minpack/minpack.html

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      MINPACK - Least Squares Minimization
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      MINPACK <br> Least Squares Minimization
    </h1>

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    <p>
      <b>MINPACK</b> 
      is a FORTRAN90 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 = "../../f_src/bvls/bvls.html">
      BVLS</a>,
      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.
    </p>

    <p>
      <a href = "../../f_src/dqed/dqed.html">
      DQED</a>,
      a FORTRAN90 library which
      solves constrained least squares problems.
    </p>

    <p>
      <a href = "../../f_src/nl2sol/nl2sol.html">
      NL2SOL</a>,
      a FORTRAN90 library which
      implements an adaptive nonlinear least-squares algorithm.
    </p>

    <p>
      <a href = "../../f_src/nms/nms.html">
      NMS</a>,
      a FORTRAN90 library which
      includes a wide variety of numerical software, including 
      solvers for linear systems of equations, interpolation of data,
      numerical quadrature, linear least squares data fitting,
      the solution of nonlinear equations, ordinary differential equations,
      optimization and nonlinear least squares, simulation and random numbers,
      trigonometric approximation and Fast Fourier Transforms.
    </p>

    <p>
      <a href = "../../f_src/praxis/praxis.html">
      PRAXIS</a>,
      a FORTRAN90 library which
      minimizes a scalar function of several variables.
    </p>

    <p>
      <a href = "../../f_src/qr_solve/qr_solve.html">
      QR_SOLVE</a>,
      a FORTRAN90 library which
      computes the least squares solution of a linear system A*x=b.
    </p>

    <p>
      <a href = "../../f_src/slatec/slatec.html">
      SLATEC</a> ,
      a FORTRAN90 library which
      includes MINPACK.
    </p>

    <p>
      <a href = "../../f_src/test_opt/test_opt.html">
      TEST_OPT</a>,
      a FORTRAN90 library which 
      defines test problems for the minimization of a scalar function 
      of several variables.
    </p>

    <p>
      <a href = "../../f_src/test_optimization/test_optimization.html">
      TEST_OPTIMIZATION</a>,
      a FORTRAN90 library which
      defines test problems for the minimization of a scalar function
      of several variables, as described by Molga and Smutnicki.
    </p>

    <p>
      <a href = "../../f_src/toms611/toms611.html">
      TOMS611</a>,
      a FORTRAN90 library which
      seeks the minimizer of a scalar functional of multiple variables.
    </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>

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      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "minpack.f90">minpack.f90</a>, the source code;
        </li>
        <li>
          <a href = "minpack.csh">minpack.csh</a>, 
          commands to compile the source code;
        </li>
      </ul>
    </p>

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "minpack_prb.f90">minpack_prb.f90</a>, sample calling code;
        </li>
        <li>
          <a href = "minpack_prb.csh">minpack_prb.csh</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>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>CHKDER</b> checks the gradients of M functions of N variables.
        </li>
        <li>
          <b>DOGLEG</b> finds the minimizing combination of Gauss-Newton and gradient steps.
        </li>
        <li>
          <b>ENORM</b> computes the Euclidean norm of a vector.
        </li>
        <li>
          <b>ENORM2</b> computes 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>HYBRD</b> seeks a zero of N nonlinear equations in N variables.
        </li>
        <li>
          <b>HYBRD1</b> seeks a zero of N nonlinear equations in N variables.
        </li>
        <li>
          <b>HYBRJ</b> seeks a zero of N nonlinear equations in N variables.
        </li>
        <li>
          <b>HYBRJ1</b> seeks a zero of N nonlinear equations in N variables by Powell's method.
        </li>
        <li>
          <b>LMDER</b> minimizes M functions in N variables by the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMDER1</b> minimizes M functions in N variables by the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMDIF</b> minimizes M functions in N variables by the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMDIF1</b> minimizes M functions in N variables using the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMPAR</b> computes a parameter for the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMSTR</b> minimizes M functions in N variables using the Levenberg-Marquardt method.
        </li>
        <li>
          <b>LMSTR1</b> minimizes M functions in N variables using the Levenberg-Marquardt method.
        </li>
        <li>
          <b>QFORM</b> produces the explicit QR factorization of a matrix.
        </li>
        <li>
          <b>QRFAC</b> computes a QR factorization using Householder transformations.
        </li>
        <li>
          <b>QRSOLV</b> solves a rectangular linear system A*x=b in the least squares sense.
        </li>
        <li>
          <b>R1MPYQ</b> computes A*Q, where Q is the product of Householder transformations.
        </li>
        <li>
          <b>R1UPDT</b> re-triangularizes a matrix after a rank one update.
        </li>
        <li>
          <b>RWUPDT</b> computes the decomposition of a triangular matrix augmented by one row.
        </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 = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

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    <i>
      Last revised on 07 April 2010.
    </i>

    <!-- John Burkardt -->
 
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