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().expand();
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(true);
81 clog << "determinant of 2x2 matrix " << m2
82 << " erroneously returned " << det << endl;
86 // check sparse symbolic 4x4 matrix determinant
87 m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d);
88 det = m4.determinant();
90 clog << "determinant of 4x4 matrix " << m4
91 << " erroneously returned " << det << endl;
95 // check characteristic polynomial
96 m3.set(0,0,a).set(0,1,-2).set(0,2,2);
97 m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
98 m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
99 ex p = m3.charpoly(a);
101 clog << "charpoly of 3x3 matrix " << m3
102 << " erroneously returned " << p << endl;
109 static unsigned matrix_invert1(void)
115 matrix m_i = m.inverse();
117 if (m_i(0,0) != pow(a,-1)) {
118 clog << "inversion of 1x1 matrix " << m
119 << " erroneously returned " << m_i << endl;
125 static unsigned matrix_invert2(void)
128 symbol a("a"), b("b"), c("c"), d("d");
129 m.set(0,0,a).set(0,1,b);
130 m.set(1,0,c).set(1,1,d);
131 matrix m_i = m.inverse();
132 ex det = m.determinant().expand();
134 if ((normal(m_i(0,0)*det) != d) ||
135 (normal(m_i(0,1)*det) != -b) ||
136 (normal(m_i(1,0)*det) != -c) ||
137 (normal(m_i(1,1)*det) != a)) {
138 clog << "inversion of 2x2 matrix " << m
139 << " erroneously returned " << m_i << endl;
145 static unsigned matrix_invert3(void)
148 symbol a("a"), b("b"), c("c");
149 symbol d("d"), e("e"), f("f");
150 symbol g("g"), h("h"), i("i");
151 m.set(0,0,a).set(0,1,b).set(0,2,c);
152 m.set(1,0,d).set(1,1,e).set(1,2,f);
153 m.set(2,0,g).set(2,1,h).set(2,2,i);
154 matrix m_i = m.inverse();
155 ex det = m.determinant().normal().expand();
157 if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
158 (normal(m_i(0,1)*det) != (c*h-b*i)) ||
159 (normal(m_i(0,2)*det) != (b*f-c*e)) ||
160 (normal(m_i(1,0)*det) != (f*g-d*i)) ||
161 (normal(m_i(1,1)*det) != (a*i-c*g)) ||
162 (normal(m_i(1,2)*det) != (c*d-a*f)) ||
163 (normal(m_i(2,0)*det) != (d*h-e*g)) ||
164 (normal(m_i(2,1)*det) != (b*g-a*h)) ||
165 (normal(m_i(2,2)*det) != (a*e-b*d))) {
166 clog << "inversion of 3x3 matrix " << m
167 << " erroneously returned " << m_i << endl;
173 static unsigned matrix_misc(void)
177 symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
178 m1.set(0,0,a).set(0,1,b);
179 m1.set(1,0,c).set(1,1,d);
182 // check a simple trace
183 if (tr.compare(a+d)) {
184 clog << "trace of 2x2 matrix " << m1
185 << " erroneously returned " << tr << endl;
189 // and two simple transpositions
190 matrix m2 = transpose(m1);
191 if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) {
192 clog << "transpose of 2x2 matrix " << m1
193 << " erroneously returned " << m2 << endl;
197 m3.set(0,0,a).set(0,1,b);
198 m3.set(1,0,c).set(1,1,d);
199 m3.set(2,0,e).set(2,1,f);
200 if (transpose(transpose(m3)) != m3) {
201 clog << "transposing 3x2 matrix " << m3 << " twice"
202 << " erroneously returned " << transpose(transpose(m3)) << endl;
206 // produce a runtime-error by inverting a singular matrix and catch it
212 } catch (std::runtime_error err) {
216 cerr << "singular 2x2 matrix " << m4
217 << " erroneously inverted to " << m5 << endl;
224 unsigned exam_matrices(void)
228 cout << "examining symbolic matrix manipulations" << flush;
229 clog << "----------symbolic matrix manipulations:" << endl;
231 result += matrix_determinants(); cout << '.' << flush;
232 result += matrix_invert1(); cout << '.' << flush;
233 result += matrix_invert2(); cout << '.' << flush;
234 result += matrix_invert3(); cout << '.' << flush;
235 result += matrix_misc(); cout << '.' << flush;
238 cout << " passed " << endl;
239 clog << "(no output)" << endl;
241 cout << " failed " << endl;