Nicholaswogan / ForwardDiff

Forward mode automatic differentiation for Fortran

ForwardDiff

ForwardDiff allows for the computation of derivatives, gradients and Jacobians of Fortran subroutines or functions using forward mode automatic differentiation (AD). To create this package I borrowed code, syntax and inspiration from DNAD, ForwardDiff.jl, and a lecture series by Chris Rackauckas.

Examples

For a comprehensive set of examples see the tests in the test directory. In particular, test/fypp_example.fypp shows how to use the fypp preprocessor to write more general, differentiable code.

Below is a simple demo that computes the derivative of the scalar function $f(x) = \sin(x)\exp(x)x^2 + 1$ at $x = 2$.

program main
  use forwarddiff, only: wp, derivative
  implicit none

  call example()

contains

  subroutine example()
    real(wp) :: x, f, dfdx
    x = 2.0_wp
    call derivative(fcn, x, f, dfdx)
    print*,'x = ',x
    print*,'f = ',f
    print*,'df/dx = ',dfdx
  end subroutine

  function fcn(x) result(f)
    use forwarddiff
    type(dual), intent(in) :: x
    type(dual) :: f
    f = sin(x)*exp(x)*x**2.0_wp + 1.0_wp
  end function

end program 

Output:

 x =    2.0000000000000000     
 f =    27.875398789713000     
 df/dx =    41.451068296868563

Building

mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
cmake --build .
# run test
./test/test_forwarddiff

Limitations

This package has the following limitations:

• The package is not compatible with all Fortran intrinsic functions. If you identify an intrinsic that should be added, please submit a pull request.

• The jacobian routine can only compute square Jacobians.