Matrix multiplication

Multiply two Matrices together, they can be of any dimension as long as the number of columns of the first matrix is equal to the number of rows of the second matrix

Ada

package Matrix_Ops is
   type Matrix is array(Natural range <>, Natural range <>) of Float;
   function "*" (Left, Right : Matrix) return Matrix;
   Dimension_Violation : exception;
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 Dimension_Violation;
      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;

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)))

Haskell

import Data.List

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]]

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;