check/genex.cpp

   1 /** @file genex.cpp
   2  *
   3  *  Provides some routines for generating expressions that are later used as
   4  *  input in the consistency checks. */
   5
   6 /*
   7  *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
   8  *
   9  *  This program is free software; you can redistribute it and/or modify
  10  *  it under the terms of the GNU General Public License as published by
  11  *  the Free Software Foundation; either version 2 of the License, or
  12  *  (at your option) any later version.
  13  *
  14  *  This program is distributed in the hope that it will be useful,
  15  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  16  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  17  *  GNU General Public License for more details.
  18  *
  19  *  You should have received a copy of the GNU General Public License
  20  *  along with this program; if not, write to the Free Software
  21  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  22  */
  23
  24 #include "ginac.h"
  25 using namespace GiNaC;
  26
  27 #include <cstdlib>
  28 using namespace std;
  29
  30 /* Create a dense univariate random polynomial in x.
  31  * (of the form 9 - 22*a - 17*a^2 + 14*a^3 + 7*a^4 + 7a^5 if degree==5) */
  32 const ex
  33 dense_univariate_poly(const symbol & x, unsigned degree)
  34 {
  35         ex unipoly;
  36
  37         for (unsigned i=0; i<=degree; ++i)
  38                 unipoly += numeric((rand()-RAND_MAX/2))*pow(x,i);
  39
  40         return unipoly;
  41 }
  42
  43 /* Create a dense bivariate random polynomial in x1 and x2.
  44  * (of the form 9 + 52*x1 - 27*x1^2 + 84*x2 + 7*x2^2 - 12*x1*x2 if degree==2)
  45  */
  46 const ex
  47 dense_bivariate_poly(const symbol & x1, const symbol & x2, unsigned degree)
  48 {
  49         ex bipoly;
  50
  51         for (unsigned i1=0; i1<=degree; ++i1)
  52                 for (unsigned i2=0; i2<=degree-i1; ++i2)
  53                         bipoly += numeric((rand()-RAND_MAX/2))*pow(x1,i1)*pow(x2,i2);
  54
  55         return bipoly;
  56 }
  57
  58 /* Chose a randum symbol or number from the argument list. */
  59 const ex
  60 random_symbol(const symbol & x,
  61                           const symbol & y,
  62                           const symbol & z,
  63                           bool rational = true,
  64                           bool complex = false)
  65 {
  66         ex e;
  67         switch (abs(rand()) % 4) {
  68                 case 0:
  69                         e = x;
  70                         break;
  71                 case 1:
  72                         e = y;
  73                         break;
  74                 case 2:
  75                         e = z;
  76                         break;
  77                 case 3: {
  78                         int c1;
  79                         do { c1 = rand()%20 - 10; } while (!c1);
  80                         int c2;
  81                         do { c2 = rand()%20 - 10; } while (!c2);
  82                         if (!rational)
  83                                 c2 = 1;
  84                         e = numeric(c1, c2);
  85                         if (complex && !(rand()%5))
  86                                 e = e*I;
  87                         break;
  88                 }
  89         }
  90         return e;
  91 }
  92
  93 /* Create a sparse random tree in three symbols. */
  94 const ex
  95 sparse_tree(const symbol & x,
  96                         const symbol & y,
  97                         const symbol & z,
  98                         int level,
  99                         bool trig = false,      // true includes trigonomatric functions
 100                         bool rational = true, // false excludes coefficients in Q
 101                         bool complex = false) // true includes complex numbers
 102 {
 103         if (level == 0)
 104                 return random_symbol(x,y,z,rational,complex);
 105         switch (abs(rand()) % 10) {
 106                 case 0:
 107                 case 1:
 108                 case 2:
 109                 case 3:
 110                         return add(sparse_tree(x,y,z,level-1, trig, rational),
 111                                            sparse_tree(x,y,z,level-1, trig, rational));
 112                 case 4:
 113                 case 5:
 114                 case 6:
 115                         return mul(sparse_tree(x,y,z,level-1, trig, rational),
 116                                            sparse_tree(x,y,z,level-1, trig, rational));
 117                 case 7:
 118                 case 8: {
 119                         ex powbase;
 120                         do {
 121                                 powbase = sparse_tree(x,y,z,level-1, trig, rational);
 122                         } while (powbase.is_zero());
 123                         return pow(powbase, abs(rand() % 4));
 124                         break;
 125                 }
 126                 case 9:
 127                         if (trig) {
 128                                 switch (abs(rand()) % 4) {
 129                                         case 0:
 130                                                 return sin(sparse_tree(x,y,z,level-1, trig, rational));
 131                                         case 1:
 132                                                 return cos(sparse_tree(x,y,z,level-1, trig, rational));
 133                                         case 2:
 134                                                 return exp(sparse_tree(x,y,z,level-1, trig, rational));
 135                                         case 3: {
 136                                                 ex logex;
 137                                                 do {
 138                                                         ex logarg;
 139                                                         do {
 140                                                                 logarg = sparse_tree(x,y,z,level-1, trig, rational);
 141                                                         } while (logarg.is_zero());
 142                                                         // Keep the evaluator from accidentally plugging an
 143                                                         // unwanted I in the tree:
 144                                                         if (!complex && logarg.info(info_flags::negative))
 145                                                                 logarg = -logarg;
 146                                                         logex = log(logarg);
 147                                                 } while (logex.is_zero());
 148                                                 return logex;
 149                                                 break;
 150                                         }
 151                                 }
 152                         } else
 153                                 return random_symbol(x,y,z,rational,complex);
 154         }
 155
 156         return 0;
 157 }