Passing an internal procedure as argument

问题:

I want to solve a differential equation lots of times for different parameters. It is more complicated than this, but for the sake of clarity let's say the ODE is y'(x) = (y+a)*x with y(0) = 0 and I want y(1). I picked the dverk algorithm from netlib for solving the ODE and it expects the function on the right hand side to be of a certain form. Now what I did with the Intel Fortran compiler is the following (simplified):

subroutine f(x,a,ans)
implicite none
double precision f,a,ans,y,tol,c(24),w(9)
...
call dverk(1,faux,x,y,1.d0,tol,ind,c,1,w)
...
contains
    subroutine faux(n,xx,yy,yprime)
           implicite none
           integer n
           double precision xx,yy(n),yprime(n)
           yprime(1) = (yy(1)+a)*xx
    end subroutine faux
end subroutine f

This works just fine with ifort, the sub-subroutine faux sees the parameter a and everything works as expected. But I'd like the code to be compatible with gfortran, and with this compiler I get the following error message:

Error: Internal procedure 'faux' is not allowed as an actual argument at (1)

I need to have the faux routine inside f, or else I don't know how to tell it the value of a, because I can't change the list of parameters, since this is what the dverk routine expects.

I would like to keep the dverk routine and understand how to solve this specific problem without a workaround, since I feel it will become important again when I need to integrate a parameterized function with different integrators.

回答1:

You could put this all in a module, and make a a global module variable. Make faux a module procedure. That way, it has access to a.

module ode_module
    double precision::a

    contains

    subroutine f(x,a,ans)
        implicit none
        double precision f,ans,y,tol,c(24),w(9)

        call dverk(1,faux,x,y,1.d0,tol,ind,c,1,w)

    end subroutine 

    subroutine faux(n,xx,yy,yprime)
       implicite none
       integer n
       double precision xx,yy(n),yprime(n)
       yprime(1) = (yy(1)+a)*xx
    end subroutine faux

end module

回答2:

You can check here which compilers support this F2008 feature:

http://fortranwiki.org/fortran/show/Fortran+2008+status

On that page, search for "Internal procedure as an actual argument" .

回答3:

Passing an internal procedure is allowed by Fortran 2008. It is not limited to module. You just have to make sure, that the containing procedure is still running. It is not possible to save the pointer and make a so called 'closure' known from LISP and many modern languages. In languages like Fortran or C the enclosing environment for future calls is not saved and pointers to internal functions become invalid.

The advantage of internal procedure over module procedure is that you can share the data without sharing it in the whole module.

It works well will reasonably old versions of GCC (gfortran), Intel Fortran and Cray Fortran (personally tested) and possibly others. I remember not being able to compile by PGI and Oracle Fortran. As shown by Daniel, it can be checked at http://fortranwiki.org/fortran/show/Fortran+2008+status (search Internal procedure as an actual argument). The most recent version of this table is periodically published in ACM SIGPLAN Fortran Forum.

There is some interesting info in this article http://software.intel.com/en-us/blogs/2009/09/02/doctor-fortran-in-think-thank-thunk/