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<html>
<head>
<title>
MINPACK - Least Squares Minimization
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MINPACK <br> Least Squares Minimization
</h1>
<hr>
<p>
<b>MINPACK</b>
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.
</p>
<p>
<b>MINPACK</b> 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.
</p>
<p>
Given a set of N nonlinear equations in N unknowns, F(X) = 0,
Powell's method is used to seek a solution X.
</p>
<p>
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)||.
</p>
<p>
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.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>MINPACK</b> is available in
<a href = "../../cpp_src/minpack/minpack.html">a C++ version</a> and
<a href = "../../f77_src/minpack/minpack.html">a FORTRAN77 version</a> and
<a href = "../../f_src/minpack/minpack.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/llsq/llsq.html">
LLSQ</a>,
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.
</p>
<p>
<a href = "../../cpp_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a C++ library which
computes the least squares solution of a linear system A*x=b.
</p>
<p>
<a href = "../../cpp_src/test_ls/test_ls.html">
TEST_LS</a>,
a C++ library which
implements linear least squares test problems of the form A*x=b.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Jorge More, Burton Garbow, Kenneth Hillstrom,<br>
User Guide for MINPACK-1,<br>
Technical Report ANL-80-74,<br>
Argonne National Laboratory, 1980.
</li>
<li>
Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom,<br>
The MINPACK Project,<br>
in Sources and Development of Mathematical Software,<br>
edited by Wayne Cowell,<br>
Prentice-Hall, 1984,<br>
ISBN: 0-13-823501-5,<br>
LC: QA76.95.S68.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "minpack.cpp">minpack.cpp</a>, the source code;
</li>
<li>
<a href = "minpack.hpp">minpack.hpp</a>, the include file;
</li>
<li>
<a href = "minpack.sh">minpack.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "minpack_prb.cpp">minpack_prb.cpp</a>, sample calling code;
</li>
<li>
<a href = "minpack_prb.sh">minpack_prb.sh</a>,
commands to compile, link and run the sample calling code;
</li>
<li>
<a href = "minpack_prb_output.txt">minpack_prb_output.txt</a>, sample output;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CHKDER</b> checks the gradients of M functions in N variables.
</li>
<li>
<b>DOGLEG</b> combines Gauss-Newton and gradient for a minimizing step.
</li>
<li>
<b>ENORM</b> returns the Euclidean norm of a vector.
</li>
<li>
<b>FDJAC1</b> estimates an N by N Jacobian matrix using forward differences.
</li>
<li>
<b>FDJAC2</b> estimates an M by N Jacobian matrix using forward differences.
</li>
<li>
<b>HYBRD1</b> is a simplified interface to HYBRD.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>QRFORM</b> constructs the standard form of Q from its factored form.
</li>
<li>
<b>QRFAC</b> computes the QR factorization of an M by N matrix.
</li>
<li>
<b>R1UPDT</b> updates the Q factor after a rank one update of the matrix.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 roundoff unit.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" R8.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_TINY</b> returns a "tiny" R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 06 April 2010.
</i>
<!-- John Burkardt -->
</body>
</html>