/** @file time_toeplitz.cpp
 *
 *  Calculates determinants of dense symbolic Toeplitz materices.
 *  For 4x4 our matrix would look like this:
 *  [[a,b,a+b,a^2+a*b+b^2], [b,a,b,a+b], [a+b,b,a,b], [a^2+a*b+b^2,a+b,b,a]]
 */

/*
 *  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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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
 */

#include "times.h"

static unsigned toeplitz_det(unsigned size)
{
	unsigned result = 0;
	symbol a("a"), b("b");
	ex p[8] = {a,
	           b,
	           a+b,
	           pow(a,2) + a*b + pow(b,2),
	           pow(a,3) + pow(a,2)*b - a*pow(b,2) + pow(b,3),
	           pow(a,4) + pow(a,3)*b + pow(a*b,2) + a*pow(b,3) + pow(b,4),
	           pow(a,5) + pow(a,4)*b + pow(a,3)*pow(b,2) - pow(a,2)*pow(b,3) + a*pow(b,4) + pow(b,5),
	           pow(a,6) + pow(a,5)*b + pow(a,4)*pow(b,2) + pow(a*b,3) + pow(a,2)*pow(b,4) + a*pow(b,5) + pow(b,6)
	};
	
	// construct Toeplitz matrix:
	matrix M(size,size);
	for (unsigned ro=0; ro<size; ++ro) {
		for (unsigned nd=ro; nd<size; ++nd) {
			M.set(nd-ro,nd,p[ro]);
			M.set(nd,nd-ro,p[ro]);
		}
	}
	
	// compute determinant:
	ex tdet = M.determinant();
	
	// dirty consistency check of result:
	if (!tdet.subs(a==0).subs(b==0).is_zero()) {
		clog << "Determaint of Toeplitz matrix " << endl
		     << "M==" << M << endl
		     << "was miscalculated: det(M)==" << tdet << endl;
		++result;
	}
	
	return result;
}

unsigned time_toeplitz(void)
{
	unsigned result = 0;
	
	cout << "timing determinant of polyvariate symbolic Toeplitz matrices" << flush;
	clog << "-------determinant of polyvariate symbolic Toeplitz matrices:" << endl;
	
	vector<unsigned> sizes;
	vector<double> times;
	timer longines;
	
	sizes.push_back(5);
	sizes.push_back(6);
	sizes.push_back(7);
	sizes.push_back(8);
	
	for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
		int count = 1;
		longines.start();
		result += toeplitz_det(*i);
		// correct for very small times:
		while (longines.read()<0.1) {
			toeplitz_det(*i);
			++count;
		}
		times.push_back(longines.read()/count);
		cout << '.' << flush;
	}
	
	if (!result) {
		cout << " passed ";
		clog << "(no output)" << endl;
	} else {
		cout << " failed ";
	}
	// print the report:
	cout << endl << "	dim:   ";
	for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
		cout << '\t' << *i << 'x' << *i;
	cout << endl << "	time/s:";
	for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
		cout << '\t' << int(1000*(*i))*0.001;
	cout << endl;
	
	return result;
}