ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables

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• 作者：Straka ; Christian W.
• 关键词：Automatic differentiation ; Derivatives ; FORTRAN 95 ; Implicit solvers
• 刊名：Computer Physics Communications
• 出版年：2005
• 出版时间：June 1, 2005
• 年：2005
• 卷：168
• 期：2
• 页码：123-139
• 全文大小：141 K

文摘

ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied to any FORTRAN 77/90/95 conforming code and requires minimal changes by the user. It provides a new derived data type that holds the value and derivatives and applies forward differencing by overloading all FORTRAN operators and intrinsic functions. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain over other available tools with operator overloading. This gain is especially pronounced for sparse systems with large number of independent variables. A wide class of numerical simulations, e.g., those employing implicit solvers, can profit from ADF95.

Program summary

Title of program: ADF95

Catalogue identifier: ADVI

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVI

Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland

Computer for which the program is designed: all platforms with a FORTRAN 95 compiler

Programming language used: FORTRAN 95

No. of lines in distributed program, including test data, etc.: 3103

No. of bytes in distributed program, including test data, etc.: 9862

Distribution format: tar.gz

Nature of problem: In many areas in the computational sciences first order partial derivatives for large and complex sets of equations are needed with machine precision accuracy. For example, any implicit or semi-implicit solver requires the computation of the Jacobian matrix, which contains the first derivatives with respect to the independent variables. ADF95 is a software module to facilitate the automatic computation of the first partial derivatives of any arbitrarily complex mathematical FORTRAN expression. The program exploits the sparsity inherited by many set of equations thereby enabling faster computations compared to alternate differentiation tools

Solution method: A class is constructed which applies the chain rule of differentiation to any FORTRAN expression, to compute the first derivatives by forward differencing. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain when sparsity can be exploited. From a users point of view, only minimal changes to his/her original code are needed in order to compute the first derivatives of any expression in the code

Restrictions: Processor and memory hardware may restrict both the possible number of independent variables and the computation time

Unusual features: ADF95 can operate on user code that makes use of the array features introduced in FORTRAN 90. A convenient extraction subroutine for the Jacobian matrix is also provided

Running time: In many realistic cases, the evaluation of the first order derivatives of a mathematical expression is only six times slower compared to the evaluation of analytically derived and hard-coded expressions. The actual factor depends on the underlying set of equations for which derivatives are to be calculated, the number of independent variables, the sparsity and on the FORTRAN 95 compiler