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vnl_adjugate_fixed.h
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1// This is core/vnl/vnl_adjugate_fixed.h
2#ifndef vnl_adjugate_fixed_h_
3#define vnl_adjugate_fixed_h_
4//:
5// \file
6// \brief Calculates adjugate or cofactor matrix of a small vnl_matrix_fixed.
7// Code is only a small adaptation from Peter Vanroose's vnl_inverse.h
8// adjugate == inverse/det
9// cofactor == adjugate^T
10// \author Floris Berendsen
11// \date 18 April 2013
12//
13// \verbatim
14// Code is only a small adaptation from Peter Vanroose's vnl_inverse.h
15// \endverbatim
16
17#include <vnl/vnl_matrix_fixed.h>
18#include <vnl/vnl_vector_fixed.h>
19#include <vnl/vnl_matrix.h>
20#include <vnl/vnl_det.h>
21
22//: Calculates adjugate of a small vnl_matrix_fixed (not using svd)
23// This allows you to write e.g.
24//
25// x = vnl_adjugate(A) * b;
26//
27// Note that this function is inlined (except for the call to vnl_det()),
28// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
29// since that one is using svd.
30//
31// \relatesalso vnl_matrix_fixed
32
33template <class T>
34vnl_matrix_fixed<T,1,1> vnl_adjugate(vnl_matrix_fixed<T,1,1> const& m)
35{
36 return vnl_matrix_fixed<T,1,1>(m(0,0));
37}
38
39//: Calculates adjugate of a small vnl_matrix_fixed (not using svd)
40// This allows you to write e.g.
41//
42// x = vnl_adjugate(A) * b;
43//
44// Note that this function is inlined (except for the call to vnl_det()),
45// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
46// since that one is using svd.
47//
48// \relatesalso vnl_matrix_fixed
49
50template <class T>
51vnl_matrix_fixed<T,2,2> vnl_adjugate(vnl_matrix_fixed<T,2,2> const& m)
52{
53 T d[4];
54 d[0] = m(1,1); d[1] = - m(0,1);
55 d[3] = m(0,0); d[2] = - m(1,0);
56 return vnl_matrix_fixed<T,2,2>(d);
57}
58
59//: Calculates adjugate of a small vnl_matrix_fixed (not using svd)
60// This allows you to write e.g.
61//
62// x = vnl_adjugate_fixed(A) * b;
63//
64// Note that this function is inlined (except for the call to vnl_det()),
65// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
66// since that one is using svd.
67//
68// \relatesalso vnl_matrix_fixed
69
70template <class T>
71vnl_matrix_fixed<T,3,3> vnl_adjugate(vnl_matrix_fixed<T,3,3> const& m)
72{
73 T d[9];
74 d[0] = (m(1,1)*m(2,2)-m(1,2)*m(2,1));
75 d[1] = (m(2,1)*m(0,2)-m(2,2)*m(0,1));
76 d[2] = (m(0,1)*m(1,2)-m(0,2)*m(1,1));
77 d[3] = (m(1,2)*m(2,0)-m(1,0)*m(2,2));
78 d[4] = (m(0,0)*m(2,2)-m(0,2)*m(2,0));
79 d[5] = (m(1,0)*m(0,2)-m(1,2)*m(0,0));
80 d[6] = (m(1,0)*m(2,1)-m(1,1)*m(2,0));
81 d[7] = (m(0,1)*m(2,0)-m(0,0)*m(2,1));
82 d[8] = (m(0,0)*m(1,1)-m(0,1)*m(1,0));
83 return vnl_matrix_fixed<T,3,3>(d);
84}
85
86//: Calculates adjugate_fixed of a small vnl_matrix_fixed (not using svd)
87// This allows you to write e.g.
88//
89// x = vnl_adjugate_fixed(A) * b;
90//
91// Note that this function is inlined (except for the call to vnl_det()),
92// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
93// since that one is using svd.
94//
95// \relatesalso vnl_matrix_fixed
96
97template <class T>
98vnl_matrix_fixed<T,4,4> vnl_adjugate(vnl_matrix_fixed<T,4,4> const& m)
99{
100 T d[16];
101 d[0] = m(1,1)*m(2,2)*m(3,3) - m(1,1)*m(2,3)*m(3,2) - m(2,1)*m(1,2)*m(3,3)
102 + m(2,1)*m(1,3)*m(3,2) + m(3,1)*m(1,2)*m(2,3) - m(3,1)*m(1,3)*m(2,2);
103 d[1] = -m(0,1)*m(2,2)*m(3,3) + m(0,1)*m(2,3)*m(3,2) + m(2,1)*m(0,2)*m(3,3)
104 - m(2,1)*m(0,3)*m(3,2) - m(3,1)*m(0,2)*m(2,3) + m(3,1)*m(0,3)*m(2,2);
105 d[2] = m(0,1)*m(1,2)*m(3,3) - m(0,1)*m(1,3)*m(3,2) - m(1,1)*m(0,2)*m(3,3)
106 + m(1,1)*m(0,3)*m(3,2) + m(3,1)*m(0,2)*m(1,3) - m(3,1)*m(0,3)*m(1,2);
107 d[3] = -m(0,1)*m(1,2)*m(2,3) + m(0,1)*m(1,3)*m(2,2) + m(1,1)*m(0,2)*m(2,3)
108 - m(1,1)*m(0,3)*m(2,2) - m(2,1)*m(0,2)*m(1,3) + m(2,1)*m(0,3)*m(1,2);
109 d[4] = -m(1,0)*m(2,2)*m(3,3) + m(1,0)*m(2,3)*m(3,2) + m(2,0)*m(1,2)*m(3,3)
110 - m(2,0)*m(1,3)*m(3,2) - m(3,0)*m(1,2)*m(2,3) + m(3,0)*m(1,3)*m(2,2);
111 d[5] = m(0,0)*m(2,2)*m(3,3) - m(0,0)*m(2,3)*m(3,2) - m(2,0)*m(0,2)*m(3,3)
112 + m(2,0)*m(0,3)*m(3,2) + m(3,0)*m(0,2)*m(2,3) - m(3,0)*m(0,3)*m(2,2);
113 d[6] = -m(0,0)*m(1,2)*m(3,3) + m(0,0)*m(1,3)*m(3,2) + m(1,0)*m(0,2)*m(3,3)
114 - m(1,0)*m(0,3)*m(3,2) - m(3,0)*m(0,2)*m(1,3) + m(3,0)*m(0,3)*m(1,2);
115 d[7] = m(0,0)*m(1,2)*m(2,3) - m(0,0)*m(1,3)*m(2,2) - m(1,0)*m(0,2)*m(2,3)
116 + m(1,0)*m(0,3)*m(2,2) + m(2,0)*m(0,2)*m(1,3) - m(2,0)*m(0,3)*m(1,2);
117 d[8] = m(1,0)*m(2,1)*m(3,3) - m(1,0)*m(2,3)*m(3,1) - m(2,0)*m(1,1)*m(3,3)
118 + m(2,0)*m(1,3)*m(3,1) + m(3,0)*m(1,1)*m(2,3) - m(3,0)*m(1,3)*m(2,1);
119 d[9] = -m(0,0)*m(2,1)*m(3,3) + m(0,0)*m(2,3)*m(3,1) + m(2,0)*m(0,1)*m(3,3)
120 - m(2,0)*m(0,3)*m(3,1) - m(3,0)*m(0,1)*m(2,3) + m(3,0)*m(0,3)*m(2,1);
121 d[10]= m(0,0)*m(1,1)*m(3,3) - m(0,0)*m(1,3)*m(3,1) - m(1,0)*m(0,1)*m(3,3)
122 + m(1,0)*m(0,3)*m(3,1) + m(3,0)*m(0,1)*m(1,3) - m(3,0)*m(0,3)*m(1,1);
123 d[11]= -m(0,0)*m(1,1)*m(2,3) + m(0,0)*m(1,3)*m(2,1) + m(1,0)*m(0,1)*m(2,3)
124 - m(1,0)*m(0,3)*m(2,1) - m(2,0)*m(0,1)*m(1,3) + m(2,0)*m(0,3)*m(1,1);
125 d[12]= -m(1,0)*m(2,1)*m(3,2) + m(1,0)*m(2,2)*m(3,1) + m(2,0)*m(1,1)*m(3,2)
126 - m(2,0)*m(1,2)*m(3,1) - m(3,0)*m(1,1)*m(2,2) + m(3,0)*m(1,2)*m(2,1);
127 d[13]= m(0,0)*m(2,1)*m(3,2) - m(0,0)*m(2,2)*m(3,1) - m(2,0)*m(0,1)*m(3,2)
128 + m(2,0)*m(0,2)*m(3,1) + m(3,0)*m(0,1)*m(2,2) - m(3,0)*m(0,2)*m(2,1);
129 d[14]= -m(0,0)*m(1,1)*m(3,2) + m(0,0)*m(1,2)*m(3,1) + m(1,0)*m(0,1)*m(3,2)
130 - m(1,0)*m(0,2)*m(3,1) - m(3,0)*m(0,1)*m(1,2) + m(3,0)*m(0,2)*m(1,1);
131 d[15]= m(0,0)*m(1,1)*m(2,2) - m(0,0)*m(1,2)*m(2,1) - m(1,0)*m(0,1)*m(2,2)
132 + m(1,0)*m(0,2)*m(2,1) + m(2,0)*m(0,1)*m(1,2) - m(2,0)*m(0,2)*m(1,1);
133 return vnl_matrix_fixed<T,4,4>(d);
134}
135
136//: Calculates adjugate_fixed of a small vnl_matrix_fixed (not using svd)
137// This allows you to write e.g.
138//
139// x = vnl_adjugate_fixed(A) * b;
140//
141// Note that this function is inlined (except for the call to vnl_det()),
142// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
143// since that one is using svd.
144//
145// \relatesalso vnl_matrix
146
147template <class T>
148vnl_matrix<T> vnl_adjugate_asfixed(vnl_matrix<T> const& m)
149{
150 assert(m.rows() == m.columns());
151 assert(m.rows() <= 4);
152 if (m.rows() == 1)
153 return vnl_matrix<T>(1,1, T(1)/m(0,0));
154 else if (m.rows() == 2)
155 return vnl_adjugate(vnl_matrix_fixed<T,2,2>(m)).as_ref();
156 else if (m.rows() == 3)
157 return vnl_adjugate(vnl_matrix_fixed<T,3,3>(m)).as_ref();
158 else
159 return vnl_adjugate(vnl_matrix_fixed<T,4,4>(m)).as_ref();
160}
161
162//: Calculates transpose of the adjugate_fixed of a small vnl_matrix_fixed (not using svd)
163// This allows you to write e.g.
164//
165// x = vnl_cofactor(A) * b;
166//
167// Note that this function is inlined (except for the call to vnl_det()),
168// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
169// since that one is using svd. This is also faster than using
170//
171// x = vnl_adjugate_fixed(A).transpose() * b;
172//
173// \relatesalso vnl_matrix_fixed
174
175template <class T>
176vnl_matrix_fixed<T,1,1> vnl_cofactor(vnl_matrix_fixed<T,1,1> const& m)
177{
178 return vnl_matrix_fixed<T,1,1>(T(1)/m(0,0));
179}
180
181//: Calculates transpose of the adjugate_fixed of a small vnl_matrix_fixed (not using svd)
182// This allows you to write e.g.
183//
184// x = vnl_cofactor(A) * b;
185//
186// Note that this function is inlined (except for the call to vnl_det()),
187// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
188// since that one is using svd. This is also faster than using
189//
190// x = vnl_adjugate_fixed(A).transpose() * b;
191//
192// \relatesalso vnl_matrix_fixed
193
194template <class T>
195vnl_matrix_fixed<T,2,2> vnl_cofactor(vnl_matrix_fixed<T,2,2> const& m)
196{
197
198 T d[4];
199 d[0] = m(1,1); d[2] = - m(0,1);
200 d[3] = m(0,0); d[1] = - m(1,0);
201 return vnl_matrix_fixed<T,2,2>(d);
202}
203
204//: Calculates transpose of the adjugate_fixed of a small vnl_matrix_fixed (not using svd)
205// This allows you to write e.g.
206//
207// x = vnl_cofactor(A) * b;
208//
209// Note that this function is inlined (except for the call to vnl_det()),
210// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
211// since that one is using svd. This is also faster than using
212//
213// x = vnl_adjugate_fixed(A).transpose() * b;
214//
215// \relatesalso vnl_matrix_fixed
216
217template <class T>
218vnl_matrix_fixed<T,3,3> vnl_cofactor(vnl_matrix_fixed<T,3,3> const& m)
219{
220
221 T d[9];
222 d[0] = (m(1,1)*m(2,2)-m(1,2)*m(2,1));
223 d[3] = (m(2,1)*m(0,2)-m(2,2)*m(0,1));
224 d[6] = (m(0,1)*m(1,2)-m(0,2)*m(1,1));
225 d[1] = (m(1,2)*m(2,0)-m(1,0)*m(2,2));
226 d[4] = (m(0,0)*m(2,2)-m(0,2)*m(2,0));
227 d[7] = (m(1,0)*m(0,2)-m(1,2)*m(0,0));
228 d[2] = (m(1,0)*m(2,1)-m(1,1)*m(2,0));
229 d[5] = (m(0,1)*m(2,0)-m(0,0)*m(2,1));
230 d[8] = (m(0,0)*m(1,1)-m(0,1)*m(1,0));
231 return vnl_matrix_fixed<T,3,3>(d);
232}
233
234//: Calculates transpose of the adjugate_fixed of a small vnl_matrix_fixed (not using svd)
235// This allows you to write e.g.
236//
237// x = vnl_cofactor(A) * b;
238//
239// Note that this function is inlined (except for the call to vnl_det()),
240// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
241// since that one is using svd. This is also faster than using
242//
243// x = vnl_adjugate_fixed(A).transpose() * b;
244//
245// \relatesalso vnl_matrix_fixed
246
247template <class T>
248vnl_matrix_fixed<T,4,4> vnl_cofactor(vnl_matrix_fixed<T,4,4> const& m)
249{
250 T d[16];
251 d[0] = m(1,1)*m(2,2)*m(3,3) - m(1,1)*m(2,3)*m(3,2) - m(2,1)*m(1,2)*m(3,3)
252 + m(2,1)*m(1,3)*m(3,2) + m(3,1)*m(1,2)*m(2,3) - m(3,1)*m(1,3)*m(2,2);
253 d[4] = -m(0,1)*m(2,2)*m(3,3) + m(0,1)*m(2,3)*m(3,2) + m(2,1)*m(0,2)*m(3,3)
254 - m(2,1)*m(0,3)*m(3,2) - m(3,1)*m(0,2)*m(2,3) + m(3,1)*m(0,3)*m(2,2);
255 d[8] = m(0,1)*m(1,2)*m(3,3) - m(0,1)*m(1,3)*m(3,2) - m(1,1)*m(0,2)*m(3,3)
256 + m(1,1)*m(0,3)*m(3,2) + m(3,1)*m(0,2)*m(1,3) - m(3,1)*m(0,3)*m(1,2);
257 d[12]= -m(0,1)*m(1,2)*m(2,3) + m(0,1)*m(1,3)*m(2,2) + m(1,1)*m(0,2)*m(2,3)
258 - m(1,1)*m(0,3)*m(2,2) - m(2,1)*m(0,2)*m(1,3) + m(2,1)*m(0,3)*m(1,2);
259 d[1] = -m(1,0)*m(2,2)*m(3,3) + m(1,0)*m(2,3)*m(3,2) + m(2,0)*m(1,2)*m(3,3)
260 - m(2,0)*m(1,3)*m(3,2) - m(3,0)*m(1,2)*m(2,3) + m(3,0)*m(1,3)*m(2,2);
261 d[5] = m(0,0)*m(2,2)*m(3,3) - m(0,0)*m(2,3)*m(3,2) - m(2,0)*m(0,2)*m(3,3)
262 + m(2,0)*m(0,3)*m(3,2) + m(3,0)*m(0,2)*m(2,3) - m(3,0)*m(0,3)*m(2,2);
263 d[9] = -m(0,0)*m(1,2)*m(3,3) + m(0,0)*m(1,3)*m(3,2) + m(1,0)*m(0,2)*m(3,3)
264 - m(1,0)*m(0,3)*m(3,2) - m(3,0)*m(0,2)*m(1,3) + m(3,0)*m(0,3)*m(1,2);
265 d[13]= m(0,0)*m(1,2)*m(2,3) - m(0,0)*m(1,3)*m(2,2) - m(1,0)*m(0,2)*m(2,3)
266 + m(1,0)*m(0,3)*m(2,2) + m(2,0)*m(0,2)*m(1,3) - m(2,0)*m(0,3)*m(1,2);
267 d[2] = m(1,0)*m(2,1)*m(3,3) - m(1,0)*m(2,3)*m(3,1) - m(2,0)*m(1,1)*m(3,3)
268 + m(2,0)*m(1,3)*m(3,1) + m(3,0)*m(1,1)*m(2,3) - m(3,0)*m(1,3)*m(2,1);
269 d[6] = -m(0,0)*m(2,1)*m(3,3) + m(0,0)*m(2,3)*m(3,1) + m(2,0)*m(0,1)*m(3,3)
270 - m(2,0)*m(0,3)*m(3,1) - m(3,0)*m(0,1)*m(2,3) + m(3,0)*m(0,3)*m(2,1);
271 d[10]= m(0,0)*m(1,1)*m(3,3) - m(0,0)*m(1,3)*m(3,1) - m(1,0)*m(0,1)*m(3,3)
272 + m(1,0)*m(0,3)*m(3,1) + m(3,0)*m(0,1)*m(1,3) - m(3,0)*m(0,3)*m(1,1);
273 d[14]= -m(0,0)*m(1,1)*m(2,3) + m(0,0)*m(1,3)*m(2,1) + m(1,0)*m(0,1)*m(2,3)
274 - m(1,0)*m(0,3)*m(2,1) - m(2,0)*m(0,1)*m(1,3) + m(2,0)*m(0,3)*m(1,1);
275 d[3] = -m(1,0)*m(2,1)*m(3,2) + m(1,0)*m(2,2)*m(3,1) + m(2,0)*m(1,1)*m(3,2)
276 - m(2,0)*m(1,2)*m(3,1) - m(3,0)*m(1,1)*m(2,2) + m(3,0)*m(1,2)*m(2,1);
277 d[7] = m(0,0)*m(2,1)*m(3,2) - m(0,0)*m(2,2)*m(3,1) - m(2,0)*m(0,1)*m(3,2)
278 + m(2,0)*m(0,2)*m(3,1) + m(3,0)*m(0,1)*m(2,2) - m(3,0)*m(0,2)*m(2,1);
279 d[11]= -m(0,0)*m(1,1)*m(3,2) + m(0,0)*m(1,2)*m(3,1) + m(1,0)*m(0,1)*m(3,2)
280 - m(1,0)*m(0,2)*m(3,1) - m(3,0)*m(0,1)*m(1,2) + m(3,0)*m(0,2)*m(1,1);
281 d[15]= m(0,0)*m(1,1)*m(2,2) - m(0,0)*m(1,2)*m(2,1) - m(1,0)*m(0,1)*m(2,2)
282 + m(1,0)*m(0,2)*m(2,1) + m(2,0)*m(0,1)*m(1,2) - m(2,0)*m(0,2)*m(1,1);
283 return vnl_matrix_fixed<T,4,4>(d);
284}
285
286//: Calculates transpose of the adjugate_fixed of a small vnl_matrix_fixed (not using svd)
287// This allows you to write e.g.
288//
289// x = vnl_cofactor(A) * b;
290//
291// Note that this function is inlined (except for the call to vnl_det()),
292// which makes it much faster than the vnl_matrix_adjugate_fixed class in vnl/algo
293// since that one is using svd. This is also faster than using
294//
295// x = vnl_adjugate_fixed(A).transpose() * b;
296//
297// \relatesalso vnl_matrix
298
299template <class T>
300vnl_matrix<T> vnl_cofactor(vnl_matrix<T> const& m)
301{
302 assert(m.rows() == m.columns());
303 assert(m.rows() <= 4);
304 if (m.rows() == 1)
305 return vnl_matrix<T>(1,1, T(1)/m(0,0));
306 else if (m.rows() == 2)
307 return vnl_cofactor(vnl_matrix_fixed<T,2,2>(m)).as_ref();
308 else if (m.rows() == 3)
309 return vnl_cofactor(vnl_matrix_fixed<T,3,3>(m)).as_ref();
310 else
311 return vnl_cofactor(vnl_matrix_fixed<T,4,4>(m)).as_ref();
312}
313
314
315template <class T>
316vnl_vector_fixed<T,3> vnl_cofactor_row1(vnl_vector_fixed<T,3> const& row2, vnl_vector_fixed<T,3> const& row3)
317{
318 T d[3];
319 d[0] = (row2[1]*row3[2]-row2[2]*row3[1]);
320 d[1] = (row2[2]*row3[0]-row2[0]*row3[2]);
321 d[2] = (row2[0]*row3[1]-row2[1]*row3[0]);
322 return vnl_vector_fixed<T,3>(d);
323}
324
325#endif // vnl_adjugate_fixed_h_
vnl_cofactor_row1
vnl_vector_fixed< T, 3 > vnl_cofactor_row1(vnl_vector_fixed< T, 3 > const &row2, vnl_vector_fixed< T, 3 > const &row3)
Definition: vnl_adjugate_fixed.h:316
vnl_adjugate_asfixed
vnl_matrix< T > vnl_adjugate_asfixed(vnl_matrix< T > const &m)
Definition: vnl_adjugate_fixed.h:148
vnl_adjugate
vnl_matrix_fixed< T, 1, 1 > vnl_adjugate(vnl_matrix_fixed< T, 1, 1 > const &m)
Definition: vnl_adjugate_fixed.h:34
vnl_cofactor
vnl_matrix_fixed< T, 1, 1 > vnl_cofactor(vnl_matrix_fixed< T, 1, 1 > const &m)
Definition: vnl_adjugate_fixed.h:176

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