Christian H. Bischof, Alan Carle, George F. Corliss, Andreas Griewank, and Paul D. Hovland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1:11--29, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....une fonction f , g en ere un programme P qui calcule certaines d eriv ees de f . L etude de la D.A. a une longue tradition a l inria [52] Il existe a l heure actuelle deux approches pour obtenir P . Soit par une transformation de source a source (outils odyss ee [42] adifor [14] [13], tamc [49] 50] padre2 [2] 70] soit par surcharge des op erateurs 9 arithm etiques (outils adol c [56] adogen [89] dans laquelle les op erateurs = etc sont modi es pour e ectuer en m eme temps les op erations sur les valeurs et leurs d eriv ees. Les d eriv ees calcul ees sont ....

Bischof C., Carle A., Corliss G., Griewank A., Hovland P. "ADIFOR: generating derivative codes from Fortran programs". Scienti c Programming, 1(1):11-29, 1992.

....code is demonstrated. References [4] and [5] are recent summaries of the studies of this work; the combination of AD and IIM to efficiently obtain consistent discrete SD s from a two dimensional (2 D) thin layer Navier Stokes code is demonstrated in [6] The AD tool ADIFOR (AD of Fortran) of [7] and [8] has been used throughout this work. Symbols and acronyms are defined as introduced in the text. The equations summarized in this paragraph can be found in greater detail in [1] 6] The conservation laws of compressible fluid flow, R, and aerodynamic functions, F , of interest can be ....

....extensive use was made of solution restart files; these inner loops are not shown in Fig. 2. The shape design loop starts at the upper left with the automated surface shaping and volume grid generation codes, which are discussed in [14] and [15] These codes are differentiated with ADIFOR ([7] and [8] to provide the grid SD s (X ) with respect to approximately 100 (wing) geometric design variables, as discussed in the appendix of [12] Both the grid (X) and its SD s (X ) are required because the geometric (shape) design variables determine the vehicle surface and its body fitted ....

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C. H. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, ADIFOR: Generating derivative codes from Fortran programs, Scientific Programming, 1 (1), (1992), pp. 11--29.

....The jth column of this matrix is given by the solutions on the interval [t i ;t i 1 ] of the equations F y (t; y; p)s ij ;s ij (t i ) e j ; 8) where e j is the jth column of the identity. As an aside, we note that these equations can be evaluated using automatic di#erentiation tools (see [3]) and solved via ODE or DAE sensitivity analysis software (see [8] They can also be evaluated using #nite di#erences (F(t; y # ij s ij ;p) F(t; y; p) where # ij is a small scalar. In the numerical example that we will consider, the matrix F(t; y; p) y is sparse and the products ....

C. Bischof, A. Carle, G. Corliss, A. Griewank, P. Hovland, ADIFOR --- generating derivative codes from Fortran programs, Sci. Programming 1 (1992) 11--29.

....function that is discontinuous, automatic differentiation tools will generate the JacobJan matrix but will not be able to detect this situation. 4 ADIFOR Figure 3. 1 shows that given the function F that defines the mixed complementarity problem, the automatic differentiator tool ADIFOR SparsLinc [3, 5] is used to produce the JacobJan matrix of F and the sparsity structure of the JacobJan matrix. This information is then fed to PATH. In this section we describe the process for generating a representation of the sparse JacobJan matrix of the function F that is submitted to the PATH solver. This ....

....to generate a sub routine of the form g fcn(n,x,gx,f ,g f) where gx is a gradient object for the independent variable x and g f is a gradient object for the function F. These objects are manipulated and accessed by PATH as described below. Further details on how to invoke ADIFOR can be found in [3, 5]. We compute the JacobJan of F by manipulating the gradient object with subroutines provided by ADIFOR in the SparsLinc [4] library. We first set the gradient object gx for the independent variable x to the identity matrix with the code segment doj =l,n cal 1 dspsd (g x (j) j, 1. dO, 1) end ....

C. BIscuor, A. CARLE, G. CORLISS, A. (RIEWANK, AND P. HOVLAND, ADIFOR: Generating derivative codes from Fortran programs, Scientific Programming, 1 (1992), pp. 1-29.

....Craig s algorithm to find s. Let s, s, be the sequence of iterates generated by the algorithm, hence for all i. sl = arg min lIVCf s Cll, s sn p, pl . Assume that I111 r and I1 11 rc. Therefore dog (1 S =aSl a)Si with It is easy to see that By convexity, Thus, c C [0, 1]. IIvcT, CII IIvcT Cll IIVCs g c11 IIVCs c11. Thus we can apply Lemma 2.1. n n 1f rSc Now suppose that s c is given by = with IIll = i otherwise. When = 1, we have when [ s[ r and When 1, we have IIC112 IIC vC II vcT slf ,2 IlCcll 2 ....

....for problems where B can be easily identified. See Dennis and Lewis [6] In either case, the uniform boundedness of Ak follows from the problem assumptions. The exact Hessian matrix perhaps can be gotten by using automatic differentia tion or an adjoint integration approach. See Bischof et al. [1]. However, an approxi mation to the Hessian of the Lagrangian can be used. Also, for example, setting Hk to a fixed matrix (e.g. H 0) for all k is valid. The question of how to use a secant approximation of the Hessian of the Lagrangian in order to produce a more efficient algorithm is a ....

C. BISCHOF, A. CARLE, G. CORLISS, A. GRIEWANK, and P. HOVLAND. Adifor - generating derivative codes from fortran progreuns. Scientific Programming, 1 (1) :11-29, 1992.

....of the objective function and constraints with respect to the optimization variables. We compute these derivatives via highly efficient DAE sensitivity software DASPK3.0 [11] The sensitivity equations to be solved by DASPK3.0 are generated via the automatic differentiation software ADIFOR2.0 [2]. This basic multiple shooting type of strategy can work very well for small to moderate size DAE systems, and has an additional advantage that it is inherently parallel. However, for large scale DAE systems there is a problem because the computational complexity grows rapidly with the dimension ....

BISCHOF, C., CARLE, A., CORLISS, G., GRIEWANK, A., AND HOVLAND, P. ADIFOR- Generating Derivative Codes from Fortran Programs. Scientific Programming I (1992), 11-29.

....the imaginary part is exactly the derivative of f times h. The end result is a sensitivity calculation method that is equivalent to the forward mode of algorithmic di#erentiation, as observed by Griewank [24] Algorithmic di#erentiation (AD) is a well established method for estimating derivatives [25, 9]. The method is based on the application of the chain rule of di#erentiation to each operation in the program flow. For each intermediate variable in the algorithm, a variation due to one input variable is carried through. As a simple example, suppose we want to di#erentiate the multiplication ....

....programs exist. These tools have been extensively developed and some of them provide the user with great functionality by including the option for using the reverse mode, for calculating higher order derivatives, or for both. Tools that use the source transformation approach include: ADIFOR [9], TAMC [19] DAFOR, GRESS [29] Odyssee [14] and PADRE2. The necessary changes to the source code are made automatically. As explained before, extending the original source code is a method that usually compromises its maintainability. The derived datatype approach is used in the following tools: ....

C. Bischof, A. Carle, G. Corliss, A. Grienwank, and P. Hoveland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1(1):11--29, 1992.

....code (where the software developer is no longer available to consult on code modifications) or spaghetti code (where the structure of the code is fragile poor) making the necessary modification very di#cult. Automatic di#erentiation (AD) tools have been developed to simplify this process [1, 16]. By viewing the original code as a sequence of unary and binary operations, taking the design parameters and returning the (approximate) solution to the PDE, AD tools read in the original code and produce software to solve for the state and sensitivity variables simultaneously. We point out that ....

C. Bischof, A. Carle, A. Griewank, and P. Hovland. ADIFOR: Generating derivative codes from Fortran programs. Technical Report MCS-P263-0991, Mathematics and Computer Science Division, Argonne National Laboratory, IL and Center for Research on Parallel Computation, Rice University, TX, 1991.

....given a program P implementing a function f , generates a program P 0 that computes some derivatives of f . A.D. has been studied at inria for a long time [52] There are two main approaches to get P 0 . One is source to source transformation. Let us quote the tools odyss#e [42] adifor [14] [13], tamc [49] 50] padre2 [2] 70] The other is overloading of arithmetic operations, as in the tools adol c [56] or adogen [89] The computed derivatives are used in various kinds of problems: a) Program sensitivity analysis [21] 37] 40] b) Analysis of propagation of truncation errors. ....

Bischof C., Carle A., Corliss G., Griewank A., Hovland P. "ADIFOR: generating derivative codes from Fortran programs". Scienti c Programming, 1(1):1129, 1992.

....of large nonlinear problems. Automatic di#erentiation can compute fast and exact 1 derivatives of any degree computationally via propagating Taylor series coe#cients using the chain rule [8] Although still in its formative stages, AD is now a very powerful tool (e.g. ADOL C [9] and ADIFOR [1] are two popular AD tools) especially when coupled with recent developments, e.g. exploitation of the user problem structure [13, 3, 2] The traditional methods of obtaining derivatives such as hand coding or finite di#erencing su#er in comparison with AD; hand coding is error prone and can be ....

....ways to implement an automatic di#erentiation tool: Source to source transformation: In source to source transformation tools the program is transformed using the above propagation rules to a derivative program which can be used to compute the derivative. One example of such a tool is ADIFOR [1]. Object oriented tools: In the rest of this section, we briefly describe how an AD tool based on object oriented technology works. Another such tool is ADOLC [9] For a survey article on AD tools, refer to [10] A typical Object oriented AD tool defines all the variables in the program to be ....

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C. H. Bischof, A. Carle, G. F. Corliss, A. Griewank, and P. Hovland, ADIFOR: Generating derivative code from FORTRAN programs, Scientific Programming, 1 (1992), pp. 11--29.

....computation. The evaluation of the function and its derivatives are calculated simultaneously using the same expressions. There are several descriptions about automatic differentiation [15, 1, 3] and also software packages Object Oriented Model for Partially Separable Functions . 13 available [9, 4]. Some packages preprocess the source code to add the necessary statements for computing the derivatives. Other packages, using programming languages that support operator overloading, implement the differentiation as a class library without the need for a separate precompilation. There are ....

Bischof C. H., Carle A., Corliss G. F., Griewank A., Hovland P.: ADIFOR: Generating derivative codes from Fortran programs, Scientific Programming, 1 (1992) 1-29.

....objective function and constraints with respect to the optimization variables. We compute these derivatives via di#erential algebraic equation (DAE) sensitivity software DASPKSO [10] The sensitivity equations to be solved by DASPKSO are generated via the automatic di#erentiation software ADIFOR [11]. The basic algorithms and software for the optimal control of dynamical systems are described in detail in [1] This basic multiple shooting type of strategy can work very well for small tomoderate size DAE systems, and has an additional advantage that it is inherently parallel. However, for ....

C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, ADIFOR--- generating derivative codes from Fortran programs, Scientific Programming, 1 (1992), pp. 11--29.

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Christian Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1(1):11--29, 1992.

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Christian Bischof, Alan Carle, George Corliss, Andreas Griewank, and Paul Hovland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1(1):11--29, 1992.

....complicated functions in an efficient way. To this end, we applied automatic differentiation to a large scale computational fluid dynamics solver, TFS, developed at Aerodynamisches Institut of Aachen University of Technology. More precisely, we used the automatic differentiation system ADIFOR [3, 4] to compute the derivatives of the density with respect to the angle of attack. The goal of this new project is twofold. On the one hand, derivatives provide valuable sensitivity information that lead to a better understanding of the simulation results and can be used for improving the robustness ....

....direction u than first determining f 0 (x) and then multiplying with u. We mention once more that AD is not only applicable to small pieces of code as given above but scales up to arbitrarily complicated codes consisting of several hundreds of thousands lines [7] Software tools such as ADIFOR [3, 4], ADIC [5] or ADOL C [18] implement the technology of automatic differentiation and can by applied in a black box fashion. A survey of AD tools will soon be available at http: www.autodiff.org: Besides the forward mode sketched above, there are further alternatives for the way how derivatives ....

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C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1(1):11--29, 1992.

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Christian H. Bischof, Alan Carle, George F. Corliss, Andreas Griewank, and Paul D. Hovland. ADIFOR: Generating derivative codes from Fortran programs. Scientific Programming, 1:11--29, 1992.

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C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland. ADIFOR - generating derivative codes from FORTRAN programs. Scientific Programming, 1:1--29, 1992. 22

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C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland. ADIFOR - Generating Derivative Codes from Fortran Programs. Scientific Programming, (1):1--29, 1992.

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Christian Bischof, Alan Carle, Andreas Griewank, and Paul Hovland. Adifor: Generating derivative codes from fortran programs. Scientific Programming, 1(1):11--29, 1992.

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Bischof, C., A. Carle, G. Corliss, A. Grienwank, P. Hoveland, "ADIFOR: Generating Derivative Codes from Fortran Programs", Scientific Programming, Vol. 1, No. 1, 1992, pp. 11-29.

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C. Bischof, A. Carle, G. Corliss, A. Griewank and P. Hovland, ADIFORGenerating derivative codes from Fortran programs, Scientific Programming (1992).

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Bischof, C., A. Carle, G. Corliss, A. Grienwank, P. Hoveland, "ADIFOR: Generating Derivative Codes from Fortran Programs", Scientific Programming, Vol. 1, No. 1, 1992, pp. 11-29.

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Christian H. Bischof, Alan Carle, George F. Corliss, Andreas Griewank, and Paul Hovland. ADIFOR: Generating derivative code from FORTRAN programs. Scientific Programming, 1:11--29., 1992.

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Bischof, C. H.; Carle, A.; Corliss, G. F.; Griewank, A.; and Hovland, P.: "ADIFOR: Generating Derivative Codes from Fortran Programs," Scientific Programming, Vol. 1, No. 1, 1992, pp. 1-29.

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Ch. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland. ADIFOR generating derivative codes from FORTRAN programs. Technical report, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, 1992.

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