SparseLU_panel_bmod.h

// 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>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@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/.

/*

 * NOTE: This file is the modified version of [s,d,c,z]panel_bmod.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_PANEL_BMOD_H
#define SPARSELU_PANEL_BMOD_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {
namespace internal {

template <typename Scalar, typename StorageIndex>
void SparseLUImpl<Scalar, StorageIndex>::panel_bmod(const Index m, const Index w, const Index jcol, const Index nseg,
                                                    ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep,
                                                    IndexVector& repfnz, GlobalLU_t& glu) {
  Index ksub, jj, nextl_col;
  Index fsupc, nsupc, nsupr, nrow;
  Index krep, kfnz;
  Index lptr;   // points to the row subscripts of a supernode
  Index luptr;  // ...
  Index segsize, no_zeros;
  // For each nonz supernode segment of U[*,j] in topological order
  Index k = nseg - 1;
  const Index PacketSize = internal::packet_traits<Scalar>::size;

  for (ksub = 0; ksub < nseg; ksub++) {  // For each updating supernode
    /* krep = representative of current k-th supernode
     * fsupc =  first supernodal column
     * nsupc = number of columns in a supernode
     * nsupr = number of rows in a supernode
     */
    krep = segrep(k);
    k--;
    fsupc = glu.xsup(glu.supno(krep));
    nsupc = krep - fsupc + 1;
    nsupr = glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
    nrow = nsupr - nsupc;
    lptr = glu.xlsub(fsupc);

    // loop over the panel columns to detect the actual number of columns and rows
    Index u_rows = 0;
    Index u_cols = 0;
    for (jj = jcol; jj < jcol + w; jj++) {
      nextl_col = (jj - jcol) * m;
      VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m);  // First nonzero column index for each row

      kfnz = repfnz_col(krep);
      if (kfnz == emptyIdxLU) continue;  // skip any zero segment

      segsize = krep - kfnz + 1;
      u_cols++;
      u_rows = (std::max)(segsize, u_rows);
    }

    if (nsupc >= 2) {
      Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);
      Map<ScalarMatrix, Aligned, OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));

      // gather U
      Index u_col = 0;
      for (jj = jcol; jj < jcol + w; jj++) {
        nextl_col = (jj - jcol) * m;
        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m);  // First nonzero column index for each row
        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m);   // Scatter/gather entire matrix column from/to here

        kfnz = repfnz_col(krep);
        if (kfnz == emptyIdxLU) continue;  // skip any zero segment

        segsize = krep - kfnz + 1;
        luptr = glu.xlusup(fsupc);
        no_zeros = kfnz - fsupc;

        Index isub = lptr + no_zeros;
        Index off = u_rows - segsize;
        for (Index i = 0; i < off; i++) U(i, u_col) = 0;
        for (Index i = 0; i < segsize; i++) {
          Index irow = glu.lsub(isub);
          U(i + off, u_col) = dense_col(irow);
          ++isub;
        }
        u_col++;
      }
      // solve U = A^-1 U
      luptr = glu.xlusup(fsupc);
      Index lda = glu.xlusup(fsupc + 1) - glu.xlusup(fsupc);
      no_zeros = (krep - u_rows + 1) - fsupc;
      luptr += lda * no_zeros + no_zeros;
      MappedMatrixBlock A(glu.lusup.data() + luptr, u_rows, u_rows, OuterStride<>(lda));
      U = A.template triangularView<UnitLower>().solve(U);

      // update
      luptr += u_rows;
      MappedMatrixBlock B(glu.lusup.data() + luptr, nrow, u_rows, OuterStride<>(lda));
      eigen_assert(tempv.size() > w * ldu + nrow * w + 1);

      Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
      Index offset = (PacketSize - internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
      MappedMatrixBlock L(tempv.data() + w * ldu + offset, nrow, u_cols, OuterStride<>(ldl));

      L.noalias() = B * U;

      // scatter U and L
      u_col = 0;
      for (jj = jcol; jj < jcol + w; jj++) {
        nextl_col = (jj - jcol) * m;
        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m);  // First nonzero column index for each row
        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m);   // Scatter/gather entire matrix column from/to here

        kfnz = repfnz_col(krep);
        if (kfnz == emptyIdxLU) continue;  // skip any zero segment

        segsize = krep - kfnz + 1;
        no_zeros = kfnz - fsupc;
        Index isub = lptr + no_zeros;

        Index off = u_rows - segsize;
        for (Index i = 0; i < segsize; i++) {
          Index irow = glu.lsub(isub++);
          dense_col(irow) = U.coeff(i + off, u_col);
          U.coeffRef(i + off, u_col) = 0;
        }

        // Scatter l into SPA dense[]
        for (Index i = 0; i < nrow; i++) {
          Index irow = glu.lsub(isub++);
          dense_col(irow) -= L.coeff(i, u_col);
          L.coeffRef(i, u_col) = 0;
        }
        u_col++;
      }
    } else  // level 2 only
    {
      // Sequence through each column in the panel
      for (jj = jcol; jj < jcol + w; jj++) {
        nextl_col = (jj - jcol) * m;
        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m);  // First nonzero column index for each row
        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m);   // Scatter/gather entire matrix column from/to here

        kfnz = repfnz_col(krep);
        if (kfnz == emptyIdxLU) continue;  // skip any zero segment

        segsize = krep - kfnz + 1;
        luptr = glu.xlusup(fsupc);

        Index lda = glu.xlusup(fsupc + 1) - glu.xlusup(fsupc);  // nsupr

        // Perform a trianglar solve and block update,
        // then scatter the result of sup-col update to dense[]
        no_zeros = kfnz - fsupc;
        if (segsize == 1)
          LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
        else if (segsize == 2)
          LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
        else if (segsize == 3)
          LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
        else
          LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr,
                                       no_zeros);
      }  // End for each column in the panel
    }

  }  // End for each updating supernode
}  // end panel bmod

}  // end namespace internal

}  // end namespace Eigen

#endif  // SPARSELU_PANEL_BMOD_H