FORTRAN Program for Matrix Multiplication

Q : A Fortran program that reads four natural numbers m,n,p,q and further reads entries of two matrices A and B of real numbers, respectively of size m x n and p x q. Further, the program checks whether the matrix product A x B is defined. If the product is defined then the program computes the product matrix, else prints a suitable message.

Ans :

Let us assume that Matrix C is the Product of   Matrices A & B.

so          

 (C)mxq =(A)mxn x (B)pxq

  The product of the matrix is defined only when n = p, that is the number of columns of  First Matrix A is equal to the number of rows of second Matrix B. This condition is used in the program to check whether the matrix is defined or not.

            Here is the listing of full program : -

DIMENSION A(100,100), B(100,100), C(100,100)

INTEGER P,Q

C*****READ THE SIZE OF MATRIX A(MXN)

C*****MAXIMUM SIZE IS ASSUMED TO 100X100

 1    WRITE( *,*) 'ENTER THE SIZE(M<100,N<100) OF MATRIX A'

  READ ( *, 2) M, N

2    FORMAT (2I3)

     WRITE( *,*) 'ENTER THE SIZE(P<100,Q<100) OF MATRIX B'

  READ ( *, 2) P,Q

C*****CHECK WHETHER P=N IF NOT THEN PRODUCT IS NOT DEFINED.

 IF(N .EQ. P) GO TO 3

 WRITE( *,*) 'THE PRODUCT OF MATRICES A & NOT DEFINED'

 WRITE( *, *) 'RE-ENTER THE SIZES OF A & B AGAIN'

 GO TO 1

C*****INPUT STARTS FOR A :

3  WRITE ( *,* ) 'ENTER MATRIX A ROW-WISE'

 DO 4 I =1, M

    WRITE (*,*) 'ENTER ROW NO :', I

4              READ (*,5) (A(I,J),J=1,N)

5    FORMAT (F8.2)

C*****INPUT STARTS FOR B :  

    WRITE ( *,* ) 'ENTER MATRIX B ROW-WISE'

 DO 7 I =1, P

    WRITE (*,*) 'ENTER ROW NO :', I

7   READ (*,5) (A(I,J),J=1,Q)

C*****START THE MULTIPLICATION

DO 8 I =1,M

DO 8 K =1,Q

C(I,K) = 0.0

DO 9 J =1,N

  9  C(I,K) = C(I,K) + A(I,J)*B(J,K)

C*****PRINT THE PRODUCT MATRIX C IN TABULAR FORM

     DO 10  I=1,M

 10  WRITE (*,11) (C(I,J), J=1,Q)

 11  FORMAT ( F8.2 )

     STOP

     END