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
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
|
#include "match.h"
#include <string.h>
#include <stdio.h>
/**
* MATLAB implementation of the hungarian algorithm (2008)
*
* modified by Henrik Rydberg (2008)
*/
const float BIG_VALUE = 1e20;
typedef unsigned short col_t;
#define GETBIT2(m, row, col) ((m[col]>>(row))&1U)
#define SETBIT2(m, row, col) (m[col]|=(1U<<(row)))
#define CLEARBIT2(m, row, col) (m[col]&=~(1U<<(row)))
/********************************************************/
static void buildixvector(int *ix, col_t *mstar, int nrows, int ncols)
{
int row, col;
for (row = 0; row < nrows; row++) {
for (col = 0; col < ncols; col++) {
if (GETBIT2(mstar, row, col)) {
ix[row] = col;
break;
}
}
}
}
/********************************************************/
static void step2a(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin);
static void step2b(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin);
static void step3 (int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin);
static void step4 (int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin, int row, int col);
static void step5 (int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin);
static void ixoptimal(int *ix, float *mdist, int nrows, int ncols)
{
float *mdistTemp, *mdistEnd, *columnEnd, value, minValue;
int nelem, dmin, row, col;
col_t ccol,crow, mstar[DIM_FINGER],mprime[DIM_FINGER],nmstar[DIM_FINGER];
ccol = crow = 0;
memset(mstar, 0, sizeof(mstar));
memset(mprime, 0, sizeof(mprime));
memset(nmstar, 0, sizeof(nmstar));
/* initialization */
for(row=0; row<nrows; row++)
ix[row] = -1;
nelem = nrows * ncols;
mdistEnd = mdist + nelem;
/* preliminary steps */
if(nrows <= ncols) {
dmin = nrows;
for(row=0; row<nrows; row++) {
/* find the smallest element in the row */
mdistTemp = mdist + row;
minValue = *mdistTemp;
mdistTemp += nrows;
while(mdistTemp < mdistEnd) {
value = *mdistTemp;
if(value < minValue)
minValue = value;
mdistTemp += nrows;
}
/* subtract the smallest element from each element of the row */
mdistTemp = mdist + row;
while(mdistTemp < mdistEnd) {
*mdistTemp -= minValue;
mdistTemp += nrows;
}
}
/* Steps 1 and 2a */
for(row=0; row<nrows; row++)
for(col=0; col<ncols; col++)
if(mdist[row + nrows*col] == 0)
if(!GETBIT(ccol, col)) {
SETBIT2(mstar, row, col);
SETBIT(ccol, col);
break;
}
}
else /* if(nrows > ncols) */
{
dmin = ncols;
for(col=0; col<ncols; col++)
{
/* find the smallest element in the column */
mdistTemp = mdist + nrows*col;
columnEnd = mdistTemp + nrows;
minValue = *mdistTemp++;
while(mdistTemp < columnEnd)
{
value = *mdistTemp++;
if(value < minValue)
minValue = value;
}
/* subtract the smallest element from each element of the column */
mdistTemp = mdist + nrows*col;
while(mdistTemp < columnEnd)
*mdistTemp++ -= minValue;
}
/* Steps 1 and 2a */
for(col=0; col<ncols; col++)
for(row=0; row<nrows; row++)
if(mdist[row + nrows*col] == 0)
if(!GETBIT(crow, row))
{
SETBIT2(mstar, row, col);
SETBIT(ccol, col);
SETBIT(crow, row);
break;
}
for(row=0; row<nrows; row++)
CLEARBIT(crow, row);
}
/* move to step 2b */
step2b(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
/********************************************************/
static void step2a(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin)
{
int col, row;
/* cover every column containing a starred zero */
for(col=0; col<ncols; col++) {
for(row=col;row<nrows;row++) {
if(GETBIT2(mstar, row, col)) {
SETBIT(ccol, col);
break;
}
}
}
/* move to step 3 */
step2b(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
/********************************************************/
static void step2b(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin)
{
int col, ncc;
/* count covered columns */
ncc = 0;
for(col=0; col<ncols; col++)
if(GETBIT(ccol, col))
ncc++;
if(ncc == dmin)
{
/* algorithm finished */
buildixvector(ix, mstar, nrows, ncols);
}
else
{
/* move to step 3 */
step3(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
}
/********************************************************/
static void step3(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin)
{
bool zerosFound;
int row, col, cstar;
zerosFound = 1;
while(zerosFound)
{
zerosFound = 0;
for(col=0; col<ncols; col++)
if(!GETBIT(ccol,col))
for(row=0; row<nrows; row++)
if((!GETBIT(crow,row)) && (mdist[row + nrows*col] == 0))
{
/* prime zero */
SETBIT2(mprime, row, col);
/* find starred zero in current row */
for(cstar=0; cstar<ncols; cstar++)
if(GETBIT2(mstar, row, cstar))
break;
if(cstar == ncols) /* no starred zero found */
{
/* move to step 4 */
step4(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin, row, col);
return;
}
else
{
SETBIT(crow, row);
CLEARBIT(ccol,cstar);
zerosFound = 1;
break;
}
}
}
/* move to step 5 */
step5(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
/********************************************************/
static void step4(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin, int row, int col)
{
int n, rstar, cstar, primeRow, primeCol;
int nelem = nrows*ncols;
/* generate temporary copy of mstar */
for(n=0; n<nelem; n++)
nmstar[n] = mstar[n];
/* star current zero */
SETBIT2(nmstar, row, col);
/* find starred zero in current column */
cstar = col;
for(rstar=0; rstar<nrows; rstar++)
if(GETBIT2(mstar, rstar, cstar))
break;
while(rstar<nrows)
{
/* unstar the starred zero */
CLEARBIT2(nmstar, rstar, cstar);
/* find primed zero in current row */
primeRow = rstar;
for(primeCol=0; primeCol<ncols; primeCol++)
if(GETBIT2(mprime, primeRow, primeCol))
break;
/* star the primed zero */
SETBIT2(nmstar, primeRow, primeCol);
/* find starred zero in current column */
cstar = primeCol;
for(rstar=0; rstar<nrows; rstar++)
if(GETBIT2(mstar, rstar, cstar))
break;
}
/* use temporary copy as new mstar */
/* delete all primes, uncover all rows */
for(n=0; n<nelem; n++)
{
mprime[n] = 0;
mstar[n] = nmstar[n];
}
for(n=0; n<nrows; n++)
CLEARBIT(crow, n);
/* move to step 2a */
step2a(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
/********************************************************/
static void step5(int *ix, float *mdist, col_t *mstar, col_t *nmstar, col_t *mprime, col_t ccol, col_t crow, int nrows, int ncols, int dmin)
{
float h, value;
int row, col;
/* find smallest uncovered element h */
h = BIG_VALUE;
for(row=0; row<nrows; row++)
if(!GETBIT(crow, row))
for(col=0; col<ncols; col++)
if(!GETBIT(ccol,col))
{
value = mdist[row + nrows*col];
if(value < h)
h = value;
}
/* add h to each covered row */
for(row=0; row<nrows; row++)
if(GETBIT(crow, row))
for(col=0; col<ncols; col++)
mdist[row + nrows*col] += h;
/* subtract h from each uncovered column */
for(col=0; col<ncols; col++)
if(!GETBIT(ccol,col))
for(row=0; row<nrows; row++)
mdist[row + nrows*col] -= h;
/* move to step 3 */
step3(ix, mdist, mstar, nmstar, mprime, ccol, crow, nrows, ncols, dmin);
}
////////////////////////////////////////////////////////
void match_fingers(int ix[DIM_FINGER], float A[DIM2_FINGER], int nrow, int ncol)
{
ixoptimal(ix, A, nrow, ncol);
}
////////////////////////////////////////////////////////
|