fortran not able to call defined functions power of matrix

Question

I just started learning Fortran and I have this function called matrix_power But I'm having difficulty trying to call the function. The file extension I'm using is .f and my compiler is gfortran.

Here is my code

function transpose_matrix(mat) result(mat_t)
    implicit none
    real, dimension(:,:), intent(in) :: mat
    real, dimension(size(mat,2),size(mat,1)) :: mat_t
    integer :: i, j
    do i = 1, size(mat,1)
    do j = 1, size(mat,2)
        mat_t(j,i) = mat(i,j)
    end do
    end do
end function transpose_matrix

function matrix_power(mat, p) result(mat_p)
    implicit none
    integer, intent(in) :: p
    real, dimension(:,:), intent(in) :: mat
    real, dimension(size(mat,1),size(mat,2)) :: mat_p
    integer :: i
    mat_p = mat
    do i = 2, p
    mat_p = matmul(mat_p, mat)
    end do
end function matrix_power


program matrix
implicit none

real, dimension(5, 5) :: matrix1 = reshape([2.0, 0.0, 0.0, 0.0, 0.0, &
                                            0.0, 2.0, 0.0, 0.0, 0.0, &
                                            0.0, 0.0, 2.0, 0.0, 0.0, &
                                            0.0, 0.0, 0.0, 2.0, 0.0, &
                                            2.0, 0.0, 0.0, 0.0, 2.0], (5, 5))

real, dimension(5, 5) :: mat_t, mat_p
integer :: i

mat_t = transpose_matrix(matrix1)

mat_p = matrix_power(matrix1, 3)
! Print the results
print *, "Matrix 1:"
print *, matrix1
print *, "Matrix 1 Transposed:"
print *, mat_t
print *, "Matrix 1 to the power of 3:"
print *, mat_p

end program matrix

I know that it's saying that there is a mismatch but it doesn't even make sense This is my definition of the mat_p

  real, dimension(m,n) :: mat_t, mat_p

Here is the error I'm receiving

here is a text based error

   Return type mismatch of function 'matrix_power' at (1) (UNKNOWN/REAL(4))
Function 'matrix_power' at (1) has no IMPLICIT type

Answer 1

As suspected by @VladimirFГероямслава in the comments, functions returning arrays must have explicit interfaces. Routines/functions with assumed shapes dummy arguments, or intent() attributes for the arguments, do also require explicit interfaces.

First of all , because you are using implicit none (which is a good practice) in the main program, you have to define the return type of all the non-intrinsic functions you are using. For instance if you had this function:

function matrix_trace(mat,n) result(t)
    implicit none
    real :: mat(n,n)
    real :: t
    integer :: i
    t = 0.0
    do i = 1, n
        t = t + mat(i,i)
    end do
end function

You would simply have to insert in your main program:

real, external :: matrix_trace

This is an implicit interface, because you don't describe how arguments are passed. The implicit interface is the legacy pre-Fortran 90 way.

In your case your have to define explicit interfaces, with two possibilities.

Interface blocks:

In your main program you insert this code:

INTERFACE
    function transpose_matrix(mat) result(mat_t)
        implicit none
        real, dimension(:,:), intent(in) :: mat
        real, dimension(size(mat,2),size(mat,1)) :: mat_t
    end function transpose_matrix

    function matrix_power(mat, p) result(mat_p)
        implicit none
        integer, intent(in) :: p
        real, dimension(:,:), intent(in) :: mat
        real, dimension(size(mat,1),size(mat,2)) :: mat_p
    end function matrix_power
END INTERFACE

Modules

Much better, use modules to encapsulate your functions:

!*****************************************
MODULE mymatfuncs

CONTAINS

function transpose_matrix(mat) result(mat_t)
    implicit none
    real, dimension(:,:), intent(in) :: mat
    real, dimension(size(mat,2),size(mat,1)) :: mat_t
    integer :: i, j
    do i = 1, size(mat,1)
    do j = 1, size(mat,2)
        mat_t(j,i) = mat(i,j)
    end do
    end do
end function transpose_matrix

function matrix_power(mat, p) result(mat_p)
    implicit none
    integer, intent(in) :: p
    real, dimension(:,:), intent(in) :: mat
    real, dimension(size(mat,1),size(mat,2)) :: mat_p
    integer :: i
    mat_p = mat
    do i = 2, p
    mat_p = matmul(mat_p, mat)
    end do
end function matrix_power

END MODULE mymatfuncs
!*****************************************




program matrix
USE mymatfuncs, only: matrix_power, transpose_matrix
implicit none

real, dimension(5, 5) :: matrix1 = reshape([2.0, 0.0, 0.0, 0.0, 0.0, &
                                            0.0, 2.0, 0.0, 0.0, 0.0, &
                                            0.0, 0.0, 2.0, 0.0, 0.0, &
                                            0.0, 0.0, 0.0, 2.0, 0.0, &
                                            2.0, 0.0, 0.0, 0.0, 2.0], (5, 5))

real, dimension(5, 5) :: mat_t, mat_p
integer :: i

mat_t = transpose_matrix(matrix1)

mat_p = matrix_power(matrix1, 3)
! Print the results
print *, "Matrix 1:"
print *, matrix1
print *, "Matrix 1 Transposed:"
print *, mat_t
print *, "Matrix 1 to the power of 3:"
print *, mat_p

end program matrix