Sparse Automatique Differentiation
This project implements a Matlab/ forward automatic differentiation method, (wikipedia definition https://en.wikipedia.org/wiki/Automatic_differentiation#Forward_accumulation) based on operator overloading. This does not provide backward mode. It enables precise and efficient computation of the Jacobian of a function. This contrasts with numerical differentiation (a.k.a finite differences) that is unprecise due to roundoff errors and that cannot exploit the sparsity of the derivatives.
In contrast with most existing automatic differentiation Matlab toolboxes:
1) Derivatives are represented as sparse matrices, which yield to large speedups when the Jacobian of the function - we aim to differentiate is sparse or when intermediate accumulated Jacobian matrices are sparse (see the image denoising example) .
2) N dimensional arrays are supported while many Matlab automatic differentiation toolboxes only support scalars, vectors and 2D matrices
It is likely that the speed could be improved by representing Jacobian matrices by their transpose, due to the way Matlab represents internally sparse matrices
a simple example using a 3D array:
>> f=@(x) sum(x.^2,3);
>> full(AutoDiffJacobianAutoDiff(f,ones(2,2,2)))
ans =
2.0000 0 0 0 2.0000 0 0 0
0 2.0000 0 0 0 2.0000 0 0
0 0 2.0000 0 0 0 2.0000 0
0 0 0 2.0000 0 0 0 2.0000
see the github page https://github.com/martinResearch/MatlabAutoDiff for more examples and a more detailed explaination
Cita come
martin de la gorce (2024). Sparse Automatique Differentiation (https://github.com/martinResearch/MatlabAutoDiff), GitHub. Recuperato .
Compatibilità della release di MATLAB
Compatibilità della piattaforma
Windows macOS LinuxCategorie
- MATLAB > Mathematics > Sparse Matrices >
Tag
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Scopri Live Editor
Crea script con codice, output e testo formattato in un unico documento eseguibile.
src
src/backports
Le versioni che utilizzano il ramo predefinito di GitHub non possono essere scaricate
Versione | Pubblicato | Note della release | |
---|---|---|---|
1.0.0.0 | improve doc
updating example
|
|