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) 1999-2002 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 #include <sstream>
  26
  27 static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
  28                                                                    unsigned degree)
  29 {
  30         const symbol a("a");
  31         matrix A(m,n);
  32         matrix B(m,p);
  33         // set the first min(m,n) rows of A and B
  34         for (unsigned ro=0; (ro<m)&&(ro<n); ++ro) {
  35                 for (unsigned co=0; co<n; ++co)
  36                         A.set(ro,co,dense_univariate_poly(a,degree));
  37                 for (unsigned co=0; co<p; ++co)
  38                         B.set(ro,co,dense_univariate_poly(a,degree));
  39         }
  40         // repeat excessive rows of A and B to avoid excessive construction of
  41         // overdetermined linear systems
  42         for (unsigned ro=n; ro<m; ++ro) {
  43                 for (unsigned co=0; co<n; ++co)
  44                         A.set(ro,co,A(ro-1,co));
  45                 for (unsigned co=0; co<p; ++co)
  46                         B.set(ro,co,B(ro-1,co));
  47         }
  48         // create a vector of n*p symbols all named "xrc" where r and c are ints
  49         vector<symbol> x;
  50         matrix X(n,p);
  51         for (unsigned i=0; i<n; ++i) {
  52                 for (unsigned j=0; j<p; ++j) {
  53                         ostringstream buf;
  54                         buf << "x" << i << j << ends;
  55                         x.push_back(symbol(buf.str()));
  56                         X.set(i,j,x[p*i+j]);
  57                 }
  58         }
  59         matrix sol(n,p);
  60         // Solve the system A*X==B:
  61         try {
  62                 sol = A.solve(X, B);
  63         } catch (const exception & err) {  // catch runtime_error
  64                 // Presumably, the coefficient matrix A was degenerate
  65                 string errwhat = err.what();
  66                 if (errwhat == "matrix::solve(): inconsistent linear system")
  67                         return 0;
  68                 else
  69                         clog << "caught exception: " << errwhat << endl;
  70                 throw;
  71         }
  72
  73         // check the result with our original matrix:
  74         bool errorflag = false;
  75         for (unsigned ro=0; ro<m; ++ro) {
  76                 for (unsigned pco=0; pco<p; ++pco) {
  77                         ex e = 0;
  78                         for (unsigned co=0; co<n; ++co)
  79                         e += A(ro,co)*sol(co,pco);
  80                         if (!(e-B(ro,pco)).normal().is_zero())
  81                                 errorflag = true;
  82                 }
  83         }
  84         if (errorflag) {
  85                 clog << "Our solve method claims that A*X==B, with matrices" << endl
  86                      << "A == " << A << endl
  87                      << "X == " << sol << endl
  88                      << "B == " << B << endl;
  89                 return 1;
  90         }
  91
  92         return 0;
  93 }
  94
  95 static unsigned check_inifcns_lsolve(unsigned n)
  96 {
  97         unsigned result = 0;
  98
  99         for (int repetition=0; repetition<100; ++repetition) {
 100                 // create two size n vectors of symbols, one for the coefficients
 101                 // a[0],..,a[n], one for indeterminates x[0]..x[n]:
 102                 vector<symbol> a;
 103                 vector<symbol> x;
 104                 for (unsigned i=0; i<n; ++i) {
 105                         ostringstream buf;
 106                         buf << i << ends;
 107                         a.push_back(symbol(string("a")+buf.str()));
 108                         x.push_back(symbol(string("x")+buf.str()));
 109                 }
 110                 lst eqns;  // equation list
 111                 lst vars;  // variable list
 112                 ex sol; // solution
 113                 // Create a random linear system...
 114                 for (unsigned i=0; i<n; ++i) {
 115                         ex lhs = rand()%201-100;
 116                         ex rhs = rand()%201-100;
 117                         for (unsigned j=0; j<n; ++j) {
 118                                 // ...with small coefficients to give degeneracy a chance...
 119                                 lhs += a[j]*(rand()%21-10);
 120                                 rhs += x[j]*(rand()%21-10);
 121                         }
 122                         eqns.append(lhs==rhs);
 123                         vars.append(x[i]);
 124                 }
 125                 // ...solve it...
 126                 sol = lsolve(eqns, vars);
 127
 128                 // ...and check the solution:
 129                 if (sol.nops() == 0) {
 130                         // no solution was found
 131                         // is the coefficient matrix really, really, really degenerate?
 132                         matrix coeffmat(n,n);
 133                         for (unsigned ro=0; ro<n; ++ro)
 134                                 for (unsigned co=0; co<n; ++co)
 135                                         coeffmat.set(ro,co,eqns.op(co).rhs().coeff(a[co],1));
 136                         if (!coeffmat.determinant().is_zero()) {
 137                                 ++result;
 138                                 clog << "solution of the system " << eqns << " for " << vars
 139                                          << " was not found" << endl;
 140                         }
 141                 } else {
 142                         // insert the solution into rhs of out equations
 143                         bool errorflag = false;
 144                         for (unsigned i=0; i<n; ++i)
 145                                 if (eqns.op(i).rhs().subs(sol) != eqns.op(i).lhs())
 146                                         errorflag = true;
 147                         if (errorflag) {
 148                                 ++result;
 149                                 clog << "solution of the system " << eqns << " for " << vars
 150                                      << " erroneously returned " << sol << endl;
 151                         }
 152                 }
 153         }
 154
 155         return result;
 156 }
 157
 158 unsigned check_lsolve(void)
 159 {
 160         unsigned result = 0;
 161
 162         cout << "checking linear solve" << flush;
 163         clog << "---------linear solve:" << endl;
 164
 165         // solve some numeric linear systems
 166         for (unsigned n=1; n<12; ++n)
 167                 result += check_matrix_solve(n, n, 1, 0);
 168         cout << '.' << flush;
 169         // solve some underdetermined numeric systems
 170         for (unsigned n=1; n<12; ++n)
 171                 result += check_matrix_solve(n+1, n, 1, 0);
 172         cout << '.' << flush;
 173         // solve some overdetermined numeric systems
 174         for (unsigned n=1; n<12; ++n)
 175                 result += check_matrix_solve(n, n+1, 1, 0);
 176         cout << '.' << flush;
 177         // solve some multiple numeric systems
 178         for (unsigned n=1; n<12; ++n)
 179                 result += check_matrix_solve(n, n, n/3+1, 0);
 180         cout << '.' << flush;
 181         // solve some symbolic linear systems
 182         for (unsigned n=1; n<7; ++n)
 183                 result += check_matrix_solve(n, n, 1, 2);
 184         cout << '.' << flush;
 185
 186         // check lsolve, the wrapper function around matrix::solve()
 187         result += check_inifcns_lsolve(2);  cout << '.' << flush;
 188         result += check_inifcns_lsolve(3);  cout << '.' << flush;
 189         result += check_inifcns_lsolve(4);  cout << '.' << flush;
 190         result += check_inifcns_lsolve(5);  cout << '.' << flush;
 191         result += check_inifcns_lsolve(6);  cout << '.' << flush;
 192
 193         if (!result) {
 194                 cout << " passed " << endl;
 195                 clog << "(no output)" << endl;
 196         } else {
 197                 cout << " failed " << endl;
 198         }
 199
 200         return result;
 201 }