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446 lines
16 KiB
446 lines
16 KiB
5 years ago
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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/*
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NOTE: this routine has been adapted from the CSparse library:
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Copyright (c) 2006, Timothy A. Davis.
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http://www.suitesparse.com
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CSparse is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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CSparse is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this Module; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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#include "../Core/util/NonMPL2.h"
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#ifndef EIGEN_SPARSE_AMD_H
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#define EIGEN_SPARSE_AMD_H
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namespace Eigen {
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namespace internal {
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template<typename T> inline T amd_flip(const T& i) { return -i-2; }
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template<typename T> inline T amd_unflip(const T& i) { return i<0 ? amd_flip(i) : i; }
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template<typename T0, typename T1> inline bool amd_marked(const T0* w, const T1& j) { return w[j]<0; }
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template<typename T0, typename T1> inline void amd_mark(const T0* w, const T1& j) { return w[j] = amd_flip(w[j]); }
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/* clear w */
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template<typename StorageIndex>
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static StorageIndex cs_wclear (StorageIndex mark, StorageIndex lemax, StorageIndex *w, StorageIndex n)
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{
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StorageIndex k;
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if(mark < 2 || (mark + lemax < 0))
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{
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for(k = 0; k < n; k++)
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if(w[k] != 0)
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w[k] = 1;
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mark = 2;
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}
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return (mark); /* at this point, w[0..n-1] < mark holds */
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}
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/* depth-first search and postorder of a tree rooted at node j */
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template<typename StorageIndex>
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StorageIndex cs_tdfs(StorageIndex j, StorageIndex k, StorageIndex *head, const StorageIndex *next, StorageIndex *post, StorageIndex *stack)
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{
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StorageIndex i, p, top = 0;
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if(!head || !next || !post || !stack) return (-1); /* check inputs */
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stack[0] = j; /* place j on the stack */
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while (top >= 0) /* while (stack is not empty) */
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{
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p = stack[top]; /* p = top of stack */
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i = head[p]; /* i = youngest child of p */
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if(i == -1)
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{
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top--; /* p has no unordered children left */
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post[k++] = p; /* node p is the kth postordered node */
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}
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else
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{
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head[p] = next[i]; /* remove i from children of p */
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stack[++top] = i; /* start dfs on child node i */
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}
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}
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return k;
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}
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/** \internal
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* \ingroup OrderingMethods_Module
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* Approximate minimum degree ordering algorithm.
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*
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* \param[in] C the input selfadjoint matrix stored in compressed column major format.
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* \param[out] perm the permutation P reducing the fill-in of the input matrix \a C
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*
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* Note that the input matrix \a C must be complete, that is both the upper and lower parts have to be stored, as well as the diagonal entries.
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* On exit the values of C are destroyed */
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template<typename Scalar, typename StorageIndex>
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void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm)
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{
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using std::sqrt;
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StorageIndex d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
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k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
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ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t, h;
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StorageIndex n = StorageIndex(C.cols());
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dense = std::max<StorageIndex> (16, StorageIndex(10 * sqrt(double(n)))); /* find dense threshold */
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dense = (std::min)(n-2, dense);
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StorageIndex cnz = StorageIndex(C.nonZeros());
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perm.resize(n+1);
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t = cnz + cnz/5 + 2*n; /* add elbow room to C */
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C.resizeNonZeros(t);
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// get workspace
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ei_declare_aligned_stack_constructed_variable(StorageIndex,W,8*(n+1),0);
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StorageIndex* len = W;
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StorageIndex* nv = W + (n+1);
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StorageIndex* next = W + 2*(n+1);
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StorageIndex* head = W + 3*(n+1);
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StorageIndex* elen = W + 4*(n+1);
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StorageIndex* degree = W + 5*(n+1);
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StorageIndex* w = W + 6*(n+1);
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StorageIndex* hhead = W + 7*(n+1);
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StorageIndex* last = perm.indices().data(); /* use P as workspace for last */
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/* --- Initialize quotient graph ---------------------------------------- */
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StorageIndex* Cp = C.outerIndexPtr();
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StorageIndex* Ci = C.innerIndexPtr();
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for(k = 0; k < n; k++)
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len[k] = Cp[k+1] - Cp[k];
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len[n] = 0;
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nzmax = t;
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for(i = 0; i <= n; i++)
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{
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head[i] = -1; // degree list i is empty
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last[i] = -1;
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next[i] = -1;
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hhead[i] = -1; // hash list i is empty
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nv[i] = 1; // node i is just one node
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w[i] = 1; // node i is alive
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elen[i] = 0; // Ek of node i is empty
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degree[i] = len[i]; // degree of node i
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}
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mark = internal::cs_wclear<StorageIndex>(0, 0, w, n); /* clear w */
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/* --- Initialize degree lists ------------------------------------------ */
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for(i = 0; i < n; i++)
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{
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bool has_diag = false;
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for(p = Cp[i]; p<Cp[i+1]; ++p)
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if(Ci[p]==i)
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{
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has_diag = true;
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break;
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}
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d = degree[i];
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if(d == 1 && has_diag) /* node i is empty */
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{
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elen[i] = -2; /* element i is dead */
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nel++;
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Cp[i] = -1; /* i is a root of assembly tree */
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w[i] = 0;
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}
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else if(d > dense || !has_diag) /* node i is dense or has no structural diagonal element */
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{
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nv[i] = 0; /* absorb i into element n */
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elen[i] = -1; /* node i is dead */
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nel++;
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Cp[i] = amd_flip (n);
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nv[n]++;
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}
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else
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{
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if(head[d] != -1) last[head[d]] = i;
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next[i] = head[d]; /* put node i in degree list d */
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head[d] = i;
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}
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}
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elen[n] = -2; /* n is a dead element */
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Cp[n] = -1; /* n is a root of assembly tree */
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w[n] = 0; /* n is a dead element */
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while (nel < n) /* while (selecting pivots) do */
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{
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/* --- Select node of minimum approximate degree -------------------- */
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for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}
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if(next[k] != -1) last[next[k]] = -1;
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head[mindeg] = next[k]; /* remove k from degree list */
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elenk = elen[k]; /* elenk = |Ek| */
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nvk = nv[k]; /* # of nodes k represents */
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nel += nvk; /* nv[k] nodes of A eliminated */
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/* --- Garbage collection ------------------------------------------- */
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if(elenk > 0 && cnz + mindeg >= nzmax)
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{
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for(j = 0; j < n; j++)
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{
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if((p = Cp[j]) >= 0) /* j is a live node or element */
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{
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Cp[j] = Ci[p]; /* save first entry of object */
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Ci[p] = amd_flip (j); /* first entry is now amd_flip(j) */
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}
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}
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for(q = 0, p = 0; p < cnz; ) /* scan all of memory */
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{
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if((j = amd_flip (Ci[p++])) >= 0) /* found object j */
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{
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Ci[q] = Cp[j]; /* restore first entry of object */
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Cp[j] = q++; /* new pointer to object j */
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for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];
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}
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}
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cnz = q; /* Ci[cnz...nzmax-1] now free */
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}
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/* --- Construct new element ---------------------------------------- */
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dk = 0;
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nv[k] = -nvk; /* flag k as in Lk */
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p = Cp[k];
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pk1 = (elenk == 0) ? p : cnz; /* do in place if elen[k] == 0 */
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pk2 = pk1;
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for(k1 = 1; k1 <= elenk + 1; k1++)
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{
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if(k1 > elenk)
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{
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e = k; /* search the nodes in k */
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pj = p; /* list of nodes starts at Ci[pj]*/
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ln = len[k] - elenk; /* length of list of nodes in k */
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}
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else
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{
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e = Ci[p++]; /* search the nodes in e */
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pj = Cp[e];
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ln = len[e]; /* length of list of nodes in e */
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}
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for(k2 = 1; k2 <= ln; k2++)
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{
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i = Ci[pj++];
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if((nvi = nv[i]) <= 0) continue; /* node i dead, or seen */
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dk += nvi; /* degree[Lk] += size of node i */
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nv[i] = -nvi; /* negate nv[i] to denote i in Lk*/
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Ci[pk2++] = i; /* place i in Lk */
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if(next[i] != -1) last[next[i]] = last[i];
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if(last[i] != -1) /* remove i from degree list */
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{
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next[last[i]] = next[i];
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}
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else
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{
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head[degree[i]] = next[i];
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}
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}
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if(e != k)
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{
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Cp[e] = amd_flip (k); /* absorb e into k */
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w[e] = 0; /* e is now a dead element */
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}
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}
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if(elenk != 0) cnz = pk2; /* Ci[cnz...nzmax] is free */
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degree[k] = dk; /* external degree of k - |Lk\i| */
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Cp[k] = pk1; /* element k is in Ci[pk1..pk2-1] */
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len[k] = pk2 - pk1;
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elen[k] = -2; /* k is now an element */
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/* --- Find set differences ----------------------------------------- */
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mark = internal::cs_wclear<StorageIndex>(mark, lemax, w, n); /* clear w if necessary */
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for(pk = pk1; pk < pk2; pk++) /* scan 1: find |Le\Lk| */
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{
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i = Ci[pk];
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if((eln = elen[i]) <= 0) continue;/* skip if elen[i] empty */
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nvi = -nv[i]; /* nv[i] was negated */
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wnvi = mark - nvi;
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for(p = Cp[i]; p <= Cp[i] + eln - 1; p++) /* scan Ei */
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{
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e = Ci[p];
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if(w[e] >= mark)
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{
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w[e] -= nvi; /* decrement |Le\Lk| */
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}
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else if(w[e] != 0) /* ensure e is a live element */
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{
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w[e] = degree[e] + wnvi; /* 1st time e seen in scan 1 */
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}
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}
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}
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/* --- Degree update ------------------------------------------------ */
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for(pk = pk1; pk < pk2; pk++) /* scan2: degree update */
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{
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i = Ci[pk]; /* consider node i in Lk */
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p1 = Cp[i];
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p2 = p1 + elen[i] - 1;
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pn = p1;
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for(h = 0, d = 0, p = p1; p <= p2; p++) /* scan Ei */
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{
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e = Ci[p];
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if(w[e] != 0) /* e is an unabsorbed element */
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{
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dext = w[e] - mark; /* dext = |Le\Lk| */
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if(dext > 0)
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{
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d += dext; /* sum up the set differences */
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Ci[pn++] = e; /* keep e in Ei */
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h += e; /* compute the hash of node i */
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}
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else
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{
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Cp[e] = amd_flip (k); /* aggressive absorb. e->k */
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w[e] = 0; /* e is a dead element */
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}
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}
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}
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elen[i] = pn - p1 + 1; /* elen[i] = |Ei| */
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p3 = pn;
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p4 = p1 + len[i];
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for(p = p2 + 1; p < p4; p++) /* prune edges in Ai */
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{
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j = Ci[p];
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if((nvj = nv[j]) <= 0) continue; /* node j dead or in Lk */
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d += nvj; /* degree(i) += |j| */
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Ci[pn++] = j; /* place j in node list of i */
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h += j; /* compute hash for node i */
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}
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if(d == 0) /* check for mass elimination */
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{
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Cp[i] = amd_flip (k); /* absorb i into k */
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nvi = -nv[i];
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dk -= nvi; /* |Lk| -= |i| */
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nvk += nvi; /* |k| += nv[i] */
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nel += nvi;
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nv[i] = 0;
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elen[i] = -1; /* node i is dead */
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}
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else
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{
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degree[i] = std::min<StorageIndex> (degree[i], d); /* update degree(i) */
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Ci[pn] = Ci[p3]; /* move first node to end */
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Ci[p3] = Ci[p1]; /* move 1st el. to end of Ei */
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Ci[p1] = k; /* add k as 1st element in of Ei */
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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<StorageIndex>(lemax, dk);
|
||
|
|
mark = internal::cs_wclear<StorageIndex>(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<StorageIndex> (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<StorageIndex> (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<StorageIndex>(i, k, head, next, perm.indices().data(), w);
|
||
|
|
}
|
||
|
|
|
||
|
|
perm.indices().conservativeResize(n);
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
|
||
|
|
} // end namespace Eigen
|
||
|
|
|
||
|
|
#endif // EIGEN_SPARSE_AMD_H
|