First Partial Differentiation by Computer with an Application to Categorical Data Analysis

Abstract

A strategy is presented for producing code to evaluate first partial derivatives of a function f by computer. Advantage is taken of the capabilities that a compiler must have simply to bring about the evaluation of f. A bound kt on the time it should take to evaluate the partials of f is developed, where f takes time t to evaluate and k is independent of f. The benefits of the differentiation strategy for weighted least squares analysis of categorical data are discussed.

Key Words:

• First partial differentiation
• Compiler
• Parse tree
• Categorical data analysis