dbleCHOL.cc

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/*

Copyright (C) 1994-2015 John W. Eaton
Copyright (C) 2008-2009 Jaroslav Hajek

This file is part of Octave.

Octave is free software; 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 3 of the License, or (at your
option) any later version.

Octave 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 General Public License
for more details.

You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <vector>

#include "dRowVector.h"
#include "dbleCHOL.h"
#include "f77-fcn.h"
#include "lo-error.h"
#include "oct-locbuf.h"
#include "oct-norm.h"
#ifndef HAVE_QRUPDATE
#include "dbleQR.h"
#endif

extern "C"
{
  F77_RET_T
  F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, double*,
                             const octave_idx_type&, octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dpotri, DPOTRI) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, double*,
                             const octave_idx_type&, octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, double*,
                             const octave_idx_type&, const double&,
                             double&, double*, octave_idx_type*,
                             octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);
#ifdef HAVE_QRUPDATE

  F77_RET_T
  F77_FUNC (dch1up, DCH1UP) (const octave_idx_type&, double*,
                             const octave_idx_type&, double*, double*);

  F77_RET_T
  F77_FUNC (dch1dn, DCH1DN) (const octave_idx_type&, double*,
                             const octave_idx_type&, double*, double*,
                             octave_idx_type&);

  F77_RET_T
  F77_FUNC (dchinx, DCHINX) (const octave_idx_type&, double*,
                             const octave_idx_type&, const octave_idx_type&,
                             double*, double*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (dchdex, DCHDEX) (const octave_idx_type&, double*,
                             const octave_idx_type&, const octave_idx_type&,
                             double*);

  F77_RET_T
  F77_FUNC (dchshx, DCHSHX) (const octave_idx_type&, double*,
                             const octave_idx_type&, const octave_idx_type&,
                             const octave_idx_type&, double*);
#endif
}

octave_idx_type
CHOL::init (const Matrix& a, bool calc_cond)
{
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (a_nr != a_nc)
    {
      (*current_liboctave_error_handler) ("CHOL requires square matrix");
      return -1;
    }

  octave_idx_type n = a_nc;
  octave_idx_type info;

  chol_mat.clear (n, n);
  for (octave_idx_type j = 0; j < n; j++)
    {
      for (octave_idx_type i = 0; i <= j; i++)
        chol_mat.xelem (i, j) = a(i, j);
      for (octave_idx_type i = j+1; i < n; i++)
        chol_mat.xelem (i, j) = 0.0;
    }
  double *h = chol_mat.fortran_vec ();

  // Calculate the norm of the matrix, for later use.
  double anorm = 0;
  if (calc_cond)
    anorm = xnorm (a, 1);

  F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 ("U", 1),
                             n, h, n, info
                             F77_CHAR_ARG_LEN (1)));

  xrcond = 0.0;
  if (info > 0)
    chol_mat.resize (info - 1, info - 1);
  else if (calc_cond)
    {
      octave_idx_type dpocon_info = 0;

      // Now calculate the condition number for non-singular matrix.
      Array<double> z (dim_vector (3*n, 1));
      double *pz = z.fortran_vec ();
      Array<octave_idx_type> iz (dim_vector (n, 1));
      octave_idx_type *piz = iz.fortran_vec ();
      F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n, h,
                                 n, anorm, xrcond, pz, piz, dpocon_info
                                 F77_CHAR_ARG_LEN (1)));

      if (dpocon_info != 0)
        info = -1;
    }

  return info;
}

static Matrix
chol2inv_internal (const Matrix& r)
{
  Matrix retval;

  octave_idx_type r_nr = r.rows ();
  octave_idx_type r_nc = r.cols ();

  if (r_nr == r_nc)
    {
      octave_idx_type n = r_nc;
      octave_idx_type info = 0;

      Matrix tmp = r;
      double *v = tmp.fortran_vec ();

      if (info == 0)
        {
          F77_XFCN (dpotri, DPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                     v, n, info
                                     F77_CHAR_ARG_LEN (1)));

          // If someone thinks of a more graceful way of doing this (or
          // faster for that matter :-)), please let me know!

          if (n > 1)
            for (octave_idx_type j = 0; j < r_nc; j++)
              for (octave_idx_type i = j+1; i < r_nr; i++)
                tmp.xelem (i, j) = tmp.xelem (j, i);

          retval = tmp;
        }
    }
  else
    (*current_liboctave_error_handler) ("chol2inv requires square matrix");

  return retval;
}

// Compute the inverse of a matrix using the Cholesky factorization.
Matrix
CHOL::inverse (void) const
{
  return chol2inv_internal (chol_mat);
}

void
CHOL::set (const Matrix& R)
{
  if (R.is_square ())
    chol_mat = R;
  else
    (*current_liboctave_error_handler) ("CHOL requires square matrix");
}

#ifdef HAVE_QRUPDATE

void
CHOL::update (const ColumnVector& u)
{
  octave_idx_type n = chol_mat.rows ();

  if (u.length () == n)
    {
      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dch1up, DCH1UP, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 utmp.fortran_vec (), w));
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");
}

octave_idx_type
CHOL::downdate (const ColumnVector& u)
{
  octave_idx_type info = -1;

  octave_idx_type n = chol_mat.rows ();

  if (u.length () == n)
    {
      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dch1dn, DCH1DN, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 utmp.fortran_vec (), w, info));
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

  return info;
}

octave_idx_type
CHOL::insert_sym (const ColumnVector& u, octave_idx_type j)
{
  octave_idx_type info = -1;

  octave_idx_type n = chol_mat.rows ();

  if (u.length () != n + 1)
    (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
  else if (j < 0 || j > n)
    (*current_liboctave_error_handler) ("cholinsert: index out of range");
  else
    {
      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      chol_mat.resize (n+1, n+1);

      F77_XFCN (dchinx, DCHINX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 j + 1, utmp.fortran_vec (), w, info));
    }

  return info;
}

void
CHOL::delete_sym (octave_idx_type j)
{
  octave_idx_type n = chol_mat.rows ();

  if (j < 0 || j > n-1)
    (*current_liboctave_error_handler) ("choldelete: index out of range");
  else
    {
      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dchdex, DCHDEX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 j + 1, w));

      chol_mat.resize (n-1, n-1);
    }
}

void
CHOL::shift_sym (octave_idx_type i, octave_idx_type j)
{
  octave_idx_type n = chol_mat.rows ();

  if (i < 0 || i > n-1 || j < 0 || j > n-1)
    (*current_liboctave_error_handler) ("cholshift: index out of range");
  else
    {
      OCTAVE_LOCAL_BUFFER (double, w, 2*n);

      F77_XFCN (dchshx, DCHSHX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 i + 1, j + 1, w));
    }
}

#else

void
CHOL::update (const ColumnVector& u)
{
  warn_qrupdate_once ();

  octave_idx_type n = chol_mat.rows ();

  if (u.length () == n)
    {
      init (chol_mat.transpose () * chol_mat
            + Matrix (u) * Matrix (u).transpose (), false);
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");
}

static bool
singular (const Matrix& a)
{
  for (octave_idx_type i = 0; i < a.rows (); i++)
    if (a(i,i) == 0.0) return true;
  return false;
}

octave_idx_type
CHOL::downdate (const ColumnVector& u)
{
  warn_qrupdate_once ();

  octave_idx_type info = -1;

  octave_idx_type n = chol_mat.rows ();

  if (u.length () == n)
    {
      if (singular (chol_mat))
        info = 2;
      else
        {
          info = init (chol_mat.transpose () * chol_mat
                       - Matrix (u) * Matrix (u).transpose (), false);
          if (info) info = 1;
        }
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

  return info;
}

octave_idx_type
CHOL::insert_sym (const ColumnVector& u, octave_idx_type j)
{
  warn_qrupdate_once ();

  octave_idx_type info = -1;

  octave_idx_type n = chol_mat.rows ();

  if (u.length () != n + 1)
    (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
  else if (j < 0 || j > n)
    (*current_liboctave_error_handler) ("cholinsert: index out of range");
  else
    {
      if (singular (chol_mat))
        info = 2;
      else
        {
          Matrix a = chol_mat.transpose () * chol_mat;
          Matrix a1 (n+1, n+1);
          for (octave_idx_type k = 0; k < n+1; k++)
            for (octave_idx_type l = 0; l < n+1; l++)
              {
                if (l == j)
                  a1(k, l) = u(k);
                else if (k == j)
                  a1(k, l) = u(l);
                else
                  a1(k, l) = a(k < j ? k : k-1, l < j ? l : l-1);
              }
          info = init (a1, false);
          if (info) info = 1;
        }
    }

  return info;
}

void
CHOL::delete_sym (octave_idx_type j)
{
  warn_qrupdate_once ();

  octave_idx_type n = chol_mat.rows ();

  if (j < 0 || j > n-1)
    (*current_liboctave_error_handler) ("choldelete: index out of range");
  else
    {
      Matrix a = chol_mat.transpose () * chol_mat;
      a.delete_elements (1, idx_vector (j));
      a.delete_elements (0, idx_vector (j));
      init (a, false);
    }
}

void
CHOL::shift_sym (octave_idx_type i, octave_idx_type j)
{
  warn_qrupdate_once ();

  octave_idx_type n = chol_mat.rows ();

  if (i < 0 || i > n-1 || j < 0 || j > n-1)
    (*current_liboctave_error_handler) ("cholshift: index out of range");
  else
    {
      Matrix a = chol_mat.transpose () * chol_mat;
      Array<octave_idx_type> p (dim_vector (n, 1));
      for (octave_idx_type k = 0; k < n; k++) p(k) = k;
      if (i < j)
        {
          for (octave_idx_type k = i; k < j; k++) p(k) = k+1;
          p(j) = i;
        }
      else if (j < i)
        {
          p(j) = i;
          for (octave_idx_type k = j+1; k < i+1; k++) p(k) = k-1;
        }

      init (a.index (idx_vector (p), idx_vector (p)), false);
    }
}

#endif

Matrix
chol2inv (const Matrix& r)
{
  return chol2inv_internal (r);
}