Open source auto-differentiation for MATLAB?

Question

Are there any open-source auto-differentiation libraries for MATLAB?

I am aware of commercial packages such as Tomlab/MAD and plenty of C++ libraries, but I can't find many more for MATLAB other than Automatic Differentiation for Matlab package on Matlab File Exchange which isn't a major package.

Added

As a bare minimum of functionality, I need to be able to handle vectors as variables. In that MathWorks package, I reference, for example, here is a test case:

val = [1 2 3]; %Some value
x = myAD(val); %Creates a vector with that value.

x .* [4 5 6]; %This should give the derivatives [4; 5; 6]
x_inner = sum(x.* x);% To get the inner product.  The derivative here is [2 4 6] here
%Ideally, the above would simply be x_inner = x * x'

Answer 1

The SINTEF Matlab Reservoir Simulation Toolbox includes a GPL-licensed AD library. The usage is mostly geared towards numerical applications in subsurface flow, but the library itself is usable for more general purposes.

Here is a basic runthrough of your example as you would run it from the base directory of MRST:

startup;
% Load ad based module
mrstModule add ad-fi


val = [1; 2; 3];
x = initVariablesADI(val);
y = x.*[4; 5; 6];
disp 'Jacobian:'
full(y.jac{1})

z = sum(x.*x);
disp 'Jacobian:'
full(z.jac{1})
Jacobian:

% MRST AD also supports multiple vector valued functions
a = ones(5, 1);
b = ones(5, 1);
[a, b] = initVariablesADI(a, b);
c = a.*b + 2.*b;
full(c.jac{1})
full(c.jac{2})

There exists a work-in-progress user guide at the website, where chapter 7 has some usage of the AD library. This library is primarily geared towards problems that require all Jacobian values and is vectorized using forward mode only. It does include some nice things though, like 2d table interpolation and so on. It has been used for moderate size non-linear problems (order of 500,000 unknowns).

The non-linear solvers and components are heavily focused on reservoir applications at the moment. This part of the library is presently being rewritten and may in the future have some use outside of this specific domain. However, if you just want the AD part, the ADI class and the initVariablesADI function should be sufficient.

Disclaimer: I am one of the developers attached to this research group.

Answer 2

This article in SIAM Review describes how to implement operator-overloading automatic differentiation in MATLAB, and gives a good introduction to the technology.

Answer 3

I realize this is an old question, but when looking for this myself today I found ADiGator, which is open source, and seems to handle vectors. I haven't tested it yet myself, but it seems to be actively developed.

Answer 4

If you are really interested in open source and like to promote/support it, then you should probably take a look at the open source matlab clone octave. There is an extension to it, called ad that supports automatic forward differentiation. Unfortunately, it seems to be unmaintained currently.

Answer 5

The wikipedia page for automatic differentiation has links to many software packages or libraries, including several for MATLAB. http://en.wikipedia.org/wiki/Automatic_differentiation#Software

Answer 6

KPP translates a (chemical or other) ODE specification into Fortran77, Fortran90, C, or Matlab simulation code that implements time derivative function, its Jacobian, and its Hessian, together with a suitable numerical integration scheme. Sparsity in Jacobian/Hessian is carefully exploited to obtain computational efficiency.

CasADi's backbone is a symbolic framework implementing forward and reverse mode of AD on expression graphs to construct gradients, large-and-sparse Jacobians and Hessians. These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or be exported to Matlab, Python, or C code.