+++ /dev/null
-/** @file matrix_checks.cpp
- *
- * Here we test manipulations on GiNaC's symbolic matrices. */
-
-/*
- * GiNaC Copyright (C) 1999-2000 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 <stdexcept>
-#include "ginac.h"
-
-#ifndef NO_NAMESPACE_GINAC
-using namespace GiNaC;
-#endif // ndef NO_NAMESPACE_GINAC
-
-static unsigned matrix_determinants(void)
-{
- unsigned result = 0;
- ex det;
- matrix m1(1,1), m2(2,2), m3(3,3);
- symbol a("a"), b("b"), c("c");
- symbol d("d"), e("e"), f("f");
- symbol g("g"), h("h"), i("i");
-
- // check symbolic trivial matrix determinant
- m1.set(0,0,a);
- det = m1.determinant();
- if (det != a) {
- clog << "determinant of 1x1 matrix " << m1
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 2x2 matrix determinant
- m2.set(0,0,a).set(0,1,b);
- m2.set(1,0,c).set(1,1,d);
- det = m2.determinant();
- if (det != (a*d-b*c)) {
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 3x3 matrix determinant
- m3.set(0,0,a).set(0,1,b).set(0,2,c);
- m3.set(1,0,d).set(1,1,e).set(1,2,f);
- m3.set(2,0,g).set(2,1,h).set(2,2,i);
- det = m3.determinant().expand();
- if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense numeric 3x3 matrix determinant
- m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
- m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
- m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
- det = m3.determinant();
- if (det != 42) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense symbolic 2x2 matrix determinant
- m2.set(0,0,a/(a-b)).set(0,1,numeric(1));
- m2.set(1,0,b/(a-b)).set(1,1,numeric(1));
- det = m2.determinant(true);
- if (det != 1) {
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check characteristic polynomial
- m3.set(0,0,a).set(0,1,-2).set(0,2,2);
- m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
- m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
- ex p = m3.charpoly(a);
- if (p != 0) {
- clog << "charpoly of 3x3 matrix " << m3
- << " erroneously returned " << p << endl;
- ++result;
- }
-
- return result;
-}
-
-static unsigned matrix_invert1(void)
-{
- matrix m(1,1);
- symbol a("a");
-
- m.set(0,0,a);
- matrix m_i = m.inverse();
-
- if (m_i(0,0) != pow(a,-1)) {
- clog << "inversion of 1x1 matrix " << m
- << " erroneously returned " << m_i << endl;
- return 1;
- }
- return 0;
-}
-
-static unsigned matrix_invert2(void)
-{
- matrix m(2,2);
- symbol a("a"), b("b"), c("c"), d("d");
- m.set(0,0,a).set(0,1,b);
- m.set(1,0,c).set(1,1,d);
- matrix m_i = m.inverse();
- ex det = m.determinant().expand();
-
- if ((normal(m_i(0,0)*det) != d) ||
- (normal(m_i(0,1)*det) != -b) ||
- (normal(m_i(1,0)*det) != -c) ||
- (normal(m_i(1,1)*det) != a)) {
- clog << "inversion of 2x2 matrix " << m
- << " erroneously returned " << m_i << endl;
- return 1;
- }
- return 0;
-}
-
-static unsigned matrix_invert3(void)
-{
- matrix m(3,3);
- symbol a("a"), b("b"), c("c");
- symbol d("d"), e("e"), f("f");
- symbol g("g"), h("h"), i("i");
- m.set(0,0,a).set(0,1,b).set(0,2,c);
- m.set(1,0,d).set(1,1,e).set(1,2,f);
- m.set(2,0,g).set(2,1,h).set(2,2,i);
- matrix m_i = m.inverse();
- ex det = m.determinant().normal().expand();
-
- if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
- (normal(m_i(0,1)*det) != (c*h-b*i)) ||
- (normal(m_i(0,2)*det) != (b*f-c*e)) ||
- (normal(m_i(1,0)*det) != (f*g-d*i)) ||
- (normal(m_i(1,1)*det) != (a*i-c*g)) ||
- (normal(m_i(1,2)*det) != (c*d-a*f)) ||
- (normal(m_i(2,0)*det) != (d*h-e*g)) ||
- (normal(m_i(2,1)*det) != (b*g-a*h)) ||
- (normal(m_i(2,2)*det) != (a*e-b*d))) {
- clog << "inversion of 3x3 matrix " << m
- << " erroneously returned " << m_i << endl;
- return 1;
- }
- return 0;
-}
-
-static unsigned matrix_misc(void)
-{
- unsigned result = 0;
- matrix m1(2,2);
- symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
- m1.set(0,0,a).set(0,1,b);
- m1.set(1,0,c).set(1,1,d);
- ex tr = trace(m1);
-
- // check a simple trace
- if (tr.compare(a+d)) {
- clog << "trace of 2x2 matrix " << m1
- << " erroneously returned " << tr << endl;
- ++result;
- }
-
- // and two simple transpositions
- matrix m2 = transpose(m1);
- if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
- clog << "transpose of 2x2 matrix " << m1
- << " erroneously returned " << m2 << endl;
- ++result;
- }
- matrix m3(3,2);
- m3.set(0,0,a).set(0,1,b);
- m3.set(1,0,c).set(1,1,d);
- m3.set(2,0,e).set(2,1,f);
- if (transpose(transpose(m3)) != m3) {
- clog << "transposing 3x2 matrix " << m3 << " twice"
- << " erroneously returned " << transpose(transpose(m3)) << endl;
- ++result;
- }
-
- // produce a runtime-error by inverting a singular matrix and catch it
- matrix m4(2,2);
- matrix m5;
- bool caught=false;
- try {
- m5 = inverse(m4);
- }
- catch (std::runtime_error err) {
- caught=true;
- }
- if (!caught) {
- cerr << "singular 2x2 matrix " << m4
- << " erroneously inverted to " << m5 << endl;
- ++result;
- }
-
- return result;
-}
-
-unsigned matrix_checks(void)
-{
- unsigned result = 0;
-
- cout << "checking symbolic matrix manipulations..." << flush;
- clog << "---------symbolic matrix manipulations:" << endl;
-
- result += matrix_determinants();
- result += matrix_invert1();
- result += matrix_invert2();
- result += matrix_invert3();
- result += matrix_misc();
-
- if (!result) {
- cout << " passed ";
- clog << "(no output)" << endl;
- } else {
- cout << " failed ";
- }
-
- return result;
-}
git://www.ginac.de / ginac.git / blobdiff