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https://github.com/jacobwilliams/numdiff
Modern Fortran Numerical Differentiation Library
https://github.com/jacobwilliams/numdiff
differentiation finite-differences graph-coloring numerical-differentiation numerical-methods optimization sparsity-optimization
Last synced: 23 days ago
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Modern Fortran Numerical Differentiation Library
- Host: GitHub
- URL: https://github.com/jacobwilliams/numdiff
- Owner: jacobwilliams
- License: other
- Created: 2016-10-31T01:18:09.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2024-02-26T23:18:47.000Z (11 months ago)
- Last Synced: 2024-11-08T03:09:19.501Z (3 months ago)
- Topics: differentiation, finite-differences, graph-coloring, numerical-differentiation, numerical-methods, optimization, sparsity-optimization
- Language: Fortran
- Homepage:
- Size: 4.33 MB
- Stars: 65
- Watchers: 8
- Forks: 7
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
============
## Brief description
**NumDiff** provides a modern Fortran interface for computing the Jacobian (derivative) matrix of `m` nonlinear functions which depend on `n` variables. The Jacobian matrix is required for various applications, including numerical optimization. It can also be used to test the accuracy of gradients computed by other means. The library also provides for computing the sparsity of this matrix, and returning the Jacobian in sparse or dense form.
## Status
[](https://github.com/jacobwilliams/NumDiff/releases/latest)
[](https://github.com/jacobwilliams/NumDiff/actions)
[](https://codecov.io/gh/jacobwilliams/NumDiff)
[](https://github.com/jacobwilliams/NumDiff/commits/master)
This is currently a work in progress. The goal is a comprehensive library that contains a full suite of computationally efficient implementations of algorithms for sparsity determination and numerical differentiation. This code is hosted on GitHub at: https://github.com/jacobwilliams/NumDiff
### To Do
- [x] Computing the nonlinear sparsity pattern
- [x] Specified by the user
- [x] Assume all elements `true`
- [x] Three random points within variable bounds (have the option to specify separate bounds for this purpose)
- [x] Various order finite different gradient methods
- [x] 2-point (backward 1, forward 1)
- [x] 3-point (backward 2, central, forward 2)
- [x] 4-point (backward 3, backward 2, forward 2, forward 3)
- [x] 5-point (backward 4, backward 3, central, forward 3, forward 4)
- [x] 6-point (backward 5, backward 4, backward 3, forward 3, forward 4, forward 5)
- [x] 7-point (backward 6, backward 5, backward 4, central, forward 4, forward 5, forward 6)
- [x] 8-point (backward 7, backward 6, backward 5, backward 4, forward 4, forward 5, forward 6, forward 7)
- [x] 9-point (backward 8, backward 7, backward 6, backward 5, central, forward 5, forward 6, forward 7, forward 8)
- [x] 11-point (central)
- [x] 13-point (central)
- [x] 15-point (central)
- [x] 17-point (central)
- [x] Perturbations should respect variable bounds
- [x] Neville's process
- [x] Ability to use different methods for different columns
- [x] Jacobian partitioning to compute multiple columns at the same time
- [ ] Estimate the optimal perturbation step size
- [ ] Computing the linear sparsity pattern (constant elements of Jacobian)
- [ ] Add other gradient methods?
- [ ] Also compute Hessian matrix?
- [ ] OpenMP or Coarrays for parallelization
- [ ] Testing for computational efficiency
- [ ] General code cleanup
## Building NumDiff
### FPM
A [Fortran Package Manager](https://github.com/fortran-lang/fpm) manifest file is included, so that the library and tests cases can be compiled with FPM. For example:
```
fpm build --profile release
fpm test --profile release
```
To use `NumDiff` within your FPM project, add the following to your `fpm.toml` file:
```toml
[dependencies]
NumDiff = { git="https://github.com/jacobwilliams/NumDiff.git" }
```
or, to use a specific version:
```toml
[dependencies]
NumDiff = { git="https://github.com/jacobwilliams/NumDiff.git", tag = "1.7.0" }
```
To generate the documentation using [FORD](https://github.com/Fortran-FOSS-Programmers/ford), run:
```
ford ford.md
```
By default, the library is built with double precision (`real64`) real values. Explicitly specifying the real kind can be done using the following processor flags:
Preprocessor flag | Kind | Number of bytes
----------------- | ----- | ---------------
`REAL32` | `real(kind=real32)` | 4
`REAL64` | `real(kind=real64)` | 8
`REAL128` | `real(kind=real128)` | 16
For example, to build a single precision version of the library, use:
```
fpm build --profile release --flag "-DREAL32"
```
Note that the [pyplot-fortran](https://github.com/jacobwilliams/pyplot-fortran) library is a dependency for one of the test cases. FPM will automatically download the right version.
## Documentation
The latest API documentation can be found [here](https://jacobwilliams.github.io/NumDiff/). This was generated from the source code using [FORD](https://github.com/Fortran-FOSS-Programmers/ford) (note that the included `build.sh` script will also generate these files).
## License
The NumDiff source code and related files and documentation are distributed under a permissive free software [license](https://github.com/jacobwilliams/NumDiff/blob/master/LICENSE) (BSD-style).
## References
* J. Oliver, "An algorithm for numerical differentiation of a function of one real variable", Journal of Computational and Applied Mathematics 6 (2) (1980) 145-160. Fortran 77 code from [NIST](ftp://math.nist.gov/pub/repository/diff/src/DIFF)
* Thomas F. Coleman, Burton S. Garbow, Jorge J. More, "Algorithm 618: FORTRAN subroutines for estimating sparse Jacobian Matrices", ACM Transactions on Mathematical Software (TOMS), Volume 10 Issue 3, Sept. 1984, Pages 346-347
* G. E. Mullges, F. Uhlig, "Numerical Algorithms with Fortran", Springer, 1996.