Add preliminary files for SparseLU

Eigen/src/SparseLU/SparseLU_pivotL.h

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+// 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>
+//
+// Eigen 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 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen 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 or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+/* 
+ 
+ * NOTE: This file is the modified version of dpivotL.c file in SuperLU 
+ 
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation.  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 or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PIVOTL_H
+#define SPARSELU_PIVOTL_H
+/**
+ * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
+ * 
+ * Here is the pivot policy :
+ * (1) 
+ * 
+ * \param jcol The current column of L
+ * \param pivrow [out] The pivot row
+ * 
+ * 
+ */
+int SparseLU::LU_pivotL(const int jcol, Index& pivrow)
+{
+  // Initialize pointers 
+  VectorXi& lsub = m_Glu.lsub; // Compressed row subscripts of ( rectangular supernodes ??)
+  VectorXi& xlsub = m_Glu.xlsub; // xlsub[j] is the starting location of the j-th column in lsub(*)
+  Scalar* lusup = m_Glu.lusup.data(); // Numerical values of the rectangular supernodes
+  VectorXi& xlusup = m_Glu.xlusup; // xlusup[j] is the starting location of the j-th column in lusup(*)
+  
+  Index fsupc = (m_Glu.xsup)((m_Glu.supno)(jcol)); // First column in the supernode containing the column jcol
+  Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
+  Index lptr = xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
+  Index nsupr = xlsub(fsupc+1) - lptr; // Number of rows in the supernode
+  Scalar* lu_sup_ptr = &(lusup[xlusup(fsupc)]); // Start of the current supernode
+  Scalar* lu_col_ptr = &(lusup[xlusup(jcol)]); // Start of jcol in the supernode
+  Index* lsub_ptr = &(lsub.data()[lptr]); // Start of row indices of the supernode
+  
+  // Determine the largest abs numerical value for partial pivoting 
+  Index diagind = m_iperm_c(jcol); // diagonal index 
+  Scalar pivmax = 0.0; 
+  Index pivptr = nsupc; 
+  Index diag = -1; 
+  Index old_pivptr = nsupc; 
+  Scalar rtemp;
+  for (isub = nsupc; isub < nsupr; ++isub) {
+    rtemp = std::abs(lu_col_ptr[isub]);
+    if (rtemp > pivmax) {
+      pivmax = rtemp; 
+      pivptr = isub;
+    } 
+    if (lsub_ptr[isub] == diagind) diag = isub;
+  }
+  
+  // Test for singularity
+  if ( pivmax == 0.0 ) {
+    pivrow = lsub_ptr[pivptr];
+    m_perm_r(pivrow) = jcol;
+    return (jcol+1);
+  }
+  
+  Scalar thresh = m_diagpivotthresh * pivmax; 
+  
+  // Choose appropriate pivotal element 
+  
+  {
+    // Test if the diagonal element can be used as a pivot (given the threshold value)
+    if (diag >= 0 ) 
+    {
+      // Diagonal element exists
+      rtemp = std::abs(lu_col_ptr[diag]);
+      if (rtemp != Scalar(0.0) && rtemp >= thresh) pivptr = diag;
+    }
+    pivrow = lsub_ptr[pivptr];
+  }
+  
+  // Record pivot row
+  perm_r(pivrow) = jcol; 
+  // Interchange row subscripts
+  if (pivptr != nsupc )
+  {
+    std::swap( lsub_ptr(pivptr), lsub_ptr(nsupc) );
+    // Interchange numerical values as well, for the two rows in the whole snode
+    // such that L is indexed the same way as A
+    for (icol = 0; icol <= nsupc; icol++)
+    {
+      itemp = pivptr + icol * nsupr; 
+      std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * nsupr]);
+    }
+  }
+  // cdiv operations
+  Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
+  for (k = nsupc+1; k < nsupr; k++)
+    lu_col_ptr[k] *= temp; 
+  return 0;
+}
+#endif