A toolbox called ADiGator is described for algorithmically differentiating mathematical functions in MATLAB. ADiGator performs source transformation via operator overloading using forward mode algorithmic differentiation and produces a file that can be evaluated to obtain the derivative of the original function at a numeric value of the input. A convenient by-product of the file generation is the sparsity pattern of the derivative function. Moreover, because both the input and output to the algorithm are source codes, the algorithm may be applied recursively to generate derivatives of any order. A key component of the algorithm is its ability to statically exploit derivative sparsity at the MATLAB operation level to improve runtime performance. The algorithm is applied to four different classes of example problems and is shown to produce runtime efficient derivative code. Due to the static nature of the approach, the algorithm is well suited and intended for use with problems requiring many repeated derivative computations.

A source transformation via operator overloading method is presented for computing derivatives of mathematical functions defined by MATLAB computer programs. The transformed derivative code that results from the method of this article computes a sparse representation of the derivative of the function defined in the original code. As in all source transformation automatic differentiation techniques, an important feature of the method is that any flow control in the original function code is preserved in the derivative code. Furthermore, the resulting derivative code relies solely upon the native MATLAB library. The method is useful in applications where it is required to repeatedly evaluate the derivative of the original function. The approach is demonstrated on several examples and is found to be highly efficient when compared to well-known MATLAB automatic differentiation programs.

An object-oriented method is presented that computes without truncation the error derivatives of functions defined by MATLAB computer codes. The method implements forward-mode automatic differentiation via operator overloading in a manner that produces a new MATLAB code that computes the derivatives of the outputs of the original function with respect to the differentiation variables. Because the derivative code has the same input as the original function code, the method can be used recursively to generate derivatives of any order desired. In addition, the approach developed in this article has the feature that the derivatives are generated by simply evaluating the function on an instance of the class, thus making the method straightforward to use while simultaneously enabling differentiation of highly complex functions. A detailed description of the method is presented and the approach is illustrated and shown to be efficient on four examples.

An approach to the architecture of distributed databases is presented, oriented around extensive embeddmg of database prinntives in the underlying distributed operating system.It is shown that this approach greatly reduces the effort required to provide high quality distributed database services.Substantial portions of this approach are implemented and are operational as extensions to the Locus distributed Unix operating system.TIns paper describes the approach, compares it with other work, argues why rt is attractive and what drawbacks are present, and lays out what has been done and what remains.