band.cc

Go to the documentation of this file.

// Banded level set routines 
//
// Author: Pierre Saramito
//
#include "rheolef/band.h"
#include "rheolef/field_expr.h"
#include "rheolef/rheostream.h"
 
namespace rheolef {
 
// extern:
template<class T, class M>
geo_basic<T,M>
level_set_internal (
    const field_basic<T,M>&,      
    const level_set_option&,
    std::vector<size_t>&,
    disarray<size_t,M>&);      
 
// =========================================================================
// part 0: utility
// =========================================================================
static Float band_epsilon = 100*std::numeric_limits<Float>::epsilon();
 
template <class T>
static
bool
band_is_zero (const T& x) {
  return fabs(x) <= band_epsilon;
}
// =========================================================================
// part I: subroutine: build vertex cc
// =========================================================================
template<class T, class M>
static
geo_element::size_type
build_vertex_connex_component (
  const geo_basic<T,M>&                        band,
  const std::vector<geo_element::size_type>&   zero_iv_list,
  const std::vector<geo_element::size_type>&   isolated_ie_list)
{
  band.neighbour_guard(); // will use neighbours
 
  typedef geo_element::size_type size_type;
  communicator comm = band.sizes().node_ownership.comm();
  size_type map_dim = band.map_dimension();
  size_type not_marked = std::numeric_limits<size_type>::max();
  //
  // 1) isolated elements are marked 0
  //    and icc-th connex component will be marked 1+icc (icc=0,1..)
  //
  distributor element_ownership = band.sizes().ownership_by_dimension[map_dim];
  disarray<size_type,M> element_mark (element_ownership, not_marked);
  for (size_type iie = 0, ine = isolated_ie_list.size(); iie < ine; iie++) {
    element_mark [isolated_ie_list [iie]] = 0;
  }
  //
  // 2) propagate a front that stop at isolated of zero marked vertices
  //
  // element_mark [ie] = 0;     when isolated
  // element_mark [ie] = 1+icc; when on the i-th connex component
  //
  size_type first_dis_ie = element_ownership.first_index();
  size_type icc = 0;
  bool cc_need_dis_fusion = false;
  std::vector<std::vector<size_type> >  cc_ie_list_table;
  size_type side_dim = map_dim-1;
  index_set ext_ie_set;
  for (size_type ie0 = 0, ne = band.size(map_dim); ie0 < ne; ie0++) {
    if (element_mark [ie0] != not_marked) continue;
    element_mark [ie0] = 1+icc;
    std::list<size_type> front;
    front.push_back (ie0);
    cc_ie_list_table.push_back (std::vector<size_type>());
    std::vector<size_type>& cc_ie_list = cc_ie_list_table [icc];
    cc_ie_list.push_back (ie0);
    while (front.size() != 0) {
      size_type ie = *(front.begin());
      front.pop_front();
      const geo_element& K = band [ie];
      for (size_type loc_isid = 0, loc_nsid = K.n_subgeo(side_dim); loc_isid < loc_nsid; loc_isid++) {
        size_type dis_je = band.neighbour (ie, loc_isid);
        if (dis_je == std::numeric_limits<size_type>::max()) continue; // no neighbour
        if (! element_ownership.is_owned (dis_je)) {
          // K' belongs to another partition: cc is split on several parts
          ext_ie_set += dis_je;
          cc_need_dis_fusion = true;
          continue;
        }
        // K' belongs to my partition
        size_type je = dis_je - first_dis_ie;
        if (element_mark [je] != not_marked) continue; // K' already studied
        element_mark[je] = 1+icc;
        front.push_back(je);
        cc_ie_list.push_back(je);
      }
    }
    icc++;
  }
  size_type ncc = cc_ie_list_table.size();
  distributor cc_ownership (distributor::decide, comm, ncc);
  size_type dis_ncc = cc_ownership.dis_size();
  size_type first_dis_icc = cc_ownership.first_index();
  //
  // 4) here, cc fusion across partitions are neded...
  //    => fusion of vertex cc that are split by partition boundaries
  //
  // non-zero marks are changed from 1+icc to 1+dis_icc numbering
  for (size_type ie = 0, ne = element_ownership.size(); ie < ne; ie++) {
    check_macro (element_mark [ie] != not_marked, "unexpected ie="<<ie<<" not marked");
    if (element_mark [ie] != 0) { element_mark [ie] += first_dis_icc; }
  }
  element_mark.set_dis_indexes (ext_ie_set);
  //
  // 5) compute the adjacency matrix A of cc across boundaries:
  //
  // send all in a pseudo-sequential matrix on process io_proc
  size_type io_proc = odiststream::io_proc();
  size_type my_proc = comm.rank();
  distributor io_cc_ownership (dis_ncc, comm, (my_proc == io_proc ? dis_ncc : 0));
  asr<Float,M> a_asr (io_cc_ownership, io_cc_ownership);
  for (size_type ie = 0, ne = element_ownership.size(); ie < ne; ie++) {
    if (element_mark [ie] == 0) continue;
    const geo_element& K1 = band [ie];
    size_type K1_dis_icc = element_mark [ie] - 1;
    for (size_type loc_isid = 0, loc_nsid = K1.n_subgeo(side_dim); loc_isid < loc_nsid; loc_isid++) {
      size_type dis_je = band.neighbour (ie, loc_isid);
      if (dis_je == std::numeric_limits<size_type>::max()) continue; // no neighbour
      size_type K2_mark = element_mark.dis_at (dis_je);
      if (K2_mark == 0) continue;
      size_type K2_dis_icc = K2_mark - 1;
      a_asr.dis_entry (K1_dis_icc, K2_dis_icc) += 1;
      a_asr.dis_entry (K2_dis_icc, K1_dis_icc) += 1;
    }
  }
  a_asr.dis_entry_assembly();
  // convert to csr:
  csr<Float,M> a_csr (a_asr);
  size_type nnz_a = a_csr.dis_nnz();
  //
  // 6) compute the closure adjacency matrix: C = lim_{n->infty} A^n
  //    A is a boolean matrix: the sequence A^n converge for a finite n
  //
  // convert A_csr to A as dense Eigen::Matrix on io_proc
  //
  // note: using "bool" instead of "int" in Eigen works with g++ but not with clang++
  Eigen::Matrix<int,Eigen::Dynamic,Eigen::Dynamic> a = Eigen::Matrix<int,Eigen::Dynamic,Eigen::Dynamic>::Zero (a_csr.nrow(), a_csr.ncol());
  typename csr<T,M>::const_iterator dia_ia = a_csr.begin();
  typename csr<T,M>::const_iterator ext_ia = a_csr.ext_begin();
  size_type first_i = a_csr.row_ownership().first_index();
  for (size_type i = 0, n = a_csr.nrow(), q = 0; i < n; i++) {
    size_type dis_i = first_i + i;
    a (dis_i,dis_i) = 1; // force auto-connection, for locally empty cc (fix a bug)
    for (typename csr<T,M>::const_data_iterator p = dia_ia[i]; p < dia_ia[i+1]; p++) {
      size_type dis_j = first_i + (*p).first;
      a (dis_i,dis_j) = 1;
    }
  }
  Eigen::Matrix<int,Eigen::Dynamic,Eigen::Dynamic> c = a;
  size_type nnz_c = nnz_a;
  for (size_type k = 0, n = a_csr.nrow(); k < n; k++) {
    Eigen::Matrix<int,Eigen::Dynamic,Eigen::Dynamic> c_tmp = c*a;
    c = c_tmp;
    size_type new_nnz_c = 0;
    for (size_type i = 0; i < n; i++)
    for (size_type j = 0; j < n; j++)
      if (c(i,j) != 0) new_nnz_c++;
    if (new_nnz_c == nnz_c) break; // converged
  }
  //
  // 7) each row of C indicates the cc that are split by a partition bdry
  // => re-number icc on io_proc into merged_icc
  //
  size_type unset = std::numeric_limits<size_type>::max();
  disarray<size_type,M> icc2merged_dis_icc (cc_ownership, unset);
  size_type merged_dis_ncc = 0;
  if (my_proc == io_proc) {
    std::vector<size_type> tmp_icc2merged_dis_icc (cc_ownership.dis_size(), unset);
    for (size_type dis_icc = 0; dis_icc < dis_ncc; dis_icc++) {
      if (tmp_icc2merged_dis_icc [dis_icc] != unset) continue;
      for (size_type dis_jcc = 0; dis_jcc < dis_ncc; dis_jcc++) {
        if (! c (dis_icc,dis_jcc)) continue;
        // here dis_icc and dis_jcc are two parts of the same cc 
        // these two parts have been cutted by a partition boundary: now merge their indexes
        check_macro (tmp_icc2merged_dis_icc [dis_jcc] == unset, "closure adjacency of connex component failed");
        tmp_icc2merged_dis_icc [dis_jcc] = merged_dis_ncc;
      }
      merged_dis_ncc++;
    }
    // distribute the tmp_icc2merged_dis_icc disarray:
    for (size_type dis_icc = 0; dis_icc < dis_ncc; dis_icc++) {
      icc2merged_dis_icc.dis_entry (dis_icc) = tmp_icc2merged_dis_icc [dis_icc];
    }
  }
  icc2merged_dis_icc.dis_entry_assembly();
#ifdef _RHEOLEF_HAVE_MPI
  if (is_distributed<M>::value) {
    mpi::broadcast (comm, merged_dis_ncc, io_proc);
  }
#endif // _RHEOLEF_HAVE_MPI
  //
  // 8) on each proc, merge parts of cc components
  //
  std::map<size_type,std::vector<size_type> > merged_cc_ie_list; // merged_cc[merged_icc] -> list of elt indexes
  for (size_type icc = 0; icc < ncc; icc++) {
    size_type merged_dis_icc = icc2merged_dis_icc [icc];
    std::vector<size_type>& merged_cc = merged_cc_ie_list [merged_dis_icc];
    index_set tmp_cc; // used to have a sorted index list
    for (std::vector<size_type>::const_iterator
          iter = cc_ie_list_table[icc].begin(),
          last = cc_ie_list_table[icc].end(); iter != last; ++iter) { 
      size_type ie = *iter;
      tmp_cc.insert (ie);
    }
    for (index_set::const_iterator
          iter = tmp_cc.begin(),
          last = tmp_cc.end(); iter != last; ++iter) {
      
      merged_cc.push_back(*iter);
    }
  }
  //
  // 9) merged icc numbering depends upon nproc: renum by sorting
  //    cc based on the smallest ios element index (nproc independant)
  //
  // mpi::reduce with std::minimum handles unsigned=size_t as signed=long
  // so use here long to reduce, otherwise leads to a bug
  using signed_size_type = long;
  const signed_size_type signed_large = -1;
  std::map<size_type,size_type> min_ios_dis_ie2dis_icc;
  for (size_type merged_dis_icc = 0; merged_dis_icc < merged_dis_ncc; merged_dis_icc++) {
    std::map<size_type,std::vector<size_type> >::const_iterator iter
        = merged_cc_ie_list.find (merged_dis_icc);
    signed_size_type min_ios_dis_ie = signed_large;
    if (iter != merged_cc_ie_list.end()) {
      const std::vector<size_type>& ie_list = (*iter).second;
      for (size_type iie = 0, ine = ie_list.size(); iie < ine; iie++) {
        size_type ie = ie_list [iie];
        size_type ios_dis_ie = band.ige2ios_dis_ige (map_dim, ie);
        min_ios_dis_ie = std::max (min_ios_dis_ie, signed_size_type(ios_dis_ie));
      }
    }
#ifdef _RHEOLEF_HAVE_MPI
    if (is_distributed<M>::value) {
      min_ios_dis_ie = mpi::all_reduce (comm, min_ios_dis_ie, mpi::maximum<signed_size_type>());
    }
#endif // _RHEOLEF_HAVE_MPI
    check_macro (min_ios_dis_ie != signed_large, "something bad appends: min_ios_dis_ie = " << min_ios_dis_ie);
    min_ios_dis_ie2dis_icc [min_ios_dis_ie] = merged_dis_icc;
  }
  check_macro (min_ios_dis_ie2dis_icc.size() == merged_dis_ncc, "something wrong appends");
  std::vector<size_type> ios_merged_dis_icc2merged_dis_icc (merged_dis_ncc, unset);
  {
    size_type ios_merged_dis_icc = 0;
    for (std::map<size_type,size_type>::const_iterator
           iter = min_ios_dis_ie2dis_icc.begin(),
           last = min_ios_dis_ie2dis_icc.end(); iter != last; ++iter, ++ios_merged_dis_icc) {
      size_type merged_dis_icc = (*iter).second;
      ios_merged_dis_icc2merged_dis_icc [ios_merged_dis_icc] = merged_dis_icc;
    }
  }
  // 10) build distributed domains from merged parts of each procs
  //
  std::vector<size_type>  merged_cc_ie_empty_list;
  for (size_type ios_merged_dis_icc = 0; ios_merged_dis_icc < merged_dis_ncc; ios_merged_dis_icc++) {
 
    size_type merged_dis_icc = ios_merged_dis_icc2merged_dis_icc [ios_merged_dis_icc];
    check_macro (merged_dis_icc < merged_dis_ncc, "merged_dis_icc="<<merged_dis_icc<<" out of range {0:"<<merged_dis_ncc<<"[");
    std::string merged_cc_name = "cc" + std::to_string (ios_merged_dis_icc);
    const std::vector<size_type>* ptr_merged_cc_ie_list;
    std::map<size_type,std::vector<size_type> >::const_iterator iter
        = merged_cc_ie_list.find (merged_dis_icc);
    if (iter != merged_cc_ie_list.end()) {
      ptr_merged_cc_ie_list = & ((*iter).second);
    } else {
      ptr_merged_cc_ie_list = & merged_cc_ie_empty_list;
    }
    domain_indirect_basic<M> merged_cc_dom (band, merged_cc_name, map_dim, comm, *ptr_merged_cc_ie_list);
    band.insert_domain_indirect (merged_cc_dom);
  }
  return merged_dis_ncc;
}
// =========================================================================
// part II: the main band constructor
// =========================================================================
template<class T, class M>
band_basic<T,M>::band_basic (
    const field_basic<T,M>& phi_h,
    const level_set_option& opt)
  : _gamma(),
    _band(),
    _sid_ie2bnd_ie(),
    _ncc(0)
{
  using namespace details;
  band_epsilon = opt.epsilon; // set global variable
  // 
  // 1) build the level set
  // 
  std::vector<size_type> bnd_dom_ie_list;
  _gamma = level_set_internal (phi_h, opt, bnd_dom_ie_list, _sid_ie2bnd_ie);
  // 
  // 2) build the band
  // 
  // 2.1) build the band domain in lambda
  const geo_basic<T,M>& lambda = phi_h.get_geo();
  check_macro(lambda.order() == 1, "Only order=1 band supported");
  size_type map_dim = lambda.map_dimension();
  communicator comm = lambda.geo_element_ownership(map_dim).comm();
  domain_indirect_basic<M> band_indirect (lambda, "band", map_dim, comm, bnd_dom_ie_list);
  geo_basic<T,M> band_domain = geo_basic<T,M> (band_indirect, lambda); 
  // 2.2) reduce phi_h to the band domain & get its geo_domain band
  field_basic<T,M> phi_h_band (phi_h [band_domain]);
  _band = phi_h_band.get_geo();
  // 
  // 3) create the "zero" containing vertices xi such that phi(xi) = 0
  // TODO: Pk and k>=2: zero is a domain of idofs: Bh.block(isolated); Bh.unblock (zeros)
  //
  check_macro(phi_h_band.get_approx() == "P1", "Only P1 level set function supported");
  std::vector<size_type>  zero_iv_list;
  for (size_type iv = 0, nv = _band.n_vertex(); iv < nv; iv++) {
    size_type idof = iv; // assume phi_h is P1
    if (band_is_zero (phi_h_band.dof(idof))) zero_iv_list.push_back (iv);
  }
  domain_indirect_basic<M> zero_dom (_band, "zero", 0, comm, zero_iv_list);
  _band.insert_domain_indirect (zero_dom);
  //
  // 4) create the "isolated" domain containing vertices xi such that:
  //    (i)  phi(xi) != 0
  //    (ii) for all element K that contains xi, 
  //         we have phi(xj) = 0 for all vertex xj of K and xj != xi
  //
  // 4.1) mark isolated vertices
  phi_h_band.dis_dof_update();
  distributor element_ownership = _band.sizes().ownership_by_dimension[map_dim];
  size_type not_marked = std::numeric_limits<size_type>::max();
  disarray<size_type,M> is_isolated  (element_ownership, 1); // 1=true, for bool
  std::vector<size_type>  isolated_ie_list;
  size_type ie = 0;
  for (typename geo_basic<T,M>::const_iterator
      iter = _band.begin(map_dim),
      last = _band.end(map_dim); iter != last; ++iter, ++ie) {
    const geo_element& K = *iter;
    size_type count_non_zero = 0;
    // TODO Pk: K is isolated when all non-zero are located inside one face exactly
    // but on this face some can be non-zero (at least 2 ?)
    // here: only for P1: only one dof is non-zero
    size_type loc_inod_isolated = std::numeric_limits<size_type>::max();
    for (size_type loc_inod = 0, loc_nnod = K.size(); loc_inod < loc_nnod; loc_inod++) {
      size_type dis_inod = K [loc_inod];
      if (! band_is_zero (phi_h_band.dis_dof (dis_inod))) {
        count_non_zero++;
        loc_inod_isolated = loc_inod;
      }
    }
    if (count_non_zero == 1) {
      is_isolated[ie] = 1;
      isolated_ie_list.push_back (ie);
    }
  }
  domain_indirect_basic<M> isolated_dom (_band, "isolated", map_dim, comm, isolated_ie_list);
  _band.insert_domain_indirect (isolated_dom);
  //
  // 5) build cc
  //
  _ncc = build_vertex_connex_component (_band, zero_iv_list, isolated_ie_list);
}
// ----------------------------------------------------------------------------
// instanciation in library
// ----------------------------------------------------------------------------
#define _RHEOLEF_instanciation(T,M)                                                     \
template class band_basic<T,M>;
 
_RHEOLEF_instanciation(Float,sequential)
#ifdef _RHEOLEF_HAVE_MPI
_RHEOLEF_instanciation(Float,distributed)
#endif // _RHEOLEF_HAVE_MPI
 
} // namespace