minpack, a Fortran77 code which solves systems of nonlinear equations, or carries out the least squares minimization of the residual of a set of linear or nonlinear equations, by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.
The code includes software for solving nonlinear equations and nonlinear least squares problems. Five algorithmic paths each include a core subroutine and an easy-to-use driver. The algorithms proceed either from an analytic specification of the Jacobian matrix 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.
Given a set of N nonlinear equations in N unknowns, F(X) = 0, Powell's method is used to seek a solution X.
Given a set of M nonlinear functions in N unknowns, F(X), the Levenberg-Marquardt method is used to seek an X which minimizes the L2 norm of the residual ||F(X)||.
The user supplies a subroutine to evaluate the nonlinear function; the jacobian matrix dFi(X)/dXj may also be supplied by the user in a subroutine, or approximated by finite differences.
The original Fortran77 version is available through the NETLIB web site.
Minpack Copyright Notice (1999) University of Chicago. All rights reserved
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minpack is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version.
bvls, a Fortran90 library which applies least squares methods to solve a linear system for which lower and upper constraints may have been placed on every variable.
dqed, a Fortran77 library which solves constrained least squares problems.
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midpoint, a Fortran77 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with a version of fsolve() handling the associated nonlinear equations, and using a fixed time step.
nl2sol, a Fortran77 code which implements an adaptive nonlinear least-squares algorithm.
praxis, a Fortran77 code which minimizes a scalar function of several variables.
qr_solve, a Fortran77 code which computes the least squares solution of a linear system A*x=b.
SLATEC, a Fortran90 code which includes minpack().
TEST_LS, a Fortran77 code which implements linear least squares test problems of the form A*x=b.
TEST_OPT, a Fortran90 code which defines test problems for the minimization of a scalar function of several variables.
TOMS611, a Fortran77 library which seeks the minimizer of a scalar functional of multiple variables.
Original Fortran77 version by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.