C. Bischof and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians, Technical Memorandum. ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Y(NEQ) PD(NROWPD,NEQ) RPAR( IPAR( Listing 2. Template for subroutine JAC 2 Using ADIFOR with VODE In this section, we go through the steps required to use ADIFOR to generate the Jacobians required by VODE. We assume that the reader is familiar with other reports showing how to use ADIFOR [1,2,3], so we give only the VODE specific information. The lesson here is that ADIFOR is a very useful tool which can relieve a user of VODE from the task of hand coding a routine for computing the Jacobian. The user of VODE ADIFOR can use the makefile and the template for VODJAC given here. The ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991. ADIFOR Working Note # 2.

....agree between a call site and the called procedure. In our experience, the interprocedural analysis phase of ADIFOR 2.0 processing is the most memory consuming and time consuming part of the process. The derivative code generated by ADIFOR 2. 0 provides, as expected from the forward mode of AD [9], the ability to compute directional derivatives. Instead of simply producing code to compute the JacobJan J, ADIFOR 2.0 produces code to compute J S, where the seed matrix S is initialized by the user. Thus, if S is the identity, ADIFOR 2.0 computes the full JacobJan, whereas if S is just a ....

C. Bischof and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians, Technical Memorandum. ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....by ADIFOR can be called by user programs in a flexible manner to be used in conjunction with standard software tools for optimization, solving nonlinear equations, or for stiff ordinary differential equations. A discussion of calling the ADIFOR generated code from users programs in included in [4]. 4 Using ADIFOR The issues of ease of use and portability have received scant attention in software for automatic differentiation. In many applications, the function whose derivatives we wish to compute is a collection of subroutines, and all that should be expected of the user is to specify ....

....selects the vari ables (in either parameter lists or common blocks) that correspond to the independent and dependent variables. ADIFOR then determines which other variables throughout the program require derivative information. A detailed description of the use of ADIFOR generated code appears in [4]. Intuitive Interface: An X windows interface for ADIFOR (called xadifor) makes it easy for the user to set up the ASCII script file that ADIFOR reads. This functional division makes it easy both to set up the problem and to rerun ADIFOR if changes in the code for the target function require a ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991.

....value of f(u) can be reused) As discussed earlier, in this application we precondition with a lagged Jacobian computed using a lower order discretization with some terms neglected. It is, however, possible to compute the full, sparse Jacobian using an appropriate seed matrix S based on coloring [6]. This reduces the cost of computing f 0 (u) to appromately k 1 times the cost of computing f(u) where k is the chromatic number for f 0 (u) 6 Experimental Results The following experiments with the Euler simulation modeled transonic flow over an ONERA M6 wing, a standard ....

C. Bischof and P. Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....code generated by ADIFOR to compute second derivatives and 2. to document some of the design decisions made in arriving at this implementation. We assume that the reader is familiar with the Fortran to Fortran source transformation tool ADIFOR (Automatic Differentiation In FORtran) as described in [1, 2, 3, 4, 6], as well as with the theoretical framework for computing second and higher order mixed partial derivatives by interpolating from sets of univariate Taylor series [5] Here, we describe the implementation in ADIFOR of the framework outlined in [5] In Section 2, we outline briefly where second ....

....are preaccumulated independently of the larger flow of control from one statement to the next. ADIFOR was the first tool for automatic differentiation to use preaccumulation of local derivatives by applying the reverse mode at the statement level for the efficient computation of first derivatives [3,6]. The hierarchy of local and global derivatives extends to higher order derivatives. If w = f(s 1 ; s k ) let rf and r 2 f denote the local gradient and Hessian, respectively, of f with respect to s 1 ; s k . If we extend Equation (3) to complicated right hand sides, we ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991. ADIFOR Working Note # 2.

No context found.

Bischof, C., and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians. ADIFOR Working Note #2, ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., 1991.

....with the working accuracy of the original function evaluation. In contrast to fully symbolic differentiation, both operations count and storage requirement can be a priori bounded in terms of the complexity of the original function code. The ADIFOR (Automatic Differentiation in Fortran) tool [2, 5, 4] provides automatic differentiation of programs written in Fortran 77. Given a Fortran subroutine (or collection of subroutines) describing a function, and an indication of which variables in parameter lists or common blocks correspond to independent and dependent variables with respect to ....

C. Bischof and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians, Tech. Report MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....derivatives slower than divided difference approaches, potential users were discouraged. Recently, however, process towards a generalpurpose automatic differentiation tool competitive with divided differences has been made with the development of ADIFOR (Automatic Differentiation in Fortran) [2, 5, 3, 1]. ADIFOR provides automatic differentiation for programs written in Fortran 77. Given a Fortran subroutine (or collection of subroutines) describing a function , and an indication which variables in parameter lists or common blocks correspond to independent and dependent variables with ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. ADIFOR Working Note #2, MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

No context found.

C. Bischof and P. Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....the correct values of the derivatives almost all of the time. This paper discusses what happens in the remaining rare events. The purpose of this paper is to make explicit the issues and alternatives associated with exception handling in ADIFOR. We assume that the reader is familiar with ADIFOR [1, 2]. The intended audience of this paper is the user of ADIFOR who wishes to better understand the error handling provided by ADIFOR and the rationale behind it. We address three questions: 1. What is an error 2. How can we detect that an error has occurred or is about to occur 3. What action ....

C. Bischof and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians, Technical Memorandum MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, October 1991.

....by ADIFOR can be called by user programs in a flexible manner to be used in conjunction with standard software tools for optimization, solving nonlinear equations, or for stiff ordinary differential equations. A discussion of calling the ADIFOR generated code from users programs in included in [4]. 4 Using ADIFOR The issues of ease of use and portability have received scant attention in software for automatic differentiation. In many applications, the function whose derivatives we wish to compute is a collection of subroutines, and all that should be expected of the user is to specify ....

....selects the variables (in either parameter lists or common blocks) that correspond to the independent and dependent variables. ADIFOR then determines which other variables throughout the program require derivative information. A detailed description of the use of ADIFOR generated code appears in [4]. Intuitive Interface: An X windows interface for ADIFOR (called xadifor) makes it easy for the user to set up the ASCII script file that ADIFOR reads. This functional division makes it easy both to set up the problem and to rerun ADIFOR if changes in the code for the target function require a ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991.

....mode to propagate overall derivatives. For example, the statement y = x(1) x(2) x(3) x(4) x(5) gets transformed into the code shown in Figure 6. Note that none of the common subexpressions x(i) x(j) is recomputed in the reverse mode section. ADIFOR generated code can be used in various ways [6]: Instead of simply producing code to compute the Jacobian J , ADIFOR produces code to compute J S, where the seed matrix S is initialized by the user. So if S is the identity, ADIFOR computes the full Jacobian, and if S is just a vector, ADIFOR computes the product of the Jacobian by a ....

....length Compressed 134,428 185,948 28.0 Sparse 5,537 31,633 4.0 Table 2: Dense versus sparse derivative propagation identity) and derivative objects fill in slowly as the computation proceeds. This effect is most noticeable in the computation of gradients of so called partially separable functions [6, 8], a rather common class of functions first described by Griewank and Toint [27] For example, on the 2 D Ginsburg Landau Superconductivity problem [1] the sparse gradient computation on a 400 Theta 400 grid requires only 7 percent of the floating point operations required for the dense version. ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. ADIFOR Working Note #2, MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

No context found.

Bischof, C. and P. Hovland. Using ADIFOR to compute dense and sparse Jacobians. ADIFOR Working Note #2, MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....how the resultant code might resemble and differ from the code that would be produced by a future version of ADIFOR. 2 Procedure This paper assumes that the user is already familiar with ADIFOR and the various files involved in its use. Those readers not familiar with ADIFOR are referred to [3,4] for an introduction. The procedure required to produce code capable of computing second derivatives is: 1. Create an ADIFOR script ( adf) file. Be sure to include a SEP line. 2. Create a composition ( comp) file. 3. Run ADIFOR (adifor func.adf func.comp) 4. Run make on the ADMakefile. 5. ....

....between the gradient objects of the first pass and the gradient objects of the second pass, and also to prevent name conflicts, a different separator character (such as ) should be used. 4 Initialization The initialization of seed matrices is nontrivial even for first derivative programs [3]. In the case of second derivatives things (can) become even more complex. The code produced by the method outlined above is capable of computing the matrix product S 1 Theta H Theta S T 2 , where H is the Hessian. The two seed matrices, S 1 and S 2 , arise from the double application of ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....variety of problems, and, like the forward mode, it has predictable storage and runtime requirements. We also see that, from a user s perspective, the ADIFOR generated code provides the directional derivative computation possibilities associated with the forward mode of automatic differentiation [15]. Instead of simply producing code to compute the Jacobian J , ADIFOR produces code to compute J S, where the seed matrix S is initialized by the user. Thus, if S is the identity, ADIFOR computes the full Jacobian; whereas if S is just a vector, ADIFOR computes the product of the Jacobian by a ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....derivatives of that function with respect to certain independent variables. ADIFOR provides a mechanism for the automatic generation of Fortran code for the computation of derivatives, using the Fortran code for the evaluation of the function as input. More information on ADIFOR can be found in [2, 3, 4, 5]. The organization of this paper is as follows. The next section is devoted to a step by step description of how to process a code using ADIFOR, and an explanation of how ADIFOR generated code may be incorporated into a program. This example is intentionally simple, and ignores many subtle issues. ....

....but, because of storage limitations, the ADIFOR generated code will be used to compute only 10 Jacobian columns at a time. Then a value of 10 for PMAX is suitable choice. Also for sparse Jacobians, PMAX need not be the total number of independent variables. These issues are discussed in detail in [5], which is available on line (see Section 8) For our example program, we choose a value of 2 for PMAX, because x is the only independent variable, and it has 2 elements. SEP: ADIFOR uses the character specified by SEP for generating names for Fortran variables used in derivative computations. ....

[Article contains additional citation context not shown here]

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS--TM--158 (also ADIFOR Working Note #2), Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....derivatives being computed, and hence the ADIFOR approach is more efficient than the normal forward mode or a divideddifference approximation when more than a few derivatives are computed at the same time. We see that ADIFOR generated code provides a directional derivative computation capability [8]: Instead of simply producing code to compute the Jacobian J , ADIFOR produces code to compute J S, where the seed matrix S is initialized by the user. Hence, if S is the identity, ADIFOR computes the full Jacobian; whereas if S is just a vector, ADIFOR computes the product of the Jacobian by a ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....than the normal forward mode or a divided difference approximation when more than a few derivatives are computed at the same time. We also see that ADIFOR generated code provides the directional derivative computation possibilities associated with the forward mode of automatic differentiation [6]. Instead of simply producing code to compute the Jacobian J , ADIFOR produces code to compute J S, where the seed matrix S is 2 Information on ADIFOR and ADIC can be found on the world wide web under http: www.mcs.anl.gov Projects autodiff index.html r 1 = x(1) x(2) r 2 = r 1 x(3) ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....by ADIFOR can be called by users programs in a flexible manner to be used in conjunction with standard software tools for optimization, solving nonlinear equations, or for stiff ordinary differential equations. A discussion of calling the ADIFOR generated code from users programs is included in [4]. 4 The Functionality of ADIFOR Generated Derivative Codes The functionality provided by ADIFOR is best understood through an example. Our example is adapted from problem C2 in the STDTST set of test problems for stiff ODE solvers [25] The routine FCN2 shown in Figure 7 that computes the ....

....Jacobian g Fval T is shown in Figure 11 as well. Here every circle denotes a nonzero entry. Now, instead of g p = 56, a size of g p = 14 is sufficient, a sizeable reduction in cost. The proper and efficient initialization of ADIFOR generated derivative codes is described in detail in [4]. o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, Ill. 60439, October 1991.

....preaccumulated independently of the larger flow of control from one statement to the next. ADIFOR was the first tool for automatic differentiation to use preaccumulation of local derivatives by applying the reverse mode at the statement level for the efficient computation of first derivatives [7,9]. The hierarchy of local and global derivatives extends to higher order derivatives. Consider the alternatives for computing first and second order derivatives of an active variable w that is given by an expression involving k active variables: w = f(s 1 ; s 2 ; s k ) There are two ....

....operations because q(n; m) is monotonically decreasing in m and equals roughly m 2 =2 m 1 when n is significantly larger than m. Thus, we have an exponential complexity reduction in terms of m. 8 Conclusions and Future Research Directions ADIFOR (Automatic Differentiation In FORtran) [7,8,9] is a source translation tool implemented by using the data abstractions and program analysis capabilities of the ParaScope Parallel Programming Environment [10] ADIFOR accepts arbitrary Fortran 77 code defining the computation of a function and writes portable Fortran 77 code for the computation ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991. ADIFOR Working Note # 2.

....by ADIFOR can be called by user programs in a flexible manner to be used in conjunction with standard software tools for optimization, solving nonlinear equations, or for stiff ordinary differential equations. A discussion of calling the ADIFOR generated code from users programs in included in [4]. The ease of use of ADIFOR follows from its basis in a sophisticated compilation environment. In many applications, the function whose derivatives we wish to compute is a collection of subroutines, and all that is expected of the user is to specify which of the variables correspond to the ....

....selects the variables (in either parameter lists or common blocks) that correspond to the independent and dependent variables. ADIFOR then determines which other variables throughout the program require derivative information. A detailed description of the use of ADIFOR generated code appears in [4]. Intuitive Interface: An X windows interface for ADIFOR (called xadifor) makes it easy for the user to create the ASCII script file that ADIFOR reads. This functional division makes it easy both to set up the problem and to rerun ADIFOR if changes in the code for the target function require a ....

[Article contains additional citation context not shown here]

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Memorandum ANL/MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill. 60439, October 1991. ADIFOR Working Note # 2.

....how the resultant code might resemble and differ from the code that would be produced by a future version of ADIFOR. 2 Procedure This paper assumes that the user is already familiar with ADIFOR and the various files involved in its use. Those readers not familiar with ADIFOR are referred to [3,4] for an introduction. The procedure required to produce code capable of computing second derivatives is as follows: 1. Create an ADIFOR script ( adf) file. Be sure to include a SEP line. 2. Create a composition ( comp) file. 3. Run ADIFOR (adifor func.adf func.comp) 4. Run make on the ....

....between the gradient objects of the first pass and the gradient objects of the second pass, and also to prevent name conflicts, a different separator character (such as ) should be used. 4 Initialization The initialization of seed matrices is nontrivial even for first derivative programs [3]. In the case of second derivatives, the situation can become even more complex. The code produced by the method outlined above is capable of computing the matrix product S 1 Theta H Theta S T 2 , where H is the Hessian. The two seed matrices, S 1 and S 2 , arise from the double application of ....

Christian Bischof and Paul Hovland. Using ADIFOR to compute dense and sparse Jacobians. Technical Report ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

....techniques and tools in the context of engineering design see [11] An introduction to the Fortran tool ADIFOR and some preliminary numerical results on a 2 D small disturbance model of transonic flow are given in [18] 4. 1 An Advanced FORTRAN Tool ADIFOR (Automatic Differentiation of Fortran) [15, 19, 16, 14] provides automatic differentiation for programs written in Fortran 77. Given a Fortran subroutine (or collection of subroutines) describing a function, and an indication of which variables in parameter lists or common blocks correspond to independent and dependent variables with respect to ....

C. H. Bischof and P. Hovland. Using ADIFOR to compute dense and sparse Jacobians. ADIFOR Working Note #2, MCS--TM--158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.

No context found.

C. Blscor AND P. HOVLAND, Using ADIFOR to compute dense and sparse Jacobians, Technical Memorandum ANL/MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991. ADIFOR Working Note 2.

No context found.

Bischof, C. H. and Hovland, P. Using ADIFOR to compute dense and sparse Jacobians. Tech. Memorandum ANL-MCS-TM-158, Mathematics and Computer Science Division, Argonne National Laboratory, 1991. (ADIFOR Working Note # 2).

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