CmplxCHOL.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 "dMatrix.h"
#include "dRowVector.h"
#include "CmplxCHOL.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 (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, Complex*,
                             const octave_idx_type&, octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);
  F77_RET_T
  F77_FUNC (zpotri, ZPOTRI) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, Complex*,
                             const octave_idx_type&, octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL,
                             const octave_idx_type&, Complex*,
                             const octave_idx_type&, const double&,
                             double&, Complex*, double*, octave_idx_type&
                             F77_CHAR_ARG_LEN_DECL);
#ifdef HAVE_QRUPDATE

  F77_RET_T
  F77_FUNC (zch1up, ZCH1UP) (const octave_idx_type&, Complex*,
                             const octave_idx_type&, Complex*, double*);

  F77_RET_T
  F77_FUNC (zch1dn, ZCH1DN) (const octave_idx_type&, Complex*,
                             const octave_idx_type&, Complex*, double*,
                             octave_idx_type&);

  F77_RET_T
  F77_FUNC (zchinx, ZCHINX) (const octave_idx_type&, Complex*,
                             const octave_idx_type&, const octave_idx_type&,
                             Complex*, double*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (zchdex, ZCHDEX) (const octave_idx_type&, Complex*,
                             const octave_idx_type&, const octave_idx_type&,
                             double*);

  F77_RET_T
  F77_FUNC (zchshx, ZCHSHX) (const octave_idx_type&, Complex*,
                             const octave_idx_type&, const octave_idx_type&,
                             const octave_idx_type&, Complex*, double*);
#endif
}

octave_idx_type
ComplexCHOL::init (const ComplexMatrix& 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)
        ("ComplexCHOL 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;
    }
  Complex *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 (zpotrf, ZPOTRF, (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 zpocon_info = 0;

      // Now calculate the condition number for non-singular matrix.
      Array<Complex> z (dim_vector (2*n, 1));
      Complex *pz = z.fortran_vec ();
      Array<double> rz (dim_vector (n, 1));
      double *prz = rz.fortran_vec ();
      F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n, h,
                                 n, anorm, xrcond, pz, prz, zpocon_info
                                 F77_CHAR_ARG_LEN (1)));

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

  return info;
}

static ComplexMatrix
chol2inv_internal (const ComplexMatrix& r)
{
  ComplexMatrix 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;

      ComplexMatrix tmp = r;

      F77_XFCN (zpotri, ZPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                 tmp.fortran_vec (), 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) = std::conj (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.
ComplexMatrix
ComplexCHOL::inverse (void) const
{
  return chol2inv_internal (chol_mat);
}

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

#ifdef HAVE_QRUPDATE

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

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

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zch1up, ZCH1UP, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 utmp.fortran_vec (), rw));
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");
}

octave_idx_type
ComplexCHOL::downdate (const ComplexColumnVector& u)
{
  octave_idx_type info = -1;

  octave_idx_type n = chol_mat.rows ();

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

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zch1dn, ZCH1DN, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 utmp.fortran_vec (), rw, info));
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

  return info;
}

octave_idx_type
ComplexCHOL::insert_sym (const ComplexColumnVector& 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
    {
      ComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, rw, n);

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

      F77_XFCN (zchinx, ZCHINX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 j + 1, utmp.fortran_vec (), rw, info));
    }

  return info;
}

void
ComplexCHOL::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, rw, n);

      F77_XFCN (zchdex, ZCHDEX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 j + 1, rw));

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

void
ComplexCHOL::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 (Complex, w, n);
      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zchshx, ZCHSHX, (n, chol_mat.fortran_vec (), chol_mat.rows (),
                                 i + 1, j + 1, w, rw));
    }
}

#else

void
ComplexCHOL::update (const ComplexColumnVector& u)
{
  warn_qrupdate_once ();

  octave_idx_type n = chol_mat.rows ();

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

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

octave_idx_type
ComplexCHOL::downdate (const ComplexColumnVector& 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.hermitian () * chol_mat
                       - ComplexMatrix (u) * ComplexMatrix (u).hermitian (),
                       false);
          if (info) info = 1;
        }
    }
  else
    (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

  return info;
}

octave_idx_type
ComplexCHOL::insert_sym (const ComplexColumnVector& 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 if (u(j).imag () != 0.0)
        info = 3;
      else
        {
          ComplexMatrix a = chol_mat.hermitian () * chol_mat;
          ComplexMatrix 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) = std::conj (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
ComplexCHOL::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
    {
      ComplexMatrix a = chol_mat.hermitian () * chol_mat;
      a.delete_elements (1, idx_vector (j));
      a.delete_elements (0, idx_vector (j));
      init (a, false);
    }
}

void
ComplexCHOL::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
    {
      ComplexMatrix a = chol_mat.hermitian () * 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

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