PermMatrix.cc

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// Copyright (C) 2008-2023 The Octave Project Developers
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#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include "PermMatrix.h"
#include "idx-vector.h"
#include "Array-util.h"
#include "oct-locbuf.h"
 
OCTAVE_NORETURN static
void
err_invalid_permutation (void)
{
  (*current_liboctave_error_handler) ("PermMatrix: invalid permutation vector");
}
 
void
PermMatrix::setup (const Array<octave_idx_type>& p, bool colp, bool check)
{
  if (check)
    {
      if (! octave::idx_vector (p).is_permutation (p.numel ()))
        err_invalid_permutation ();
    }
 
  if (! colp)
    *this = this->transpose ();
}
 
PermMatrix::PermMatrix (const Array<octave_idx_type>& p, bool colp, bool check)
  : Array<octave_idx_type> (p)
{
  setup (p, colp, check);
}
 
void
PermMatrix::setup (const octave::idx_vector& idx, bool colp, octave_idx_type n)
{
  octave_idx_type len = idx.length (n);
 
  if (! idx.is_permutation (len))
    err_invalid_permutation ();
 
  Array<octave_idx_type> idxa (dim_vector (len, 1));
  for (octave_idx_type i = 0; i < len; i++) idxa(i) = idx(i);
  Array<octave_idx_type>::operator = (idxa);
 
  if (! colp)
    *this = this->transpose ();
}
 
PermMatrix::PermMatrix (const octave::idx_vector& idx, bool colp, octave_idx_type n)
  : Array<octave_idx_type> ()
{
  setup (idx, colp, n);
}
 
PermMatrix::PermMatrix (octave_idx_type n)
  : Array<octave_idx_type> (dim_vector (n, 1))
{
  for (octave_idx_type i = 0; i < n; i++)
    xelem (i) = i;
}
 
octave_idx_type
PermMatrix::checkelem (octave_idx_type i, octave_idx_type j) const
{
  octave_idx_type len = Array<octave_idx_type>::numel ();
  if (i < 0 || j < 0 || i > len || j > len)
    (*current_liboctave_error_handler) ("index out of range");
 
  return elem (i, j);
}
 
PermMatrix
PermMatrix::transpose (void) const
{
  octave_idx_type len = Array<octave_idx_type>::numel ();
 
  PermMatrix retval (len);
 
  for (octave_idx_type i = 0; i < len; ++i)
    retval.xelem (xelem (i)) = i;
 
  return retval;
}
 
PermMatrix
PermMatrix::inverse (void) const
{
  return transpose ();
}
 
octave_idx_type
PermMatrix::determinant (void) const
{
  // Determine the sign of a permutation in linear time.
  // Is this widely known?
 
  octave_idx_type len = perm_length ();
  const octave_idx_type *pa = data ();
 
  OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, q, len);
 
  for (octave_idx_type i = 0; i < len; i++)
    {
      p[i] = pa[i];
      q[p[i]] = i;
    }
 
  bool neg = false;
 
  for (octave_idx_type i = 0; i < len; i++)
    {
      octave_idx_type j = p[i];
      octave_idx_type k = q[i];
      if (j != i)
        {
          p[k] = p[i];
          q[j] = q[i];
          neg = ! neg;
        }
    }
 
  return neg ? -1 : 1;
}
 
PermMatrix
PermMatrix::power(octave_idx_type m) const
{
  if (m < 0)
    return inverse ().pos_power (-m);
  else if (m > 0)
    return pos_power (m);
  else
    return PermMatrix (rows ());
}
 
PermMatrix
PermMatrix::pos_power (octave_idx_type m) const
{
  octave_idx_type n = rows ();
 
  const octave_idx_type *p = data ();
  Array<octave_idx_type> res_pvec (dim_vector (n, 1), -1);
  octave_idx_type *q = res_pvec.fortran_vec ();
 
  for (octave_idx_type ics = 0; ics < n; ics++)
    {
      if (q[ics] > 0)
        continue;
 
      // go forward m steps or until a cycle is found.
      octave_idx_type ic, j;
      for (j = 1, ic = p[ics]; j != m && ic != ics; j++, ic = p[ic]) ;
      if (ic == ics)
        {
          // reduce power.
          octave_idx_type mm = m % j;
          // go forward mm steps.
          for (j = 0, ic = ics; j != mm; j++, ic = p[ic]) ;
        }
 
      // now ic = p^m[ics].  Loop through the whole cycle.
      octave_idx_type jcs = ics;
      do
        {
          q[jcs] = ic;
          jcs = p[jcs]; ic = p[ic];
        }
      while (jcs != ics);
 
    }
 
  return PermMatrix (res_pvec, true, false);
}
 
PermMatrix
PermMatrix::eye (octave_idx_type n)
{
  return PermMatrix (n);
}
 
PermMatrix
operator *(const PermMatrix& a, const PermMatrix& b)
{
  PermMatrix r;
 
  const Array<octave_idx_type> ia = a.col_perm_vec ();
  const Array<octave_idx_type> ib = b.col_perm_vec ();
 
  octave_idx_type n = a.columns ();
 
  if (n != b.rows ())
    octave::err_nonconformant ("operator *", n, n, b.rows (), b.rows ());
 
  r = PermMatrix (ia.index (octave::idx_vector (ib)), true, false);
 
  return r;
}