* Here we examine manipulations on GiNaC's symbolic matrices. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 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 <stdexcept>
#include "exams.h"
-static unsigned matrix_determinants(void)
+static unsigned matrix_determinants()
{
unsigned result = 0;
ex det;
det = m1.determinant();
if (det != a) {
clog << "determinant of 1x1 matrix " << m1
- << " erroneously returned " << det << endl;
+ << " erroneously returned " << det << endl;
++result;
}
det = m2.determinant();
if (det != (a*d-b*c)) {
clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
+ << " erroneously returned " << det << endl;
++result;
}
det = m3.determinant();
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;
+ << " erroneously returned " << det << endl;
++result;
}
det = m3.determinant();
if (det != 42) {
clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
+ << " erroneously returned " << det << endl;
++result;
}
if (det != 1) {
if (det.normal() == 1) // only half wrong
clog << "determinant of 2x2 matrix " << m2
- << " was returned unnormalized as " << det << endl;
+ << " was returned unnormalized as " << det << endl;
else // totally wrong
clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
+ << " erroneously returned " << det << endl;
++result;
}
det = m4.determinant();
if (det != a*b*c*d) {
clog << "determinant of 4x4 matrix " << m4
- << " erroneously returned " << det << endl;
+ << " erroneously returned " << det << endl;
++result;
}
ex p = m3.charpoly(a);
if (p != 0) {
clog << "charpoly of 3x3 matrix " << m3
- << " erroneously returned " << p << endl;
+ << " erroneously returned " << p << endl;
++result;
}
return result;
}
-static unsigned matrix_invert1(void)
+static unsigned matrix_invert1()
{
unsigned result = 0;
matrix m(1,1);
if (m_i(0,0) != pow(a,-1)) {
clog << "inversion of 1x1 matrix " << m
- << " erroneously returned " << m_i << endl;
+ << " erroneously returned " << m_i << endl;
++result;
}
return result;
}
-static unsigned matrix_invert2(void)
+static unsigned matrix_invert2()
{
unsigned result = 0;
matrix m(2,2);
(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;
+ << " erroneously returned " << m_i << endl;
++result;
}
return result;
}
-static unsigned matrix_invert3(void)
+static unsigned matrix_invert3()
{
unsigned result = 0;
matrix m(3,3);
ex det = m.determinant();
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))) {
+ (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;
+ << " erroneously returned " << m_i << endl;
++result;
}
return result;
}
-static unsigned matrix_solve2(void)
+static unsigned matrix_solve2()
{
// check the solution of the multiple system A*X = B:
// [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
result = 1;
if (result) {
clog << "Solving " << A << " * " << X << " == " << B << endl
- << "erroneously returned " << sol << endl;
+ << "erroneously returned " << sol << endl;
}
return result;
}
-static unsigned matrix_misc(void)
+static unsigned matrix_evalm()
+{
+ unsigned result = 0;
+
+ matrix S(2, 2, lst(
+ 1, 2,
+ 3, 4
+ )), T(2, 2, lst(
+ 1, 1,
+ 2, -1
+ )), R(2, 2, lst(
+ 27, 14,
+ 36, 26
+ ));
+
+ ex e = ((S + T) * (S + 2*T));
+ ex f = e.evalm();
+ if (!f.is_equal(R)) {
+ clog << "Evaluating " << e << " erroneously returned " << f << " instead of " << R << endl;
+ result++;
+ }
+
+ return result;
+}
+
+static unsigned matrix_rank()
+{
+ unsigned result = 0;
+ symbol x("x"), y("y");
+ matrix m(3,3);
+
+ // the zero matrix always has rank 0
+ if (m.rank() != 0) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // a trivial rank one example
+ m = 1, 0, 0,
+ 2, 0, 0,
+ 3, 0, 0;
+ if (m.rank() != 1) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // an example from Maple's help with rank two
+ m = x, 1, 0,
+ 0, 0, 1,
+ x*y, y, 1;
+ if (m.rank() != 2) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ // the 3x3 unit matrix has rank 3
+ m = ex_to<matrix>(unit_matrix(3,3));
+ if (m.rank() != 3) {
+ clog << "The rank of " << m << " was not computed correctly." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned matrix_misc()
{
unsigned result = 0;
matrix m1(2,2);
// check a simple trace
if (tr.compare(a+d)) {
clog << "trace of 2x2 matrix " << m1
- << " erroneously returned " << tr << endl;
+ << " erroneously returned " << tr << endl;
++result;
}
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;
+ << " erroneously returned " << transpose(transpose(m3)) << endl;
++result;
}
}
if (!caught) {
cerr << "singular 2x2 matrix " << m4
- << " erroneously inverted to " << m5 << endl;
+ << " erroneously inverted to " << m5 << endl;
++result;
}
return result;
}
-unsigned exam_matrices(void)
+unsigned exam_matrices()
{
unsigned result = 0;
result += matrix_invert2(); cout << '.' << flush;
result += matrix_invert3(); cout << '.' << flush;
result += matrix_solve2(); cout << '.' << flush;
+ result += matrix_evalm(); cout << "." << flush;
+ result += matrix_rank(); cout << "." << flush;
result += matrix_misc(); cout << '.' << flush;
if (!result) {
git://www.ginac.de / ginac.git / blobdiff