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https://github.com/jacobwilliams/diff
Numerical Differentiation of a User Defined Function
https://github.com/jacobwilliams/diff
differentiation numerical-differentiation
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Numerical Differentiation of a User Defined Function
- Host: GitHub
- URL: https://github.com/jacobwilliams/diff
- Owner: jacobwilliams
- License: other
- Created: 2014-02-20T03:45:05.000Z (over 10 years ago)
- Default Branch: master
- Last Pushed: 2022-05-22T20:58:33.000Z (over 2 years ago)
- Last Synced: 2023-03-24T05:55:58.030Z (over 1 year ago)
- Topics: differentiation, numerical-differentiation
- Language: Fortran
- Homepage:
- Size: 658 KB
- Stars: 2
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
diff
============
Numerical Differentiation of a User Defined Function
### Status
[](https://github.com/jacobwilliams/diff/releases/latest)
[](https://github.com/jacobwilliams/diff/actions)
[](https://codecov.io/gh/jacobwilliams/diff)
[](https://github.com/jacobwilliams/diff/commits/master)
### Overview
This code is a modern Fortran update of the DIFF subroutine found here: `ftp://math.nist.gov/pub/repository/diff/`
The DIFF subroutine computes the first, second or third derivative of a real function of a single real variable. The user provides the function, a real interval `[xmin,xmax]` on which the function is continuous, and a point `x0` lying in `[xmin,xmax]`. Optionally, the user may provide an estimate of the absolute or relative accuracy of function evaluation in `[xmin,xmax]` and the absolute or relative error tolerance that is acceptable in the computed derivative. The subroutine returns the computed derivative and an estimated upper bound on the absolute error of the computed derivative. The method used is Neville's process of extrapolating from a sequence of interpolating polynomials with interpolating points distributed symmetrically about `x0` or, if this is not possible, to one side of `x0`.
The original sourcecode was produced by the National Bureau of Standards, and is presumed to be in the public domain.
### Compiling
A [Fortran Package Manager](https://github.com/fortran-lang/fpm) manifest file is included, so that the library and test cases can be compiled with FPM. For example:
```
fpm build --profile release
fpm test --profile release
```
To use `diff` within your fpm project, add the following to your `fpm.toml` file:
```toml
[dependencies]
diff = { git="https://github.com/jacobwilliams/diff.git" }
```
### Example Usage
```fortran
program example
use diff_module
use iso_fortran_env, only: wp => real64 !use double precision
implicit none
integer,parameter :: iord = 1
real(wp),parameter :: x0 = 0.12345_wp
real(wp),parameter :: xmin = 0.0_wp
real(wp),parameter :: xmax = 1.0_wp
real(wp),parameter :: eps = 1.0e-9_wp
real(wp),parameter :: acc = 0.0_wp
real(wp) :: deriv, error
integer :: ifail
type(diff_func) :: d
call d%set_function(sin_func) !set function
call d%compute_derivative(iord,x0,xmin,xmax,eps,acc,deriv,error,ifail)
write(*,'(A)') ''
write(*,'(A,I5)') 'ifail :', ifail
write(*,'(A,E25.16)') 'estimated derivative :', deriv
write(*,'(A,E25.16)') 'actual derivative :', cos(x0)
write(*,'(A,E25.16)') 'estimated error :', error
write(*,'(A,E25.16)') 'actual error :', cos(x0) - deriv
write(*,'(A)') ''
contains
function sin_func(me,x) result(fx)
implicit none
class(diff_func),intent(inout) :: me
real(wp),intent(in) :: x
real(wp) :: fx
fx = sin(x)
end function sin_func
end program example
```
Which produces:
```
ifail : 0
estimated derivative : 0.9923897210998529E+00
actual derivative : 0.9923897211114882E+00
estimated error : 0.5805992701806732E-09
actual error : 0.1163524832037410E-10
```
### Documentation
* The API documentation for the current ```master``` branch can be found [here](https://jacobwilliams.github.io/diff/). This is generated by processing the source files with [FORD](https://github.com/Fortran-FOSS-Programmers/ford).
### Notes
Alan Miller's [to_f90](http://jblevins.org/mirror/amiller/to_f90.f90) program was used to assist in the conversion to modern Fortran.
### See also
* DIFF has been incorporated into the [NumDiff](https://github.com/jacobwilliams/NumDiff) library.