Differentiation-Enabled Fortran 95 Compiler Technology (CompAD-II)

给定一个Fortran程序，它从输入值的向量x数值计算标量输出y=f（x），我们经常对计算梯度向量g=f '（x）感兴趣，其分量是导数（灵敏度）dy/dx。自动微分是一组用于将计算f的程序自动转换为计算f '的程序的技术。特别是伴随，或反向，模式的自动微分将产生数值的梯度g的所有组件在计算成本约五个评估f，无论数量的组件在x和g。这一建议是继续的工作开始在GR/R 55252。NAGWare Fortran 95编译器中自动微分功能的集成将被扩展到包含反向在已经引入的CompAD-I主动数据类型的基础上，将建立基本反向模式，并通过基本块的局部雅可比矩阵成功地扩展到具有用户的单个分配的最佳预累积梯度，这将是世界上第一次伴随模式AD与工业级Fortran编译器完全集成。在Hatfield开发编译器（和必要的伴随理论）的同时，该项目将结合克兰菲尔德和Qinetiq的参考问题的开发和经验。这个项目的主要目的是探索替代算法和表示的语义转换与伴随在这种情况下，为了奠定基础，为未来的进展。然而，这个项目产生的Fortran编译器被设计成在科学计算中广泛直接使用（见下一节）。

Given a Fortran program which evaluates numerically a scalar output y=f(x) from a vector x of input values, we are frequently interested in evaluating the gradient vector g=f '(x) whose components are the derivatives (sensitivities) dy/dx.Automatic Differentiation is a set of techniques for the automatic transformation of the program for evaluating f into a program for evaluating f '. In particular the adjoint, or reverse, mode of Automatic Differentiation will produce numerical values for all components of the gradient g at a computational cost of about five evaluations of f, regardless of the number of components in x and g.This proposal is for continuation of the work begun in GR/R55252. The integration of Automatic Differentiation capabilities into the NAGWare Fortran 95 Compiler will be extended to incorporate the reverse (or adjoint) mode of operation.Building on the CompAD-I active data type already introduced, basic reverse mode will be built and sucessively extended through local Jacobians of basic blocks through to optimally pre-accumulated gradients of single assignments with user-defined checkpointing.This will be the first time in the world that adjoint mode AD has been fully integrated with an industrial strength Fortran compiler. In parallel with development of the compiler (and the necessary adjoint theory) at Hatfield, the project will incorporate development of, and experience with, reference problems at Cranfield and Qinetiq. A primary purpose of this project is to explore alternative algorithms and representations for the semantic transformations associated with adjoints in this context, in order to lay the groundwork for future progress. However the Fortran Compiler resulting from this project is designed to be of widespread direct use in scientific computing (see next section).