jburkardt

MINPACK\ Least Squares Minimization {#minpack-least-squares-minimization align=”center”} ==========================

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MINPACK is a C++ library which solves systems of nonlinear equations, or carries out the least squares minimization of the residual of a set of linear or nonlinear equations.

MINPACK 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.

License: {#license align=”center”}

This code may freely be copied, modified, and used for any purpose.

Languages: {#languages align=”center”}

MINPACK is available in a C++ version and a FORTRAN90 version.

Related Data and Programs: {#related-data-and-programs align=”center”}

LLSQ, a C++ library which solves the simple linear least squares problem of finding the formula of a straight line y=a*x+b which minimizes the root-mean-square error to a set of N data points.

QR_SOLVE, a C++ library which computes the least squares solution of a linear system A*x=b.

TEST_LS, a C++ library which implements linear least squares test problems of the form A*x=b.

Reference: {#reference align=”center”}

1. Jorge More, Burton Garbow, Kenneth Hillstrom,\ User Guide for MINPACK-1,\ Technical Report ANL-80-74,\ Argonne National Laboratory, 1980.
2. Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom,\ The MINPACK Project,\ in Sources and Development of Mathematical Software,\ edited by Wayne Cowell,\ Prentice-Hall, 1984,\ ISBN: 0-13-823501-5,\ LC: QA76.95.S68.

Source Code: {#source-code align=”center”}

• minpack.cpp, the source code;
• minpack.hpp, the include file;

Examples and Tests: {#examples-and-tests align=”center”}

• minpack_test.cpp, sample calling code;
• minpack_test.txt, sample output;

List of Routines: {#list-of-routines align=”center”}

• CHKDER checks the gradients of M functions in N variables.
• DOGLEG combines Gauss-Newton and gradient for a minimizing step.
• ENORM returns the Euclidean norm of a vector.
• FDJAC1 estimates an N by N Jacobian matrix using forward differences.
• FDJAC2 estimates an M by N Jacobian matrix using forward differences.
• HYBRD1 is a simplified interface to HYBRD.
• I4_MIN returns the minimum of two I4’s.
• QRFORM constructs the standard form of Q from its factored form.
• QRFAC computes the QR factorization of an M by N matrix.
• R1UPDT updates the Q factor after a rank one update of the matrix.
• R8_ABS returns the absolute value of an R8.
• R8_EPSILON returns the R8 roundoff unit.
• R8_HUGE returns a “huge” R8.
• R8_MAX returns the maximum of two R8’s.
• R8_MIN returns the minimum of two R8’s.
• R8_TINY returns a “tiny” R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

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Last revised on 06 April 2010.