1 #include "cs.h"
2 /* find an augmenting path starting at column k and extend the match if found */
cs_augment(CS_INT k,const cs * A,CS_INT * jmatch,CS_INT * cheap,CS_INT * w,CS_INT * js,CS_INT * is,CS_INT * ps)3 static void cs_augment (CS_INT k, const cs *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w,
4 CS_INT *js, CS_INT *is, CS_INT *ps)
5 {
6 CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ;
7 js [0] = k ; /* start with just node k in jstack */
8 while (head >= 0)
9 {
10 /* --- Start (or continue) depth-first-search at node j ------------- */
11 j = js [head] ; /* get j from top of jstack */
12 if (w [j] != k) /* 1st time j visited for kth path */
13 {
14 w [j] = k ; /* mark j as visited for kth path */
15 for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
16 {
17 i = Ai [p] ; /* try a cheap assignment (i,j) */
18 found = (jmatch [i] == -1) ;
19 }
20 cheap [j] = p ; /* start here next time j is traversed*/
21 if (found)
22 {
23 is [head] = i ; /* column j matched with row i */
24 break ; /* end of augmenting path */
25 }
26 ps [head] = Ap [j] ; /* no cheap match: start dfs for j */
27 }
28 /* --- Depth-first-search of neighbors of j ------------------------- */
29 for (p = ps [head] ; p < Ap [j+1] ; p++)
30 {
31 i = Ai [p] ; /* consider row i */
32 if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */
33 ps [head] = p + 1 ; /* pause dfs of node j */
34 is [head] = i ; /* i will be matched with j if found */
35 js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */
36 break ;
37 }
38 if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */
39 } /* augment the match if path found: */
40 if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ;
41 }
42
43 /* find a maximum transveral */
cs_maxtrans(const cs * A,CS_INT seed)44 CS_INT *cs_maxtrans (const cs *A, CS_INT seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/
45 {
46 CS_INT i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is,
47 *ps, *Ai, *Cp, *jmatch, *imatch, *q ;
48 cs *C ;
49 if (!CS_CSC (A)) return (NULL) ; /* check inputs */
50 n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ;
51 w = jimatch = cs_calloc (m+n, sizeof (CS_INT)) ; /* allocate result */
52 if (!jimatch) return (NULL) ;
53 for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */
54 {
55 n2 += (Ap [j] < Ap [j+1]) ;
56 for (p = Ap [j] ; p < Ap [j+1] ; p++)
57 {
58 w [Ai [p]] = 1 ;
59 k += (j == Ai [p]) ; /* count entries already on diagonal */
60 }
61 }
62 if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */
63 {
64 jmatch = jimatch ; imatch = jimatch + m ;
65 for (i = 0 ; i < k ; i++) jmatch [i] = i ;
66 for ( ; i < m ; i++) jmatch [i] = -1 ;
67 for (j = 0 ; j < k ; j++) imatch [j] = j ;
68 for ( ; j < n ; j++) imatch [j] = -1 ;
69 return (cs_idone (jimatch, NULL, NULL, 1)) ;
70 }
71 for (i = 0 ; i < m ; i++) m2 += w [i] ;
72 C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */
73 if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ;
74 n = C->n ; m = C->m ; Cp = C->p ;
75 jmatch = (m2 < n2) ? jimatch + n : jimatch ;
76 imatch = (m2 < n2) ? jimatch : jimatch + m ;
77 w = cs_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */
78 if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ;
79 cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ;
80 for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */
81 for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
82 for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */
83 q = cs_randperm (n, seed) ; /* q = random permutation */
84 for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */
85 {
86 cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ;
87 }
88 cs_free (q) ;
89 for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */
90 for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
91 return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ;
92 }
93