1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
|
//:
// \file
// \author Tim Cootes
// \date 25-Apr-2001
// \brief Various specialised versions of matrix product operations
#include "mbl_matrix_products.h"
#include <vnl/vnl_vector.h>
#include <vnl/vnl_matrix.h>
#include <vcl_cassert.h>
#include <vcl_cstdlib.h> // for vcl_abort()
#include <vcl_iostream.h>
//=======================================================================
//: Compute product AB = A * B
//=======================================================================
void mbl_matrix_product(vnl_matrix<double>& AB, const vnl_matrix<double>& A,
const vnl_matrix<double>& B)
{
unsigned int nr1 = A.rows();
unsigned int nc1 = A.cols();
unsigned int nr2 = B.rows();
unsigned int nc2 = B.cols();
if ( nr2 != nc1 )
{
vcl_cerr<<"Product : B.rows != A.cols\n";
vcl_abort() ;
}
if ( (AB.rows()!=nr1) || (AB.cols()!= nc2) )
AB.set_size( nr1, nc2 ) ;
const double *const * AData = A.data_array();
const double *const * BData = B.data_array();
double ** RData = AB.data_array();
// Zero the elements of AB
AB.fill(0);
for (unsigned int r=0; r < nr1; ++r)
{
const double* A_row = AData[r];
double* R_row = RData[r]-1;
for (unsigned int c=0; c < nc1 ; ++c )
{
double a = A_row[c];
if (a==0.0) continue;
const double* B_row = BData[c]-1;
int i = nc2+1;
while (--i)
{
R_row[i] += a * B_row[i];
}
}
}
}
//=======================================================================
//: Compute product ABt = A * B.transpose()
//=======================================================================
void mbl_matrix_product_a_bt(vnl_matrix<double>& ABt,
const vnl_matrix<double>& A,
const vnl_matrix<double>& B)
{
int nc1 = A.columns();
#ifndef NDEBUG
int nc2 = B.columns();
if ( nc2 != nc1 )
{
vcl_cerr<<"mbl_matrix_product_a_bt : B.columns != A.columns\n";
vcl_abort();
}
#endif //!NDEBUG
mbl_matrix_product_a_bt(ABt,A,B,nc1);
}
//=======================================================================
//: Compute product ABt = A * B.transpose(), using only nc cols of A and B
//=======================================================================
void mbl_matrix_product_a_bt(vnl_matrix<double>& ABt,
const vnl_matrix<double>& A,
const vnl_matrix<double>& B,
int nc)
{
unsigned int nr1 = A.rows();
unsigned int nr2 = B.rows();
assert(A.columns()>=(unsigned int)nc);
assert(B.columns()>=(unsigned int)nc);
if ( (ABt.rows()!=nr1) || (ABt.columns()!= nr2) )
ABt.set_size( nr1, nr2 ) ;
double const *const * A_data = A.data_array();
double const *const * B_data = B.data_array();
double ** R_data = ABt.data_array();
for (unsigned int r=0;r<nr1;++r)
{
const double* A_row = A_data[r];
double* R_row = R_data[r];
for (unsigned int c=0;c<nr2;++c)
{
const double* B_row = B_data[c];
R_row[c] = vnl_c_vector<double>::dot_product(A_row,B_row,nc);
}
}
}
//=======================================================================
//: Compute product AtB = A.transpose() * B
//=======================================================================
void mbl_matrix_product_at_b(vnl_matrix<double>& AtB,
const vnl_matrix<double>& A,
const vnl_matrix<double>& B)
{
mbl_matrix_product_at_b(AtB,A,B,A.columns());
}
//=======================================================================
//: Compute AAt = A * A.transpose(), using only first nr x nc partition of A
// Uses symmetry of result to improve speed
//=======================================================================
void mbl_matrix_product_a_at(vnl_matrix<double>& AAt,
const vnl_matrix<double>& A,
unsigned nr, unsigned nc)
{
assert(nr<=A.rows());
assert(nc<=A.columns());
if ( (AAt.rows()!=nr) || (AAt.columns()!= nr) )
AAt.set_size( nr, nr ) ;
double const *const * A_data = A.data_array();
double ** R_data = AAt.data_array();
// Fill in upper triangle of symmetric matrix
for (unsigned int r=0;r<nr;++r)
{
const double* A_row = A_data[r];
double* R_row = R_data[r];
for (unsigned int c=r;c<nr;++c)
{
const double* B_row = A_data[c];
R_row[c] = vnl_c_vector<double>::dot_product(A_row,B_row,nc);
}
}
// Copy upper triangle to lower triangle
for (unsigned int r=1;r<nr;++r)
for (unsigned int c=0;c<r;++c)
AAt(r,c)=AAt(c,r);
}
//=======================================================================
//: Compute product AAt = A * A.transpose()
// Uses symmetry of result to be approx twice as fast as
// mbl_matrix_product_a_bt(AAt,A,A)
//=======================================================================
void mbl_matrix_product_a_at(vnl_matrix<double>& AAt,
const vnl_matrix<double>& A)
{
mbl_matrix_product_a_at(AAt,A,A.rows(),A.columns());
}
//=======================================================================
//: Compute product AtB = A.transpose() * B, using nc_a cols of A
//=======================================================================
void mbl_matrix_product_at_b(vnl_matrix<double>& AtB,
const vnl_matrix<double>& A,
const vnl_matrix<double>& B,
int nc_a)
{
assert(nc_a >= 0 && A.columns()>=(unsigned int)nc_a);
unsigned int nr1 = A.rows();
unsigned int nr2 = B.rows();
unsigned int nc2 = B.columns();
if ( nr2 != nr1 )
{
vcl_cerr<<"TC_ProductAtB : B.rows != A.rows\n";
vcl_abort();
}
if ( (AtB.rows()!=(unsigned int)nc_a) || (AtB.columns()!= nc2) )
AtB.set_size( nc_a, nc2 ) ;
double const *const * A_data = A.data_array();
double const *const * B_data = B.data_array();
double ** R_data = AtB.data_array()-1;
AtB.fill(0);
for (unsigned int r1 = 0; r1<nr1; ++r1)
{
const double* A_row = A_data[r1]-1;
const double* B_row = B_data[r1]-1;
double a;
int c1 = nc_a+1;
while (--c1)
{
double *R_row = R_data[c1]-1;
a = A_row[c1];
int c2 = nc2+1;
while (--c2)
{
R_row[c2] +=a*B_row[c2];
}
}
}
}
//=======================================================================
//: Compute product AtA = A.transpose() * A using nc cols of A
//=======================================================================
void mbl_matrix_product_at_a(vnl_matrix<double>& AtA,
const vnl_matrix<double>& A,
unsigned nc)
{
assert(A.columns()>=nc);
unsigned int nr = A.rows();
if ( AtA.rows()!=nr || (AtA.columns()!= nc) )
AtA.set_size( nc, nc ) ;
double const *const * A_data = A.data_array();
double ** R_data = AtA.data_array()-1;
AtA.fill(0);
for (unsigned int r = 0; r<nr; ++r)
{
const double* A_row = A_data[r]-1;
double a;
int c1 = nc+1;
while (--c1)
{
double *R_row = R_data[c1]-1;
a = A_row[c1];
int c2 = nc+1;
while (--c2)
{
R_row[c2] +=a*A_row[c2];
}
}
}
}
//=======================================================================
//: Compute product AtA = A.transpose() * A
//=======================================================================
void mbl_matrix_product_at_a(vnl_matrix<double>& AtA,
const vnl_matrix<double>& A)
{
mbl_matrix_product_at_a(AtA,A,A.columns());
}
//: Returns ADB = A * D * B
// where D is diagonal with elements d
void mbl_matrix_product_adb(vnl_matrix<double>& ADB,
const vnl_matrix<double>& A,
const vnl_vector<double>& d,
const vnl_matrix<double>& B)
{
unsigned int nr1 = A.rows();
unsigned int nc1 = A.cols();
unsigned int nc2 = B.cols();
assert ( B.rows() == nc1 ); //Product : B.nrows != A.ncols
assert ( B.rows() == d.size() ); // Product : d.nelems != A.ncols
if ( (ADB.rows()!=nr1) || (ADB.cols()!= nc2) )
ADB.set_size( nr1, nc2 ) ;
const double * const* AData = A.data_array();
const double * const* BData = B.data_array();
const double * d_data = d.data_block();
double ** ADBdata = ADB.data_array();
ADB.fill(0);
for (unsigned int r=0; r < nr1; ++r)
{
const double* A_row = AData[r];
double* ADB_row = ADBdata[r]-1;
for (unsigned int c=0; c < nc1 ; ++c )
{
double ad = A_row[c] * d_data[c];
if (ad==0.0) continue;
const double* B_row = BData[c]-1;
int i = nc2+1;
while (--i)
{
ADB_row[i] += ad * B_row[i];
}
}
}
}
|
