* symbolic equations. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 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
*/
#include "checks.h"
+#include <sstream>
-static unsigned lsolve1(int size)
+static unsigned check_matrix_solve(unsigned m, unsigned n, unsigned p,
+ unsigned degree)
{
- // 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;
+ 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 lsolve2(int size)
+static unsigned check_inifcns_lsolve(unsigned n)
{
- // 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;
+
+ for (int repetition=0; repetition<100; ++repetition) {
+ // create two size n vectors of symbols, one for the coefficients
+ // a[0],..,a[n], one for indeterminates x[0]..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;
}
unsigned check_lsolve(void)
{
- 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;
+ unsigned result = 0;
+
+ cout << "checking linear solve" << flush;
+ clog << "---------linear solve:" << endl;
+
+ // solve some numeric linear systems
+ for (unsigned n=1; n<12; ++n)
+ result += check_matrix_solve(n, n, 1, 0);
+ cout << '.' << flush;
+ // solve some underdetermined numeric systems
+ for (unsigned n=1; n<12; ++n)
+ result += check_matrix_solve(n+1, n, 1, 0);
+ cout << '.' << flush;
+ // solve some overdetermined numeric systems
+ for (unsigned n=1; n<12; ++n)
+ result += check_matrix_solve(n, n+1, 1, 0);
+ cout << '.' << flush;
+ // solve some multiple numeric systems
+ for (unsigned n=1; n<12; ++n)
+ result += check_matrix_solve(n, n, n/3+1, 0);
+ cout << '.' << flush;
+ // solve some symbolic linear systems
+ for (unsigned n=1; n<7; ++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;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
}
git://www.ginac.de / ginac.git / blobdiff