index 4d1f23730aeda0acb20b388ec522a692835acb75..226b6c2d3a0d8144d126f0f6f83fb584c43767ec 100644 (file)
@@ -1,10 +1,11 @@
/** @file check_lsolve.cpp
*
*  These test routines do some simple checks on solving linear systems of
- *  symbolic equations. */
+ *  symbolic equations.  They are a well-tried resource for cross-checking
+ *  the underlying symbolic manipulations. */

/*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
*
*  This program is free software; you can redistribute it and/or modify
*  it under the terms of the GNU General Public License as published by
*
*  You should have received a copy of the GNU General Public License
*  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
*/

-#include "checks.h"
+#include <iostream>
+#include <sstream>
+#include <cstdlib> // rand()
+#include "ginac.h"
+using namespace std;
+using namespace GiNaC;

-static unsigned lsolve1(int size)
+extern const ex
+dense_univariate_poly(const symbol & x, unsigned degree);
+
+static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
+                                                                  unsigned degree)
+{
+       const symbol a("a");
+       matrix A(m,n);
+       matrix B(m,p);
+       // set the first min(m,n) rows of A and B
+       for (unsigned ro=0; (ro<m)&&(ro<n); ++ro) {
+               for (unsigned co=0; co<n; ++co)
+                       A.set(ro,co,dense_univariate_poly(a,degree));
+               for (unsigned co=0; co<p; ++co)
+                       B.set(ro,co,dense_univariate_poly(a,degree));
+       }
+       // repeat excessive rows of A and B to avoid excessive construction of
+       // overdetermined linear systems
+       for (unsigned ro=n; ro<m; ++ro) {
+               for (unsigned co=0; co<n; ++co)
+                       A.set(ro,co,A(ro-1,co));
+               for (unsigned co=0; co<p; ++co)
+                       B.set(ro,co,B(ro-1,co));
+       }
+       // create a vector of n*p symbols all named "xrc" where r and c are ints
+       vector<symbol> x;
+       matrix X(n,p);
+       for (unsigned i=0; i<n; ++i) {
+               for (unsigned j=0; j<p; ++j) {
+                       ostringstream buf;
+                       buf << "x" << i << j << ends;
+                       x.push_back(symbol(buf.str()));
+                       X.set(i,j,x[p*i+j]);
+               }
+       }
+       matrix sol(n,p);
+       // Solve the system A*X==B:
+       try {
+               sol = A.solve(X, B);
+       } catch (const exception & err) {  // catch runtime_error
+               // Presumably, the coefficient matrix A was degenerate
+               string errwhat = err.what();
+               if (errwhat == "matrix::solve(): inconsistent linear system")
+                       return 0;
+               else
+                       clog << "caught exception: " << errwhat << endl;
+               throw;
+       }
+
+       // check the result with our original matrix:
+       bool errorflag = false;
+       for (unsigned ro=0; ro<m; ++ro) {
+               for (unsigned pco=0; pco<p; ++pco) {
+                       ex e = 0;
+                       for (unsigned co=0; co<n; ++co)
+                       e += A(ro,co)*sol(co,pco);
+                       if (!(e-B(ro,pco)).normal().is_zero())
+                               errorflag = true;
+               }
+       }
+       if (errorflag) {
+               clog << "Our solve method claims that A*X==B, with matrices" << endl
+                    << "A == " << A << endl
+                    << "X == " << sol << endl
+                    << "B == " << B << endl;
+               return 1;
+       }
+
+       return 0;
+}
+
+static unsigned check_inifcns_lsolve(unsigned n)
{
-    // A dense size x size matrix in dense univariate random polynomials
-    // of order 4.
-    unsigned result = 0;
-    symbol a("a");
-    ex sol;
-
-    // Create two dense linear matrices A and B where all entries are random
-    // univariate polynomials
-    matrix A(size,size), B(size,2), X(size,2);
-    for (int ro=0; ro<size; ++ro) {
-        for (int co=0; co<size; ++co)
-            A.set(ro,co,dense_univariate_poly(a, 5));
-        for (int co=0; co<2; ++co)
-            B.set(ro,co,dense_univariate_poly(a, 5));
-    }
-    if (A.determinant().is_zero())
-        clog << "lsolve1: singular system!" << endl;
-
-    // Solve the system A*X==B:
-    X = A.old_solve(B);
-
-    // check the result:
-    bool errorflag = false;
-    matrix Aux(size,2);
-    Aux = A.mul(X).sub(B);
-    for (int ro=0; ro<size && !errorflag; ++ro)
-        for (int co=0; co<2; ++co)
-            if (!(Aux(ro,co)).normal().is_zero())
-                errorflag = true;
-    if (errorflag) {
-        clog << "Our solve method claims that A*X==B, with matrices" << endl
-             << "A == " << A << endl
-             << "X == " << X << endl
-             << "B == " << B << endl;
-        ++result;
-    }
-    return result;
+       unsigned result = 0;
+
+       for (int repetition=0; repetition<200; ++repetition) {
+               // create two size n vectors of symbols, one for the coefficients
+               // a,..,a[n], one for indeterminates x..x[n]:
+               vector<symbol> a;
+               vector<symbol> x;
+               for (unsigned i=0; i<n; ++i) {
+                       ostringstream buf;
+                       buf << i << ends;
+                       a.push_back(symbol(string("a")+buf.str()));
+                       x.push_back(symbol(string("x")+buf.str()));
+               }
+               lst eqns;  // equation list
+               lst vars;  // variable list
+               ex sol; // solution
+               // Create a random linear system...
+               for (unsigned i=0; i<n; ++i) {
+                       ex lhs = rand()%201-100;
+                       ex rhs = rand()%201-100;
+                       for (unsigned j=0; j<n; ++j) {
+                               // ...with small coefficients to give degeneracy a chance...
+                               lhs += a[j]*(rand()%21-10);
+                               rhs += x[j]*(rand()%21-10);
+                       }
+                       eqns.append(lhs==rhs);
+                       vars.append(x[i]);
+               }
+               // ...solve it...
+               sol = lsolve(eqns, vars);
+
+               // ...and check the solution:
+               if (sol.nops() == 0) {
+                       // no solution was found
+                       // is the coefficient matrix really, really, really degenerate?
+                       matrix coeffmat(n,n);
+                       for (unsigned ro=0; ro<n; ++ro)
+                               for (unsigned co=0; co<n; ++co)
+                                       coeffmat.set(ro,co,eqns.op(co).rhs().coeff(a[co],1));
+                       if (!coeffmat.determinant().is_zero()) {
+                               ++result;
+                               clog << "solution of the system " << eqns << " for " << vars
+                                        << " was not found" << endl;
+                       }
+               } else {
+                       // insert the solution into rhs of out equations
+                       bool errorflag = false;
+                       for (unsigned i=0; i<n; ++i)
+                               if (eqns.op(i).rhs().subs(sol) != eqns.op(i).lhs())
+                                       errorflag = true;
+                       if (errorflag) {
+                               ++result;
+                               clog << "solution of the system " << eqns << " for " << vars
+                                    << " erroneously returned " << sol << endl;
+                       }
+               }
+       }
+
+       return result;
}

-static unsigned lsolve2(int size)
+unsigned check_lsolve()
{
-    // A dense size x size matrix in dense bivariate random polynomials
-    // of order 2.
-    unsigned result = 0;
-    symbol a("a"), b("b");
-    ex sol;
-
-    // Create two dense linear matrices A and B where all entries are dense random
-    // bivariate polynomials:
-    matrix A(size,size), B(size,2), X(size,2);
-    for (int ro=0; ro<size; ++ro) {
-        for (int co=0; co<size; ++co)
-            A.set(ro,co,dense_bivariate_poly(a,b,2));
-        for (int co=0; co<2; ++co)
-            B.set(ro,co,dense_bivariate_poly(a,b,2));
-    }
-    if (A.determinant().is_zero())
-        clog << "lsolve2: singular system!" << endl;
-
-    // Solve the system A*X==B:
-    X = A.old_solve(B);
-
-    // check the result:
-    bool errorflag = false;
-    matrix Aux(size,2);
-    Aux = A.mul(X).sub(B);
-    for (int ro=0; ro<size && !errorflag; ++ro)
-        for (int co=0; co<2; ++co)
-            if (!(Aux(ro,co)).normal().is_zero())
-                errorflag = true;
-    if (errorflag) {
-        clog << "Our solve method claims that A*X==B, with matrices" << endl
-             << "A == " << A << endl
-             << "X == " << X << endl
-             << "B == " << B << endl;
-        ++result;
-    }
-    return result;
+       unsigned result = 0;
+
+       cout << "checking linear solve" << flush;
+
+       // solve some numeric linear systems
+       for (unsigned n=1; n<14; ++n)
+               result += check_matrix_solve(n, n, 1, 0);
+       cout << '.' << flush;
+       // solve some underdetermined numeric systems
+       for (unsigned n=1; n<14; ++n)
+               result += check_matrix_solve(n+1, n, 1, 0);
+       cout << '.' << flush;
+       // solve some overdetermined numeric systems
+       for (unsigned n=1; n<14; ++n)
+               result += check_matrix_solve(n, n+1, 1, 0);
+       cout << '.' << flush;
+       // solve some multiple numeric systems
+       for (unsigned n=1; n<14; ++n)
+               result += check_matrix_solve(n, n, n/3+1, 0);
+       cout << '.' << flush;
+       // solve some symbolic linear systems
+       for (unsigned n=1; n<8; ++n)
+               result += check_matrix_solve(n, n, 1, 2);
+       cout << '.' << flush;
+
+       // check lsolve, the wrapper function around matrix::solve()
+       result += check_inifcns_lsolve(2);  cout << '.' << flush;
+       result += check_inifcns_lsolve(3);  cout << '.' << flush;
+       result += check_inifcns_lsolve(4);  cout << '.' << flush;
+       result += check_inifcns_lsolve(5);  cout << '.' << flush;
+       result += check_inifcns_lsolve(6);  cout << '.' << flush;
+
+       return result;
}

-unsigned check_lsolve(void)
+int main(int argc, char** argv)
{
-    unsigned result = 0;
-
-    cout << "checking linear solve" << flush;
-    clog << "---------linear solve:" << endl;
-
-    //result += lsolve1(2);  cout << '.' << flush;
-    //result += lsolve1(3);  cout << '.' << flush;
-    //result += lsolve2(2);  cout << '.' << flush;
-    //result += lsolve2(3);  cout << '.' << flush;
-
-    if (!result) {
-        cout << " passed " << endl;
-        clog << "(no output)" << endl;
-    } else {
-        cout << " failed " << endl;
-    }
-
-    return result;
+       return check_lsolve();
}