max.cc

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/*

Copyright (C) 1996-2017 John W. Eaton
Copyright (C) 2009 VZLU Prague

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/>.

*/

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "lo-ieee.h"
#include "lo-mappers.h"
#include "lo-math.h"
#include "dNDArray.h"
#include "CNDArray.h"
#include "quit.h"

#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"

#include "ov-cx-mat.h"
#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"

template <typename ArrayType>
static octave_value_list
do_minmax_red_op (const octave_value& arg,
                  int nargout, int dim, bool ismin)
{
  octave_value_list retval (nargout > 1 ? 2 : 1);
  ArrayType array = octave_value_extract<ArrayType> (arg);

  if (nargout <= 1)
    {
      if (ismin)
        retval(0) = array.min (dim);
      else
        retval(0) = array.max (dim);
    }
  else
    {
      Array<octave_idx_type> idx;
      if (ismin)
        retval(0) = array.min (idx, dim);
      else
        retval(0) = array.max (idx, dim);

      retval(1) = octave_value (idx, true, true);
    }

  return retval;
}

// Matlab returns double arrays for min/max operations on character
// arrays, so we specialize here to get that behavior.  Other possible
// solutions are to convert the argument to double here and call the
// code for double, but that could waste memory, or to have the
// underlying charNDArray::min/max functions return NDArray instead of
// charNDArray, but that is inconsistent with the way other min/max
// functions work.

template <>
octave_value_list
do_minmax_red_op<charNDArray> (const octave_value& arg,
                               int nargout, int dim, bool ismin)
{
  octave_value_list retval (nargout > 1 ? 2 : 1);
  charNDArray array = octave_value_extract<charNDArray> (arg);

  if (nargout <= 1)
    {
      if (ismin)
        retval(0) = NDArray (array.min (dim));
      else
        retval(0) = NDArray (array.max (dim));
    }
  else
    {
      Array<octave_idx_type> idx;
      if (ismin)
        retval(0) = NDArray (array.min (idx, dim));
      else
        retval(0) = NDArray (array.max (idx, dim));

      retval(1) = octave_value (idx, true, true);
    }

  return retval;
}

// Specialization for bool arrays (dense or sparse).
template <>
octave_value_list
do_minmax_red_op<boolNDArray> (const octave_value& arg,
                               int nargout, int dim, bool ismin)
{
  octave_value_list retval;

  if (! arg.is_sparse_type ())
    {
      if (nargout <= 1)
        {
          // This case can be handled using any/all.
          boolNDArray array = arg.bool_array_value ();

          if (array.is_empty ())
            retval(0) = array;
          else if (ismin)
            retval(0) = array.all (dim);
          else
            retval(0) = array.any (dim);
        }
      else
        {
          // any/all don't have indexed versions, so do it via a conversion.
          retval = do_minmax_red_op<int8NDArray> (arg, nargout, dim, ismin);

          retval(0) = retval(0).bool_array_value ();
        }
    }
  else
    {
      // Sparse: Don't use any/all trick, as full matrix could exceed memory.
      // Instead, convert to double.
      retval = do_minmax_red_op<SparseMatrix> (arg, nargout, dim, ismin);

      retval(0) = retval(0).sparse_bool_matrix_value ();
    }

  return retval;
}

template <typename ArrayType>
static octave_value
do_minmax_bin_op (const octave_value& argx, const octave_value& argy,
                  bool ismin)
{
  typedef typename ArrayType::element_type ScalarType;

  octave_value retval;

  if (argx.is_scalar_type ())
    {
      ScalarType x = octave_value_extract<ScalarType> (argx);
      ArrayType y = octave_value_extract<ArrayType> (argy);

      if (ismin)
        retval = min (x, y);
      else
        retval = max (x, y);
    }
  else if (argy.is_scalar_type ())
    {
      ArrayType x = octave_value_extract<ArrayType> (argx);
      ScalarType y = octave_value_extract<ScalarType> (argy);

      if (ismin)
        retval = min (x, y);
      else
        retval = max (x, y);
    }
  else
    {
      ArrayType x = octave_value_extract<ArrayType> (argx);
      ArrayType y = octave_value_extract<ArrayType> (argy);

      if (ismin)
        retval = min (x, y);
      else
        retval = max (x, y);
    }

  return retval;
}

// Matlab returns double arrays for min/max operations on character
// arrays, so we specialize here to get that behavior.  Other possible
// solutions are to convert the arguments to double here and call the
// code for double, but that could waste a lot of memory, or to have the
// underlying charNDArray::min/max functions return NDArray instead of
// charNDArray, but that is inconsistent with the way other min/max
// functions work.

template <>
octave_value
do_minmax_bin_op<charNDArray> (const octave_value& argx,
                               const octave_value& argy, bool ismin)
{
  octave_value retval;

  charNDArray x = octave_value_extract<charNDArray> (argx);
  charNDArray y = octave_value_extract<charNDArray> (argy);

  if (ismin)
    {
      if (x.numel () == 1)
        retval = NDArray (min (x(0), y));
      else if (y.numel () == 1)
        retval = NDArray (min (x, y(0)));
      else
        retval = NDArray (min (x, y));
    }
  else
    {
      if (x.numel () == 1)
        retval = NDArray (max (x(0), y));
      else if (y.numel () == 1)
        retval = NDArray (max (x, y(0)));
      else
        retval = NDArray (max (x, y));
    }

  return retval;
}

static octave_value_list
do_minmax_body (const octave_value_list& args,
                int nargout, bool ismin)
{
  int nargin = args.length ();

  if (nargin < 1 || nargin > 3)
    print_usage ();

  octave_value_list retval (nargout > 1 ? 2 : 1);

  const char *func = ismin ? "min" : "max";

  if (nargin == 3 || nargin == 1)
    {
      octave_value arg = args(0);
      int dim = -1;
      if (nargin == 3)
        {
          dim = args(2).int_value (true) - 1;

          if (dim < 0)
            error ("%s: DIM must be a valid dimension", func);

          if (! args(1).is_empty ())
            warning ("%s: second argument is ignored", func);
        }

      switch (arg.builtin_type ())
        {
        case btyp_double:
          {
            if (arg.is_range () && (dim == -1 || dim == 1))
              {
                Range range = arg.range_value ();
                if (range.numel () < 1)
                  {
                    retval(0) = arg;
                    if (nargout > 1)
                      retval(1) = arg;
                  }
                else if (ismin)
                  {
                    retval(0) = range.min ();
                    if (nargout > 1)
                      retval(1) = static_cast<double>
                                  (range.inc () < 0 ? range.numel () : 1);
                  }
                else
                  {
                    retval(0) = range.max ();
                    if (nargout > 1)
                      retval(1) = static_cast<double>
                                  (range.inc () >= 0 ? range.numel () : 1);
                  }
              }
            else if (arg.is_sparse_type ())
              retval = do_minmax_red_op<SparseMatrix> (arg, nargout, dim,
                                                       ismin);
            else
              retval = do_minmax_red_op<NDArray> (arg, nargout, dim, ismin);

          }
          break;

        case btyp_complex:
          {
            if (arg.is_sparse_type ())
              retval = do_minmax_red_op<SparseComplexMatrix> (arg, nargout, dim,
                                                              ismin);
            else
              retval = do_minmax_red_op<ComplexNDArray> (arg, nargout, dim,
                                                         ismin);
          }
          break;

        case btyp_float:
          retval = do_minmax_red_op<FloatNDArray> (arg, nargout, dim, ismin);
          break;

        case btyp_float_complex:
          retval = do_minmax_red_op<FloatComplexNDArray> (arg, nargout, dim,
                                                          ismin);
          break;

        case btyp_char:
          retval = do_minmax_red_op<charNDArray> (arg, nargout, dim, ismin);
          break;

#define MAKE_INT_BRANCH(X)                                                    \
        case btyp_ ## X:                                                      \
          retval = do_minmax_red_op<X ## NDArray> (arg, nargout, dim, ismin); \
          break;

        MAKE_INT_BRANCH (int8);
        MAKE_INT_BRANCH (int16);
        MAKE_INT_BRANCH (int32);
        MAKE_INT_BRANCH (int64);
        MAKE_INT_BRANCH (uint8);
        MAKE_INT_BRANCH (uint16);
        MAKE_INT_BRANCH (uint32);
        MAKE_INT_BRANCH (uint64);

#undef MAKE_INT_BRANCH

        case btyp_bool:
          retval = do_minmax_red_op<boolNDArray> (arg, nargout, dim, ismin);
          break;

        default:
          err_wrong_type_arg (func, arg);
        }
    }
  else
    {
      octave_value argx = args(0);
      octave_value argy = args(1);
      builtin_type_t xtyp = argx.builtin_type ();
      builtin_type_t ytyp = argy.builtin_type ();
      builtin_type_t rtyp;
      if (xtyp == btyp_char && ytyp == btyp_char)
        rtyp = btyp_char;
      // FIXME: This is what should happen when boolNDArray has max()
      // else if (xtyp == btyp_bool && ytyp == btyp_bool)
      //   rtyp = btyp_bool;
      else
        rtyp = btyp_mixed_numeric (xtyp, ytyp);

      switch (rtyp)
        {
        case btyp_double:
          {
            if ((argx.is_sparse_type ()
                 && (argy.is_sparse_type () || argy.is_scalar_type ()))
                || (argy.is_sparse_type () && argx.is_scalar_type ()))
              retval = do_minmax_bin_op<SparseMatrix> (argx, argy, ismin);
            else
              retval = do_minmax_bin_op<NDArray> (argx, argy, ismin);
          }
          break;

        case btyp_complex:
          {
            if ((argx.is_sparse_type ()
                 && (argy.is_sparse_type () || argy.is_scalar_type ()))
                || (argy.is_sparse_type () && argx.is_scalar_type ()))
              retval = do_minmax_bin_op<SparseComplexMatrix> (argx, argy,
                                                              ismin);
            else
              retval = do_minmax_bin_op<ComplexNDArray> (argx, argy, ismin);
          }
          break;

        case btyp_float:
          retval = do_minmax_bin_op<FloatNDArray> (argx, argy, ismin);
          break;

        case btyp_float_complex:
          retval = do_minmax_bin_op<FloatComplexNDArray> (argx, argy, ismin);
          break;

        case btyp_char:
          retval = do_minmax_bin_op<charNDArray> (argx, argy, ismin);
          break;

#define MAKE_INT_BRANCH(X)                                             \
        case btyp_ ## X:                                               \
          retval = do_minmax_bin_op<X ## NDArray> (argx, argy, ismin); \
          break;

        MAKE_INT_BRANCH (int8);
        MAKE_INT_BRANCH (int16);
        MAKE_INT_BRANCH (int32);
        MAKE_INT_BRANCH (int64);
        MAKE_INT_BRANCH (uint8);
        MAKE_INT_BRANCH (uint16);
        MAKE_INT_BRANCH (uint32);
        MAKE_INT_BRANCH (uint64);

#undef MAKE_INT_BRANCH

        // FIXME: This is what should happen when boolNDArray has max()
        // case btyp_bool:
        //   retval = do_minmax_bin_op<boolNDArray> (argx, argy, ismin);
        //   break;

        default:
          error ("%s: cannot compute %s (%s, %s)", func, func,
                 argx.type_name ().c_str (), argy.type_name ().c_str ());
        }

      // FIXME: Delete when boolNDArray has max()
      if (xtyp == btyp_bool && ytyp == btyp_bool)
        retval(0) = retval(0).bool_array_value ();

    }

  return retval;
}

DEFUN (min, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} min (@var{x})
@deftypefnx {} {} min (@var{x}, [], @var{dim})
@deftypefnx {} {[@var{w}, @var{iw}] =} min (@var{x})
@deftypefnx {} {} min (@var{x}, @var{y})
Find minimum values in the array @var{x}.

For a vector argument, return the minimum value.  For a matrix argument,
return a row vector with the minimum value of each column.  For a
multi-dimensional array, @code{min} operates along the first non-singleton
dimension.

If the optional third argument @var{dim} is present then operate along
this dimension.  In this case the second argument is ignored and should be
set to the empty matrix.

For two matrices (or a matrix and a scalar), return the pairwise minimum.

Thus,

@example
min (min (@var{x}))
@end example

@noindent
returns the smallest element of the 2-D matrix @var{x}, and

@example
@group
min (2:5, pi)
    @result{}  2.0000  3.0000  3.1416  3.1416
@end group
@end example

@noindent
compares each element of the range @code{2:5} with @code{pi}, and returns a
row vector of the minimum values.

For complex arguments, the magnitude of the elements are used for
comparison.  If the magnitudes are identical, then the results are ordered
by phase angle in the range (-pi, pi].  Hence,

@example
@group
min ([-1 i 1 -i])
    @result{} -i
@end group
@end example

@noindent
because all entries have magnitude 1, but -i has the smallest phase angle
with value -pi/2.

If called with one input and two output arguments, @code{min} also returns
the first index of the minimum value(s).  Thus,

@example
@group
[x, ix] = min ([1, 3, 0, 2, 0])
    @result{}  x = 0
        ix = 3
@end group
@end example
@seealso{max, cummin, cummax}
@end deftypefn */)
{
  return do_minmax_body (args, nargout, true);
}

/*
## Test generic double class
%!assert (min ([1, 4, 2, 3]), 1)
%!assert (min ([1; -10; 5; -2]), -10)
%!assert (min ([4, 2i 4.999; -2, 2, 3+4i]), [-2, 2, 4.999])
## Special routines for char arrays
%!assert (min (["abc", "ABC"]), 65)
%!assert (min (["abc"; "CBA"]), [67 66 65])
## Special routines for logical arrays
%!assert (min (logical ([])), logical ([]))
%!assert (min (logical ([0 0 1 0])), false)
%!assert (min (logical ([0 0 1 0; 0 1 1 0])), logical ([0 0 1 0]))
## Single values
%!assert (min (single ([1, 4, 2, 3])), single (1))
%!assert (min (single ([1; -10; 5; -2])), single (-10))
%!assert (min (single ([4, 2i 4.999; -2, 2, 3+4i])), single ([-2, 2, 4.999]))
## Integer values
%!assert (min (uint8 ([1, 4, 2, 3])), uint8 (1))
%!assert (min (uint8 ([1; -10; 5; -2])), uint8 (-10))
%!assert (min (int8 ([1, 4, 2, 3])), int8 (1))
%!assert (min (int8 ([1; -10; 5; -2])), int8 (-10))
%!assert (min (uint16 ([1, 4, 2, 3])), uint16 (1))
%!assert (min (uint16 ([1; -10; 5; -2])), uint16 (-10))
%!assert (min (int16 ([1, 4, 2, 3])), int16 (1))
%!assert (min (int16 ([1; -10; 5; -2])), int16 (-10))
%!assert (min (uint32 ([1, 4, 2, 3])), uint32 (1))
%!assert (min (uint32 ([1; -10; 5; -2])), uint32 (-10))
%!assert (min (int32 ([1, 4, 2, 3])), int32 (1))
%!assert (min (int32 ([1; -10; 5; -2])), int32 (-10))
%!assert (min (uint64 ([1, 4, 2, 3])), uint64 (1))
%!assert (min (uint64 ([1; -10; 5; -2])), uint64 (-10))
%!assert (min (int64 ([1, 4, 2, 3])), int64 (1))
%!assert (min (int64 ([1; -10; 5; -2])), int64 (-10))
## Sparse double values
%!assert (min (sparse ([1, 4, 2, 3])), sparse (1))
%!assert (min (sparse ([1; -10; 5; -2])), sparse(-10))
## FIXME: sparse doesn't order complex values by phase angle
%!xtest
%! assert (min (sparse ([4, 2i 4.999; -2, 2, 3+4i])), sparse ([-2, 2, 4.999]));

## Test dimension argument
%!test
%! x = reshape (1:8, [2,2,2]);
%! assert (min (x, [], 1), reshape ([1, 3, 5, 7], [1,2,2]));
%! assert (min (x, [], 2), reshape ([1, 2, 5, 6], [2,1,2]));
%! [y, i] = min (x, [], 3);
%! assert (ndims (y), 2);
%! assert (y, [1, 3; 2, 4]);
%! assert (ndims (i), 2);
%! assert (i, [1, 1; 1, 1]);

## Test 2-output forms for various arg types
## Special routines for char arrays
%!test
%! [y, i] = min (["abc", "ABC"]);
%! assert (y, 65);
%! assert (i, 4);
## Special routines for logical arrays
%!test
%! x = logical ([0 0 1 0]);
%! [y, i] = min (x);
%! assert (y, false);
%! assert (i, 1);
## Special handling of ranges
%!test
%! rng = 1:2:10;
%! [y, i] = min (rng);
%! assert (y, 1);
%! assert (i, 1);
%! rng = 10:-2:1;
%! [y, i] = min (rng);
%! assert (y, 2);
%! assert (i, 5);

## Test 2-input calling form for various arg types
## Test generic double class
%!test
%! x = [1, 2, 3, 4];  y = fliplr (x);
%! assert (min (x, y), [1 2 2 1]);
%! assert (min (x, 3), [1 2 3 3]);
%! assert (min (2, x), [1 2 2 2]);
%! assert (min (x, 2.1i), [1 2 2.1i 2.1i]);
## FIXME: Ordering of complex results with equal magnitude is not by phase
##        angle in the 2-input form.  Instead, it is in the order in which it
##        appears in the argument list.
%!xtest
%! x = [1, 2, 3, 4];  y = fliplr (x);
%! assert (min (x, 2i), [2i 2i 3 4]);
## Special routines for char arrays
%!assert (min ("abc", "b"), [97 98 98])
%!assert (min ("b", "cba"), [98 98 97])
## Special handling for logical arrays
%!assert (min ([true false], false), [false false])
%!assert (min (true, [true false]), [true false])
## Single values
%!test
%! x = single ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), single ([1 2 2 1]));
%! assert (min (x, 3), single ([1 2 3 3]));
%! assert (min (2, x), single ([1 2 2 2]));
%! assert (min (x, 2.1i), single ([1 2 2.1i 2.1i]));
## Integer values
%!test
%! x = uint8 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), uint8 ([1 2 2 1]));
%! assert (min (x, 3), uint8 ([1 2 3 3]));
%! assert (min (2, x), uint8 ([1 2 2 2]));
%! x = int8 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), int8 ([1 2 2 1]));
%! assert (min (x, 3), int8 ([1 2 3 3]));
%! assert (min (2, x), int8 ([1 2 2 2]));
%! x = uint16 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), uint16 ([1 2 2 1]));
%! assert (min (x, 3), uint16 ([1 2 3 3]));
%! assert (min (2, x), uint16 ([1 2 2 2]));
%! x = int16 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), int16 ([1 2 2 1]));
%! assert (min (x, 3), int16 ([1 2 3 3]));
%! assert (min (2, x), int16 ([1 2 2 2]));
%! x = uint32 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), uint32 ([1 2 2 1]));
%! assert (min (x, 3), uint32 ([1 2 3 3]));
%! assert (min (2, x), uint32 ([1 2 2 2]));
%! x = int32 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), int32 ([1 2 2 1]));
%! assert (min (x, 3), int32 ([1 2 3 3]));
%! assert (min (2, x), int32 ([1 2 2 2]));
%! x = uint64 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), uint64 ([1 2 2 1]));
%! assert (min (x, 3), uint64 ([1 2 3 3]));
%! assert (min (2, x), uint64 ([1 2 2 2]));
%! x = int64 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), int64 ([1 2 2 1]));
%! assert (min (x, 3), int64 ([1 2 3 3]));
%! assert (min (2, x), int64 ([1 2 2 2]));
## Sparse double values
%!test
%! x = sparse ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (min (x, y), sparse ([1 2 2 1]));
%! assert (min (x, 3), sparse ([1 2 3 3]));
%! assert (min (2, x), sparse ([1 2 2 2]));
%! assert (min (x, 2.1i), sparse ([1 2 2.1i 2.1i]));

%!error min ()
%!error min (1, 2, 3, 4)
%!error <DIM must be a valid dimension> min ([1 2; 3 4], [], -3)
%!warning <second argument is ignored> min ([1 2 3 4], 2, 2);
%!error <wrong type argument 'cell'> min ({1 2 3 4})
%!error <cannot compute min \(cell, scalar\)> min ({1, 2, 3}, 2)
*/

DEFUN (max, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} max (@var{x})
@deftypefnx {} {} max (@var{x}, [], @var{dim})
@deftypefnx {} {[@var{w}, @var{iw}] =} max (@var{x})
@deftypefnx {} {} max (@var{x}, @var{y})
Find maximum values in the array @var{x}.

For a vector argument, return the maximum value.  For a matrix argument,
return a row vector with the maximum value of each column.  For a
multi-dimensional array, @code{max} operates along the first non-singleton
dimension.

If the optional third argument @var{dim} is present then operate along
this dimension.  In this case the second argument is ignored and should be
set to the empty matrix.

For two matrices (or a matrix and a scalar), return the pairwise maximum.

Thus,

@example
max (max (@var{x}))
@end example

@noindent
returns the largest element of the 2-D matrix @var{x}, and

@example
@group
max (2:5, pi)
    @result{}  3.1416  3.1416  4.0000  5.0000
@end group
@end example

@noindent
compares each element of the range @code{2:5} with @code{pi}, and returns a
row vector of the maximum values.

For complex arguments, the magnitude of the elements are used for
comparison.  If the magnitudes are identical, then the results are ordered
by phase angle in the range (-pi, pi].  Hence,

@example
@group
max ([-1 i 1 -i])
    @result{} -1
@end group
@end example

@noindent
because all entries have magnitude 1, but -1 has the largest phase angle
with value pi.

If called with one input and two output arguments, @code{max} also returns
the first index of the maximum value(s).  Thus,

@example
@group
[x, ix] = max ([1, 3, 5, 2, 5])
    @result{}  x = 5
        ix = 3
@end group
@end example
@seealso{min, cummax, cummin}
@end deftypefn */)
{
  return do_minmax_body (args, nargout, false);
}

/*
## Test generic double class
%!assert (max ([1, 4, 2, 3]), 4)
%!assert (max ([1; -10; 5; -2]), 5)
%!assert (max ([4, 2i 4.999; -2, 2, 3+4i]), [4, 2i, 3+4i])
## Special routines for char arrays
%!assert (max (["abc", "ABC"]), 99)
%!assert (max (["abc"; "CBA"]), [97 98 99])
## Special routines for logical arrays
%!assert (max (logical ([])), logical ([]))
%!assert (max (logical ([0 0 1 0])), true)
%!assert (max (logical ([0 0 1 0; 0 1 0 0])), logical ([0 1 1 0]))
## Single values
%!assert (max (single ([1, 4, 2, 3])), single (4))
%!assert (max (single ([1; -10; 5; -2])), single (5))
%!assert (max (single ([4, 2i 4.999; -2, 2, 3+4i])), single ([4, 2i, 3+4i]))
## Integer values
%!assert (max (uint8 ([1, 4, 2, 3])), uint8 (4))
%!assert (max (uint8 ([1; -10; 5; -2])), uint8 (5))
%!assert (max (int8 ([1, 4, 2, 3])), int8 (4))
%!assert (max (int8 ([1; -10; 5; -2])), int8 (5))
%!assert (max (uint16 ([1, 4, 2, 3])), uint16 (4))
%!assert (max (uint16 ([1; -10; 5; -2])), uint16 (5))
%!assert (max (int16 ([1, 4, 2, 3])), int16 (4))
%!assert (max (int16 ([1; -10; 5; -2])), int16 (5))
%!assert (max (uint32 ([1, 4, 2, 3])), uint32 (4))
%!assert (max (uint32 ([1; -10; 5; -2])), uint32 (5))
%!assert (max (int32 ([1, 4, 2, 3])), int32 (4))
%!assert (max (int32 ([1; -10; 5; -2])), int32 (5))
%!assert (max (uint64 ([1, 4, 2, 3])), uint64 (4))
%!assert (max (uint64 ([1; -10; 5; -2])), uint64 (5))
%!assert (max (int64 ([1, 4, 2, 3])), int64 (4))
%!assert (max (int64 ([1; -10; 5; -2])), int64 (5))
## Sparse double values
%!assert (max (sparse ([1, 4, 2, 3])), sparse (4))
%!assert (max (sparse ([1; -10; 5; -2])), sparse(5))
%!assert (max (sparse ([4, 2i 4.999; -2, 2, 3+4i])), sparse ([4, 2i, 3+4i]))

## Test dimension argument
%!test
%! x = reshape (1:8, [2,2,2]);
%! assert (min (x, [], 1), reshape ([1, 3, 5, 7], [1,2,2]));
%! assert (min (x, [], 2), reshape ([1, 2, 5, 6], [2,1,2]));
%! [y, i] = min (x, [], 3);
%! assert (ndims (y), 2);
%! assert (y, [1, 3; 2, 4]);
%! assert (ndims (i), 2);
%! assert (i, [1, 1; 1, 1]);

## Test 2-output forms for various arg types
## Special routines for char arrays
%!test
%! [y, i] = max (["abc", "ABC"]);
%! assert (y, 99);
%! assert (i, 3);
## Special routines for logical arrays
%!test
%! x = logical ([0 0 1 0]);
%! [y, i] = max (x);
%! assert (y, true);
%! assert (i, 3);
## Special handling of ranges
%!test
%! rng = 1:2:10;
%! [y, i] = max (rng);
%! assert (y, 9);
%! assert (i, 5);
%! rng = 10:-2:1;
%! [y, i] = max (rng);
%! assert (y, 10);
%! assert (i, 1);

## Test 2-input calling form for various arg types
## Test generic double class
%!test
%! x = [1, 2, 3, 4];  y = fliplr (x);
%! assert (max (x, y), [4 3 3 4]);
%! assert (max (x, 3), [3 3 3 4]);
%! assert (max (2, x), [2 2 3 4]);
%! assert (max (x, 2.1i), [2.1i 2.1i 3 4]);
## FIXME: Ordering of complex results with equal magnitude is not by phase
##        angle in the 2-input form.  Instead, it is in the order in which it
##        appears in the argument list.
%!xtest
%! x = [1, 2, 3, 4];  y = fliplr (x);
%! assert (max (x, 2i), [2i 2i 3 4]);
## Special routines for char arrays
%!assert (max ("abc", "b"), [98 98 99])
%!assert (max ("b", "cba"), [99 98 98])
## Special handling for logical arrays
%!assert (max ([true false], false), [true false])
%!assert (max (true, [false false]), [true true])
## Single values
%!test
%! x = single ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), single ([4 3 3 4]));
%! assert (max (x, 3), single ([3 3 3 4]));
%! assert (max (2, x), single ([2 2 3 4]));
%! assert (max (x, 2.1i), single ([2.1i 2.1i 3 4]));
## Integer values
%!test
%! x = uint8 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), uint8 ([4 3 3 4]));
%! assert (max (x, 3), uint8 ([3 3 3 4]));
%! assert (max (2, x), uint8 ([2 2 3 4]));
%! x = int8 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), int8 ([4 3 3 4]));
%! assert (max (x, 3), int8 ([3 3 3 4]));
%! assert (max (2, x), int8 ([2 2 3 4]));
%! x = uint16 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), uint16 ([4 3 3 4]));
%! assert (max (x, 3), uint16 ([3 3 3 4]));
%! assert (max (2, x), uint16 ([2 2 3 4]));
%! x = int16 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), int16 ([4 3 3 4]));
%! assert (max (x, 3), int16 ([3 3 3 4]));
%! assert (max (2, x), int16 ([2 2 3 4]));
%! x = uint32 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), uint32 ([4 3 3 4]));
%! assert (max (x, 3), uint32 ([3 3 3 4]));
%! assert (max (2, x), uint32 ([2 2 3 4]));
%! x = int32 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), int32 ([4 3 3 4]));
%! assert (max (x, 3), int32 ([3 3 3 4]));
%! assert (max (2, x), int32 ([2 2 3 4]));
%! x = uint64 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), uint64 ([4 3 3 4]));
%! assert (max (x, 3), uint64 ([3 3 3 4]));
%! assert (max (2, x), uint64 ([2 2 3 4]));
%! x = int64 ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), int64 ([4 3 3 4]));
%! assert (max (x, 3), int64 ([3 3 3 4]));
%! assert (max (2, x), int64 ([2 2 3 4]));
## Sparse double values
%!test
%! x = sparse ([1, 2, 3, 4]);  y = fliplr (x);
%! assert (max (x, y), sparse ([4 3 3 4]));
%! assert (max (x, 3), sparse ([3 3 3 4]));
%! assert (max (2, x), sparse ([2 2 3 4]));
%! assert (max (x, 2.1i), sparse ([2.1i 2.1i 3 4]));

## Test for bug #40743
%!assert <40743> (max (zeros (1,0), ones (1,1)), zeros (1,0))
%!assert <40743> (max (sparse (zeros (1,0)), sparse (ones (1,1))),
                  sparse (zeros (1,0)))

%!error max ()
%!error max (1, 2, 3, 4)
%!error <DIM must be a valid dimension> max ([1 2; 3 4], [], -3)
%!warning <second argument is ignored> max ([1 2 3 4], 2, 2);
%!error <wrong type argument 'cell'> max ({1 2 3 4})
%!error <cannot compute max \(cell, scalar\)> max ({1, 2, 3}, 2)

*/

template <typename ArrayType>
static octave_value_list
do_cumminmax_red_op (const octave_value& arg,
                     int nargout, int dim, bool ismin)
{
  octave_value_list retval (nargout > 1 ? 2 : 1);
  ArrayType array = octave_value_extract<ArrayType> (arg);

  if (nargout <= 1)
    {
      if (ismin)
        retval(0) = array.cummin (dim);
      else
        retval(0) = array.cummax (dim);
    }
  else
    {
      retval.resize (2);
      Array<octave_idx_type> idx;
      if (ismin)
        retval(0) = array.cummin (idx, dim);
      else
        retval(0) = array.cummax (idx, dim);

      retval(1) = octave_value (idx, true, true);
    }

  return retval;
}

static octave_value_list
do_cumminmax_body (const octave_value_list& args,
                   int nargout, bool ismin)
{
  int nargin = args.length ();

  if (nargin < 1 || nargin > 2)
    print_usage ();

  const char *func = ismin ? "cummin" : "cummax";

  octave_value arg = args(0);
  int dim = -1;
  if (nargin == 2)
    {
      dim = args(1).int_value (true) - 1;

      if (dim < 0)
        error ("%s: DIM must be a valid dimension", func);
    }

  octave_value_list retval;

  switch (arg.builtin_type ())
    {
    case btyp_double:
      retval = do_cumminmax_red_op<NDArray> (arg, nargout, dim, ismin);
      break;

    case btyp_complex:
      retval = do_cumminmax_red_op<ComplexNDArray> (arg, nargout, dim,
                                                    ismin);
      break;

    case btyp_float:
      retval = do_cumminmax_red_op<FloatNDArray> (arg, nargout, dim, ismin);
      break;

    case btyp_float_complex:
      retval = do_cumminmax_red_op<FloatComplexNDArray> (arg, nargout, dim,
                                                         ismin);
      break;

#define MAKE_INT_BRANCH(X)                                                   \
    case btyp_ ## X:                                                         \
      retval = do_cumminmax_red_op<X ## NDArray> (arg, nargout, dim, ismin); \
      break;

      MAKE_INT_BRANCH (int8);
      MAKE_INT_BRANCH (int16);
      MAKE_INT_BRANCH (int32);
      MAKE_INT_BRANCH (int64);
      MAKE_INT_BRANCH (uint8);
      MAKE_INT_BRANCH (uint16);
      MAKE_INT_BRANCH (uint32);
      MAKE_INT_BRANCH (uint64);

#undef MAKE_INT_BRANCH

    case btyp_bool:
      {
        retval = do_cumminmax_red_op<int8NDArray> (arg, nargout, dim,
                                                   ismin);
        if (retval.length () > 0)
          retval(0) = retval(0).bool_array_value ();
      }
      break;

    default:
      err_wrong_type_arg (func, arg);
    }

  return retval;
}

DEFUN (cummin, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} cummin (@var{x})
@deftypefnx {} {} cummin (@var{x}, @var{dim})
@deftypefnx {} {[@var{w}, @var{iw}] =} cummin (@var{x})
Return the cumulative minimum values along dimension @var{dim}.

If @var{dim} is unspecified it defaults to column-wise operation.  For
example:

@example
@group
cummin ([5 4 6 2 3 1])
   @result{}  5  4  4  2  2  1
@end group
@end example

If called with two output arguments the index of the minimum value is also
returned.

@example
@group
[w, iw] = cummin ([5 4 6 2 3 1])
@result{}
w =  5  4  4  2  2  1
iw = 1  2  2  4  4  6
@end group
@end example

@seealso{cummax, min, max}
@end deftypefn */)
{
  return do_cumminmax_body (args, nargout, true);
}

/*
%!assert (cummin ([1, 4, 2, 3]), [1 1 1 1])
%!assert (cummin ([1; -10; 5; -2]), [1; -10; -10; -10])
%!assert (cummin ([4, i; -2, 2]), [4, i; -2, i])
%!assert (cummin ([1 2; NaN 1], 2), [1 1; NaN 1])

%!test
%! x = reshape (1:8, [2,2,2]);
%! assert (cummin (x, 1), reshape ([1 1 3 3 5 5 7 7], [2,2,2]));
%! assert (cummin (x, 2), reshape ([1 2 1 2 5 6 5 6], [2,2,2]));
%! [w, iw] = cummin (x, 3);
%! assert (ndims (w), 3);
%! assert (w, repmat ([1 3; 2 4], [1 1 2]));
%! assert (ndims (iw), 3);
%! assert (iw, ones (2,2,2));

%!error cummin ()
%!error cummin (1, 2, 3)
*/

DEFUN (cummax, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} cummax (@var{x})
@deftypefnx {} {} cummax (@var{x}, @var{dim})
@deftypefnx {} {[@var{w}, @var{iw}] =} cummax (@dots{})
Return the cumulative maximum values along dimension @var{dim}.

If @var{dim} is unspecified it defaults to column-wise operation.  For
example:

@example
@group
cummax ([1 3 2 6 4 5])
   @result{}  1  3  3  6  6  6
@end group
@end example

If called with two output arguments the index of the maximum value is also
returned.

@example
@group
[w, iw] = cummax ([1 3 2 6 4 5])
@result{}
w =  1  3  3  6  6  6
iw = 1  2  2  4  4  4
@end group
@end example

@seealso{cummin, max, min}
@end deftypefn */)
{
  return do_cumminmax_body (args, nargout, false);
}

/*
%!assert (cummax ([1, 4, 2, 3]), [1 4 4 4])
%!assert (cummax ([1; -10; 5; -2]), [1; 1; 5; 5])
%!assert (cummax ([4, i 4.9, -2, 2, 3+4i]), [4, 4, 4.9, 4.9, 4.9, 3+4i])
%!assert (cummax ([1 NaN 0; NaN NaN 1], 2), [1 1 1; NaN NaN 1])

%!test
%! x = reshape (8:-1:1, [2,2,2]);
%! assert (cummax (x, 1), reshape ([8 8 6 6 4 4 2 2], [2,2,2]));
%! assert (cummax (x, 2), reshape ([8 7 8 7 4 3 4 3], [2,2,2]));
%! [w, iw] = cummax (x, 3);
%! assert (ndims (w), 3);
%! assert (w, repmat ([8 6; 7 5], [1 1 2]));
%! assert (ndims (iw), 3);
%! assert (iw, ones (2,2,2));

%!error cummax ()
%!error cummax (1, 2, 3)
*/