dDiagMatrix.cc

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//
// Copyright (C) 1994-2021 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 <ostream>
 
#include "Array-util.h"
#include "lo-error.h"
#include "mx-base.h"
#include "mx-inlines.cc"
#include "oct-cmplx.h"
 
// Diagonal Matrix class.
 
bool
DiagMatrix::operator == (const DiagMatrix& a) const
{
  if (rows () != a.rows () || cols () != a.cols ())
    return 0;
 
  return mx_inline_equal (length (), data (), a.data ());
}
 
bool
DiagMatrix::operator != (const DiagMatrix& a) const
{
  return !(*this == a);
}
 
DiagMatrix&
DiagMatrix::fill (double val)
{
  for (octave_idx_type i = 0; i < length (); i++)
    elem (i, i) = val;
  return *this;
}
 
DiagMatrix&
DiagMatrix::fill (double val, octave_idx_type beg, octave_idx_type end)
{
  if (beg < 0 || end >= length () || end < beg)
    (*current_liboctave_error_handler) ("range error for fill");
 
  for (octave_idx_type i = beg; i <= end; i++)
    elem (i, i) = val;
 
  return *this;
}
 
DiagMatrix&
DiagMatrix::fill (const ColumnVector& a)
{
  octave_idx_type len = length ();
  if (a.numel () != len)
    (*current_liboctave_error_handler) ("range error for fill");
 
  for (octave_idx_type i = 0; i < len; i++)
    elem (i, i) = a.elem (i);
 
  return *this;
}
 
DiagMatrix&
DiagMatrix::fill (const RowVector& a)
{
  octave_idx_type len = length ();
  if (a.numel () != len)
    (*current_liboctave_error_handler) ("range error for fill");
 
  for (octave_idx_type i = 0; i < len; i++)
    elem (i, i) = a.elem (i);
 
  return *this;
}
 
DiagMatrix&
DiagMatrix::fill (const ColumnVector& a, octave_idx_type beg)
{
  octave_idx_type a_len = a.numel ();
  if (beg < 0 || beg + a_len >= length ())
    (*current_liboctave_error_handler) ("range error for fill");
 
  for (octave_idx_type i = 0; i < a_len; i++)
    elem (i+beg, i+beg) = a.elem (i);
 
  return *this;
}
 
DiagMatrix&
DiagMatrix::fill (const RowVector& a, octave_idx_type beg)
{
  octave_idx_type a_len = a.numel ();
  if (beg < 0 || beg + a_len >= length ())
    (*current_liboctave_error_handler) ("range error for fill");
 
  for (octave_idx_type i = 0; i < a_len; i++)
    elem (i+beg, i+beg) = a.elem (i);
 
  return *this;
}
 
DiagMatrix
DiagMatrix::abs (void) const
{
  return DiagMatrix (extract_diag ().abs (), rows (), columns ());
}
 
DiagMatrix
real (const ComplexDiagMatrix& a)
{
  return DiagMatrix (real (a.extract_diag ()), a.rows (), a.cols ());
}
 
DiagMatrix
imag (const ComplexDiagMatrix& a)
{
  return DiagMatrix (imag (a.extract_diag ()), a.rows (), a.cols ());
}
 
Matrix
DiagMatrix::extract (octave_idx_type r1, octave_idx_type c1,
                     octave_idx_type r2, octave_idx_type c2) const
{
  if (r1 > r2) { std::swap (r1, r2); }
  if (c1 > c2) { std::swap (c1, c2); }
 
  octave_idx_type new_r = r2 - r1 + 1;
  octave_idx_type new_c = c2 - c1 + 1;
 
  Matrix result (new_r, new_c);
 
  for (octave_idx_type j = 0; j < new_c; j++)
    for (octave_idx_type i = 0; i < new_r; i++)
      result.elem (i, j) = elem (r1+i, c1+j);
 
  return result;
}
 
// extract row or column i.
 
RowVector
DiagMatrix::row (octave_idx_type i) const
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
  if (i < 0 || i >= r)
    (*current_liboctave_error_handler) ("invalid row selection");
 
  RowVector retval (c, 0.0);
  if (r <= c || i < c)
    retval.elem (i) = elem (i, i);
 
  return retval;
}
 
RowVector
DiagMatrix::row (char *s) const
{
  if (! s)
    (*current_liboctave_error_handler) ("invalid row selection");
 
  char c = s[0];
  if (c == 'f' || c == 'F')
    return row (static_cast<octave_idx_type> (0));
  else if (c == 'l' || c == 'L')
    return row (rows () - 1);
  else
    (*current_liboctave_error_handler) ("invalid row selection");
}
 
ColumnVector
DiagMatrix::column (octave_idx_type i) const
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
  if (i < 0 || i >= c)
    (*current_liboctave_error_handler) ("invalid column selection");
 
  ColumnVector retval (r, 0.0);
  if (r >= c || i < r)
    retval.elem (i) = elem (i, i);
 
  return retval;
}
 
ColumnVector
DiagMatrix::column (char *s) const
{
  if (! s)
    (*current_liboctave_error_handler) ("invalid column selection");
 
  char c = s[0];
  if (c == 'f' || c == 'F')
    return column (static_cast<octave_idx_type> (0));
  else if (c == 'l' || c == 'L')
    return column (cols () - 1);
  else
    (*current_liboctave_error_handler) ("invalid column selection");
}
 
DiagMatrix
DiagMatrix::inverse (void) const
{
  octave_idx_type info;
  return inverse (info);
}
 
DiagMatrix
DiagMatrix::inverse (octave_idx_type& info) const
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
  if (r != c)
    (*current_liboctave_error_handler) ("inverse requires square matrix");
 
  DiagMatrix retval (r, c);
 
  info = 0;
  octave_idx_type len = r;        // alias for readability
  octave_idx_type z_count  = 0;   // zeros
  octave_idx_type nz_count = 0;   // non-zeros
  for (octave_idx_type i = 0; i < len; i++)
    {
      if (xelem (i, i) == 0.0)
        {
          z_count++;
          if (nz_count > 0)
            break;
        }
      else
        {
          nz_count++;
          if (z_count > 0)
            break;
          retval.elem (i, i) = 1.0 / xelem (i, i);
        }
    }
  if (nz_count == 0)
    {
      (*current_liboctave_error_handler)
        ("inverse of the null matrix not defined");
    }
  else if (z_count > 0)
    {
      info = -1;
      element_type *data = retval.fortran_vec ();
      std::fill (data, data + len, octave::numeric_limits<double>::Inf ());
    }
 
  return retval;
}
 
DiagMatrix
DiagMatrix::pseudo_inverse (double tol) const
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
  octave_idx_type len = length ();
 
  DiagMatrix retval (c, r);
 
  for (octave_idx_type i = 0; i < len; i++)
    {
      double val = std::abs (elem (i, i));
      if (val < tol || val == 0.0)
        retval.elem (i, i) = 0.0;
      else
        retval.elem (i, i) = 1.0 / elem (i, i);
    }
 
  return retval;
}
 
// diagonal matrix by diagonal matrix -> diagonal matrix operations
 
// diagonal matrix by diagonal matrix -> diagonal matrix operations
 
DiagMatrix
operator * (const DiagMatrix& a, const DiagMatrix& b)
{
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();
 
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();
 
  if (a_nc != b_nr)
    octave::err_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc);
 
  DiagMatrix c (a_nr, b_nc);
 
  octave_idx_type len = c.length ();
  octave_idx_type lenm = (len < a_nc ? len : a_nc);
 
  for (octave_idx_type i = 0; i < lenm; i++)
    c.dgxelem (i) = a.dgelem (i) * b.dgelem (i);
  for (octave_idx_type i = lenm; i < len; i++)
    c.dgxelem (i) = 0.0;
 
  return c;
}
 
// other operations
 
DET
DiagMatrix::determinant (void) const
{
  DET det (1.0);
  if (rows () != cols ())
    (*current_liboctave_error_handler) ("determinant requires square matrix");
 
  octave_idx_type len = length ();
  for (octave_idx_type i = 0; i < len; i++)
    det *= elem (i, i);
 
  return det;
}
 
double
DiagMatrix::rcond (void) const
{
  ColumnVector av = extract_diag (0).map<double> (fabs);
  double amx = av.max ();
  double amn = av.min ();
  return amx == 0 ? 0.0 : amn / amx;
}
 
std::ostream&
operator << (std::ostream& os, const DiagMatrix& a)
{
//  int field_width = os.precision () + 7;
 
  for (octave_idx_type i = 0; i < a.rows (); i++)
    {
      for (octave_idx_type j = 0; j < a.cols (); j++)
        {
          if (i == j)
            os << ' ' /* setw (field_width) */ << a.elem (i, i);
          else
            os << ' ' /* setw (field_width) */ << 0.0;
        }
      os << "\n";
    }
  return os;
}