# Fazang: a reverse-mode automatic differentiation library

**URL:** <https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714>\
**Category:** Announcements\
**Created:** [February 2, 2022, 12:10am UTC](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714 "2022-02-02T00:10:00Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![yizhang](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/yizhang/32/1209_2.png) [@yizhang](https://fortran-lang.discourse.group/u/yizhang)\
**Post date:** [February 16, 2022, 11:01pm UTC](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714/21 "2022-02-16T23:01:28Z")

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`Fazang` now supports ODE sensitivity solution (based on `CVODES`) with respect to given parameters  
without explicitly asking for Jacobian. For that the user-defined ODE must include right-hand-side (RHS) definitions for `var` type and `real` types, due to the lack of meta-programming.

User-defined RHS would be like this.

```fortran
module ode_mod
  use fazang
  use, intrinsic :: iso_c_binding
  implicit none

  real(rk), parameter :: omega = 0.5d0
  real(rk), parameter :: d1 = 1.0d0
  real(rk), parameter :: d2 = 1.0d0

contains
  ! right-hand-side for data input
  subroutine eval_rhs(t, y, fy)
    implicit none
    real(c_double), intent(in) :: t, y(:)
    real(c_double), intent(inout) :: fy(size(y))
    fy(1) = y(2)
    fy(2) = sin(omega * d1 * d2 * t)
  end subroutine eval_rhs

  ! right-hand-side for var input with parameters
  ! y, p, and output fy must all be of var type
  subroutine eval_rhs_pvar(t, y, fy, p)
    implicit none
    real(c_double), intent(in) :: t
    type(var), intent(in) :: y(:), p(:)
    type(var), intent(inout) :: fy(size(y))
    fy(1) = y(2)
    fy(2) = sin(p(1) * p(2) * p(3) * t)
  end subroutine eval_rhs_pvar
end module ode_mod

```

Now we can solve the defined ODE

```fortran
program cvodes_demo
  use ode_mod
  use fazang
  implicit none

  type(var) :: yt(2, 3)
  type(cvodes_tol) :: tol
  real(rk), parameter :: ts(3) = [1.2d0, 2.4d0, 4.8d0]
  real(rk), parameter :: y00(2) = [0.2d0, 0.8d0]
  type(var) :: param(3)
  real(rk) :: y0(2), ga(2)
  integer :: i, j

  y0 = y00 ! init condition
  param = var([omega, d1, d2]) ! parameters
  tol = cvodes_tol(CV_BDF, 1.d-10, 1.d-10, 1000_8)

  yt = cvodes_sol(0.d0, y0, ts, param, eval_rhs,&
       & eval_rhs_pvar, tol)
! ...
end program cvodes_demo

```

Note that the call to `cvodes_sol` includes parameter argument `param` and **two** RHS functions, one for `real` input and one for `var` input.

The sensitivities are obtained the same way by calling `grad` and `adj` on the output and input, respectively.

```fortran
  call yt(1, 1) % grad()
  write(*, *) "dy_1/ d_omega at time ts(1):", param(1)%adj()

```

See [examples](https://github.com/yizhang-yiz/fazang/tree/main/example/ode) and [user doc](https://github.com/yizhang-yiz/fazang/blob/main/doc/fazang_user_guide.pdf) for details.

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<div class="post-metadata">

**Author:** ![fedebenelli](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/fedebenelli/32/1823_2.png) [@fedebenelli](https://fortran-lang.discourse.group/u/fedebenelli)\
**Post date:** [February 23, 2023, 11:45pm UTC](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714/22 "2023-02-23T23:45:45Z")

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This seems like a REALLY interesting and useful project! For me a lot since I’m starting to learn and use automatic differentiation. I’ll give this project a try but I would also love `fpm` compatibility to easily add it to my projects

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<div class="post-metadata">

**Author:** ![yizhang](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/yizhang/32/1209_2.png) [@yizhang](https://fortran-lang.discourse.group/u/yizhang)\
**Post date:** [February 23, 2023, 11:56pm UTC](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714/23 "2023-02-23T23:56:14Z")

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I’m hopelessly overwhelmed in past a few months and lack bandwidth to revisit this. Also I’m not familiar with fpm so any help is appreciated.

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<div class="post-metadata">

**Author:** ![fedebenelli](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/fedebenelli/32/1823_2.png) [@fedebenelli](https://fortran-lang.discourse.group/u/fedebenelli)\
**Post date:** [February 24, 2023, 12:05am UTC](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714/24 "2023-02-24T00:05:31Z")

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I’ve just realized this post was from a whole year ago! I’ll check if I can help you with fpm compatibility. I don’t have much experience with packages with this complexity (mostly the sundials bit), but this can also be a learning experience for me 🙂

[Previous page](https://fortran-lang.discourse.group/t/fazang-a-reverse-mode-automatic-differentiation-library/2714.md?page=1)