ADIFOR–Generating Derivative Codes from Fortran Programs

Abstract

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function I : R" ~ Rm. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution. Automatic Differentiation of FORtran (ADIFOR) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem. ADIFOR employs the data analysis capabilities of the ParaScope Parallel Programming Environment, which enable us to handle arbitrary Fortran 77 codes and to exploit the computational context in the computation of derivatives. Experimental results show that ADIFOR can handle real-life codes and that ADIFOR-generated codes are competitive with divided-difference approximations of derivatives. In addition, studies suggest that the source transformation approach to automatic differentiation may improve the time to compute derivatives by orders of magnitude.

Algorithmic differentiation techniques for global optimization in the COCONUT environment

“…That can, e.g., be derived from Figure 5 for the point (1, 3, 3). On the lower right + operator this point evaluates to 6, which is clearly outside the range [8,12]. Hence, (1, 3, 3) / ∈ M , which cannot easily be seen without propagating through the DAG.…”

“…If we then consider the constraints for problem (8) componentwise, for every component F j (x) ∈ F j the constraints Q j (x) ≤ F j and Q j (x) ≥ F j are valid quadratic constraints; here Q j (x) and Q j (x) are the quadratic under-and overestimating functions for F j (x). Together with the quadratic underestimating function q(x) of the objective function f , we get the QCQP (quadratically constrained quadratic program) relaxation min q(x) s.t.…”

On Combining Computational Differentiation and Toolkits for Parallel Scientific Computing

“…Given a computer code for the objective function in virtually any high-level programming language such as Fortran, C, or C++, automatic differentiation tools such as ADIFOR [4,5], ADIC [6], or ADOL-C [13] can by applied in a black-box fashion. A survey of AD tools can be found at http: //www .mcs.…”

“…The differences in execution time between these three approaches increase with increasing the dimension, r, of the free parameter vector s. While the CD approach turns out to be clearly the best of the three discussed approaches, its performance can be improved significantly. The linear systems (4) involving the same coefficient matrix but r different right-hand sides are solved in [14] by running r times a typical Krylov subspace method for a linear system with a single right-hand side. In contrast to these successive runs, so-called block versions of Krylov subspace methods are suitable candidates for solving systems with multiple right-hand sides; see [7,15] and the references given there.…”

Sensitivity technologies for large scale simulation.

“…Obviously this is a difficult task and clearly not always achievable. Nevertheless, significant work has been done on tools that use source transformation [38,100,37] and can be very effective as a general or initial approach to calculating derivatives. An alternative strategy for applying AD in C++ based codes is to use template overloading.…”