CDiagMatrix.cc

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//
// Copyright (C) 1994-2021 The Octave Project Developers
//
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// 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 "lo-ieee.h"
#include "mx-base.h"
#include "mx-inlines.cc"
#include "oct-cmplx.h"
 
// Complex Diagonal Matrix class
 
ComplexDiagMatrix::ComplexDiagMatrix (const DiagMatrix& a)
  : MDiagArray2<Complex> (a.rows (), a.cols ())
{
  for (octave_idx_type i = 0; i < length (); i++)
    elem (i, i) = a.elem (i, i);
}
 
bool
ComplexDiagMatrix::operator == (const ComplexDiagMatrix& a) const
{
  if (rows () != a.rows () || cols () != a.cols ())
    return 0;
 
  return mx_inline_equal (length (), data (), a.data ());
}
 
bool
ComplexDiagMatrix::operator != (const ComplexDiagMatrix& a) const
{
  return !(*this == a);
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (double val)
{
  for (octave_idx_type i = 0; i < length (); i++)
    elem (i, i) = val;
  return *this;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const Complex& val)
{
  for (octave_idx_type i = 0; i < length (); i++)
    elem (i, i) = val;
  return *this;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const Complex& 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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const ComplexColumnVector& 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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const ComplexRowVector& 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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const ComplexColumnVector& 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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::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;
}
 
ComplexDiagMatrix&
ComplexDiagMatrix::fill (const ComplexRowVector& 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
ComplexDiagMatrix::abs (void) const
{
  return DiagMatrix (extract_diag ().abs (), rows (), columns ());
}
 
ComplexDiagMatrix
conj (const ComplexDiagMatrix& a)
{
  return ComplexDiagMatrix (conj (a.extract_diag ()), a.rows (), a.columns ());
}
 
// resize is the destructive analog for this one
 
ComplexMatrix
ComplexDiagMatrix::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;
 
  ComplexMatrix 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.
 
ComplexRowVector
ComplexDiagMatrix::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");
 
  ComplexRowVector retval (c, 0.0);
  if (r <= c || i < c)
    retval.elem (i) = elem (i, i);
 
  return retval;
}
 
ComplexRowVector
ComplexDiagMatrix::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");
}
 
ComplexColumnVector
ComplexDiagMatrix::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");
 
  ComplexColumnVector retval (r, 0.0);
  if (r >= c || i < r)
    retval.elem (i) = elem (i, i);
 
  return retval;
}
 
ComplexColumnVector
ComplexDiagMatrix::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");
}
 
ComplexDiagMatrix
ComplexDiagMatrix::inverse (void) const
{
  octave_idx_type info;
  return inverse (info);
}
 
ComplexDiagMatrix
ComplexDiagMatrix::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");
 
  ComplexDiagMatrix 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;
}
 
ComplexDiagMatrix
ComplexDiagMatrix::pseudo_inverse (double tol) const
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
  octave_idx_type len = length ();
 
  ComplexDiagMatrix 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;
}
 
bool
ComplexDiagMatrix::all_elements_are_real (void) const
{
  return mx_inline_all_real (length (), data ());
}
 
// diagonal matrix by diagonal matrix -> diagonal matrix operations
 
ComplexDiagMatrix&
ComplexDiagMatrix::operator += (const DiagMatrix& a)
{
  octave_idx_type r = rows ();
  octave_idx_type c = cols ();
 
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();
 
  if (r != a_nr || c != a_nc)
    octave::err_nonconformant ("operator +=", r, c, a_nr, a_nc);
 
  if (r == 0 || c == 0)
    return *this;
 
  Complex *d = fortran_vec (); // Ensures only one reference to my privates!
 
  mx_inline_add2 (length (), d, a.data ());
  return *this;
}
 
ComplexDiagMatrix
operator * (const ComplexDiagMatrix& 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);
 
  ComplexDiagMatrix 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;
}
 
ComplexDiagMatrix
operator * (const DiagMatrix& a, const ComplexDiagMatrix& 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);
 
  if (a_nr == 0 || a_nc == 0 || b_nc == 0)
    return ComplexDiagMatrix (a_nr, a_nc, 0.0);
 
  ComplexDiagMatrix c (a_nr, b_nc);
 
  octave_idx_type len = (a_nr < b_nc ? a_nr : b_nc);
 
  for (octave_idx_type i = 0; i < len; i++)
    {
      double a_element = a.elem (i, i);
      Complex b_element = b.elem (i, i);
 
      c.elem (i, i) = a_element * b_element;
    }
 
  return c;
}
 
ComplexDiagMatrix
operator * (const ComplexDiagMatrix& a, const ComplexDiagMatrix& 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);
 
  if (a_nr == 0 || a_nc == 0 || b_nc == 0)
    return ComplexDiagMatrix (a_nr, a_nc, 0.0);
 
  ComplexDiagMatrix c (a_nr, b_nc);
 
  octave_idx_type len = (a_nr < b_nc ? a_nr : b_nc);
 
  for (octave_idx_type i = 0; i < len; i++)
    {
      Complex a_element = a.elem (i, i);
      Complex b_element = b.elem (i, i);
 
      c.elem (i, i) = a_element * b_element;
    }
 
  return c;
}
 
// other operations
 
ComplexDET
ComplexDiagMatrix::determinant (void) const
{
  ComplexDET 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
ComplexDiagMatrix::rcond (void) const
{
  ColumnVector av = extract_diag (0).map<double> (std::abs);
  double amx = av.max ();
  double amn = av.min ();
  return amx == 0 ? 0.0 : amn / amx;
}
 
// i/o
 
std::ostream&
operator << (std::ostream& os, const ComplexDiagMatrix& a)
{
  Complex ZERO (0.0);
//  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) */ << ZERO;
        }
      os << "\n";
    }
  return os;
}