# Matrix multiplication

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

Multiply two matrices together.

They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.

## 360 Assembly

*        Matrix multiplication     06/08/2015MATRIXRC CSECT                     Matrix multiplication         USING  MATRIXRC,R13SAVEARA  B      STM-SAVEARA(R15)         DC     17F'0'STM      STM    R14,R12,12(R13)         ST     R13,4(R15)         ST     R15,8(R13)         LR     R13,R15         LA     R7,1               i=1LOOPI1   CH     R7,M               do i=1 to m (R7)         BH     ELOOPI1         LA     R8,1               j=1LOOPJ1   CH     R8,P               do j=1 to p (R8)         BH     ELOOPJ1         LR     R1,R7              i         BCTR   R1,0         MH     R1,P         LR     R6,R8              j         BCTR   R6,0         AR     R1,R6         SLA    R1,2         LA     R6,0         ST     R6,C(R1)           c(i,j)=0         LA     R9,1               k=1LOOPK1   CH     R9,N               do k=1 to n (R9)         BH     ELOOPK1         LR     R1,R7              i         BCTR   R1,0         MH     R1,P         LR     R6,R8              j         BCTR   R6,0         AR     R1,R6         SLA    R1,2         L      R2,C(R1)           R2=c(i,j)         LR     R10,R1             R10=offset(i,j)         LR     R1,R7              i         BCTR   R1,0         MH     R1,N         LR     R6,R9              k         BCTR   R6,0         AR     R1,R6         SLA    R1,2         L      R3,A(R1)           R3=a(i,k)         LR     R1,R9              k         BCTR   R1,0         MH     R1,P         LR     R6,R8              j         BCTR   R6,0         AR     R1,R6         SLA    R1,2         L      R4,B(R1)           R4=b(k,j)         LR     R15,R3             a(i,k)         MR     R14,R4             a(i,k)*b(k,j)         LR     R3,R15         AR     R2,R3              R2=R2+a(i,k)*b(k,j)         ST     R2,C(R10)          c(i,j)=c(i,j)+a(i,k)*b(k,j)         LA     R9,1(R9)           k=k+1         B      LOOPK1ELOOPK1  LA     R8,1(R8)           j=j+1         B      LOOPJ1ELOOPJ1  LA     R7,1(R7)           i=i+1         B      LOOPI1ELOOPI1  MVC    Z,=CL80' '         clear buffer         LA     R7,1LOOPI2   CH     R7,M               do i=1 to m         BH     ELOOPI2         LA     R8,1LOOPJ2   CH     R8,P               do j=1 to p         BH     ELOOPJ2         LR     R1,R7              i         BCTR   R1,0         MH     R1,P         LR     R6,R8              j         BCTR   R6,0         AR     R1,R6         SLA    R1,2         L      R6,C(R1)           c(i,j)         LA     R3,Z         AH     R3,IZ         XDECO  R6,W         MVC    0(5,R3),W+7        output c(i,j)         LH     R3,IZ         LA     R3,5(R3)         STH    R3,IZ         LA     R8,1(R8)           j=j+1         B      LOOPJ2ELOOPJ2  XPRNT  Z,80               print buffer         MVC    IZ,=H'0'         LA     R7,1(R7)           i=i+1         B      LOOPI2ELOOPI2  L      R13,4(0,R13)         LM     R14,R12,12(R13)         XR     R15,R15         BR     R14A        DC     F'1',F'2',F'3',F'4',F'5',F'6',F'7',F'8'  a(4,2)B        DC     F'1',F'2',F'3',F'4',F'5',F'6'            b(2,3)C        DS     12F                                      c(4,3)N        DC     H'2'               dim(a,2)=dim(b,1) M        DC     H'4'               dim(a,1) P        DC     H'3'               dim(b,2)Z        DS     CL80IZ       DC     H'0'W        DS     CL16         YREGS           END    MATRIXRC
Output:
    9   12   15
19   26   33
29   40   51
39   54   69

Ada has matrix multiplication predefined for any floating-point or complex type. The implementation is provided by the standard library packages Ada.Numerics.Generic_Real_Arrays and Ada.Numerics.Generic_Complex_Arrays correspondingly. The following example illustrates use of real matrix multiplication for the type Float:

with Ada.Text_IO;               use Ada.Text_IO;with Ada.Numerics.Real_Arrays;  use Ada.Numerics.Real_Arrays; procedure Matrix_Product is    procedure Put (X : Real_Matrix) is      type Fixed is delta 0.01 range -100.0..100.0;   begin      for I in X'Range (1) loop         for J in X'Range (2) loop            Put (Fixed'Image (Fixed (X (I, J))));         end loop;         New_Line;      end loop;   end Put;    A : constant Real_Matrix :=         (  ( 1.0,  1.0,  1.0,   1.0),            ( 2.0,  4.0,  8.0,  16.0),            ( 3.0,  9.0, 27.0,  81.0),            ( 4.0, 16.0, 64.0, 256.0)         );   B : constant Real_Matrix :=         (  (  4.0,     -3.0,      4.0/3.0,  -1.0/4.0 ),            (-13.0/3.0, 19.0/4.0, -7.0/3.0,  11.0/24.0),            (  3.0/2.0, -2.0,      7.0/6.0,  -1.0/4.0 ),            ( -1.0/6.0,  1.0/4.0, -1.0/6.0,   1.0/24.0)         );begin   Put (A * B);end Matrix_Product;
Output:
 1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00


The following code illustrates how matrix multiplication could be implemented from scratch:

package Matrix_Ops is   type Matrix is array (Natural range <>, Natural range <>) of Float;   function "*" (Left, Right : Matrix) return Matrix;end Matrix_Ops; package body Matrix_Ops is   ---------   -- "*" --   ---------   function "*" (Left, Right : Matrix) return Matrix is      Temp : Matrix(Left'Range(1), Right'Range(2)) := (others =>(others => 0.0));   begin      if Left'Length(2) /= Right'Length(1) then         raise Constraint_Error;      end if;       for I in Left'range(1) loop         for J in Right'range(2) loop            for K in Left'range(2) loop               Temp(I,J) := Temp(I,J) + Left(I, K)*Right(K, J);            end loop;         end loop;      end loop;      return Temp;   end "*";end Matrix_Ops;

## ALGOL 68

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

An example of user defined Vector and Matrix Multiplication Operators:

MODE FIELD = LONG REAL; # field type is LONG REAL #INT default upb:=3;MODE VECTOR = [default upb]FIELD;MODE MATRIX = [default upb,default upb]FIELD; # crude exception handling #PROC VOID raise index error := VOID: GOTO exception index error; # define the vector/matrix operators #OP * = (VECTOR a,b)FIELD: ( # basically the dot product #    FIELD result:=0;    IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;    FOR i FROM LWB a TO UPB a DO result+:= a[i]*b[i] OD;    result  );  OP * = (VECTOR a, MATRIX b)VECTOR: ( # overload vector times matrix #    [2 LWB b:2 UPB b]FIELD result;    IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;    FOR j FROM 2 LWB b TO 2 UPB b DO result[j]:=a*b[,j] OD;    result  );# this is the task portion #OP * = (MATRIX a, b)MATRIX: ( # overload matrix times matrix #    [LWB a:UPB a, 2 LWB b:2 UPB b]FIELD result;    IF 2 LWB a/=LWB b OR 2 UPB a/=UPB b THEN raise index error FI;    FOR k FROM LWB result TO UPB result DO result[k,]:=a[k,]*b OD;    result  );  # Some sample matrices to test #test:(  MATRIX a=((1,  1,  1,   1), # matrix A #            (2,  4,  8,  16),            (3,  9, 27,  81),            (4, 16, 64, 256));   MATRIX b=((  4  , -3  ,  4/3,  -1/4 ), # matrix B #            (-13/3, 19/4, -7/3,  11/24),            (  3/2, -2  ,  7/6,  -1/4 ),            ( -1/6,  1/4, -1/6,   1/24));   MATRIX prod = a * b; # actual multiplication example of A x B #   FORMAT real fmt = $g(-6,2)$; # width of 6, with no '+' sign, 2 decimals #  PROC real matrix printf= (FORMAT real fmt, MATRIX m)VOID:(    FORMAT vector fmt = $"("n(2 UPB m-1)(f(real fmt)",")f(real fmt)")"$;    FORMAT matrix fmt = $x"("n(UPB m-1)(f(vector fmt)","lxx)f(vector fmt)");"$;    # finally print the result #    printf((matrix fmt,m))  );   # finally print the result #  print(("Product of a and b: ",new line));  real matrix printf(real fmt, prod)  EXIT    exception index error:     putf(stand error, $x"Exception: index error."l$))
Output:
 Product of a and b:
((  1.00, -0.00, -0.00, -0.00),
( -0.00,  1.00, -0.00, -0.00),
( -0.00, -0.00,  1.00, -0.00),
( -0.00, -0.00, -0.00,  1.00));


### Parallel processing

Alternatively - for multicore CPUs - use the following parallel code... The next step might be to augment with Strassen's O(n^log2(7)) recursive matrix multiplication algorithm:

int default upb := 3;
mode field = long real;
mode vector = [default upb]field;
mode matrix = [default upb, default upb]field;

¢ crude exception handling ¢
proc void raise index error := void: goto exception index error;

sema idle cpus = level ( 8 - 1 ); ¢ 8 = number of CPU cores minus parent CPU ¢

¢ define an operator to slice array into quarters ¢
op top = (matrix m)int: ( ⌊m + ⌈m ) %2,
bot = (matrix m)int: top m + 1,
left = (matrix m)int: ( 2 ⌊m + 2 ⌈m ) %2,
right = (matrix m)int: left m + 1,
left = (vector v)int: ( ⌊v + ⌈v ) %2,
right = (vector v)int: left v + 1;
prio top = 8, bot = 8, left = 8, right = 8; ¢ Operator priority - same as LWB & UPB ¢

op × = (vector a, b)field: ( ¢ dot product ¢
if (⌊a, ⌈a) ≠ (⌊b, ⌈b) then raise index error fi;
if ⌊a = ⌈a then
a[⌈a] × b[⌈b]
else
field begin, end;
[]proc void schedule=(
void: begin:=a[:left a] × b[:left b],
void: end  :=a[right a:] × b[right b:]
);
if level idle cpus = 0 then ¢ use current CPU ¢
else
par ( ¢ run vector in parallel ¢
schedule[1], ¢ assume parent CPU ¢
( ↓idle cpus; schedule[2]; ↑idle cpus)
)
fi;
begin+end
fi
);

op × = (matrix a, b)matrix: ¢ matrix multiply ¢
if (⌊a, 2 ⌊b) = (⌈a, 2 ⌈b) then
a[⌊a, ] × b[, 2 ⌈b] ¢ dot product ¢
else
[⌈a, 2 ⌈b] field out;
if (2 ⌊a, 2 ⌈a) ≠ (⌊b, ⌈b) then raise index error fi;
[]struct(bool required, proc void thread) schedule = (
( true, ¢ calculate top left corner ¢
void: out[:top a, :left b] := a[:top a, ] × b[, :left b]),
( ⌊a ≠ ⌈a, ¢ calculate bottom left corner ¢
void: out[bot a:, :left b] := a[bot a:, ] × b[, :left b]),
( 2 ⌊b ≠ 2 ⌈b, ¢ calculate top right corner ¢
void: out[:top a, right b:] := a[:top a, ] × b[, right b:]),
( (⌊a, 2 ⌊b) ≠ (⌈a, 2 ⌈b) , ¢ calculate bottom right corner ¢
void: out[bot a:, right b:] := a[bot a:, ] × b[, right b:])
);
if level idle cpus = 0 then ¢ use current CPU ¢
else
par ( ¢ run vector in parallel ¢
thread →schedule[1], ¢ thread is always required, and assume parent CPU ¢
( required →schedule[4] | ↓idle cpus; thread →schedule[4]; ↑idle cpus),
¢ try to do opposite corners of matrix in parallel if CPUs are limited ¢
( required →schedule[3] | ↓idle cpus; thread →schedule[3]; ↑idle cpus),
( required →schedule[2] | ↓idle cpus; thread →schedule[2]; ↑idle cpus)
)
fi;
out
fi;

format real fmt = $g(-6,2)$; ¢ width of 6, with no '+' sign, 2 decimals ¢
proc real matrix printf= (format real fmt, matrix m)void:(
format vector fmt = $"("n(2 ⌈m-1)(f(real fmt)",")f(real fmt)")"$;
format matrix fmt = $x"("n(⌈m-1)(f(vector fmt)","lxx)f(vector fmt)");"$;
¢ finally print the result ¢
printf((matrix fmt,m))
);

¢ Some sample matrices to test ¢
matrix a=((1,  1,  1,   1), ¢ matrix A ¢
(2,  4,  8,  16),
(3,  9, 27,  81),
(4, 16, 64, 256));

matrix b=((  4  , -3  ,  4/3,  -1/4 ), ¢ matrix B ¢
(-13/3, 19/4, -7/3,  11/24),
(  3/2, -2  ,  7/6,  -1/4 ),
( -1/6,  1/4, -1/6,   1/24));

matrix c = a × b; ¢ actual multiplication example of A x B ¢

print((" A x B =",new line));
real matrix printf(real fmt, c).

exception index error:
putf(stand error, $x"Exception: index error."l$)


## AppleScript

Translation of: JavaScript
-- matrixMultiply :: Num a => [[a]] -> [[a]] -> [[a]]to matrixMultiply(a, b)    script rows        property xs : transpose(b)         on |λ|(row)            script columns                on |λ|(col)                    my dotProduct(row, col)                end |λ|            end script             map(columns, xs)        end |λ|    end script     map(rows, a)end matrixMultiply  -- TEST -----------------------------------------------------------on run    matrixMultiply({¬        {-1, 1, 4}, ¬        {6, -4, 2}, ¬        {-3, 5, 0}, ¬        {3, 7, -2} ¬            }, {¬        {-1, 1, 4, 8}, ¬        {6, 9, 10, 2}, ¬        {11, -4, 5, -3}})     --> {{51, -8, 26, -18}, {-8, -38, -6, 34},     --     {33, 42, 38, -14}, {17, 74, 72, 44}}end run  -- GENERIC FUNCTIONS ---------------------------------------------- -- dotProduct :: [n] -> [n] -> Maybe non dotProduct(xs, ys)    script mult        on |λ|(a, b)            a * b        end |λ|    end script     if length of xs is not length of ys then        missing value    else        sum(zipWith(mult, xs, ys))    end ifend dotProduct -- foldr :: (a -> b -> a) -> a -> [b] -> aon foldr(f, startValue, xs)    tell mReturn(f)        set v to startValue        set lng to length of xs        repeat with i from lng to 1 by -1            set v to |λ|(v, item i of xs, i, xs)        end repeat        return v    end tellend foldr -- map :: (a -> b) -> [a] -> [b]on map(f, xs)    tell mReturn(f)        set lng to length of xs        set lst to {}        repeat with i from 1 to lng            set end of lst to |λ|(item i of xs, i, xs)        end repeat        return lst    end tellend map -- min :: Ord a => a -> a -> aon min(x, y)    if y < x then        y    else        x    end ifend min -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Scripton mReturn(f)    if class of f is script then        f    else        script            property |λ| : f        end script    end ifend mReturn -- product :: Num a => [a] -> aon product(xs)    script mult        on |λ|(a, b)            a * b        end |λ|    end script     foldr(mult, 1, xs)end product -- sum :: Num a => [a] -> aon sum(xs)    script add        on |λ|(a, b)            a + b        end |λ|    end script     foldr(add, 0, xs)end sum -- transpose :: [[a]] -> [[a]]on transpose(xss)    script column        on |λ|(_, iCol)            script row                on |λ|(xs)                    item iCol of xs                end |λ|            end script             map(row, xss)        end |λ|    end script     map(column, item 1 of xss)end transpose -- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]on zipWith(f, xs, ys)    set lng to min(length of xs, length of ys)    set lst to {}    tell mReturn(f)        repeat with i from 1 to lng            set end of lst to |λ|(item i of xs, item i of ys)        end repeat        return lst    end tellend zipWith
Output:
{{51, -8, 26, -18}, {-8, -38, -6, 34}, {33, 42, 38, -14}, {17, 74, 72, 44}}

## APL

Matrix multiply in APL is just +.×. For example:

    x  ←  +.×     A  ←  ↑A*¨⊂A←⍳4   ⍝  Same  A  as in other examples (1 1 1 1⍪ 2 4 8 16⍪ 3 9 27 81,[0.5] 4 16 64 256)     B  ←  ⌹A          ⍝  Matrix inverse of A     'F6.2' ⎕FMT A x B1.00  0.00  0.00  0.000.00  1.00  0.00  0.000.00  0.00  1.00  0.000.00  0.00  0.00  1.00

By contrast, A×B is for element-by-element multiplication of arrays of the same shape, and if they are simple elements, this is ordinary multiplication.

## AutoHotkey

ahk discussion

Matrix("b","  ; rows separated by ",", 1   2       ; entries separated by space or tab, 2   3, 3   0")MsgBox % "Bnn" MatrixPrint(b)Matrix("c",", 1 2 3, 3 2 1")MsgBox % "Cnn" MatrixPrint(c) MatrixMul("a",b,c)MsgBox % "B * Cnn" MatrixPrint(a) MsgBox % MatrixMul("x",b,b)  Matrix(_a,_v) { ; Matrix structure: m_0_0 = #rows, m_0_1 = #columns, m_i_j = element[i,j], i,j > 0   Local _i, _j = 0   Loop Parse, _v, ,      If (A_LoopField != "") {         _i := 0, _j ++         Loop Parse, A_LoopField, %A_Space%%A_Tab%            If (A_LoopField != "")               _i++, %_a%_%_i%_%_j% := A_LoopField      }   %_a% := _a, %_a%_0_0 := _j, %_a%_0_1 := _i}MatrixPrint(_a) {   Local _i = 0, _t   Loop % %_a%_0_0 {      _i++      Loop % %_a%_0_1         _t .= %_a%_%A_Index%_%_i% "t"      _t .= "n"   }   Return _t}MatrixMul(_a,_b,_c) {   Local _i = 0, _j, _k, _s   If (%_b%_0_0 != %_c%_0_1)      Return "ERROR: inner dimensions " %_b%_0_0 " != " %_c%_0_1   %_a% := _a, %_a%_0_0 := %_b%_0_0, %_a%_0_1 := %_c%_0_1   Loop % %_c%_0_1 {      _i++, _j := 0      Loop % %_b%_0_0 {         _j++, _k := _s := 0         Loop % %_b%_0_1            _k++, _s += %_b%_%_k%_%_j% * %_c%_%_i%_%_k%         %_a%_%_i%_%_j% := _s      }   }}

### Using Objects

Multiply_Matrix(A,B){	if (A[1].MaxIndex() <> B.MaxIndex())		return	RCols := A[1].MaxIndex()>B[1].MaxIndex()?A[1].MaxIndex():B[1].MaxIndex()	RRows := A.MaxIndex()>B.MaxIndex()?A.MaxIndex():B.MaxIndex(),	 R := []	Loop, % RRows {		RRow:=A_Index		loop, % RCols {			RCol:=A_Index,			v := 0			loop % A[1].MaxIndex()				col := A_Index,		v += A[RRow, col] * B[col,RCol]			R[RRow,RCol] := v		}	}	return R}
Examples:
A := [[1,2]	, [3,4]	, [5,6]	, [7,8]] B := [[1,2,3]	, [4,5,6]] if Res := Multiply_Matrix(A,B)	MsgBox % Print(Res)else	MsgBox ErrorreturnPrint(M){	for i, row in M		for j, col in row			Res .= (A_Index=1?"":"t") col (Mod(A_Index,M[1].MaxIndex())?"":"n")	return Trim(Res,"n")}
Output:
9	12	15
19	26	33
29	40	51
39	54	69

## BASIC

Works with: QuickBasic version 4.5
Translation of: Java
Assume the matrices TO be multiplied are a AND b IF (LEN(a,2) = LEN(b)) 'if valid dims        n = LEN(a,2)        m = LEN(a)        p = LEN(b,2)         DIM ans(0 TO m - 1, 0 TO p - 1)         FOR i = 0 TO m - 1                FOR j = 0 TO p - 1                        FOR k = 0 TO n - 1                                ans(i, j) = ans(i, j) + (a(i, k) * b(k, j))                        NEXT k, j, i         'print answer        FOR i = 0 TO m - 1                FOR j = 0 TO p - 1                        PRINT ans(i, j);                NEXT j                PRINT        NEXT i ELSE        PRINT "invalid dimensions" END IF

## BBC BASIC

BBC BASIC has built-in matrix multiplication (assumes default lower bound of 0):

      DIM matrix1(3,1), matrix2(1,2), product(3,2)       matrix1() = 1, 2, \      \           3, 4, \      \           5, 6, \      \           7, 8       matrix2() = 1, 2, 3, \      \           4, 5, 6       product() = matrix1() . matrix2()       FOR row% = 0 TO DIM(product(),1)        FOR col% = 0 TO DIM(product(),2)          PRINT product(row%,col%),;        NEXT        PRINT      NEXT
Output:
         9        12        15
19        26        33
29        40        51
39        54        69

## Burlesque

 blsq ) {{1 2}{3 4}{5 6}{7 8}}{{1 2 3}{4 5 6}}mmsp9 12 1519 26 3329 40 5139 54 69

## C

For performance critical work involving matrices, especially large or sparse ones, always consider using an established library such as BLAS first.

#include <stdio.h>#include <stdlib.h> /* Make the data structure self-contained.  Element at row i and col j   is x[i * w + j].  More often than not, though,  you might want   to represent a matrix some other way */typedef struct { int h, w; double *x;} matrix_t, *matrix; inline double dot(double *a, double *b, int len, int step){	double r = 0;	while (len--) {		r += *a++ * *b;		b += step;	}	return r;} matrix mat_new(int h, int w){	matrix r = malloc(sizeof(matrix_t) + sizeof(double) * w * h);	r->h = h, r->w = w;	r->x = (double*)(r + 1);	return r;} matrix mat_mul(matrix a, matrix b){	matrix r;	double *p, *pa;	int i, j;	if (a->w != b->h) return 0; 	r = mat_new(a->h, b->w);	p = r->x;	for (pa = a->x, i = 0; i < a->h; i++, pa += a->w)		for (j = 0; j < b->w; j++)			*p++ = dot(pa, b->x + j, a->w, b->w);	return r;} void mat_show(matrix a){	int i, j;	double *p = a->x;	for (i = 0; i < a->h; i++, putchar('\n'))		for (j = 0; j < a->w; j++)			printf("\t%7.3f", *p++);	putchar('\n');} int main(){	double da[] = {	1, 1,  1,   1,			2, 4,  8,  16,			3, 9, 27,  81,			4,16, 64, 256	};	double db[] = {     4.0,   -3.0,  4.0/3,			-13.0/3, 19.0/4, -7.0/3,			  3.0/2,   -2.0,  7.0/6,			 -1.0/6,  1.0/4, -1.0/6}; 	matrix_t a = { 4, 4, da }, b = { 4, 3, db };	matrix c = mat_mul(&a, &b); 	/* mat_show(&a), mat_show(&b); */	mat_show(c);	/* free(c) */	return 0;}

## C#

This code should work with any version of the .NET Framework and C# language

public class Matrix{	int n;	int m;	double[,] a; 	public Matrix(int n, int m)	{		if (n <= 0 || m <= 0)			throw new ArgumentException("Matrix dimensions must be positive");		this.n = n;		this.m = m;		a = new double[n, m];	} 	//indices start from one	public double this[int i, int j]	{		get { return a[i - 1, j - 1]; }		set { a[i - 1, j - 1] = value; }	} 	public int N { get { return n; } }	public int M { get { return m; } } 	public static Matrix operator*(Matrix _a, Matrix b)	{		int n = _a.N;		int m = b.M;		int l = _a.M;		if (l != b.N)			throw new ArgumentException("Illegal matrix dimensions for multiplication. _a.M must be equal b.N");		Matrix result = new Matrix(_a.N, b.M);		for(int i = 0; i < n; i++)			for (int j = 0; j < m; j++)			{				double sum = 0.0;				for (int k = 0; k < l; k++)					sum += _a.a[i, k]*b.a[k, j];				result.a[i, j] = sum;			}		return result;	}}

## C++

Works with: Visual C++ 2010
Library: Blitz++
#include <iostream>#include <blitz/tinymat.h> int main(){  using namespace blitz;   TinyMatrix<double,3,3> A, B, C;   A = 1, 2, 3,      4, 5, 6,      7, 8, 9;   B = 1, 0, 0,      0, 1, 0,      0, 0, 1;   C = product(A, B);   std::cout << C << std::endl;}
Output:
(3,3):
[          1         2         3 ]
[          4         5         6 ]
[          7         8         9 ]


### Generic solution

main.cpp

 #include <iostream>#include "matrix.h" #if !defined(ARRAY_SIZE)    #define ARRAY_SIZE(x) (sizeof((x)) / sizeof((x)[0]))#endif int main() {    int  am[2][3] = {        {1,2,3},        {4,5,6},    };    int  bm[3][2] = {        {1,2},        {3,4},        {5,6}    };     Matrix<int> a(ARRAY_SIZE(am), ARRAY_SIZE(am[0]), am[0], ARRAY_SIZE(am)*ARRAY_SIZE(am[0]));    Matrix<int> b(ARRAY_SIZE(bm), ARRAY_SIZE(bm[0]), bm[0], ARRAY_SIZE(bm)*ARRAY_SIZE(bm[0]));    Matrix<int> c;     try {        c = a * b;        for (unsigned int i = 0; i < c.rowNum(); i++) {            for (unsigned int j = 0; j < c.colNum(); j++) {                std::cout <<  c[i][j] << "  ";            }            std::cout << std::endl;        }    } catch (MatrixException& e) {        std::cerr << e.message() << std::endl;        return e.errorCode();    } } /* main() */

matrix.h

 #ifndef _MATRIX_H#define	_MATRIX_H #include <sstream>#include <string>#include <vector> #define MATRIX_ERROR_CODE_COUNT 5#define MATRIX_ERR_UNDEFINED "1 Undefined exception!"#define MATRIX_ERR_WRONG_ROW_INDEX "2 The row index is out of range."#define MATRIX_ERR_MUL_ROW_AND_COL_NOT_EQUAL "3 The row number of second matrix must be equal with the column number of first matrix!"#define MATRIX_ERR_MUL_ROW_AND_COL_BE_GREATER_THAN_ZERO "4 The number of rows and columns must be greater than zero!"#define MATRIX_ERR_TOO_FEW_DATA "5 Too few data in matrix." class MatrixException {private:    std::string message_;    int errorCode_;public:    MatrixException(std::string message = MATRIX_ERR_UNDEFINED);     inline std::string message() {        return message_;    };     inline int errorCode() {        return errorCode_;    };}; MatrixException::MatrixException(std::string message) {    errorCode_ = MATRIX_ERROR_CODE_COUNT + 1;    std::stringstream ss(message);    ss >> errorCode_;    if (errorCode_ < 1) {        errorCode_ = MATRIX_ERROR_CODE_COUNT + 1;    }    std::string::size_type pos = message.find(' ');    if (errorCode_ <= MATRIX_ERROR_CODE_COUNT && pos != std::string::npos) {        message_ = message.substr(pos + 1);    } else {        message_ = message + " (This an unknown and unsupported exception!)";    }} /** * Generic class for matrices. */template <class T>class Matrix {private:    std::vector<T> v; // the data of matrix    unsigned int m;   // the number of rows    unsigned int n;   // the number of columnsprotected:     virtual void clear() {        v.clear();        m = n = 0;    }public:     Matrix() {        clear();    }    Matrix(unsigned int, unsigned int, T* = 0, unsigned int = 0);    Matrix(unsigned int, unsigned int, const std::vector<T>&);     virtual ~Matrix() {        clear();    }    Matrix& operator=(const Matrix&);    std::vector<T> operator[](unsigned int) const;    Matrix operator*(const Matrix&);     inline unsigned int rowNum() const {        return m;    }     inline unsigned int colNum() const {        return n;    }     inline unsigned int size() const {        return v.size();    }     inline void add(const T& t) {        v.push_back(t);    }}; template <class T>Matrix<T>::Matrix(unsigned int row, unsigned int col, T* data, unsigned int dataLength) {    clear();    if (row > 0 && col > 0) {        m = row;        n = col;        unsigned int mxn = m * n;        if (dataLength && data) {            for (unsigned int i = 0; i < dataLength && i < mxn; i++) {                v.push_back(data[i]);            }        }    }} template <class T>Matrix<T>::Matrix(unsigned int row, unsigned int col, const std::vector<T>& data) {    clear();    if (row > 0 && col > 0) {        m = row;        n = col;        unsigned int mxn = m * n;        if (data.size() > 0) {            for (unsigned int i = 0; i < mxn && i < data.size(); i++) {                v.push_back(data[i]);            }        }    }} template<class T>Matrix<T>& Matrix<T>::operator=(const Matrix<T>& other) {    clear();    if (other.m > 0 && other.n > 0) {        m = other.m;        n = other.n;        unsigned int mxn = m * n;        for (unsigned int i = 0; i < mxn && i < other.size(); i++) {            v.push_back(other.v[i]);        }    }    return *this;} template<class T>std::vector<T> Matrix<T>::operator[](unsigned int index) const {    std::vector<T> result;    if (index >= m) {        throw MatrixException(MATRIX_ERR_WRONG_ROW_INDEX);    } else if ((index + 1) * n > size()) {        throw MatrixException(MATRIX_ERR_TOO_FEW_DATA);    } else {        unsigned int begin = index * n;        unsigned int end = begin + n;        for (unsigned int i = begin; i < end; i++) {            result.push_back(v[i]);        }    }    return result;} template<class T>Matrix<T> Matrix<T>::operator*(const Matrix<T>& other) {    Matrix result(m, other.n);    if (n != other.m) {        throw MatrixException(MATRIX_ERR_MUL_ROW_AND_COL_NOT_EQUAL);    } else if (m <= 0 || n <= 0 || other.n <= 0) {        throw MatrixException(MATRIX_ERR_MUL_ROW_AND_COL_BE_GREATER_THAN_ZERO);    } else if (m * n > size() || other.m * other.n > other.size()) {        throw MatrixException(MATRIX_ERR_TOO_FEW_DATA);    } else {        for (unsigned int i = 0; i < m; i++) {            for (unsigned int j = 0; j < other.n; j++) {                T temp = v[i * n] * other.v[j];                for (unsigned int k = 1; k < n; k++) {                    temp += v[i * n + k] * other.v[k * other.n + j];                }                result.v.push_back(temp);            }        }    }    return result;} #endif	/* _MATRIX_H */
Output:
22  28
49  64


## Clojure

 (defn transpose  [s]  (apply map vector s)) (defn nested-for  [f x y]  (map (fn [a]         (map (fn [b]                 (f a b)) y))       x)) (defn matrix-mult  [a b]  (nested-for (fn [x y] (reduce + (map * x y))) a (transpose b))) (def ma [[1 1 1 1] [2 4 8 16] [3 9 27 81] [4 16 64 256]])(def mb [[4 -3 4/3 -1/4] [-13/3 19/4 -7/3 11/24] [3/2 -2 7/6 -1/4] [-1/6 1/4 -1/6 1/24]])
Output:
=> (matrix-mult ma mb)
((1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1))


## Common Lisp

(defun matrix-multiply (a b)  (flet ((col (mat i) (mapcar #'(lambda (row) (elt row i)) mat))         (row (mat i) (elt mat i)))    (loop for row from 0 below (length a)          collect (loop for col from 0 below (length (row b 0))                        collect (apply #'+ (mapcar #'* (row a row) (col b col))))))) ;; example use:(matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4)))
(defun matrix-multiply (matrix1 matrix2) (mapcar  (lambda (row)   (apply #'mapcar    (lambda (&rest column)     (apply #'+ (mapcar #'* row column))) matrix2)) matrix1))

The following version uses 2D arrays as inputs.

(defun mmul (A B)  (let* ((m (car (array-dimensions A)))         (n (cadr (array-dimensions A)))         (l (cadr (array-dimensions B)))         (C (make-array (,m ,l) :initial-element 0)))    (loop for i from 0 to (- m 1) do              (loop for k from 0 to (- l 1) do                    (setf (aref C i k)                          (loop for j from 0 to (- n 1)                                sum (* (aref A i j)                                       (aref B j k))))))    C))

Example use:

(mmul #2a((1 2) (3 4)) #2a((-3 -8 3) (-2 1 4)))#2A((-7 -6 11) (-17 -20 25)) 

Another version:

(defun mmult (a b)  (loop       with m = (array-dimension a 0)       with n = (array-dimension a 1)       with l = (array-dimension b 1)       with c = (make-array (list m l) :initial-element 0)       for i below m do              (loop for k below l do                    (setf (aref c i k)                          (loop for j below n                                sum (* (aref a i j)                                       (aref b j k)))))       finally (return c)))

## Chapel

Overload the '*' operator for arrays

proc *(a:[], b:[]) {     if (a.eltType != b.eltType) then        writeln("type mismatch: ", a.eltType, " ", b.eltType);     var ad = a.domain.dims();    var bd = b.domain.dims();    var (arows, acols) = ad;    var (brows, bcols) = bd;    if (arows != bcols) then        writeln("dimension mismatch: ", ad, " ", bd);     var c:[{arows, bcols}] a.eltType = 0;     for i in arows do        for j in bcols do            for k in acols do                c(i,j) += a(i,k) * b(k,j);     return c;}

example usage (I could not figure out the syntax for multi-dimensional array literals)

var m1:[{1..2, 1..2}] int;m1(1,1) = 1; m1(1,2) = 2;m1(2,1) = 3; m1(2,2) = 4;writeln(m1); var m2:[{1..2, 1..2}] int;m2(1,1) = 2; m2(1,2) = 3;m2(2,1) = 4; m2(2,2) = 5;writeln(m2); var m3 = m1 * m2;writeln(m3); var m4:[{1..2, 1..3}] int;m4(1, 1) = 1; m4(1, 2) = 2; m4(1, 3) = 3;m4(2, 1) = 4; m4(2, 2) = 5; m4(2, 3) = 6;writeln(m4); var m5:[{1..3, 1..2}] int;m5(1, 1) = 6; m5(1, 2) = -1;m5(2, 1) = 3; m5(2, 2) =  2;m5(3, 1) = 0; m5(3, 2) = -3;writeln(m5); writeln(m4 * m5);

## D

### Basic Version

import std.stdio, std.string, std.conv, std.numeric,       std.array, std.algorithm; bool isRectangular(T)(in T[][] M) pure nothrow {    return M.all!(row => row.length == M[0].length);} T[][] matrixMul(T)(in T[][] A, in T[][] B) pure nothrowin {    assert(A.isRectangular && B.isRectangular &&           !A.empty && !B.empty && A[0].length == B.length);} body {    auto result = new T[][](A.length, B[0].length);    auto aux = new T[B.length];     foreach (immutable j; 0 .. B[0].length) {        foreach (immutable k, const row; B)            aux[k] = row[j];        foreach (immutable i, const ai; A)            result[i][j] = dotProduct(ai, aux);    }     return result;} void main() {    immutable a = [[1, 2], [3, 4], [3, 6]];    immutable b = [[-3, -8, 3,], [-2, 1, 4]];     immutable form = "[%([%(%d, %)],\n %)]]";    writefln("A = \n" ~ form ~ "\n", a);    writefln("B = \n" ~ form ~ "\n", b);    writefln("A * B = \n" ~ form, matrixMul(a, b));}
Output:
A =
[[1, 2],
[3, 4],
[3, 6]]

B =
[[-3, -8, 3],
[-2, 1, 4]]

A * B =
[[-7, -6, 11],
[-17, -20, 25],
[-21, -18, 33]]

### Short Version

import std.stdio, std.range, std.array, std.numeric, std.algorithm; T[][] matMul(T)(in T[][] A, in T[][] B) pure nothrow /*@safe*/ {    const Bt = B[0].length.iota.map!(i=> B.transversal(i).array).array;    return A.map!(a => Bt.map!(b => a.dotProduct(b)).array).array;} void main() {    immutable a = [[1, 2], [3, 4], [3, 6]];    immutable b = [[-3, -8, 3,], [-2, 1, 4]];     immutable form = "[%([%(%d, %)],\n %)]]";    writefln("A = \n" ~ form ~ "\n", a);    writefln("B = \n" ~ form ~ "\n", b);    writefln("A * B = \n" ~ form, matMul(a, b));}

The output is the same.

### Pure Short Version

import std.stdio, std.range, std.numeric, std.algorithm; T[][] matMul(T)(immutable T[][] A, immutable T[][] B) pure nothrow {    immutable Bt = B[0].length.iota.map!(i=> B.transversal(i).array)                   .array;    return A.map!((in a) => Bt.map!(b => a.dotProduct(b)).array).array;} void main() {    immutable a = [[1, 2], [3, 4], [3, 6]];    immutable b = [[-3, -8, 3,], [-2, 1, 4]];     immutable form = "[%([%(%d, %)],\n %)]]";    writefln("A = \n" ~ form ~ "\n", a);    writefln("B = \n" ~ form ~ "\n", b);    writefln("A * B = \n" ~ form, matMul(a, b));}

The output is the same.

### Stronger Statically Typed Version

All array sizes are verified at compile-time (and no matrix is copied). Same output.

import std.stdio, std.string, std.numeric, std.algorithm, std.traits; alias TMMul_helper(M1, M2) = Unqual!(ForeachType!(ForeachType!M1))                             [M2.init[0].length][M1.length]; void matrixMul(T, T2, size_t k, size_t m, size_t n)              (in ref T[m][k] A, in ref T[n][m] B,               /*out*/ ref T2[n][k] result) pure nothrow /*@safe*/ @nogcif (is(T2 == Unqual!T)) {    static if (hasIndirections!T)        T2[m] aux;    else        T2[m] aux = void;     foreach (immutable j; 0 .. n) {        foreach (immutable i, const ref bi; B)            aux[i] = bi[j];        foreach (immutable i, const ref ai; A)            result[i][j] = dotProduct(ai, aux);    }} void main() {    immutable int[2][3] a = [[1, 2], [3, 4], [3, 6]];    immutable int[3][2] b = [[-3, -8, 3,], [-2, 1, 4]];     enum form = "[%([%(%d, %)],\n %)]]";    writefln("A = \n" ~ form ~ "\n", a);    writefln("B = \n" ~ form ~ "\n", b);    TMMul_helper!(typeof(a), typeof(b)) result = void;    matrixMul(a, b, result);    writefln("A * B = \n" ~ form, result);}

open list mmult a b = [ [ sum $zipWith (*) ar bc \\ bc <- (transpose b) ] \\ ar <- a ] [[1, 2], [3, 4]] mmult [[-3, -8, 3], [-2, 1, 4]] ## ELLA Sample originally from ftp://ftp.dra.hmg.gb/pub/ella (a now dead link) - Public release. Code for matrix multiplication hardware design verification: MAC ZIP = ([INT n]TYPE t: vector1 vector2) -> [n][2]t: [INT k = 1..n](vector1[k], vector2[k]). MAC TRANSPOSE = ([INT n][INT m]TYPE t: matrix) -> [m][n]t: [INT i = 1..m] [INT j = 1..n] matrix[j][i]. MAC INNER_PRODUCT{FN * = [2]TYPE t -> TYPE s, FN + = [2]s -> s} = ([INT n][2]t: vector) -> s: IF n = 1 THEN *vector[1] ELSE *vector[1] + INNER_PRODUCT {*,+} vector[2..n] FI. MAC MATRIX_MULT {FN * = [2]TYPE t->TYPE s, FN + = [2]s->s} =([INT n][INT m]t: matrix1, [m][INT p]t: matrix2) -> [n][p]s:BEGIN LET transposed_matrix2 = TRANSPOSE matrix2.OUTPUT [INT i = 1..n][INT j = 1..p] INNER_PRODUCT{*,+}ZIP(matrix1[i],transposed_matrix2[j])END. TYPE element = NEW elt/(1..20), product = NEW prd/(1..1200). FN PLUS = (product: integer1 integer2) -> product: ARITH integer1 + integer2. FN MULT = (element: integer1 integer2) -> product: ARITH integer1 * integer2. FN MULT_234 = ([2][3]element:matrix1, [3][4]element:matrix2) -> [2][4]product: MATRIX_MULT{MULT,PLUS}(matrix1, matrix2). FN TEST = () -> [2][4]product:( LET m1 = ((elt/2, elt/1, elt/1), (elt/3, elt/6, elt/9)), m2 = ((elt/6, elt/1, elt/3, elt/4), (elt/9, elt/2, elt/8, elt/3), (elt/6, elt/4, elt/1, elt/2)). OUTPUT MULT_234 (m1, m2)). COM test: just displaysignal MOC ## Euphoria function matrix_mul(sequence a, sequence b) sequence c if length(a[1]) != length(b) then return 0 else c = repeat(repeat(0,length(b[1])),length(a)) for i = 1 to length(a) do for j = 1 to length(b[1]) do for k = 1 to length(a[1]) do c[i][j] += a[i][k]*b[k][j] end for end for end for return c end ifend function ## EGL  program Matrix_multiplication type BasicProgram {} function main() a float[][] = [[1,2,3],[4,5,6]]; b float[][] = [[1,2],[3,4],[5,6]]; c float[][] = mult(a, b); end function mult(a float[][], b float[][]) returns(float[][]) if(a.getSize() == 0) return (new float[0][0]); end if(a[1].getSize() != b.getSize()) return (null); //invalid dims end n int = a[1].getSize(); m int = a.getSize(); p int = b[1].getSize(); ans float[0][0]; ans.resizeAll([m, p]); // Calculate dot product. for(i int from 1 to m) for(j int from 1 to p) for(k int from 1 to n) ans[i][j] += a[i][k] * b[k][j]; end end end return (ans); endend  ## Elixir  def mult(m1, m2) do Enum.map m1, fn (x) -> Enum.map t(m2), fn (y) -> Enum.zip(x, y) |> Enum.map(fn {x, y} -> x * y end) |> Enum.sum end end end def t(m) do # transpose List.zip(m) |> Enum.map(&Tuple.to_list(&1)) end  ## Erlang  %% Multiplies two matrices. Usage example:%%$ matrix:multiply([[1,2,3],[4,5,6]], [[4,4],[0,0],[1,4]])%% If the dimentions are incompatible, an error is thrown.%%%% The erl shell may encode the lists output as strings. In order to prevent such%% behaviour, BEFORE running matrix:multiply, run shell:strings(false) to disable%% auto-encoding. When finished, run shell:strings(true) to reset the defaults. -module(matrix).-export([multiply/2]). transpose([[]|_]) ->    [];transpose(B) ->  [lists:map(fun hd/1, B) | transpose(lists:map(fun tl/1, B))].  red(Pair, Sum) ->    X = element(1, Pair),   %gets X    Y = element(2, Pair),   %gets Y    X * Y + Sum. %% Mathematical dot product. A x B = d%% A, B = 1-dimension vector%% d    = scalardot_product(A, B) ->    lists:foldl(fun red/2, 0, lists:zip(A, B)).  %% Exposed function. Expected result is C = A x B.multiply(A, B) ->    %% First transposes B, to facilitate the calculations (It's easier to fetch    %% row than column wise).    multiply_internal(A, transpose(B)).  %% This function does the actual multiplication, but expects the second matrix%% to be transposed.multiply_internal([Head | Rest], B) ->    % multiply each row by Y    Element = multiply_row_by_col(Head, B),     % concatenate the result of this multiplication with the next ones    [Element | multiply_internal(Rest, B)]; multiply_internal([], B) ->    % concatenating and empty list to the end of a list, changes nothing.    [].  multiply_row_by_col(Row, [Col_Head | Col_Rest]) ->    Scalar = dot_product(Row, Col_Head),     [Scalar | multiply_row_by_col(Row, Col_Rest)]; multiply_row_by_col(Row, []) ->    []. 
Output:
[[7,16],[22,40]]


## ERRE

 PROGRAM MAT_PROD DIM A[3,1],B[1,2],ANS[3,2] BEGIN DATA(1,2,3,4,5,6,7,8)DATA(1,2,3,4,5,6) FOR I=0 TO 3 DO   FOR J=0 TO 1 DO      READ(A[I,J])   END FOREND FOR FOR I=0 TO 1 DO   FOR J=0 TO 2 DO      READ(B[I,J])   END FOREND FOR FOR I=0 TO UBOUND(ANS,1) DO  FOR J=0 TO UBOUND(ANS,2) DO     FOR K=0 TO UBOUND(A,2) DO        ANS[I,J]=ANS[I,J]+(A[I,K]*B[K,J])     END FOR  END FOREND FOR! print answer  FOR I=0 TO UBOUND(ANS,1) DO     FOR J=0 TO UBOUND(ANS,2) DO        PRINT(ANS[I,J],)     END FOR     PRINT  END FOR END PROGRAM 
Output:

9        12        15
19        26        33
29        40        51
39        54        69



## F#

 let MatrixMultiply (matrix1 : _[,] , matrix2 : _[,]) =    let result_row = (matrix1.GetLength 0)    let result_column = (matrix2.GetLength 1)    let ret = Array2D.create result_row result_column 0    for x in 0 .. result_row - 1 do        for y in 0 .. result_column - 1 do            let mutable acc = 0            for z in 0 .. (matrix1.GetLength 1) - 1 do                acc <- acc + matrix1.[x,z] * matrix2.[z,y]            ret.[x,y] <- acc    ret  

## Factor

The built-in word m. multiplies matrices:

( scratchpad ) USE: math.matrices
{ { 1 2 } { 3 4 } }  { { -3 -8 3 } { -2 1 4 } } m. .
{ { -7 -6 11 } { -17 -20 25 } }


## Fantom

Using a list of lists representation. The multiplication is done using three nested loops.

### With Array

A more efficient version, based on arrays:

import Data.Array  mmult :: (Ix i, Num a) => Array (i,i) a -> Array (i,i) a -> Array (i,i) a  mmult x y    | x1 /= y0 || x1' /= y0'  = error "range mismatch"   | otherwise               = array ((x0,y1),(x0',y1')) l   where     ((x0,x1),(x0',x1')) = bounds x     ((y0,y1),(y0',y1')) = bounds y     ir = range (x0,x0')     jr = range (y1,y1')     kr = range (x1,x1')     l  = [((i,j), sum [x!(i,k) * y!(k,j) | k <- kr]) | i <- ir, j <- jr]

### With List and without transpose

 foldlZipWith::(a -> b -> c) -> (d -> c -> d) -> d -> [a] -> [b]  -> dfoldlZipWith _ _ u [] _          = ufoldlZipWith _ _ u _ []          = ufoldlZipWith f g u (x:xs) (y:ys) = foldlZipWith f g (g u (f x y)) xs ys foldl1ZipWith::(a -> b -> c) -> (c -> c -> c) -> [a] -> [b] -> cfoldl1ZipWith _ _ [] _          = error "First list is empty"foldl1ZipWith _ _ _ []          = error "Second list is empty"foldl1ZipWith f g (x:xs) (y:ys) = foldlZipWith f g (f x y) xs ys multAdd::(a -> b -> c) -> (c -> c -> c) -> [[a]] -> [[b]] -> [[c]]multAdd f g xs ys = map (\us -> foldl1ZipWith (\u vs -> map (f u) vs) (zipWith g) us ys) xs mult:: Num a => [[a]] -> [[a]] -> [[a]]mult xs ys = multAdd (*) (+) xs ys test a b = do  let c = mult a b  putStrLn "a ="  mapM_ print a  putStrLn "b ="  mapM_ print b  putStrLn "c = a * b = mult a b ="  mapM_ print c main = test [[1, 2],[3, 4]] [[-3, -8, 3],[-2,  1, 4]] 
Output:
a =
[1,2]
[3,4]
b =
[-3,-8,3]
[-2,1,4]
c = a * b = mult a b =
[-7,-6,11]
[-17,-20,25]


## HicEst

REAL :: m=4, n=2, p=3, a(m,n), b(n,p), res(m,p) a = $! initialize to 1, 2, ..., m*nb =$ ! initialize to 1, 2, ..., n*p res = 0DO i = 1, m  DO j = 1, p    DO k = 1, n      res(i,j) = res(i,j) + a(i,k) * b(k,j)    ENDDO  ENDDOENDDO DLG(DefWidth=4, Text=a, Text=b,Y=0, Text=res,Y=0)
a         b              res1    2    1    2    3    9    12   15   3    4    4    5    6    19   26   33   5    6                   29   40   51   7    8                   39   54   69   

## Icon and Unicon

Using the provided matrix library:

 link matrix procedure main ()  m1 := [[1,2,3], [4,5,6]]  m2 := [[1,2],[3,4],[5,6]]  m3 := mult_matrix (m1, m2)  write ("Multiply:")  write_matrix ("", m1) # first argument is filename, or "" for stdout  write ("by:")  write_matrix ("", m2)  write ("Result: ")  write_matrix ("", m3)end 

And a hand-crafted multiply procedure:

 procedure multiply_matrix (m1, m2)  result := [] # to hold the final matrix  every row1 := !m1 do { # loop through each row in the first matrix    row := []    every colIndex := 1 to *m1 do { # and each column index of the result      value := 0      every rowIndex := 1 to *m2 do {         value +:= row1[rowIndex] * m2[rowIndex][colIndex]      }      put (row, value)     }    put (result, row) # add each row as it is complete  }  return resultend 
Output:
Multiply:
1 2 3
4 5 6
by:
1 2
3 4
5 6
Result:
22 28
49 64


## IDL

result = arr1 # arr2

## Idris

import Data.Vect Matrix : Nat -> Nat -> Type -> TypeMatrix m n t = Vect m (Vect n t) multiply : Num t => Matrix m1 n t -> Matrix n m2 t -> Matrix m1 m2 tmultiply a b = multiply' a (transpose b)  where         dot : Num t => Vect n t -> Vect n t -> t        dot v1 v2 = sum $map (\(s1, s2) => (s1 * s2)) (zip v1 v2) multiply' : Num t => Matrix m1 n t -> Matrix m2 n t -> Matrix m1 m2 t multiply' (a::as) b = map (dot a) b :: multiply' as b multiply' [] _ = [] ## J Matrix multiply in J is +/ .*. For example:  mp =: +/ .* NB. Matrix product A =: ^/~>:i. 4 NB. Same A as in other examples (1 1 1 1, 2 4 8 16, 3 9 27 81,:4 16 64 256) B =: %.A NB. Matrix inverse of A '6.2' 8!:2 A mp B1.00 0.00 0.00 0.000.00 1.00 0.00 0.000.00 0.00 1.00 0.000.00 0.00 0.00 1.00 The notation is for a generalized inner product so that x ~:/ .*. y NB. boolean inner product ( ~: is "not equal" (exclusive or) and *. is "and")x *./ .= y NB. which rows of x are the same as vector y?x + / .= y NB. number of places where a value in row x equals the corresponding value in y The general inner product extends to multidimensional arrays, requiring only that x and y be conformable (trailing dimension of array x equals the leading dimension of array y). For example, the matrix multiplication of two dimensional arrays requires x to have the same numbers of rows as y has columns, as you would expect. Note also that mp=: +/@:*"1 _ functions identically. Perhaps it would have made more sense to define something more like dot=: conjunction def 'u/@:v"1 _' so that matrix multiplication would be +dot* -- this would also correspond to the original APL implementation. ## Java public static double[][] mult(double a[][], double b[][]){//a[m][n], b[n][p] if(a.length == 0) return new double[0][0]; if(a[0].length != b.length) return null; //invalid dims int n = a[0].length; int m = a.length; int p = b[0].length; double ans[][] = new double[m][p]; for(int i = 0;i < m;i++){ for(int j = 0;j < p;j++){ for(int k = 0;k < n;k++){ ans[i][j] += a[i][k] * b[k][j]; } } } return ans;} ## JavaScript ### ES5 #### Iterative Works with: SpiderMonkey for the print() function Extends Matrix Transpose#JavaScript // returns a new matrixMatrix.prototype.mult = function(other) { if (this.width != other.height) { throw "error: incompatible sizes"; } var result = []; for (var i = 0; i < this.height; i++) { result[i] = []; for (var j = 0; j < other.width; j++) { var sum = 0; for (var k = 0; k < this.width; k++) { sum += this.mtx[i][k] * other.mtx[k][j]; } result[i][j] = sum; } } return new Matrix(result); } var a = new Matrix([[1,2],[3,4]])var b = new Matrix([[-3,-8,3],[-2,1,4]]);print(a.mult(b)); Output: -7,-6,11 -17,-20,25 #### Functional (function () { 'use strict'; // matrixMultiply:: [[n]] -> [[n]] -> [[n]] function matrixMultiply(a, b) { var bCols = transpose(b); return a.map(function (aRow) { return bCols.map(function (bCol) { return dotProduct(aRow, bCol); }); }); } // [[n]] -> [[n]] -> [[n]] function dotProduct(xs, ys) { return sum(zipWith(product, xs, ys)); } return matrixMultiply( [[-1, 1, 4], [ 6, -4, 2], [-3, 5, 0], [ 3, 7, -2]], [[-1, 1, 4, 8], [ 6, 9, 10, 2], [11, -4, 5, -3]] ); // --> [[51, -8, 26, -18], [-8, -38, -6, 34], // [33, 42, 38, -14], [17, 74, 72, 44]] // GENERIC LIBRARY FUNCTIONS // (a -> b -> c) -> [a] -> [b] -> [c] function zipWith(f, xs, ys) { return xs.length === ys.length ? ( xs.map(function (x, i) { return f(x, ys[i]); }) ) : undefined; } // [[a]] -> [[a]] function transpose(lst) { return lst[0].map(function (_, iCol) { return lst.map(function (row) { return row[iCol]; }); }); } // sum :: (Num a) => [a] -> a function sum(xs) { return xs.reduce(function (a, x) { return a + x; }, 0); } // product :: n -> n -> n function product(a, b) { return a * b; } })(); Output: [[51, -8, 26, -18], [-8, -38, -6, 34], [33, 42, 38, -14], [17, 74, 72, 44]] ### ES6 ((() => { 'use strict'; // matrixMultiply :: Num a => [[a]] -> [[a]] -> [[a]] const matrixMultiply = (a, b) => { const bCols = transpose(b); return a.map(aRow => bCols.map(bCol => dotProduct(aRow, bCol))); } // dotProduct :: Num a => [[a]] -> [[a]] -> [[a]] const dotProduct = (xs, ys) => sum(zipWith(product, xs, ys)); // GENERIC // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] const zipWith = (f, xs, ys) => xs.length === ys.length ? ( xs.map((x, i) => f(x, ys[i])) ) : undefined; // transpose :: [[a]] -> [[a]] const transpose = xs => xs[0].map((_, iCol) => xs.map(row => row[iCol])); // sum :: (Num a) => [a] -> a const sum = xs => xs.reduce((a, x) => a + x, 0); // product :: Num a => a -> a -> a const product = (a, b) => a * b; // TEST return matrixMultiply( [ [-1, 1, 4], [6, -4, 2], [-3, 5, 0], [3, 7, -2] ], [ [-1, 1, 4, 8], [6, 9, 10, 2], [11, -4, 5, -3] ] ); // --> [[51, -8, 26, -18], [-8, -38, -6, 34], // [33, 42, 38, -14], [17, 74, 72, 44]]}))(); Output: [[51, -8, 26, -18], [-8, -38, -6, 34], [33, 42, 38, -14], [17, 74, 72, 44]] ## jq In the following, an m by n matrix is represented by an array of m arrays, each of which is of length n. The function multiply(A;B) assumes its arguments are numeric matrices of the proper dimensions. Note that preallocating the resultant matrix would actually slow things down. def dot_product(a; b): a as$a | b as $b | reduce range(0;$a|length) as $i (0; . + ($a[$i] *$b[$i]) ); # transpose/0 expects its input to be a rectangular matrix (an array of equal-length arrays)def transpose: if (.[0] | length) == 0 then [] else [map(.[0])] + (map(.[1:]) | transpose) end ; # A and B should both be numeric matrices, A being m by n, and B being n by p.def multiply(A; B): A as$A | B as $B | ($B[0]|length) as $p | ($B|transpose) as $BT | reduce range(0;$A|length) as $i ([]; reduce range(0;$p) as $j (.; .[$i][$j] = dot_product($A[$i];$BT[$j] ) )) ; Example ((2|sqrt)/2) as$r | [ [$r,$r],  [(-($r)),$r]] as $R | multiply($R;$R)  Output: [[0,1.0000000000000002],[-1.0000000000000002,0]]  ## Julia The multiplication is denoted by * julia> [1 2 3 ; 4 5 6] * [1 2 ; 3 4 ; 5 6] # product of a 2x3 by a 3x22x2 Array{Int64,2}: 22 28 49 64 julia> [1 2 3] * [1,2,3] # product of a row vector by a column vector1-element Array{Int64,1}: 14  ## K  (1 2;3 4)_mul (5 6;7 8)(19 22 43 50) ## Klong  mul::{[a b];b::+y;{a::x;+/'{a*x}'b}'x} [[1 2] [3 4]] mul [[5 6] [7 8]][[19 22] [43 50]] ## Kotlin // version 1.1.3 typealias Vector = DoubleArraytypealias Matrix = Array<Vector> operator fun Matrix.times(other: Matrix): Matrix { val rows1 = this.size val cols1 = this[0].size val rows2 = other.size val cols2 = other[0].size require(cols1 == rows2) val result = Matrix(rows1) { Vector(cols2) } for (i in 0 until rows1) { for (j in 0 until cols2) { for (k in 0 until rows2) { result[i][j] += this[i][k] * other[k][j] } } } return result} fun printMatrix(m: Matrix) { for (i in 0 until m.size) println(m[i].contentToString())} fun main(args: Array<String>) { val m1 = arrayOf( doubleArrayOf(-1.0, 1.0, 4.0), doubleArrayOf( 6.0, -4.0, 2.0), doubleArrayOf(-3.0, 5.0, 0.0), doubleArrayOf( 3.0, 7.0, -2.0) ) val m2 = arrayOf( doubleArrayOf(-1.0, 1.0, 4.0, 8.0), doubleArrayOf( 6.0, 9.0, 10.0, 2.0), doubleArrayOf(11.0, -4.0, 5.0, -3.0) ) printMatrix(m1 * m2)} Output: [51.0, -8.0, 26.0, -18.0] [-8.0, -38.0, -6.0, 34.0] [33.0, 42.0, 38.0, -14.0] [17.0, 74.0, 72.0, 44.0]  ## Lang5 [[1 2 3] [4 5 6]] 'm dress[[1 2] [3 4] [5 6]] 'm dress * . Output: [ [ 22 28 ] [ 49 64 ] ] ## LFE Use the LFE transpose/1 function from Matrix transposition.  (defun matrix* (matrix-1 matrix-2) (list-comp ((<- a matrix-1)) (list-comp ((<- b (transpose matrix-2))) (lists:foldl #'+/2 0 (lists:zipwith #'*/2 a b)))))  Usage example in the LFE REPL:  > (set ma '((1 2) (3 4) (5 6) (7 8)))((1 2) (3 4) (5 6) (7 8))> (set mb (transpose ma))((1 3 5 7) (2 4 6 8))> (matrix* ma mb)((5 11 17 23) (11 25 39 53) (17 39 61 83) (23 53 83 113))  ## Liberty BASIC There is no native matrix capability. A set of functions is available at http://www.diga.me.uk/RCMatrixFuncs.bas implementing matrices of arbitrary dimension in a string format.  MatrixA$ ="4, 4,         1,  1,  1,  1,         2,  4,  8,  16,             3,  9, 27,  81,          4, 16, 64, 256"MatrixB$="4, 4, 4, -3, 4/3, -1/4 , -13/3, 19/4, -7/3, 11/24, 3/2, -2, 7/6, -1/4, -1/6, 1/4, -1/6, 1/24" print "Product of two matrices"call DisplayMatrix MatrixA$print "         *"call DisplayMatrix MatrixB$print " ="MatrixP$ =MatrixMultiply$( MatrixA$, MatrixB$)call DisplayMatrix MatrixP$ 
Output:
Product of two matrices
| 1.00000 1.00000 1.00000 1.00000 |
| 2.00000 4.00000 8.00000 16.00000 |
| 3.00000 9.00000 27.00000 81.00000 |
| 4.00000 16.00000 64.00000 256.00000 |

*
| 4.00000 -3.00000 1.33333 -0.25000 |
| -4.33333 4.75000 -2.33333 0.45833 |
| 1.50000 -2.00000 1.16667 -0.25000 |
| -0.16667 0.25000 -0.16667 0.04167 |

=
| 1.00000 0.00000 0.00000 0.00000 |
| 0.00000 1.00000 0.00000 0.00000 |
| 0.00000 0.00000 1.00000 0.00000 |
| 0.00000 0.00000 0.00000 1.00000 |

## Logo

TO LISTVMD :A :F :C :NV;PROCEDURE LISTVMD;A = LIST;F = ROWS;C = COLS;NV = NAME OF MATRIX / VECTOR NEW;this procedure transform a list in matrix / vector square or rect (LOCAL "CF "CC "NV "T "W)MAKE "CF 1MAKE "CC 1MAKE "NV (MDARRAY (LIST :F :C) 1)MAKE "T :F * :CFOR [Z 1 :T][MAKE "W ITEM :Z :AMDSETITEM (LIST :CF :CC) :NV :WMAKE "CC :CC + 1IF :CC = :C + 1 [MAKE "CF :CF + 1 MAKE "CC 1]]OUTPUT :NVEND::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::  TO XX; MAIN PROGRAM;LRCVS 10.04.12; THIS PROGRAM multiplies two "square" matrices / vector ONLY!!!; THE RECTANGULAR NOT WORK!!! CT CS HT ; FIRST DATA MATRIX / VECTORMAKE "A [1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49]MAKE "FA 5 ;"ROWSMAKE "CA 5 ;"COLS ; SECOND DATA MATRIX / VECTORMAKE "B [2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50]MAKE "FB 5 ;"ROWSMAKE "CB 5 ;"COLS  IF (OR :FA <> :CA :FB <>:CB) [PRINT "Las_matrices/vector_no_son_cuadradas THROW"TOPLEVEL ]IFELSE (OR :CA <> :FB :FA <> :CB) [PRINT"Las_matrices/vector_no_son_compatibles THROW "TOPLEVEL ][MAKE "MA LISTVMD :A:FA :CA "MA MAKE "MB LISTVMD :B :FB :CB "MB] ;APPLICATION <<< "LISTVMD" PRINT (LIST "THIS_IS: "ROWS "X "COLS)PRINT []PRINT (LIST :MA "=_M1 :FA "ROWS "X :CA "COLS)PRINT []PRINT (LIST :MB "=_M2 :FA "ROWS "X :CA "COLS)PRINT []  MAKE "T :FA * :CBMAKE "RE (ARRAY :T 1)  MAKE "CO 0FOR [AF 1 :CA][FOR [AC 1 :CA][MAKE "TEMP 0FOR [I 1 :CA ][MAKE "TEMP :TEMP + (MDITEM (LIST :I :AF) :MA) * (MDITEM (LIST :AC :I) :MB)]MAKE "CO :CO + 1SETITEM :CO :RE :TEMP]]  PRINT []PRINT (LIST "THIS_IS: :FA "ROWS "X :CB "COLS)SHOW LISTVMD :RE :FA :CB "TO ;APPLICATION <<< "LISTVMD"END  ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::\                 M1 * M2 RESULT / SOLUTION  1  3  5  7  9    2  4  6  8 10    830 1880 2930 3980 503011 13 15 17 19   12 14 16 18 20    890 2040 3190 4340 549021 23 25 27 29 X 22 24 26 28 30 =  950 2200 3450 4700 595031 33 35 37 39   32 34 36 38 40   1010 2360 3710 5060 641041 43 45 47 49   42 44 46 48 50   1070 2520 3970 5420 6870 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::\  NOW IN LOGO!!!!  THIS_IS: ROWS X COLS {{1 3 5 7 9} {11 13 15 17 19} {21 23 25 27 29} {31 33 35 37 39} {41 43 45 4749}} =_M1 5 ROWS X 5 COLS {{2 4 6 8 10} {12 14 16 18 20} {22 24 26 28 30} {32 34 36 38 40} {42 44 46 4850}} =_M2 5 ROWS X 5 COLS  THIS_IS: 5 ROWS X 5 COLS{{830 1880 2930 3980 5030} {890 2040 3190 4340 5490} {950 2200 3450 4700 5950}{1010 2360 3710 5060 6410} {1070 2520 3970 5420 6870}}

## Lua

function MatMul( m1, m2 )    if #m1[1] ~= #m2 then       -- inner matrix-dimensions must agree        return nil          end      local res = {}     for i = 1, #m1 do        res[i] = {}        for j = 1, #m2[1] do            res[i][j] = 0            for k = 1, #m2 do                res[i][j] = res[i][j] + m1[i][k] * m2[k][j]            end        end    end     return resend -- Test for MatMulmat1 = { { 1, 2, 3 }, { 4, 5, 6 } }mat2 = { { 1, 2 }, { 3, 4 }, { 5, 6 } }erg = MatMul( mat1, mat2 )for i = 1, #erg do    for j = 1, #erg[1] do        io.write( erg[i][j] )        io.write("  ")    end    io.write("\n")end 

### SciLua

Using the sci.alg library from scilua.org

local alg = require("sci.alg")mat1 = alg.tomat{{1, 2, 3}, {4, 5, 6}}mat2 = alg.tomat{{1, 2}, {3, 4}, {5, 6}}mat3 = mat1[] ** mat2[]print(mat3)
Output:
+22.00000,+28.00000
+49.00000,+64.00000

## Maple

A := <<1|2|3>,<4|5|6>>; B := <<1,2,3>|<4,5,6>|<7,8,9>|<10,11,12>>; A . B;
Output:
                                    [1  2  3]
A := [       ]
[4  5  6]

[1  4  7  10]
[           ]
B := [2  5  8  11]
[           ]
[3  6  9  12]

[14  32   50   68]
[                ]
[32  77  122  167]

## MathCortex

 >> A = [2,3; -2,1] 2           3         -2           1          >> B = [1,2;4,2] 1           2          4           2          >> A * B 14          10         2          -2   

## Mathematica

The Wolfram Language supports both dot products and element-wise multiplication of matrices.

This computes a dot product:

Dot[{{a, b}, {c, d}}, {{w, x}, {y, z}}]

With the following output:

{{a w + b y, a x + b z}, {c w + d y, c x + d z}}

This also computes a dot product, using the infix . notation:

{{a, b}, {c, d}} . {{w, x}, {y, z}}

This does element-wise multiplication of matrices:

Times[{{a, b}, {c, d}}, {{w, x}, {y, z}}]

With the following output:

{{a w, b x}, {c y, d z}}

Alternative infix notations '*' and ' ' (space, indicating multiplication):

{{a, b}, {c, d}}*{{w, x}, {y, z}}
{{a, b}, {c, d}} {{w, x}, {y, z}}

In all cases matrices can be fully symbolic or numeric or mixed symbolic and numeric. Numeric matrices support arbitrary numerical magnitudes, arbitrary precision as well as complex numbers:

Dot[{{85, 60, 65}, {54, 99, 33}, {46, 52, 87}}, {{89, 77, 98}, {55, 27, 25}, {80, 68, 85}}]

With the following output:

{{16065, 12585, 15355}, {12891, 9075, 10572}, {13914, 10862, 13203}}

## MATLAB

Matlab contains two methods of multiplying matrices: by using the "mtimes(matrix,matrix)" function, or the "*" operator.

>> A = [1 2;3 4] A =      1     2     3     4 >> B = [5 6;7 8] B =      5     6     7     8 >> A * B ans =     19    22    43    50 >> mtimes(A,B) ans =     19    22    43    50

## Maxima

a: matrix([1, 2],          [3, 4],          [5, 6],          [7, 8])$b: matrix([1, 2, 3], [4, 5, 6])$ a . b;/* matrix([ 9, 12, 15],          [19, 26, 33],          [29, 40, 51],          [39, 54, 69]) */

## Nial

|A :=  4 4 reshape 1 1 1 1 2 4 8 16 3 9 27 81 4 16 64 256=1  1  1   1=2  4  8  16=3  9 27  81=4 16 64 256|B := inverse A |A innerproduct B=1.        0.     8.3e-17     -2.9e-16=1.3e-15   1.     -4.4e-16    -3.3e-16=0.        0.      1.         4.4e-16=0.        0.      0.         1.

import strfmt type Matrix[M,N: static[int]] = array[M, array[N, float]] let a = [[1.0,  1.0,  1.0,   1.0],         [2.0,  4.0,  8.0,  16.0],         [3.0,  9.0, 27.0,  81.0],         [4.0, 16.0, 64.0, 256.0]] let b = [[  4.0  , -3.0  ,  4/3.0,  -1/4.0 ],         [-13/3.0, 19/4.0, -7/3.0,  11/24.0],         [  3/2.0, -2.0  ,  7/6.0,  -1/4.0 ],         [ -1/6.0,  1/4.0, -1/6.0,   1/24.0]] proc $(m: Matrix): string = result = "([" for r in m: if result.len > 2: result.add "]\n [" for val in r: result.add val.format("8.2f") result.add "])" proc *[M,P,N](a: Matrix[M,P]; b: Matrix[P,N]): Matrix[M,N] = for i in result.low .. result.high: for j in result[0].low .. result[0].high: for k in a[0].low .. a[0].high: result[i][j] += a[i][k] * b[k][j] echo aecho becho a * becho b * a ## OCaml This version works on arrays of arrays of ints: let matrix_multiply x y = let x0 = Array.length x and y0 = Array.length y in let y1 = if y0 = 0 then 0 else Array.length y.(0) in let z = Array.make_matrix x0 y1 0 in for i = 0 to x0-1 do for j = 0 to y1-1 do for k = 0 to y0-1 do z.(i).(j) <- z.(i).(j) + x.(i).(k) * y.(k).(j) done done done; z # matrix_multiply [|[|1;2|];[|3;4|]|] [|[|-3;-8;3|];[|-2;1;4|]|];; - : int array array = [|[|-7; -6; 11|]; [|-17; -20; 25|]|]  Translation of: Scheme This version works on lists of lists of ints: (* equivalent to (apply map ...) *)let rec mapn f lists = assert (lists <> []); if List.mem [] lists then [] else f (List.map List.hd lists) :: mapn f (List.map List.tl lists) let matrix_multiply m1 m2 = List.map (fun row -> mapn (fun column -> List.fold_left (+) 0 (List.map2 ( * ) row column)) m2) m1 # matrix_multiply [[1;2];[3;4]] [[-3;-8;3];[-2;1;4]];; - : int list list = [[-7; -6; 11]; [-17; -20; 25]]  ## Octave a = zeros(4);% prepare the matrix% 1 1 1 1% 2 4 8 16% 3 9 27 81% 4 16 64 256for i = 1:4 for j = 1:4 a(i, j) = i^j; endforendforb = inverse(a);a * b ## Ol Translation of: Scheme This version works on lists of lists:  (define (matrix-multiply matrix1 matrix2)(map (lambda (row) (apply map (lambda column (apply + (map * row column))) matrix2)) matrix1))  > (matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4))) ((-7 -6 11) (-17 -20 25))  ## OxygenBasic When using matrices in Video graphics, speed is important. Here is a matrix multiplier written in OxygenBasics's x86 Assembly code.  'Example of matrix layout mapped to an array of 4x4 cells ' ' 0 4 8 C ' 1 5 9 D ' 2 6 A E ' 3 7 B F ' % MatrixType double sub MatrixMul(MatrixType *A,*B,*C, sys n) '======================================== ' ' #if leftmatch matrixtype single % OneStep 4 % mtype single #endif ' #if leftmatch matrixtype double % OneStep 8 % mtype double #endif sys [email protected], [email protected], [email protected] sys ColStep=OneStep*n mov ecx,pa mov edx,pb mov eax,pc mov esi,n ( call column : dec esi : jg repeat ) exit sub column: '====== mov edi,n ( call cell : dec edi : jg repeat ) add edx,ColStep sub ecx,ColStep ret cell: ' row A * column B '======================= 'matrix data is stored ascending vertically then horizontally 'thus rows are minor, columns are major ' push ecx push edx push eax mov eax,4 fldz ( fld mtype [ecx] fmul mtype [edx] faddp st1 add ecx,ColStep 'next column of matrix A add edx,OneStep 'next row of matrix B dec eax jnz repeat ) pop eax fstp mtype [eax] 'assign to next row of matrix C ' pop edx pop ecx add eax,OneStep 'next cell in column of matrix C (columns then rows) add ecx,OneStep 'next row of matrix A ret ' end sub function ShowMatrix(MatrixType*A,sys n) as string '================================================ string cr=chr(13)+chr(10), tab=chr(9) function="MATRIX " n "x" n cr cr sys i,j,m ' for i=1 to n m=0 for j=1 to n function+=str( A[m+i] ) tab m+=n next function+=cr next end function 'TEST '==== % n 4 MatrixType A[n*n],B[n*n],C[n*n] 'reading vertically (minor) then left to right (major) A <= 4,0,0,1, 0,4,0,0, 0,0,4,0, 0,0,0,4 B <= 2,0,0,2, 0,2,0,0, 0,0,2,0, 0,0,0,2 MatrixMul A,B,C,n Print ShowMatrix C,n  ## PARI/GP M*N ## Perl For most applications involving extensive matrix arithmetic, using the CPAN module called "PDL" (that stands for "Perl Data Language") would probably be the easiest and most efficient approach. That said, here's an implementation of matrix multiplication in plain Perl. This function takes two references to arrays of arrays and returns the product as a reference to a new anonymous array of arrays. sub mmult { our @a; local *a = shift; our @b; local *b = shift; my @p = []; my$rows = @a;  my $cols = @{$b[0] };  my $n = @b - 1; for (my$r = 0 ; $r <$rows ; ++$r) { for (my$c = 0 ; $c <$cols ; ++$c) {$p[$r][$c] += $a[$r][$_] *$b[$_][$c]           foreach 0 .. $n; } } return [@p]; } sub display { join("\n" => map join(" " => map(sprintf("%4d",$_), @$_)), @{+shift})."\n" } @a =( [1, 2], [3, 4]); @b = ( [-3, -8, 3], [-2, 1, 4]);$c = mmult(\@a,\@b);display($c) Output:  -7 -6 11 -17 -20 25 ## Perl 6 Translation of: Perl 5 Works with: Rakudo version 2015-09-22 There are three ways in which this example differs significantly from the original Perl 5 code. These are not esoteric differences; all three of these features typically find heavy use in Perl 6. First, we can use a real signature that can bind two arrays as arguments, because the default in Perl 6 is not to flatten arguments unless the signature specifically requests it. We don't need to pass the arrays with backslashes because the binding choice is made lazily by the signature itself at run time; in Perl 5 this choice must be made at compile time. Also, we can bind the arrays to formal parameters that are really lexical variable names; in Perl 5 they can only be bound to global array objects (via a typeglob assignment). Second, we use the X cross operator in conjunction with a two-parameter closure to avoid writing nested loops. The X cross operator, along with Z, the zip operator, is a member of a class of operators that expect lists on both sides, so we call them "list infix" operators. We tend to define these operators using capital letters so that they stand out visually from the lists on both sides. The cross operator makes every possible combination of the one value from the first list followed by one value from the second. The right side varies most rapidly, just like an inner loop. (The X and Z operators may both also be used as meta-operators, Xop or Zop, distributing some other operator "op" over their generated list. All metaoperators in Perl 6 may be applied to user-defined operators as well.) Third is the use of prefix ^ to generate a list of numbers in a range. Here it is used on an array to generate all the indexes of the array. We have a way of indicating a range by the infix .. operator, and you can put a ^ on either end to exclude that endpoint. We found ourselves writing 0 ..^ @a so often that we made ^@a a shorthand for that. It's pronounced "upto". The array is evaluated in a numeric context, so it returns the number of elements it contains, which is exactly what you want for the exclusive limit of the range. sub mmult(@a,@b) { my @p; for ^@a X ^@b[0] -> ($r, $c) { @p[$r][$c] += @a[$r][$_] * @b[$_][$c] for ^@b; } @p;} my @a = [1, 1, 1, 1], [2, 4, 8, 16], [3, 9, 27, 81], [4, 16, 64, 256]; my @b = [ 4 , -3 , 4/3, -1/4 ], [-13/3, 19/4, -7/3, 11/24], [ 3/2, -2 , 7/6, -1/4 ], [ -1/6, 1/4, -1/6, 1/24]; .say for mmult(@a,@b); Output: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] Note that these are not rounded values, but exact, since all the math was done in rationals. Hence we need not rely on format tricks to hide floating-point inaccuracies. Just for the fun of it, here's a functional version that uses no temp variables or side effects. Some people will find this more readable and elegant, and others will, well, not. sub mmult(\a,\b) { [ for ^a -> \r { [ for ^b[0] -> \c { [+] a[r;^b] Z* b[^b;c] } ] } ]} Here we use Z with an "op" of *, which is a zip with multiply. This, along with the [+] reduction operator, replaces the inner loop. We chose to split the outer X loop back into two loops to make it convenient to collect each subarray value in [...]. It just collects all the returned values from the inner loop and makes an array of them. The outer loop simply returns the outer array. ## Phix Copy of Euphoria function matrix_mul(sequence a, sequence b)sequence c if length(a[1]) != length(b) then return 0 else c = repeat(repeat(0,length(b[1])),length(a)) for i=1 to length(a) do for j=1 to length(b[1]) do for k=1 to length(a[1]) do c[i][j] += a[i][k]*b[k][j] end for end for end for return c end ifend function ## PicoLisp (de matMul (Mat1 Mat2) (mapcar '((Row) (apply mapcar Mat2 '(@ (sum * Row (rest))) ) ) Mat1 ) ) (matMul '((1 2 3) (4 5 6)) '((6 -1) (3 2) (0 -3)) ) Output: -> ((12 -6) (39 -12)) ## PL/I  /* Matrix multiplication of A by B, yielding C */MMULT: procedure (a, b, c); declare (a, b, c)(*,*) float controlled; declare (i, j, m, n, p) fixed binary; if hbound(a,2) ^= hbound(b,1) then do; put skip list ('Matrices are incompatible for matrix multiplication'); signal error; end; m = hbound(a, 1); p = hbound(b, 2); if allocation(c) > 0 then free c; allocate c(m,p); do i = 1 to m; do j = 1 to p; c(i,j) = sum(a(i,*) * b(*,j) ); end; end;end MMULT;  ## Pop11 define matmul(a, b) -> c; lvars ba = boundslist(a), bb = boundslist(b); lvars i, i0 = ba(1), i1 = ba(2); lvars j, j0 = bb(1), j1 = bb(2); lvars k, k0 = bb(3), k1 = bb(4); if length(ba) /= 4 then throw([need_2d_array ^a]) endif; if length(bb) /= 4 then throw([need_2d_array ^b]) endif; if ba(3) /= j0 or ba(4) /= j1 then throw([dimensions_do_not_match ^a ^b]); endif; newarray([^i0 ^i1 ^k0 ^k1], 0) -> c; for i from i0 to i1 do for k from k0 to k1 do for j from j0 to j1 do c(i, k) + a(i, j)*b(j, k) -> c(i, k); endfor; endfor; endfor;enddefine; ## PowerShell  function multarrays($a, $b) {$c = @()    if($a -and$b) {        $n =$a.count - 1        $m =$b[0].count - 1        $c = @(0)*($n+1)        foreach ($i in 0..$n) {                $c[$i] = foreach ($j in 0..$m) {                 $sum = 0 foreach ($k in 0..$n){$sum += $a[$i][$k]*$b[$k][$j]}                $sum } } }$c}function show($a) { if($a) {         0..($a.count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }    }}$a = @(@(1,2),@(3,4))$b = @(@(5,6),@(7,8))$c = @(5,6)"$a ="show $a"""$b ="show $b"""$c ="$c"""$a * $b ="show (multarrays$a $b)" ""$a * $c ="show (multarrays$a $c)  Output: $a =
1 2
3 4

$b = 5 6 7 8$c =
5
6

$a *$b =
19 22
43 50

$a *$c =
17
39


## Prolog

Translation of: Scheme
Works with: SWI Prolog version 5.9.9
% SWI-Prolog has transpose/2 in its clpfd library:- use_module(library(clpfd)). % N is the dot product of lists V1 and V2.dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N).product(N1,N2,N3) :- N3 is N1*N2. % Matrix multiplication with matrices represented% as lists of lists. M3 is the product of M1 and M2mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3).mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3).

## PureBasic

Matrices represented as integer arrays with rows in the first dimension and columns in the second.

Procedure multiplyMatrix(Array a(2), Array b(2), Array prd(2))  Protected ar = ArraySize(a())    ;#rows for matrix a  Protected ac = ArraySize(a(), 2) ;#cols for matrix a  Protected br = ArraySize(b())    ;#rows for matrix b  Protected bc = ArraySize(b(), 2) ;#cols for matrix b   If ac = br    Dim prd(ar, bc)     Protected i, j, k    For i = 0 To ar      For j = 0 To bc         For k = 0 To br ;ac          prd(i, j) = prd(i, j) + (a(i, k) * b(k, j))        Next      Next    Next     ProcedureReturn #True  ;multiplication performed, product in prd()  Else    ProcedureReturn #False ;multiplication not performed, dimensions invalid   EndIf EndProcedure

DataSection  Data.i 2,3           ;matrix a (#rows, #cols)  Data.i 1,2,3, 4,5,6  ;elements by row   Data.i 3,1           ;matrix b (#rows, #cols)  Data.i 1, 5, 9       ;elements by rowEndDataSection Procedure displayMatrix(Array a(2), text.s)  Protected i, j   Protected columns = ArraySize(a(), 2), rows = ArraySize(a(), 1)   PrintN(text + ": (" + Str(rows + 1) + ", " + Str(columns + 1) + ")")  For i = 0 To rows    For j = 0 To columns      Print(LSet(Str(a(i, j)), 4, " "))    Next    PrintN("")  Next  PrintN("")EndProcedure Procedure loadMatrix(Array a(2))  Protected rows, columns, i, j  Read.i rows  Read.i columns   Dim a(rows - 1, columns - 1)   For i = 0 To rows - 1    For j = 0 To columns - 1      Read.i a(i, j)    Next  NextEndProcedure Dim a(0,0)Dim b(0,0)Dim c(0,0) If OpenConsole()  loadMatrix(a()): displayMatrix(a(), "matrix a")  loadMatrix(b()): displayMatrix(b(), "matrix b")   If multiplyMatrix(a(), b(), c())    displayMatrix(c(), "product of a * b")  Else    PrintN("product of a * b is undefined")  EndIf    Print(#CRLF$+ #CRLF$ + "Press ENTER to exit")  Input()  CloseConsole()EndIf
Output:
matrix a: (2, 3)
1   2   3
4   5   6

matrix b: (3, 1)
1
5
9

product of a * b: (2, 1)
38
83

## Python

a=((1,  1,  1,   1), # matrix A #     (2,  4,  8,  16),     (3,  9, 27,  81),     (4, 16, 64, 256)) b=((  4  , -3  ,  4/3.,  -1/4. ), # matrix B #     (-13/3., 19/4., -7/3.,  11/24.),     (  3/2., -2.  ,  7/6.,  -1/4. ),     ( -1/6.,  1/4., -1/6.,   1/24.))   def MatrixMul( mtx_a, mtx_b):    tpos_b = zip( *mtx_b)    rtn = [[ sum( ea*eb for ea,eb in zip(a,b)) for b in tpos_b] for a in mtx_a]    return rtn  v = MatrixMul( a, b ) print 'v = ('for r in v:    print '[',     for val in r:        print '%8.2f '%val,     print ']'print ')'  u = MatrixMul(b,a) print 'u = 'for r in u:    print '[',     for val in r:        print '%8.2f '%val,     print ']'print ')'
Another one,
Translation of: Scheme
from operator import mul def matrixMul(m1, m2):  return map(    lambda row:      map(        lambda *column:          sum(map(mul, row, column)),        *m2),    m1)

Using list comprehensions, multiplying matrices represented as lists of lists. (Input is not validated):

def mm(A, B):    return [[sum(x * B[i][col] for i,x in enumerate(row)) for col in range(len(B[0]))] for row in A]

Another one, use numpy the most popular array package for python

 import numpy as npnp.dot(a,b)#or if a is an arraya.dot(b)

## R

a %*% b

## Racket

Translation of: Scheme
 #lang racket(define (m-mult m1 m2)  (for/list ([r m1])    (for/list ([c (apply map list m2)])      (apply + (map * r c)))))(m-mult '((1 2) (3 4)) '((5 6) (7 8)));; -> '((19 22) (43 50))

Alternative:

 #lang racket(require math)(matrix* (matrix [[1 2] [3 4]]) (matrix [[5 6] [7 8]]));; -> (array #[#[19 22] #[43 50]])

## Rascal

public rel[real, real, real] matrixMultiplication(rel[real x, real y, real v] matrix1, rel[real x, real y, real v] matrix2){	if (max(matrix1.x) == max(matrix2.y)){		p = {<x1,y1,x2,y2, v1*v2> | <x1,y1,v1> <- matrix1, <x2,y2,v2> <- matrix2}; 		result = {};		for (y <- matrix1.y){			for (x <- matrix2.x){				v = (0.0 | it + v | <x1, y1, x2, y2, v> <- p,  x==x2 && y==y1, x1==y2 && y2==x1);				result += <x,y,v>;			}		}		return result;	}	else throw "Matrix sizes do not match."; //a matrix, given by a relation of the x-coordinate, y-coordinate and 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>};

## REXX

/*REXX program multiplies two matrices together, displays the matrices and the results. */x.=;  x.1=1 2                                    /*╔═══════════════════════════════════╗*/      x.2=3 4                                    /*║ As none of the matrix values have ║*/      x.3=5 6                                    /*║ a sign,  quotes aren't needed.    ║*/      x.4=7 8                                    /*╚═══════════════════════════════════╝*/                 do   r=1  while x.r\==''        /*build the "A" matrix from X. numbers.*/                   do c=1  while x.r\=='';   parse var x.r a.r.c x.r;      end  /*c*/                 end   /*r*/Arows=r-1                                        /*adjust the number of rows  (DO loop).*/Acols=c-1                                        /*   "    "     "    " cols    "   "  .*/y.=;  y.1=1 2 3      y.2=4 5 6                 do   r=1  while y.r\==''        /*build the "B" matrix from Y. numbers.*/                   do c=1  while y.r\=='';   parse var y.r b.r.c y.r;      end  /*c*/                 end   /*r*/Brows=r-1                                        /*adjust the number of rows  (DO loop).*/Bcols=c-1                                        /*   "     "    "    " cols    "   "   */c.=0;  w=0                                       /*W  is max width of an matrix element.*/            do       i=1  for Arows              /*multiply matrix  A  and  B  ───►   C */              do     j=1  for Bcols                  do k=1  for Acols;    c.i.j=c.i.j  +  a.i.k * b.k.j                                                     w=max(w, length(c.i.j))                  end   /*k*/                    /*  ↑                                  */              end       /*j*/                    /*  └──◄─── maximum width of elements. */            end         /*i*/ call showMatrix  'A',  Arows,  Acols             /*display matrix  A ───►  the terminal.*/call showMatrix  'B',  Brows,  Bcols             /*   "       "    B ───►   "     "     */call showMatrix  'C',  Arows,  Bcols             /*   "       "    C ───►   "     "     */exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/showMatrix: parse arg mat,rows,cols;   say;   say center(mat 'matrix', cols*(w+1) +4, "─")                    do   r=1  for rows;  _=                      do c=1  for cols;  _=_ right(value(mat'.'r"."c), w);  end;     say _                    end   /*r*/            return

output

─A matrix─
1  2
3  4
5  6
7  8

──B matrix───
1  2  3
4  5  6

──C matrix───
9 12 15
19 26 33
29 40 51
39 54 69


## Ring

 load "stdlib.ring"n = 3C = newlist(n,n)A = [[1,2,3], [4,5,6], [7,8,9]]B = [[1,0,0], [0,1,0], [0,0,1]]for i = 1 to n    for j = 1 to n       for k = 1 to n           C[i][k] += A[i][j] * B[j][k]       next    nextnextfor i = 1 to n    for j = 1 to n        see C[i][j] + " "    next    see nlnext

Output:

123
456
789


## Ruby

Using 'matrix' from the standard library:

require 'matrix' Matrix[[1, 2],       [3, 4]] * Matrix[[-3, -8, 3],                        [-2,  1, 4]]
Output:
Matrix[[-7, -6, 11], [-17, -20, 25]]

Version for lists:
def matrix_mult(a, b)  a.map do |ar|    b.transpose.map do |bc|      ar.zip(bc).map(&:*).inject(&:+)    end  endend

## Rust

 struct Matrix {    dat: [[f32; 3]; 3]} impl Matrix {    pub fn mult_m(a: Matrix, b: Matrix) -> Matrix    {        let mut out = Matrix {            dat: [[0., 0., 0.],                  [0., 0., 0.],                  [0., 0., 0.]                  ]        };         for i in 0..3{            for j in 0..3 {                for k in 0..3 {                    out.dat[i][j] += a.dat[i][k] * b.dat[k][j];                }            }        }         out    }     pub fn print(self)    {        for i in 0..3 {            for j in 0..3 {                print!("{} ", self.dat[i][j]);            }            print!("\n");        }    }} fn main(){    let  a = Matrix {        dat: [[1., 2., 3.],              [4., 5., 6.],              [7., 8., 9.]              ]    };     let  b = Matrix {        dat: [[1., 0., 0.],              [0., 1., 0.],              [0., 0., 1.]]    };           let c = Matrix::mult_m(a, b);      c.print();}

## Scala

Works with: Scala version 2.8

Assuming an array of arrays representation:

def mult[A](a: Array[Array[A]], b: Array[Array[A]])(implicit n: Numeric[A]) = {  import n._  for (row <- a)  yield for(col <- b.transpose)        yield row zip col map Function.tupled(_*_) reduceLeft (_+_)}

For any subclass of Seq (which does not include Java-specific arrays):

def mult[A, CC[X] <: Seq[X], DD[Y] <: Seq[Y]](a: CC[DD[A]], b: CC[DD[A]])(implicit n: Numeric[A]): CC[DD[A]] = {  import n._  for (row <- a)  yield for(col <- b.transpose)        yield row zip col map Function.tupled(_*_) reduceLeft (_+_)}

Examples:

scala> Array(Array(1, 2), Array(3, 4))
res0: Array[Array[Int]] = Array(Array(1, 2), Array(3, 4))

scala> Array(Array(-3, -8, 3), Array(-2, 1, 4))
res1: Array[Array[Int]] = Array(Array(-3, -8, 3), Array(-2, 1, 4))

scala> mult(res0, res1)
res2: Array[scala.collection.mutable.GenericArray[Int]] = Array(GenericArray(-7, -6, 11), GenericArray(-17, -20, 25))

scala> res0.map(_.toList).toList
res5: List[List[Int]] = List(List(1, 2), List(3, 4))

scala> res1.map(_.toList).toList
res6: List[List[Int]] = List(List(-3, -8, 3), List(-2, 1, 4))

scala> mult(res5, res6)
res7: Seq[Seq[Int]] = List(List(-7, -6, 11), List(-17, -20, 25))


A fully generic multiplication that returns the same collection as received is possible, but much more verbose.

## Scheme

Translation of: Common Lisp

This version works on lists of lists:

(define (matrix-multiply matrix1 matrix2)  (map   (lambda (row)    (apply map     (lambda column      (apply + (map * row column)))     matrix2))   matrix1))
> (matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4)))
((-7 -6 11) (-17 -20 25))


## Seed7

const type: matrix is array array float; const func matrix: (in matrix: left) * (in matrix: right) is func  result    var matrix: result is matrix.value;  local    var integer: i is 0;    var integer: j is 0;    var integer: k is 0;    var float: accumulator is 0.0;  begin    if length(left[1]) <> length(right) then      raise RANGE_ERROR;    else      result := length(left) times length(right[1]) times 0.0;      for i range 1 to length(left) do        for j range 1 to length(right) do          accumulator := 0.0;          for k range 1 to length(left) do            accumulator +:= left[i][k] * right[k][j];          end for;          result[i][j] := accumulator;        end for;      end for;    end if;  end func;

Original source: [1]

## SequenceL

The product of the m×p matrix A with the p×n matrix B is the m×n matrix whose (i,j)'th entry is
${\displaystyle \sum _{k=1}^{p}A(i,k)B(k,j)}$

The SequenceL definition mirrors that definition more or less exactly:

matmul(A(2), B(2)) [i,j] :=         let k := 1...size(B);         in  sum( A[i,k] * B[k,j] ); //Example Usea := [[1, 2],      [3, 4]]; b := [[-3, -8, 3],       [-2,  1, 4]]; test := matmul(a, b);

It can be written a little more simply using the all keyword:

matmul(A(2), B(2)) [i,j] := sum( A[i,all] * B[all,j] );

## Sidef

func matrix_multi(a, b) {    var m = [[]]    for r in ^a {        for c in ^b[0] {            for i in ^b {                m[r][c] := 0 += (a[r][i] * b[i][c])            }        }    }    return m} var a = [          [1, 2],          [3, 4],          [5, 6],          [7, 8]        ] var b = [          [1, 2, 3],          [4, 5, 6]        ] for line in matrix_multi(a, b) {    say line.map{|i|'%3d' % i }.join(', ')}
Output:
  9,  12,  15
19,  26,  33
29,  40,  51
39,  54,  69

Works with: FriCAS
Works with: OpenAxiom
Works with: Axiom
(1) -> A:=matrix [[1,2],[3,4],[5,6],[7,8]]         +1  2+        |    |        |3  4|   (1)  |    |        |5  6|        |    |        +7  8+                                                        Type: Matrix(Integer)(2) -> B:=matrix [[1,2,3],[4,5,6]]         +1  2  3+   (2)  |       |        +4  5  6+                                                        Type: Matrix(Integer)(3) -> A*B         +9   12  15+        |          |        |19  26  33|   (3)  |          |        |29  40  51|        |          |        +39  54  69+                                                        Type: Matrix(Integer)

Domain:Matrix(R)

## SQL

CREATE TABLE a (x INTEGER, y INTEGER, e REAL);CREATE TABLE b (x INTEGER, y INTEGER, e REAL); -- test data-- A is a 2x2 matrixINSERT INTO a VALUES(0,0,1); INSERT INTO a VALUES(1,0,2);INSERT INTO a VALUES(0,1,3); INSERT INTO a VALUES(1,1,4); -- B is a 2x3 matrixINSERT INTO b VALUES(0,0,-3); INSERT INTO b VALUES(1,0,-8); INSERT INTO b VALUES(2,0,3);INSERT INTO b VALUES(0,1,-2); INSERT INTO b VALUES(1,1, 1); INSERT INTO b VALUES(2,1,4); -- C is 2x2 * 2x3 so will be a 2x3 matrixSELECT rhs.x, lhs.y, (SELECT SUM(a.e*b.e) FROM a, b                             WHERE a.y = lhs.y                               AND b.x = rhs.x                               AND a.x = b.y)       INTO TABLE c       FROM a AS lhs, b AS rhs       WHERE lhs.x = 0 AND rhs.y = 0;

## Stata

### Stata matrices

. mat a=1,2,3\4,5,6. mat b=1,1,0,0\1,0,0,1\0,0,1,1. mat c=a*b. mat list c c[2,4]    c1  c2  c3  c4r1   3   1   3   5r2   9   4   6  11

### Mata

: a=1,2,3\4,5,6: b=1,1,0,0\1,0,0,1\0,0,1,1: a*b        1    2    3    4    +---------------------+  1 |   3    1    3    5  |  2 |   9    4    6   11  |    +---------------------+

## Tcl

Works with: Tcl version 8.5

## Ursala

There is a library function for matrix multiplication of IEEE double precision floating point numbers. This example shows how to define and use a matrix multiplication function over any chosen field given only the relevant product and sum functions, in this case for the built in rational number type.

#import rat a = <   <1/1,  1/1,  1/1,   1/1>,   <2/1,  4/1,  8/1,  16/1>,   <3/1,  9/1, 27/1,  81/1>,   <4/1, 16/1, 64/1, 256/1>> b = <   <  4/1, -3/1,  4/3,  -1/4>,   <-13/3, 19/4, -7/3,  11/24>,   <  3/2, -2/1,  7/6,  -1/4>,   < -1/6,  1/4, -1/6,   1/24>> mmult = *rK7lD *rlD sum:-0.+ product*p #cast %qLL test = mmult(a,b)
Output:
<
<1/1,0/1,0/1,0/1>,
<0/1,1/1,0/1,0/1>,
<0/1,0/1,1/1,0/1>,
<0/1,0/1,0/1,1/1>>

## VBScript

 Dim matrix1(2,2)matrix1(0,0) = 3 : matrix1(0,1) = 7 : matrix1(0,2) = 4matrix1(1,0) = 5 : matrix1(1,1) = -2 : matrix1(1,2) = 9matrix1(2,0) = 8 : matrix1(2,1) = -6 : matrix1(2,2) = -5Dim matrix2(2,2)matrix2(0,0) = 9 : matrix2(0,1) = 2 : matrix2(0,2) = 1matrix2(1,0) = -7 : matrix2(1,1) = 3 : matrix2(1,2) = -10matrix2(2,0) = 4 : matrix2(2,1) = 5 : matrix2(2,2) = -6 Call multiply_matrix(matrix1,matrix2) Sub multiply_matrix(arr1,arr2)	For i = 0 To UBound(arr1)		For j = 0 To 2			WScript.StdOut.Write (arr1(i,j) * arr2(i,j)) & vbTab 		Next		WScript.StdOut.WriteLine	NextEnd Sub
Output:
27	14	4
-35	-6	-90
32	-30	30


## Visual FoxPro

 LOCAL ARRAY a[4,2], b[2,3], c[4,3]CLOSE DATABASES ALL*!* The arrays could be created directly but I prefer to do this:CREATE CURSOR mat1 (c1 I, c2 I)CREATE CURSOR mat2 (c1 I, c2 I, c3 I)*!* Since matrix multiplication of integer arrays *!* involves only multiplication and addition, *!* the result will contain integersCREATE CURSOR result (c1 I, c2 I, c3 I)INSERT INTO mat1 VALUES (1, 2)INSERT INTO mat1 VALUES (3, 4)INSERT INTO mat1 VALUES (5, 6)INSERT INTO mat1 VALUES (7, 8)SELECT * FROM mat1 INTO ARRAY a INSERT INTO mat2 VALUES (1, 2, 3)INSERT INTO mat2 VALUES (4, 5, 6)SELECT * FROM mat2 INTO ARRAY bSTORE 0 TO cMatMult(@a,@b,@c)SELECT resultAPPEND FROM ARRAY cBROWSE   PROCEDURE MatMult(aa, bb, cc)LOCAL n As Integer, m As Integer, p As Integer, i As Integer, j As Integer, k As IntegerIF ALEN(aa,2) = ALEN(bb,1) 	n = ALEN(aa,2)	m = ALEN(aa,1)	p = ALEN(bb,2)	FOR i = 1 TO m		FOR j = 1 TO p 			FOR k = 1 TO n				cc[i,j] = cc[i,j] + aa[i,k]*bb[k,j]			ENDFOR		ENDFOR	ENDFOR		ELSE	? "Invalid dimensions"ENDIFENDPROC

## XPL0

proc Mat4x1Mul(M, V);   \Multiply matrix M times column vector Vreal M,     \4x4 matrix  [M] * [V] -> [V]     V;     \column vectorreal W(4);  \working copy of column vectorint  R;     \row[for R:= 0 to 4-1 do    W(R):= M(R,0)*V(0) + M(R,1)*V(1) + M(R,2)*V(2) + M(R,3)*V(3);for R:= 0 to 4-1 do V(R):= W(R);]; proc Mat4x4Mul(M, N);   \Multiply matrix M times matrix Nreal M, N;   \4x4 matrices       [M] * [N] -> [N]real W(4,4); \working copy of matrix Nint  C;      \column[for C:= 0 to 4-1 do       [W(0,C):= M(0,0)*N(0,C) + M(0,1)*N(1,C) + M(0,2)*N(2,C) + M(0,3)*N(3,C);        W(1,C):= M(1,0)*N(0,C) + M(1,1)*N(1,C) + M(1,2)*N(2,C) + M(1,3)*N(3,C);        W(2,C):= M(2,0)*N(0,C) + M(2,1)*N(1,C) + M(2,2)*N(2,C) + M(2,3)*N(3,C);        W(3,C):= M(3,0)*N(0,C) + M(3,1)*N(1,C) + M(3,2)*N(2,C) + M(3,3)*N(3,C);        ];for C:= 0 to 4-1 do       [N(0,C):= W(0,C);        N(1,C):= W(1,C);        N(2,C):= W(2,C);        N(3,C):= W(3,C);        ];];

## XSLT 1.0

With input document ...

<?xml-stylesheet href="matmul.templ.xsl" type="text/xsl"?><mult>  <A>    <r><c>1</c><c>2</c></r>    <r><c>3</c><c>4</c></r>    <r><c>5</c><c>6</c></r>    <r><c>7</c><c>8</c></r>  </A>  <B>    <r><c>1</c><c>2</c><c>3</c></r>    <r><c>4</c><c>5</c><c>6</c></r>  </B></mult>

... and this referenced stylesheet ...

<xsl:stylesheet version="1.0"  xmlns:xsl="http://www.w3.org/1999/XSL/Transform">  <xsl:output method="html"/>   <xsl:template match="/mult">    <table>      <tr><td>╭</td><td colspan="{count(*[2]/*[1]/*)}"/><td>╮</td></tr>      <xsl:call-template name="prodMM">        <xsl:with-param name="A" select="*[1]/*"/>        <xsl:with-param name="B" select="*[2]/*"/>      </xsl:call-template>      <tr><td>╰</td><td colspan="{count(*[2]/*[1]/*)}"/><td>╯</td></tr>    </table>  </xsl:template>   <xsl:template name="prodMM">    <xsl:param name="A"/>    <xsl:param name="B"/>     <xsl:if test="$A/*"> <tr> <td>│</td> <xsl:call-template name="prodVM"> <xsl:with-param name="a" select="$A[1]/*"/>          <xsl:with-param name="B" select="$B"/> </xsl:call-template> <td>│</td> </tr> <xsl:call-template name="prodMM"> <xsl:with-param name="A" select="$A[position()>1]"/>        <xsl:with-param name="B" select="$B"/> </xsl:call-template> </xsl:if> </xsl:template> <xsl:template name="prodVM"> <xsl:param name="a"/> <xsl:param name="B"/> <xsl:param name="col" select="1"/> <xsl:if test="$B/*[col]"> <td align="right"> <xsl:call-template name="prod"> <xsl:with-param name="a" select="a"/>          <xsl:with-param name="b" select="$B/*[$col]"/>        </xsl:call-template>      </td>       <xsl:call-template name="prodVM">        <xsl:with-param name="a"   select="$a"/> <xsl:with-param name="B" select="$B"/>        <xsl:with-param name="col" select="$col+1"/> </xsl:call-template> </xsl:if> </xsl:template> <xsl:template name="prod"> <xsl:param name="a"/> <xsl:param name="b"/> <xsl:if test="not($a)">0</xsl:if>     <xsl:if test="$a"> <xsl:variable name="res"> <xsl:call-template name="prod"> <xsl:with-param name="a" select="$a[position()>1]"/>          <xsl:with-param name="b" select="$b[position()>1]"/> </xsl:call-template> </xsl:variable> <xsl:value-of select="$a[1] * $b[1] +$res"/>    </xsl:if>         </xsl:template> </xsl:stylesheet>
Output:
(in a browser):
╭          ╮
│  9 12	15 │
│ 19 26	33 │
│ 29 40	51 │
│ 39 54	69 │
╰          ╯


You may try in your browser: [[2]]

A slightly smaller version of above stylesheet making use of (Non-"XSLT 1.0") EXSLT functions can be founde here: [[3]]

## zkl

Using the GNU Scientific Library:

var [const] GSL=Import("zklGSL");	// libGSL (GNU Scientific Library)A:=GSL.Matrix(4,2).set(1,2, 3,4, 5,6, 7,8);B:=GSL.Matrix(2,3).set(1,2,3, 4,5,6);(A*B).format().println();   // creates a new matrix
Output:
      9.00,     12.00,     15.00
19.00,     26.00,     33.00
29.00,     40.00,     51.00
39.00,     54.00,     69.00


Or, using lists:

Translation of: BASIC
fcn matMult(a,b){   n,m,p:=a[0].len(),a.len(),b[0].len();   ans:=(0).pump(m,List().write, (0).pump(p,List,0).copy); // matrix of zeros   foreach i,j,k in (m,p,n){ ans[i][j]+=a[i][k]*b[k][j]; }   ans}
a:=L( L(1,2,), L(3,4,), L(5,6,), L(7,8) );b:=L( L(1,2,3,), L(4,5,6) );printM(matMult(a,b)); fcn printM(m){ m.pump(Console.println,rowFmt) }fcn rowFmt(row){ ("%4d "*row.len()).fmt(row.xplode()) }
Output:
   9   12   15
19   26   33
29   40   51
39   54   69


## zonnon

 module MatrixOps;type	Matrix = array {math} *,* of integer;  	procedure WriteMatrix(x: array {math} *,* of integer);	var		i,j: integer;	begin		for i := 0 to len(x,0) - 1 do			for j := 0 to len(x,1) - 1 do				write(x[i,j]);			end;			writeln;		end		end WriteMatrix; 	procedure Multiplication;	var		a,b: Matrix;	begin		a := [[1,2],[3,4],[5,6],[7,8]];		b := [[1,2,3],[4,5,6]];		WriteMatrix(a * b);	end Multiplication; begin	Multiplication;end MatrixOps.

## ZPL

 program matmultSUMMA; prototype GetSingleDim(infile:file):integer;prototype GetInnerDim(infile1:file; infile2:file):integer; config var           Afilename: string = "";          Bfilename: string = "";           Afile: file = open(Afilename,file_read);          Bfile: file = open(Bfilename,file_read);           default_size:integer = 4;          m:integer = GetSingleDim(Afile);          n:integer = GetInnerDim(Afile,Bfile);          p:integer = GetSingleDim(Bfile);           iters: integer = 1;           printinput: boolean = false;          verbose: boolean = true;          dotiming: boolean = false; region           RA = [1..m,1..n];       RB = [1..n,1..p];       RC = [1..m,1..p];       FCol = [1..m,*];       FRow = [*,1..p]; var    A : [RA] double;    B : [RB] double;    C : [RC] double;    Aflood : [FCol] double;    Bflood : [FRow] double;  procedure ReadA();var step:double;[RA] begin       if (Afile != znull) then         read(Afile,A);       else         step := 1.0/(m*n);         A := ((Index1-1)*n + Index2)*step + 1.0;       end;     end;  procedure ReadB();var step:double;[RB] begin       if (Bfile != znull) then         read(Bfile,B);       else         step := 1.0/(n*p);         B := ((Index1-1)*p + Index2)*step + 1.0;       end;     end;  procedure matmultSUMMA();var    i: integer;    it: integer;    runtime: double;[RC] begin       ReadA();       ReadB();        if (printinput) then         [RA] writeln("A is:\n",A);         [RB] writeln("B is:\n",B);       end;        ResetTimer();        for it := 1 to iters do          C := 0.0;                       -- zero C          for i := 1 to n do           [FCol] Aflood := >>[,i] A;       -- flood A col           [FRow] Bflood := >>[i,] B;       -- flood B row            C += (Aflood * Bflood);   -- multiply         end;       end;        runtime := CheckTimer();        if (verbose) then         writeln("C is:\n",C);       end;        if (dotiming) then         writeln("total runtime  = %12.6f":runtime);         writeln("actual runtime = %12.6f":runtime/iters);       end;     end;  procedure GetSingleDim(infile:file):integer;var dim:integer;begin  if (infile != znull) then    read(infile,dim);  else    dim := default_size;  end;  return dim;end;  procedure GetInnerDim(infile1:file; infile2:file):integer;var   col:integer;   row:integer;   retval:integer;begin  retval := -1;  if (infile1 != znull) then    read(infile1,col);    retval := col;  end;  if (infile2 != znull) then    read(infile2,row);    if (retval = -1) then      retval := row;    else      if (row != col) then        halt("ERROR: Inner dimensions don't match");      end;    end;  end;  if (retval = -1) then    retval := default_size;  end;  return retval;end;