Matrix multiplication

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Task
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.

Contents

[edit] Ada

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;

Sample 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;

[edit] 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));

[edit] Parallel processing

Alternatively - for multicore CPUs - use the following reinvention of 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 ¢
      for thread to ⌈schedule do schedule[thread] od
    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 ¢
      for thread to ⌈schedule do (required →schedule[thread] | thread →schedule[thread] ) od
    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, $x"Exception: index error."l$)

[edit] 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 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

[edit] AutoHotkey

ahk discussion

Matrix("b","  ; rows separated by ","
, 1 2  ; entries separated by space or tab
, 2 3
, 3 0"
)
MsgBox % "B`n`n" MatrixPrint(b)
Matrix("c","
, 1 2 3
, 3 2 1"
)
MsgBox % "C`n`n" MatrixPrint(c)
 
MatrixMul("a",b,c)
MsgBox % "B * C`n`n" 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
}
}
}

[edit] 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 Error
return
Print(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")
}
Outputs:
9	12	15
19	26	33
29	40	51
39	54	69


[edit] 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

[edit] 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


[edit] Burlesque

 
blsq ) {{1 2}{3 4}{5 6}{7 8}}{{1 2 3}{4 5 6}}mmsp
9 12 15
19 26 33
29 40 51
39 54 69
 

[edit] 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;
}

[edit] 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;
}
}

[edit] 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 ]

[edit] 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 columns
protected:
 
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  

[edit] 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))

[edit] 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)))

[edit] 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);

[edit] D

[edit] 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 nothrow
in {
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]]

[edit] Short Version

import std.stdio, std.range, std.array, std.numeric, std.algorithm;
 
T[][] matMul(T)(in T[][] A, in T[][] B) /*pure*/ nothrow {
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.

[edit] 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.

[edit] 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
if (is(T2 == Unqual!T)) {
T2[m] aux;
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);
}

[edit] 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

[edit] 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 if
end function

[edit] 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);
end
end
 

[edit] 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 } }

[edit] Fantom

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

 
class Main
{
// multiply two matrices (with no error checking)
public static Int[][] multiply (Int[][] m1, Int[][] m2)
{
Int[][] result := [,]
m1.each |Int[] row1|
{
Int[] row := [,]
m2[0].size.times |Int colNumber|
{
Int value := 0
m2.each |Int[] row2, Int index|
{
value += row1[index] * row2[colNumber]
}
row.add (value)
}
result.add (row)
}
return result
}
 
public static Void main ()
{
m1 := [[1,2,3],[4,5,6]]
m2 := [[1,2],[3,4],[5,6]]
 
echo ("${m1} times ${m2} = ${multiply(m1,m2)}")
}
}
 

Output:

[[1, 2, 3], [4, 5, 6]] times [[1, 2], [3, 4], [5, 6]] = [[22, 28], [49, 64]]

[edit] Forth

include fsl-util.f
 
3 3 float matrix A{{
A{{ 3 3 }}fread 1e 2e 3e 4e 5e 6e 7e 8e 9e
3 3 float matrix B{{
B{{ 3 3 }}fread 3e 3e 3e 2e 2e 2e 1e 1e 1e
3 3 float matrix C{{ \ result
 
A{{ B{{ C{{ mat*
C{{ }}print

[edit] Fortran

In ISO Fortran 90 or later, use the MATMUL intrinsic function to perform Matrix Multiply; use RESHAPE and SIZE intrinsic functions to form the matrices themselves:

real, dimension(n,m) :: a = reshape( (/ (i, i=1, n*m) /), (/ n, m /) )
real, dimension(m,k) :: b = reshape( (/ (i, i=1, m*k) /), (/ m, k /) )
real, dimension(size(a,1), size(b,2)) :: c ! C is an array whose first dimension (row) size
! is the same as A's first dimension size, and
! whose second dimension (column) size is the same
! as B's second dimension size.
 
c = matmul( a, b )
 
print *, 'A'
do i = 1, n
print *, a(i,:)
end do
 
print *,
print *, 'B'
do i = 1, m
print *, b(i,:)
end do
 
print *,
print *, 'C = AB'
do i = 1, n
print *, c(i,:)
end do

[edit] Frink

matprod[a is array, b is array] :=
{
c = makeArray[[length[a], length[b@0]], 0]
 
a_row = length[a]-1
a_col = length[a@0]-1
b_col = length[b]-1
 
for row = 0 to a_row
for col = 0 to b_col
for inc = 0 to a_col
c@row@col = c@row@col + (a@row@inc * b@inc@col)
 
return c
}

[edit] GAP

# Built-in
A := [[1, 2], [3, 4], [5, 6], [7, 8]];
B := [[1, 2, 3], [4, 5, 6]];
 
PrintArray(A);
# [ [ 1, 2 ],
# [ 3, 4 ],
# [ 5, 6 ],
# [ 7, 8 ] ]
 
PrintArray(B);
# [ [ 1, 2, 3 ],
# [ 4, 5, 6 ] ]
 
PrintArray(A * B);
# [ [ 9, 12, 15 ],
# [ 19, 26, 33 ],
# [ 29, 40, 51 ],
# [ 39, 54, 69 ] ]

[edit] Go

[edit] 2D representation

package main
 
import "fmt"
 
type Value float64
type Matrix [][]Value
 
func Multiply(m1, m2 Matrix) (m3 Matrix, ok bool) {
rows, cols, extra := len(m1), len(m2[0]), len(m2)
if len(m1[0]) != extra { return nil, false }
m3 = make(Matrix, rows)
for i := 0; i < rows; i++ {
m3[i] = make([]Value,cols)
for j := 0; j < cols; j++ {
for k := 0; k < extra; k++ {
m3[i][j] += m1[i][k] * m2[k][j]
}
}
}
return m3, true
}
 
func (m Matrix) String() string {
rows := len(m)
cols := len(m[0])
out := "["
for r := 0; r < rows; r++ {
if r > 0 { out += ",\n " }
out += "[ "
for c := 0; c < cols; c++ {
if c > 0 { out += ", " }
out += fmt.Sprintf("%7.3f", m[r][c])
}
out += " ]"
}
out += "]"
return out
}
 
func main() {
A := Matrix{[]Value{1, 1, 1, 1},
[]Value{2, 4, 8, 16},
[]Value{3, 9, 27, 81},
[]Value{4, 16, 64, 256}}
B := Matrix{[]Value{ 4.0 , -3.0 , 4.0/3, -1.0/4 },
[]Value{-13.0/3, 19.0/4, -7.0/3, 11.0/24},
[]Value{ 3.0/2, -2.0 , 7.0/6, -1.0/4 },
[]Value{ -1.0/6, 1.0/4, -1.0/6, 1.0/24}}
P,ok := Multiply(A,B)
if !ok { panic("Invalid dimensions") }
fmt.Printf("Matrix A:\n%s\n\n", A)
fmt.Printf("Matrix B:\n%s\n\n", B)
fmt.Printf("Product of A and B:\n%s\n\n", P)
}
Output:
Matrix A:
[[   1.000,   1.000,   1.000,   1.000 ],
 [   2.000,   4.000,   8.000,  16.000 ],
 [   3.000,   9.000,  27.000,  81.000 ],
 [   4.000,  16.000,  64.000, 256.000 ]]

Matrix B:
[[   4.000,  -3.000,   1.333,  -0.250 ],
 [  -4.333,   4.750,  -2.333,   0.458 ],
 [   1.500,  -2.000,   1.167,  -0.250 ],
 [  -0.167,   0.250,  -0.167,   0.042 ]]

Product of A and B:
[[   1.000,   0.000,  -0.000,  -0.000 ],
 [   0.000,   1.000,  -0.000,  -0.000 ],
 [   0.000,   0.000,   1.000,  -0.000 ],
 [   0.000,   0.000,   0.000,   1.000 ]]

[edit] Flat representation

package main
 
import "fmt"
 
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 (m *matrix) print(heading string) {
if heading > "" {
fmt.Print("\n", heading, "\n")
}
for e := 0; e < len(m.ele); e += m.stride {
fmt.Printf("%6.3f ", m.ele[e:e+m.stride])
fmt.Println()
}
}
 
func (m1 *matrix) multiply(m2 *matrix) (m3 *matrix, ok bool) {
if m1.stride*m2.stride != len(m2.ele) {
return nil, false
}
m3 = &matrix{make([]float64, (len(m1.ele)/m1.stride)*m2.stride), m2.stride}
for m1c0, m3x := 0, 0; m1c0 < len(m1.ele); m1c0 += m1.stride {
for m2r0 := 0; m2r0 < m2.stride; m2r0++ {
for m1x, m2x := m1c0, m2r0; m2x < len(m2.ele); m2x += m2.stride {
m3.ele[m3x] += m1.ele[m1x] * m2.ele[m2x]
m1x++
}
m3x++
}
}
return m3, true
}
 
func main() {
a := matrixFromRows([][]float64{
{1, 1, 1, 1},
{2, 4, 8, 16},
{3, 9, 27, 81},
{4, 16, 64, 256},
})
b := matrixFromRows([][]float64{
{
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,
},
})
p, ok := a.multiply(b)
a.print("Matrix A:")
b.print("Matrix B:")
if !ok {
fmt.Println("not conformable for matrix multiplication")
return
}
p.print("Product of A and B:")
}

Output is similar to 2D version.

[edit] Library

package main
 
import (
"fmt"
 
mat "github.com/skelterjohn/go.matrix"
)
 
func main() {
a := mat.MakeDenseMatrixStacked([][]float64{
{1, 1, 1, 1},
{2, 4, 8, 16},
{3, 9, 27, 81},
{4, 16, 64, 256},
})
b := mat.MakeDenseMatrixStacked([][]float64{
{
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,
},
})
p, err := a.TimesDense(b)
fmt.Printf("Matrix A:\n%v\n", a)
fmt.Printf("Matrix B:\n%v\n", b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("Product of A and B:\n%v\n", p)
}
Output:
Matrix A:
{  1,   1,   1,   1,
   2,   4,   8,  16,
   3,   9,  27,  81,
   4,  16,  64, 256}
Matrix B:
{        4,        -3,  1.333333,     -0.25,
 -4.333333,      4.75, -2.333333,  0.458333,
       1.5,        -2,  1.166667,     -0.25,
 -0.166667,      0.25, -0.166667,  0.041667}
Product of A and B:
{ 1,  0, -0, -0,
  0,  1, -0, -0,
  0,  0,  1,  0,
  0,  0,  0,  1}

[edit] Groovy

[edit] Without Indexed Loops

Uses transposition to avoid indirect element access via ranges of indexes. "assertConformability()" asserts that a & b are both rectangular lists of lists, and that row-length (number of columns) of a is equal to the column-length (number of rows) of b.

def assertConformable = { a, b ->
assert a instanceof List
assert b instanceof List
assert a.every { it instanceof List && it.size() == b.size() }
assert b.every { it instanceof List && it.size() == b[0].size() }
}
 
def matmulWOIL = { a, b ->
assertConformable(a, b)
 
def bt = b.transpose()
a.collect { ai ->
bt.collect { btj ->
[ai, btj].transpose().collect { it[0] * it[1] }.sum()
}
}
}

[edit] Without Transposition

Uses ranges of indexes, the way that matrix multiplication is typically defined. Not as elegant, but it avoids expensive transpositions. Reuses "assertConformable()" from above.

def matmulWOT = { a, b ->
assertConformable(a, b)
 
(0..<a.size()).collect { i ->
(0..<b[0].size()).collect { j ->
(0..<b.size()).collect { k -> a[i][k] * b[k][j] }.sum()
}
}
}

Test:

def m4by2 = [ [  1,  2 ],
[ 3, 4 ],
[ 5, 6 ],
[ 7, 8 ] ]
 
def m2by3 = [ [ 1, 2, 3 ],
[ 4, 5, 6 ] ]
 
matmulWOIL(m4by2, m2by3).each { println it }
println()
matmulWOT(m4by2, m2by3).each { println it }

Output:

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

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

[edit] Haskell

A somewhat inefficient version with lists (transpose is expensive):

import Data.List
 
mmult :: Num a => [[a]] -> [[a]] -> [[a]]
mmult a b = [ [ sum $ zipWith (*) ar bc | bc <- (transpose b) ] | ar <- a ]
 
-- Example use:
test = [[1, 2],
[3, 4]] `mmult` [[-3, -8, 3],
[-2, 1, 4]]

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]

[edit] HicEst

REAL :: m=4, n=2, p=3, a(m,n), b(n,p), res(m,p)
 
a = $ ! initialize to 1, 2, ..., m*n
b = $ ! initialize to 1, 2, ..., n*p
 
res = 0
DO i = 1, m
DO j = 1, p
DO k = 1, n
res(i,j) = res(i,j) + a(i,k) * b(k,j)
ENDDO
ENDDO
ENDDO
 
DLG(DefWidth=4, Text=a, Text=b,Y=0, Text=res,Y=0)
a         b              res
1 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

[edit] 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 result
end
 

Output:

Multiply:
1 2 3 
4 5 6 
by:
1 2 
3 4 
5 6 
Result: 
22 28 
49 64

[edit] IDL

result = arr1 # arr2

[edit] 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 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

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

etc.

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.

[edit] 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;
}

[edit] JavaScript

Works with: SpiderMonkey
for the print() function

Extends Matrix Transpose#JavaScript

// returns a new matrix
Matrix.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

[edit] 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 3x2
2x2 Array{Int64,2}:
22 28
49 64
 
julia> [1 2 3] * [1,2,3] # product of a row vector by a column vector
1-element Array{Int64,1}:
14
 

[edit] K

  (1 2;3 4)_mul (5 6;7 8)
(19 22
43 50)

[edit] Lang5

[[1 2 3] [4 5 6]] 'm dress
[[1 2] [3 4] [5 6]] 'm dress * .
Output:
[
  [   22    28  ]
  [   49    64  ]
]

[edit] 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$)
call DisplayMatrix MatrixP$
 

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 |

[edit]

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 1
MAKE "CC 1
MAKE "NV (MDARRAY (LIST :F :C) 1)
MAKE "T :F * :C
FOR [Z 1 :T][MAKE "W ITEM :Z :A
MDSETITEM (LIST :CF :CC) :NV :W
MAKE "CC :CC + 1
IF :CC = :C + 1 [MAKE "CF :CF + 1 MAKE "CC 1]]
OUTPUT :NV
END
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
 
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 / VECTOR
MAKE "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 ;"ROWS
MAKE "CA 5 ;"COLS
 
; SECOND DATA MATRIX / VECTOR
MAKE "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 ;"ROWS
MAKE "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 * :CB
MAKE "RE (ARRAY :T 1)
 
 
MAKE "CO 0
FOR [AF 1 :CA][
FOR [AC 1 :CA][
MAKE "TEMP 0
FOR [I 1 :CA ][
MAKE "TEMP :TEMP + (MDITEM (LIST :I :AF) :MA) * (MDITEM (LIST :AC :I) :MB)]
MAKE "CO :CO + 1
SETITEM :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 5030
11 13 15 17 19 12 14 16 18 20 890 2040 3190 4340 5490
21 23 25 27 29 X 22 24 26 28 30 = 950 2200 3450 4700 5950
31 33 35 37 39 32 34 36 38 40 1010 2360 3710 5060 6410
41 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 47
49}} =_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 48
50}} =_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}}

[edit] 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 res
end
 
-- Test for MatMul
mat1 = { { 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


[edit] 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]

[edit] Mathematica

M1 = {{1, 2},
{3, 4},
{5, 6},
{7, 8}}
M2 = {{1, 2, 3},
{4, 5, 6}}
M = M1.M2

Or without the variables:

{{1, 2}, {3, 4}, {5, 6}, {7, 8}}.{{1, 2, 3}, {4, 5, 6}}

The result is:

{{9, 12, 15}, {19, 26, 33}, {29, 40, 51}, {39, 54, 69}}
matrixMul[m1_, m2_] := Table[Times @@ {a, b} // Tr, {a, m1}, {b, Transpose@m2}]
matrixMul2[m1_, m2_] :=Table[Sum[Times @@ i, {i, Transpose@{a, b}}], {a, m1}, {b, Transpose@m2}]
 
a = {{1, 2}, {3, 4}, {5, 6}, {7, 8}};
b = {{1, 2, 3}, {4, 5, 6}};
matrixMul[a, b]
matrixMul2[a, b]

[edit] MATLAB / Octave

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

[edit] 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]) */

[edit] 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.

[edit] Nimrod

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,N,M2,N2](a: Matrix[M,N2]; b: Matrix[M2,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 a
echo b
echo a * b
echo b * a

[edit] 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]]

[edit] Octave

a = zeros(4);
% prepare the matrix
% 1 1 1 1
% 2 4 8 16
% 3 9 27 81
% 4 16 64 256
for i = 1:4
for j = 1:4
a(i, j) = i^j;
endfor
endfor
b = inverse(a);
a * b


[edit] 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 pa=@A, pb=@B, pc=@C
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
 

[edit] PARI/GP

M*N

[edit] 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.

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];
}

This function takes two references to arrays of arrays and returns the product as a reference to a new anonymous array of arrays.

[edit] Perl 6

Translation of: Perl 5
Works with: Rakudo version 2010.09

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 list of arrays. We also had to sneak in a » metaoperator (known as "hyper") to do a parallel subscript lookup. Eventually we'll have shaped arrays, and a multidimensional subscript will automatically slice in all its dimensions--but rakudo doesn't do that yet.

[edit] 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))

[edit] 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;
 

[edit] 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;

[edit] 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 M2
mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3).
mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3).

[edit] 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

Additional code to demonstrate use.

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 row
EndDataSection
 
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
Next
EndProcedure
 
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

Sample 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

[edit] 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 np
np.dot(a,b)
#or if a is an array
a.dot(b)

[edit] R

a %*% b

[edit] 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]])
 

[edit] 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>
};

[edit] REXX

/*REXX program multiplies two matrixes together, shows matrixes & result*/
x.=
x.1 = '1 2'
x.2 = '3 4'
x.3 = "5 6" /*either kind of quote works. */
x.4 = '7 8'
do r=1 while x.r\=='' /*build the "A" matric from X. #s*/
do c=1 while x.r\==''; parse var x.r a.r.c x.r; end
end
Arows=r-1; Acols=c-1
y.=
y.1 = 1 2 3 /*if all values are positive, */
y.2 = 4 5 6 /*can eliminate the quotes. */
do r=1 while y.r\=='' /*build the "B" matric from Y. #s*/
do c=1 while y.r\==''; parse var y.r b.r.c y.r; end
end
Brows=r-1; Bcols=c-1
c.=0; L=0 /*L is max width of an element. */
do i =1 for Arows /*multiply matrix A & B ──� C */
do j =1 for Bcols
do k=1 for Acols
c.i.j = c.i.j + a.i.k * b.k.j; L=max(L,length(c.i.j))
end /*k*/
end /*j*/
end /*i*/
 
call showMat 'A', Arows, Acols
call showMat 'B', Brows, Bcols
call showMat 'C', Arows, Bcols
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────SHOWMAT subroutine──────────────────*/
showMat: parse arg mat,rows,cols; say
say center(mat 'matrix',cols*(L+1)+4,"─")
do r =1 for rows; _=
do c=1 for cols; _=_ right(value(mat'.'r'.'c),L); end; say _
end
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

[edit] 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:
Translation of: Haskell
def matrix_mult(a, b)
a.map do |ar|
b.transpose.map do |bc|
ar.zip(bc).map(&:*).inject(&:+)
end
end
end

[edit] 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.

[edit] 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))

[edit] 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]

[edit] 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 matrix
INSERT 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 matrix
INSERT 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 matrix
SELECT 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;

[edit] Tcl

Works with: Tcl version 8.5
package require Tcl 8.5
namespace path ::tcl::mathop
proc matrix_multiply {a b} {
lassign [size $a] a_rows a_cols
lassign [size $b] b_rows b_cols
if {$a_cols != $b_rows} {
error "incompatible sizes: a($a_rows, $a_cols), b($b_rows, $b_cols)"
}
set temp [lrepeat $a_rows [lrepeat $b_cols 0]]
for {set i 0} {$i < $a_rows} {incr i} {
for {set j 0} {$j < $b_cols} {incr j} {
set sum 0
for {set k 0} {$k < $a_cols} {incr k} {
set sum [+ $sum [* [lindex $a $i $k] [lindex $b $k $j]]]
}
lset temp $i $j $sum
}
}
return $temp
}

Using the print_matrix procedure defined in Matrix Transpose#Tcl

% print_matrix [matrix_multiply {{1 2} {3 4}} {{-3 -8 3} {-2 1 4}}]
 -7  -6 11 
-17 -20 25 

[edit] TI-83 BASIC

Store your matrices in [A] and [B].

Disp [A]*[B]

An error will show if the matrices have invalid dimensions for multiplication.

[edit] TI-89 BASIC

Translation of: Mathematica
[1,2; 3,4; 5,6; 7,8] → m1
[1,2,3; 4,5,6] → m2
m1 * m2

Or without the variables:

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

The result (without prettyprinting) is:

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

[edit] UNIX Shell

 
#!/bin/bash
 
DELAY=0 # increase this if printing of matrices should be slower
 
echo "This script takes two matrices, henceforth called A and B,
and returns their product, AB.
 
For the time being, matrices can have integer components only.
 
"

 
read -p "Number of rows of matrix A: " arows
read -p "Number of columns of matrix A: " acols
brows="$acols"
echo
echo "Number of rows of matrix B: "$brows
read -p "Number of columns of matrix B: " bcols
 
crows="$arows"
ccols="$bcols"
echo
 
echo "Number of rows of matrix AB: " $crows
echo "Number of columns of matrix AB: " $ccols
echo
echo
 
matrixa=( )
matrixb=( )
 
# input matrix A
 
maxlengtha=0
for ((row=1; row<=arows; row++)); do
for ((col=1; col<=acols; col++)); do
checkentry="false"
while [ "$checkentry" != "true" ]; do
read -p "Enter component A[$row, $col]: " number
index=$(((row-1)*acols+col))
matrixa[$index]="$number"
[ "${matrixa[$index]}" -eq "$number" ] && checkentry="true"
echo
done
entry="${matrixa[$index]}"
[ "${#entry}" -gt "$maxlengtha" ] && maxlengtha="${#entry}"
done
echo
done
 
# print matrix A to guard against errors
 
if [ "$maxlengtha" -le "5" ]; then
width=8
else
width=$((maxlengtha + 3))
fi
 
echo "This is matrix A:
 
"

 
for ((row=1; row<=arows; row++)); do
for ((col=1; col<=acols; col++)); do
 
index=$(((row-1)*acols+col))
printf "%${width}d" "${matrixa[$index]}"
sleep "$DELAY"
 
done
echo; echo # printf %s "\n\n" does not work...
done
 
echo
echo
 
# input matrix B
 
maxlengthb=0
for ((row=1; row<=brows; row++)); do
for ((col=1; col<=bcols; col++)); do
checkentry="false"
while [ "$checkentry" != "true" ]; do
read -p "Enter component B[$row, $col]: " number
index=$(((row-1)*bcols+col))
matrixb[$index]="$number"
[ "${matrixb[$index]}" -eq "$number" ] && checkentry="true"
echo
done
entry="${matrixb[$index]}"
[ "${#entry}" -gt "$maxlengthb" ] && maxlengthb="${#entry}"
done
echo
done
 
# print matrix B to guard against errors
 
if [ "$maxlengthb" -le "5" ]; then
width=8
else
width=$((maxlengthb + 3))
fi
 
echo "This is matrix B:
 
"

 
for ((row=1; row<=brows; row++)); do
for ((col=1; col<=bcols; col++)); do
 
index=$(((row-1)*bcols+col))
printf "%${width}d" "${matrixb[$index]}"
sleep "$DELAY"
 
done
echo; echo # printf %s "\n\n" does not work...
done
 
read -p "Hit enter to continue"
 
# calculate matrix C := AB
 
maxlengthc=0
time for ((row=1; row<=crows; row++)); do
for ((col=1; col<=ccols; col++)); do
 
# calculate component C[$row, $col]
 
runningtotal=0
for ((j=1; j<=acols; j++)); do
rowa="$row"
cola="$j"
indexa=$(((rowa-1)*acols+cola))
rowb="$j"
colb="$col"
indexb=$(((rowb-1)*bcols+colb))
 
entry_from_A=${matrixa[$indexa]}
entry_from_B=${matrixb[$indexb]}
 
subtotal=$((entry_from_A * entry_from_B))
((runningtotal+=subtotal))
done
 
number="$runningtotal"
 
# store component in the result array
index=$(((row-1)*ccols+col))
matrixc[$index]="$number"
 
entry="${matrixc[$index]}"
[ "${#entry}" -gt "$maxlengthc" ] && maxlengthc="${#entry}"
done
done
 
echo
read -p "Hit enter to continue"
echo
 
# print the matrix C
 
if [ "$maxlengthc" -le "5" ]; then
width=8
else
width=$((maxlengthc + 3))
fi
 
echo "The product matrix is:
 
"

 
for ((row=1; row<=crows; row++)); do
for ((col=1; col<=ccols; col++)); do
 
index=$(((row-1)*ccols+col))
printf "%${width}d" "${matrixc[$index]}"
sleep "$DELAY"
 
done
echo; echo # printf %s "\n\n" does not work...
done
 
echo
echo
 

[edit] 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>>

[edit] XPL0

proc Mat4x1Mul(M, V);   \Multiply matrix M times column vector V
real M, \4x4 matrix [M] * [V] -> [V]
V; \column vector
real W(4); \working copy of column vector
int 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 N
real M, N; \4x4 matrices [M] * [N] -> [N]
real W(4,4); \working copy of matrix N
int 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);
];
];

[edit] 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>

... this output will be produced (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]]

[edit] 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;
 
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