Using functions as arguments - how to call?

Question

I have the following code, where I call a function from a subroutine, all of them in the same module:

      module mymodule
      implicit none
      contains  

      subroutine mycode
      real :: y0(3), a = 0.0, b = 1.0
      integer :: i, N = 10
      real, allocatable :: y(:,:)
      y0(:) = [1.0, 1.0, 1.0]
      y = AB2(od, a, b, N, y0)
      do i = 1, N
          print *, y(:,i)
      end do      
      end subroutine mycode

      function AB2(f, a, b, N, y0)
          real, allocatable :: AB2(:,:)
          interface
              function f(x, y)
                  real, allocatable :: f(:)
                  real, intent(in) :: x, y(:)
              end function
          end interface
          real, intent(in) :: a, b
          integer, intent(in) :: N
          real, intent(in) :: y0(:)
          real :: xn0, xn1, step
          real, allocatable :: yn0(:), yn1(:)
          integer :: i
          allocate(AB2(size(y0),N))
          step = (b-a)/(N-1)
          AB2(:,1) = y0
          AB2(:,2) = y0 + step*f(a, y0)
          do i = 3, N
              xn0 = a+(i-2)*step
              xn1 = a+(i-1)*step
              yn0 = AB2(:,i-2)
              yn1 = AB2(:,i-1)
              AB2(:,i) = AB2(:,i-1) + step*(3.0/2.0*f(xn1,yn1)
     &             -0.5*f(xn0,yn0))
          end do
      end function

      function od(x, y)
          real, allocatable :: od(:)
          real, intent(in) :: x, y(:)
          allocate(od(3))
          od(1) =  x + y(1)
          od(2) = -y(3) - y(2) - x
          od(3) =  x - y(1) + y(3)
      end function

      end module mymodule

If I want to give another parameter to the function od, say c, I have to include it on this line

real, intent(in) :: x, c, y(:)

and also

   function od(x,c,y)

However, where do I provide the value for this argument? There is no option in the call

y = AB2(od, a, b, N, y0)

Answer 1

This answer does not try to duplicate answers to Fortran minimization of a function with additional arguments Passing external function of multiple variables as a function of one variable in Fortran or Implementing anonymous functions in Fortran but to introduce the problem on a very basic level.

Suppose you have a function AB2 and another small function od.

They are used in such a way that AB2 accepts od as an argument, so you call

y = AB2(od)

the functions look like

real function AB2(f)
  interface
    real function f(x)
      real x
    end function
  end interface
  ... call f(x) here ...
end function

real function od(x)
  real x
end function

You need to pass additional data c to od. How to do that?

You cannot just change od by adding an argument for c and keep AB2 unchanged. AB2 contains a description of the interface of the argument f and od(x,c) would not be compatible with f(x).

Also, you would not be able to pass the data to AB2. You certainly cannot do

y = AB2(od(c))

by doing od(c) you are computing a number by calling od(x) you would then try to pass this number to AB2 instead of the function that should be passed.

There are several ways how to mitigate this. They are described in the answers linked above. I will show one simple possibility.

Let's say we nave have function od(b,x) and wee need to pass c to b, but we don't know how to do that with our AB2.

 real function od(b,x)
   real b, x
 end function

In our calling code we create a wrapper function that calls od with c for us. It can be an internal function or a module function. And we pass the wrapper to AB2.

subroutine caller(c)
  y = AB2(wrapper)
contains
  real function wrapper(x)
    real x
    !we must be able to see c from here, by host association or by using a module
    wrapper = od(c,x)
  end function
end subroutine