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. */
   5
   6 /*
   7  *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  22  */
  23
  24 #include "checks.h"
  25
  26 static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
  27                                                                    unsigned degree)
  28 {
  29         const symbol a("a");
  30         matrix A(m,n);
  31         matrix B(m,p);
  32         // set the first min(m,n) rows of A and B
  33         for (unsigned ro=0; (ro<m)&&(ro<n); ++ro) {
  34                 for (unsigned co=0; co<n; ++co)
  35                         A.set(ro,co,dense_univariate_poly(a,degree));
  36                 for (unsigned co=0; co<p; ++co)
  37                         B.set(ro,co,dense_univariate_poly(a,degree));
  38         }
  39         // repeat excessive rows of A and B to avoid excessive construction of
  40         // overdetermined linear systems
  41         for (unsigned ro=n; ro<m; ++ro) {
  42                 for (unsigned co=0; co<n; ++co)
  43                         A.set(ro,co,A(ro-1,co));
  44                 for (unsigned co=0; co<p; ++co)
  45                         B.set(ro,co,B(ro-1,co));
  46         }
  47         // create a vector of n*p symbols all named "xrc" where r and c are ints
  48         vector<symbol> x;
  49         matrix X(n,p);
  50         for (unsigned i=0; i<n; ++i) {
  51                 for (unsigned j=0; j<p; ++j) {
  52                         char buf[4];
  53                         ostrstream(buf,sizeof(buf)) << i << j << ends;
  54                         x.push_back(symbol(string("x")+buf));
  55                         X.set(i,j,x[p*i+j]);
  56                 }
  57         }
  58         matrix sol(n,p);
  59         // Solve the system A*X==B:
  60         try {
  61                 sol = A.solve(X, B);
  62         } catch (const exception & err) {  // catch runtime_error
  63                 // Presumably, the coefficient matrix A was degenerate
  64                 string errwhat = err.what();
  65                 if (errwhat == "matrix::solve(): inconsistent linear system")
  66                         return 0;
  67                 else
  68                         clog << "caught exception: " << errwhat << endl;
  69                 throw;
  70         }
  71
  72         // check the result with our original matrix:
  73         bool errorflag = false;
  74         for (unsigned ro=0; ro<m; ++ro) {
  75                 for (unsigned pco=0; pco<p; ++pco) {
  76                         ex e = 0;
  77                         for (unsigned co=0; co<n; ++co)
  78                         e += A(ro,co)*sol(co,pco);
  79                         if (!(e-B(ro,pco)).normal().is_zero())
  80                                 errorflag = true;
  81                 }
  82         }
  83         if (errorflag) {
  84                 clog << "Our solve method claims that A*X==B, with matrices" << endl
  85                      << "A == " << A << endl
  86                      << "X == " << sol << endl
  87                      << "B == " << B << endl;
  88                 return 1;
  89         }
  90
  91         return 0;
  92 }
  93
  94 static unsigned check_inifcns_lsolve(unsigned n)
  95 {
  96         unsigned result = 0;
  97
  98         for (int repetition=0; repetition<100; ++repetition) {
  99                 // create two size n vectors of symbols, one for the coefficients
 100                 // a[0],..,a[n], one for indeterminates x[0]..x[n]:
 101                 vector<symbol> a;
 102                 vector<symbol> x;
 103                 for (unsigned i=0; i<n; ++i) {
 104                         char buf[3];
 105                         ostrstream(buf,sizeof(buf)) << i << ends;
 106                         a.push_back(symbol(string("a")+buf));
 107                         x.push_back(symbol(string("x")+buf));
 108                 }
 109                 lst eqns;  // equation list
 110                 lst vars;  // variable list
 111                 ex sol; // solution
 112                 // Create a random linear system...
 113                 for (unsigned i=0; i<n; ++i) {
 114                         ex lhs = rand()%201-100;
 115                         ex rhs = rand()%201-100;
 116                         for (unsigned j=0; j<n; ++j) {
 117                                 // ...with small coefficients to give degeneracy a chance...
 118                                 lhs += a[j]*(rand()%21-10);
 119                                 rhs += x[j]*(rand()%21-10);
 120                         }
 121                         eqns.append(lhs==rhs);
 122                         vars.append(x[i]);
 123                 }
 124                 // ...solve it...
 125                 sol = lsolve(eqns, vars);
 126
 127                 // ...and check the solution:
 128                 if (sol.nops() == 0) {
 129                         // no solution was found
 130                         // is the coefficient matrix really, really, really degenerate?
 131                         matrix coeffmat(n,n);
 132                         for (unsigned ro=0; ro<n; ++ro)
 133                                 for (unsigned co=0; co<n; ++co)
 134                                         coeffmat.set(ro,co,eqns.op(co).rhs().coeff(a[co],1));
 135                         if (!coeffmat.determinant().is_zero()) {
 136                                 ++result;
 137                                 clog << "solution of the system " << eqns << " for " << vars
 138                                          << " was not found" << endl;
 139                         }
 140                 } else {
 141                         // insert the solution into rhs of out equations
 142                         bool errorflag = false;
 143                         for (unsigned i=0; i<n; ++i)
 144                                 if (eqns.op(i).rhs().subs(sol) != eqns.op(i).lhs())
 145                                         errorflag = true;
 146                         if (errorflag) {
 147                                 ++result;
 148                                 clog << "solution of the system " << eqns << " for " << vars
 149                                      << " erroneously returned " << sol << endl;
 150                         }
 151                 }
 152         }
 153
 154         return result;
 155 }
 156
 157 unsigned check_lsolve(void)
 158 {
 159         unsigned result = 0;
 160
 161         cout << "checking linear solve" << flush;
 162         clog << "---------linear solve:" << endl;
 163
 164         // solve some numeric linear systems
 165         for (unsigned n=1; n<12; ++n)
 166                 result += check_matrix_solve(n, n, 1, 0);
 167         cout << '.' << flush;
 168         // solve some underdetermined numeric systems
 169         for (unsigned n=1; n<12; ++n)
 170                 result += check_matrix_solve(n+1, n, 1, 0);
 171         cout << '.' << flush;
 172         // solve some overdetermined numeric systems
 173         for (unsigned n=1; n<12; ++n)
 174                 result += check_matrix_solve(n, n+1, 1, 0);
 175         cout << '.' << flush;
 176         // solve some multiple numeric systems
 177         for (unsigned n=1; n<12; ++n)
 178                 result += check_matrix_solve(n, n, n/3+1, 0);
 179         cout << '.' << flush;
 180         // solve some symbolic linear systems
 181         for (unsigned n=1; n<7; ++n)
 182                 result += check_matrix_solve(n, n, 1, 2);
 183         cout << '.' << flush;
 184
 185         // check lsolve, the wrapper function around matrix::solve()
 186         result += check_inifcns_lsolve(2);  cout << '.' << flush;
 187         result += check_inifcns_lsolve(3);  cout << '.' << flush;
 188         result += check_inifcns_lsolve(4);  cout << '.' << flush;
 189         result += check_inifcns_lsolve(5);  cout << '.' << flush;
 190         result += check_inifcns_lsolve(6);  cout << '.' << flush;
 191
 192         if (!result) {
 193                 cout << " passed " << endl;
 194                 clog << "(no output)" << endl;
 195         } else {
 196                 cout << " failed " << endl;
 197         }
 198
 199         return result;
 200 }