don't index Eigen

3 files changed, 0 insertions, 2445 deletions

diff --git a/eigen/Eigen/src/OrderingMethods/Amd.h b/eigen/Eigen/src/OrderingMethods/Amd.h
deleted file mode 100644
index f91ecb2..0000000
--- a/eigen/Eigen/src/OrderingMethods/Amd.h
+++ /dev/null
@@ -1,445 +0,0 @@
-// 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.suitesparse.com
-
-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 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);     /* at this point, w[0..n-1] < mark holds */
-}
-
-/* depth-first search and postorder of a tree rooted at node j */
-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);    /* 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.
-  *
-  * \param[in] C the input selfadjoint matrix stored in compressed column major format.
-  * \param[out] perm the permutation P reducing the fill-in of the input matrix \a C
-  *
-  * 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.
-  * On exit the values of C are destroyed */
-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))));   /* find dense threshold */
-  dense = (std::min)(n-2, dense);
-  
-  StorageIndex cnz = StorageIndex(C.nonZeros());
-  perm.resize(n+1);
-  t = cnz + cnz/5 + 2*n;                 /* add elbow room to C */
-  C.resizeNonZeros(t);
-  
-  // get workspace
-  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();                              /* use P as workspace for last */
-  
-  /* --- Initialize quotient graph ---------------------------------------- */
-  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;                     // 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<StorageIndex>(0, 0, w, n);         /* clear w */
-  
-  /* --- 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 && has_diag)           /* 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<StorageIndex>(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<StorageIndex> (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<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
diff --git a/eigen/Eigen/src/OrderingMethods/Eigen_Colamd.h b/eigen/Eigen/src/OrderingMethods/Eigen_Colamd.h
deleted file mode 100644
index da85b4d..0000000
--- a/eigen/Eigen/src/OrderingMethods/Eigen_Colamd.h
+++ /dev/null
@@ -1,1843 +0,0 @@
-// // This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-// This file is modified from the colamd/symamd library. The copyright is below
-
-//   The authors of the code itself are Stefan I. Larimore and Timothy A.
-//   Davis (davis@cise.ufl.edu), University of Florida.  The algorithm was
-//   developed in collaboration with John Gilbert, Xerox PARC, and Esmond
-//   Ng, Oak Ridge National Laboratory.
-// 
-//     Date:
-// 
-//   September 8, 2003.  Version 2.3.
-// 
-//     Acknowledgements:
-// 
-//   This work was supported by the National Science Foundation, under
-//   grants DMS-9504974 and DMS-9803599.
-// 
-//     Notice:
-// 
-//   Copyright (c) 1998-2003 by the University of Florida.
-//   All Rights Reserved.
-// 
-//   THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
-//   EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
-// 
-//   Permission is hereby granted to use, copy, modify, and/or distribute
-//   this program, provided that the Copyright, this License, and the
-//   Availability of the original version is retained on all copies and made
-//   accessible to the end-user of any code or package that includes COLAMD
-//   or any modified version of COLAMD. 
-// 
-//     Availability:
-// 
-//   The colamd/symamd library is available at
-// 
-//       http://www.suitesparse.com
-
-  
-#ifndef EIGEN_COLAMD_H
-#define EIGEN_COLAMD_H
-
-namespace internal {
-/* Ensure that debugging is turned off: */
-#ifndef COLAMD_NDEBUG
-#define COLAMD_NDEBUG
-#endif /* NDEBUG */
-/* ========================================================================== */
-/* === Knob and statistics definitions ====================================== */
-/* ========================================================================== */
-
-/* size of the knobs [ ] array.  Only knobs [0..1] are currently used. */
-#define COLAMD_KNOBS 20
-
-/* number of output statistics.  Only stats [0..6] are currently used. */
-#define COLAMD_STATS 20 
-
-/* knobs [0] and stats [0]: dense row knob and output statistic. */
-#define COLAMD_DENSE_ROW 0
-
-/* knobs [1] and stats [1]: dense column knob and output statistic. */
-#define COLAMD_DENSE_COL 1
-
-/* stats [2]: memory defragmentation count output statistic */
-#define COLAMD_DEFRAG_COUNT 2
-
-/* stats [3]: colamd status:  zero OK, > 0 warning or notice, < 0 error */
-#define COLAMD_STATUS 3
-
-/* stats [4..6]: error info, or info on jumbled columns */ 
-#define COLAMD_INFO1 4
-#define COLAMD_INFO2 5
-#define COLAMD_INFO3 6
-
-/* error codes returned in stats [3]: */
-#define COLAMD_OK       (0)
-#define COLAMD_OK_BUT_JUMBLED     (1)
-#define COLAMD_ERROR_A_not_present    (-1)
-#define COLAMD_ERROR_p_not_present    (-2)
-#define COLAMD_ERROR_nrow_negative    (-3)
-#define COLAMD_ERROR_ncol_negative    (-4)
-#define COLAMD_ERROR_nnz_negative   (-5)
-#define COLAMD_ERROR_p0_nonzero     (-6)
-#define COLAMD_ERROR_A_too_small    (-7)
-#define COLAMD_ERROR_col_length_negative  (-8)
-#define COLAMD_ERROR_row_index_out_of_bounds  (-9)
-#define COLAMD_ERROR_out_of_memory    (-10)
-#define COLAMD_ERROR_internal_error   (-999)
-
-/* ========================================================================== */
-/* === Definitions ========================================================== */
-/* ========================================================================== */
-
-#define ONES_COMPLEMENT(r) (-(r)-1)
-
-/* -------------------------------------------------------------------------- */
-
-#define COLAMD_EMPTY (-1)
-
-/* Row and column status */
-#define ALIVE (0)
-#define DEAD  (-1)
-
-/* Column status */
-#define DEAD_PRINCIPAL    (-1)
-#define DEAD_NON_PRINCIPAL  (-2)
-
-/* Macros for row and column status update and checking. */
-#define ROW_IS_DEAD(r)      ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
-#define ROW_IS_MARKED_DEAD(row_mark)  (row_mark < ALIVE)
-#define ROW_IS_ALIVE(r)     (Row [r].shared2.mark >= ALIVE)
-#define COL_IS_DEAD(c)      (Col [c].start < ALIVE)
-#define COL_IS_ALIVE(c)     (Col [c].start >= ALIVE)
-#define COL_IS_DEAD_PRINCIPAL(c)  (Col [c].start == DEAD_PRINCIPAL)
-#define KILL_ROW(r)     { Row [r].shared2.mark = DEAD ; }
-#define KILL_PRINCIPAL_COL(c)   { Col [c].start = DEAD_PRINCIPAL ; }
-#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
-
-/* ========================================================================== */
-/* === Colamd reporting mechanism =========================================== */
-/* ========================================================================== */
-
-// == Row and Column structures ==
-template <typename IndexType>
-struct colamd_col
-{
-  IndexType start ;   /* index for A of first row in this column, or DEAD */
-  /* if column is dead */
-  IndexType length ;  /* number of rows in this column */
-  union
-  {
-    IndexType thickness ; /* number of original columns represented by this */
-    /* col, if the column is alive */
-    IndexType parent ;  /* parent in parent tree super-column structure, if */
-    /* the column is dead */
-  } shared1 ;
-  union
-  {
-    IndexType score ; /* the score used to maintain heap, if col is alive */
-    IndexType order ; /* pivot ordering of this column, if col is dead */
-  } shared2 ;
-  union
-  {
-    IndexType headhash ;  /* head of a hash bucket, if col is at the head of */
-    /* a degree list */
-    IndexType hash ;  /* hash value, if col is not in a degree list */
-    IndexType prev ;  /* previous column in degree list, if col is in a */
-    /* degree list (but not at the head of a degree list) */
-  } shared3 ;
-  union
-  {
-    IndexType degree_next ; /* next column, if col is in a degree list */
-    IndexType hash_next ;   /* next column, if col is in a hash list */
-  } shared4 ;
-  
-};
- 
-template <typename IndexType>
-struct Colamd_Row
-{
-  IndexType start ;   /* index for A of first col in this row */
-  IndexType length ;  /* number of principal columns in this row */
-  union
-  {
-    IndexType degree ;  /* number of principal & non-principal columns in row */
-    IndexType p ;   /* used as a row pointer in init_rows_cols () */
-  } shared1 ;
-  union
-  {
-    IndexType mark ;  /* for computing set differences and marking dead rows*/
-    IndexType first_column ;/* first column in row (used in garbage collection) */
-  } shared2 ;
-  
-};
- 
-/* ========================================================================== */
-/* === Colamd recommended memory size ======================================= */
-/* ========================================================================== */
- 
-/*
-  The recommended length Alen of the array A passed to colamd is given by
-  the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro.  It returns -1 if any
-  argument is negative.  2*nnz space is required for the row and column
-  indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is
-  required for the Col and Row arrays, respectively, which are internal to
-  colamd.  An additional n_col space is the minimal amount of "elbow room",
-  and nnz/5 more space is recommended for run time efficiency.
-  
-  This macro is not needed when using symamd.
-  
-  Explicit typecast to IndexType added Sept. 23, 2002, COLAMD version 2.2, to avoid
-  gcc -pedantic warning messages.
-*/
-template <typename IndexType>
-inline IndexType colamd_c(IndexType n_col) 
-{ return IndexType( ((n_col) + 1) * sizeof (colamd_col<IndexType>) / sizeof (IndexType) ) ; }
-
-template <typename IndexType>
-inline IndexType  colamd_r(IndexType n_row)
-{ return IndexType(((n_row) + 1) * sizeof (Colamd_Row<IndexType>) / sizeof (IndexType)); }
-
-// Prototypes of non-user callable routines
-template <typename IndexType>
-static IndexType init_rows_cols (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> col [], IndexType A [], IndexType p [], IndexType stats[COLAMD_STATS] ); 
-
-template <typename IndexType>
-static void init_scoring (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType head [], double knobs[COLAMD_KNOBS], IndexType *p_n_row2, IndexType *p_n_col2, IndexType *p_max_deg);
-
-template <typename IndexType>
-static IndexType find_ordering (IndexType n_row, IndexType n_col, IndexType Alen, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType head [], IndexType n_col2, IndexType max_deg, IndexType pfree);
-
-template <typename IndexType>
-static void order_children (IndexType n_col, colamd_col<IndexType> Col [], IndexType p []);
-
-template <typename IndexType>
-static void detect_super_cols (colamd_col<IndexType> Col [], IndexType A [], IndexType head [], IndexType row_start, IndexType row_length ) ;
-
-template <typename IndexType>
-static IndexType garbage_collection (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType *pfree) ;
-
-template <typename IndexType>
-static inline  IndexType clear_mark (IndexType n_row, Colamd_Row<IndexType> Row [] ) ;
-
-/* === No debugging ========================================================= */
-
-#define COLAMD_DEBUG0(params) ;
-#define COLAMD_DEBUG1(params) ;
-#define COLAMD_DEBUG2(params) ;
-#define COLAMD_DEBUG3(params) ;
-#define COLAMD_DEBUG4(params) ;
-
-#define COLAMD_ASSERT(expression) ((void) 0)
-
-
-/**
- * \brief Returns the recommended value of Alen 
- * 
- * Returns recommended value of Alen for use by colamd.  
- * Returns -1 if any input argument is negative.  
- * The use of this routine or macro is optional.  
- * Note that the macro uses its arguments   more than once, 
- * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.  
- * 
- * \param nnz nonzeros in A
- * \param n_row number of rows in A
- * \param n_col number of columns in A
- * \return recommended value of Alen for use by colamd
- */
-template <typename IndexType>
-inline IndexType colamd_recommended ( IndexType nnz, IndexType n_row, IndexType n_col)
-{
-  if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)
-    return (-1);
-  else
-    return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5)); 
-}
-
-/**
- * \brief set default parameters  The use of this routine is optional.
- * 
- * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col)
- * entries are removed prior to ordering.  Columns with more than
- * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to
- * ordering, and placed last in the output column ordering. 
- *
- * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
- * respectively, in colamd.h.  Default values of these two knobs
- * are both 0.5.  Currently, only knobs [0] and knobs [1] are
- * used, but future versions may use more knobs.  If so, they will
- * be properly set to their defaults by the future version of
- * colamd_set_defaults, so that the code that calls colamd will
- * not need to change, assuming that you either use
- * colamd_set_defaults, or pass a (double *) NULL pointer as the
- * knobs array to colamd or symamd.
- * 
- * \param knobs parameter settings for colamd
- */
-
-static inline void colamd_set_defaults(double knobs[COLAMD_KNOBS])
-{
-  /* === Local variables ================================================== */
-  
-  int i ;
-
-  if (!knobs)
-  {
-    return ;      /* no knobs to initialize */
-  }
-  for (i = 0 ; i < COLAMD_KNOBS ; i++)
-  {
-    knobs [i] = 0 ;
-  }
-  knobs [COLAMD_DENSE_ROW] = 0.5 ;  /* ignore rows over 50% dense */
-  knobs [COLAMD_DENSE_COL] = 0.5 ;  /* ignore columns over 50% dense */
-}
-
-/** 
- * \brief  Computes a column ordering using the column approximate minimum degree ordering
- * 
- * Computes a column ordering (Q) of A such that P(AQ)=LU or
- * (AQ)'AQ=LL' have less fill-in and require fewer floating point
- * operations than factorizing the unpermuted matrix A or A'A,
- * respectively.
- * 
- * 
- * \param n_row number of rows in A
- * \param n_col number of columns in A
- * \param Alen, size of the array A
- * \param A row indices of the matrix, of size ALen
- * \param p column pointers of A, of size n_col+1
- * \param knobs parameter settings for colamd
- * \param stats colamd output statistics and error codes
- */
-template <typename IndexType>
-static bool colamd(IndexType n_row, IndexType n_col, IndexType Alen, IndexType *A, IndexType *p, double knobs[COLAMD_KNOBS], IndexType stats[COLAMD_STATS])
-{
-  /* === Local variables ================================================== */
-  
-  IndexType i ;     /* loop index */
-  IndexType nnz ;     /* nonzeros in A */
-  IndexType Row_size ;    /* size of Row [], in integers */
-  IndexType Col_size ;    /* size of Col [], in integers */
-  IndexType need ;      /* minimum required length of A */
-  Colamd_Row<IndexType> *Row ;   /* pointer into A of Row [0..n_row] array */
-  colamd_col<IndexType> *Col ;   /* pointer into A of Col [0..n_col] array */
-  IndexType n_col2 ;    /* number of non-dense, non-empty columns */
-  IndexType n_row2 ;    /* number of non-dense, non-empty rows */
-  IndexType ngarbage ;    /* number of garbage collections performed */
-  IndexType max_deg ;   /* maximum row degree */
-  double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
-  
-  
-  /* === Check the input arguments ======================================== */
-  
-  if (!stats)
-  {
-    COLAMD_DEBUG0 (("colamd: stats not present\n")) ;
-    return (false) ;
-  }
-  for (i = 0 ; i < COLAMD_STATS ; i++)
-  {
-    stats [i] = 0 ;
-  }
-  stats [COLAMD_STATUS] = COLAMD_OK ;
-  stats [COLAMD_INFO1] = -1 ;
-  stats [COLAMD_INFO2] = -1 ;
-  
-  if (!A)   /* A is not present */
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
-    COLAMD_DEBUG0 (("colamd: A not present\n")) ;
-    return (false) ;
-  }
-  
-  if (!p)   /* p is not present */
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
-    COLAMD_DEBUG0 (("colamd: p not present\n")) ;
-    return (false) ;
-  }
-  
-  if (n_row < 0)  /* n_row must be >= 0 */
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
-    stats [COLAMD_INFO1] = n_row ;
-    COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
-    return (false) ;
-  }
-  
-  if (n_col < 0)  /* n_col must be >= 0 */
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
-    stats [COLAMD_INFO1] = n_col ;
-    COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
-    return (false) ;
-  }
-  
-  nnz = p [n_col] ;
-  if (nnz < 0)  /* nnz must be >= 0 */
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
-    stats [COLAMD_INFO1] = nnz ;
-    COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
-    return (false) ;
-  }
-  
-  if (p [0] != 0)
-  {
-    stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
-    stats [COLAMD_INFO1] = p [0] ;
-    COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
-    return (false) ;
-  }
-  
-  /* === If no knobs, set default knobs =================================== */
-  
-  if (!knobs)
-  {
-    colamd_set_defaults (default_knobs) ;
-    knobs = default_knobs ;
-  }
-  
-  /* === Allocate the Row and Col arrays from array A ===================== */
-  
-  Col_size = colamd_c (n_col) ;
-  Row_size = colamd_r (n_row) ;
-  need = 2*nnz + n_col + Col_size + Row_size ;
-  
-  if (need > Alen)
-  {
-    /* not enough space in array A to perform the ordering */
-    stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
-    stats [COLAMD_INFO1] = need ;
-    stats [COLAMD_INFO2] = Alen ;
-    COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
-    return (false) ;
-  }
-  
-  Alen -= Col_size + Row_size ;
-  Col = (colamd_col<IndexType> *) &A [Alen] ;
-  Row = (Colamd_Row<IndexType> *) &A [Alen + Col_size] ;
-
-  /* === Construct the row and column data structures ===================== */
-  
-  if (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
-  {
-    /* input matrix is invalid */
-    COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ;
-    return (false) ;
-  }
-  
-  /* === Initialize scores, kill dense rows/columns ======================= */
-
-  Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs,
-		&n_row2, &n_col2, &max_deg) ;
-  
-  /* === Order the supercolumns =========================================== */
-  
-  ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p,
-			    n_col2, max_deg, 2*nnz) ;
-  
-  /* === Order the non-principal columns ================================== */
-  
-  Eigen::internal::order_children (n_col, Col, p) ;
-  
-  /* === Return statistics in stats ======================================= */
-  
-  stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;
-  stats [COLAMD_DENSE_COL] = n_col - n_col2 ;
-  stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
-  COLAMD_DEBUG0 (("colamd: done.\n")) ; 
-  return (true) ;
-}
-
-/* ========================================================================== */
-/* === NON-USER-CALLABLE ROUTINES: ========================================== */
-/* ========================================================================== */
-
-/* There are no user-callable routines beyond this point in the file */
-
-
-/* ========================================================================== */
-/* === init_rows_cols ======================================================= */
-/* ========================================================================== */
-
-/*
-  Takes the column form of the matrix in A and creates the row form of the
-  matrix.  Also, row and column attributes are stored in the Col and Row
-  structs.  If the columns are un-sorted or contain duplicate row indices,
-  this routine will also sort and remove duplicate row indices from the
-  column form of the matrix.  Returns false if the matrix is invalid,
-  true otherwise.  Not user-callable.
-*/
-template <typename IndexType>
-static IndexType init_rows_cols  /* returns true if OK, or false otherwise */
-  (
-    /* === Parameters ======================================================= */
-
-    IndexType n_row,      /* number of rows of A */
-    IndexType n_col,      /* number of columns of A */
-    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */
-    colamd_col<IndexType> Col [],    /* of size n_col+1 */
-    IndexType A [],     /* row indices of A, of size Alen */
-    IndexType p [],     /* pointers to columns in A, of size n_col+1 */
-    IndexType stats [COLAMD_STATS]  /* colamd statistics */ 
-    )
-{
-  /* === Local variables ================================================== */
-
-  IndexType col ;     /* a column index */
-  IndexType row ;     /* a row index */
-  IndexType *cp ;     /* a column pointer */
-  IndexType *cp_end ;   /* a pointer to the end of a column */
-  IndexType *rp ;     /* a row pointer */
-  IndexType *rp_end ;   /* a pointer to the end of a row */
-  IndexType last_row ;    /* previous row */
-
-  /* === Initialize columns, and check column pointers ==================== */
-
-  for (col = 0 ; col < n_col ; col++)
-  {
-    Col [col].start = p [col] ;
-    Col [col].length = p [col+1] - p [col] ;
-
-    if ((Col [col].length) < 0) // extra parentheses to work-around gcc bug 10200
-    {
-      /* column pointers must be non-decreasing */
-      stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
-      stats [COLAMD_INFO1] = col ;
-      stats [COLAMD_INFO2] = Col [col].length ;
-      COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
-      return (false) ;
-    }
-
-    Col [col].shared1.thickness = 1 ;
-    Col [col].shared2.score = 0 ;
-    Col [col].shared3.prev = COLAMD_EMPTY ;
-    Col [col].shared4.degree_next = COLAMD_EMPTY ;
-  }
-
-  /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
-
-  /* === Scan columns, compute row degrees, and check row indices ========= */
-
-  stats [COLAMD_INFO3] = 0 ;  /* number of duplicate or unsorted row indices*/
-
-  for (row = 0 ; row < n_row ; row++)
-  {
-    Row [row].length = 0 ;
-    Row [row].shared2.mark = -1 ;
-  }
-
-  for (col = 0 ; col < n_col ; col++)
-  {
-    last_row = -1 ;
-
-    cp = &A [p [col]] ;
-    cp_end = &A [p [col+1]] ;
-
-    while (cp < cp_end)
-    {
-      row = *cp++ ;
-
-      /* make sure row indices within range */
-      if (row < 0 || row >= n_row)
-      {
-	stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
-	stats [COLAMD_INFO1] = col ;
-	stats [COLAMD_INFO2] = row ;
-	stats [COLAMD_INFO3] = n_row ;
-	COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
-	return (false) ;
-      }
-
-      if (row <= last_row || Row [row].shared2.mark == col)
-      {
-	/* row index are unsorted or repeated (or both), thus col */
-	/* is jumbled.  This is a notice, not an error condition. */
-	stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
-	stats [COLAMD_INFO1] = col ;
-	stats [COLAMD_INFO2] = row ;
-	(stats [COLAMD_INFO3]) ++ ;
-	COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
-      }
-
-      if (Row [row].shared2.mark != col)
-      {
-	Row [row].length++ ;
-      }
-      else
-      {
-	/* this is a repeated entry in the column, */
-	/* it will be removed */
-	Col [col].length-- ;
-      }
-
-      /* mark the row as having been seen in this column */
-      Row [row].shared2.mark = col ;
-
-      last_row = row ;
-    }
-  }
-
-  /* === Compute row pointers ============================================= */
-
-  /* row form of the matrix starts directly after the column */
-  /* form of matrix in A */
-  Row [0].start = p [n_col] ;
-  Row [0].shared1.p = Row [0].start ;
-  Row [0].shared2.mark = -1 ;
-  for (row = 1 ; row < n_row ; row++)
-  {
-    Row [row].start = Row [row-1].start + Row [row-1].length ;
-    Row [row].shared1.p = Row [row].start ;
-    Row [row].shared2.mark = -1 ;
-  }
-
-  /* === Create row form ================================================== */
-
-  if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
-  {
-    /* if cols jumbled, watch for repeated row indices */
-    for (col = 0 ; col < n_col ; col++)
-    {
-      cp = &A [p [col]] ;
-      cp_end = &A [p [col+1]] ;
-      while (cp < cp_end)
-      {
-	row = *cp++ ;
-	if (Row [row].shared2.mark != col)
-	{
-	  A [(Row [row].shared1.p)++] = col ;
-	  Row [row].shared2.mark = col ;
-	}
-      }
-    }
-  }
-  else
-  {
-    /* if cols not jumbled, we don't need the mark (this is faster) */
-    for (col = 0 ; col < n_col ; col++)
-    {
-      cp = &A [p [col]] ;
-      cp_end = &A [p [col+1]] ;
-      while (cp < cp_end)
-      {
-	A [(Row [*cp++].shared1.p)++] = col ;
-      }
-    }
-  }
-
-  /* === Clear the row marks and set row degrees ========================== */
-
-  for (row = 0 ; row < n_row ; row++)
-  {
-    Row [row].shared2.mark = 0 ;
-    Row [row].shared1.degree = Row [row].length ;
-  }
-
-  /* === See if we need to re-create columns ============================== */
-
-  if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
-  {
-    COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
-
-
-    /* === Compute col pointers ========================================= */
-
-    /* col form of the matrix starts at A [0]. */
-    /* Note, we may have a gap between the col form and the row */
-    /* form if there were duplicate entries, if so, it will be */
-    /* removed upon the first garbage collection */
-    Col [0].start = 0 ;
-    p [0] = Col [0].start ;
-    for (col = 1 ; col < n_col ; col++)
-    {
-      /* note that the lengths here are for pruned columns, i.e. */
-      /* no duplicate row indices will exist for these columns */
-      Col [col].start = Col [col-1].start + Col [col-1].length ;
-      p [col] = Col [col].start ;
-    }
-
-    /* === Re-create col form =========================================== */
-
-    for (row = 0 ; row < n_row ; row++)
-    {
-      rp = &A [Row [row].start] ;
-      rp_end = rp + Row [row].length ;
-      while (rp < rp_end)
-      {
-	A [(p [*rp++])++] = row ;
-      }
-    }
-  }
-
-  /* === Done.  Matrix is not (or no longer) jumbled ====================== */
-
-  return (true) ;
-}
-
-
-/* ========================================================================== */
-/* === init_scoring ========================================================= */
-/* ========================================================================== */
-
-/*
-  Kills dense or empty columns and rows, calculates an initial score for
-  each column, and places all columns in the degree lists.  Not user-callable.
-*/
-template <typename IndexType>
-static void init_scoring
-  (
-    /* === Parameters ======================================================= */
-
-    IndexType n_row,      /* number of rows of A */
-    IndexType n_col,      /* number of columns of A */
-    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */
-    colamd_col<IndexType> Col [],    /* of size n_col+1 */
-    IndexType A [],     /* column form and row form of A */
-    IndexType head [],    /* of size n_col+1 */
-    double knobs [COLAMD_KNOBS],/* parameters */
-    IndexType *p_n_row2,    /* number of non-dense, non-empty rows */
-    IndexType *p_n_col2,    /* number of non-dense, non-empty columns */
-    IndexType *p_max_deg    /* maximum row degree */
-    )
-{
-  /* === Local variables ================================================== */
-
-  IndexType c ;     /* a column index */
-  IndexType r, row ;    /* a row index */
-  IndexType *cp ;     /* a column pointer */
-  IndexType deg ;     /* degree of a row or column */
-  IndexType *cp_end ;   /* a pointer to the end of a column */
-  IndexType *new_cp ;   /* new column pointer */
-  IndexType col_length ;    /* length of pruned column */
-  IndexType score ;     /* current column score */
-  IndexType n_col2 ;    /* number of non-dense, non-empty columns */
-  IndexType n_row2 ;    /* number of non-dense, non-empty rows */
-  IndexType dense_row_count ; /* remove rows with more entries than this */
-  IndexType dense_col_count ; /* remove cols with more entries than this */
-  IndexType min_score ;   /* smallest column score */
-  IndexType max_deg ;   /* maximum row degree */
-  IndexType next_col ;    /* Used to add to degree list.*/
-
-
-  /* === Extract knobs ==================================================== */
-
-  dense_row_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [COLAMD_DENSE_ROW] * n_col), n_col)) ;
-  dense_col_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [COLAMD_DENSE_COL] * n_row), n_row)) ;
-  COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
-  max_deg = 0 ;
-  n_col2 = n_col ;
-  n_row2 = n_row ;
-
-  /* === Kill empty columns =============================================== */
-
-  /* Put the empty columns at the end in their natural order, so that LU */
-  /* factorization can proceed as far as possible. */
-  for (c = n_col-1 ; c >= 0 ; c--)
-  {
-    deg = Col [c].length ;
-    if (deg == 0)
-    {
-      /* this is a empty column, kill and order it last */
-      Col [c].shared2.order = --n_col2 ;
-      KILL_PRINCIPAL_COL (c) ;
-    }
-  }
-  COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
-
-  /* === Kill dense columns =============================================== */
-
-  /* Put the dense columns at the end, in their natural order */
-  for (c = n_col-1 ; c >= 0 ; c--)
-  {
-    /* skip any dead columns */
-    if (COL_IS_DEAD (c))
-    {
-      continue ;
-    }
-    deg = Col [c].length ;
-    if (deg > dense_col_count)
-    {
-      /* this is a dense column, kill and order it last */
-      Col [c].shared2.order = --n_col2 ;
-      /* decrement the row degrees */
-      cp = &A [Col [c].start] ;
-      cp_end = cp + Col [c].length ;
-      while (cp < cp_end)
-      {
-	Row [*cp++].shared1.degree-- ;
-      }
-      KILL_PRINCIPAL_COL (c) ;
-    }
-  }
-  COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
-
-  /* === Kill dense and empty rows ======================================== */
-
-  for (r = 0 ; r < n_row ; r++)
-  {
-    deg = Row [r].shared1.degree ;
-    COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;
-    if (deg > dense_row_count || deg == 0)
-    {
-      /* kill a dense or empty row */
-      KILL_ROW (r) ;
-      --n_row2 ;
-    }
-    else
-    {
-      /* keep track of max degree of remaining rows */
-      max_deg = numext::maxi(max_deg, deg) ;
-    }
-  }
-  COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
-
-  /* === Compute initial column scores ==================================== */
-
-  /* At this point the row degrees are accurate.  They reflect the number */
-  /* of "live" (non-dense) columns in each row.  No empty rows exist. */
-  /* Some "live" columns may contain only dead rows, however.  These are */
-  /* pruned in the code below. */
-
-  /* now find the initial matlab score for each column */
-  for (c = n_col-1 ; c >= 0 ; c--)
-  {
-    /* skip dead column */
-    if (COL_IS_DEAD (c))
-    {
-      continue ;
-    }
-    score = 0 ;
-    cp = &A [Col [c].start] ;
-    new_cp = cp ;
-    cp_end = cp + Col [c].length ;
-    while (cp < cp_end)
-    {
-      /* get a row */
-      row = *cp++ ;
-      /* skip if dead */
-      if (ROW_IS_DEAD (row))
-      {
-	continue ;
-      }
-      /* compact the column */
-      *new_cp++ = row ;
-      /* add row's external degree */
-      score += Row [row].shared1.degree - 1 ;
-      /* guard against integer overflow */
-      score = numext::mini(score, n_col) ;
-    }
-    /* determine pruned column length */
-    col_length = (IndexType) (new_cp - &A [Col [c].start]) ;
-    if (col_length == 0)
-    {
-      /* a newly-made null column (all rows in this col are "dense" */
-      /* and have already been killed) */
-      COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ;
-      Col [c].shared2.order = --n_col2 ;
-      KILL_PRINCIPAL_COL (c) ;
-    }
-    else
-    {
-      /* set column length and set score */
-      COLAMD_ASSERT (score >= 0) ;
-      COLAMD_ASSERT (score <= n_col) ;
-      Col [c].length = col_length ;
-      Col [c].shared2.score = score ;
-    }
-  }
-  COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
-		  n_col-n_col2)) ;
-
-  /* At this point, all empty rows and columns are dead.  All live columns */
-  /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
-  /* yet).  Rows may contain dead columns, but all live rows contain at */
-  /* least one live column. */
-
-  /* === Initialize degree lists ========================================== */
-
-
-  /* clear the hash buckets */
-  for (c = 0 ; c <= n_col ; c++)
-  {
-    head [c] = COLAMD_EMPTY ;
-  }
-  min_score = n_col ;
-  /* place in reverse order, so low column indices are at the front */
-  /* of the lists.  This is to encourage natural tie-breaking */
-  for (c = n_col-1 ; c >= 0 ; c--)
-  {
-    /* only add principal columns to degree lists */
-    if (COL_IS_ALIVE (c))
-    {
-      COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n",
-		      c, Col [c].shared2.score, min_score, n_col)) ;
-
-      /* === Add columns score to DList =============================== */
-
-      score = Col [c].shared2.score ;
-
-      COLAMD_ASSERT (min_score >= 0) ;
-      COLAMD_ASSERT (min_score <= n_col) ;
-      COLAMD_ASSERT (score >= 0) ;
-      COLAMD_ASSERT (score <= n_col) ;
-      COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ;
-
-      /* now add this column to dList at proper score location */
-      next_col = head [score] ;
-      Col [c].shared3.prev = COLAMD_EMPTY ;
-      Col [c].shared4.degree_next = next_col ;
-
-      /* if there already was a column with the same score, set its */
-      /* previous pointer to this new column */
-      if (next_col != COLAMD_EMPTY)
-      {
-	Col [next_col].shared3.prev = c ;
-      }
-      head [score] = c ;
-
-      /* see if this score is less than current min */
-      min_score = numext::mini(min_score, score) ;
-
-
-    }
-  }
-
-
-  /* === Return number of remaining columns, and max row degree =========== */
-
-  *p_n_col2 = n_col2 ;
-  *p_n_row2 = n_row2 ;
-  *p_max_deg = max_deg ;
-}
-
-
-/* ========================================================================== */
-/* === find_ordering ======================================================== */
-/* ========================================================================== */
-
-/*
-  Order the principal columns of the supercolumn form of the matrix
-  (no supercolumns on input).  Uses a minimum approximate column minimum
-  degree ordering method.  Not user-callable.
-*/
-template <typename IndexType>
-static IndexType find_ordering /* return the number of garbage collections */
-  (
-    /* === Parameters ======================================================= */
-
-    IndexType n_row,      /* number of rows of A */
-    IndexType n_col,      /* number of columns of A */
-    IndexType Alen,     /* size of A, 2*nnz + n_col or larger */
-    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */
-    colamd_col<IndexType> Col [],    /* of size n_col+1 */
-    IndexType A [],     /* column form and row form of A */
-    IndexType head [],    /* of size n_col+1 */
-    IndexType n_col2,     /* Remaining columns to order */
-    IndexType max_deg,    /* Maximum row degree */
-    IndexType pfree     /* index of first free slot (2*nnz on entry) */
-    )
-{
-  /* === Local variables ================================================== */
-
-  IndexType k ;     /* current pivot ordering step */
-  IndexType pivot_col ;   /* current pivot column */
-  IndexType *cp ;     /* a column pointer */
-  IndexType *rp ;     /* a row pointer */
-  IndexType pivot_row ;   /* current pivot row */
-  IndexType *new_cp ;   /* modified column pointer */
-  IndexType *new_rp ;   /* modified row pointer */
-  IndexType pivot_row_start ; /* pointer to start of pivot row */
-  IndexType pivot_row_degree ;  /* number of columns in pivot row */
-  IndexType pivot_row_length ;  /* number of supercolumns in pivot row */
-  IndexType pivot_col_score ; /* score of pivot column */
-  IndexType needed_memory ;   /* free space needed for pivot row */
-  IndexType *cp_end ;   /* pointer to the end of a column */
-  IndexType *rp_end ;   /* pointer to the end of a row */
-  IndexType row ;     /* a row index */
-  IndexType col ;     /* a column index */
-  IndexType max_score ;   /* maximum possible score */
-  IndexType cur_score ;   /* score of current column */
-  unsigned int hash ;   /* hash value for supernode detection */
-  IndexType head_column ;   /* head of hash bucket */
-  IndexType first_col ;   /* first column in hash bucket */
-  IndexType tag_mark ;    /* marker value for mark array */
-  IndexType row_mark ;    /* Row [row].shared2.mark */
-  IndexType set_difference ;  /* set difference size of row with pivot row */
-  IndexType min_score ;   /* smallest column score */
-  IndexType col_thickness ;   /* "thickness" (no. of columns in a supercol) */
-  IndexType max_mark ;    /* maximum value of tag_mark */
-  IndexType pivot_col_thickness ; /* number of columns represented by pivot col */
-  IndexType prev_col ;    /* Used by Dlist operations. */
-  IndexType next_col ;    /* Used by Dlist operations. */
-  IndexType ngarbage ;    /* number of garbage collections performed */
-
-
-  /* === Initialization and clear mark ==================================== */
-
-  max_mark = INT_MAX - n_col ;  /* INT_MAX defined in <limits.h> */
-  tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
-  min_score = 0 ;
-  ngarbage = 0 ;
-  COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
-
-  /* === Order the columns ================================================ */
-
-  for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
-  {
-
-    /* === Select pivot column, and order it ============================ */
-
-    /* make sure degree list isn't empty */
-    COLAMD_ASSERT (min_score >= 0) ;
-    COLAMD_ASSERT (min_score <= n_col) ;
-    COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ;
-
-    /* get pivot column from head of minimum degree list */
-    while (min_score < n_col && head [min_score] == COLAMD_EMPTY)
-    {
-      min_score++ ;
-    }
-    pivot_col = head [min_score] ;
-    COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
-    next_col = Col [pivot_col].shared4.degree_next ;
-    head [min_score] = next_col ;
-    if (next_col != COLAMD_EMPTY)
-    {
-      Col [next_col].shared3.prev = COLAMD_EMPTY ;
-    }
-
-    COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ;
-    COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ;
-
-    /* remember score for defrag check */
-    pivot_col_score = Col [pivot_col].shared2.score ;
-
-    /* the pivot column is the kth column in the pivot order */
-    Col [pivot_col].shared2.order = k ;
-
-    /* increment order count by column thickness */
-    pivot_col_thickness = Col [pivot_col].shared1.thickness ;
-    k += pivot_col_thickness ;
-    COLAMD_ASSERT (pivot_col_thickness > 0) ;
-
-    /* === Garbage_collection, if necessary ============================= */
-
-    needed_memory = numext::mini(pivot_col_score, n_col - k) ;
-    if (pfree + needed_memory >= Alen)
-    {
-      pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
-      ngarbage++ ;
-      /* after garbage collection we will have enough */
-      COLAMD_ASSERT (pfree + needed_memory < Alen) ;
-      /* garbage collection has wiped out the Row[].shared2.mark array */
-      tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
-
-    }
-
-    /* === Compute pivot row pattern ==================================== */
-
-    /* get starting location for this new merged row */
-    pivot_row_start = pfree ;
-
-    /* initialize new row counts to zero */
-    pivot_row_degree = 0 ;
-
-    /* tag pivot column as having been visited so it isn't included */
-    /* in merged pivot row */
-    Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
-
-    /* pivot row is the union of all rows in the pivot column pattern */
-    cp = &A [Col [pivot_col].start] ;
-    cp_end = cp + Col [pivot_col].length ;
-    while (cp < cp_end)
-    {
-      /* get a row */
-      row = *cp++ ;
-      COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ;
-      /* skip if row is dead */
-      if (ROW_IS_DEAD (row))
-      {
-	continue ;
-      }
-      rp = &A [Row [row].start] ;
-      rp_end = rp + Row [row].length ;
-      while (rp < rp_end)
-      {
-	/* get a column */
-	col = *rp++ ;
-	/* add the column, if alive and untagged */
-	col_thickness = Col [col].shared1.thickness ;
-	if (col_thickness > 0 && COL_IS_ALIVE (col))
-	{
-	  /* tag column in pivot row */
-	  Col [col].shared1.thickness = -col_thickness ;
-	  COLAMD_ASSERT (pfree < Alen) ;
-	  /* place column in pivot row */
-	  A [pfree++] = col ;
-	  pivot_row_degree += col_thickness ;
-	}
-      }
-    }
-
-    /* clear tag on pivot column */
-    Col [pivot_col].shared1.thickness = pivot_col_thickness ;
-    max_deg = numext::maxi(max_deg, pivot_row_degree) ;
-
-
-    /* === Kill all rows used to construct pivot row ==================== */
-
-    /* also kill pivot row, temporarily */
-    cp = &A [Col [pivot_col].start] ;
-    cp_end = cp + Col [pivot_col].length ;
-    while (cp < cp_end)
-    {
-      /* may be killing an already dead row */
-      row = *cp++ ;
-      COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
-      KILL_ROW (row) ;
-    }
-
-    /* === Select a row index to use as the new pivot row =============== */
-
-    pivot_row_length = pfree - pivot_row_start ;
-    if (pivot_row_length > 0)
-    {
-      /* pick the "pivot" row arbitrarily (first row in col) */
-      pivot_row = A [Col [pivot_col].start] ;
-      COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
-    }
-    else
-    {
-      /* there is no pivot row, since it is of zero length */
-      pivot_row = COLAMD_EMPTY ;
-      COLAMD_ASSERT (pivot_row_length == 0) ;
-    }
-    COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
-
-    /* === Approximate degree computation =============================== */
-
-    /* Here begins the computation of the approximate degree.  The column */
-    /* score is the sum of the pivot row "length", plus the size of the */
-    /* set differences of each row in the column minus the pattern of the */
-    /* pivot row itself.  The column ("thickness") itself is also */
-    /* excluded from the column score (we thus use an approximate */
-    /* external degree). */
-
-    /* The time taken by the following code (compute set differences, and */
-    /* add them up) is proportional to the size of the data structure */
-    /* being scanned - that is, the sum of the sizes of each column in */
-    /* the pivot row.  Thus, the amortized time to compute a column score */
-    /* is proportional to the size of that column (where size, in this */
-    /* context, is the column "length", or the number of row indices */
-    /* in that column).  The number of row indices in a column is */
-    /* monotonically non-decreasing, from the length of the original */
-    /* column on input to colamd. */
-
-    /* === Compute set differences ====================================== */
-
-    COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ;
-
-    /* pivot row is currently dead - it will be revived later. */
-
-    COLAMD_DEBUG3 (("Pivot row: ")) ;
-    /* for each column in pivot row */
-    rp = &A [pivot_row_start] ;
-    rp_end = rp + pivot_row_length ;
-    while (rp < rp_end)
-    {
-      col = *rp++ ;
-      COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
-      COLAMD_DEBUG3 (("Col: %d\n", col)) ;
-
-      /* clear tags used to construct pivot row pattern */
-      col_thickness = -Col [col].shared1.thickness ;
-      COLAMD_ASSERT (col_thickness > 0) ;
-      Col [col].shared1.thickness = col_thickness ;
-
-      /* === Remove column from degree list =========================== */
-
-      cur_score = Col [col].shared2.score ;
-      prev_col = Col [col].shared3.prev ;
-      next_col = Col [col].shared4.degree_next ;
-      COLAMD_ASSERT (cur_score >= 0) ;
-      COLAMD_ASSERT (cur_score <= n_col) ;
-      COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ;
-      if (prev_col == COLAMD_EMPTY)
-      {
-	head [cur_score] = next_col ;
-      }
-      else
-      {
-	Col [prev_col].shared4.degree_next = next_col ;
-      }
-      if (next_col != COLAMD_EMPTY)
-      {
-	Col [next_col].shared3.prev = prev_col ;
-      }
-
-      /* === Scan the column ========================================== */
-
-      cp = &A [Col [col].start] ;
-      cp_end = cp + Col [col].length ;
-      while (cp < cp_end)
-      {
-	/* get a row */
-	row = *cp++ ;
-	row_mark = Row [row].shared2.mark ;
-	/* skip if dead */
-	if (ROW_IS_MARKED_DEAD (row_mark))
-	{
-	  continue ;
-	}
-	COLAMD_ASSERT (row != pivot_row) ;
-	set_difference = row_mark - tag_mark ;
-	/* check if the row has been seen yet */
-	if (set_difference < 0)
-	{
-	  COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;
-	  set_difference = Row [row].shared1.degree ;
-	}
-	/* subtract column thickness from this row's set difference */
-	set_difference -= col_thickness ;
-	COLAMD_ASSERT (set_difference >= 0) ;
-	/* absorb this row if the set difference becomes zero */
-	if (set_difference == 0)
-	{
-	  COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
-	  KILL_ROW (row) ;
-	}
-	else
-	{
-	  /* save the new mark */
-	  Row [row].shared2.mark = set_difference + tag_mark ;
-	}
-      }
-    }
-
-
-    /* === Add up set differences for each column ======================= */
-
-    COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ;
-
-    /* for each column in pivot row */
-    rp = &A [pivot_row_start] ;
-    rp_end = rp + pivot_row_length ;
-    while (rp < rp_end)
-    {
-      /* get a column */
-      col = *rp++ ;
-      COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
-      hash = 0 ;
-      cur_score = 0 ;
-      cp = &A [Col [col].start] ;
-      /* compact the column */
-      new_cp = cp ;
-      cp_end = cp + Col [col].length ;
-
-      COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
-
-      while (cp < cp_end)
-      {
-	/* get a row */
-	row = *cp++ ;
-	COLAMD_ASSERT(row >= 0 && row < n_row) ;
-	row_mark = Row [row].shared2.mark ;
-	/* skip if dead */
-	if (ROW_IS_MARKED_DEAD (row_mark))
-	{
-	  continue ;
-	}
-	COLAMD_ASSERT (row_mark > tag_mark) ;
-	/* compact the column */
-	*new_cp++ = row ;
-	/* compute hash function */
-	hash += row ;
-	/* add set difference */
-	cur_score += row_mark - tag_mark ;
-	/* integer overflow... */
-	cur_score = numext::mini(cur_score, n_col) ;
-      }
-
-      /* recompute the column's length */
-      Col [col].length = (IndexType) (new_cp - &A [Col [col].start]) ;
-
-      /* === Further mass elimination ================================= */
-
-      if (Col [col].length == 0)
-      {
-	COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
-	/* nothing left but the pivot row in this column */
-	KILL_PRINCIPAL_COL (col) ;
-	pivot_row_degree -= Col [col].shared1.thickness ;
-	COLAMD_ASSERT (pivot_row_degree >= 0) ;
-	/* order it */
-	Col [col].shared2.order = k ;
-	/* increment order count by column thickness */
-	k += Col [col].shared1.thickness ;
-      }
-      else
-      {
-	/* === Prepare for supercolumn detection ==================== */
-
-	COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
-
-	/* save score so far */
-	Col [col].shared2.score = cur_score ;
-
-	/* add column to hash table, for supercolumn detection */
-	hash %= n_col + 1 ;
-
-	COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
-	COLAMD_ASSERT (hash <= n_col) ;
-
-	head_column = head [hash] ;
-	if (head_column > COLAMD_EMPTY)
-	{
-	  /* degree list "hash" is non-empty, use prev (shared3) of */
-	  /* first column in degree list as head of hash bucket */
-	  first_col = Col [head_column].shared3.headhash ;
-	  Col [head_column].shared3.headhash = col ;
-	}
-	else
-	{
-	  /* degree list "hash" is empty, use head as hash bucket */
-	  first_col = - (head_column + 2) ;
-	  head [hash] = - (col + 2) ;
-	}
-	Col [col].shared4.hash_next = first_col ;
-
-	/* save hash function in Col [col].shared3.hash */
-	Col [col].shared3.hash = (IndexType) hash ;
-	COLAMD_ASSERT (COL_IS_ALIVE (col)) ;
-      }
-    }
-
-    /* The approximate external column degree is now computed.  */
-
-    /* === Supercolumn detection ======================================== */
-
-    COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ;
-
-    Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;
-
-    /* === Kill the pivotal column ====================================== */
-
-    KILL_PRINCIPAL_COL (pivot_col) ;
-
-    /* === Clear mark =================================================== */
-
-    tag_mark += (max_deg + 1) ;
-    if (tag_mark >= max_mark)
-    {
-      COLAMD_DEBUG2 (("clearing tag_mark\n")) ;
-      tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
-    }
-
-    /* === Finalize the new pivot row, and column scores ================ */
-
-    COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ;
-
-    /* for each column in pivot row */
-    rp = &A [pivot_row_start] ;
-    /* compact the pivot row */
-    new_rp = rp ;
-    rp_end = rp + pivot_row_length ;
-    while (rp < rp_end)
-    {
-      col = *rp++ ;
-      /* skip dead columns */
-      if (COL_IS_DEAD (col))
-      {
-	continue ;
-      }
-      *new_rp++ = col ;
-      /* add new pivot row to column */
-      A [Col [col].start + (Col [col].length++)] = pivot_row ;
-
-      /* retrieve score so far and add on pivot row's degree. */
-      /* (we wait until here for this in case the pivot */
-      /* row's degree was reduced due to mass elimination). */
-      cur_score = Col [col].shared2.score + pivot_row_degree ;
-
-      /* calculate the max possible score as the number of */
-      /* external columns minus the 'k' value minus the */
-      /* columns thickness */
-      max_score = n_col - k - Col [col].shared1.thickness ;
-
-      /* make the score the external degree of the union-of-rows */
-      cur_score -= Col [col].shared1.thickness ;
-
-      /* make sure score is less or equal than the max score */
-      cur_score = numext::mini(cur_score, max_score) ;
-      COLAMD_ASSERT (cur_score >= 0) ;
-
-      /* store updated score */
-      Col [col].shared2.score = cur_score ;
-
-      /* === Place column back in degree list ========================= */
-
-      COLAMD_ASSERT (min_score >= 0) ;
-      COLAMD_ASSERT (min_score <= n_col) ;
-      COLAMD_ASSERT (cur_score >= 0) ;
-      COLAMD_ASSERT (cur_score <= n_col) ;
-      COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ;
-      next_col = head [cur_score] ;
-      Col [col].shared4.degree_next = next_col ;
-      Col [col].shared3.prev = COLAMD_EMPTY ;
-      if (next_col != COLAMD_EMPTY)
-      {
-	Col [next_col].shared3.prev = col ;
-      }
-      head [cur_score] = col ;
-
-      /* see if this score is less than current min */
-      min_score = numext::mini(min_score, cur_score) ;
-
-    }
-
-    /* === Resurrect the new pivot row ================================== */
-
-    if (pivot_row_degree > 0)
-    {
-      /* update pivot row length to reflect any cols that were killed */
-      /* during super-col detection and mass elimination */
-      Row [pivot_row].start  = pivot_row_start ;
-      Row [pivot_row].length = (IndexType) (new_rp - &A[pivot_row_start]) ;
-      Row [pivot_row].shared1.degree = pivot_row_degree ;
-      Row [pivot_row].shared2.mark = 0 ;
-      /* pivot row is no longer dead */
-    }
-  }
-
-  /* === All principal columns have now been ordered ====================== */
-
-  return (ngarbage) ;
-}
-
-
-/* ========================================================================== */
-/* === order_children ======================================================= */
-/* ========================================================================== */
-
-/*
-  The find_ordering routine has ordered all of the principal columns (the
-  representatives of the supercolumns).  The non-principal columns have not
-  yet been ordered.  This routine orders those columns by walking up the
-  parent tree (a column is a child of the column which absorbed it).  The
-  final permutation vector is then placed in p [0 ... n_col-1], with p [0]
-  being the first column, and p [n_col-1] being the last.  It doesn't look
-  like it at first glance, but be assured that this routine takes time linear
-  in the number of columns.  Although not immediately obvious, the time
-  taken by this routine is O (n_col), that is, linear in the number of
-  columns.  Not user-callable.
-*/
-template <typename IndexType>
-static inline  void order_children
-(
-  /* === Parameters ======================================================= */
-
-  IndexType n_col,      /* number of columns of A */
-  colamd_col<IndexType> Col [],    /* of size n_col+1 */
-  IndexType p []      /* p [0 ... n_col-1] is the column permutation*/
-  )
-{
-  /* === Local variables ================================================== */
-
-  IndexType i ;     /* loop counter for all columns */
-  IndexType c ;     /* column index */
-  IndexType parent ;    /* index of column's parent */
-  IndexType order ;     /* column's order */
-
-  /* === Order each non-principal column ================================== */
-
-  for (i = 0 ; i < n_col ; i++)
-  {
-    /* find an un-ordered non-principal column */
-    COLAMD_ASSERT (COL_IS_DEAD (i)) ;
-    if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY)
-    {
-      parent = i ;
-      /* once found, find its principal parent */
-      do
-      {
-	parent = Col [parent].shared1.parent ;
-      } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;
-
-      /* now, order all un-ordered non-principal columns along path */
-      /* to this parent.  collapse tree at the same time */
-      c = i ;
-      /* get order of parent */
-      order = Col [parent].shared2.order ;
-
-      do
-      {
-	COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ;
-
-	/* order this column */
-	Col [c].shared2.order = order++ ;
-	/* collaps tree */
-	Col [c].shared1.parent = parent ;
-
-	/* get immediate parent of this column */
-	c = Col [c].shared1.parent ;
-
-	/* continue until we hit an ordered column.  There are */
-	/* guarranteed not to be anymore unordered columns */
-	/* above an ordered column */
-      } while (Col [c].shared2.order == COLAMD_EMPTY) ;
-
-      /* re-order the super_col parent to largest order for this group */
-      Col [parent].shared2.order = order ;
-    }
-  }
-
-  /* === Generate the permutation ========================================= */
-
-  for (c = 0 ; c < n_col ; c++)
-  {
-    p [Col [c].shared2.order] = c ;
-  }
-}
-
-
-/* ========================================================================== */
-/* === detect_super_cols ==================================================== */
-/* ========================================================================== */
-
-/*
-  Detects supercolumns by finding matches between columns in the hash buckets.
-  Check amongst columns in the set A [row_start ... row_start + row_length-1].
-  The columns under consideration are currently *not* in the degree lists,
-  and have already been placed in the hash buckets.
-
-  The hash bucket for columns whose hash function is equal to h is stored
-  as follows:
-
-  if head [h] is >= 0, then head [h] contains a degree list, so:
-
-  head [h] is the first column in degree bucket h.
-  Col [head [h]].headhash gives the first column in hash bucket h.
-
-  otherwise, the degree list is empty, and:
-
-  -(head [h] + 2) is the first column in hash bucket h.
-
-  For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
-  column" pointer.  Col [c].shared3.hash is used instead as the hash number
-  for that column.  The value of Col [c].shared4.hash_next is the next column
-  in the same hash bucket.
-
-  Assuming no, or "few" hash collisions, the time taken by this routine is
-  linear in the sum of the sizes (lengths) of each column whose score has
-  just been computed in the approximate degree computation.
-  Not user-callable.
-*/
-template <typename IndexType>
-static void detect_super_cols
-(
-  /* === Parameters ======================================================= */
-  
-  colamd_col<IndexType> Col [],    /* of size n_col+1 */
-  IndexType A [],     /* row indices of A */
-  IndexType head [],    /* head of degree lists and hash buckets */
-  IndexType row_start,    /* pointer to set of columns to check */
-  IndexType row_length    /* number of columns to check */
-)
-{
-  /* === Local variables ================================================== */
-
-  IndexType hash ;      /* hash value for a column */
-  IndexType *rp ;     /* pointer to a row */
-  IndexType c ;     /* a column index */
-  IndexType super_c ;   /* column index of the column to absorb into */
-  IndexType *cp1 ;      /* column pointer for column super_c */
-  IndexType *cp2 ;      /* column pointer for column c */
-  IndexType length ;    /* length of column super_c */
-  IndexType prev_c ;    /* column preceding c in hash bucket */
-  IndexType i ;     /* loop counter */
-  IndexType *rp_end ;   /* pointer to the end of the row */
-  IndexType col ;     /* a column index in the row to check */
-  IndexType head_column ;   /* first column in hash bucket or degree list */
-  IndexType first_col ;   /* first column in hash bucket */
-
-  /* === Consider each column in the row ================================== */
-
-  rp = &A [row_start] ;
-  rp_end = rp + row_length ;
-  while (rp < rp_end)
-  {
-    col = *rp++ ;
-    if (COL_IS_DEAD (col))
-    {
-      continue ;
-    }
-
-    /* get hash number for this column */
-    hash = Col [col].shared3.hash ;
-    COLAMD_ASSERT (hash <= n_col) ;
-
-    /* === Get the first column in this hash bucket ===================== */
-
-    head_column = head [hash] ;
-    if (head_column > COLAMD_EMPTY)
-    {
-      first_col = Col [head_column].shared3.headhash ;
-    }
-    else
-    {
-      first_col = - (head_column + 2) ;
-    }
-
-    /* === Consider each column in the hash bucket ====================== */
-
-    for (super_c = first_col ; super_c != COLAMD_EMPTY ;
-	 super_c = Col [super_c].shared4.hash_next)
-    {
-      COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ;
-      COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;
-      length = Col [super_c].length ;
-
-      /* prev_c is the column preceding column c in the hash bucket */
-      prev_c = super_c ;
-
-      /* === Compare super_c with all columns after it ================ */
-
-      for (c = Col [super_c].shared4.hash_next ;
-	   c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next)
-      {
-	COLAMD_ASSERT (c != super_c) ;
-	COLAMD_ASSERT (COL_IS_ALIVE (c)) ;
-	COLAMD_ASSERT (Col [c].shared3.hash == hash) ;
-
-	/* not identical if lengths or scores are different */
-	if (Col [c].length != length ||
-	    Col [c].shared2.score != Col [super_c].shared2.score)
-	{
-	  prev_c = c ;
-	  continue ;
-	}
-
-	/* compare the two columns */
-	cp1 = &A [Col [super_c].start] ;
-	cp2 = &A [Col [c].start] ;
-
-	for (i = 0 ; i < length ; i++)
-	{
-	  /* the columns are "clean" (no dead rows) */
-	  COLAMD_ASSERT (ROW_IS_ALIVE (*cp1))  ;
-	  COLAMD_ASSERT (ROW_IS_ALIVE (*cp2))  ;
-	  /* row indices will same order for both supercols, */
-	  /* no gather scatter nessasary */
-	  if (*cp1++ != *cp2++)
-	  {
-	    break ;
-	  }
-	}
-
-	/* the two columns are different if the for-loop "broke" */
-	if (i != length)
-	{
-	  prev_c = c ;
-	  continue ;
-	}
-
-	/* === Got it!  two columns are identical =================== */
-
-	COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
-
-	Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
-	Col [c].shared1.parent = super_c ;
-	KILL_NON_PRINCIPAL_COL (c) ;
-	/* order c later, in order_children() */
-	Col [c].shared2.order = COLAMD_EMPTY ;
-	/* remove c from hash bucket */
-	Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
-      }
-    }
-
-    /* === Empty this hash bucket ======================================= */
-
-    if (head_column > COLAMD_EMPTY)
-    {
-      /* corresponding degree list "hash" is not empty */
-      Col [head_column].shared3.headhash = COLAMD_EMPTY ;
-    }
-    else
-    {
-      /* corresponding degree list "hash" is empty */
-      head [hash] = COLAMD_EMPTY ;
-    }
-  }
-}
-
-
-/* ========================================================================== */
-/* === garbage_collection =================================================== */
-/* ========================================================================== */
-
-/*
-  Defragments and compacts columns and rows in the workspace A.  Used when
-  all avaliable memory has been used while performing row merging.  Returns
-  the index of the first free position in A, after garbage collection.  The
-  time taken by this routine is linear is the size of the array A, which is
-  itself linear in the number of nonzeros in the input matrix.
-  Not user-callable.
-*/
-template <typename IndexType>
-static IndexType garbage_collection  /* returns the new value of pfree */
-  (
-    /* === Parameters ======================================================= */
-    
-    IndexType n_row,      /* number of rows */
-    IndexType n_col,      /* number of columns */
-    Colamd_Row<IndexType> Row [],    /* row info */
-    colamd_col<IndexType> Col [],    /* column info */
-    IndexType A [],     /* A [0 ... Alen-1] holds the matrix */
-    IndexType *pfree      /* &A [0] ... pfree is in use */
-    )
-{
-  /* === Local variables ================================================== */
-
-  IndexType *psrc ;     /* source pointer */
-  IndexType *pdest ;    /* destination pointer */
-  IndexType j ;     /* counter */
-  IndexType r ;     /* a row index */
-  IndexType c ;     /* a column index */
-  IndexType length ;    /* length of a row or column */
-
-  /* === Defragment the columns =========================================== */
-
-  pdest = &A[0] ;
-  for (c = 0 ; c < n_col ; c++)
-  {
-    if (COL_IS_ALIVE (c))
-    {
-      psrc = &A [Col [c].start] ;
-
-      /* move and compact the column */
-      COLAMD_ASSERT (pdest <= psrc) ;
-      Col [c].start = (IndexType) (pdest - &A [0]) ;
-      length = Col [c].length ;
-      for (j = 0 ; j < length ; j++)
-      {
-	r = *psrc++ ;
-	if (ROW_IS_ALIVE (r))
-	{
-	  *pdest++ = r ;
-	}
-      }
-      Col [c].length = (IndexType) (pdest - &A [Col [c].start]) ;
-    }
-  }
-
-  /* === Prepare to defragment the rows =================================== */
-
-  for (r = 0 ; r < n_row ; r++)
-  {
-    if (ROW_IS_ALIVE (r))
-    {
-      if (Row [r].length == 0)
-      {
-	/* this row is of zero length.  cannot compact it, so kill it */
-	COLAMD_DEBUG3 (("Defrag row kill\n")) ;
-	KILL_ROW (r) ;
-      }
-      else
-      {
-	/* save first column index in Row [r].shared2.first_column */
-	psrc = &A [Row [r].start] ;
-	Row [r].shared2.first_column = *psrc ;
-	COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
-	/* flag the start of the row with the one's complement of row */
-	*psrc = ONES_COMPLEMENT (r) ;
-
-      }
-    }
-  }
-
-  /* === Defragment the rows ============================================== */
-
-  psrc = pdest ;
-  while (psrc < pfree)
-  {
-    /* find a negative number ... the start of a row */
-    if (*psrc++ < 0)
-    {
-      psrc-- ;
-      /* get the row index */
-      r = ONES_COMPLEMENT (*psrc) ;
-      COLAMD_ASSERT (r >= 0 && r < n_row) ;
-      /* restore first column index */
-      *psrc = Row [r].shared2.first_column ;
-      COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
-
-      /* move and compact the row */
-      COLAMD_ASSERT (pdest <= psrc) ;
-      Row [r].start = (IndexType) (pdest - &A [0]) ;
-      length = Row [r].length ;
-      for (j = 0 ; j < length ; j++)
-      {
-	c = *psrc++ ;
-	if (COL_IS_ALIVE (c))
-	{
-	  *pdest++ = c ;
-	}
-      }
-      Row [r].length = (IndexType) (pdest - &A [Row [r].start]) ;
-
-    }
-  }
-  /* ensure we found all the rows */
-  COLAMD_ASSERT (debug_rows == 0) ;
-
-  /* === Return the new value of pfree ==================================== */
-
-  return ((IndexType) (pdest - &A [0])) ;
-}
-
-
-/* ========================================================================== */
-/* === clear_mark =========================================================== */
-/* ========================================================================== */
-
-/*
-  Clears the Row [].shared2.mark array, and returns the new tag_mark.
-  Return value is the new tag_mark.  Not user-callable.
-*/
-template <typename IndexType>
-static inline  IndexType clear_mark  /* return the new value for tag_mark */
-  (
-      /* === Parameters ======================================================= */
-
-    IndexType n_row,    /* number of rows in A */
-    Colamd_Row<IndexType> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
-    )
-{
-  /* === Local variables ================================================== */
-
-  IndexType r ;
-
-  for (r = 0 ; r < n_row ; r++)
-  {
-    if (ROW_IS_ALIVE (r))
-    {
-      Row [r].shared2.mark = 0 ;
-    }
-  }
-  return (1) ;
-}
-
-
-} // namespace internal 
-#endif
diff --git a/eigen/Eigen/src/OrderingMethods/Ordering.h b/eigen/Eigen/src/OrderingMethods/Ordering.h
deleted file mode 100644
index 7ea9b14..0000000
--- a/eigen/Eigen/src/OrderingMethods/Ordering.h
+++ /dev/null
@@ -1,157 +0,0 @@
- 
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2012  Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_ORDERING_H
-#define EIGEN_ORDERING_H
-
-namespace Eigen {
-  
-#include "Eigen_Colamd.h"
-
-namespace internal {
-    
-/** \internal
-  * \ingroup OrderingMethods_Module
-  * \param[in] A the input non-symmetric matrix
-  * \param[out] symmat the symmetric pattern A^T+A from the input matrix \a A.
-  * FIXME: The values should not be considered here
-  */
-template<typename MatrixType> 
-void ordering_helper_at_plus_a(const MatrixType& A, MatrixType& symmat)
-{
-  MatrixType C;
-  C = A.transpose(); // NOTE: Could be  costly
-  for (int i = 0; i < C.rows(); i++) 
-  {
-      for (typename MatrixType::InnerIterator it(C, i); it; ++it)
-        it.valueRef() = 0.0;
-  }
-  symmat = C + A;
-}
-    
-}
-
-#ifndef EIGEN_MPL2_ONLY
-
-/** \ingroup OrderingMethods_Module
-  * \class AMDOrdering
-  *
-  * Functor computing the \em approximate \em minimum \em degree ordering
-  * If the matrix is not structurally symmetric, an ordering of A^T+A is computed
-  * \tparam  StorageIndex The type of indices of the matrix 
-  * \sa COLAMDOrdering
-  */
-template <typename StorageIndex>
-class AMDOrdering
-{
-  public:
-    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
-    
-    /** Compute the permutation vector from a sparse matrix
-     * This routine is much faster if the input matrix is column-major     
-     */
-    template <typename MatrixType>
-    void operator()(const MatrixType& mat, PermutationType& perm)
-    {
-      // Compute the symmetric pattern
-      SparseMatrix<typename MatrixType::Scalar, ColMajor, StorageIndex> symm;
-      internal::ordering_helper_at_plus_a(mat,symm); 
-    
-      // Call the AMD routine 
-      //m_mat.prune(keep_diag());
-      internal::minimum_degree_ordering(symm, perm);
-    }
-    
-    /** Compute the permutation with a selfadjoint matrix */
-    template <typename SrcType, unsigned int SrcUpLo> 
-    void operator()(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat, PermutationType& perm)
-    { 
-      SparseMatrix<typename SrcType::Scalar, ColMajor, StorageIndex> C; C = mat;
-      
-      // Call the AMD routine 
-      // m_mat.prune(keep_diag()); //Remove the diagonal elements 
-      internal::minimum_degree_ordering(C, perm);
-    }
-};
-
-#endif // EIGEN_MPL2_ONLY
-
-/** \ingroup OrderingMethods_Module
-  * \class NaturalOrdering
-  *
-  * Functor computing the natural ordering (identity)
-  * 
-  * \note Returns an empty permutation matrix
-  * \tparam  StorageIndex The type of indices of the matrix 
-  */
-template <typename StorageIndex>
-class NaturalOrdering
-{
-  public:
-    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
-    
-    /** Compute the permutation vector from a column-major sparse matrix */
-    template <typename MatrixType>
-    void operator()(const MatrixType& /*mat*/, PermutationType& perm)
-    {
-      perm.resize(0); 
-    }
-    
-};
-
-/** \ingroup OrderingMethods_Module
-  * \class COLAMDOrdering
-  *
-  * \tparam  StorageIndex The type of indices of the matrix 
-  * 
-  * Functor computing the \em column \em approximate \em minimum \em degree ordering 
-  * The matrix should be in column-major and \b compressed format (see SparseMatrix::makeCompressed()).
-  */
-template<typename StorageIndex>
-class COLAMDOrdering
-{
-  public:
-    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType; 
-    typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;
-    
-    /** Compute the permutation vector \a perm form the sparse matrix \a mat
-      * \warning The input sparse matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
-      */
-    template <typename MatrixType>
-    void operator() (const MatrixType& mat, PermutationType& perm)
-    {
-      eigen_assert(mat.isCompressed() && "COLAMDOrdering requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to COLAMDOrdering");
-      
-      StorageIndex m = StorageIndex(mat.rows());
-      StorageIndex n = StorageIndex(mat.cols());
-      StorageIndex nnz = StorageIndex(mat.nonZeros());
-      // Get the recommended value of Alen to be used by colamd
-      StorageIndex Alen = internal::colamd_recommended(nnz, m, n); 
-      // Set the default parameters
-      double knobs [COLAMD_KNOBS]; 
-      StorageIndex stats [COLAMD_STATS];
-      internal::colamd_set_defaults(knobs);
-      
-      IndexVector p(n+1), A(Alen); 
-      for(StorageIndex i=0; i <= n; i++)   p(i) = mat.outerIndexPtr()[i];
-      for(StorageIndex i=0; i < nnz; i++)  A(i) = mat.innerIndexPtr()[i];
-      // Call Colamd routine to compute the ordering 
-      StorageIndex info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats); 
-      EIGEN_UNUSED_VARIABLE(info);
-      eigen_assert( info && "COLAMD failed " );
-      
-      perm.resize(n);
-      for (StorageIndex i = 0; i < n; i++) perm.indices()(p(i)) = i;
-    }
-};
-
-} // end namespace Eigen
-
-#endif