1 /** @file exam_matrices.cpp
3 * Here we examine manipulations on GiNaC's symbolic matrices. */
6 * GiNaC Copyright (C) 1999-2000 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
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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.
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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,numeric(1));
78 m2.set(1,0,b/(a-b)).set(1,1,numeric(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_misc(void)
187 symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
188 m1.set(0,0,a).set(0,1,b);
189 m1.set(1,0,c).set(1,1,d);
192 // check a simple trace
193 if (tr.compare(a+d)) {
194 clog << "trace of 2x2 matrix " << m1
195 << " erroneously returned " << tr << endl;
199 // and two simple transpositions
200 matrix m2 = transpose(m1);
201 if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
202 clog << "transpose of 2x2 matrix " << m1
203 << " erroneously returned " << m2 << endl;
207 m3.set(0,0,a).set(0,1,b);
208 m3.set(1,0,c).set(1,1,d);
209 m3.set(2,0,e).set(2,1,f);
210 if (transpose(transpose(m3)) != m3) {
211 clog << "transposing 3x2 matrix " << m3 << " twice"
212 << " erroneously returned " << transpose(transpose(m3)) << endl;
216 // produce a runtime-error by inverting a singular matrix and catch it
222 } catch (std::runtime_error err) {
226 cerr << "singular 2x2 matrix " << m4
227 << " erroneously inverted to " << m5 << endl;
234 unsigned exam_matrices(void)
238 cout << "examining symbolic matrix manipulations" << flush;
239 clog << "----------symbolic matrix manipulations:" << endl;
241 result += matrix_determinants(); cout << '.' << flush;
242 result += matrix_invert1(); cout << '.' << flush;
243 result += matrix_invert2(); cout << '.' << flush;
244 result += matrix_invert3(); cout << '.' << flush;
245 result += matrix_misc(); cout << '.' << flush;
248 cout << " passed " << endl;
249 clog << "(no output)" << endl;
251 cout << " failed " << endl;