| |
| |
| |
| |
| |
| |
| |
| |
|
|
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|
|
| #ifndef EIGEN_SPARSE_AMD_H |
| #define EIGEN_SPARSE_AMD_H |
|
|
| namespace Eigen { |
|
|
| namespace internal { |
| |
| template<typename T> inline T amd_flip(const T& i) { return -i-2; } |
| template<typename T> inline T amd_unflip(const T& i) { return i<0 ? amd_flip(i) : i; } |
| template<typename T0, typename T1> inline bool amd_marked(const T0* w, const T1& j) { return w[j]<0; } |
| template<typename T0, typename T1> inline void amd_mark(const T0* w, const T1& j) { return w[j] = amd_flip(w[j]); } |
|
|
| |
| template<typename StorageIndex> |
| static StorageIndex cs_wclear (StorageIndex mark, StorageIndex lemax, StorageIndex *w, StorageIndex n) |
| { |
| StorageIndex k; |
| if(mark < 2 || (mark + lemax < 0)) |
| { |
| for(k = 0; k < n; k++) |
| if(w[k] != 0) |
| w[k] = 1; |
| mark = 2; |
| } |
| return (mark); |
| } |
|
|
| |
| template<typename StorageIndex> |
| StorageIndex cs_tdfs(StorageIndex j, StorageIndex k, StorageIndex *head, const StorageIndex *next, StorageIndex *post, StorageIndex *stack) |
| { |
| StorageIndex i, p, top = 0; |
| if(!head || !next || !post || !stack) return (-1); |
| stack[0] = j; |
| while (top >= 0) |
| { |
| p = stack[top]; |
| i = head[p]; |
| if(i == -1) |
| { |
| top--; |
| post[k++] = p; |
| } |
| else |
| { |
| head[p] = next[i]; |
| stack[++top] = i; |
| } |
| } |
| return k; |
| } |
|
|
|
|
| |
| |
| |
| |
| |
| |
| |
| |
| |
| template<typename Scalar, typename StorageIndex> |
| void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) |
| { |
| using std::sqrt; |
| |
| StorageIndex d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1, |
| k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi, |
| ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t, h; |
| |
| StorageIndex n = StorageIndex(C.cols()); |
| dense = std::max<StorageIndex> (16, StorageIndex(10 * sqrt(double(n)))); |
| dense = (std::min)(n-2, dense); |
| |
| StorageIndex cnz = StorageIndex(C.nonZeros()); |
| perm.resize(n+1); |
| t = cnz + cnz/5 + 2*n; |
| C.resizeNonZeros(t); |
| |
| |
| ei_declare_aligned_stack_constructed_variable(StorageIndex,W,8*(n+1),0); |
| StorageIndex* len = W; |
| StorageIndex* nv = W + (n+1); |
| StorageIndex* next = W + 2*(n+1); |
| StorageIndex* head = W + 3*(n+1); |
| StorageIndex* elen = W + 4*(n+1); |
| StorageIndex* degree = W + 5*(n+1); |
| StorageIndex* w = W + 6*(n+1); |
| StorageIndex* hhead = W + 7*(n+1); |
| StorageIndex* last = perm.indices().data(); |
| |
| |
| StorageIndex* Cp = C.outerIndexPtr(); |
| StorageIndex* Ci = C.innerIndexPtr(); |
| for(k = 0; k < n; k++) |
| len[k] = Cp[k+1] - Cp[k]; |
| len[n] = 0; |
| nzmax = t; |
| |
| for(i = 0; i <= n; i++) |
| { |
| head[i] = -1; |
| last[i] = -1; |
| next[i] = -1; |
| hhead[i] = -1; |
| nv[i] = 1; |
| w[i] = 1; |
| elen[i] = 0; |
| degree[i] = len[i]; |
| } |
| mark = internal::cs_wclear<StorageIndex>(0, 0, w, n); |
| |
| |
| for(i = 0; i < n; i++) |
| { |
| bool has_diag = false; |
| for(p = Cp[i]; p<Cp[i+1]; ++p) |
| if(Ci[p]==i) |
| { |
| has_diag = true; |
| break; |
| } |
| |
| d = degree[i]; |
| if(d == 1 && has_diag) |
| { |
| elen[i] = -2; |
| nel++; |
| Cp[i] = -1; |
| w[i] = 0; |
| } |
| else if(d > dense || !has_diag) |
| { |
| nv[i] = 0; |
| elen[i] = -1; |
| nel++; |
| Cp[i] = amd_flip (n); |
| nv[n]++; |
| } |
| else |
| { |
| if(head[d] != -1) last[head[d]] = i; |
| next[i] = head[d]; |
| head[d] = i; |
| } |
| } |
| |
| elen[n] = -2; |
| Cp[n] = -1; |
| w[n] = 0; |
| |
| while (nel < n) |
| { |
| |
| for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {} |
| if(next[k] != -1) last[next[k]] = -1; |
| head[mindeg] = next[k]; |
| elenk = elen[k]; |
| nvk = nv[k]; |
| nel += nvk; |
| |
| |
| if(elenk > 0 && cnz + mindeg >= nzmax) |
| { |
| for(j = 0; j < n; j++) |
| { |
| if((p = Cp[j]) >= 0) |
| { |
| Cp[j] = Ci[p]; |
| Ci[p] = amd_flip (j); |
| } |
| } |
| for(q = 0, p = 0; p < cnz; ) |
| { |
| if((j = amd_flip (Ci[p++])) >= 0) |
| { |
| Ci[q] = Cp[j]; |
| Cp[j] = q++; |
| for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++]; |
| } |
| } |
| cnz = q; |
| } |
| |
| |
| dk = 0; |
| nv[k] = -nvk; |
| p = Cp[k]; |
| pk1 = (elenk == 0) ? p : cnz; |
| pk2 = pk1; |
| for(k1 = 1; k1 <= elenk + 1; k1++) |
| { |
| if(k1 > elenk) |
| { |
| e = k; |
| pj = p; |
| ln = len[k] - elenk; |
| } |
| else |
| { |
| e = Ci[p++]; |
| pj = Cp[e]; |
| ln = len[e]; |
| } |
| for(k2 = 1; k2 <= ln; k2++) |
| { |
| i = Ci[pj++]; |
| if((nvi = nv[i]) <= 0) continue; |
| dk += nvi; |
| nv[i] = -nvi; |
| Ci[pk2++] = i; |
| if(next[i] != -1) last[next[i]] = last[i]; |
| if(last[i] != -1) |
| { |
| next[last[i]] = next[i]; |
| } |
| else |
| { |
| head[degree[i]] = next[i]; |
| } |
| } |
| if(e != k) |
| { |
| Cp[e] = amd_flip (k); |
| w[e] = 0; |
| } |
| } |
| if(elenk != 0) cnz = pk2; |
| degree[k] = dk; |
| Cp[k] = pk1; |
| len[k] = pk2 - pk1; |
| elen[k] = -2; |
| |
| |
| mark = internal::cs_wclear<StorageIndex>(mark, lemax, w, n); |
| for(pk = pk1; pk < pk2; pk++) |
| { |
| i = Ci[pk]; |
| if((eln = elen[i]) <= 0) continue; |
| nvi = -nv[i]; |
| wnvi = mark - nvi; |
| for(p = Cp[i]; p <= Cp[i] + eln - 1; p++) |
| { |
| e = Ci[p]; |
| if(w[e] >= mark) |
| { |
| w[e] -= nvi; |
| } |
| else if(w[e] != 0) |
| { |
| w[e] = degree[e] + wnvi; |
| } |
| } |
| } |
| |
| |
| for(pk = pk1; pk < pk2; pk++) |
| { |
| i = Ci[pk]; |
| p1 = Cp[i]; |
| p2 = p1 + elen[i] - 1; |
| pn = p1; |
| for(h = 0, d = 0, p = p1; p <= p2; p++) |
| { |
| e = Ci[p]; |
| if(w[e] != 0) |
| { |
| dext = w[e] - mark; |
| if(dext > 0) |
| { |
| d += dext; |
| Ci[pn++] = e; |
| h += e; |
| } |
| else |
| { |
| Cp[e] = amd_flip (k); |
| w[e] = 0; |
| } |
| } |
| } |
| elen[i] = pn - p1 + 1; |
| p3 = pn; |
| p4 = p1 + len[i]; |
| for(p = p2 + 1; p < p4; p++) |
| { |
| j = Ci[p]; |
| if((nvj = nv[j]) <= 0) continue; |
| d += nvj; |
| Ci[pn++] = j; |
| h += j; |
| } |
| if(d == 0) |
| { |
| Cp[i] = amd_flip (k); |
| nvi = -nv[i]; |
| dk -= nvi; |
| nvk += nvi; |
| nel += nvi; |
| nv[i] = 0; |
| elen[i] = -1; |
| } |
| else |
| { |
| degree[i] = std::min<StorageIndex> (degree[i], d); |
| Ci[pn] = Ci[p3]; |
| Ci[p3] = Ci[p1]; |
| Ci[p1] = k; |
| len[i] = pn - p1 + 1; |
| h %= n; |
| next[i] = hhead[h]; |
| hhead[h] = i; |
| last[i] = h; |
| } |
| } |
| degree[k] = dk; |
| lemax = std::max<StorageIndex>(lemax, dk); |
| mark = internal::cs_wclear<StorageIndex>(mark+lemax, lemax, w, n); |
| |
| |
| for(pk = pk1; pk < pk2; pk++) |
| { |
| i = Ci[pk]; |
| if(nv[i] >= 0) continue; |
| h = last[i]; |
| i = hhead[h]; |
| hhead[h] = -1; |
| for(; i != -1 && next[i] != -1; i = next[i], mark++) |
| { |
| ln = len[i]; |
| eln = elen[i]; |
| for(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark; |
| jlast = i; |
| for(j = next[i]; j != -1; ) |
| { |
| ok = (len[j] == ln) && (elen[j] == eln); |
| for(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++) |
| { |
| if(w[Ci[p]] != mark) ok = 0; |
| } |
| if(ok) |
| { |
| Cp[j] = amd_flip (i); |
| nv[i] += nv[j]; |
| nv[j] = 0; |
| elen[j] = -1; |
| j = next[j]; |
| next[jlast] = j; |
| } |
| else |
| { |
| jlast = j; |
| j = next[j]; |
| } |
| } |
| } |
| } |
| |
| |
| for(p = pk1, pk = pk1; pk < pk2; pk++) |
| { |
| i = Ci[pk]; |
| if((nvi = -nv[i]) <= 0) continue; |
| nv[i] = nvi; |
| d = degree[i] + dk - nvi; |
| d = std::min<StorageIndex> (d, n - nel - nvi); |
| if(head[d] != -1) last[head[d]] = i; |
| next[i] = head[d]; |
| last[i] = -1; |
| head[d] = i; |
| mindeg = std::min<StorageIndex> (mindeg, d); |
| degree[i] = d; |
| Ci[p++] = i; |
| } |
| nv[k] = nvk; |
| if((len[k] = p-pk1) == 0) |
| { |
| Cp[k] = -1; |
| w[k] = 0; |
| } |
| if(elenk != 0) cnz = p; |
| } |
| |
| |
| for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]); |
| for(j = 0; j <= n; j++) head[j] = -1; |
| for(j = n; j >= 0; j--) |
| { |
| if(nv[j] > 0) continue; |
| next[j] = head[Cp[j]]; |
| head[Cp[j]] = j; |
| } |
| for(e = n; e >= 0; e--) |
| { |
| if(nv[e] <= 0) continue; |
| if(Cp[e] != -1) |
| { |
| next[e] = head[Cp[e]]; |
| head[Cp[e]] = e; |
| } |
| } |
| for(k = 0, i = 0; i <= n; i++) |
| { |
| if(Cp[i] == -1) k = internal::cs_tdfs<StorageIndex>(i, k, head, next, perm.indices().data(), w); |
| } |
| |
| perm.indices().conservativeResize(n); |
| } |
|
|
| } |
|
|
| } |
|
|
| #endif |
|
|