Libadjoint has moved to bitbucket: https://bitbucket.org/dolfin-adjoint/libadjoint

Much computational science deals with the approximate solution of models described by systems of partial differential equations; these are used across the entire breadth of the quantitative sciences. Such a model takes as input the physical state at some initial time and runs forward in time to compute the state at some later time of interest; that is, it maps cause to effect, and so it is referred to as the forward model. For a given forward model, one can associate an adjoint model, which does the opposite: it maps from effect back to cause, and so runs backwards in time. Once an adjoint model is available, it makes possible a number of very powerful techniques: optimise engineering designs, assimilate data from physical measurements, estimate unknown parameters in the forward model, and estimate the approximation error in quantities of interest. Such applications are of huge interest and importance across all of engineering and the quantitative sciences. As computational science moves from mere simulation to optimisation, adjoint modelling will only grow in importance.

The fundamental abstraction of algorithmic differentiation is that it treats the model as a sequence of primitive instructions, each of which may be differentiated in turn and composed using the chain rule. libadjoint explores a similar, but higher-level abstraction: that the model is a sequence of linear solves. In this approach, the model is instrumented with library calls that record what operators it is assembling and what they are being applied to, in an analogous manner to building a tape for reverse-mode AD. The model developer then provides callback routines that compute the action of or assemble these operators to the library. With this information, the library may then assemble the adjoint of each equation solved in the forward model automatically. This promises to make adjointing models significantly easier than it currently is.