Multiplication of Matrices in Fortran

Question

I am encountering a problem to compile a program in Fortran. The build error accuses that the Shape of the matrices are not compliant. However, I understand that it is mathematically allowed to multiply a 2x3 Matrix by a 3x2 matrix2.

mtx1 = | 2 4 1 |      mtx2 = | 3 4 |    Resultado esperado: | 12  18 |
       | 1 3 6 |             | 1 1 |                        | 15  25 |
                             | 2 3 |

This is the build error message:

print*, mtx1*mtx2 1 2 Error: Shapes for operands at (1) and (2) are not conformable

---

source code

program test
integer :: mtx1(2,3) = reshape((/2,4,1, 1,3,6/),(/2,3/))
integer :: mtx2(3,2) = reshape((/3,4, 1,1, 2,3/),(/3,2/))

print*, mtx1*mtx2

end program teste

Answer 1

The Fortran language does not multiply multidimensional matrices directly, only vectors (one-dimensional).

To multiply multidimensional matrices, use the function matmul (Fortran 90):

program test

  integer :: mtx1(2,3) = reshape((/2,4,1, 1,3,6/),(/2,3/))
  integer :: mtx2(3,2) = reshape((/3,4, 1,1, 2,3/),(/3,2/))

  ! -----
  ! Aqui: trocar pela funcao matmul
  ! -----
  print*, matmul(mtx1, mtx2)

end program test

After execution, the multiplication result is printed correctly:

13          22          13          24

Answer 2

The Fortran language uses the model column-major to store the contents of a array contiguously in memory. Therefore, it is necessary to keep this in mind when assigning values in the constructor of a variable of type array (dimension); Further considering this and the response of @Gumball (use the function matmul for amultiplicar matrices in Fortran), the program with the correct result can be the one of the following source code:

    program test
    
      integer :: mtx1(2,3) = reshape((/2,1, 4,3, 1,6/),(/2,3/)) !column-major
      integer :: mtx2(3,2) = reshape((/3,1,2 ,4,1,3/),(/3,2/))
    
      print ('(" | ",i2,2x,i2," | ")'), matmul(mtx1,mtx2)
    
    end program test

Producing the desired result:

| 12  18 |                                                                                      
| 15  25 |