X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fcheck_lsolve.cpp;h=4c98fc510c5605454795a6d166e20fb508b041b2;hp=4d1f23730aeda0acb20b388ec522a692835acb75;hb=b3283b8904fbc9617cb6293791c7a653e255ebbe;hpb=f4ea690a3f118bf364190f0ef3c3f6d2ccdf6206

diff --git a/check/check_lsolve.cpp b/check/check_lsolve.cpp
index 4d1f2373..4c98fc51 100644
--- a/check/check_lsolve.cpp
+++ b/check/check_lsolve.cpp
@@ -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) 1999-2003 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
@@ -22,107 +23,180 @@
  */
 
 #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<200; ++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 check_lsolve()
 {
-    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<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;
+		
+	if (!result) {
+		cout << " passed " << endl;
+		clog << "(no output)" << endl;
+	} else {
+		cout << " failed " << endl;
+	}
+	
+	return result;
 }