applications/testlib.c

   1 /* main.c
   2      COPYRIGHT
   3           Both this software and its documentation are
   4
   5               Copyright 1993 by IRISA /Universite de Rennes I - France,
   6               Copyright 1995,1996 by BYU
   7                          all rights reserved.
   8
   9           Permission is granted to copy, use, and distribute
  10           for any commercial or noncommercial purpose under the terms
  11           of the GNU General Public license, version 2, June 1991
  12           (see file : LICENSING).
  13
  14    This file along with polyhedron.c and vector.c do the following functions:
  15     - Extraction of a minimal set of constraints from some set of constraints
  16     - Intersection of two convexes
  17     - Application of a linear function to some convex
  18     - Verification that a convex is included in some other convex
  19
  20    They are compiled together into an executable file called "test".
  21    The file test.in contains sample input data for the program.
  22    The file test.out contains the output produced by the program.
  23
  24    This directory also contains a makefile to build and run the test.
  25
  26    This file is a tutorial on how to use the library.  The comments
  27    explain whats going on.  You can use this file as a pattern for your
  28    own program.  Good Luck !
  29
  30    --Doran
  31 */
  32
  33 #include <stdio.h>
  34
  35 #include <polylib/polylib.h>
  36
  37
  38 int main() {
  39
  40   Matrix *a, *b, *t;
  41   Polyhedron *A, *B, *C, *D;
  42
  43   printf("Polyhedral Library Test\n\n");
  44
  45   /* read in a matrix containing your equations */
  46   /* for example, run this program and type in these five  lines:
  47      4 4
  48      1 0 1 -1
  49      1 -1 0 6
  50      1 0 -1 7
  51      1 1 0 -2
  52      This is a matrix for the following inequalities
  53      1 = inequality,  0x +  1y -1 >=0  -->      y >= 1
  54      1 = inequality, -1x +  0y +6 >=0  -->      x <= 6
  55      1 = inequality,  0x + -1y +7 >=0  -->      y <= 7
  56      1 = inequality,  1x +  0y -2 >=0  -->      x >= 2
  57      If the first number is a 0 instead of a 1, then that constraint
  58      is an 'equality' instead of an 'inequality'.
  59   */
  60   a = Matrix_Read();
  61
  62   /* read in a second matrix containing a second set of constraints:
  63      for example :
  64      4 4
  65      1 1 0 -1
  66      1 -1 0 3
  67      1 0 -1 5
  68      1 0 1 -2
  69   */
  70   b = Matrix_Read();
  71
  72   /* Convert the constraints to a Polyhedron.
  73      This operation 1. Computes the dual ray/vertice form of the
  74      system, and 2. Eliminates redundant constraints and reduces
  75      them to a minimal form.
  76   */
  77   A = Constraints2Polyhedron(a, 200);
  78   B = Constraints2Polyhedron(b, 200);
  79
  80   /* the 200 is the size of the working space (in terms of number
  81      of rays) that is allocated temporarily
  82      -- you can enlarge or reduce it as needed */
  83
  84   /* There is likewise a rays to polyhedron procedure */
  85
  86   /* Since you are done with the matrices a and b, be a good citizen
  87      and clean up your garbage */
  88   Matrix_Free(a);
  89   Matrix_Free(b);
  90
  91   /* If you want the the reduced set of equations back, you can
  92      either learn to read the polyhedron structure (not hard,
  93      look in "types.h"...
  94      or you can get the matrix back in the same format it started
  95      in... */
  96   a = Polyhedron2Constraints(A);
  97   b = Polyhedron2Constraints(B);
  98
  99   /* Take a look at them if you want */
 100   printf("\na =");
 101   Matrix_Print(stdout,P_VALUE_FMT,a);
 102   printf("\nb =");
 103   Matrix_Print(stdout,P_VALUE_FMT,b);
 104
 105   /* To intersect the two systems, use the polyhedron formats... */
 106   C = DomainIntersection(A, B, 200);
 107
 108   /* Again, the 200 is the size of the working space */
 109
 110   /* This time, lets look a the polyhedron itself... */
 111   printf("\nC = A and B =");
 112   Polyhedron_Print(stdout,P_VALUE_FMT,C);
 113
 114   /*
 115    * The operations DomainUnion, DomainDifference, and DomainConvex
 116    * are also available
 117    */
 118
 119   /*
 120    * Read in a third matrix containing a transformation matrix,
 121    * this one swaps the indices (x,y --> y,x):
 122    * 3 3
 123    * 0 1 0
 124    * 1 0 0
 125    * 0 0 1
 126    */
 127
 128
 129   t = Matrix_Read();
 130
 131   /* Take the preimage (transform the equations) of the domain C to
 132      get D.  Are you catching on to this 200 thing yet ??? */
 133
 134   D = Polyhedron_Preimage(C, t, 200);
 135
 136   /* cleanup please */
 137   Matrix_Free(t);
 138
 139   printf("\nD = transformed C =");
 140   Polyhedron_Print(stdout,P_VALUE_FMT,D);
 141   Domain_Free(D);
 142
 143   /* in a similar way, Polyhedron_Image(dom, mat, 200), takes the image
 144      of dom under matrix mat  (transforms the vertices/rays) */
 145
 146   /* The function PolyhedronIncludes(Pol1, Pol2) returns 1 if Pol1
 147      includes (covers) Pol2, and a 0 otherwise */
 148
 149   if (PolyhedronIncludes(A,C))
 150     printf("\nWe expected A to cover C since C = A intersect B\n");
 151   if (!PolyhedronIncludes(C,B))
 152     printf("and C does not cover B...\n");
 153
 154   /* Final note:  some functions are defined for Domains, others
 155    * for Polyhedrons.  A domain is simply a list of polyhedrons.
 156    * Every polyhedron structure has a "next" pointer used to
 157    * make a list of polyhedrons...  For instance, the union of
 158    * two disjoint polyhedra is a domain consisting of two polyhedra.
 159    * If you want the convex domain... you have to call
 160    * DomainConvex(Pol1, 200) explicity.
 161    * Note that includes does not work on domains, only on simple
 162    * polyhedrons...
 163    * Thats the end of the demo...  write me if you have questions.
 164    * And remember to clean up...
 165    */
 166
 167   Domain_Free(A);
 168   Domain_Free(B);
 169   Domain_Free(C);
 170
 171   return 0;
 172 }
 173
 174