Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/OrderingMethods/Amd.h b/Eigen/src/OrderingMethods/Amd.h
new file mode 100644
index 0000000..1c28bdf
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Amd.h
@@ -0,0 +1,447 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+/*
+
+NOTE: this routine has been adapted from the CSparse library:
+
+Copyright (c) 2006, Timothy A. Davis.
+http://www.cise.ufl.edu/research/sparse/CSparse
+
+CSparse is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+CSparse is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+*/
+
+#include "../Core/util/NonMPL2.h"
+
+#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]); }
+
+/* clear w */
+template<typename Index>
+static int cs_wclear (Index mark, Index lemax, Index *w, Index n)
+{
+ Index k;
+ if(mark < 2 || (mark + lemax < 0))
+ {
+ for(k = 0; k < n; k++)
+ if(w[k] != 0)
+ w[k] = 1;
+ mark = 2;
+ }
+ return (mark); /* at this point, w[0..n-1] < mark holds */
+}
+
+/* depth-first search and postorder of a tree rooted at node j */
+template<typename Index>
+Index cs_tdfs(Index j, Index k, Index *head, const Index *next, Index *post, Index *stack)
+{
+ int i, p, top = 0;
+ if(!head || !next || !post || !stack) return (-1); /* check inputs */
+ stack[0] = j; /* place j on the stack */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack[top]; /* p = top of stack */
+ i = head[p]; /* i = youngest child of p */
+ if(i == -1)
+ {
+ top--; /* p has no unordered children left */
+ post[k++] = p; /* node p is the kth postordered node */
+ }
+ else
+ {
+ head[p] = next[i]; /* remove i from children of p */
+ stack[++top] = i; /* start dfs on child node i */
+ }
+ }
+ return k;
+}
+
+
+/** \internal
+ * \ingroup OrderingMethods_Module
+ * Approximate minimum degree ordering algorithm.
+ * \returns the permutation P reducing the fill-in of the input matrix \a C
+ * The input matrix \a C must be a selfadjoint compressed column major SparseMatrix object. Both the upper and lower parts have to be stored, but the diagonal entries are optional.
+ * On exit the values of C are destroyed */
+template<typename Scalar, typename Index>
+void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,Index>& C, PermutationMatrix<Dynamic,Dynamic,Index>& perm)
+{
+ using std::sqrt;
+
+ int 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;
+ unsigned int h;
+
+ Index n = C.cols();
+ dense = std::max<Index> (16, Index(10 * sqrt(double(n)))); /* find dense threshold */
+ dense = std::min<Index> (n-2, dense);
+
+ Index cnz = C.nonZeros();
+ perm.resize(n+1);
+ t = cnz + cnz/5 + 2*n; /* add elbow room to C */
+ C.resizeNonZeros(t);
+
+ Index* W = new Index[8*(n+1)]; /* get workspace */
+ Index* len = W;
+ Index* nv = W + (n+1);
+ Index* next = W + 2*(n+1);
+ Index* head = W + 3*(n+1);
+ Index* elen = W + 4*(n+1);
+ Index* degree = W + 5*(n+1);
+ Index* w = W + 6*(n+1);
+ Index* hhead = W + 7*(n+1);
+ Index* last = perm.indices().data(); /* use P as workspace for last */
+
+ /* --- Initialize quotient graph ---------------------------------------- */
+ Index* Cp = C.outerIndexPtr();
+ Index* 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; // degree list i is empty
+ last[i] = -1;
+ next[i] = -1;
+ hhead[i] = -1; // hash list i is empty
+ nv[i] = 1; // node i is just one node
+ w[i] = 1; // node i is alive
+ elen[i] = 0; // Ek of node i is empty
+ degree[i] = len[i]; // degree of node i
+ }
+ mark = internal::cs_wclear<Index>(0, 0, w, n); /* clear w */
+ elen[n] = -2; /* n is a dead element */
+ Cp[n] = -1; /* n is a root of assembly tree */
+ w[n] = 0; /* n is a dead element */
+
+ /* --- Initialize degree lists ------------------------------------------ */
+ 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) /* node i is empty */
+ {
+ elen[i] = -2; /* element i is dead */
+ nel++;
+ Cp[i] = -1; /* i is a root of assembly tree */
+ w[i] = 0;
+ }
+ else if(d > dense || !has_diag) /* node i is dense or has no structural diagonal element */
+ {
+ nv[i] = 0; /* absorb i into element n */
+ elen[i] = -1; /* node i is dead */
+ nel++;
+ Cp[i] = amd_flip (n);
+ nv[n]++;
+ }
+ else
+ {
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put node i in degree list d */
+ head[d] = i;
+ }
+ }
+
+ elen[n] = -2; /* n is a dead element */
+ Cp[n] = -1; /* n is a root of assembly tree */
+ w[n] = 0; /* n is a dead element */
+
+ while (nel < n) /* while (selecting pivots) do */
+ {
+ /* --- Select node of minimum approximate degree -------------------- */
+ for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}
+ if(next[k] != -1) last[next[k]] = -1;
+ head[mindeg] = next[k]; /* remove k from degree list */
+ elenk = elen[k]; /* elenk = |Ek| */
+ nvk = nv[k]; /* # of nodes k represents */
+ nel += nvk; /* nv[k] nodes of A eliminated */
+
+ /* --- Garbage collection ------------------------------------------- */
+ if(elenk > 0 && cnz + mindeg >= nzmax)
+ {
+ for(j = 0; j < n; j++)
+ {
+ if((p = Cp[j]) >= 0) /* j is a live node or element */
+ {
+ Cp[j] = Ci[p]; /* save first entry of object */
+ Ci[p] = amd_flip (j); /* first entry is now amd_flip(j) */
+ }
+ }
+ for(q = 0, p = 0; p < cnz; ) /* scan all of memory */
+ {
+ if((j = amd_flip (Ci[p++])) >= 0) /* found object j */
+ {
+ Ci[q] = Cp[j]; /* restore first entry of object */
+ Cp[j] = q++; /* new pointer to object j */
+ for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];
+ }
+ }
+ cnz = q; /* Ci[cnz...nzmax-1] now free */
+ }
+
+ /* --- Construct new element ---------------------------------------- */
+ dk = 0;
+ nv[k] = -nvk; /* flag k as in Lk */
+ p = Cp[k];
+ pk1 = (elenk == 0) ? p : cnz; /* do in place if elen[k] == 0 */
+ pk2 = pk1;
+ for(k1 = 1; k1 <= elenk + 1; k1++)
+ {
+ if(k1 > elenk)
+ {
+ e = k; /* search the nodes in k */
+ pj = p; /* list of nodes starts at Ci[pj]*/
+ ln = len[k] - elenk; /* length of list of nodes in k */
+ }
+ else
+ {
+ e = Ci[p++]; /* search the nodes in e */
+ pj = Cp[e];
+ ln = len[e]; /* length of list of nodes in e */
+ }
+ for(k2 = 1; k2 <= ln; k2++)
+ {
+ i = Ci[pj++];
+ if((nvi = nv[i]) <= 0) continue; /* node i dead, or seen */
+ dk += nvi; /* degree[Lk] += size of node i */
+ nv[i] = -nvi; /* negate nv[i] to denote i in Lk*/
+ Ci[pk2++] = i; /* place i in Lk */
+ if(next[i] != -1) last[next[i]] = last[i];
+ if(last[i] != -1) /* remove i from degree list */
+ {
+ next[last[i]] = next[i];
+ }
+ else
+ {
+ head[degree[i]] = next[i];
+ }
+ }
+ if(e != k)
+ {
+ Cp[e] = amd_flip (k); /* absorb e into k */
+ w[e] = 0; /* e is now a dead element */
+ }
+ }
+ if(elenk != 0) cnz = pk2; /* Ci[cnz...nzmax] is free */
+ degree[k] = dk; /* external degree of k - |Lk\i| */
+ Cp[k] = pk1; /* element k is in Ci[pk1..pk2-1] */
+ len[k] = pk2 - pk1;
+ elen[k] = -2; /* k is now an element */
+
+ /* --- Find set differences ----------------------------------------- */
+ mark = internal::cs_wclear<Index>(mark, lemax, w, n); /* clear w if necessary */
+ for(pk = pk1; pk < pk2; pk++) /* scan 1: find |Le\Lk| */
+ {
+ i = Ci[pk];
+ if((eln = elen[i]) <= 0) continue;/* skip if elen[i] empty */
+ nvi = -nv[i]; /* nv[i] was negated */
+ wnvi = mark - nvi;
+ for(p = Cp[i]; p <= Cp[i] + eln - 1; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] >= mark)
+ {
+ w[e] -= nvi; /* decrement |Le\Lk| */
+ }
+ else if(w[e] != 0) /* ensure e is a live element */
+ {
+ w[e] = degree[e] + wnvi; /* 1st time e seen in scan 1 */
+ }
+ }
+ }
+
+ /* --- Degree update ------------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++) /* scan2: degree update */
+ {
+ i = Ci[pk]; /* consider node i in Lk */
+ p1 = Cp[i];
+ p2 = p1 + elen[i] - 1;
+ pn = p1;
+ for(h = 0, d = 0, p = p1; p <= p2; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] != 0) /* e is an unabsorbed element */
+ {
+ dext = w[e] - mark; /* dext = |Le\Lk| */
+ if(dext > 0)
+ {
+ d += dext; /* sum up the set differences */
+ Ci[pn++] = e; /* keep e in Ei */
+ h += e; /* compute the hash of node i */
+ }
+ else
+ {
+ Cp[e] = amd_flip (k); /* aggressive absorb. e->k */
+ w[e] = 0; /* e is a dead element */
+ }
+ }
+ }
+ elen[i] = pn - p1 + 1; /* elen[i] = |Ei| */
+ p3 = pn;
+ p4 = p1 + len[i];
+ for(p = p2 + 1; p < p4; p++) /* prune edges in Ai */
+ {
+ j = Ci[p];
+ if((nvj = nv[j]) <= 0) continue; /* node j dead or in Lk */
+ d += nvj; /* degree(i) += |j| */
+ Ci[pn++] = j; /* place j in node list of i */
+ h += j; /* compute hash for node i */
+ }
+ if(d == 0) /* check for mass elimination */
+ {
+ Cp[i] = amd_flip (k); /* absorb i into k */
+ nvi = -nv[i];
+ dk -= nvi; /* |Lk| -= |i| */
+ nvk += nvi; /* |k| += nv[i] */
+ nel += nvi;
+ nv[i] = 0;
+ elen[i] = -1; /* node i is dead */
+ }
+ else
+ {
+ degree[i] = std::min<Index> (degree[i], d); /* update degree(i) */
+ Ci[pn] = Ci[p3]; /* move first node to end */
+ Ci[p3] = Ci[p1]; /* move 1st el. to end of Ei */
+ Ci[p1] = k; /* add k as 1st element in of Ei */
+ len[i] = pn - p1 + 1; /* new len of adj. list of node i */
+ h %= n; /* finalize hash of i */
+ next[i] = hhead[h]; /* place i in hash bucket */
+ hhead[h] = i;
+ last[i] = h; /* save hash of i in last[i] */
+ }
+ } /* scan2 is done */
+ degree[k] = dk; /* finalize |Lk| */
+ lemax = std::max<Index>(lemax, dk);
+ mark = internal::cs_wclear<Index>(mark+lemax, lemax, w, n); /* clear w */
+
+ /* --- Supernode detection ------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++)
+ {
+ i = Ci[pk];
+ if(nv[i] >= 0) continue; /* skip if i is dead */
+ h = last[i]; /* scan hash bucket of node i */
+ i = hhead[h];
+ hhead[h] = -1; /* hash bucket will be empty */
+ 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; ) /* compare i with all j */
+ {
+ 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; /* compare i and j*/
+ }
+ if(ok) /* i and j are identical */
+ {
+ Cp[j] = amd_flip (i); /* absorb j into i */
+ nv[i] += nv[j];
+ nv[j] = 0;
+ elen[j] = -1; /* node j is dead */
+ j = next[j]; /* delete j from hash bucket */
+ next[jlast] = j;
+ }
+ else
+ {
+ jlast = j; /* j and i are different */
+ j = next[j];
+ }
+ }
+ }
+ }
+
+ /* --- Finalize new element------------------------------------------ */
+ for(p = pk1, pk = pk1; pk < pk2; pk++) /* finalize Lk */
+ {
+ i = Ci[pk];
+ if((nvi = -nv[i]) <= 0) continue;/* skip if i is dead */
+ nv[i] = nvi; /* restore nv[i] */
+ d = degree[i] + dk - nvi; /* compute external degree(i) */
+ d = std::min<Index> (d, n - nel - nvi);
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put i back in degree list */
+ last[i] = -1;
+ head[d] = i;
+ mindeg = std::min<Index> (mindeg, d); /* find new minimum degree */
+ degree[i] = d;
+ Ci[p++] = i; /* place i in Lk */
+ }
+ nv[k] = nvk; /* # nodes absorbed into k */
+ if((len[k] = p-pk1) == 0) /* length of adj list of element k*/
+ {
+ Cp[k] = -1; /* k is a root of the tree */
+ w[k] = 0; /* k is now a dead element */
+ }
+ if(elenk != 0) cnz = p; /* free unused space in Lk */
+ }
+
+ /* --- Postordering ----------------------------------------------------- */
+ for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);/* fix assembly tree */
+ for(j = 0; j <= n; j++) head[j] = -1;
+ for(j = n; j >= 0; j--) /* place unordered nodes in lists */
+ {
+ if(nv[j] > 0) continue; /* skip if j is an element */
+ next[j] = head[Cp[j]]; /* place j in list of its parent */
+ head[Cp[j]] = j;
+ }
+ for(e = n; e >= 0; e--) /* place elements in lists */
+ {
+ if(nv[e] <= 0) continue; /* skip unless e is an element */
+ if(Cp[e] != -1)
+ {
+ next[e] = head[Cp[e]]; /* place e in list of its parent */
+ head[Cp[e]] = e;
+ }
+ }
+ for(k = 0, i = 0; i <= n; i++) /* postorder the assembly tree */
+ {
+ if(Cp[i] == -1) k = internal::cs_tdfs<Index>(i, k, head, next, perm.indices().data(), w);
+ }
+
+ perm.indices().conservativeResize(n);
+
+ delete[] W;
+}
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_AMD_H