A Dimension Abstraction Approach to Vectorization in Matlab

Matlab is a matrix-processing language that offers very efficient built-in operations for data organized in arrays. However Matlab operation is slow when the program accesses data through interpreted loops. Often during the development of a Matlab application writing loop-based code is more intuitive than crafting the data organization into arrays. Furthermore, many Matlab users do not command the linear algebra expertise necessary to write efficient code. Thus loop-based Matlab coding is a fairly common practice. This paper presents a tool that automatically converts loop-based Matlab code into equivalent array-based form and built-in Matlab constructs. Array-based code is produced by checking the input and output dimensions of equations within loops, and by transposing terms when necessary to generate correct code. This paper also describes an extensible loop pattern database that allows user-defined patterns to be discovered and replaced by more efficient Matlab routines that perform the same computation. The safe conversion of loop-based into more efficient array-based code is made possible by the introduction of a new abstract representation for dimensions