sparse-chol.cc

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//
// Copyright (C) 1998-2022 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
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////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include <cstddef>
 
#include "CSparse.h"
#include "MatrixType.h"
#include "dRowVector.h"
#include "dSparse.h"
#include "lo-error.h"
#include "oct-cmplx.h"
#include "oct-sparse.h"
#include "oct-spparms.h"
#include "quit.h"
#include "sparse-chol.h"
#include "sparse-util.h"
 
namespace octave
{
  namespace math
  {
    template <typename chol_type>
    class sparse_chol<chol_type>::sparse_chol_rep
    {
    public:
 
      sparse_chol_rep (void)
        : m_is_pd (false), m_minor_p (0), m_perm (), m_rcond (0)
#if defined (HAVE_CHOLMOD)
        , m_L (nullptr), m_common ()
#endif
      { }
 
      sparse_chol_rep (const chol_type& a, bool natural, bool force)
        : m_is_pd (false), m_minor_p (0), m_perm (), m_rcond (0)
#if defined (HAVE_CHOLMOD)
        , m_L (nullptr), m_common ()
#endif
      {
        init (a, natural, force);
      }
 
      sparse_chol_rep (const chol_type& a, octave_idx_type& info,
                       bool natural, bool force)
        : m_is_pd (false), m_minor_p (0), m_perm (), m_rcond (0)
#if defined (HAVE_CHOLMOD)
        , m_L (nullptr), m_common ()
#endif
      {
        info = init (a, natural, force);
      }
 
      // No copying!
 
      sparse_chol_rep (const sparse_chol_rep&) = delete;
 
      sparse_chol_rep& operator = (const sparse_chol_rep&) = delete;
 
      ~sparse_chol_rep (void)
      {
#if defined (HAVE_CHOLMOD)
        if (m_L)
          CHOLMOD_NAME (free_sparse) (&m_L, &m_common);
 
        CHOLMOD_NAME(finish) (&m_common);
#endif
      }
 
#if defined (HAVE_CHOLMOD)
      cholmod_sparse * L (void) const
      {
        return m_L;
      }
#endif
 
      octave_idx_type P (void) const
      {
#if defined (HAVE_CHOLMOD)
        return (m_minor_p == static_cast<octave_idx_type> (m_L->ncol) ?
                0 : m_minor_p + 1);
#else
        return 0;
#endif
      }
 
      RowVector perm (void) const { return m_perm + 1; }
 
      SparseMatrix Q (void) const;
 
      bool is_positive_definite (void) const { return m_is_pd; }
 
      double rcond (void) const { return m_rcond; }
 
    private:
 
      bool m_is_pd;
 
      octave_idx_type m_minor_p;
 
      RowVector m_perm;
 
      double m_rcond;
 
#if defined (HAVE_CHOLMOD)
      cholmod_sparse *m_L;
 
      cholmod_common m_common;
 
      void drop_zeros (const cholmod_sparse *S);
#endif
 
      octave_idx_type init (const chol_type& a, bool natural, bool force);
    };
 
#if defined (HAVE_CHOLMOD)
 
    // Can't use CHOLMOD_NAME(drop)(0.0, S, cm) because it doesn't treat
    // complex matrices.
 
    template <typename chol_type>
    void
    sparse_chol<chol_type>::sparse_chol_rep::drop_zeros (const cholmod_sparse *S)
    {
      if (! S)
        return;
 
      octave_idx_type *Sp = static_cast<octave_idx_type *>(S->p);
      octave_idx_type *Si = static_cast<octave_idx_type *>(S->i);
      chol_elt *Sx = static_cast<chol_elt *>(S->x);
 
      octave_idx_type pdest = 0;
      octave_idx_type ncol = S->ncol;
 
      for (octave_idx_type k = 0; k < ncol; k++)
        {
          octave_idx_type p = Sp[k];
          octave_idx_type pend = Sp[k+1];
          Sp[k] = pdest;
 
          for (; p < pend; p++)
            {
              chol_elt sik = Sx[p];
 
              if (CHOLMOD_IS_NONZERO (sik))
                {
                  if (p != pdest)
                    {
                      Si[pdest] = Si[p];
                      Sx[pdest] = sik;
                    }
 
                  pdest++;
                }
            }
        }
 
      Sp[ncol] = pdest;
    }
 
    // Must provide a specialization for this function.
    template <typename T>
    int
    get_xtype (void);
 
    template <>
    inline int
    get_xtype<double> (void)
    {
      return CHOLMOD_REAL;
    }
 
    template <>
    inline int
    get_xtype<Complex> (void)
    {
      return CHOLMOD_COMPLEX;
    }
 
#endif
 
    template <typename chol_type>
    octave_idx_type
    sparse_chol<chol_type>::sparse_chol_rep::init (const chol_type& a,
                                                   bool natural, bool force)
    {
      volatile octave_idx_type info = 0;
 
#if defined (HAVE_CHOLMOD)
 
      octave_idx_type a_nr = a.rows ();
      octave_idx_type a_nc = a.cols ();
 
      if (a_nr != a_nc)
        (*current_liboctave_error_handler)
          ("sparse_chol requires square matrix");
 
      cholmod_common *cm = &m_common;
 
      // Setup initial parameters
 
      CHOLMOD_NAME(start) (cm);
      cm->prefer_zomplex = false;
 
      double spu = sparse_params::get_key ("spumoni");
 
      if (spu == 0.)
        {
          cm->print = -1;
          SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr);
        }
      else
        {
          cm->print = static_cast<int> (spu) + 2;
          SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function,
                                   &SparseCholPrint);
        }
 
      cm->error_handler = &SparseCholError;
 
      SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide,
                                divcomplex);
 
      SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);
 
      cm->final_asis = false;
      cm->final_super = false;
      cm->final_ll = true;
      cm->final_pack = true;
      cm->final_monotonic = true;
      cm->final_resymbol = false;
 
      cholmod_sparse A;
      cholmod_sparse *ac = &A;
      double dummy;
 
      ac->nrow = a_nr;
      ac->ncol = a_nc;
 
      ac->p = a.cidx ();
      ac->i = a.ridx ();
      ac->nzmax = a.nnz ();
      ac->packed = true;
      ac->sorted = true;
      ac->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
      ac->itype = CHOLMOD_LONG;
#else
      ac->itype = CHOLMOD_INT;
#endif
      ac->dtype = CHOLMOD_DOUBLE;
      ac->stype = 1;
      ac->xtype = get_xtype<chol_elt> ();
 
      if (a_nr < 1)
        ac->x = &dummy;
      else
        ac->x = a.data ();
 
      // use natural ordering if no q output parameter
      if (natural)
        {
          cm->nmethods = 1;
          cm->method[0].ordering = CHOLMOD_NATURAL;
          cm->postorder = false;
        }
 
      cholmod_factor *Lfactor = CHOLMOD_NAME(analyze) (ac, cm);
      CHOLMOD_NAME(factorize) (ac, Lfactor, cm);
 
      m_is_pd = cm->status == CHOLMOD_OK;
      info = (m_is_pd ? 0 : cm->status);
 
      if (m_is_pd || force)
        {
          m_rcond = CHOLMOD_NAME(rcond) (Lfactor, cm);
 
          m_minor_p = Lfactor->minor;
 
          m_L = CHOLMOD_NAME(factor_to_sparse) (Lfactor, cm);
 
          if (m_minor_p > 0 && m_minor_p < a_nr)
            {
              std::size_t n1 = a_nr + 1;
              m_L->p = CHOLMOD_NAME(realloc) (m_minor_p+1,
                                              sizeof(octave_idx_type),
                                              m_L->p, &n1, cm);
 
              CHOLMOD_NAME(reallocate_sparse)
                (static_cast<octave_idx_type *>(m_L->p)[m_minor_p],
                 m_L, cm);
 
              m_L->ncol = m_minor_p;
            }
 
          drop_zeros (m_L);
 
          if (! natural)
            {
              m_perm.resize (a_nr);
              for (octave_idx_type i = 0; i < a_nr; i++)
                m_perm(i) = static_cast<octave_idx_type *>(Lfactor->Perm)[i];
            }
        }
 
      // NAME used to prefix statistics report from print_common
      static char blank_name[] = " ";
 
      CHOLMOD_NAME(print_common) (blank_name, cm);
      CHOLMOD_NAME(free_factor) (&Lfactor, cm);
 
      return info;
 
#else
 
      octave_unused_parameter (a);
      octave_unused_parameter (natural);
      octave_unused_parameter (force);
 
      (*current_liboctave_error_handler)
        ("support for CHOLMOD was unavailable or disabled when liboctave was built");
 
      return info;
 
#endif
    }
 
    template <typename chol_type>
    SparseMatrix
    sparse_chol<chol_type>::sparse_chol_rep::Q (void) const
    {
#if defined (HAVE_CHOLMOD)
 
      octave_idx_type n = m_L->nrow;
      SparseMatrix p (n, n, n);
 
      for (octave_idx_type i = 0; i < n; i++)
        {
          p.xcidx (i) = i;
          p.xridx (i) = static_cast<octave_idx_type> (m_perm (i));
          p.xdata (i) = 1;
        }
 
      p.xcidx (n) = n;
 
      return p;
 
#else
 
      return SparseMatrix ();
 
#endif
    }
 
    template <typename chol_type>
    sparse_chol<chol_type>::sparse_chol (void)
      : m_rep (new typename sparse_chol<chol_type>::sparse_chol_rep ())
    { }
 
    template <typename chol_type>
    sparse_chol<chol_type>::sparse_chol (const chol_type& a, bool natural,
                                         bool force)
      : m_rep (new typename
               sparse_chol<chol_type>::sparse_chol_rep (a, natural, force))
    { }
 
    template <typename chol_type>
    sparse_chol<chol_type>::sparse_chol (const chol_type& a,
                                         octave_idx_type& info,
                                         bool natural, bool force)
      : m_rep (new typename
               sparse_chol<chol_type>::sparse_chol_rep (a, info, natural, force))
    { }
 
    template <typename chol_type>
    sparse_chol<chol_type>::sparse_chol (const chol_type& a,
                                         octave_idx_type& info,
                                         bool natural)
      : m_rep (new typename
               sparse_chol<chol_type>::sparse_chol_rep (a, info, natural, false))
    { }
 
    template <typename chol_type>
    sparse_chol<chol_type>::sparse_chol (const chol_type& a,
                                         octave_idx_type& info)
      : m_rep (new typename
               sparse_chol<chol_type>::sparse_chol_rep (a, info, false, false))
    { }
 
    template <typename chol_type>
    chol_type
    sparse_chol<chol_type>::L (void) const
    {
#if defined (HAVE_CHOLMOD)
 
      cholmod_sparse *m = m_rep->L ();
 
      octave_idx_type nc = m->ncol;
      octave_idx_type nnz = m->nzmax;
 
      chol_type ret (m->nrow, nc, nnz);
 
      for (octave_idx_type j = 0; j < nc+1; j++)
        ret.xcidx (j) = static_cast<octave_idx_type *>(m->p)[j];
 
      for (octave_idx_type i = 0; i < nnz; i++)
        {
          ret.xridx (i) = static_cast<octave_idx_type *>(m->i)[i];
          ret.xdata (i) = static_cast<chol_elt *>(m->x)[i];
        }
 
      return ret;
 
#else
 
      return chol_type ();
 
#endif
    }
 
    template <typename chol_type>
    octave_idx_type
    sparse_chol<chol_type>::P (void) const
    {
      return m_rep->P ();
    }
 
    template <typename chol_type>
    RowVector
    sparse_chol<chol_type>::perm (void) const
    {
      return m_rep->perm ();
    }
 
    template <typename chol_type>
    SparseMatrix
    sparse_chol<chol_type>::Q (void) const
    {
      return m_rep->Q ();
    }
 
    template <typename chol_type>
    bool
    sparse_chol<chol_type>::is_positive_definite (void) const
    {
      return m_rep->is_positive_definite ();
    }
 
    template <typename chol_type>
    double
    sparse_chol<chol_type>::rcond (void) const
    {
      return m_rep->rcond ();
    }
 
    template <typename chol_type>
    chol_type
    sparse_chol<chol_type>::inverse (void) const
    {
      chol_type retval;
 
#if defined (HAVE_CHOLMOD)
 
      cholmod_sparse *m = m_rep->L ();
      octave_idx_type n = m->ncol;
      RowVector m_perm = m_rep->perm ();
      double rcond2;
      octave_idx_type info;
      MatrixType mattype (MatrixType::Upper);
      chol_type linv = L ().hermitian ().inverse (mattype, info, rcond2, 1, 0);
 
      if (m_perm.numel () == n)
        {
          SparseMatrix Qc = Q ();
 
          retval = Qc * linv * linv.hermitian () * Qc.transpose ();
        }
      else
        retval = linv * linv.hermitian ();
 
#endif
 
      return retval;
    }
 
    template <typename chol_type>
    chol_type
    chol2inv (const chol_type& r)
    {
      octave_idx_type r_nr = r.rows ();
      octave_idx_type r_nc = r.cols ();
      chol_type retval;
 
      if (r_nr != r_nc)
        (*current_liboctave_error_handler) ("U must be a square matrix");
 
      MatrixType mattype (r);
      int typ = mattype.type (false);
      double rcond;
      octave_idx_type info;
      chol_type rtra, multip;
 
      if (typ == MatrixType::Upper)
        {
          rtra = r.transpose ();
          multip = (rtra*r);
        }
      else if (typ == MatrixType::Lower)
        {
          rtra = r.transpose ();
          multip = (r*rtra);
        }
      else
        (*current_liboctave_error_handler) ("U must be a triangular matrix");
 
      MatrixType mattypenew (multip);
      retval = multip.inverse (mattypenew, info, rcond, true, false);
      return retval;
    }
 
    // SparseComplexMatrix specialization (the value for the NATURAL
    // parameter in the sparse_chol<T>::sparse_chol_rep constructor is
    // different from the default).
 
    template <>
    OCTAVE_API
    sparse_chol<SparseComplexMatrix>::sparse_chol (const SparseComplexMatrix& a,
                                                   octave_idx_type& info)
      : m_rep (new sparse_chol<SparseComplexMatrix>::sparse_chol_rep (a, info,
                                                                      true,
                                                                      false))
    { }
 
    // Instantiations we need.
 
    template class OCTAVE_API sparse_chol<SparseMatrix>;
 
    template class sparse_chol<SparseComplexMatrix>;
 
    template OCTAVE_API SparseMatrix
    chol2inv<SparseMatrix> (const SparseMatrix& r);
 
    template OCTAVE_API SparseComplexMatrix
    chol2inv<SparseComplexMatrix> (const SparseComplexMatrix& r);
 
  }
}