7,1],[8,2,2]] as $m2 | ( ($m1|elementwise(.[0] + .[1]; $m2) ), 

   ($m1|elementwise(.[0] + 2 * .[1]; $m2) ),
   ($m1|elementwise(.[0] < .[1]; $m2) ) )

</lang>

Output:

<lang sh>[[5,8,5],[9,7,11]] [[7,15,6],[17,9,13]] [[false,true,false],[true,false,false]] </lang>

Part 2

In elementwise2, the operator can be any jq filter e.g. (.[0] < .[1]), where .[0] refers to an element in self and .[1] to the corresponding element in other, but if it is one of the strings "+", "-", "*", "/", "%", "//", "**", "^" or "pow", then the corresponding operator will be applied. Note that in jq, operators are in general polymorphic. For example, + is defined on strings and other types besides numbers. <lang jq>def elementwise2( operator; other ): 

 def pow(i): . as $in | reduce range(0;i) as $i (1; .*$in);
 def operation(x; op; y):
   [x,y] | op as $op
   | if $op == "+" then x+y
     elif $op == "-" then x-y
     elif $op == "*" then x*y
     elif $op == "/" then x/y
     elif $op == "%" then x%y
     elif $op == "//" then x/y|floor
     elif $op == "**" or $op == "^" or $op == "pow" then x|pow(y)
     else $op
     end;

 length as $rows
 | if $rows == 0 then .
   else . as $self
   | other as $other
   | ($self[0]|length) as $cols
   | reduce range(0; $rows) as $i
       ([]; reduce range(0; $cols) as $j
         (.; .[$i][$j] = operation($self[$i][$j]; operator; $other[$i][$j] ) ) )
   end;</lang>

Example: <lang jq>[[3,1,4],[1,5,9]] as $m1 | [[2,7,1],[8,2,2]] as $m2 

 | ( ($m1|elementwise2("+"; $m2) ),
     ($m1|elementwise2("//"; $m2)),
     ($m1|elementwise2(.[0] < .[1]; $m2) ) )</lang>
Output:

<lang sh>[[5,8,5],[9,7,11]] [[1,0,4],[0,2,4]] [[false,true,false],[true,false,false]] </lang>

K

Translation of: J

<lang K> scalar: 10 

  vector: 2 3 5
  matrix: 3 3 # 7 11 13  17 19 23  29 31 37

  scalar * scalar

100 

  scalar * vector

20 30 50 

  scalar * matrix

(70 110 130 

170 190 230
290 310 370)
  
  vector * vector

4 9 25 

  vector * matrix

(14 22 26 

51 57 69
145 155 185)
  
  matrix * matrix

(49 121 169 

289 361 529
841 961 1369)

</lang> And similarly for +, -, % (division), and ^ .

Mathematica / Wolfram Language

<lang Mathematica>S = 10 ; M = {{7, 11, 13}, {17 , 19, 23} , {29, 31, 37}}; M + S M - S M * S M / S M ^ S

M + M M - M M * M M / M M ^ M

Gives:

->{{17, 21, 23}, {27, 29, 33}, {39, 41, 47}} ->{{-3, 1, 3}, {7, 9, 13}, {19, 21, 27}} ->{{70, 110, 130}, {170, 190, 230}, {290, 310, 370}} ->{{7/10, 11/10, 13/10}, {17/10, 19/10, 23/10}, {29/10, 31/10, 37/10}} ->{{282475249, 25937424601, 137858491849}, {2015993900449, 

 6131066257801, 41426511213649}, {420707233300201, 819628286980801, 
 4808584372417849}}

->{{14, 22, 26}, {34, 38, 46}, {58, 62, 74}} ->{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} ->{{49, 121, 169}, {289, 361, 529}, {841, 961, 1369}} ->{{1, 1, 1}, {1, 1, 1}, {1, 1, 1}} ->{{823543, 285311670611, 302875106592253}, {827240261886336764177, 

 1978419655660313589123979, 
 20880467999847912034355032910567}, {2567686153161211134561828214731016126483469, 
 17069174130723235958610643029059314756044734431, 
 10555134955777783414078330085995832946127396083370199442517}}</lang>

MATLAB

<lang Matlab>a = rand; b = rand(10,10); scalar_matrix = a * b; component_wise = b .* b;</lang>

Maxima

<lang maxima>a: matrix([1, 2], [3, 4]); b: matrix([2, 4], [3, 1]);

a * b; a / b; a + b; a - b; a^3; a^b; /* won't work */ fullmapl("^", a, b); sin(a);</lang>

PARI/GP

GP already implements element-wise matrix-matrix addition and subtraction and element-wise scalar-matrix multiplication and division. Other element-wise matrix-matrix functions: <lang parigp>multMM(A,B)=matrix(#A[,1],#A,i,j,A[i,j]*B[i,j]); divMM(A,B)=matrix(#A[,1],#A,i,j,A[i,j]/B[i,j]); powMM(A,B)=matrix(#A[,1],#A,i,j,A[i,j]^B[i,j]);</lang>

Other element-wise scalar-matrix functions: <lang parigp>addMs(A,s)=A+matrix(#A[,1],#A,i,j,s); subMs(A,s)=A-matrix(#A[,1],#A,i,j,s); powMs(A,s)=matrix(#A[,1],#A,i,j,A[i,j]^s);</lang>

PARI implements convenience functions vecmul (element-wise matrix-matrix multiplication), vecdiv (element-wise matrix-matrix division), and vecpow (element-wise matrix-scalar exponentiation), as well as vecmodii and vecinv. These operate on vectors, but a t_MAT is simply an array of vectors in PARI so it applies fairly easily.

Perl

There's no need to use real multi-dimentional arrays to represent matrix. Since matrices have fixed row length, they can be represented by flat array.

This example demonstrates Perl's operator overload ability and bulk list operations using map.

File Elementwise.pm: <lang perl>package Elementwise;

use Exporter 'import';

use overload '=' => sub { $_[0]->clone() }, '+' => sub { $_[0]->add($_[1]) }, '-' => sub { $_[0]->sub($_[1]) }, '*' => sub { $_[0]->mul($_[1]) }, '/' => sub { $_[0]->div($_[1]) }, '**' => sub { $_[0]->exp($_[1]) },

sub new { my ($class, $v) = @_; return bless $v, $class; }

sub clone { my @ret = @{$_[0]}; return bless \@ret, ref($_[0]); }

sub add { new Elementwise ref($_[1]) ? [map { $_[0][$_] + $_[1][$_] } 0 .. $#{$_[0]} ] : [map { $_[0][$_] + $_[1] } 0 .. $#{$_[0]} ] } sub sub { new Elementwise ref($_[1]) ? [map { $_[0][$_] - $_[1][$_] } 0 .. $#{$_[0]} ] : [map { $_[0][$_] - $_[1] } 0 .. $#{$_[0]} ] } sub mul { new Elementwise ref($_[1]) ? [map { $_[0][$_] * $_[1][$_] } 0 .. $#{$_[0]} ] : [map { $_[0][$_] * $_[1] } 0 .. $#{$_[0]} ] } sub div { new Elementwise ref($_[1]) ? [map { $_[0][$_] / $_[1][$_] } 0 .. $#{$_[0]} ] : [map { $_[0][$_] / $_[1] } 0 .. $#{$_[0]} ] } sub exp { new Elementwise ref($_[1]) ? [map { $_[0][$_] ** $_[1][$_] } 0 .. $#{$_[0]} ] : [map { $_[0][$_] ** $_[1] } 0 .. $#{$_[0]} ] }

1;</lang>

File test.pl: <lang perl>use Elementwise;

$a = new Elementwise [ 1,2,3, 4,5,6, 7,8,9 ];

print << "_E"; a @$a a OP a + @{$a+$a} - @{$a-$a}

  • @{$a*$a}

/ @{$a/$a} ^ @{$a**$a} a OP 5 + @{$a+5} - @{$a-5}

  • @{$a*5}

/ @{$a/5} ^ @{$a**5} _E</lang>

Output:
a  1 2 3 4 5 6 7 8 9
a OP a
+  2 4 6 8 10 12 14 16 18
-  0 0 0 0 0 0 0 0 0
*  1 4 9 16 25 36 49 64 81
/  1 1 1 1 1 1 1 1 1
^  1 4 27 256 3125 46656 823543 16777216 387420489
a OP 5
+  6 7 8 9 10 11 12 13 14
-  -4 -3 -2 -1 0 1 2 3 4
*  5 10 15 20 25 30 35 40 45
/  0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
^  1 32 243 1024 3125 7776 16807 32768 59049

Perl 6

Works with: rakudo version 2016.05

Perl 6 already implements this and other metaoperators as higher-order functions (cross, zip, reduce, triangle, etc.) that are usually accessed through a meta-operator syntactic sugar that is productive over all appropriate operators, including user-defined ones. In this case, a dwimmy element-wise operator (generically known as a "hyper") is indicated by surrounding the operator with double angle quotes. Hypers dwim on the pointy end with cyclic APL semantics as necessary. You can turn the quote the other way to suppress dwimmery on that end. In this case we could have used »op» instead of «op» since the short side is always on the right.<lang perl6>my @a = 

   [1,2,3],
   [4,5,6],
   [7,8,9];

sub msay(@x) { 

   for @x -> @row {
       print ' ', $_%1 ?? $_.nude.join('/') !! $_ for @row;
       say ;
   }
   say ;

}

msay @a «+» @a; msay @a «-» @a; msay @a «*» @a; msay @a «/» @a; msay @a «+» [1,2,3]; msay @a «-» [1,2,3]; msay @a «*» [1,2,3]; msay @a «/» [1,2,3]; msay @a «+» 2; msay @a «-» 2; msay @a «*» 2; msay @a «/» 2;</lang>

Output:
 2 4 6
 8 10 12
 14 16 18

 0 0 0
 0 0 0
 0 0 0

 1 4 9
 16 25 36
 49 64 81

 1 1 1
 1 1 1
 1 1 1

 2 3 4
 6 7 8
 10 11 12

 0 1 2
 2 3 4
 4 5 6

 1 2 3
 8 10 12
 21 24 27

 1 2 3
 2 5/2 3
 7/3 8/3 3

 3 4 5
 6 7 8
 9 10 11

 -1 0 1
 2 3 4
 5 6 7

 2 4 6
 8 10 12
 14 16 18

 1/2 1 3/2
 2 5/2 3
 7/2 4 9/2

In addition to calling the underlying higher-order functions directly, it's possible to name a function.

<lang perl6>sub infix:<M+> (\l,\r) { l <<+>> r }

msay @a M+ @a; msay @a M+ [1,2,3]; msay @a M+ 2;</lang>

Output:
 2 4 6
 8 10 12
 14 16 18

 2 3 4
 6 7 8
 10 11 12

 3 4 5
 6 7 8
 9 10 11

Phix

Phix has builtin sequence ops, which work fine with a multi-dimensional array / matrix: <lang Phix>constant m = {{7, 8, 7},{4, 0, 9}}, 

        m2 = {{4, 5, 1},{6, 2, 1}}

?{m,"+",m2,"=",sq_add(m,m2)} ?{m,"-",m2,"=",sq_sub(m,m2)} ?{m,"*",m2,"=",sq_mul(m,m2)} ?{m,"/",m2,"=",sq_div(m,m2)} ?{m,"^",m2,"=",sq_power(m,m2)} ?{m,"+ 3 =",sq_add(m,3)} ?{m,"- 3 =",sq_sub(m,3)} ?{m,"* 3 =",sq_mul(m,3)} ?{m,"/ 3 =",sq_div(m,3)} ?{m,"^ 3 =",sq_power(m,3)}</lang>

Output:
{{{7,8,7},{4,0,9}},"+",{{4,5,1},{6,2,1}},"=",{{11,13,8},{10,2,10}}}
{{{7,8,7},{4,0,9}},"-",{{4,5,1},{6,2,1}},"=",{{3,3,6},{-2,-2,8}}}
{{{7,8,7},{4,0,9}},"*",{{4,5,1},{6,2,1}},"=",{{28,40,7},{24,0,9}}}
{{{7,8,7},{4,0,9}},"/",{{4,5,1},{6,2,1}},"=",{{1.75,1.6,7},{0.6666666667,0,9}}}
{{{7,8,7},{4,0,9}},"^",{{4,5,1},{6,2,1}},"=",{{2401,32768,7},{4096,0,9}}}
{{{7,8,7},{4,0,9}},"+ 3 =",{{10,11,10},{7,3,12}}}
{{{7,8,7},{4,0,9}},"- 3 =",{{4,5,4},{1,-3,6}}}
{{{7,8,7},{4,0,9}},"* 3 =",{{21,24,21},{12,0,27}}}
{{{7,8,7},{4,0,9}},"/ 3 =",{{2.333333333,2.666666667,2.333333333},{1.333333333,0,3}}}
{{{7,8,7},{4,0,9}},"^ 3 =",{{343,512,343},{64,0,729}}}

PicoLisp

<lang PicoLisp>(de elementWiseMatrix (Fun Mat1 Mat2) 

  (mapcar '((L1 L2) (mapcar Fun L1 L2)) Mat1 Mat2) )

(de elementWiseScalar (Fun Mat Scalar) 

  (elementWiseMatrix Fun Mat (circ (circ Scalar))) )</lang>

Test: 

(let (S 10  M '((7 11 13) (17 19 23) (29 31 37)))
   (println (elementWiseScalar + M S))
   (println (elementWiseScalar - M S))
   (println (elementWiseScalar * M S))
   (println (elementWiseScalar / M S))
   (println (elementWiseScalar ** M S))
   (prinl)
   (println (elementWiseMatrix + M M))
   (println (elementWiseMatrix - M M))
   (println (elementWiseMatrix * M M))
   (println (elementWiseMatrix / M M))
   (println (elementWiseMatrix ** M M)) )
Output:
((17 21 23) (27 29 33) (39 41 47))
((-3 1 3) (7 9 13) (19 21 27))
((70 110 130) (170 190 230) (290 310 370))
((0 1 1) (1 1 2) (2 3 3))
((282475249 25937424601 137858491849) (2015993900449 6131066257801 ...

((14 22 26) (34 38 46) (58 62 74))
((0 0 0) (0 0 0) (0 0 0))
((49 121 169) (289 361 529) (841 961 1369))
((1 1 1) (1 1 1) (1 1 1))
((823543 285311670611 302875106592253) (827240261886336764177 ...

PL/I

Any arithmetic operation can be applied to elements of arrays. These examples illustrate element-by-element multiplication, but addition, subtraction, division, and exponentiation can also be written. <lang PL/I>declare (matrix(3,3), vector(3), scalar) fixed; declare (m(3,3), v(3) fixed;

m = scalar * matrix; m = vector * matrix; m = matrix * matrix;

v = scalar * vector; v = vector * vector;</lang>

Python

<lang python>>>> import random >>> from operator import add, sub, mul, floordiv >>> from pprint import pprint as pp >>> >>> def ewise(matrix1, matrix2, op): return [[op(e1,e2) for e1,e2 in zip(row1, row2)] for row1,row2 in zip(matrix1, matrix2)]

>>> m,n = 3,4 # array dimensions >>> a0 = [[random.randint(1,9) for y in range(n)] for x in range(m)] >>> a1 = [[random.randint(1,9) for y in range(n)] for x in range(m)] >>> pp(a0); pp(a1) [[7, 8, 7, 4], [4, 9, 4, 1], [2, 3, 6, 4]] [[4, 5, 1, 6], [6, 8, 3, 4], [2, 2, 6, 3]] >>> pp(ewise(a0, a1, add)) [[11, 13, 8, 10], [10, 17, 7, 5], [4, 5, 12, 7]] >>> pp(ewise(a0, a1, sub)) [[3, 3, 6, -2], [-2, 1, 1, -3], [0, 1, 0, 1]] >>> pp(ewise(a0, a1, mul)) [[28, 40, 7, 24], [24, 72, 12, 4], [4, 6, 36, 12]] >>> pp(ewise(a0, a1, floordiv)) [[1, 1, 7, 0], [0, 1, 1, 0], [1, 1, 1, 1]] >>> pp(ewise(a0, a1, pow)) [[2401, 32768, 7, 4096], [4096, 43046721, 64, 1], [4, 9, 46656, 64]] >>> pp(ewise(a0, a1, lambda x, y:2*x - y)) [[10, 11, 13, 2], [2, 10, 5, -2], [2, 4, 6, 5]] >>> >>> def s_ewise(scalar1, matrix1, op): return [[op(scalar1, e1) for e1 in row1] for row1 in matrix1]

>>> scalar = 10 >>> a0 [[7, 8, 7, 4], [4, 9, 4, 1], [2, 3, 6, 4]] >>> for op in ( add, sub, mul, floordiv, pow, lambda x, y:2*x - y ): print("%10s :" % op.__name__, s_ewise(scalar, a0, op)) 


      add : [[17, 18, 17, 14], [14, 19, 14, 11], [12, 13, 16, 14]]
      sub : [[3, 2, 3, 6], [6, 1, 6, 9], [8, 7, 4, 6]]
      mul : [[70, 80, 70, 40], [40, 90, 40, 10], [20, 30, 60, 40]]
 floordiv : [[1, 1, 1, 2], [2, 1, 2, 10], [5, 3, 1, 2]]
      pow : [[10000000, 100000000, 10000000, 10000], [10000, 1000000000, 10000, 10], [100, 1000, 1000000, 10000]]
 <lambda> : [[13, 12, 13, 16], [16, 11, 16, 19], [18, 17, 14, 16]]

>>> </lang>

R

In R most operations work on vectors and matrices:

<lang R># create a 2-times-2 matrix mat <- matrix(1:4, 2, 2)

  1. matrix with scalar

mat + 2 mat * 2 mat ^ 2

  1. matrix with matrix

mat + mat mat * mat mat ^ mat</lang>

Output:
> mat <- matrix(1:4, 2, 2)
     [,1] [,2]
[1,]    1    3
[2,]    2    4

> mat + 2
     [,1] [,2]
[1,]    3    5
[2,]    4    6

> mat * 2
     [,1] [,2]
[1,]    2    6
[2,]    4    8

> mat ^ 2
     [,1] [,2]
[1,]    1    9
[2,]    4   16

> mat + mat
     [,1] [,2]
[1,]    2    6
[2,]    4    8

> mat * mat
     [,1] [,2]
[1,]    1    9
[2,]    4   16

> mat ^ mat
     [,1] [,2]
[1,]    1   27
[2,]    4  256

Racket

Translation of: R

<lang racket>#lang racket(require math/array)

(define mat (list->array #(2 2) '(1 3 2 4)))

mat (array+ mat (array 2)) (array* mat (array 2)) (array-map expt mat (array 2))

(array+ mat mat) (array* mat mat) (array-map expt mat mat) </lang>

Output:
(array #[#[1 3] #[2 4]])
(array #[#[3 5] #[4 6]])
(array #[#[2 6] #[4 8]])
(array #[#[1 9] #[4 16]])
(array #[#[2 6] #[4 8]])
(array #[#[1 9] #[4 16]])
(array #[#[1 27] #[4 256]])

REXX

discrete

<lang rexx>/*REXX program multiplies two matrixes together, displays the matrixes and the result.*/ m=(1 2 3) (4 5 6) (7 8 9) w=words(m); do k=1; if k*k>=w then leave; end /*k*/; rows=k; cols=k call showMat M, 'M matrix' answer=matAdd(m, 2 ); call showMat answer, 'M matrix, added 2' answer=matSub(m, 7 ); call showMat answer, 'M matrix, subtracted 7' answer=matMul(m, 2.5); call showMat answer, 'M matrix, multiplied by 2½' answer=matPow(m, 3 ); call showMat answer, 'M matrix, cubed' answer=matDiv(m, 4 ); call showMat answer, 'M matrix, divided by 4' answer=matIdv(m, 2 ); call showMat answer, 'M matrix, integer halved' answer=matMod(m, 3 ); call showMat answer, 'M matrix, modulus 3' exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ matAdd: parse arg @,#; call mat#; do j=1 for w; !.j=!.j+#; end; return mat@() matSub: parse arg @,#; call mat#; do j=1 for w; !.j=!.j-#; end; return mat@() matMul: parse arg @,#; call mat#; do j=1 for w; !.j=!.j*#; end; return mat@() matDiv: parse arg @,#; call mat#; do j=1 for w; !.j=!.j/#; end; return mat@() matIdv: parse arg @,#; call mat#; do j=1 for w; !.j=!.j%#; end; return mat@() matPow: parse arg @,#; call mat#; do j=1 for w; !.j=!.j**#; end; return mat@() matMod: parse arg @,#; call mat#; do j=1 for w; !.j=!.j//#; end; return mat@() mat#: w=words(@); do j=1 for w; !.j=word(@,j); end; return mat@: @=!.1; do j=2 to w; @=@ !.j; end; return @ /*──────────────────────────────────────────────────────────────────────────────────────*/ showMat: parse arg @, hdr; L=0; say 

                                       do j=1  for w;  L=max(L,length(word(@,j)));  end
         say  center(hdr, max(length(hdr)+4, cols*(L+1)+4), "─")
         n=0
                   do r    =1 for rows;         _=
                       do c=1 for cols; n=n+1;  _=_ right(word(@,n),L); end;    say _
                   end
         return</lang>

output 

──M matrix──
 1 2 3
 4 5 6
 7 8 9

──M matrix, added 2──
  3  4  5
  6  7  8
  9 10 11

──M matrix, subtracted 7──
 -6 -5 -4
 -3 -2 -1
  0  1  2

──M matrix, multiplied by 2½──
  2.5  5.0  7.5
 10.0 12.5 15.0
 17.5 20.0 22.5

──M matrix, cubed──
   1   8  27
  64 125 216
 343 512 729

──M matrix, divided by 4──
 0.25  0.5 0.75
    1 1.25  1.5
 1.75    2 2.25

──M matrix, integer halved──
 0 1 1
 2 2 3
 3 4 4

──M matrix, modulus 3──
 1 2 0
 1 2 0
 1 2 0

generalized

<lang rexx>/*REXX program multiplies two matrixes together, displays the matrixes and the result. */ m=(1 2 3) (4 5 6) (7 8 9) w=words(m); do k=1; if k*k>=w then leave; end /*k*/; rows=k; cols=k call showMat M, 'M matrix' ans=matOp(m, '+2' ); call showMat ans, "M matrix, added 2" ans=matOp(m, '-7' ); call showMat ans, "M matrix, subtracted 7" ans=matOp(m, '*2.5' ); call showMat ans, "M matrix, multiplied by 2½" ans=matOp(m, '**3' ); call showMat ans, "M matrix, cubed" ans=matOp(m, '/4' ); call showMat ans, "M matrix, divided by 4" ans=matOp(m, '%2' ); call showMat ans, "M matrix, integer halved" ans=matOp(m, '//3' ); call showMat ans, "M matrix, modulus 3" ans=matOp(m, '*3-1' ); call showMat ans, "M matrix, tripled, less one" exit /*stick a fork in it, we"re all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ matOp: parse arg @,#; call mat#; do j=1 for w; interpret '!.'j"=!."j #;end; return mat@() mat#: w=words(@); do j=1 for w; !.j=word(@,j); end; return mat@: @=!.1; do j=2 to w; @=@ !.j; end; return @ /*──────────────────────────────────────────────────────────────────────────────────────*/ showMat: parse arg @, hdr; say 

         L=0;                    do j=1  for w;     L=max(L,length(word(@,j)));   end
         say;   say center(hdr,max(length(hdr)+4,cols*(L+1)+4),"─")
         n=0
                   do r    =1 for rows;         _=
                       do c=1 for cols; n=n+1;  _=_ right(word(@,n),L); end;    say _
                   end
         return</lang>

output 

──M matrix──
 1 2 3
 4 5 6
 7 8 9


──M matrix, added 2──
  3  4  5
  6  7  8
  9 10 11


──M matrix, subtracted 7──
 -6 -5 -4
 -3 -2 -1
  0  1  2


──M matrix, multiplied by 2½──
  2.5  5.0  7.5
 10.0 12.5 15.0
 17.5 20.0 22.5


──M matrix, cubed──
   1   8  27
  64 125 216
 343 512 729


──M matrix, divided by 4──
 0.25  0.5 0.75
    1 1.25  1.5
 1.75    2 2.25


──M matrix, integer halved──
 0 1 1
 2 2 3
 3 4 4


──M matrix, modulus 3──
 1 2 0
 1 2 0
 1 2 0


──M matrix, tripled, less one──
  2  5  8
 11 14 17
 20 23 26

Ruby

<lang ruby>require 'matrix'

class Matrix 

 def element_wise( operator, other )
   Matrix.build(row_size, column_size) do |row, col|
     self[row, col].send(operator, other[row, col])
   end
 end

end

m1, m2 = Matrix[[3,1,4],[1,5,9]], Matrix[[2,7,1],[8,2,2]] puts "m1: #{m1}\nm2: #{m2}\n\n"

[:+, :-, :*, :/, :fdiv, :**, :%].each do |op| 

 puts "m1 %-4s m2  =  %s" % [op, m1.element_wise(op, m2)]

end</lang>

Output:
m1: Matrix[[3, 1, 4], [1, 5, 9]]
m2: Matrix[[2, 7, 1], [8, 2, 2]]

m1 +    m2  =  Matrix[[5, 8, 5], [9, 7, 11]]
m1 -    m2  =  Matrix[[1, -6, 3], [-7, 3, 7]]
m1 *    m2  =  Matrix[[6, 7, 4], [8, 10, 18]]
m1 /    m2  =  Matrix[[1, 0, 4], [0, 2, 4]]
m1 fdiv m2  =  Matrix[[1.5, 0.14285714285714285, 4.0], [0.125, 2.5, 4.5]]
m1 **   m2  =  Matrix[[9, 1, 4], [1, 25, 81]]
m1 %    m2  =  Matrix[[1, 1, 0], [1, 1, 1]]

Tcl

<lang tcl>package require Tcl 8.5 proc alias {name args} {uplevel 1 [list interp alias {} $name {} {*}$args]}

  1. Engine for elementwise operations between matrices

proc elementwiseMatMat {lambda A B} { 

   set C {}
   foreach rA $A rB $B {

set rC {} foreach vA $rA vB $rB { lappend rC [apply $lambda $vA $vB] } lappend C $rC 

   }
   return $C

}

  1. Lift some basic math ops

alias m+ elementwiseMatMat {{a b} {expr {$a+$b}}} alias m- elementwiseMatMat {{a b} {expr {$a-$b}}} alias m* elementwiseMatMat {{a b} {expr {$a*$b}}} alias m/ elementwiseMatMat {{a b} {expr {$a/$b}}} alias m** elementwiseMatMat {{a b} {expr {$a**$b}}}

  1. Engine for elementwise operations between a matrix and a scalar

proc elementwiseMatSca {lambda A b} { 

   set C {}
   foreach rA $A {

set rC {} foreach vA $rA { lappend rC [apply $lambda $vA $b] } lappend C $rC 

   }
   return $C

}

  1. Lift some basic math ops

alias .+ elementwiseMatSca {{a b} {expr {$a+$b}}} alias .- elementwiseMatSca {{a b} {expr {$a-$b}}} alias .* elementwiseMatSca {{a b} {expr {$a*$b}}} alias ./ elementwiseMatSca {{a b} {expr {$a/$b}}} alias .** elementwiseMatSca {{a b} {expr {$a**$b}}}</lang>

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