Compiling Fast Partial Derivatives of Functions Given by Algorithms

摘要

If the gradient of the function y = f(x sub 1 ,..., x/sub n/) is desired, where f is given by an algoritym Af(x, n, y), most numerical analysts will use numerical differencing. This is a sampling scheme that approximates derivatives by the slope of secants in closely spaced points. Symbolic methods that make full use of the program text of Af should be able to come up with a better way to evaluate the gradient of F. The system Jake described produces gradients significantly faster than numerical differencing. Jake can handle algorithms Af with arbitrary flow of control. Measurements performed on one particular machine suggest that Jake is faster than numerical differencing for n > 8. Somewhat weaker results were obtained for the problem of computing Jacobians of arbitrary shape. (ERA citation 05:028237)