Annealing

Annealing

This document describes version 0.4a0 of Annealing, a C language library extension the for GSL, the GNU Scientific Library, attempting a redesign of the simulated annealing module.

The package is distributed under the terms of the GNU General Public License (GPL) and can be downloaded from:

Copyright © 1996, 1997, 1998, 1999, 2000 by Mark Galassi
Copyright © 2007, 2009 by Marco Maggi marcomaggi@gna.org

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with Invariant Sections being “GNU Free Documentation License” and “GNU General Public License”, no Front–Cover Texts, and no Back–Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”.

• overview: Overview of the package.
• annealing: Simulated annealing.
• misc: Miscellaneous functions.

Appendices

• References: Bibliography and references.
• Documentation License: GNU Free Documentation License.
• Package License: GNU General Public License.
• library version: How to interpret the library version.

Indexes

• Concept Index: An entry for each concept.
• Function Index: An entry for each function.
• Variable Index: An entry for each variable.
• Type Index: An entry for each type.

--- The Detailed Node Listing ---

Overview of the package

• overview using: Using the library.
• overview autoconf: Using GNU Autoconf.
• overview pkgconfig: Using pkgconfig.

Simulated annealing

• annealing algorithm: The basic algorithm.
• annealing types: Data types.
• annealing basic: Interface to the basic algorithm.
• annealing multi: Interface to the multi-best algorithm.
• annealing many: Interface to the many-tries algorithm.

Miscellaneous functions

• misc version: Version functions.

1 Overview of the package

Annealing is a C language extension library for GSL, the GNU Scientific Library, attempting a redesign of the simulated annealing module.

The library is developed and tested under the Linux+GNU system and officially it supports only the GNU infrastructure: requires the GNU C library and compiles fine with the GNU C compiler (-std=c99 -pedantic switches). The building infrastructure requires GNU Make, GNU Bash and the other common tools (rm, mkdir, ...).

Notice that Annealing's API violates the GSL's Design Document; specifically the requirement of section 3.18: “Algorithm decomposition”. Annealing uses callbacks everywhere, while the Document requires for the algorithm to be split into an initialise, iterate, test form.

• overview using: Using the library.
• overview autoconf: Using GNU Autoconf.
• overview pkgconfig: Using pkgconfig.

1.1 Using the library

In the following we assume that the library is installed under the /usr/local hierarchy.

A shell script is installed on the system to provide informations about version numbers and installation directories; it should be /usr/local/bin/annealing-config. Run annealing-config without arguments for the usage screen. An example of output for the important options is:

     $ annealing-config --package-version
     0.2.0
     
     $ annealing-config --library-interface-version
     1.0
     
     $ annealing-config --pkgincludedir
     /usr/local/include/annealing/0.2a1
     
     $ annealing-config --libdir
     /usr/local/lib
     
     $ annealing-config --library-id
     annealing1.0

There is a single header file that must be included in C sources: annealing.h; in our source code we can put:

     #include <annealing.h>

and use the output of annealing-config --pkgincludedir as argument to the -I option of the C preprocessor.

The libraries (shared and static) are installed under the directory obtained by running annealing-config --libdir; we can use its output as argument of the -L option to the linker.

If we want to link with the shared or static library we take the output of annealing-config --library-id and use it as value for the -l option to the linker.

1.2 Using GNU Autoconf

If we use GNU Autoconf to configure our application we can embed in our project the file annealing.m4, installed under $prefix/share/aclocal, and load it in our configure.ac by putting:

     m4_include(annealing.m4)

in aclocal.m4. Notice that GSL distributes its own Autoconf plug–in, a file named gsl.m4. The annealing.m4 macro file defines a macro that can be invoked with:

     ANNEALING_LIBRARY(1,0)

it finds and invokes annealing-config to acquire installation directories and library names. The macro accepts two arguments: the major and minor interface version numbers that are needed (library version); both of the arguments are optional, but it is recommended to specify them.

ANNEALING_LIBRARY defines the following symbols:

@ANNEALING_INCLUDEDIR@

The directory under which header files are installed, example:

          /usr/local/include/annealing/0.2a1

@ANNEALING_CPPFLAGS@

The preprocessor option -I with the value of @ANNEALING_INCLUDEDIR@ attached, example:

          -I/usr/local/include/annealing/0.2a1

@ANNEALING_LIBDIR@

The directory under which shared and static libraries are installed, example: /usr/local/lib.

@ANNEALING_LDFLAGS@

The linker option -L with the value of @ANNEALING_LIBDIR@ appended, example: -L/usr/local/lib.

@ANNEALING_LIBRARY_ID@

The identifier of the shared or static library, example: annealing1.0.

@ANNEALING_LIBS@

The linker option -l with the value of @ANNEALING_LIBRARY_ID@ appended, example: -lannealing1.0.

1.3 Using pkgconfig

pkg-config is a program (a compiled executable) that inspects a database of package meta informations and prints to its standard output channel informations about installed packages and libraries. Annealing installs a meta data file for use with pkg-config, it should be:

     ${libdir}/pkgconfig/annealing.pc

notice that the GSL distributes its own pkg-config meta file, a file named gsl.pc.

For the full list of available informations look in the file itself, and remember that the value of all the variables set in the meta file can be printed with:

     $ pkg-config annealing --variable=<VARNAME>

an example of output for the important variables is:

     $ pkg-config annealing --variable=PACKAGE_VERSION
     0.2.0
     
     $ pkg-config annealing --variable=library_interface_version
     1.0
     
     $ pkg-config annealing --variable=pkgincludedir
     /usr/local/include/annealing/0.2a1
     
     $ pkg-config annealing --variable=libdir
     /usr/local/lib
     
     $ pkg-config annealing --variable=library_id
     annealing1.0

The --libs option outputs something like:

     $ pkg-config annealing --libs
     -L/usr/local/lib -lannealing1.0 -lgsl -lgslcblas -lm

while the list of preprocessor options is:

     $ pkg-config annealing --cflags
     -I/usr/local/include/annealing/0.2a1 -I/usr/local/include

Notice that:

     $ pkg-config annealing --modversion
     1.0

because what matters is the version of the API, not the package distribution version.

2 Simulated annealing

Stochastic search techniques are used when the structure of a space is not well understood or is not smooth, so that techniques like Newton's method (which requires calculating Jacobian derivative matrices) cannot be used. In particular, these techniques are frequently used to solve combinatorial optimization problems, such as the traveling salesman problem.

The goal is to find a point in the space at which a real valued “energy function” (or “cost function”) is minimized. Simulated annealing is a minimization technique which has given good results in avoiding local minima; it is based on the idea of taking a random walk through the space at successively lower temperatures, where the probability of taking a step is given by a Boltzmann distribution.

• annealing algorithm: The basic algorithm.
• annealing types: Data types.
• annealing basic: Interface to the basic algorithm.
• annealing multi: Interface to the multi-best algorithm.
• annealing many: Interface to the many-tries algorithm.

2.1 The basic algorithm

Here is an explanation of the basic algorithm. The idea is to generate at random new configurations in the solution's space, and apply two criteria to decide if the a new configuration must be accepted or not. The criteria are: if lower energy accept, if upper energy accept with a probability from a Boltzmann distribution.

It goes like this:

1. interpret the start configuration as current and also register it as best so far;
2. start a number of iterations at fixed temperature:
   1. compute a new configuration by taking a random step from the current configuration;
   2. evaluate new configuration's energy:
      • if new_E <= best_E: register the new configuration as both best so far and current;
      • else if new_E <= current_E: register the new configuration as current;
      • else compute:

                            R = exp(-(new_E - best_E)/(k * T))
        

        where T is the current temperature and k the Boltzmann constant; if R is greater than a random number in the range [0, 1): register the new configuration as current;

      • else: discard the new configuration;
   3. if not done all the iterations: go back to a;
3. cool the temperature, the new value is:

             T_new = T / mu
   

   where mu is the damping factor: it must be a number greater than 1;

4. if the new temperature is less than the selected minimum value: stop and report the better configuration as result;
5. go to 2.

Additionally some algorithms allow restarting, between steps 4 and 5: if the new temperature is less than the selected restart value, discard the current configuration replacing it with the best so far.

Notes:

• there are two nested loops: the outer does as many iterations as required to cool the temperature from the initial value to the minimum; the inner does a fixed number of iterations at the same temperature;
• at least one outer iteration is performed, so the number of outer iterations can be computed like this:

            initial = 100;
            minimum = 1;
            damping = 1.005;
            count   = 1;
            
            for (l = initial; l >= miminum; l /= damping, ++count)
              ;
            /* count = 925 */
  

• the cooling waveform of the temperature is somewhat like an exponential; for the example above the application of nonlinear multifitting with the exponential model returns the following:

            T(x) = A exp(-lam x)    A=99.9999999173883  lam=4.60350080940739
  

  which fits very well the curve;

• the value:

            R = exp(-(new_E - best_E)/(k * T))
  

  is computed only if new_E > best_E, so it is always:

            new_E - best_E > 0  => R \in [0, 1)
  

  with R near 1 when k * T is high, and near 0 when k * T is low;

• during the first iterations: the temperature drops rapidly and its value is high; this means that a worse configuration is more likely to be accepted;
• during the last iterations: the temperature drops slowly and its value is low; this means that a worse configuration is less likely to be accepted;
• with the basic algorithm only three configuration objects are in existence at any instant: current, best so far, new; so the memory space required to hold them can be allocated at the beginning of the algorithm and released at the end by the user code;
• the algorithm as no need to report errors if:
  1. we avoid memory allocation in the code that builds new configurations;
  2. building a new configuration from an existent one cannot fail.

2.2 Data types

2.2.1 Data structures

2.2.2 User supplied functions

In the following function types:

• when the function is invoked by annealing_simple_solve() the argument S references a structure of type annealing_simple_workspace_t.
• when the function is invoked by annealing_multibest_solve() the argument S references a structure of type annealing_multibest_workspace_t;
• when the function is invoked by annealing_manytries_solve() the argument S references a structure of type annealing_manytries_workspace_t.

The configuration parameters are the values in the data field of annealing_configuration_t structures.

2.3 Interface to the basic algorithm

2.3.1 Examples

Find the minimum of f(t) = -sin(t)/t.

     /** ------------------------------------------------------------
      ** Headers.
      ** ----------------------------------------------------------*/
     
     #include <stdio.h>
     #include <stdlib.h>
     #include <math.h>
     #include <float.h>
     #include <gsl/gsl_rng.h>
     #include "annealing.h"
     
     
     static  annealing_energy_fun_t      energy_function;
     static  annealing_step_fun_t        step_function;
     static  annealing_log_fun_t         log_function;
     static  annealing_copy_fun_t        copy_function;
     
     /** ------------------------------------------------------------
      ** Main.
      ** ----------------------------------------------------------*/
     
     int
     main (void)
     {
       annealing_simple_workspace_t      S;
       double        configurations[3];
       double        max_step = 10.0;
     
     
       printf("sinc minimisation with simulated annealing\n");
     
       S.number_of_iterations_at_fixed_temperature = 10;
       S.max_step_value              = &max_step;
     
       S.temperature                 = 10.0;
       S.minimum_temperature         = 1.0e-6;
       S.restart_temperature         = DBL_MIN; /* do not restart */
       S.boltzmann_constant          = 1.0;
       S.damping_factor              = 1.005;
     
       S.energy_function             = energy_function;
       S.step_function               = step_function;
       S.copy_function               = copy_function;
       S.log_function                = log_function;
       S.cooling_function            = NULL;
     
       S.numbers_generator           = gsl_rng_alloc(gsl_rng_rand);
       gsl_rng_set(S.numbers_generator, 15);
     
       S.current_configuration.data  = &(configurations[0]);
       S.best_configuration.data     = &(configurations[1]);
       S.new_configuration.data      = &(configurations[2]);
     
       configurations[0] = 100.0;
     
       annealing_simple_solve(&S);
     
       printf("final best solution: %f, expected 0.0\n",
              configurations[1]);
     
       gsl_rng_free(S.numbers_generator);
       exit(EXIT_SUCCESS);
     }
     
     /** ------------------------------------------------------------
      ** Iteration functions.
      ** ----------------------------------------------------------*/
     
     static double
     alea (annealing_simple_workspace_t * S)
     {
       double        max_step = *((double *)S->max_step_value);
     
       return (2.0 * gsl_rng_uniform(S->numbers_generator) - 1.0) * max_step;
     }
     
     /* ------------------------------------------------------------ */
     
     double
     energy_function (void * dummy, void * configuration)
     {
       double        C = *((double *)configuration);
     
       return -sin(C)/C;
     }
     void
     step_function (void * W, void * configuration)
     {
       annealing_simple_workspace_t * S = W;
       double *      C = (double *)configuration;
       double        c;
     
       do c = *C + alea(S); while (fabs(c) > 120.0);
       *C = c;
     }
     void
     log_function (void * W)
     {
       annealing_simple_workspace_t * S = W;
       double        current = *((double *)S->current_configuration.data);
       double        best    = *((double *)S->best_configuration.data);
     
       printf("current %f (energy %f), best %f (energy %f)\n",
              current, S->current_configuration.energy,
              best,    S->best_configuration.energy);
     }
     
     /** ------------------------------------------------------------
      ** Configuration handling functions.
      ** ----------------------------------------------------------*/
     
     void
     copy_function (void * dummy,
                    void * dst_configuration, void * src_configuration)
     {
       double *      dst = dst_configuration;
       double *      src = src_configuration;
     
       *dst = *src;
     }
     
     /* end of file */

2.4 Interface to the multi–best algorithm

To understand this section you have to read annealing algorithm first.

The multi–best algorithm works like the simple one, but keeps as result a number of best configurations. It allows a two step search:

1. find N promising configurations using annealing_multibest_solve();
2. explore the neighbourhood of each of the best configurations using annealing_simple_solve();

When using the multi–best algorithm there is no restart option.

2.4.1 Examples

Find 4 local minima of f(t) = -sin(t)/t.

     /** ------------------------------------------------------------
      ** Headers.
      ** ----------------------------------------------------------*/
     
     #include <stdio.h>
     #include <stdlib.h>
     #include <math.h>
     #include <float.h>
     #include <gsl/gsl_rng.h>
     #include "annealing.h"
     
     
     static  annealing_energy_fun_t      energy_function;
     static  annealing_step_fun_t        step_function;
     static  annealing_metric_fun_t      metric_function;
     static  annealing_log_fun_t         log_function;
     static  annealing_copy_fun_t        copy_function;
     
     /** ------------------------------------------------------------
      ** Main.
      ** ----------------------------------------------------------*/
     
     int
     main (void)
     {
       annealing_multibest_workspace_t   S;
       annealing_configuration_t         array[4];
       double        configurations[2+4]; /* new, current and 4 best */
       double        max_step = 10.0;
     
     
       printf("multi-best sinc minimisation with simulated annealing\n");
     
       S.number_of_iterations_at_fixed_temperature = 10;
       S.max_step_value              = &max_step;
       S.minimum_acceptance_distance = 2.0;
     
       S.temperature                 = 10.0;
       S.minimum_temperature         = 1.0e-6;
       S.boltzmann_constant          = 1.0;
       S.damping_factor              = 1.005;
     
       S.energy_function             = energy_function;
       S.step_function               = step_function;
       S.copy_function               = copy_function;
       S.log_function                = log_function;
       S.metric_function             = metric_function;
       S.cooling_function            = NULL;
     
       S.numbers_generator           = gsl_rng_alloc(gsl_rng_rand);
       gsl_rng_set(S.numbers_generator, 15);
     
       S.max_number_of_best_configurations = 4;
       S.current_configuration.data  = &(configurations[0]);
       S.new_configuration.data      = &(configurations[1]);
       S.best_configurations         = array;
     
       array[0].data         = &(configurations[2]);
       array[1].data         = &(configurations[3]);
       array[2].data         = &(configurations[4]);
       array[3].data         = &(configurations[5]);
       configurations[0] = 100.0;
     
       annealing_multibest_solve(&S);
     
       printf("found %u best solutions:", S.best_configurations_count);
       for (size_t i=0; i<S.best_configurations_count; ++i)
         {
           double *	value = array[i].data;
           printf(" %.5f", *value);
         }
     
       gsl_rng_free(S.numbers_generator);
       exit(EXIT_SUCCESS);
     }
     
     /** ------------------------------------------------------------
      ** Iteration functions.
      ** ----------------------------------------------------------*/
     
     static double
     alea (annealing_multibest_workspace_t * S)
     {
       double        max_step = *((double *)S->max_step_value);
     
       return (2.0 * gsl_rng_uniform(S->numbers_generator) - 1.0) * max_step;
     }
     
     /* ------------------------------------------------------------ */
     
     double
     energy_function (void * dummy, void * configuration)
     {
       double        C = *((double *)configuration);
     
       return -sin(C)/C;
     }
     void
     step_function (void * W, void * configuration)
     {
       annealing_multibest_workspace_t * S = W;
       double *      C = (double *)configuration;
       double        c;
     
       do c = *C + alea(S); while (fabs(c) > 120.0);
       *C = c;
     }
     double
     metric_function (void * dummy, void * configuration_a, void * configuration_b)
     {
       double        A = *((double *)configuration_a);
       double        B = *((double *)configuration_b);
     
       return fabs(A - B);
     }
     void
     log_function (void * W)
     {
       annealing_multibest_workspace_t * S = W;
       double        current = *((double *)S->current_configuration.data);
     
     
       printf("current %5.5g (energy %.4f), worst best energy %.4f, best (%u):",
              current, S->current_configuration.energy,
              S->best_configurations[S->best_configurations_count-1].energy,
              S->best_configurations_count);
       for (size_t i=0; i<S->best_configurations_count; ++i)
         {
           double *	value = S->best_configurations[i].data;
           printf(" %.5f", *value);
         }
       printf("\n");
     }
     
     /** ------------------------------------------------------------
      ** Configuration handling functions.
      ** ----------------------------------------------------------*/
     
     void
     copy_function (void * dummy, void * dst_configuration, void * src_configuration)
     {
       double *      dst = dst_configuration;
       double *      src = src_configuration;
     
       *dst = *src;
     }
     
     /* end of file */

2.5 Interface to the many–tries algorithm

To understand this section you have to read annealing algorithm first.

The many–tries algorithm makes use of the Monte Carlo method to select the new configuration. The algorithm itself is very simple, but its meaning is not immediate to understand if one does not know the Boltzmann distribution.

2.5.1 The Boltzmann distribution

Let's consider a volume of gas composed by N particles at a temperature T. We can partition the particles in I sets, indexed by i \in [1, I], such that the number of particles in the i–th set is N_i and:

         I
     N = S N_i
        i=1

We do the partition so that: in each set all the particles share the same energy level E_i.

The Boltzmann distribution equation is:

              g_i exp(-E_i / (k T))
     N_i/N = ------------------------
              I
              S g_j exp(-E_j / (k T))
             j=1

where k is the Boltzmann constant; if we know the temperature T and all the possible energy states E_i, we can compute the fraction of particles in each state.

Altenatively: the fraction N_i/N is the probability that a particle randomly selected in the gas is in the state E_i.

Given two numbers N_i and N_j, and assuming g_i = g_j, we can write:

               g_i exp(-E_i / (k T))
     N_i/N_j = --------------------- = exp(-(E_i - E_j) / (k T))
               g_j exp(-E_j / (k T))

which gives us the probability centred around the state E_j.

2.5.2 Monte Carlo method

Let's say that we have a gas with I possible states, for which we can compute the energies E_i, i \in [1, I]. Using the Boltzmann distribution centred around a known level E having N particles:

     N_i/N = exp(-(E_i - E) / (k T))            i \in [1, I]

we can compute the fractions N_i/N.

The Monte Carlo method simulates the random extraction of a particle and the determination of its energy state:

1. compute samples of a coordinate X:

             X_0 = 0      X_i = N_i/N + X_{i-1}       i \in [1, I]
   

2. generate a random number x from a uniform distribution in the range [0, X_I];
3. select the interval for which x \in [X_{i-1}, X_i];

the result of the simulation is that the particle has energy state E_i, so it is in the state i.

2.5.3 Application to simulated annealing

To apply the method we substitute the number of iterations at fixed temperature with the following process:

1. create a number I-1 of new configurations; add the current configuration, obtaining a set of I configurations;
2. for each configuration: compute the energy level E_i centred around the energy of the current configuration;
3. apply the Monte Carlo method to select a state;

the configuration associated to the selected state is the new configuration.

We notice that:

• the fraction associated to the current configuration is:

            N_cur/N = exp(-(E - E) / (k T)) = 1
  

• the fraction associated to a configuration with energy higher than E is:

            E_hi > E     =>      (E_hi - E) > 0
                         =>      N_hi/N = exp(-(E_hi - E) / (k T)) < 1
  

  when the temperature is low the exponential becomes infinitesimal and the library forces the fraction to the value of 0.0;

• the fraction associated to a configuration with energy lower than E is:

            E_lo < E     =>      (E_lo - E) < 0
                         =>      N_lo/N = exp(-(E_lo - E) / (k T)) > 1
  

  when the temperature is low the exponential becomes huge and the library forces the fraction to the value of 10.0;

so the lower energy configurations have more probability to be selected than the current and higher energy ones, but still there is the possibility to select a higher energy configuration.

2.5.4 Interface

2.5.5 Examples

Find minimum of f(t) = -sin(t)/t.

     /** ------------------------------------------------------------
      ** Headers.
      ** ----------------------------------------------------------*/
     
     #include <stdio.h>
     #include <stdlib.h>
     #include <math.h>
     #include <float.h>
     #include <gsl/gsl_rng.h>
     #include "annealing.h"
     
     
     static	annealing_energy_fun_t	energy_function;
     static	annealing_step_fun_t	step_function;
     static	annealing_log_fun_t		log_function;
     static	annealing_copy_fun_t	copy_function;
     
     /** ------------------------------------------------------------
      ** Main.
      ** ----------------------------------------------------------*/
     
     #define TRIES   10
     
     int
     main (int argc, char ** argv)
     {
       annealing_manytries_workspace_t   S;
       annealing_configuration_t         array[TRIES];
       double        configurations[2 + TRIES]; /* best, current and new tries */
       double        monte_carlo_coordinates[TRIES];
       double        max_step = 10.0;
     
     
       printf("many-tries sinc minimisation with simulated annealing\n");
     
       S.max_step_value              = &max_step;
     
       S.temperature                 = 10.0;
       S.minimum_temperature         = 1.0e-6;
       S.restart_temperature         = DBL_MIN; /* do not restart */
       S.boltzmann_constant          = 1.0;
       S.damping_factor              = 1.005;
     
       S.energy_function             = energy_function;
       S.step_function               = step_function;
       S.copy_function               = copy_function;
       S.log_function                = log_function;
       S.cooling_function            = NULL;
     
       S.numbers_generator           = gsl_rng_alloc(gsl_rng_rand);
       gsl_rng_set(S.numbers_generator, 15);
     
       S.current_configuration.data  = &(configurations[0]);
       S.best_configuration.data     = &(configurations[1]);
       S.new_configurations          = array;
       S.monte_carlo_coordinates     = monte_carlo_coordinates;
       S.number_of_tries             = TRIES;
     
       for (size_t i=0; i<S.number_of_tries; ++i)
         array[i].data = &(configurations[i+2]);
     
       configurations[0] = 100.0;
     
       annealing_manytries_solve(&S);
     
       printf("final best solution: %f, global 0.0\n", configurations[1]);
     
       gsl_rng_free(S.numbers_generator);
       exit(EXIT_SUCCESS);
     }
     
     /** ------------------------------------------------------------
      ** Iteration functions.
      ** ----------------------------------------------------------*/
     
     static double
     alea (annealing_manytries_workspace_t * S)
     {
       double        max_step = *((double *)S->max_step_value);
     
       return (2.0 * gsl_rng_uniform(S->numbers_generator) - 1.0) * max_step;
     }
     
     /* ------------------------------------------------------------ */
     
     double
     energy_function (void * dummy, void * configuration)
     {
       double        C = *((double *)configuration);
     
       return -sin(C)/C;
     }
     void
     step_function (void * W, void * configuration)
     {
       annealing_manytries_workspace_t * S = W;
       double *      C = (double *)configuration;
       double        c;
     
       do c = *C + alea(S); while (fabs(c) > 120.0);
       *C = c;
     }
     void
     log_function (void * W)
     {
       annealing_manytries_workspace_t * S = W;
       double *      current = (double *)S->current_configuration.data;
       double *      best    = (double *)S->best_configuration.data;
     
       printf("current %f (energy %f), best %f (energy %f)\n",
              *current, S->current_configuration.energy,
              *best,    S->best_configuration.energy);
     }
     
     /** ------------------------------------------------------------
      ** Configuration handling functions.
      ** ----------------------------------------------------------*/
     
     void
     copy_function (void * dummy, void * dst_configuration, void * src_configuration)
     {
       double *      dst = dst_configuration;
       double *      src = src_configuration;
     
       *dst = *src;
     }
     
     /* end of file */

3 Miscellaneous functions

• misc version: Version functions.

3.1 Version functions

library version for details on version numbers.

Appendix A Bibliography and references

“Boltzmann distribution.” Wikipedia, The Free Encyclopedia. 24 Jan 2007, 14:52 UTC. Wikimedia Foundation, Inc. 26 Feb 2007 http://en.wikipedia.org/w/index.php?title=Boltzmann_distribution&oldid=102908405.

Appendix B GNU Free Documentation License

     Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
     http://fsf.org/
     
     Everyone is permitted to copy and distribute verbatim copies
     of this license document, but changing it is not allowed.

0. PREAMBLE

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   This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

   We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

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ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

       Copyright (C)  year  your name.
       Permission is granted to copy, distribute and/or modify this document
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       or any later version published by the Free Software Foundation;
       with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
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If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with...Texts.” line with this:

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If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

Appendix C GNU General Public License

     Copyright © 2007 Free Software Foundation, Inc. http://fsf.org/
     
     Everyone is permitted to copy and distribute verbatim copies of this
     license document, but changing it is not allowed.

Preamble

The GNU General Public License is a free, copyleft license for software and other kinds of works.

The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program—to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things.

To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others.

For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.

Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it.

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7. Additional Terms.

   “Additional permissions” are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions.

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9. Acceptance Not Required for Having Copies.

   You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.

10. Automatic Licensing of Downstream Recipients.

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17. Interpretation of Sections 15 and 16.

    If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.

     one line to give the program's name and a brief idea of what it does.
     Copyright (C) year name of author
     
     This program is free software: you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
     the Free Software Foundation, either version 3 of the License, or (at
     your option) any later version.
     
     This program is distributed in the hope that it will be useful, but
     WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     General Public License for more details.
     
     You should have received a copy of the GNU General Public License
     along with this program.  If not, see http://www.gnu.org/licenses/.

Also add information on how to contact you by electronic and paper mail.

If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:

     program Copyright (C) year name of author
     This program comes with ABSOLUTELY NO WARRANTY; for details type ‘show w’.
     This is free software, and you are welcome to redistribute it
     under certain conditions; type ‘show c’ for details.

The hypothetical commands ‘show w’ and ‘show c’ should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an “about box”.

You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyright disclaimer” for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see http://www.gnu.org/licenses/.

The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read http://www.gnu.org/philosophy/why-not-lgpl.html.

Appendix D How to interpret the library version

NOTE This section is not specific to this package; it is an explanation of library interface version numbering that the author uses for all its C libraries.

This package is distributing one or more libraries; this package has a version number and each library has an interface version number, package and interface versions are independent.

D.1 Package version

The package version tracks the development of the source code: every time the source code is modified the package version is incremented. There are three numbers: major, minor, patch level.

major

Incremented before big rewritings or additions.

minor

Incremented to track incremental development of the code.

patch level

For stable versions: incremented for bug fixes and very small additions that were forgotten in the last minor update.

The package has also a letter that indicates the status of the release: a for experimental or “alpha”, b for testing or “beta”, . for stable.

A full version number looks like this:

1.2a3

major 1, minor 2, patch level 3, status alpha;

10.23b34

major 10, minor 23, patch level 34, status beta;

1.2.3

major 1, minor 2, patch level 3, status stable.

The reason for the letter to be between the minor number and the patch level is that it is more important:

• when starting to develop version 1.2 (major 1, minor 2), the last stable version of the 1.1 branch is taken and the project starts with alpha versions; each alpha has a patch level: 1.2a0, 1.2a1, ...;
• when experimental development, is finished the package is moved to testing and the status to beta: 1.2b0, 1.2b1, ... so the first beta version is newer than the last alpha version;
• when testing is finished, the package is moved to stable status: 1.2.0, 1.2.1, ... so the first stable version is newer than the last beta version.

summary:

     1.1.x < 1.2a0 < 1.2a1 < ... < 1.2b0 < 1.2b1 < ... < 1.2.0 < 1.2.1

D.2 Interface version

The interface version changes only when the public interface of a library (public function prototypes and data types) is modified. There are two numbers: major and minor.

major

Establishes a set of: functions, data types, code behaviour that will not change until the next major number update. Code written for the first release of the library with a major interface number (1.0), will work unchanged with all the libraries with the same major interface number (1.1, 1.2, ...); if it does not: it is a library bug, please signal this to the author using the bug tracking system.

The only exception to this rule is the wrong behaviour caused by bugs; code that relies on buggy behaviour of a package version may not work with subsequent package versions with the same major interface number.

minor

Establishes a set of: functions, data types, code behaviour that will not change until the next major number update. This set is added to the set of the previous interface version.

The library file installed on our system has name composed with the interface number; example: if the package has version 1.2.3 and the interface has version 1.1, the library file is called libmy1.1.so.

Even if the interface number has not changed, and the library file has the same name: when an installed shared library is updated to a new package version, programs and libraries depending on it will have to be recompiled, because the internals of the library file will have changed.

Appendix E An entry for each concept

• FDL, GNU Free Documentation License: Documentation License

Appendix F An entry for each function.

• annealing_cooling_fun_t: annealing types
• annealing_copy_fun_t: annealing types
• annealing_energy_fun_t: annealing types
• annealing_library_major_version: misc version
• annealing_library_minor_version: misc version
• annealing_log_fun_t: annealing types
• annealing_manytries_solve: annealing many
• annealing_metric_fun_t: annealing types
• annealing_multibest_solve: annealing multi
• annealing_simple_solve: annealing basic
• annealing_step_fun_t: annealing types
• annealing_version: misc version

Appendix G An entry for each variable.

Appendix H An entry for each type.

• annealing_configuration_t: annealing types
• annealing_manytries_workspace_t: annealing many
• annealing_multibest_workspace_t: annealing multi
• annealing_simple_workspace_t: annealing basic