MINPACK
Least Squares Minimization

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.

Languages:

MINPACK is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

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:

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:

• minpack.cpp, the source code;
• minpack.hpp, the include file;
• minpack.sh, commands to compile the source code;

Examples and Tests:

• minpack_prb.cpp, sample calling code;
• minpack_prb.sh, commands to compile, link and run the sample calling code;
• minpack_prb_output.txt, sample output;

List of Routines:

• 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.