// Matrix manipulations.
/*

Copyright (C) 2008, 2009 Jaroslav Hajek
Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002,
              2003, 2004, 2005, 2006, 2007 John W. Eaton

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 <cfloat>

#include <iostream>
#include <vector>

// FIXME
#ifdef HAVE_SYS_TYPES_H
#include <sys/types.h>
#endif

#include "Array-util.h"
#include "fCMatrix.h"
#include "DET.h"
#include "fCmplxSCHUR.h"
#include "fCmplxSVD.h"
#include "fCmplxCHOL.h"
#include "f77-fcn.h"
#include "functor.h"
#include "lo-error.h"
#include "oct-locbuf.h"
#include "lo-ieee.h"
#include "lo-mappers.h"
#include "lo-utils.h"
#include "mx-base.h"
#include "mx-fcm-fdm.h"
#include "mx-fdm-fcm.h"
#include "mx-fcm-fs.h"
#include "mx-inlines.cc"
#include "mx-op-defs.h"
#include "oct-cmplx.h"
#include "oct-norm.h"

#if defined (HAVE_FFTW3)
#include "oct-fftw.h"
#endif

// Fortran functions we call.

extern "C"
{
  F77_RET_T
  F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL,
			       F77_CONST_CHAR_ARG_DECL,
			       const octave_idx_type&, const octave_idx_type&,
			       const octave_idx_type&, const octave_idx_type&,
			       octave_idx_type&
			       F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgebal, CGEBAL) (F77_CONST_CHAR_ARG_DECL,
			     const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type&,
			     octave_idx_type&, float*, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (sgebak, SGEBAK) (F77_CONST_CHAR_ARG_DECL,
			     F77_CONST_CHAR_ARG_DECL,
			     const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, float*,
			     const octave_idx_type&, float*, const octave_idx_type&, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgemm, CGEMM) (F77_CONST_CHAR_ARG_DECL,
			   F77_CONST_CHAR_ARG_DECL,
			   const octave_idx_type&, const octave_idx_type&, const octave_idx_type&,
			   const FloatComplex&, const FloatComplex*, const octave_idx_type&,
			   const FloatComplex*, const octave_idx_type&, const FloatComplex&,
			   FloatComplex*, const octave_idx_type&
			   F77_CHAR_ARG_LEN_DECL
			   F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgemv, CGEMV) (F77_CONST_CHAR_ARG_DECL,
                           const octave_idx_type&, const octave_idx_type&, const FloatComplex&,
                           const FloatComplex*, const octave_idx_type&, const FloatComplex*,
                           const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type&
                           F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (xcdotu, XCDOTU) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&,
			     const FloatComplex*, const octave_idx_type&, FloatComplex&);

  F77_RET_T
  F77_FUNC (xcdotc, XCDOTC) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&,
			     const FloatComplex*, const octave_idx_type&, FloatComplex&);

  F77_RET_T
  F77_FUNC (csyrk, CSYRK) (F77_CONST_CHAR_ARG_DECL,
			   F77_CONST_CHAR_ARG_DECL,
			   const octave_idx_type&, const octave_idx_type&, 
			   const FloatComplex&, const FloatComplex*, const octave_idx_type&,
			   const FloatComplex&, FloatComplex*, const octave_idx_type&
			   F77_CHAR_ARG_LEN_DECL
			   F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cherk, CHERK) (F77_CONST_CHAR_ARG_DECL,
			   F77_CONST_CHAR_ARG_DECL,
			   const octave_idx_type&, const octave_idx_type&, 
			   const FloatComplex&, const FloatComplex*, const octave_idx_type&,
			   const FloatComplex&, FloatComplex*, const octave_idx_type&
			   F77_CHAR_ARG_LEN_DECL
			   F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgetrf, CGETRF) (const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&,
			     octave_idx_type*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (cgetrs, CGETRS) (F77_CONST_CHAR_ARG_DECL,
			     const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&,
			     const octave_idx_type*, FloatComplex*, const octave_idx_type&, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgetri, CGETRI) (const octave_idx_type&, FloatComplex*, const octave_idx_type&, const octave_idx_type*,
			     FloatComplex*, const octave_idx_type&, octave_idx_type&);

  F77_RET_T
  F77_FUNC (cgecon, CGECON) (F77_CONST_CHAR_ARG_DECL,
			     const octave_idx_type&, FloatComplex*, 
			     const octave_idx_type&, const float&, float&, 
			     FloatComplex*, float*, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cgelsy, CGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&,
			     FloatComplex*, const octave_idx_type&, FloatComplex*,
			     const octave_idx_type&, octave_idx_type*, float&, octave_idx_type&,
			     FloatComplex*, const octave_idx_type&, float*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (cgelsd, CGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&,
			     FloatComplex*, const octave_idx_type&, FloatComplex*,
			     const octave_idx_type&, float*, float&, octave_idx_type&,
			     FloatComplex*, const octave_idx_type&, float*, 
			     octave_idx_type*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (cpotrf, CPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
			     FloatComplex*, const octave_idx_type&, 
			     octave_idx_type& F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cpocon, CPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
			     FloatComplex*, const octave_idx_type&, const float&,
			     float&, FloatComplex*, float*,
			     octave_idx_type& F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cpotrs, CPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
			     const octave_idx_type&, const FloatComplex*, 
			     const octave_idx_type&, FloatComplex*, 
			     const octave_idx_type&, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (ctrtri, CTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, 
			     const octave_idx_type&, const FloatComplex*, 
			     const octave_idx_type&, octave_idx_type& 
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (ctrcon, CTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, 
			     F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
			     const FloatComplex*, const octave_idx_type&, float&,
			     FloatComplex*, float*, octave_idx_type& 
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (ctrtrs, CTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, 
			     F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
			     const octave_idx_type&, const FloatComplex*, 
			     const octave_idx_type&, FloatComplex*, 
			     const octave_idx_type&, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (cffti, CFFTI) (const octave_idx_type&, FloatComplex*);

  F77_RET_T
  F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, FloatComplex*, FloatComplex*);

  F77_RET_T
  F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, FloatComplex*, FloatComplex*);

  F77_RET_T
  F77_FUNC (clartg, CLARTG) (const FloatComplex&, const FloatComplex&,
			     float&, FloatComplex&, FloatComplex&);

  F77_RET_T
  F77_FUNC (ctrsyl, CTRSYL) (F77_CONST_CHAR_ARG_DECL,
			     F77_CONST_CHAR_ARG_DECL,
			     const octave_idx_type&, const octave_idx_type&, const octave_idx_type&,
			     const FloatComplex*, const octave_idx_type&,
			     const FloatComplex*, const octave_idx_type&,
			     const FloatComplex*, const octave_idx_type&, float&, octave_idx_type&
			     F77_CHAR_ARG_LEN_DECL
			     F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (xclange, XCLANGE) (F77_CONST_CHAR_ARG_DECL,
			       const octave_idx_type&, const octave_idx_type&, const FloatComplex*,
			       const octave_idx_type&, float*, float&
			       F77_CHAR_ARG_LEN_DECL);
}

static const FloatComplex FloatComplex_NaN_result (octave_Float_NaN, octave_Float_NaN);

// FloatComplex Matrix class

FloatComplexMatrix::FloatComplexMatrix (const FloatMatrix& a)
  : MArray2<FloatComplex> (a.rows (), a.cols ())
{
  for (octave_idx_type j = 0; j < cols (); j++)
    for (octave_idx_type i = 0; i < rows (); i++)
      elem (i, j) = a.elem (i, j);
}

FloatComplexMatrix::FloatComplexMatrix (const FloatRowVector& rv)
  : MArray2<FloatComplex> (1, rv.length (), 0.0)
{
  for (octave_idx_type i = 0; i < rv.length (); i++)
    elem (0, i) = rv.elem (i);
}

FloatComplexMatrix::FloatComplexMatrix (const FloatColumnVector& cv)
  : MArray2<FloatComplex> (cv.length (), 1, 0.0)
{
  for (octave_idx_type i = 0; i < cv.length (); i++)
    elem (i, 0) = cv.elem (i);
}

FloatComplexMatrix::FloatComplexMatrix (const FloatDiagMatrix& a)
  : MArray2<FloatComplex> (a.rows (), a.cols (), 0.0)
{
  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) = a.elem (i, i);
}

FloatComplexMatrix::FloatComplexMatrix (const FloatComplexRowVector& rv)
  : MArray2<FloatComplex> (Array2<FloatComplex> (rv, 1, rv.length ()))
{
}

FloatComplexMatrix::FloatComplexMatrix (const FloatComplexColumnVector& cv)
  : MArray2<FloatComplex> (Array2<FloatComplex> (cv, cv.length (), 1))
{
}

FloatComplexMatrix::FloatComplexMatrix (const FloatComplexDiagMatrix& a)
  : MArray2<FloatComplex> (a.rows (), a.cols (), 0.0)
{
  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) = a.elem (i, i);
}

// FIXME -- could we use a templated mixed-type copy function
// here?

FloatComplexMatrix::FloatComplexMatrix (const boolMatrix& a)
  : MArray2<FloatComplex> (a.rows (), a.cols (), 0.0)
{
  for (octave_idx_type i = 0; i < a.rows (); i++)
    for (octave_idx_type j = 0; j < a.cols (); j++)
      elem (i, j) = a.elem (i, j);
}

FloatComplexMatrix::FloatComplexMatrix (const charMatrix& a)
  : MArray2<FloatComplex> (a.rows (), a.cols (), 0.0)
{
  for (octave_idx_type i = 0; i < a.rows (); i++)
    for (octave_idx_type j = 0; j < a.cols (); j++)
      elem (i, j) = static_cast<unsigned char> (a.elem (i, j));
}

bool
FloatComplexMatrix::operator == (const FloatComplexMatrix& a) const
{
  if (rows () != a.rows () || cols () != a.cols ())
    return false;

  return mx_inline_equal (data (), a.data (), length ());
}

bool
FloatComplexMatrix::operator != (const FloatComplexMatrix& a) const
{
  return !(*this == a);
}

bool
FloatComplexMatrix::is_hermitian (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (is_square () && nr > 0)
    {
      for (octave_idx_type i = 0; i < nr; i++)
	for (octave_idx_type j = i; j < nc; j++)
	  if (elem (i, j) != conj (elem (j, i)))
	    return false;

      return true;
    }

  return false;
}

// destructive insert/delete/reorder operations

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatMatrix& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  if (a_nr >0 && a_nc > 0)
    {
      make_unique ();

      for (octave_idx_type j = 0; j < a_nc; j++)
	for (octave_idx_type i = 0; i < a_nr; i++)
	  xelem (r+i, c+j) = a.elem (i, j);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatRowVector& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_len = a.length ();

  if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  if (a_len > 0)
    {
      make_unique ();

      for (octave_idx_type i = 0; i < a_len; i++)
	xelem (r, c+i) = a.elem (i);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatColumnVector& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_len = a.length ();

  if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  if (a_len > 0)
    {
      make_unique ();

      for (octave_idx_type i = 0; i < a_len; i++)
	xelem (r+i, c) = a.elem (i);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatDiagMatrix& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1);

  octave_idx_type a_len = a.length ();

  if (a_len > 0)
    {
      make_unique ();

      for (octave_idx_type i = 0; i < a_len; i++)
	xelem (r+i, c+i) = a.elem (i, i);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatComplexMatrix& a, octave_idx_type r, octave_idx_type c)
{
  Array2<FloatComplex>::insert (a, r, c);
  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatComplexRowVector& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_len = a.length ();
  if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  for (octave_idx_type i = 0; i < a_len; i++)
    elem (r, c+i) = a.elem (i);

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatComplexColumnVector& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_len = a.length ();

  if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  if (a_len > 0)
    {
      make_unique ();

      for (octave_idx_type i = 0; i < a_len; i++)
	xelem (r+i, c) = a.elem (i);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::insert (const FloatComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c)
{
  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ())
    {
      (*current_liboctave_error_handler) ("range error for insert");
      return *this;
    }

  fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1);

  octave_idx_type a_len = a.length ();

  if (a_len > 0)
    {
      make_unique ();

      for (octave_idx_type i = 0; i < a_len; i++)
	xelem (r+i, c+i) = a.elem (i, i);
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::fill (float val)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      make_unique ();

      for (octave_idx_type j = 0; j < nc; j++)
	for (octave_idx_type i = 0; i < nr; i++)
	  xelem (i, j) = val;
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::fill (const FloatComplex& val)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      make_unique ();

      for (octave_idx_type j = 0; j < nc; j++)
	for (octave_idx_type i = 0; i < nr; i++)
	  xelem (i, j) = val;
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::fill (float val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0
      || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc)
    {
      (*current_liboctave_error_handler) ("range error for fill");
      return *this;
    }

  if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; }
  if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; }

  if (r2 >= r1 && c2 >= c1)
    {
      make_unique ();

      for (octave_idx_type j = c1; j <= c2; j++)
	for (octave_idx_type i = r1; i <= r2; i++)
	  xelem (i, j) = val;
    }

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::fill (const FloatComplex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0
      || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc)
    {
      (*current_liboctave_error_handler) ("range error for fill");
      return *this;
    }

  if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; }
  if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; }

  if (r2 >= r1 && c2 >=c1)
    {
      make_unique ();

      for (octave_idx_type j = c1; j <= c2; j++)
	for (octave_idx_type i = r1; i <= r2; i++)
	  xelem (i, j) = val;
    }

  return *this;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.rows ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.cols ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatRowVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != 1)
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.length ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatColumnVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.length ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + 1);
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatDiagMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.rows ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.cols ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatComplexMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.rows ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.cols ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatComplexRowVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != 1)
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.length ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatComplexColumnVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.length ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + 1);
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::append (const FloatComplexDiagMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nr != a.rows ())
    {
      (*current_liboctave_error_handler) ("row dimension mismatch for append");
      return *this;
    }

  octave_idx_type nc_insert = nc;
  FloatComplexMatrix retval (nr, nc + a.cols ());
  retval.insert (*this, 0, 0);
  retval.insert (a, 0, nc_insert);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.cols ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.rows (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatRowVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.length ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + 1, nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatColumnVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != 1)
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.length (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatDiagMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.cols ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.rows (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatComplexMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.cols ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.rows (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatComplexRowVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.length ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + 1, nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatComplexColumnVector& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != 1)
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.length (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::stack (const FloatComplexDiagMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  if (nc != a.cols ())
    {
      (*current_liboctave_error_handler)
	("column dimension mismatch for stack");
      return *this;
    }

  octave_idx_type nr_insert = nr;
  FloatComplexMatrix retval (nr + a.rows (), nc);
  retval.insert (*this, 0, 0);
  retval.insert (a, nr_insert, 0);
  return retval;
}

FloatComplexMatrix
conj (const FloatComplexMatrix& a)
{
  return FloatComplexMatrix (mx_inline_conj_dup (a.data (), a.length ()),
                             a.rows (), a.cols ());
}

// resize is the destructive equivalent for this one

FloatComplexMatrix
FloatComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const
{
  if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; }
  if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; }

  octave_idx_type new_r = r2 - r1 + 1;
  octave_idx_type new_c = c2 - c1 + 1;

  FloatComplexMatrix 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.xelem (i, j) = elem (r1+i, c1+j);

  return result;
}

FloatComplexMatrix
FloatComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const
{
  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      result.xelem (i, j) = elem (r1+i, c1+j);

  return result;
}

// extract row or column i.

FloatComplexRowVector
FloatComplexMatrix::row (octave_idx_type i) const
{
  return MArray<FloatComplex> (index (idx_vector (i), idx_vector::colon));
}

FloatComplexColumnVector
FloatComplexMatrix::column (octave_idx_type i) const
{
  return MArray<FloatComplex> (index (idx_vector::colon, idx_vector (i)));
}

FloatComplexMatrix
FloatComplexMatrix::inverse (void) const
{
  octave_idx_type info;
  float rcon;
  MatrixType mattype (*this);
  return inverse (mattype, info, rcon, 0, 0);
}

FloatComplexMatrix
FloatComplexMatrix::inverse (octave_idx_type& info) const
{
  float rcon;
  MatrixType mattype (*this);
  return inverse (mattype, info, rcon, 0, 0);
}

FloatComplexMatrix
FloatComplexMatrix::inverse (octave_idx_type& info, float& rcon, int force,
			int calc_cond) const
{
  MatrixType mattype (*this);
  return inverse (mattype, info, rcon, force, calc_cond);
}

FloatComplexMatrix
FloatComplexMatrix::inverse (MatrixType &mattype) const
{
  octave_idx_type info;
  float rcon;
  return inverse (mattype, info, rcon, 0, 0);
}

FloatComplexMatrix
FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const
{
  float rcon;
  return inverse (mattype, info, rcon, 0, 0);
}

FloatComplexMatrix
FloatComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info,
			 float& rcon, int force, int calc_cond) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != nc || nr == 0 || nc == 0)
    (*current_liboctave_error_handler) ("inverse requires square matrix");
  else
    {
      int typ = mattype.type ();
      char uplo = (typ == MatrixType::Lower ? 'L' : 'U');
      char udiag = 'N';
      retval = *this;
      FloatComplex *tmp_data = retval.fortran_vec ();

      F77_XFCN (ctrtri, CTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1),
				 F77_CONST_CHAR_ARG2 (&udiag, 1),
				 nr, tmp_data, nr, info 
				 F77_CHAR_ARG_LEN (1)
				 F77_CHAR_ARG_LEN (1)));

      // Throw-away extra info LAPACK gives so as to not change output.
      rcon = 0.0;
      if (info != 0) 
	info = -1;
      else if (calc_cond) 
	{
	  octave_idx_type ztrcon_info = 0;
	  char job = '1';

	  OCTAVE_LOCAL_BUFFER (FloatComplex, cwork, 2*nr);
	  OCTAVE_LOCAL_BUFFER (float, rwork, nr);

	  F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&job, 1),
				     F77_CONST_CHAR_ARG2 (&uplo, 1),
				     F77_CONST_CHAR_ARG2 (&udiag, 1),
				     nr, tmp_data, nr, rcon, 
				     cwork, rwork, ztrcon_info 
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)));

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

      if (info == -1 && ! force)
	retval = *this; // Restore matrix contents.
    }

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info,
			 float& rcon, int force, int calc_cond) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != nc)
    (*current_liboctave_error_handler) ("inverse requires square matrix");
  else
    {
      Array<octave_idx_type> ipvt (nr);
      octave_idx_type *pipvt = ipvt.fortran_vec ();

      retval = *this;
      FloatComplex *tmp_data = retval.fortran_vec ();

      Array<FloatComplex> z(1);
      octave_idx_type lwork = -1;

      // Query the optimum work array size.

      F77_XFCN (cgetri, CGETRI, (nc, tmp_data, nr, pipvt, 
				 z.fortran_vec (), lwork, info));

      lwork = static_cast<octave_idx_type> (std::real(z(0)));
      lwork = (lwork <  2 *nc ? 2*nc : lwork);
      z.resize (lwork);
      FloatComplex *pz = z.fortran_vec ();

      info = 0;

      // Calculate the norm of the matrix, for later use.
      float anorm;
      if (calc_cond)
	anorm  = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max();

      F77_XFCN (cgetrf, CGETRF, (nc, nc, tmp_data, nr, pipvt, info));

      // Throw-away extra info LAPACK gives so as to not change output.
      rcon = 0.0;
      if (info != 0) 
	info = -1;
      else if (calc_cond) 
	{
	  // Now calculate the condition number for non-singular matrix.
	  octave_idx_type zgecon_info = 0;
	  char job = '1';
	  Array<float> rz (2 * nc);
	  float *prz = rz.fortran_vec ();
	  F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1),
				     nc, tmp_data, nr, anorm, 
				     rcon, pz, prz, zgecon_info
				     F77_CHAR_ARG_LEN (1)));

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

      if (info == -1 && ! force)
	retval = *this;  // Restore contents.
      else
	{
	  octave_idx_type zgetri_info = 0;

	  F77_XFCN (cgetri, CGETRI, (nc, tmp_data, nr, pipvt,
				     pz, lwork, zgetri_info));

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

      if (info != 0)
	mattype.mark_as_rectangular();
    }
  
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info,
			float& rcon, int force, int calc_cond) const
{
  int typ = mattype.type (false);
  FloatComplexMatrix ret;

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  if (typ == MatrixType::Upper || typ == MatrixType::Lower)
    ret = tinverse (mattype, info, rcon, force, calc_cond);
  else
    {
      if (mattype.is_hermitian ())
	{
	  FloatComplexCHOL chol (*this, info, calc_cond);
	  if (info == 0)
	    {
	      if (calc_cond)
		rcon = chol.rcond();
	      else
		rcon = 1.0;
	      ret = chol.inverse ();
	    }
	  else
	    mattype.mark_as_unsymmetric ();
	}

      if (!mattype.is_hermitian ())
	ret = finverse(mattype, info, rcon, force, calc_cond);

      if ((mattype.is_hermitian () || calc_cond) && rcon == 0.)
	ret = FloatComplexMatrix (rows (), columns (), FloatComplex (octave_Float_Inf, 0.));
    }

  return ret;
}

FloatComplexMatrix
FloatComplexMatrix::pseudo_inverse (float tol) const
{
  FloatComplexMatrix retval;

  FloatComplexSVD result (*this, SVD::economy);

  FloatDiagMatrix S = result.singular_values ();
  FloatComplexMatrix U = result.left_singular_matrix ();
  FloatComplexMatrix V = result.right_singular_matrix ();

  FloatColumnVector sigma = S.diag ();

  octave_idx_type r = sigma.length () - 1;
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (tol <= 0.0)
    {
      if (nr > nc)
	tol = nr * sigma.elem (0) * DBL_EPSILON;
      else
	tol = nc * sigma.elem (0) * DBL_EPSILON;
    }

  while (r >= 0 && sigma.elem (r) < tol)
    r--;

  if (r < 0)
    retval = FloatComplexMatrix (nc, nr, 0.0);
  else
    {
      FloatComplexMatrix Ur = U.extract (0, 0, nr-1, r);
      FloatDiagMatrix D = FloatDiagMatrix (sigma.extract (0, r)) . inverse ();
      FloatComplexMatrix Vr = V.extract (0, 0, nc-1, r);
      retval = Vr * D * Ur.hermitian ();
    }

  return retval;
}

#if defined (HAVE_FFTW3)

FloatComplexMatrix
FloatComplexMatrix::fourier (void) const
{
  size_t nr = rows ();
  size_t nc = cols ();

  FloatComplexMatrix retval (nr, nc);

  size_t npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  const FloatComplex *in (data ());
  FloatComplex *out (retval.fortran_vec ());

  octave_fftw::fft (in, out, npts, nsamples); 

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::ifourier (void) const
{
  size_t nr = rows ();
  size_t nc = cols ();

  FloatComplexMatrix retval (nr, nc);

  size_t npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  const FloatComplex *in (data ());
  FloatComplex *out (retval.fortran_vec ());

  octave_fftw::ifft (in, out, npts, nsamples); 

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::fourier2d (void) const
{
  dim_vector dv(rows (), cols ());

  FloatComplexMatrix retval (rows (), cols ());
  const FloatComplex *in (data ());
  FloatComplex *out (retval.fortran_vec ());

  octave_fftw::fftNd (in, out, 2, dv);

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::ifourier2d (void) const
{
  dim_vector dv(rows (), cols ());

  FloatComplexMatrix retval (rows (), cols ());
  const FloatComplex *in (data ());
  FloatComplex *out (retval.fortran_vec ());

  octave_fftw::ifftNd (in, out, 2, dv);

  return retval;
}

#else

FloatComplexMatrix
FloatComplexMatrix::fourier (void) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  octave_idx_type nn = 4*npts+15;

  Array<FloatComplex> wsave (nn);
  FloatComplex *pwsave = wsave.fortran_vec ();

  retval = *this;
  FloatComplex *tmp_data = retval.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave);
    }

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::ifourier (void) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  octave_idx_type nn = 4*npts+15;

  Array<FloatComplex> wsave (nn);
  FloatComplex *pwsave = wsave.fortran_vec ();

  retval = *this;
  FloatComplex *tmp_data = retval.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave);
    }

  for (octave_idx_type j = 0; j < npts*nsamples; j++)
    tmp_data[j] = tmp_data[j] / static_cast<float> (npts);

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::fourier2d (void) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  octave_idx_type nn = 4*npts+15;

  Array<FloatComplex> wsave (nn);
  FloatComplex *pwsave = wsave.fortran_vec ();

  retval = *this;
  FloatComplex *tmp_data = retval.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave);
    }

  npts = nc;
  nsamples = nr;
  nn = 4*npts+15;

  wsave.resize (nn);
  pwsave = wsave.fortran_vec ();

  Array<FloatComplex> tmp (npts);
  FloatComplex *prow = tmp.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      for (octave_idx_type i = 0; i < npts; i++)
	prow[i] = tmp_data[i*nr + j];

      F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave);

      for (octave_idx_type i = 0; i < npts; i++)
	tmp_data[i*nr + j] = prow[i];
    }

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::ifourier2d (void) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type npts, nsamples;

  if (nr == 1 || nc == 1)
    {
      npts = nr > nc ? nr : nc;
      nsamples = 1;
    }
  else
    {
      npts = nr;
      nsamples = nc;
    }

  octave_idx_type nn = 4*npts+15;

  Array<FloatComplex> wsave (nn);
  FloatComplex *pwsave = wsave.fortran_vec ();

  retval = *this;
  FloatComplex *tmp_data = retval.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave);
    }

  for (octave_idx_type j = 0; j < npts*nsamples; j++)
    tmp_data[j] = tmp_data[j] / static_cast<float> (npts);

  npts = nc;
  nsamples = nr;
  nn = 4*npts+15;

  wsave.resize (nn);
  pwsave = wsave.fortran_vec ();

  Array<FloatComplex> tmp (npts);
  FloatComplex *prow = tmp.fortran_vec ();

  F77_FUNC (cffti, CFFTI) (npts, pwsave);

  for (octave_idx_type j = 0; j < nsamples; j++)
    {
      OCTAVE_QUIT;

      for (octave_idx_type i = 0; i < npts; i++)
	prow[i] = tmp_data[i*nr + j];

      F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave);

      for (octave_idx_type i = 0; i < npts; i++)
	tmp_data[i*nr + j] = prow[i] / static_cast<float> (npts);
    }

  return retval;
}

#endif

FloatComplexDET
FloatComplexMatrix::determinant (void) const
{
  octave_idx_type info;
  float rcon;
  return determinant (info, rcon, 0);
}

FloatComplexDET
FloatComplexMatrix::determinant (octave_idx_type& info) const
{
  float rcon;
  return determinant (info, rcon, 0);
}

FloatComplexDET
FloatComplexMatrix::determinant (octave_idx_type& info, float& rcon, int calc_cond) const
{
  MatrixType mattype (*this);
  return determinant (mattype, info, rcon, calc_cond);
}

FloatComplexDET
FloatComplexMatrix::determinant (MatrixType& mattype,
                                 octave_idx_type& info, float& rcon, int calc_cond) const
{
  FloatComplexDET retval (1.0);

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != nc)
    (*current_liboctave_error_handler) ("matrix must be square");
  else
    {
      volatile int typ = mattype.type ();

      if (typ == MatrixType::Unknown)
        typ = mattype.type (*this);

      if (typ == MatrixType::Lower || typ == MatrixType::Upper)
        {
          for (octave_idx_type i = 0; i < nc; i++) 
            retval *= elem (i,i);
        }
      else if (typ == MatrixType::Hermitian)
        {
          FloatComplexMatrix atmp = *this;
          FloatComplex *tmp_data = atmp.fortran_vec ();

          info = 0;
          float anorm = 0;
          if (calc_cond) anorm = xnorm (*this, 1);


          char job = 'L';
          F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 
                                     tmp_data, nr, info
                                     F77_CHAR_ARG_LEN (1)));

          if (info != 0) 
            {
              rcon = 0.0;
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Full;
            }
          else 
            {
              Array<FloatComplex> z (2 * nc);
              FloatComplex *pz = z.fortran_vec ();
              Array<float> rz (nc);
              float *prz = rz.fortran_vec ();

              F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1),
                                         nr, tmp_data, nr, anorm,
                                         rcon, pz, prz, info
                                         F77_CHAR_ARG_LEN (1)));

              if (info != 0) 
                rcon = 0.0;

              for (octave_idx_type i = 0; i < nc; i++) 
                retval *= atmp (i,i);

              retval = retval.square ();
            }
        }
      else if (typ != MatrixType::Full)
        (*current_liboctave_error_handler) ("det: invalid dense matrix type");

      if (typ == MatrixType::Full)
        {
          Array<octave_idx_type> ipvt (nr);
          octave_idx_type *pipvt = ipvt.fortran_vec ();

          FloatComplexMatrix atmp = *this;
          FloatComplex *tmp_data = atmp.fortran_vec ();

          info = 0;

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

          F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info));

          // Throw-away extra info LAPACK gives so as to not change output.
          rcon = 0.0;
          if (info != 0) 
            {
              info = -1;
              retval = FloatComplexDET ();
            } 
          else 
            {
              if (calc_cond) 
                {
                  // Now calc the condition number for non-singular matrix.
                  char job = '1';
                  Array<FloatComplex> z (2 * nc);
                  FloatComplex *pz = z.fortran_vec ();
                  Array<float> rz (2 * nc);
                  float *prz = rz.fortran_vec ();

                  F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1),
                                             nc, tmp_data, nr, anorm, 
                                             rcon, pz, prz, info
                                             F77_CHAR_ARG_LEN (1)));
                }

              if (info != 0) 
                {
                  info = -1;
                  retval = FloatComplexDET ();
                } 
              else 
                {
                  for (octave_idx_type i = 0; i < nc; i++) 
                    {
                      FloatComplex c = atmp(i,i);
                      retval *= (ipvt(i) != (i+1)) ? -c : c;
                    }
                }
            }
        }
    }

  return retval;
}

float
FloatComplexMatrix::rcond (void) const
{
  MatrixType mattype (*this);
  return rcond (mattype);
}

float
FloatComplexMatrix::rcond (MatrixType &mattype) const
{
  float rcon;
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != nc)
    (*current_liboctave_error_handler) ("matrix must be square");
  else if (nr == 0 || nc == 0)
    rcon = octave_Inf;
  else
    {
      int typ = mattype.type ();

      if (typ == MatrixType::Unknown)
	typ = mattype.type (*this);

      // Only calculate the condition number for LU/Cholesky
      if (typ == MatrixType::Upper)
	{
	  const FloatComplex *tmp_data = fortran_vec ();
	  octave_idx_type info = 0;
	  char norm = '1';
	  char uplo = 'U';
	  char dia = 'N';

	  Array<FloatComplex> z (2 * nc);
	  FloatComplex *pz = z.fortran_vec ();
	  Array<float> rz (nc);
	  float *prz = rz.fortran_vec ();

	  F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), 
				     F77_CONST_CHAR_ARG2 (&uplo, 1), 
				     F77_CONST_CHAR_ARG2 (&dia, 1), 
				     nr, tmp_data, nr, rcon,
				     pz, prz, info
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)));

	  if (info != 0) 
	    rcon = 0;
	}
      else if  (typ == MatrixType::Permuted_Upper)
	(*current_liboctave_error_handler)
	  ("permuted triangular matrix not implemented");
      else if (typ == MatrixType::Lower)
	{
	  const FloatComplex *tmp_data = fortran_vec ();
	  octave_idx_type info = 0;
	  char norm = '1';
	  char uplo = 'L';
	  char dia = 'N';

	  Array<FloatComplex> z (2 * nc);
	  FloatComplex *pz = z.fortran_vec ();
	  Array<float> rz (nc);
	  float *prz = rz.fortran_vec ();

	  F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), 
				     F77_CONST_CHAR_ARG2 (&uplo, 1), 
				     F77_CONST_CHAR_ARG2 (&dia, 1), 
				     nr, tmp_data, nr, rcon,
				     pz, prz, info
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)
				     F77_CHAR_ARG_LEN (1)));

	  if (info != 0) 
	    rcon = 0.0;
	}
      else if (typ == MatrixType::Permuted_Lower)
	(*current_liboctave_error_handler)
	  ("permuted triangular matrix not implemented");
      else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
	{
	  float anorm = -1.0;
	  FloatComplexMatrix atmp = *this;
	  FloatComplex *tmp_data = atmp.fortran_vec ();

	  if (typ == MatrixType::Hermitian)
	    {
	      octave_idx_type info = 0;
	      char job = 'L';
	      anorm = atmp.abs().sum().
		row(static_cast<octave_idx_type>(0)).max();

	      F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 
					 tmp_data, nr, info
					 F77_CHAR_ARG_LEN (1)));

	      if (info != 0) 
		{
		  rcon = 0.0;

		  mattype.mark_as_unsymmetric ();
		  typ = MatrixType::Full;
		}
	      else 
		{
		  Array<FloatComplex> z (2 * nc);
		  FloatComplex *pz = z.fortran_vec ();
		  Array<float> rz (nc);
		  float *prz = rz.fortran_vec ();

		  F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nr, tmp_data, nr, anorm,
					     rcon, pz, prz, info
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    rcon = 0.0;
		}
	    }


	  if (typ == MatrixType::Full)
	    {
	      octave_idx_type info = 0;

	      Array<octave_idx_type> ipvt (nr);
	      octave_idx_type *pipvt = ipvt.fortran_vec ();

	      if(anorm < 0.)
		anorm = atmp.abs().sum().
		  row(static_cast<octave_idx_type>(0)).max();

	      Array<FloatComplex> z (2 * nc);
	      FloatComplex *pz = z.fortran_vec ();
	      Array<float> rz (2 * nc);
	      float *prz = rz.fortran_vec ();

	      F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info));

	      if (info != 0) 
		{ 
		  rcon = 0.0;
		  mattype.mark_as_rectangular ();
		} 
	      else 
		{
		  char job = '1';
		  F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nc, tmp_data, nr, anorm, 
					     rcon, pz, prz, info
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    rcon = 0.0;
		}
	    }
	}
      else
	rcon = 0.0;
    }

  return rcon;
}

FloatComplexMatrix
FloatComplexMatrix::utsolve (MatrixType &mattype, const FloatComplexMatrix& b, 
			octave_idx_type& info, float& rcon, 
			solve_singularity_handler sing_handler,
			bool calc_cond) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");
  else if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0));
  else
    {
      volatile int typ = mattype.type ();

      if (typ == MatrixType::Permuted_Upper ||
	  typ == MatrixType::Upper)
	{
	  octave_idx_type b_nc = b.cols ();
	  rcon = 1.;
	  info = 0;

	  if (typ == MatrixType::Permuted_Upper)
	    {
	      (*current_liboctave_error_handler)
		("permuted triangular matrix not implemented");
	    }
	  else
	    {
	      const FloatComplex *tmp_data = fortran_vec ();

	      if (calc_cond)
		{
		  char norm = '1';
		  char uplo = 'U';
		  char dia = 'N';

		  Array<FloatComplex> z (2 * nc);
		  FloatComplex *pz = z.fortran_vec ();
		  Array<float> rz (nc);
		  float *prz = rz.fortran_vec ();

		  F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), 
					     F77_CONST_CHAR_ARG2 (&uplo, 1), 
					     F77_CONST_CHAR_ARG2 (&dia, 1), 
					     nr, tmp_data, nr, rcon,
					     pz, prz, info
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    info = -2;

		  volatile float rcond_plus_one = rcon + 1.0;

		  if (rcond_plus_one == 1.0 || xisnan (rcon))
		    {
		      info = -2;

		      if (sing_handler)
			sing_handler (rcon);
		      else
			(*current_liboctave_error_handler)
			  ("matrix singular to machine precision, rcond = %g",
			   rcon);
		    }
		}

	      if (info == 0)
		{
		  retval = b;
		  FloatComplex *result = retval.fortran_vec ();

		  char uplo = 'U';
		  char trans = 'N';
		  char dia = 'N';

		  F77_XFCN (ctrtrs, CTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), 
					     F77_CONST_CHAR_ARG2 (&trans, 1), 
					     F77_CONST_CHAR_ARG2 (&dia, 1), 
					     nr, b_nc, tmp_data, nr,
					     result, nr, info
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)));
		}
	    }
	}
      else
	(*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::ltsolve (MatrixType &mattype, const FloatComplexMatrix& b, 
			octave_idx_type& info, float& rcon, 
			solve_singularity_handler sing_handler,
			bool calc_cond) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");
  else if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0));
  else
    {
      volatile int typ = mattype.type ();

      if (typ == MatrixType::Permuted_Lower ||
	  typ == MatrixType::Lower)
	{
	  octave_idx_type b_nc = b.cols ();
	  rcon = 1.;
	  info = 0;

	  if (typ == MatrixType::Permuted_Lower)
	    {
	      (*current_liboctave_error_handler)
		("permuted triangular matrix not implemented");
	    }
	  else
	    {
	      const FloatComplex *tmp_data = fortran_vec ();

	      if (calc_cond)
		{
		  char norm = '1';
		  char uplo = 'L';
		  char dia = 'N';

		  Array<FloatComplex> z (2 * nc);
		  FloatComplex *pz = z.fortran_vec ();
		  Array<float> rz (nc);
		  float *prz = rz.fortran_vec ();

		  F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), 
					     F77_CONST_CHAR_ARG2 (&uplo, 1), 
					     F77_CONST_CHAR_ARG2 (&dia, 1), 
					     nr, tmp_data, nr, rcon,
					     pz, prz, info
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    info = -2;

		  volatile float rcond_plus_one = rcon + 1.0;

		  if (rcond_plus_one == 1.0 || xisnan (rcon))
		    {
		      info = -2;

		      if (sing_handler)
			sing_handler (rcon);
		      else
			(*current_liboctave_error_handler)
			  ("matrix singular to machine precision, rcond = %g",
			   rcon);
		    }
		}

	      if (info == 0)
		{
		  retval = b;
		  FloatComplex *result = retval.fortran_vec ();

		  char uplo = 'L';
		  char trans = 'N';
		  char dia = 'N';

		  F77_XFCN (ctrtrs, CTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), 
					     F77_CONST_CHAR_ARG2 (&trans, 1), 
					     F77_CONST_CHAR_ARG2 (&dia, 1), 
					     nr, b_nc, tmp_data, nr,
					     result, nr, info
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)
					     F77_CHAR_ARG_LEN (1)));
		}
	    }
	}
      else
	(*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::fsolve (MatrixType &mattype, const FloatComplexMatrix& b, 
		       octave_idx_type& info, float& rcon,
		       solve_singularity_handler sing_handler,
		       bool calc_cond) const
{
  FloatComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();


  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");
  else if (nr == 0 || b.cols () == 0)
    retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0));
  else
    {
      volatile int typ = mattype.type ();
 
     // Calculate the norm of the matrix, for later use.
      float anorm = -1.;

      if (typ == MatrixType::Hermitian)
	{
	  info = 0;
	  char job = 'L';
	  FloatComplexMatrix atmp = *this;
	  FloatComplex *tmp_data = atmp.fortran_vec ();
	  anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max();

	  F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 
				     tmp_data, nr, info
				     F77_CHAR_ARG_LEN (1)));

	  // Throw-away extra info LAPACK gives so as to not change output.
	  rcon = 0.0;
	  if (info != 0) 
	    {
	      info = -2;

	      mattype.mark_as_unsymmetric ();
	      typ = MatrixType::Full;
	    }
	  else 
	    {
	      if (calc_cond)
		{
		  Array<FloatComplex> z (2 * nc);
		  FloatComplex *pz = z.fortran_vec ();
		  Array<float> rz (nc);
		  float *prz = rz.fortran_vec ();

		  F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nr, tmp_data, nr, anorm,
					     rcon, pz, prz, info
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    info = -2;

		  volatile float rcond_plus_one = rcon + 1.0;

		  if (rcond_plus_one == 1.0 || xisnan (rcon))
		    {
		      info = -2;

		      if (sing_handler)
			sing_handler (rcon);
		      else
			(*current_liboctave_error_handler)
			  ("matrix singular to machine precision, rcond = %g",
			   rcon);
		    }
		}

	      if (info == 0)
		{
		  retval = b;
		  FloatComplex *result = retval.fortran_vec ();

		  octave_idx_type b_nc = b.cols ();

		  F77_XFCN (cpotrs, CPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nr, b_nc, tmp_data, nr,
					     result, b.rows(), info
					     F77_CHAR_ARG_LEN (1)));
		}
	      else
		{
		  mattype.mark_as_unsymmetric ();
		  typ = MatrixType::Full;
		}
	    }
	}

      if (typ == MatrixType::Full)
	{
	  info = 0;

	  Array<octave_idx_type> ipvt (nr);
	  octave_idx_type *pipvt = ipvt.fortran_vec ();

	  FloatComplexMatrix atmp = *this;
	  FloatComplex *tmp_data = atmp.fortran_vec ();

	  Array<FloatComplex> z (2 * nc);
	  FloatComplex *pz = z.fortran_vec ();
	  Array<float> rz (2 * nc);
	  float *prz = rz.fortran_vec ();

	  // Calculate the norm of the matrix, for later use.
	  if (anorm < 0.)
	    anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max();

	  F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info));

	  // Throw-away extra info LAPACK gives so as to not change output.
	  rcon = 0.0;
	  if (info != 0) 
	    { 
	      info = -2;

	      if (sing_handler)
		sing_handler (rcon);
	      else
		(*current_liboctave_error_handler)
		  ("matrix singular to machine precision");

	      mattype.mark_as_rectangular ();
	    } 
	  else 
	    {
	      if (calc_cond)
		{
		  // Now calculate the condition number for 
		  // non-singular matrix.
		  char job = '1';
		  F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nc, tmp_data, nr, anorm, 
					     rcon, pz, prz, info
					     F77_CHAR_ARG_LEN (1)));

		  if (info != 0) 
		    info = -2;

		  volatile float rcond_plus_one = rcon + 1.0;

		  if (rcond_plus_one == 1.0 || xisnan (rcon))
		    {
		      info = -2;

		      if (sing_handler)
			sing_handler (rcon);
		      else
			(*current_liboctave_error_handler)
			  ("matrix singular to machine precision, rcond = %g",
			   rcon);
		    }
		}

	      if (info == 0)
		{
		  retval = b;
		  FloatComplex *result = retval.fortran_vec ();

		  octave_idx_type b_nc = b.cols ();

		  char job = 'N';
		  F77_XFCN (cgetrs, CGETRS, (F77_CONST_CHAR_ARG2 (&job, 1),
					     nr, b_nc, tmp_data, nr,
					     pipvt, result, b.rows(), info
					     F77_CHAR_ARG_LEN (1))); 
		}
	      else
		mattype.mark_as_rectangular ();		    
	    }
	}
    }
  
  return retval;
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, 
		      octave_idx_type& info) const
{
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info,
		      float& rcon) const
{
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, 
		      float& rcon, solve_singularity_handler sing_handler,
		      bool singular_fallback) const
{
  FloatComplexMatrix tmp (b);
  return solve (typ, tmp, info, rcon, sing_handler, singular_fallback);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, 
		      octave_idx_type& info) const
{
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, 
		      octave_idx_type& info, float& rcon) const
{
  return solve (typ, b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (MatrixType &mattype, const FloatComplexMatrix& b, 
		      octave_idx_type& info, float& rcon,
		      solve_singularity_handler sing_handler,
		      bool singular_fallback) const
{
  FloatComplexMatrix retval;
  int typ = mattype.type ();

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  // Only calculate the condition number for LU/Cholesky
  if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    retval = utsolve (mattype, b, info, rcon, sing_handler, false);
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    retval = ltsolve (mattype, b, info, rcon, sing_handler, false);
  else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
    retval = fsolve (mattype, b, info, rcon, sing_handler, true);
  else if (typ != MatrixType::Rectangular)
    {
      (*current_liboctave_error_handler) ("unknown matrix type");
      return FloatComplexMatrix ();
    }

  // Rectangular or one of the above solvers flags a singular matrix
  if (singular_fallback && mattype.type () == MatrixType::Rectangular)
    {
      octave_idx_type rank;
      retval = lssolve (b, info, rank, rcon);
    }

  return retval;
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (typ, FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, 
		      octave_idx_type& info) const
{
  float rcon;
  return solve (typ, FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, 
		      octave_idx_type& info, float& rcon) const
{
  return solve (typ, FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, 
		      octave_idx_type& info, float& rcon,
		      solve_singularity_handler sing_handler) const
{
  return solve (typ, FloatComplexColumnVector (b), info, rcon, sing_handler);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, 
		      octave_idx_type& info) const
{
  float rcon;
  return solve (typ, b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b,
		      octave_idx_type& info, float& rcon) const
{
  return solve (typ, b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b,
		      octave_idx_type& info, float& rcon,
		      solve_singularity_handler sing_handler) const
{

  FloatComplexMatrix tmp (b);
  return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0));
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatMatrix& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info) const
{
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon) const
{
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon,
		      solve_singularity_handler sing_handler) const
{
  FloatComplexMatrix tmp (b);
  return solve (tmp, info, rcon, sing_handler);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatComplexMatrix& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info) const
{
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon) const
{
  return solve (b, info, rcon, 0);
}

FloatComplexMatrix
FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon,
		      solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, info, rcon, sing_handler);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatColumnVector& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info) const
{
  float rcon;
  return solve (FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, 
		      float& rcon) const
{
  return solve (FloatComplexColumnVector (b), info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, 
		      float& rcon, 
		      solve_singularity_handler sing_handler) const
{
  return solve (FloatComplexColumnVector (b), info, rcon, sing_handler);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatComplexColumnVector& b) const
{
  octave_idx_type info;
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info) const
{
  float rcon;
  return solve (b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info,
		      float& rcon) const
{
  return solve (b, info, rcon, 0);
}

FloatComplexColumnVector
FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info,
		      float& rcon,
		      solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, info, rcon, sing_handler);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatMatrix& b) const
{
  octave_idx_type info;
  octave_idx_type rank;
  float rcon;
  return lssolve (FloatComplexMatrix (b), info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info) const
{
  octave_idx_type rank;
  float rcon;
  return lssolve (FloatComplexMatrix (b), info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info,
			octave_idx_type& rank) const
{
  float rcon;
  return lssolve (FloatComplexMatrix (b), info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info,
			octave_idx_type& rank, float& rcon) const
{
  return lssolve (FloatComplexMatrix (b), info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatComplexMatrix& b) const
{
  octave_idx_type info;
  octave_idx_type rank;
  float rcon;
  return lssolve (b, info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info) const
{
  octave_idx_type rank;
  float rcon;
  return lssolve (b, info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info,
			octave_idx_type& rank) const
{
  float rcon;
  return lssolve (b, info, rank, rcon);
}

FloatComplexMatrix
FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, 
			octave_idx_type& rank, float& rcon) const
{
  FloatComplexMatrix retval;

  octave_idx_type nrhs = b.cols ();

  octave_idx_type m = rows ();
  octave_idx_type n = cols ();

  if (m != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");
  else if (m== 0 || n == 0 || b.cols () == 0)
    retval = FloatComplexMatrix (n, b.cols (), FloatComplex (0.0, 0.0));
  else
    {
      volatile octave_idx_type minmn = (m < n ? m : n);
      octave_idx_type maxmn = m > n ? m : n;
      rcon = -1.0;

      if (m != n)
	{
	  retval = FloatComplexMatrix (maxmn, nrhs);

	  for (octave_idx_type j = 0; j < nrhs; j++)
	    for (octave_idx_type i = 0; i < m; i++)
	      retval.elem (i, j) = b.elem (i, j);
	}
      else
	retval = b;

      FloatComplexMatrix atmp = *this;
      FloatComplex *tmp_data = atmp.fortran_vec ();

      FloatComplex *pretval = retval.fortran_vec ();
      Array<float> s (minmn);
      float *ps = s.fortran_vec ();

      // Ask ZGELSD what the dimension of WORK should be.
      octave_idx_type lwork = -1;

      Array<FloatComplex> work (1);

      octave_idx_type smlsiz;
      F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 6),
				   F77_CONST_CHAR_ARG2 (" ", 1),
				   0, 0, 0, 0, smlsiz
				   F77_CHAR_ARG_LEN (6)
				   F77_CHAR_ARG_LEN (1));

      octave_idx_type mnthr;
      F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("CGELSD", 6),
				   F77_CONST_CHAR_ARG2 (" ", 1),
				   m, n, nrhs, -1, mnthr
				   F77_CHAR_ARG_LEN (6)
				   F77_CHAR_ARG_LEN (1));

      // We compute the size of rwork and iwork because ZGELSD in
      // older versions of LAPACK does not return them on a query
      // call.
      float dminmn = static_cast<float> (minmn);
      float dsmlsizp1 = static_cast<float> (smlsiz+1);
#if defined (HAVE_LOG2)
      float tmp = log2 (dminmn / dsmlsizp1);
#else
      float tmp = log (dminmn / dsmlsizp1) / log (2.0);
#endif
      octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1;
      if (nlvl < 0)
	nlvl = 0;

      octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl)
	+ 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1);
      if (lrwork < 1)
	lrwork = 1;
      Array<float> rwork (lrwork);
      float *prwork = rwork.fortran_vec ();

      octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn;
      if (liwork < 1)
	liwork = 1;
      Array<octave_idx_type> iwork (liwork);
      octave_idx_type* piwork = iwork.fortran_vec ();

      F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn,
				 ps, rcon, rank, work.fortran_vec (),
				 lwork, prwork, piwork, info));

      // The workspace query is broken in at least LAPACK 3.0.0
      // through 3.1.1 when n >= mnthr.  The obtuse formula below
      // should provide sufficient workspace for ZGELSD to operate
      // efficiently.
      if (n >= mnthr)
	{
	  octave_idx_type addend = m;

	  if (2*m-4 > addend)
	    addend = 2*m-4;

	  if (nrhs > addend)
	    addend = nrhs;

	  if (n-3*m > addend)
	    addend = n-3*m;

	  const octave_idx_type lworkaround = 4*m + m*m + addend;

	  if (std::real (work(0)) < lworkaround)
	    work(0) = lworkaround;
	}
      else if (m >= n)
	{
	  octave_idx_type lworkaround = 2*m + m*nrhs;

	  if (std::real (work(0)) < lworkaround)
	    work(0) = lworkaround;
	}

      lwork = static_cast<octave_idx_type> (std::real (work(0)));
      work.resize (lwork);

      F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval,
				 maxmn, ps, rcon, rank,
				 work.fortran_vec (), lwork, 
				 prwork, piwork, info));

      if (rank < minmn)
	(*current_liboctave_warning_handler) 
	  ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e",
	   m, n, rank, rcon);

      if (s.elem (0) == 0.0)
	rcon = 0.0;
      else
	rcon = s.elem (minmn - 1) / s.elem (0);

      retval.resize (n, nrhs);
    }

  return retval;
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatColumnVector& b) const
{
  octave_idx_type info;
  octave_idx_type rank;
  float rcon;
  return lssolve (FloatComplexColumnVector (b), info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info) const
{
  octave_idx_type rank;
  float rcon;
  return lssolve (FloatComplexColumnVector (b), info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, 
			octave_idx_type& rank) const
{
  float rcon;
  return lssolve (FloatComplexColumnVector (b), info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, 
			octave_idx_type& rank, float& rcon) const
{
  return lssolve (FloatComplexColumnVector (b), info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b) const
{
  octave_idx_type info;
  octave_idx_type rank;
  float rcon;
  return lssolve (b, info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info) const
{
  octave_idx_type rank;
  float rcon;
  return lssolve (b, info, rank, rcon);
}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info,
			octave_idx_type& rank) const
{
  float rcon;
  return lssolve (b, info, rank, rcon);

}

FloatComplexColumnVector
FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info,
			octave_idx_type& rank, float& rcon) const
{
  FloatComplexColumnVector retval;

  octave_idx_type nrhs = 1;

  octave_idx_type m = rows ();
  octave_idx_type n = cols ();

  if (m != b.length ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");
  else if (m == 0 || n == 0 || b.cols () == 0)
    retval = FloatComplexColumnVector (n, FloatComplex (0.0, 0.0));
  else
    {
      volatile octave_idx_type minmn = (m < n ? m : n);
      octave_idx_type maxmn = m > n ? m : n;
      rcon = -1.0;

      if (m != n)
	{
	  retval = FloatComplexColumnVector (maxmn);

	  for (octave_idx_type i = 0; i < m; i++)
	    retval.elem (i) = b.elem (i);
	}
      else
	retval = b;

      FloatComplexMatrix atmp = *this;
      FloatComplex *tmp_data = atmp.fortran_vec ();

      FloatComplex *pretval = retval.fortran_vec ();
      Array<float> s (minmn);
      float *ps = s.fortran_vec ();

      // Ask ZGELSD what the dimension of WORK should be.
      octave_idx_type lwork = -1;

      Array<FloatComplex> work (1);

      octave_idx_type smlsiz;
      F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 6),
				   F77_CONST_CHAR_ARG2 (" ", 1),
				   0, 0, 0, 0, smlsiz
				   F77_CHAR_ARG_LEN (6)
				   F77_CHAR_ARG_LEN (1));

      // We compute the size of rwork and iwork because ZGELSD in
      // older versions of LAPACK does not return them on a query
      // call.
      float dminmn = static_cast<float> (minmn);
      float dsmlsizp1 = static_cast<float> (smlsiz+1);
#if defined (HAVE_LOG2)
      float tmp = log2 (dminmn / dsmlsizp1);
#else
      float tmp = log (dminmn / dsmlsizp1) / log (2.0);
#endif
      octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1;
      if (nlvl < 0)
	nlvl = 0;

      octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl)
	+ 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1);
      if (lrwork < 1)
	lrwork = 1;
      Array<float> rwork (lrwork);
      float *prwork = rwork.fortran_vec ();

      octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn;
      if (liwork < 1)
	liwork = 1;
      Array<octave_idx_type> iwork (liwork);
      octave_idx_type* piwork = iwork.fortran_vec ();

      F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn,
				 ps, rcon, rank, work.fortran_vec (),
				 lwork, prwork, piwork, info));

      lwork = static_cast<octave_idx_type> (std::real (work(0)));
      work.resize (lwork);
      rwork.resize (static_cast<octave_idx_type> (rwork(0)));
      iwork.resize (iwork(0));

      F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval,
				 maxmn, ps, rcon, rank,
				 work.fortran_vec (), lwork, 
				 prwork, piwork, info));

      if (rank < minmn)
	{
	  if (rank < minmn)
	    (*current_liboctave_warning_handler) 
	      ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e",
	       m, n, rank, rcon);

	  if (s.elem (0) == 0.0)
	    rcon = 0.0;
	  else
	    rcon = s.elem (minmn - 1) / s.elem (0);

	  retval.resize (n, nrhs);
	}
    }

  return retval;
}

// column vector by row vector -> matrix operations

FloatComplexMatrix
operator * (const FloatColumnVector& v, const FloatComplexRowVector& a)
{
  FloatComplexColumnVector tmp (v);
  return tmp * a;
}

FloatComplexMatrix
operator * (const FloatComplexColumnVector& a, const FloatRowVector& b)
{
  FloatComplexRowVector tmp (b);
  return a * tmp;
}

FloatComplexMatrix
operator * (const FloatComplexColumnVector& v, const FloatComplexRowVector& a)
{
  FloatComplexMatrix retval;

  octave_idx_type len = v.length ();

  if (len != 0)
    {
      octave_idx_type a_len = a.length ();

      retval.resize (len, a_len);
      FloatComplex *c = retval.fortran_vec ();

      F77_XFCN (cgemm, CGEMM, (F77_CONST_CHAR_ARG2 ("N", 1),
			       F77_CONST_CHAR_ARG2 ("N", 1),
			       len, a_len, 1, 1.0, v.data (), len,
			       a.data (), 1, 0.0, c, len
			       F77_CHAR_ARG_LEN (1)
			       F77_CHAR_ARG_LEN (1)));
    }

  return retval;
}

// matrix by diagonal matrix -> matrix operations

FloatComplexMatrix&
FloatComplexMatrix::operator += (const FloatDiagMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = rows ();
  octave_idx_type a_nc = cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc);
      return *this;
    }

  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) += a.elem (i, i);

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::operator -= (const FloatDiagMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = rows ();
  octave_idx_type a_nc = cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc);
      return *this;
    }

  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) -= a.elem (i, i);

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::operator += (const FloatComplexDiagMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = rows ();
  octave_idx_type a_nc = cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc);
      return *this;
    }

  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) += a.elem (i, i);

  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::operator -= (const FloatComplexDiagMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = rows ();
  octave_idx_type a_nc = cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc);
      return *this;
    }

  for (octave_idx_type i = 0; i < a.length (); i++)
    elem (i, i) -= a.elem (i, i);

  return *this;
}

// matrix by matrix -> matrix operations

FloatComplexMatrix&
FloatComplexMatrix::operator += (const FloatMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc);
      return *this;
    }

  if (nr == 0 || nc == 0)
    return *this;

  FloatComplex *d = fortran_vec (); // Ensures only one reference to my privates!

  mx_inline_add2 (d, a.data (), length ());
  return *this;
}

FloatComplexMatrix&
FloatComplexMatrix::operator -= (const FloatMatrix& a)
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();

  if (nr != a_nr || nc != a_nc)
    {
      gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc);
      return *this;
    }

  if (nr == 0 || nc == 0)
    return *this;

  FloatComplex *d = fortran_vec (); // Ensures only one reference to my privates!

  mx_inline_subtract2 (d, a.data (), length ());
  return *this;
}

// unary operations

boolMatrix
FloatComplexMatrix::operator ! (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  boolMatrix b (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      b.elem (i, j) = elem (i, j) == static_cast<float> (0.0);

  return b;
}

// other operations

FloatMatrix
FloatComplexMatrix::map (dmapper fcn) const
{
  return MArray2<FloatComplex>::map<float> (func_ptr (fcn));
}

FloatComplexMatrix
FloatComplexMatrix::map (cmapper fcn) const
{
  return MArray2<FloatComplex>::map<FloatComplex> (func_ptr (fcn));
}

boolMatrix
FloatComplexMatrix::map (bmapper fcn) const
{
  return MArray2<FloatComplex>::map<bool> (func_ptr (fcn));
}

bool
FloatComplexMatrix::any_element_is_nan (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	FloatComplex val = elem (i, j);
	if (xisnan (val))
	  return true;
      }

  return false;
}

bool
FloatComplexMatrix::any_element_is_inf_or_nan (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	FloatComplex val = elem (i, j);
	if (xisinf (val) || xisnan (val))
	  return true;
      }

  return false;
}

// Return true if no elements have imaginary components.

bool
FloatComplexMatrix::all_elements_are_real (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  for (octave_idx_type j = 0; j < nc; j++)
    {
      for (octave_idx_type i = 0; i < nr; i++)
	{
	  float ip = std::imag (elem (i, j));

	  if (ip != 0.0 || lo_ieee_signbit (ip))
	    return false;
	}
    }

  return true;
}

// Return nonzero if any element of CM has a non-integer real or
// imaginary part.  Also extract the largest and smallest (real or
// imaginary) values and return them in MAX_VAL and MIN_VAL. 

bool
FloatComplexMatrix::all_integers (float& max_val, float& min_val) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      FloatComplex val = elem (0, 0);

      float r_val = std::real (val);
      float i_val = std::imag (val);

      max_val = r_val;
      min_val = r_val;

      if (i_val > max_val)
	max_val = i_val;

      if (i_val < max_val)
	min_val = i_val;
    }
  else
    return false;

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	FloatComplex val = elem (i, j);

	float r_val = std::real (val);
	float i_val = std::imag (val);

	if (r_val > max_val)
	  max_val = r_val;

	if (i_val > max_val)
	  max_val = i_val;

	if (r_val < min_val)
	  min_val = r_val;

	if (i_val < min_val)
	  min_val = i_val;

	if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val)
	  return false;
      }

  return true;
}

bool
FloatComplexMatrix::too_large_for_float (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	FloatComplex val = elem (i, j);

	float r_val = std::real (val);
	float i_val = std::imag (val);

	if ((! (xisnan (r_val) || xisinf (r_val))
	     && fabs (r_val) > FLT_MAX)
	    || (! (xisnan (i_val) || xisinf (i_val))
		&& fabs (i_val) > FLT_MAX))
	  return true;
      }

  return false;
}

// FIXME Do these really belong here?  Maybe they should be
// in a base class?

boolMatrix
FloatComplexMatrix::all (int dim) const
{
  return do_mx_red_op<boolMatrix, FloatComplex> (*this, dim, mx_inline_all);
}

boolMatrix
FloatComplexMatrix::any (int dim) const
{
  return do_mx_red_op<boolMatrix, FloatComplex> (*this, dim, mx_inline_any);
}

FloatComplexMatrix
FloatComplexMatrix::cumprod (int dim) const
{
  return do_mx_cum_op<FloatComplexMatrix, FloatComplex> (*this, dim, mx_inline_cumprod);
}

FloatComplexMatrix
FloatComplexMatrix::cumsum (int dim) const
{
  return do_mx_cum_op<FloatComplexMatrix, FloatComplex> (*this, dim, mx_inline_cumsum);
}

FloatComplexMatrix
FloatComplexMatrix::prod (int dim) const
{
  return do_mx_red_op<FloatComplexMatrix, FloatComplex> (*this, dim, mx_inline_prod);
}

FloatComplexMatrix
FloatComplexMatrix::sum (int dim) const
{
  return do_mx_red_op<FloatComplexMatrix, FloatComplex> (*this, dim, mx_inline_sum);
}

FloatComplexMatrix
FloatComplexMatrix::sumsq (int dim) const
{
  return do_mx_red_op<FloatMatrix, FloatComplex> (*this, dim, mx_inline_sumsq);
}

FloatMatrix FloatComplexMatrix::abs (void) const
{
  return FloatMatrix (mx_inline_cabs_dup (data (), length ()),
                      rows (), cols ());
}

FloatComplexMatrix
FloatComplexMatrix::diag (octave_idx_type k) const
{
  return MArray2<FloatComplex>::diag (k);
}

bool
FloatComplexMatrix::row_is_real_only (octave_idx_type i) const
{
  bool retval = true;

  octave_idx_type nc = columns ();

  for (octave_idx_type j = 0; j < nc; j++)
    {
      if (std::imag (elem (i, j)) != 0.0)
	{
	  retval = false;
	  break;
	}
    }

  return retval;	      
}

bool
FloatComplexMatrix::column_is_real_only (octave_idx_type j) const
{
  bool retval = true;

  octave_idx_type nr = rows ();

  for (octave_idx_type i = 0; i < nr; i++)
    {
      if (std::imag (elem (i, j)) != 0.0)
	{
	  retval = false;
	  break;
	}
    }

  return retval;	      
}

FloatComplexColumnVector
FloatComplexMatrix::row_min (void) const
{
  Array<octave_idx_type> dummy_idx;
  return row_min (dummy_idx);
}

FloatComplexColumnVector
FloatComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const
{
  FloatComplexColumnVector result;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      result.resize (nr);
      idx_arg.resize (nr);

      for (octave_idx_type i = 0; i < nr; i++)
        {
	  bool real_only = row_is_real_only (i);

	  octave_idx_type idx_j;

	  FloatComplex tmp_min;

	  float abs_min = octave_Float_NaN;

	  for (idx_j = 0; idx_j < nc; idx_j++)
	    {
	      tmp_min = elem (i, idx_j);

	      if (! xisnan (tmp_min))
		{
		  abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min);
		  break;
		}
	    }

	  for (octave_idx_type j = idx_j+1; j < nc; j++)
	    {
	      FloatComplex tmp = elem (i, j);

	      if (xisnan (tmp))
		continue;

	      float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp);

	      if (abs_tmp < abs_min)
		{
		  idx_j = j;
		  tmp_min = tmp;
		  abs_min = abs_tmp;
		}
	    }

	  if (xisnan (tmp_min))
	    {
	      result.elem (i) = FloatComplex_NaN_result;
	      idx_arg.elem (i) = 0;
	    }
	  else
	    {
	      result.elem (i) = tmp_min;
	      idx_arg.elem (i) = idx_j;
	    }
        }
    }

  return result;
}

FloatComplexColumnVector
FloatComplexMatrix::row_max (void) const
{
  Array<octave_idx_type> dummy_idx;
  return row_max (dummy_idx);
}

FloatComplexColumnVector
FloatComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const
{
  FloatComplexColumnVector result;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      result.resize (nr);
      idx_arg.resize (nr);

      for (octave_idx_type i = 0; i < nr; i++)
        {
	  bool real_only = row_is_real_only (i);

	  octave_idx_type idx_j;

	  FloatComplex tmp_max;

	  float abs_max = octave_Float_NaN;

	  for (idx_j = 0; idx_j < nc; idx_j++)
	    {
	      tmp_max = elem (i, idx_j);

	      if (! xisnan (tmp_max))
		{
		  abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max);
		  break;
		}
	    }

	  for (octave_idx_type j = idx_j+1; j < nc; j++)
	    {
	      FloatComplex tmp = elem (i, j);

	      if (xisnan (tmp))
		continue;

	      float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp);

	      if (abs_tmp > abs_max)
		{
		  idx_j = j;
		  tmp_max = tmp;
		  abs_max = abs_tmp;
		}
	    }

	  if (xisnan (tmp_max))
	    {
	      result.elem (i) = FloatComplex_NaN_result;
	      idx_arg.elem (i) = 0;
	    }
	  else
	    {
	      result.elem (i) = tmp_max;
	      idx_arg.elem (i) = idx_j;
	    }
        }
    }

  return result;
}

FloatComplexRowVector
FloatComplexMatrix::column_min (void) const
{
  Array<octave_idx_type> dummy_idx;
  return column_min (dummy_idx);
}

FloatComplexRowVector
FloatComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const
{
  FloatComplexRowVector result;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      result.resize (nc);
      idx_arg.resize (nc);

      for (octave_idx_type j = 0; j < nc; j++)
        {
	  bool real_only = column_is_real_only (j);

	  octave_idx_type idx_i;

	  FloatComplex tmp_min;

	  float abs_min = octave_Float_NaN;

	  for (idx_i = 0; idx_i < nr; idx_i++)
	    {
	      tmp_min = elem (idx_i, j);

	      if (! xisnan (tmp_min))
		{
		  abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min);
		  break;
		}
	    }

	  for (octave_idx_type i = idx_i+1; i < nr; i++)
	    {
	      FloatComplex tmp = elem (i, j);

	      if (xisnan (tmp))
		continue;

	      float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp);

	      if (abs_tmp < abs_min)
		{
		  idx_i = i;
		  tmp_min = tmp;
		  abs_min = abs_tmp;
		}
	    }

	  if (xisnan (tmp_min))
	    {
	      result.elem (j) = FloatComplex_NaN_result;
	      idx_arg.elem (j) = 0;
	    }
	  else
	    {
	      result.elem (j) = tmp_min;
	      idx_arg.elem (j) = idx_i;
	    }
        }
    }

  return result;
}

FloatComplexRowVector
FloatComplexMatrix::column_max (void) const
{
  Array<octave_idx_type> dummy_idx;
  return column_max (dummy_idx);
}

FloatComplexRowVector
FloatComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const
{
  FloatComplexRowVector result;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr > 0 && nc > 0)
    {
      result.resize (nc);
      idx_arg.resize (nc);

      for (octave_idx_type j = 0; j < nc; j++)
        {
	  bool real_only = column_is_real_only (j);

	  octave_idx_type idx_i;

	  FloatComplex tmp_max;

	  float abs_max = octave_Float_NaN;

	  for (idx_i = 0; idx_i < nr; idx_i++)
	    {
	      tmp_max = elem (idx_i, j);

	      if (! xisnan (tmp_max))
		{
		  abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max);
		  break;
		}
	    }

	  for (octave_idx_type i = idx_i+1; i < nr; i++)
	    {
	      FloatComplex tmp = elem (i, j);

	      if (xisnan (tmp))
		continue;

	      float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp);

	      if (abs_tmp > abs_max)
		{
		  idx_i = i;
		  tmp_max = tmp;
		  abs_max = abs_tmp;
		}
	    }

	  if (xisnan (tmp_max))
	    {
	      result.elem (j) = FloatComplex_NaN_result;
	      idx_arg.elem (j) = 0;
	    }
	  else
	    {
	      result.elem (j) = tmp_max;
	      idx_arg.elem (j) = idx_i;
	    }
        }
    }

  return result;
}

// i/o

std::ostream&
operator << (std::ostream& os, const FloatComplexMatrix& a)
{
  for (octave_idx_type i = 0; i < a.rows (); i++)
    {
      for (octave_idx_type j = 0; j < a.cols (); j++)
	{
	  os << " ";
	  octave_write_complex (os, a.elem (i, j));
	}
      os << "\n";
    }
  return os;
}

std::istream&
operator >> (std::istream& is, FloatComplexMatrix& a)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  if (nr > 0 && nc > 0)
    {
      FloatComplex tmp;
      for (octave_idx_type i = 0; i < nr; i++)
	for (octave_idx_type j = 0; j < nc; j++)
	  {
	    tmp = octave_read_complex (is);
	    if (is)
	      a.elem (i, j) = tmp;
	    else
	      goto done;
	  }
    }

done:

  return is;
}

FloatComplexMatrix
Givens (const FloatComplex& x, const FloatComplex& y)
{
  float cc;
  FloatComplex cs, temp_r;
 
  F77_FUNC (clartg, CLARTG) (x, y, cc, cs, temp_r);

  FloatComplexMatrix g (2, 2);

  g.elem (0, 0) = cc;
  g.elem (1, 1) = cc;
  g.elem (0, 1) = cs;
  g.elem (1, 0) = -conj (cs);

  return g;
}

FloatComplexMatrix
Sylvester (const FloatComplexMatrix& a, const FloatComplexMatrix& b,
	   const FloatComplexMatrix& c)
{
  FloatComplexMatrix retval;

  // FIXME -- need to check that a, b, and c are all the same
  // size.

  // Compute Schur decompositions

  FloatComplexSCHUR as (a, "U");
  FloatComplexSCHUR bs (b, "U");
  
  // Transform c to new coordinates.

  FloatComplexMatrix ua = as.unitary_matrix ();
  FloatComplexMatrix sch_a = as.schur_matrix ();

  FloatComplexMatrix ub = bs.unitary_matrix ();
  FloatComplexMatrix sch_b = bs.schur_matrix ();
  
  FloatComplexMatrix cx = ua.hermitian () * c * ub;

  // Solve the sylvester equation, back-transform, and return the
  // solution.

  octave_idx_type a_nr = a.rows ();
  octave_idx_type b_nr = b.rows ();

  float scale;
  octave_idx_type info;

  FloatComplex *pa = sch_a.fortran_vec ();
  FloatComplex *pb = sch_b.fortran_vec ();
  FloatComplex *px = cx.fortran_vec ();
  
  F77_XFCN (ctrsyl, CTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1),
			     F77_CONST_CHAR_ARG2 ("N", 1),
			     1, a_nr, b_nr, pa, a_nr, pb,
			     b_nr, px, a_nr, scale, info
			     F77_CHAR_ARG_LEN (1)
			     F77_CHAR_ARG_LEN (1)));

  // FIXME -- check info?

  retval = -ua * cx * ub.hermitian ();

  return retval;
}

FloatComplexMatrix
operator * (const FloatComplexMatrix& m, const FloatMatrix& a)
{
  FloatComplexMatrix tmp (a);
  return m * tmp;
}

FloatComplexMatrix
operator * (const FloatMatrix& m, const FloatComplexMatrix& a)
{
  FloatComplexMatrix tmp (m);
  return tmp * a;
}

/* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests
%!assert([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14)
%!assert([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14)
%!assert([1+i 2+i ; 3+i 4+i ] * [5+i 6+i ; 7+i 8+i], [17 + 15i 20 + 17i; 41 + 19i 48 + 21i], 1e-14)
*/

/* Test some simple identities
%!shared M, cv, rv
%! M = randn(10,10)+i*rand(10,10);
%! cv = randn(10,1)+i*rand(10,1);
%! rv = randn(1,10)+i*rand(1,10);
%!assert([M*cv,M*cv],M*[cv,cv],1e-14)
%!assert([rv*M;rv*M],[rv;rv]*M,1e-14)
%!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14)
*/

static const char *
get_blas_trans_arg (bool trans, bool conj)
{
  static char blas_notrans = 'N', blas_trans = 'T', blas_conj_trans = 'C';
  return trans ? (conj ? &blas_conj_trans : &blas_trans) : &blas_notrans;
}

// the general GEMM operation

FloatComplexMatrix
xgemm (bool transa, bool conja, const FloatComplexMatrix& a, 
       bool transb, bool conjb, const FloatComplexMatrix& b)
{
  FloatComplexMatrix retval;

  // conjugacy is ignored if no transpose
  conja = conja && transa;
  conjb = conjb && transb;

  octave_idx_type a_nr = transa ? a.cols () : a.rows ();
  octave_idx_type a_nc = transa ? a.rows () : a.cols ();

  octave_idx_type b_nr = transb ? b.cols () : b.rows ();
  octave_idx_type b_nc = transb ? b.rows () : b.cols ();

  if (a_nc != b_nr)
    gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc);
  else
    {
      if (a_nr == 0 || a_nc == 0 || b_nc == 0)
	retval.resize (a_nr, b_nc, 0.0);
      else if (a.data () == b.data () && a_nr == b_nc && transa != transb)
        {
	  octave_idx_type lda = a.rows ();

          retval.resize (a_nr, b_nc);
	  FloatComplex *c = retval.fortran_vec ();

          const char *ctransa = get_blas_trans_arg (transa, conja);
          if (conja || conjb)
            {
              F77_XFCN (cherk, CHERK, (F77_CONST_CHAR_ARG2 ("U", 1),
                                       F77_CONST_CHAR_ARG2 (ctransa, 1),
                                       a_nr, a_nc, 1.0,
                                       a.data (), lda, 0.0, c, a_nr
                                       F77_CHAR_ARG_LEN (1)
                                       F77_CHAR_ARG_LEN (1)));
              for (int j = 0; j < a_nr; j++)
                for (int i = 0; i < j; i++)
                  retval.xelem (j,i) = std::conj (retval.xelem (i,j));
            }
          else
            {
              F77_XFCN (csyrk, CSYRK, (F77_CONST_CHAR_ARG2 ("U", 1),
                                       F77_CONST_CHAR_ARG2 (ctransa, 1),
                                       a_nr, a_nc, 1.0,
                                       a.data (), lda, 0.0, c, a_nr
                                       F77_CHAR_ARG_LEN (1)
                                       F77_CHAR_ARG_LEN (1)));
              for (int j = 0; j < a_nr; j++)
                for (int i = 0; i < j; i++)
                  retval.xelem (j,i) = retval.xelem (i,j);

            }

        }
      else
	{
	  octave_idx_type lda = a.rows (), tda = a.cols ();
	  octave_idx_type ldb = b.rows (), tdb = b.cols ();

	  retval.resize (a_nr, b_nc);
	  FloatComplex *c = retval.fortran_vec ();

	  if (b_nc == 1 && a_nr == 1)
	    {
              if (conja == conjb)
                {
                  F77_FUNC (xcdotu, XCDOTU) (a_nc, a.data (), 1, b.data (), 1, *c);
                  if (conja) *c = std::conj (*c);
                }
              else if (conjb)
                  F77_FUNC (xcdotc, XCDOTC) (a_nc, a.data (), 1, b.data (), 1, *c);
              else
                  F77_FUNC (xcdotc, XCDOTC) (a_nc, b.data (), 1, a.data (), 1, *c);
            }
          else if (b_nc == 1 && ! conjb)
            {
              const char *ctransa = get_blas_trans_arg (transa, conja);
              F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (ctransa, 1),
                                       lda, tda, 1.0,  a.data (), lda,
                                       b.data (), 1, 0.0, c, 1
                                       F77_CHAR_ARG_LEN (1)));
            }
          else if (a_nr == 1 && ! conja)
            {
              const char *crevtransb = get_blas_trans_arg (! transb, conjb);
              F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (crevtransb, 1),
                                       ldb, tdb, 1.0,  b.data (), ldb,
                                       a.data (), 1, 0.0, c, 1
                                       F77_CHAR_ARG_LEN (1)));
            }
	  else
	    {
              const char *ctransa = get_blas_trans_arg (transa, conja);
              const char *ctransb = get_blas_trans_arg (transb, conjb);
	      F77_XFCN (cgemm, CGEMM, (F77_CONST_CHAR_ARG2 (ctransa, 1),
				       F77_CONST_CHAR_ARG2 (ctransb, 1),
				       a_nr, b_nc, a_nc, 1.0, a.data (),
				       lda, b.data (), ldb, 0.0, c, a_nr
				       F77_CHAR_ARG_LEN (1)
				       F77_CHAR_ARG_LEN (1)));
	    }
	}
    }

  return retval;
}

FloatComplexMatrix
operator * (const FloatComplexMatrix& a, const FloatComplexMatrix& b)
{
  return xgemm (false, false, a, false, false, b);
}

// FIXME -- it would be nice to share code among the min/max
// functions below.

#define EMPTY_RETURN_CHECK(T) \
  if (nr == 0 || nc == 0) \
    return T (nr, nc);

FloatComplexMatrix
min (const FloatComplex& c, const FloatComplexMatrix& m)
{
  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	OCTAVE_QUIT;
	result (i, j) = xmin (c, m (i, j));
      }

  return result;
}

FloatComplexMatrix
min (const FloatComplexMatrix& m, const FloatComplex& c)
{
  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	OCTAVE_QUIT;
	result (i, j) = xmin (m (i, j), c);
      }

  return result;
}

FloatComplexMatrix
min (const FloatComplexMatrix& a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.columns ();

  if (nr != b.rows () || nc != b.columns ())
    {
      (*current_liboctave_error_handler)
	("two-arg min expecting args of same size");
      return FloatComplexMatrix ();
    }

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    {
      int columns_are_real_only = 1;
      for (octave_idx_type i = 0; i < nr; i++)
	{
	  OCTAVE_QUIT;
	  if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0)
	    {
	      columns_are_real_only = 0;
	      break;
	    }
	}

      if (columns_are_real_only)
	{
	  for (octave_idx_type i = 0; i < nr; i++)
	    result (i, j) = xmin (std::real (a (i, j)), std::real (b (i, j)));
	}
      else
	{
	  for (octave_idx_type i = 0; i < nr; i++)
	    {
	      OCTAVE_QUIT;
	      result (i, j) = xmin (a (i, j), b (i, j));
	    }
	}
    }

  return result;
}

FloatComplexMatrix
max (const FloatComplex& c, const FloatComplexMatrix& m)
{
  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	OCTAVE_QUIT;
	result (i, j) = xmax (c, m (i, j));
      }

  return result;
}

FloatComplexMatrix
max (const FloatComplexMatrix& m, const FloatComplex& c)
{
  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
	OCTAVE_QUIT;
	result (i, j) = xmax (m (i, j), c);
      }

  return result;
}

FloatComplexMatrix
max (const FloatComplexMatrix& a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.columns ();

  if (nr != b.rows () || nc != b.columns ())
    {
      (*current_liboctave_error_handler)
	("two-arg max expecting args of same size");
      return FloatComplexMatrix ();
    }

  EMPTY_RETURN_CHECK (FloatComplexMatrix);

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    {
      int columns_are_real_only = 1;
      for (octave_idx_type i = 0; i < nr; i++)
	{
	  OCTAVE_QUIT;
	  if (std::imag (a (i, j)) != 0.0 || std::imag (b (i, j)) != 0.0)
	    {
	      columns_are_real_only = 0;
	      break;
	    }
	}

      if (columns_are_real_only)
	{
	  for (octave_idx_type i = 0; i < nr; i++)
	    {
	      OCTAVE_QUIT;
	      result (i, j) = xmax (std::real (a (i, j)), std::real (b (i, j)));
	    }
	}
      else
	{
	  for (octave_idx_type i = 0; i < nr; i++)
	    {
	      OCTAVE_QUIT;
	      result (i, j) = xmax (a (i, j), b (i, j));
	    }
	}
    }

  return result;
}

MS_CMP_OPS(FloatComplexMatrix, std::real, FloatComplex, std::real)
MS_BOOL_OPS(FloatComplexMatrix, FloatComplex, static_cast<float> (0.0))

SM_CMP_OPS(FloatComplex, std::real, FloatComplexMatrix, std::real)
SM_BOOL_OPS(FloatComplex, FloatComplexMatrix, static_cast<float> (0.0))

MM_CMP_OPS(FloatComplexMatrix, std::real, FloatComplexMatrix, std::real)
MM_BOOL_OPS(FloatComplexMatrix, FloatComplexMatrix, static_cast<float> (0.0))

/*
;;; Local Variables: ***
;;; mode: C++ ***
;;; End: ***
*/
