check/check_lsolve.cpp

   1 /** @file check_lsolve.cpp
   2  *
   3  *  These test routines do some simple checks on solving linear systems of
   4  *  symbolic equations.  They are a well-tried resource for cross-checking
   5  *  the underlying symbolic manipulations. */
   6
   7 /*
   8  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
   9  *
  10  *  This program is free software; you can redistribute it and/or modify
  11  *  it under the terms of the GNU General Public License as published by
  12  *  the Free Software Foundation; either version 2 of the License, or
  13  *  (at your option) any later version.
  14  *
  15  *  This program is distributed in the hope that it will be useful,
  16  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  17  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18  *  GNU General Public License for more details.
  19  *
  20  *  You should have received a copy of the GNU General Public License
  21  *  along with this program; if not, write to the Free Software
  22  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  23  */
  24
  25 #include "checks.h"
  26 #include <sstream>
  27
  28 static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
  29                                                                    unsigned degree)
  30 {
  31         const symbol a("a");
  32         matrix A(m,n);
  33         matrix B(m,p);
  34         // set the first min(m,n) rows of A and B
  35         for (unsigned ro=0; (ro<m)&&(ro<n); ++ro) {
  36                 for (unsigned co=0; co<n; ++co)
  37                         A.set(ro,co,dense_univariate_poly(a,degree));
  38                 for (unsigned co=0; co<p; ++co)
  39                         B.set(ro,co,dense_univariate_poly(a,degree));
  40         }
  41         // repeat excessive rows of A and B to avoid excessive construction of
  42         // overdetermined linear systems
  43         for (unsigned ro=n; ro<m; ++ro) {
  44                 for (unsigned co=0; co<n; ++co)
  45                         A.set(ro,co,A(ro-1,co));
  46                 for (unsigned co=0; co<p; ++co)
  47                         B.set(ro,co,B(ro-1,co));
  48         }
  49         // create a vector of n*p symbols all named "xrc" where r and c are ints
  50         vector<symbol> x;
  51         matrix X(n,p);
  52         for (unsigned i=0; i<n; ++i) {
  53                 for (unsigned j=0; j<p; ++j) {
  54                         ostringstream buf;
  55                         buf << "x" << i << j << ends;
  56                         x.push_back(symbol(buf.str()));
  57                         X.set(i,j,x[p*i+j]);
  58                 }
  59         }
  60         matrix sol(n,p);
  61         // Solve the system A*X==B:
  62         try {
  63                 sol = A.solve(X, B);
  64         } catch (const exception & err) {  // catch runtime_error
  65                 // Presumably, the coefficient matrix A was degenerate
  66                 string errwhat = err.what();
  67                 if (errwhat == "matrix::solve(): inconsistent linear system")
  68                         return 0;
  69                 else
  70                         clog << "caught exception: " << errwhat << endl;
  71                 throw;
  72         }
  73
  74         // check the result with our original matrix:
  75         bool errorflag = false;
  76         for (unsigned ro=0; ro<m; ++ro) {
  77                 for (unsigned pco=0; pco<p; ++pco) {
  78                         ex e = 0;
  79                         for (unsigned co=0; co<n; ++co)
  80                         e += A(ro,co)*sol(co,pco);
  81                         if (!(e-B(ro,pco)).normal().is_zero())
  82                                 errorflag = true;
  83                 }
  84         }
  85         if (errorflag) {
  86                 clog << "Our solve method claims that A*X==B, with matrices" << endl
  87                      << "A == " << A << endl
  88                      << "X == " << sol << endl
  89                      << "B == " << B << endl;
  90                 return 1;
  91         }
  92
  93         return 0;
  94 }
  95
  96 static unsigned check_inifcns_lsolve(unsigned n)
  97 {
  98         unsigned result = 0;
  99
 100         for (int repetition=0; repetition<200; ++repetition) {
 101                 // create two size n vectors of symbols, one for the coefficients
 102                 // a[0],..,a[n], one for indeterminates x[0]..x[n]:
 103                 vector<symbol> a;
 104                 vector<symbol> x;
 105                 for (unsigned i=0; i<n; ++i) {
 106                         ostringstream buf;
 107                         buf << i << ends;
 108                         a.push_back(symbol(string("a")+buf.str()));
 109                         x.push_back(symbol(string("x")+buf.str()));
 110                 }
 111                 lst eqns;  // equation list
 112                 lst vars;  // variable list
 113                 ex sol; // solution
 114                 // Create a random linear system...
 115                 for (unsigned i=0; i<n; ++i) {
 116                         ex lhs = rand()%201-100;
 117                         ex rhs = rand()%201-100;
 118                         for (unsigned j=0; j<n; ++j) {
 119                                 // ...with small coefficients to give degeneracy a chance...
 120                                 lhs += a[j]*(rand()%21-10);
 121                                 rhs += x[j]*(rand()%21-10);
 122                         }
 123                         eqns.append(lhs==rhs);
 124                         vars.append(x[i]);
 125                 }
 126                 // ...solve it...
 127                 sol = lsolve(eqns, vars);
 128
 129                 // ...and check the solution:
 130                 if (sol.nops() == 0) {
 131                         // no solution was found
 132                         // is the coefficient matrix really, really, really degenerate?
 133                         matrix coeffmat(n,n);
 134                         for (unsigned ro=0; ro<n; ++ro)
 135                                 for (unsigned co=0; co<n; ++co)
 136                                         coeffmat.set(ro,co,eqns.op(co).rhs().coeff(a[co],1));
 137                         if (!coeffmat.determinant().is_zero()) {
 138                                 ++result;
 139                                 clog << "solution of the system " << eqns << " for " << vars
 140                                          << " was not found" << endl;
 141                         }
 142                 } else {
 143                         // insert the solution into rhs of out equations
 144                         bool errorflag = false;
 145                         for (unsigned i=0; i<n; ++i)
 146                                 if (eqns.op(i).rhs().subs(sol) != eqns.op(i).lhs())
 147                                         errorflag = true;
 148                         if (errorflag) {
 149                                 ++result;
 150                                 clog << "solution of the system " << eqns << " for " << vars
 151                                      << " erroneously returned " << sol << endl;
 152                         }
 153                 }
 154         }
 155
 156         return result;
 157 }
 158
 159 unsigned check_lsolve()
 160 {
 161         unsigned result = 0;
 162
 163         cout << "checking linear solve" << flush;
 164         clog << "---------linear solve:" << endl;
 165
 166         // solve some numeric linear systems
 167         for (unsigned n=1; n<14; ++n)
 168                 result += check_matrix_solve(n, n, 1, 0);
 169         cout << '.' << flush;
 170         // solve some underdetermined numeric systems
 171         for (unsigned n=1; n<14; ++n)
 172                 result += check_matrix_solve(n+1, n, 1, 0);
 173         cout << '.' << flush;
 174         // solve some overdetermined numeric systems
 175         for (unsigned n=1; n<14; ++n)
 176                 result += check_matrix_solve(n, n+1, 1, 0);
 177         cout << '.' << flush;
 178         // solve some multiple numeric systems
 179         for (unsigned n=1; n<14; ++n)
 180                 result += check_matrix_solve(n, n, n/3+1, 0);
 181         cout << '.' << flush;
 182         // solve some symbolic linear systems
 183         for (unsigned n=1; n<8; ++n)
 184                 result += check_matrix_solve(n, n, 1, 2);
 185         cout << '.' << flush;
 186
 187         // check lsolve, the wrapper function around matrix::solve()
 188         result += check_inifcns_lsolve(2);  cout << '.' << flush;
 189         result += check_inifcns_lsolve(3);  cout << '.' << flush;
 190         result += check_inifcns_lsolve(4);  cout << '.' << flush;
 191         result += check_inifcns_lsolve(5);  cout << '.' << flush;
 192         result += check_inifcns_lsolve(6);  cout << '.' << flush;
 193
 194         if (!result) {
 195                 cout << " passed " << endl;
 196                 clog << "(no output)" << endl;
 197         } else {
 198                 cout << " failed " << endl;
 199         }
 200
 201         return result;
 202 }