MINPACK is a library of
Fortran subroutines for the solving of
systems of nonlinear equations, or the
least-squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The me ...
minimization of the residual of a set of
linear
In mathematics, the term ''linear'' is used in two distinct senses for two different properties:
* linearity of a '' function'' (or '' mapping'');
* linearity of a '' polynomial''.
An example of a linear function is the function defined by f(x) ...
or nonlinear equations.
MINPACK, along with other similar libraries such as
LINPACK and
EISPACK EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating the eigenvalues of nine classes of matrices: complex general, complex Hermitian, real ...
, originated from the Mathematics and Computer Science Division Software (MCS) of
Argonne National Laboratory
Argonne National Laboratory is a Federally funded research and development centers, federally funded research and development center in Lemont, Illinois, Lemont, Illinois, United States. Founded in 1946, the laboratory is owned by the United Sta ...
. Written by
Jorge Moré,
Burt Garbow, and
Ken Hillstrom, MINPACK is free and designed to be highly
portable
Portable may refer to:
General
* Portable building, a manufactured structure that is built off site and moved in upon completion of site and utility work
* Portable classroom, a temporary building installed on the grounds of a school to provide a ...
, robust and reliable. The quality of its implementation of the
Levenberg–Marquardt algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least s ...
is attested by Dennis and Schnabel.
Five algorithmic paths each include a core subroutine and a driver routine. The algorithms proceed either from an analytic specification of the
Jacobian matrix
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of component ...
or directly from the problem functions. The paths include facilities for systems of equations with a
banded Jacobian matrix, for least-squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions.
References
* J. J. Moré, B. S. Garbow, and K. E. Hillstrom
User Guide for MINPACK-1 Argonne National Laboratory Report ANL-80-74, Argonne, Ill., 1980.
* J. J. Moré, D. C. Sorensen, K. E. Hillstrom, and B. S. Garbow, The MINPACK Project, in Sources and Development of Mathematical Software, W. J. Cowell, ed., Prentice-Hall, pages 88–111, 1984.
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External links
Netlib download siteUser Guide for MINPACK-1, Chapters 1 to 3 from J. J. Moré website
User Guide for MINPACK-1, Chapter 4 from J. J. Moré website
Fortran libraries
Numerical software