Source Transformation for the Optimized Utilization of the Matlab Runtime System for Automatic Differentiation

Operator overloading in Matlab allows for user-defined types to semantically augment existing Matlab codes without changes. However, given sufficient knowledge about types and operand semantics, operator overloading can be replaced by equivalent function calls. The ADiMat software tool provides automatic differentiation of Matlab functions using a hybrid approach that combines source transformation and operator overloading. It can also be used as a general framework for user-defined transformations of Matlab codes. Tests showed the potential for performance improvement in a derivative class providing essential linear algebra functionality for ADiMat. The Matlab runtime environment was benchmarked regarding function and method call overheads as well as property access overhead with Matlab's objects. These tests identify the cell class property access as the main performance culprit. Hence, an automatic method, transforming the XML based abstract syntax tree created with ADiMat's toolchain through a set of stylesheets, was developed. This process completely removes the derivative object usage and hence the opreator overloading and the property access overhead from any derivative function created with ADiMat. Experimental results show that performance is improved considerably depending on the data container storing the derivative directions