Vector and Matrix Multiply Intrinsics

There are two types of intrinsic matrix multiplication these should always be used when appropriate as they will be the most efficient method of calculation:

• DOT_PRODUCT(VEC1, VEC2)

  This is the inner (dot) product of two rank 1 arrays. Clearly, VEC1, VEC2 must conform in size and must be one dimensional. Care must be taken not confuse this intrinsic with DPROD the DOUBLE PRECISION product function or PRODUCT the intra-matrix product (see Section 3.2.5).

  An example of use is,

      DP = DOT_PRODUCT(A,B)

  which is equivalent to:

      DP = A(1)*B(1) + A(2)*B(2) + ...

  or

      DP = SUM(A*B)

  The result is also defined for COMPLEX and LOGICAL array arguments. For COMPLEX the result is,

      DP = SUM(CONJG(A)*B)

  and for LOGICAL,

      DP = LA(1).AND.LB(1) .OR. LA(2).AND.LB(2) .OR. ...

• MATMUL(MAT1, MAT2)

  This is the `traditional' matrix-matrix multiplication and is not equivalent to MAT1*MAT2. There are certain restrictions placed on the function arguments which say that the arrays must match in specific dimensions, they do not have to be conformable:

  • if MAT1 has shape (n, m) and MAT2 shape (m, k) then the result has shape (n, k);
  • if MAT1 has shape (m) and MAT2 shape (m, k) then the result has shape (k);
  • if MAT1 has shape (n, m) and MAT2 shape (m) then the result has shape (n);

  Element (i,j) of the result is,

      SUM(MAT1(i,:)*MAT2(:,j))

  The result is also defined for LOGICAL arguments,

      ANY(MAT1(i,:).AND.MAT2(:,j))

If A and B are set up as follows,

and

then the following program

    PROGRAM DEMO
     INTEGER :: A(2,4)
     INTEGER :: B(4,2)
     A(1,:) = (/1,2,3,4/)
     A(2,:) = (/5,6,7,8/)
     B(:,1) = (/4,3,2,1/)
     B(:,2) = (/8,7,6,5/)
     PRINT*, "DOT_PRODUCT(A(1,:),A(2,:)) = ", DOT_PRODUCT(A(1,:),A(2,:))
     PRINT*, "MATMUL(A,B) = ",MATMUL(A,B)
    END PROGRAM DEMO

gives

    DOT_PRODUCT(A(1,:),A(2,:)) =  70
    MATMUL(A,B) = 20 60 60 164