21#ifndef EIGEN_SPARSE_AMD_H
22#define EIGEN_SPARSE_AMD_H
28template<
typename T>
inline T amd_flip(
const T& i) {
return -i-2; }
29template<
typename T>
inline T amd_unflip(
const T& i) {
return i<0 ? amd_flip(i) : i; }
30template<
typename T0,
typename T1>
inline bool amd_marked(
const T0* w,
const T1& j) {
return w[j]<0; }
31template<
typename T0,
typename T1>
inline void amd_mark(
const T0* w,
const T1& j) {
return w[j] = amd_flip(w[j]); }
34template<
typename StorageIndex>
35static StorageIndex cs_wclear (StorageIndex mark, StorageIndex lemax, StorageIndex *w, StorageIndex n)
38 if(mark < 2 || (mark + lemax < 0))
40 for(k = 0; k < n; k++)
49template<
typename StorageIndex>
50StorageIndex cs_tdfs(StorageIndex j, StorageIndex k, StorageIndex *head,
const StorageIndex *next, StorageIndex *post, StorageIndex *stack)
52 StorageIndex i, p, top = 0;
53 if(!head || !next || !post || !stack)
return (-1);
83template<
typename Scalar,
typename StorageIndex>
84void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm)
88 StorageIndex d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
89 k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
90 ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t, h;
92 StorageIndex n = StorageIndex(C.cols());
93 dense = std::max<StorageIndex> (16, StorageIndex(10 * sqrt(
double(n))));
94 dense = (std::min)(n-2, dense);
96 StorageIndex cnz = StorageIndex(C.nonZeros());
98 t = cnz + cnz/5 + 2*n;
102 ei_declare_aligned_stack_constructed_variable(StorageIndex,W,8*(n+1),0);
103 StorageIndex* len = W;
104 StorageIndex* nv = W + (n+1);
105 StorageIndex* next = W + 2*(n+1);
106 StorageIndex* head = W + 3*(n+1);
107 StorageIndex* elen = W + 4*(n+1);
108 StorageIndex* degree = W + 5*(n+1);
109 StorageIndex* w = W + 6*(n+1);
110 StorageIndex* hhead = W + 7*(n+1);
111 StorageIndex*
last = perm.indices().data();
114 StorageIndex* Cp = C.outerIndexPtr();
115 StorageIndex* Ci = C.innerIndexPtr();
116 for(k = 0; k < n; k++)
117 len[k] = Cp[k+1] - Cp[k];
121 for(i = 0; i <= n; i++)
132 mark = internal::cs_wclear<StorageIndex>(0, 0, w, n);
135 for(i = 0; i < n; i++)
137 bool has_diag =
false;
138 for(p = Cp[i]; p<Cp[i+1]; ++p)
146 if(d == 1 && has_diag)
153 else if(d > dense || !has_diag)
158 Cp[i] = amd_flip (n);
163 if(head[d] != -1)
last[head[d]] = i;
176 for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}
177 if(next[k] != -1)
last[next[k]] = -1;
178 head[mindeg] = next[k];
184 if(elenk > 0 && cnz + mindeg >= nzmax)
186 for(j = 0; j < n; j++)
191 Ci[p] = amd_flip (j);
194 for(q = 0, p = 0; p < cnz; )
196 if((j = amd_flip (Ci[p++])) >= 0)
200 for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];
210 pk1 = (elenk == 0) ? p : cnz;
212 for(k1 = 1; k1 <= elenk + 1; k1++)
226 for(k2 = 1; k2 <= ln; k2++)
229 if((nvi = nv[i]) <= 0)
continue;
233 if(next[i] != -1)
last[next[i]] =
last[i];
236 next[
last[i]] = next[i];
240 head[degree[i]] = next[i];
245 Cp[e] = amd_flip (k);
249 if(elenk != 0) cnz = pk2;
256 mark = internal::cs_wclear<StorageIndex>(mark, lemax, w, n);
257 for(pk = pk1; pk < pk2; pk++)
260 if((eln = elen[i]) <= 0)
continue;
263 for(p = Cp[i]; p <= Cp[i] + eln - 1; p++)
272 w[e] = degree[e] + wnvi;
278 for(pk = pk1; pk < pk2; pk++)
282 p2 = p1 + elen[i] - 1;
284 for(h = 0, d = 0, p = p1; p <= p2; p++)
298 Cp[e] = amd_flip (k);
303 elen[i] = pn - p1 + 1;
306 for(p = p2 + 1; p < p4; p++)
309 if((nvj = nv[j]) <= 0)
continue;
316 Cp[i] = amd_flip (k);
326 degree[i] = std::min<StorageIndex> (degree[i], d);
330 len[i] = pn - p1 + 1;
338 lemax = std::max<StorageIndex>(lemax, dk);
339 mark = internal::cs_wclear<StorageIndex>(mark+lemax, lemax, w, n);
342 for(pk = pk1; pk < pk2; pk++)
345 if(nv[i] >= 0)
continue;
349 for(; i != -1 && next[i] != -1; i = next[i], mark++)
353 for(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark;
355 for(j = next[i]; j != -1; )
357 ok = (len[j] == ln) && (elen[j] == eln);
358 for(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++)
360 if(w[Ci[p]] != mark) ok = 0;
364 Cp[j] = amd_flip (i);
381 for(p = pk1, pk = pk1; pk < pk2; pk++)
384 if((nvi = -nv[i]) <= 0)
continue;
386 d = degree[i] + dk - nvi;
387 d = std::min<StorageIndex> (d, n - nel - nvi);
388 if(head[d] != -1)
last[head[d]] = i;
392 mindeg = std::min<StorageIndex> (mindeg, d);
397 if((len[k] = p-pk1) == 0)
402 if(elenk != 0) cnz = p;
406 for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);
407 for(j = 0; j <= n; j++) head[j] = -1;
408 for(j = n; j >= 0; j--)
410 if(nv[j] > 0)
continue;
411 next[j] = head[Cp[j]];
414 for(e = n; e >= 0; e--)
416 if(nv[e] <= 0)
continue;
419 next[e] = head[Cp[e]];
423 for(k = 0, i = 0; i <= n; i++)
425 if(Cp[i] == -1) k = internal::cs_tdfs<StorageIndex>(i, k, head, next, perm.indices().data(), w);
428 perm.indices().conservativeResize(n);
static const symbolic::SymbolExpr< internal::symbolic_last_tag > last
Definition: IndexedViewHelper.h:38
Namespace containing all symbols from the Eigen library.
Definition: Core:141