# Is creating nested subroutines/functions considered good practice in Fortran?

**URL:** <https://fortran-lang.discourse.group/t/is-creating-nested-subroutines-functions-considered-good-practice-in-fortran/6545>\
**Category:** Help\
**Created:** [September 21, 2023, 6:59pm UTC](https://fortran-lang.discourse.group/t/is-creating-nested-subroutines-functions-considered-good-practice-in-fortran/6545 "2023-09-21T18:59:35Z")\
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**Author:** ![ivanpribec](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/ivanpribec/32/3290_2.png) [@ivanpribec](https://fortran-lang.discourse.group/u/ivanpribec)\
**Post date:** [September 23, 2023, 9:05pm UTC](https://fortran-lang.discourse.group/t/is-creating-nested-subroutines-functions-considered-good-practice-in-fortran/6545/17 "2023-09-23T21:05:45Z")

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The concept is known as a [callback](https://en.wikipedia.org/wiki/Callback_(computer_programming)). In other words you have a subroutine that takes another subroutine or function as argument.

The classic example would be a numerical solver and a parametrized function of some sort. We can take root-solving as an example:

```fortran
  ! find the root f(x) = 0, in the interval [ax,bx]
  x = zeroin(ax,bx,f,tol)

```

The function `f` passed as a parameter to `zeroin` must match a particular interface:

```auto
interface
  real(dp) function f(x)
    import dp
    real(dp), intent(in) :: x
  end function
end interface

```

To make this more concrete, say you had to find the friction factor f prescribed by the [Colebrook-White](https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae#Colebrook%E2%80%93White_equation) equation:

\frac{1}{\sqrt{f}} = -2 \log \left( \frac{\epsilon}{3.7 D\_\text{h}} + \frac{2.51}{\mathit{Re} \sqrt f} \right)

Finding f can be recast as finding the root of the equation:

G(f) = \frac{1}{\sqrt{f}} +2 \log \left( \frac{\epsilon}{3.7 D\_\text{h}} + \frac{2.51}{\mathit{Re} \sqrt f} \right) = 0

In Fortran you might do this as follows:

```fortran
real(dp) :: f, Re, Dh, eps
real(dp), parameter :: tol = 1.0e-9_dp

Re = 10000
Dh = 0.2_dp ! in meters
eps = 0.002_dp ! 2 mm

f = zeroin(0.001_dp, 0.01_dp,friction_equation,tol)
print *, f

contains

  real(dp) function friction_equation(f) result(y)
    import, only: Re, Dh, eps ! if supported by your Fortran compiler
    real(dp), intent(in) :: f
    y = 1.0_dp/sqrt(f) + 2*log(eps/(3.7_dp*Dh) + 2.51_dp/(Re*sqrt(f))) 
  end function

```

This could be made part of general subroutine taking Re, D\_h and \epsilon as inputs, making sure they are valid and finally returning the friction factor f as output.

---

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