ODRPACK

Nonlinear least squares (NLS) and orthogonal distance regression (ODR) problems, including those with implicit models and multiresponse data

The NLS and ODR algorithms in ODRPACK are based on a trust-region Levenberg-Marquardt method. The procedure uses scaling to automatically accommodate problems in which the estimated values have widely varying magnitudes. The structure of the {ODR} problem is exploited so that the computational cost per iteration is equal to that of the {NLS} problem. When the model is implicit, the solution is found using the classic quadratic penalty function method.

For both NLS and ODR, the algorithm can approximate the necessary Jacobian matrices using either forward or central finite differences when the user does not supply the code to compute them. If the user does supply this code, it can be verified by a derivative-checking procedure. The ODRPACK weighting facility allows the user to easily compensate for correlation between the responses within a given observation, and also to compensate for unequal precision between the observations. The covariance matrix and the standard errors of the estimators are optionally provided.

ODRPACK is a portable ANSI Fortran subroutine library, with no restrictions on problem size other than those imposed by the memory limits of the machine on which it is installed. Both single- and double-precision versions are available. Machine dependencies are restricted to three integer constants that must be specified within two subroutines.

The ODRPACK code is in the public domain and can be obtained via netlib (send index from odrpack)

Need more info?

Contact:

Janet E. Rogers 
Applied and Computational Mathematics Division 
National Institute of Standards and Technology
325 Broadway 
Boulder, CO 80303-3328 
Phone: (303) 497-5114  
jrogers@bldr.nist.gov

Reference:

P. T. Boggs, R. H. Byrd, J. E. Rogers, and R. B. Schnabel, User's reference guide for ODRPACK version 2.01 software for weighted orthogonal distance regression, National Institute of Standards and Technology NISTIR 4834,1992.

P. T. Boggs, R. H. Byrd, and R. B. Schnabel, A stable and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. Statist. Comput. 8 (1987), pp. 1052--1078.

P. T. Boggs, J. R. Donaldson, R. H. Byrd, and R. B. Schnabel, ODRPACK software for weighted orthogonal distance regression, ACM Trans. Math. Software 15 (1989), pp. 348--364.

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