1 /** @file exam_matrices.cpp
3 * Here we examine manipulations on GiNaC's symbolic matrices. */
6 * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 static unsigned matrix_determinants(void)
30 matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4);
31 symbol a("a"), b("b"), c("c");
32 symbol d("d"), e("e"), f("f");
33 symbol g("g"), h("h"), i("i");
35 // check symbolic trivial matrix determinant
37 det = m1.determinant();
39 clog << "determinant of 1x1 matrix " << m1
40 << " erroneously returned " << det << endl;
44 // check generic dense symbolic 2x2 matrix determinant
45 m2.set(0,0,a).set(0,1,b);
46 m2.set(1,0,c).set(1,1,d);
47 det = m2.determinant();
48 if (det != (a*d-b*c)) {
49 clog << "determinant of 2x2 matrix " << m2
50 << " erroneously returned " << det << endl;
54 // check generic dense symbolic 3x3 matrix determinant
55 m3.set(0,0,a).set(0,1,b).set(0,2,c);
56 m3.set(1,0,d).set(1,1,e).set(1,2,f);
57 m3.set(2,0,g).set(2,1,h).set(2,2,i);
58 det = m3.determinant();
59 if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
60 clog << "determinant of 3x3 matrix " << m3
61 << " erroneously returned " << det << endl;
65 // check dense numeric 3x3 matrix determinant
66 m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
67 m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
68 m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
69 det = m3.determinant();
71 clog << "determinant of 3x3 matrix " << m3
72 << " erroneously returned " << det << endl;
76 // check dense symbolic 2x2 matrix determinant
77 m2.set(0,0,a/(a-b)).set(0,1,1);
78 m2.set(1,0,b/(a-b)).set(1,1,1);
79 det = m2.determinant();
81 if (det.normal() == 1) // only half wrong
82 clog << "determinant of 2x2 matrix " << m2
83 << " was returned unnormalized as " << det << endl;
85 clog << "determinant of 2x2 matrix " << m2
86 << " erroneously returned " << det << endl;
90 // check sparse symbolic 4x4 matrix determinant
91 m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d);
92 det = m4.determinant();
94 clog << "determinant of 4x4 matrix " << m4
95 << " erroneously returned " << det << endl;
99 // check characteristic polynomial
100 m3.set(0,0,a).set(0,1,-2).set(0,2,2);
101 m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
102 m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
103 ex p = m3.charpoly(a);
105 clog << "charpoly of 3x3 matrix " << m3
106 << " erroneously returned " << p << endl;
113 static unsigned matrix_invert1(void)
120 matrix m_i = m.inverse();
122 if (m_i(0,0) != pow(a,-1)) {
123 clog << "inversion of 1x1 matrix " << m
124 << " erroneously returned " << m_i << endl;
131 static unsigned matrix_invert2(void)
135 symbol a("a"), b("b"), c("c"), d("d");
136 m.set(0,0,a).set(0,1,b);
137 m.set(1,0,c).set(1,1,d);
138 matrix m_i = m.inverse();
139 ex det = m.determinant();
141 if ((normal(m_i(0,0)*det) != d) ||
142 (normal(m_i(0,1)*det) != -b) ||
143 (normal(m_i(1,0)*det) != -c) ||
144 (normal(m_i(1,1)*det) != a)) {
145 clog << "inversion of 2x2 matrix " << m
146 << " erroneously returned " << m_i << endl;
153 static unsigned matrix_invert3(void)
157 symbol a("a"), b("b"), c("c");
158 symbol d("d"), e("e"), f("f");
159 symbol g("g"), h("h"), i("i");
160 m.set(0,0,a).set(0,1,b).set(0,2,c);
161 m.set(1,0,d).set(1,1,e).set(1,2,f);
162 m.set(2,0,g).set(2,1,h).set(2,2,i);
163 matrix m_i = m.inverse();
164 ex det = m.determinant();
166 if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
167 (normal(m_i(0,1)*det) != (c*h-b*i)) ||
168 (normal(m_i(0,2)*det) != (b*f-c*e)) ||
169 (normal(m_i(1,0)*det) != (f*g-d*i)) ||
170 (normal(m_i(1,1)*det) != (a*i-c*g)) ||
171 (normal(m_i(1,2)*det) != (c*d-a*f)) ||
172 (normal(m_i(2,0)*det) != (d*h-e*g)) ||
173 (normal(m_i(2,1)*det) != (b*g-a*h)) ||
174 (normal(m_i(2,2)*det) != (a*e-b*d))) {
175 clog << "inversion of 3x3 matrix " << m
176 << " erroneously returned " << m_i << endl;
183 static unsigned matrix_solve2(void)
185 // check the solution of the multiple system A*X = B:
186 // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
187 // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ]
188 // [ a -2 2 ] [ x2 y2 ] [ a 4 ]
191 symbol x0("x0"), x1("x1"), x2("x2");
192 symbol y0("y0"), y1("y1"), y2("y2");
194 A.set(0,0,1).set(0,1,2).set(0,2,-1);
195 A.set(1,0,1).set(1,1,4).set(1,2,-2);
196 A.set(2,0,a).set(2,1,-2).set(2,2,2);
198 B.set(0,0,4).set(1,0,7).set(2,0,a);
199 B.set(0,1,0).set(1,1,0).set(2,1,4);
201 X.set(0,0,x0).set(1,0,x1).set(2,0,x2);
202 X.set(0,1,y0).set(1,1,y1).set(2,1,y2);
204 cmp.set(0,0,1).set(1,0,3).set(2,0,3);
205 cmp.set(0,1,0).set(1,1,2).set(2,1,4);
206 matrix sol(A.solve(X, B));
207 for (unsigned ro=0; ro<3; ++ro)
208 for (unsigned co=0; co<2; ++co)
209 if (cmp(ro,co) != sol(ro,co))
212 clog << "Solving " << A << " * " << X << " == " << B << endl
213 << "erroneously returned " << sol << endl;
219 static unsigned matrix_evalm(void)
234 ex e = ((S + T) * (S + 2*T));
236 if (!f.is_equal(R)) {
237 clog << "Evaluating " << e << " erroneously returned " << f << " instead of " << R << endl;
244 static unsigned matrix_misc(void)
248 symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
249 m1.set(0,0,a).set(0,1,b);
250 m1.set(1,0,c).set(1,1,d);
253 // check a simple trace
254 if (tr.compare(a+d)) {
255 clog << "trace of 2x2 matrix " << m1
256 << " erroneously returned " << tr << endl;
260 // and two simple transpositions
261 matrix m2 = transpose(m1);
262 if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
263 clog << "transpose of 2x2 matrix " << m1
264 << " erroneously returned " << m2 << endl;
268 m3.set(0,0,a).set(0,1,b);
269 m3.set(1,0,c).set(1,1,d);
270 m3.set(2,0,e).set(2,1,f);
271 if (transpose(transpose(m3)) != m3) {
272 clog << "transposing 3x2 matrix " << m3 << " twice"
273 << " erroneously returned " << transpose(transpose(m3)) << endl;
277 // produce a runtime-error by inverting a singular matrix and catch it
283 } catch (std::runtime_error err) {
287 cerr << "singular 2x2 matrix " << m4
288 << " erroneously inverted to " << m5 << endl;
295 unsigned exam_matrices(void)
299 cout << "examining symbolic matrix manipulations" << flush;
300 clog << "----------symbolic matrix manipulations:" << endl;
302 result += matrix_determinants(); cout << '.' << flush;
303 result += matrix_invert1(); cout << '.' << flush;
304 result += matrix_invert2(); cout << '.' << flush;
305 result += matrix_invert3(); cout << '.' << flush;
306 result += matrix_solve2(); cout << '.' << flush;
307 result += matrix_evalm(); cout << "." << flush;
308 result += matrix_misc(); cout << '.' << flush;
311 cout << " passed " << endl;
312 clog << "(no output)" << endl;
314 cout << " failed " << endl;