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<html>
<head>
<title>
TEST_CON - Continuation Tests
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_CON <br> Continuation Tests
</h1>
<hr>
<p>
<b>TEST_CON</b>
is a FORTRAN90 library which
defines test functions for continuation codes.
</p>
<p>
A simple continuation code is an algorithm
for producing a sequence of solutions of the system of equations
F(X) = 0, where there are fewer equations F than variables X.
Commonly, there is one more variable than equation, resulting in
one degree of freedom. The set of solutions will then generally
describe a curve.
</p>
<p>
A continuation code might carry out the following steps:
<ol>
<li>
choose a problem by picking an index number.
</li>
<li>
for problems with several options, pick an option index.
</li>
<li>
find out the number of variables.
</li>
<li>
get a starting point <b>X0</b>.
</li>
<li>
get a suggested stepsize H.
</li>
<li>
get the tangent vector T at <b>X0</b>.
</li>
<li>
use the estimate <b>X1=X0+H*T</b> as a starting point for
a new point on the curve; use Newton method to refine the estimate.
</li>
<li>
If the Newton iteration failed, reduce H and try again.
</li>
<li>
If the new point was computed "easily", increase H.
</li>
<li>
Go back to step 6 if another point is desired.
</li>
</ol>
</p>
<p>
<b>TEST_CON</b> includes routines to
<ul>
<li>
return the number of problems available (<b>p00_problem_num</b>);
</li>
<li>
return the number of different "options" for each problem (<b>p00_option_num</b>);
</li>
<li>
return the problem size NVAR (<b>p00_nvar</b>);
</li>
<li>
provide a starting point X0 (<b>p00_start</b>);
</li>
<li>
provide a suggested stepsize H (<b>p00_stepsize</b>);
</li>
<li>
determine the tangent vector T(X) (<b>p00_tan</b>);
</li>
<li>
apply Newton's method to an approximate solution (<b>p00_newton</b>);
</li>
<li>
take a single continuation step (compute the "next" point) (<b>p00_step</b>);
</li>
<li>
compute a target point, for which one component has a selected value
(<b>p00_target</b>);
</li>
<li>
choose the continuation parameter index (<b>p00_par_index</b>);
</li>
<li>
evaluate the function F(X) (<b>p00_fun</b>);
</li>
<li>
evaluate the jacobian J(X) (<b>p00_problem_jac</b>);
</li>
<li>
return the problem title (<b>p00_title</b>);
</li>
</ul>
</p>
<p>
The list of problems includes:
<ol>
<li>
The Freudenstein-Roth function
</li>
<li>
The Boggs function
</li>
<li>
The Powell function
</li>
<li>
The Broyden function
</li>
<li>
The Wacker function
</li>
<li>
The Aircraft stability function
</li>
<li>
The Cell kinetic function
</li>
<li>
The Riks mechanical problem
</li>
<li>
The Oden mechanical problem
</li>
<li>
Torsion of a square rod, finite difference solution
</li>
<li>
Torsion of a square rod, finite element solution
</li>
<li>
The materially nonlinear problem
</li>
<li>
Simpson's mildly nonlinear boundary value problem
</li>
<li>
Keller's boundary value problem
</li>
<li>
The Trigger Circuit
</li>
<li>
The Moore-Spence Chemical Reaction Integral Equation
</li>
<li>
The Bremermann Propane Combustion System
</li>
<li>
The semiconductor problem
</li>
<li>
The Nitric acid absorption flash
</li>
<li>
The Buckling Spring
</li>
</ol>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_CON</b> is available in
<a href = "../../f77_src/test_con/test_con.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_con/test_con.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_con/test_con.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f77_src/pitcon66/pitcon66.html">
PITCON66</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this is version 6.6 of ACM TOMS algorithm 596.
</p>
<p>
<a href = "../../f_src/pitcon7/pitcon7.html">
PITCON7</a>,
a FORTRAN90 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this is version 7.0 of ACM TOMS algorithm 596.
</p>
<p>
<a href = "../../datasets/test_con/test_con.html">
TEST_CON</a>,
a dataset directory which
contains sequences of points that lie on multidimensional curves defined by
sets of nonlinear equations;
</p>
<p>
<a href = "../../f77_src/toms502/toms502.html">
TOMS502</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this library is commonly called <b>DERPAR</b>;<br>
this is ACM TOMS algorithm 502.
</p>
<p>
<a href = "../../f77_src/toms596/toms596.html">
TOMS596</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this library is commonly called <b>PITCON</b>;<br>
this is ACM TOMS algorithm 596.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Ivo Babuska, Werner Rheinboldt,<br>
Reliable Error Estimations and Mesh Adaptation for the Finite
Element Method,<br>
in International Conference on Computational Methods
in Nonlinear Mechanics,<br>
edited by John Oden,<br>
Elsevier, 1980,<br>
ISBN: 0444853820,<br>
LC: QA808.I57.
</li>
<li>
Paul Boggs,<br>
The Solution of Nonlinear Systems by A-stable
Integration Techniques,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 8, Number 4, December 1971, pages 767-785.
</li>
<li>
Hans Bremermann,<br>
Calculation of Equilibrium Points for Models of Ecological and
Chemical Systems,<br>
in Proceedings of a Conference on the Applications of Undergraduate
Mathematics in the Engineering, Life, Managerial
and Social Sciences,<br>
Georgia Institute of Technology, June 1973, pages 198-217.
</li>
<li>
Charles Broyden,<br>
A New Method of Solving Nonlinear Simultaneous Equations,<br>
The Computer Journal,<br>
Volume 12, 1969, pages 94-99.
</li>
<li>
Tama Copeman,<br>
Air Products and Chemicals, Inc.<br>
Box 538,<br>
Allentown, Pennsylvania, 18105.
</li>
<li>
Cor denHeijer, Werner Rheinboldt,<br>
On Steplength Algorithms for a Class of Continuation Methods,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 18, Number 5, October 1981, pages 925-947.
</li>
<li>
Ferdinand Freudenstein, Bernhard Roth,<br>
Numerical Solutions of Nonlinear Equations,<br>
Journal of the ACM,<br>
Volume 10, Number 4, October 1963, pages 550-556.
</li>
<li>
Kathie Hiebert,<br>
A Comparison of Software Which Solves Systems of Nonlinear
Equations,<br>
Technical Report SAND-80-0181,<br>
Sandia National Laboratory, 1980.
</li>
<li>
Herbert Keller,<br>
Numerical Methods for Two-point Boundary Value Problems,<br>
Dover, 1992,<br>
ISBN: 0486669254,<br>
LC: QA372.K42.
</li>
<li>
Raman Mehra, William Kessel, James Carroll,<br>
Global stability and contral analysis of aircraft at high angles of attack,<br>
Technical Report CR-215-248-1, -2, -3,<br>
Office of Naval Research, June 1977.
</li>
<li>
Rami Melhem, Werner Rheinboldt,<br>
A Comparison of Methods for Determining Turning Points of Nonlinear Equations,<br>
Computing,<br>
Volume 29, Number 3, September 1982, pages 201-226.
</li>
<li>
Gerald Moore, Alastair Spence,<br>
The Calculation of Turning Points of Nonlinear Equations,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 17, Number 4, August 1980, pages 567-576.
</li>
<li>
John Oden,<br>
Finite Elements of Nonlinear Continua,<br>
Dover, 2006,<br>
ISBN: 0486449734,<br>
LC: QA808.2.O33.
</li>
<li>
Gerd Poenisch, Hubert Schwetlick,<br>
Computing Turning Points of Curves Implicitly Defined by Nonlinear
Equations Depending on a Parameter,<br>
Computing,<br>
Volume 26, Number 2, June 1981, pages 107-121.
</li>
<li>
SJ Polak, A Wachten, H Vaes, A deBeer, Cor denHeijer,<br>
A Continuation Method for the Calculation of Electrostatic
Potentials in Semiconductors,<br>
Technical Report ISA-TIS/CARD,<br>
NV Philips Gloeilampen-Fabrieken, 1979.
</li>
<li>
Tim Poston, Ian Stewart,<br>
Catastrophe Theory and its Applications,<br>
Dover, 1996,<br>
ISBN13: 978-0486692715,<br>
LC: QA614.58.P66.
</li>
<li>
Michael Powell,<br>
A Fortran Subroutine for Solving Systems of Nonlinear
Algebraic Equations,<br>
in Numerical Methods for Nonlinear Algebraic Equations,<br>
edited by Philip Rabinowitz,<br>
Gordon and Breach, 1970,<br>
ISBN13: 978-0677142302,<br>
LC: QA218.N85.
</li>
<li>
Werner Rheinboldt,<br>
Computation of Critical Boundaries on Equilibrium Manifolds,<br>
SIAM Journal on Numerical analysis,<br>
Volume 19, Number 3, June 1982, pages 653-669.
</li>
<li>
Werner Rheinboldt, John Burkardt,<br>
A Locally Parameterized Continuation Process,<br>
ACM Transactions on Mathematical Software,<br>
Volume 9, Number 2, June 1983, pages 215-235.
</li>
<li>
Werner Rheinboldt, John Burkardt, <br>
Algorithm 596:
A Program for a Locally Parameterized
Continuation Process,<br>
ACM Transactions on Mathematical Software,<br>
Volume 9, Number 2, June 1983, pages 236-241.
</li>
<li>
Werner Rheinboldt,<br>
Numerical Analysis of Parameterized Nonlinear Equations,<br>
Wiley, 1986,<br>
ISBN: 0-471-88814-1,<br>
LC: QA372.R54.
</li>
<li>
Werner Rheinboldt,<br>
Sample Problems for Continuation Processes,<br>
Technical Report ICMA-80-?,<br>
Institute for Computational Mathematics and Applications,<br>
Department of Mathematics,<br>
University of Pittsburgh, November 1980.
</li>
<li>
Werner Rheinboldt,<br>
Solution Fields of Nonlinear Equations and Continuation Methods,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 17, Number 2, April 1980, pages 221-237.
</li>
<li>
Werner Rheinboldt,<br>
On the Solution of Some Nonlinear Equations Arising in the
Application of Finite Element Methods,<br>
in The Mathematics of Finite Elements and Applications II,<br>
edited by John Whiteman,<br>
Academic Press, 1976,<br>
LC: TA347.F5.M37.
</li>
<li>
E Riks,<br>
The Application of Newton's Method to the Problem of Elastic
Stability,<br>
Transactions of the ASME, Journal of Applied Mechanics,<br>
December 1972, pages 1060-1065.
</li>
<li>
Albert Schy, Margery Hannah,<br>
Prediction of Jump Phenomena in Roll-coupled Maneuvers
of Airplanes,<br>
Journal of Aircraft,<br>
Volume 14, Number 4, 1977, pages 375-382.
</li>
<li>
Bruce Simpson,<br>
A Method for the Numerical Determination of Bifurcation
States of Nonlinear Systems of Equations,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 12, Number 3, June 1975, pages 439-451.
</li>
<li>
Hans-Joerg Wacker, Erich Zarzer, Werner Zulehner,<br>
Optimal Stepsize Control for the Globalized Newton Method,<br>
in Continuation Methods,<br>
edited by Hans-Joerg Wacker,<br>
Academic Press, 1978,<br>
ISBN: 0127292500,<br>
LC: QA1.S899.
</li>
<li>
John Young, Albert Schy, Katherine Johnson,<br>
Prediction of Jump Phenomena in Aircraft Maneuvers, Including
Nonlinear Aerodynamic Effects,<br>
Journal of Guidance and Control,<br>
Volume 1, Number 1, 1978, pages 26-31.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_con.f90">test_con.f90</a>, the source code;
</li>
<li>
<a href = "test_con.sh">test_con.sh</a>, commands to compile
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_con_prb.f90">test_con_prb.f90</a>, the calling program;
</li>
<li>
<a href = "test_con_prb.sh">test_con_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "test_con_prb_output.txt">test_con_prb_output.txt</a>, the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>FILE_NAME_INC</b> increments a partially numeric filename.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>P00_FUN</b> evaluates the function for any problem.
</li>
<li>
<b>P00_JAC</b> evaluates the jacobian for any problem.
</li>
<li>
<b>P00_JAC_CHECK</b> compares the jacobian with a finite difference estimate.
</li>
<li>
<b>P00_JAC_DIF</b> estimates the jacobian via finite differences.
</li>
<li>
<b>P00_NEWTON</b> applies Newton's method to an approximate root.
</li>
<li>
<b>P00_NVAR</b> sets the number of variables for any problem.
</li>
<li>
<b>P00_OPTION_NUM</b> returns the number of options available for a problem.
</li>
<li>
<b>P00_PAR_INDEX</b> chooses the index of the continuation parameter.
</li>
<li>
<b>P00_PROBLEM_NUM</b> returns the number of problems available.
</li>
<li>
<b>P00_START</b> returns a starting point for any problem.
</li>
<li>
<b>P00_STEP</b> takes one continuation step.
</li>
<li>
<b>P00_STEPSIZE</b> returns step sizes for any problem.
</li>
<li>
<b>P00_TAN</b> determines a tangent vector at X.
</li>
<li>
<b>P00_TARGET</b> computes a solution with a given component value.
</li>
<li>
<b>P00_TITLE</b> sets the title for any problem.
</li>
<li>
<b>P01_FUN</b> evaluates the function for problem 1.
</li>
<li>
<b>P01_GX</b> evaluates the underlying function for problem 1.
</li>
<li>
<b>P01_JAC</b> evaluates the jacobian for problem 1.
</li>
<li>
<b>P01_NVAR</b> sets the number of variables for problem 1.
</li>
<li>
<b>P01_OPTION_NUM</b> returns the number of options for problem 1.
</li>
<li>
<b>P01_START</b> returns a starting point for problem 1.
</li>
<li>
<b>P01_STEPSIZE</b> returns step sizes for problem 1.
</li>
<li>
<b>P01_TITLE</b> sets the title for problem 1.
</li>
<li>
<b>P02_FUN</b> evaluates the function for problem 2.
</li>
<li>
<b>P02_GX</b> evaluates the underlying function for problem 2.
</li>
<li>
<b>P02_JAC</b> evaluates the jacobian for problem 2.
</li>
<li>
<b>P02_NVAR</b> sets the number of variables for problem 2.
</li>
<li>
<b>P02_OPTION_NUM</b> returns the number of options for problem 2.
</li>
<li>
<b>P02_START</b> returns a starting point for problem 2.
</li>
<li>
<b>P02_STEPSIZE</b> returns step sizes for problem 2.
</li>
<li>
<b>P02_TITLE</b> sets the title for problem 2.
</li>
<li>
<b>P03_FUN</b> evaluates the function for problem 3.
</li>
<li>
<b>P03_GX</b> evaluates the underlying function for problem 3.
</li>
<li>
<b>P03_JAC</b> evaluates the jacobian for problem 3.
</li>
<li>
<b>P03_NVAR</b> sets the number of variables for problem 3.
</li>
<li>
<b>P03_OPTION_NUM</b> returns the number of options for problem 3.
</li>
<li>
<b>P03_START</b> returns a starting point for problem 3.
</li>
<li>
<b>P03_STEPSIZE</b> returns step sizes for problem 3.
</li>
<li>
<b>P03_TITLE</b> sets the title for problem 3.
</li>
<li>
<b>P04_FUN</b> evaluates the function for problem 4.
</li>
<li>
<b>P04_GX</b> evaluates the underlying function for problem 4.
</li>
<li>
<b>P04_JAC</b> evaluates the jacobian for problem 4.
</li>
<li>
<b>P04_NVAR</b> sets the number of variables for problem 4.
</li>
<li>
<b>P04_OPTION_NUM</b> returns the number of options for problem 4.
</li>
<li>
<b>P04_START</b> returns a starting point for problem 4.
</li>
<li>
<b>P04_STEPSIZE</b> returns step sizes for problem 4.
</li>
<li>
<b>P04_TITLE</b> sets the title for problem 4.
</li>
<li>
<b>P05_FUN</b> evaluates the function for problem 5.
</li>
<li>
<b>P05_JAC</b> evaluates the jacobian for problem 5.
</li>
<li>
<b>P05_NVAR</b> sets the number of variables for problem 5.
</li>
<li>
<b>P05_OPTION_NUM</b> returns the number of options for problem 5.
</li>
<li>
<b>P05_START</b> returns a starting point for problem 5.
</li>
<li>
<b>P05_STEPSIZE</b> returns step sizes for problem 5.
</li>
<li>
<b>P05_TITLE</b> sets the title for problem 5.
</li>
<li>
<b>P06_BARRAY</b> sets the B array.
</li>
<li>
<b>P06_CARRAY</b> sets the C array.
</li>
<li>
<b>P06_FUN</b> evaluates the function for problem 6.
</li>
<li>
<b>P06_JAC</b> evaluates the jacobian for problem 6.
</li>
<li>
<b>P06_NVAR</b> sets the number of variables for problem 6.
</li>
<li>
<b>P06_OPTION_NUM</b> returns the number of options for problem 6.
</li>
<li>
<b>P06_START</b> returns a starting point for problem 6.
</li>
<li>
<b>P06_STEPSIZE</b> returns step sizes for problem 6.
</li>
<li>
<b>P06_TITLE</b> sets the title for problem 6.
</li>
<li>
<b>P07_FUN</b> evaluates the function for problem 7.
</li>
<li>
<b>P07_JAC</b> evaluates the jacobian for problem 7.
</li>
<li>
<b>P07_NVAR</b> sets the number of variables for problem 7.
</li>
<li>
<b>P07_OPTION_NUM</b> returns the number of options for problem 7.
</li>
<li>
<b>P07_START</b> returns a starting point for problem 7.
</li>
<li>
<b>P07_STEPSIZE</b> returns step sizes for problem 7.
</li>
<li>
<b>P07_TITLE</b> sets the title for problem 7.
</li>
<li>
<b>P08_FUN</b> evaluates the function for problem 8.
</li>
<li>
<b>P08_GX</b> sets data used for Rik's mechanical problem.
</li>
<li>
<b>P08_HX</b> reports the constraint equation data.
</li>
<li>
<b>P08_JAC</b> evaluates the jacobian for problem 8.
</li>
<li>
<b>P08_NVAR</b> sets the number of variables for problem 8.
</li>
<li>
<b>P08_OPTION_NUM</b> returns the number of options for problem 8.
</li>
<li>
<b>P08_START</b> returns a starting point for problem 8.
</li>
<li>
<b>P08_STEPSIZE</b> returns step sizes for problem 8.
</li>
<li>
<b>P08_TITLE</b> sets the title for problem 8.
</li>
<li>
<b>P09_FUN</b> evaluates the function for problem 9.
</li>
<li>
<b>P09_GX</b> is used by problem 9.
</li>
<li>
<b>P09_JAC</b> evaluates the jacobian for problem 9.
</li>
<li>
<b>P09_NVAR</b> sets the number of variables for problem 9.
</li>
<li>
<b>P09_OPTION_NUM</b> returns the number of options for problem 9.
</li>
<li>
<b>P09_START</b> returns a starting point for problem 9.
</li>
<li>
<b>P09_STEPSIZE</b> returns step sizes for problem 9.
</li>
<li>
<b>P09_TITLE</b> sets the title for problem 9.
</li>
<li>
<b>P10_FUN</b> evaluates the function for problem 10.
</li>
<li>
<b>P10_GX</b> is used by problem 10.
</li>
<li>
<b>P10_JAC</b> evaluates the jacobian for problem 10.
</li>
<li>
<b>P10_NVAR</b> sets the number of variables for problem 10.
</li>
<li>
<b>P10_OPTION_NUM</b> returns the number of options for problem 10.
</li>
<li>
<b>P10_START</b> returns a starting point for problem 10.
</li>
<li>
<b>P10_STEPSIZE</b> returns step sizes for problem 10.
</li>
<li>
<b>P10_TITLE</b> sets the title for problem 10.
</li>
<li>
<b>P11_FUN</b> evaluates the function for problem 11.
</li>
<li>
<b>P11_GAUSS</b> returns the Gauss quadrature abscissas and weights.
</li>
<li>
<b>P11_GUL</b> computes G(U,LAMBDA) and dG/dU and dG/dLAMBDA.
</li>
<li>
<b>P11_JAC</b> evaluates the jacobian for problem 11.
</li>
<li>
<b>P11_NVAR</b> sets the number of variables for problem 11.
</li>
<li>
<b>P11_OPTION_NUM</b> returns the number of options for problem 11.
</li>
<li>
<b>P11_PHI</b> is used by problem 11.
</li>
<li>
<b>P11_SHAPE</b> evaluates the shape functions for problem 11.
</li>
<li>
<b>P11_START</b> returns a starting point for problem 11.
</li>
<li>
<b>P11_STEPSIZE</b> returns step sizes for problem 11.
</li>
<li>
<b>P11_TITLE</b> sets the title for problem 11.
</li>
<li>
<b>P12_FUN</b> evaluates the function for problem 12.
</li>
<li>
<b>P12_GAUSS8</b> returns an 8 point Gauss quadrature rule.
</li>
<li>
<b>P12_JAC</b> evaluates the jacobian for problem 12.
</li>
<li>
<b>P12_LEGENDRE_VAL</b> evaluates the Legendre polynomials and derivatives.
</li>
<li>
<b>P12_NVAR</b> sets the number of variables for problem 12.
</li>
<li>
<b>P12_OPTION_NUM</b> returns the number of options for problem 12.
</li>
<li>
<b>P12_START</b> returns a starting point for problem 12.
</li>
<li>
<b>P12_STEPSIZE</b> returns step sizes for problem 12.
</li>
<li>
<b>P12_THETA</b> is a utility routine used in problem 12.
</li>
<li>
<b>P12_TITLE</b> sets the title for problem 12.
</li>
<li>
<b>P13_FUN</b> evaluates the function for problem 13.
</li>
<li>
<b>P13_FX2</b> computes the function by recasting it on a square grid.
</li>
<li>
<b>P13_GP</b> evaluates the derivative of the right hand side function.
</li>
<li>
<b>P13_GX</b> evaluates the right hand side function.
</li>
<li>
<b>P13_JAC</b> evaluates the jacobian for problem 13.
</li>
<li>
<b>P13_JAC2</b> computes the jacobian by recasting it on a square grid.
</li>
<li>
<b>P13_NVAR</b> sets the number of variables for problem 13.
</li>
<li>
<b>P13_OPTION_NUM</b> returns the number of options for problem 13.
</li>
<li>
<b>P13_START</b> returns a starting point for problem 13.
</li>
<li>
<b>P13_STEPSIZE</b> returns step sizes for problem 13.
</li>
<li>
<b>P13_TITLE</b> sets the title for problem 13.
</li>
<li>
<b>P14_FU</b> computes the auxilliary function F(LAMBDA,U).
</li>
<li>
<b>P14_FUDL</b> computes d F(LAMBDA,U) / d LAMBDA.
</li>
<li>
<b>P14_FUDU</b> computes d F(LAMBDA,U) / d U
</li>
<li>
<b>P14_FUN</b> computes the function for problem 14.
</li>
<li>
<b>P14_GU</b> computes the auxilliary function G(U).
</li>
<li>
<b>P14_GUDU</b> computes d G(U) / d U.
</li>
<li>
<b>P14_JAC</b> computes the jacobian of problem 14.
</li>
<li>
<b>P14_NVAR</b> sets the number of variables for problem 14.
</li>
<li>
<b>P14_OPTION_NUM</b> returns the number of options for problem 14.
</li>
<li>
<b>P14_START</b> returns a starting point for problem 14.
</li>
<li>
<b>P14_STEPSIZE</b> returns step sizes for problem 14.
</li>
<li>
<b>P14_TITLE</b> sets the title for problem 14.
</li>
<li>
<b>P15_FUN</b> evaluates the function for problem 15.
</li>
<li>
<b>P15_GX</b> returns the coefficients of the linear portion of the function.
</li>
<li>
<b>P15_JAC</b> computes the jacobian for problem 15.
</li>
<li>
<b>P15_NVAR</b> sets the number of variables for problem 15.
</li>
<li>
<b>P15_OPTION_NUM</b> returns the number of options for problem 15.
</li>
<li>
<b>P15_START</b> returns a starting point for problem 15.
</li>
<li>
<b>P15_STEPSIZE</b> returns step sizes for problem 15.
</li>
<li>
<b>P15_TITLE</b> sets the title for problem 15.
</li>
<li>
<b>P16_FUN</b> evaluates the function for problem 16.
</li>
<li>
<b>P16_JAC</b> computes the jacobian for problem 16.
</li>
<li>
<b>P16_NVAR</b> sets the number of variables for problem 16.
</li>
<li>
<b>P16_OPTION_NUM</b> returns the number of options for problem 16.
</li>
<li>
<b>P16_START</b> returns a starting point for problem 16.
</li>
<li>
<b>P16_STEPSIZE</b> returns step sizes for problem 16.
</li>
<li>
<b>P16_TITLE</b> sets the title for problem 16.
</li>
<li>
<b>P17_FUN</b> evaluates the function for problem 17.
</li>
<li>
<b>P17_JAC</b> evaluates the jacobian for problem 17.
</li>
<li>
<b>P17_NVAR</b> sets the number of variables for problem 17.
</li>
<li>
<b>P17_OPTION_NUM</b> returns the number of options for problem 17.
</li>
<li>
<b>P17_START</b> returns a starting point for problem 17.
</li>
<li>
<b>P17_STEPSIZE</b> returns step sizes for problem 17.
</li>
<li>
<b>P17_TITLE</b> sets the title for problem 17.