Use array valued function as argument to another function

Question

I have transformed a problem from a more complex f90-code into the following:

module userfunctions

implicit none

contains

    function Function1(Argument,ArgumentSize)

        ! Input
        integer, intent(in)                         ::      ArgumentSize
        real,dimension(ArgumentSize),intent(in)     ::      Argument

        ! Output
        real,dimension(ArgumentSize)                ::      Function1    

        ! Local
        integer                 ::      i

        Function1 = Argument

        ! Random operation on argument, resembling generic vector function
        do i=1,ArgumentSize

            Function1(i) = Function1(i)**2

        end do

    end function Function1


    function Function2(RandomFunction,Argument,ArgumentSize)


    ! Input
    integer, intent(in)                         ::      ArgumentSize
    real,dimension(ArgumentSize), intent(in)    ::      Argument

    ! Array-type function of dimension ArgumentSize
    real,external                       ::      RandomFunction

    ! Evaluate RandomFunction to
    real,dimension(ArgumentSize)       ::      Value

    ! Output
    real                                ::      Function2

    ! assign evaluation of RandomFunction to Value
    Value = RandomFunction(Argument,ArgumentSize)

    Function2 = dot_product(Value,Value)

    end function Function2

end module userfunctions



    program Fortran_Console_002

        use userfunctions

        implicit none

        real                    ::      Result1
        real,dimension(6)       ::      Vector1

        Vector1 = 2

        Result1 = Function2(Function1,Vector1,6)

        write(*,*) Result1


    end program Fortran_Console_002

The result should be "96". Compiling this with Visual Studio 2013 and Intel Fortran produces the following error:

Error 1 error #6634: The shape matching rules of actual arguments and dummy arguments have been violated. [FUNCTION1]

In real context I do need to pass an array-valued function from a subroutine to a function defined in a module (a solver for nonlinear functions which takes functions as arguments). I do know how to do this for a scalar-valued function, but failed to apply this to an array.

I use Visual Studio 2013 for this because of convenience. The real piece has to be compiled using Compaq Visual Fortran 6 on a virtual machine which is, as of my knowledge, only compatible up to fortran90.

Answer 1

See How to pass subroutine names as arguments in Fortran? for general rules.

Don't use external here. It is incompatible with advanced features like array valued functions. Generally, external is only for old programs in FORTRAN 77 style. Make an interface block (see the link) or try

   procedure(Function1) :: RandomFunction

instead (Fortran 2003).