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) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  23  */
  24
  25 #include <iostream>
  26 #include <sstream>
  27 #include <cstdlib> // rand()
  28 #include "ginac.h"
  29 using namespace std;
  30 using namespace GiNaC;
  31
  32 extern const ex
  33 dense_univariate_poly(const symbol & x, unsigned degree);
  34
  35 static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
  36                                                                    unsigned degree)
  37 {
  38         const symbol a("a");
  39         matrix A(m,n);
  40         matrix B(m,p);
  41         // set the first min(m,n) rows of A and B
  42         for (unsigned ro=0; (ro<m)&&(ro<n); ++ro) {
  43                 for (unsigned co=0; co<n; ++co)
  44                         A.set(ro,co,dense_univariate_poly(a,degree));
  45                 for (unsigned co=0; co<p; ++co)
  46                         B.set(ro,co,dense_univariate_poly(a,degree));
  47         }
  48         // repeat excessive rows of A and B to avoid excessive construction of
  49         // overdetermined linear systems
  50         for (unsigned ro=n; ro<m; ++ro) {
  51                 for (unsigned co=0; co<n; ++co)
  52                         A.set(ro,co,A(ro-1,co));
  53                 for (unsigned co=0; co<p; ++co)
  54                         B.set(ro,co,B(ro-1,co));
  55         }
  56         // create a vector of n*p symbols all named "xrc" where r and c are ints
  57         vector<symbol> x;
  58         matrix X(n,p);
  59         for (unsigned i=0; i<n; ++i) {
  60                 for (unsigned j=0; j<p; ++j) {
  61                         ostringstream buf;
  62                         buf << "x" << i << j << ends;
  63                         x.push_back(symbol(buf.str()));
  64                         X.set(i,j,x[p*i+j]);
  65                 }
  66         }
  67         matrix sol(n,p);
  68         // Solve the system A*X==B:
  69         try {
  70                 sol = A.solve(X, B);
  71         } catch (const exception & err) {  // catch runtime_error
  72                 // Presumably, the coefficient matrix A was degenerate
  73                 string errwhat = err.what();
  74                 if (errwhat == "matrix::solve(): inconsistent linear system")
  75                         return 0;
  76                 else
  77                         clog << "caught exception: " << errwhat << endl;
  78                 throw;
  79         }
  80
  81         // check the result with our original matrix:
  82         bool errorflag = false;
  83         for (unsigned ro=0; ro<m; ++ro) {
  84                 for (unsigned pco=0; pco<p; ++pco) {
  85                         ex e = 0;
  86                         for (unsigned co=0; co<n; ++co)
  87                         e += A(ro,co)*sol(co,pco);
  88                         if (!(e-B(ro,pco)).normal().is_zero())
  89                                 errorflag = true;
  90                 }
  91         }
  92         if (errorflag) {
  93                 clog << "Our solve method claims that A*X==B, with matrices" << endl
  94                      << "A == " << A << endl
  95                      << "X == " << sol << endl
  96                      << "B == " << B << endl;
  97                 return 1;
  98         }
  99
 100         return 0;
 101 }
 102
 103 static unsigned check_inifcns_lsolve(unsigned n)
 104 {
 105         unsigned result = 0;
 106
 107         for (int repetition=0; repetition<200; ++repetition) {
 108                 // create two size n vectors of symbols, one for the coefficients
 109                 // a[0],..,a[n], one for indeterminates x[0]..x[n]:
 110                 vector<symbol> a;
 111                 vector<symbol> x;
 112                 for (unsigned i=0; i<n; ++i) {
 113                         ostringstream buf;
 114                         buf << i << ends;
 115                         a.push_back(symbol(string("a")+buf.str()));
 116                         x.push_back(symbol(string("x")+buf.str()));
 117                 }
 118                 lst eqns;  // equation list
 119                 lst vars;  // variable list
 120                 ex sol; // solution
 121                 // Create a random linear system...
 122                 for (unsigned i=0; i<n; ++i) {
 123                         ex lhs = rand()%201-100;
 124                         ex rhs = rand()%201-100;
 125                         for (unsigned j=0; j<n; ++j) {
 126                                 // ...with small coefficients to give degeneracy a chance...
 127                                 lhs += a[j]*(rand()%21-10);
 128                                 rhs += x[j]*(rand()%21-10);
 129                         }
 130                         eqns.append(lhs==rhs);
 131                         vars.append(x[i]);
 132                 }
 133                 // ...solve it...
 134                 sol = lsolve(eqns, vars);
 135
 136                 // ...and check the solution:
 137                 if (sol.nops() == 0) {
 138                         // no solution was found
 139                         // is the coefficient matrix really, really, really degenerate?
 140                         matrix coeffmat(n,n);
 141                         for (unsigned ro=0; ro<n; ++ro)
 142                                 for (unsigned co=0; co<n; ++co)
 143                                         coeffmat.set(ro,co,eqns.op(co).rhs().coeff(a[co],1));
 144                         if (!coeffmat.determinant().is_zero()) {
 145                                 ++result;
 146                                 clog << "solution of the system " << eqns << " for " << vars
 147                                          << " was not found" << endl;
 148                         }
 149                 } else {
 150                         // insert the solution into rhs of out equations
 151                         bool errorflag = false;
 152                         for (unsigned i=0; i<n; ++i)
 153                                 if (eqns.op(i).rhs().subs(sol) != eqns.op(i).lhs())
 154                                         errorflag = true;
 155                         if (errorflag) {
 156                                 ++result;
 157                                 clog << "solution of the system " << eqns << " for " << vars
 158                                      << " erroneously returned " << sol << endl;
 159                         }
 160                 }
 161         }
 162
 163         return result;
 164 }
 165
 166 unsigned check_lsolve()
 167 {
 168         unsigned result = 0;
 169
 170         cout << "checking linear solve" << flush;
 171
 172         // solve some numeric linear systems
 173         for (unsigned n=1; n<14; ++n)
 174                 result += check_matrix_solve(n, n, 1, 0);
 175         cout << '.' << flush;
 176         // solve some underdetermined numeric systems
 177         for (unsigned n=1; n<14; ++n)
 178                 result += check_matrix_solve(n+1, n, 1, 0);
 179         cout << '.' << flush;
 180         // solve some overdetermined numeric systems
 181         for (unsigned n=1; n<14; ++n)
 182                 result += check_matrix_solve(n, n+1, 1, 0);
 183         cout << '.' << flush;
 184         // solve some multiple numeric systems
 185         for (unsigned n=1; n<14; ++n)
 186                 result += check_matrix_solve(n, n, n/3+1, 0);
 187         cout << '.' << flush;
 188         // solve some symbolic linear systems
 189         for (unsigned n=1; n<8; ++n)
 190                 result += check_matrix_solve(n, n, 1, 2);
 191         cout << '.' << flush;
 192
 193         // check lsolve, the wrapper function around matrix::solve()
 194         result += check_inifcns_lsolve(2);  cout << '.' << flush;
 195         result += check_inifcns_lsolve(3);  cout << '.' << flush;
 196         result += check_inifcns_lsolve(4);  cout << '.' << flush;
 197         result += check_inifcns_lsolve(5);  cout << '.' << flush;
 198         result += check_inifcns_lsolve(6);  cout << '.' << flush;
 199
 200         return result;
 201 }
 202
 203 int main(int argc, char** argv)
 204 {
 205         return check_lsolve();
 206 }