## Copyright (C) 2024-2026 Andreas Bertsatos <abertsatos@biol.uoa.gr>
##
## This file is part of the datatypes package for GNU Octave.
##
## This program 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.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.

classdef duration
  ## -*- texinfo -*-
  ## @deftp {datatypes} duration
  ##
  ## Array representing durations of time using fixed-length time units.
  ##
  ## @qcode{duration} values are stored internally as @qcode{double} type array
  ## representing numbers of elapsed days as a fixed-length time unit.  By
  ## default, fractional seconds of duration values are not displayed, but their
  ## actual precision is closer to nanoseconds for typical time lengths.
  ##
  ## @code{duration} arrays can be created through their constructor by
  ## combining numeric arrays representing individual fixed-length elapsed time
  ## units or through the functions @code{years}, @code{days}, @code{hours},
  ## @code{minutes}, @code{seconds}, and @code{calyears}, which create
  ## fixed-length durations in terms of a single duration units.  These
  ## functions are also available as methods of @code{duration} arrays to
  ## extract individual duration units as numeric arrays.
  ##
  ## @seealso{calendarDuration, datetime}
  ## @end deftp

  properties
    ## -*- texinfo -*-
    ## @deftp {duration} {property} Format
    ##
    ## Display format
    ##
    ## Display format, specified as a character vector or string scalar.  If
    ## specified as a string scalar, it is converted and stored internally as
    ## a character vector.
    ##
    ## @end deftp
    Format = 'hh:mm:ss'
  endproperties

  properties (SetAccess = private, Hidden)
    ## Duration length in milliseconds.  MATLAB stores a duration this way too,
    ## and its representable set follows from it: 'eps' of a duration is the
    ## spacing of a double at that many milliseconds, which is what this class
    ## reproduces.  Storing days instead put the grid somewhere else and cost
    ## about three significant digits on every conversion back to seconds.
    Millis = 0
  endproperties

  methods (Hidden)

    ## Custom display
    function display (this)
      in_name = inputname (1);
      if (! isempty (in_name))
        fprintf ('%s =\n', in_name);
      endif
      __disp__ (this, 'duration', in_name);
    endfunction

    ## Custom display
    function disp (this)
      __disp__ (this, 'duration');
    endfunction

  endmethods

  methods (Static, Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{E} =} duration.empty ()
    ## @deftypefnx {duration} {@var{E} =} duration.empty (@var{sz})
    ## @deftypefnx {duration} {@var{E} =} duration.empty (@var{m}, @var{n}, @dots{})
    ##
    ## Create an empty duration array.
    ##
    ## @code{@var{E} = duration.empty ()} returns a @math{0*0} empty duration
    ## array.  @code{duration.empty (@var{m}, @var{n}, @dots{})} or
    ## @code{duration.empty (@var{sz})} returns an empty duration array of the
    ## requested size, which must have at least one dimension equal to zero.  A
    ## lone dimension gives a square size, so @code{duration.empty (3)} is an
    ## error while @code{duration.empty (0)} is @math{0*0}.  As for
    ## @code{zeros}, a negative dimension counts as zero, and a size vector with
    ## nothing in it names no size and gives @math{0*0}.
    ##
    ## @end deftypefn
    function E = empty (varargin)
      if (nargin == 0)
        sz = [0, 0];
      elseif (nargin == 1 && ! isscalar (varargin{1}))
        sz = double (varargin{1}(:)).';
      else
        sz = [varargin{:}];
      endif
      if (! (isnumeric (sz) && isrow (sz) && all (sz == fix (sz))))
        error ("duration.empty: dimensions must be integer values.");
      endif
      ## A negative dimension is no smaller than none at all, and a size vector
      ## holding no dimensions names no size: 'zeros' and every other array
      ## constructor read both the same way.
      sz = max (sz, 0);
      if (isempty (sz))
        sz = [0, 0];
      elseif (isscalar (sz))
        sz = [sz, sz];
      endif
      if (all (sz != 0))
        error (strcat ("duration.empty: at least one dimension must be", ...
                       " zero for an empty array."));
      endif
      E = duration (zeros (sz), zeros (sz), zeros (sz));
    endfunction

  endmethods

################################################################################
##                 ** Create and convert 'duration' type **                   ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'duration'         'dispstrings'      'cellstr'          'char'            ##
## 'datevec'          'datenum'          'hms'              'years'           ##
## 'days'             'hours'            'minutes'          'seconds'         ##
## 'milliseconds'                                                             ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{D} =} duration (@var{X})
    ## @deftypefnx {duration} {@var{D} =} duration (@var{H}, @var{MI}, @var{S})
    ## @deftypefnx {duration} {@var{D} =} duration (@var{H}, @var{MI}, @var{S}, @var{MS})
    ## @deftypefnx {duration} {@var{D} =} duration (@var{TimeStrings})
    ## @deftypefnx {duration} {@var{D} =} duration (@var{TimeStrings}, @qcode{'InputFormat'}, @var{INFMT})
    ## @deftypefnx {duration} {@var{D} =} duration (@dots{}, @qcode{'Format'}, @var{FMT})
    ##
    ## Create a new array of fixed-length time durations.
    ##
    ## @code{@var{D} = duration (@var{X})} creates a column vector of durations
    ## from a numeric matrix.
    ##
    ## @code{@var{D} = duration (@var{H}, @var{MI}, @var{S})} creates a duration
    ## array from numeric arrays containing the number of hours, minutes, and
    ## seconds specified by @var{H}, @var{MI} and @var{S}, respectively.
    ##
    ## @code{@var{D} = duration (@var{H}, @var{MI}, @var{S}, @var{MS})} creates
    ## a duration array from numeric arrays containing the number of hours,
    ## minutes, seconds, and milliseconds specified by @var{H}, @var{MI},
    ## @var{S}, and @var{MS}, respectively.
    ##
    ## @code{@var{D} = duration (@var{TimeStrings})} creates a duration array
    ## from text that represents elapsed times.  @var{TimeStrings} can be a
    ## character vector, a cell array of character vectors, or a string array
    ## representing times using either the @qcode{'hh:mm:ss'} or the
    ## @qcode{'dd:hh:mm:ss'} format.
    ##
    ## @code{@var{D} = duration (@var{TimeStrings}, @qcode{'InputFormat'},
    ## @var{INFMT})} creates a duration array from text that represents elapsed
    ## times according to the format specified by @var{INFMT}, which can be any
    ## of the following:
    ##
    ## @itemize
    ## @item @qcode{'dd:hh:mm:ss'}
    ## @item @qcode{'hh:mm:ss'}
    ## @item @qcode{'mm:ss'}
    ## @item @qcode{'hh:mm'}
    ## @item Any of the first three formats can also be appended with up to nine
    ## @qcode{S} characters to indicate fractional second digits, such as
    ## @qcode{'dd:hh:mm:ss.SS'} or @qcode{'mm:ss.SS'}.
    ## @end itemize
    ##
    ## @code{@var{D} = duration (@dots{}, @qcode{'Format'}, @var{FMT})}
    ## specifies the format in which @var{D} is displayed.  @var{FMT} can
    ## specify either a digital timer, which can have any of the valid formats
    ## for @qcode{'InputFormat'} as shown above or a single number with time
    ## units by specifying one of the following:
    ##
    ## @itemize
    ## @item @qcode{'y'} fixed-length years (1 year equals 365.2425 days)
    ## @item @qcode{'d'} fixed-length days (1 day equals 24 hours)
    ## @item @qcode{'h'} hours
    ## @item @qcode{'m'} minutes
    ## @item @qcode{'s'} seconds
    ## @end itemize
    ##
    ## @code{@var{D} = duration ()} returns a scalar array of durations with an
    ## elapsed time value of zero.  To create an empty duration array, use
    ## @code{duration ([], [], [])}.
    ##
    ## @seealso{years, days, hours, minutes, seconds, milliseconds, duration,
    ## isduration, calendarDuration, datetime}
    ## @end deftypefn
    function this = duration (varargin)

      ## Return a scalar duration object
      if (nargin == 0)
        return
      endif

      ## Parse optional Name-Value paired arguments
      optNames = {'Format', 'InputFormat'};
      dfValues = {[], []};
      [Format, inputFormat, args] = ...
            parsePairedArguments (optNames, dfValues, varargin(:));

      ## Check optional 'Format' and 'InputFormat' arguments
      if (! isempty (Format))
        ## Convert string to character vector if necessary
        if (isstring (Format))
          if (! isscalar (Format))
            error (strcat ("duration: 'Format' must be a character", ...
                           " vector or a string scalar."));
          endif
          Format = char (Format);
        elseif (! (ischar (Format) && isrow (Format)))
          error (strcat ("duration: 'Format' must be a character", ...
                         " vector or a string scalar."));
        endif
        errmsg = checkFormatString (Format);
        if (! isempty (errmsg))
          error ("duration: %s", errmsg);
        endif
        this.Format = Format;
      endif
      if (! isempty (inputFormat))
        ## Convert string to character vector if necessary
        if (isstring (inputFormat))
          if (! isscalar (inputFormat))
            error (strcat ("duration: 'InputFormat' must be a", ...
                           " character vector or a string scalar."));
          endif
          inputFormat = char (inputFormat);
        elseif (! (ischar (inputFormat) && isrow (inputFormat)))
          error (strcat ("duration: 'InputFormat' must be a character", ...
                         " vector or a string scalar."));
        endif
        errmsg = checkInputFormatString (inputFormat);
        if (! isempty (errmsg))
          error ("duration: %s", errmsg);
        endif
      endif

      ## Parse inputs
      switch (numel (args))

        ## this = duration ()
        case 0
          return

        ## this = duration (X)
        case 1
          X = args{1};
          if (isnumeric (X))
            if (! ismatrix (X))
              error ("duration: numeric X must be a matrix.");
            endif
            if (! isreal (X))
              error ("duration: numeric X must be real.");
            endif
            if (size (X, 2) == 3)
              H  = X(:,1);
              MI = X(:,2);
              S  = X(:,3);
            else
              error ("duration: X must have 3 columns.");
            endif
            [~, this.Millis] = hms2millis (H, MI, S);
            ## Return a warning if InputFormat is defined
            if (! isempty (inputFormat))
              warning (strcat ("duration: 'InputFormat' has no effect", ...
                               " on numeric data."));
            endif

          elseif (iscellstr (X) || ischar (X) || isa (X, "string"))
            if (! iscellstr (X))
              X = cellstr (X);
            endif
            this.Millis = timestrings2millis (X, inputFormat);
          else
            error ("duration: invalid type of single input data argument.");
          endif

        ## this = duration (H, MI, S)
        case 3
          [H, MI, S] = args{:};
          if (! (isnumeric (H) && isnumeric (MI) && isnumeric (S)))
            error ("duration: H, MI, and S must be numeric arrays.");
          endif
          if (! (isreal (H) && isreal (MI) && isreal (S)))
            error ("duration: H, MI, and S must be real.");
          endif
          ## Expansion is handled by the helper function
          [err, millis] = hms2millis (H, MI, S);
          if (err > 0)
            error ("duration: H, MI, and S must be of common size or scalars.");
          endif
          this.Millis = millis;
          ## Return a warning if InputFormat is defined
          if (! isempty (inputFormat))
            warning ("duration: 'InputFormat' has no effect on numeric data.");
          endif

        ## this = duration (H, MI, S, MS)
        case 4
          [H, MI, S, MS] = args{:};
          if (! (isnumeric (H) && isnumeric (MI) && isnumeric (S) && ...
                 isnumeric (MS)))
            error ("duration: H, MI, S, and MS must be numeric arrays.");
          endif
          if (! (isreal (H) && isreal (MI) && isreal (S) && isreal (MS)))
            error ("duration: H, MI, S, and MS must be real.");
          endif
          ## Expansion is handled by the helper function
          [err, millis] = hms2millis (H, MI, S, MS);
          if (err > 0)
            error (strcat ("duration: H, MI, S, and MS must be of", ...
                           " common size or scalars."));
          endif
          this.Millis = millis;
          ## Return a warning if InputFormat is defined
          if (! isempty (inputFormat))
            warning ("duration: 'InputFormat' has no effect on numeric data.");
          endif

        otherwise
          error ("duration: invalid number of input arguments.");

      endswitch

    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{cstr} =} dispstrings (@var{D})
    ##
    ## Get display formatted strings for each element of a duration array.
    ##
    ## @code{@var{cstr} = dispstrings (@var{D})} returns a cellstr array of
    ## character vectors, @var{cstr}, which has the same size as the input
    ## duration @var{D}.
    ##
    ## @end deftypefn
    function cstr = dispstrings (this)
      ## Get display format
      fmt = strsplit (this.Format, '.')';
      if (numel (fmt) == 1)
        fmt = fmt{1};
        fracSec = false;
      else
        fracSec = true;
        fdigits = numel (fmt{2});
        pat = sprintf ('.%%0%dd', fdigits);
        fmt = fmt{1};
      endif
      ## Process all elements
      sz = size (this);
      cstr = cell (sz);
      for i = 1:prod (sz)
        ## The format branches below work in days, as they always have;
        ## only the stored unit changed underneath them.
        d = this.Millis(i) / 86400000;
        ## Handle NaNs and Infs early
        if (! isfinite (d))
          switch (fmt)
            case 'y'
              cstr{i} = sprintf ('%g yrs', d);
            case 'd'
              cstr{i} = sprintf ('%g days', d);
            case 'h'
              cstr{i} = sprintf ('%g hr', d);
            case 'm'
              cstr{i} = sprintf ('%g min', d);
            case 's'
              cstr{i} = sprintf ('%g sec', d);
            otherwise
              cstr{i} = sprintf ('%g', d);
          endswitch
        else
          ## Get sign for positive/negative duration
          str = '';
          if (d < 0)
            str = [str, '-'];
            d = abs (d);
          endif
          ## Build string according to display format
          if (strcmp (fmt, 'y'))
            years = d / 365.2425;
            if (years == 1)
              str = [str, sprintf('%g yr', years)];
            else
              str = [str, sprintf('%g yrs', years)];
            endif
          elseif (strcmp (fmt, 'd'))
            if (d == 1)
              str = [str, sprintf('%g day', d)];
            else
              str = [str, sprintf('%g days', d)];
            endif
          elseif (strcmp (fmt, 'h'))
            str = [str, sprintf('%g hr', d * 24)];
          elseif (strcmp (fmt, 'm'))
            str = [str, sprintf('%g min', d * 1440)];
          elseif (strcmp (fmt, 's'))
            str = [str, sprintf('%g sec', d * 86400)];
          elseif (strcmp (fmt, 'hh:mm'))
            ## Convert to minutes
            x = d * 1440;
            ## Calculate hours
            tmp = x / 60;
            h = fix (tmp);
            ## Fix round-off errors with threshold scaled by hours
            if (abs (tmp - h - 1) < 1e-13 * (1 + h))
              h++;
            endif
            ## Calculate remaining minutes
            tmp = x - h * 60;
            m = fix (tmp);
            ## Fix round-off errors with threshold scaled by minutes
            if (abs (tmp - m - 1) < 1e-13 * (1 + m))
              m++;
            endif
            str = [str, sprintf('%02d:%02d', h, m)];
          elseif (strcmp (fmt, 'mm:ss'))
            ## Convert to seconds
            x = d * 86400;
            ## Calculate minutes
            tmp = x / 60;
            m = fix (tmp);
            ## Fix round-off errors with threshold scaled by minutes
            if (abs (tmp - m - 1) < 1e-13 * (1 + m))
              m++;
            endif
            ## Calculate remaining seconds
            tmp = x - m * 60;
            s = fix (tmp);
            ## Fix round-off errors with threshold scaled by seconds
            if (abs (tmp - s - 1) < 1e-12 * (1 + s))
              s++;
            endif
            str = [str, sprintf('%02d:%02d', m, s)];
            if (fracSec)
              fs = rem (x, 60) - s; # fraction of a second
              ## Promote to integer value according to requested digits
              ms = abs (fix (fs * 10 ^ fdigits));
              str = [str, sprintf(pat, ms)];
            endif
          elseif (strcmp (fmt, 'hh:mm:ss'))
            ## Convert to seconds
            x = d * 86400;
            ## Calculate hours
            tmp = x / 3600;
            h = fix (tmp);
            ## Fix round-off errors with threshold scaled by hours
            if (abs (tmp - h - 1) < 1e-13 * (1 + h))
              h++;
            endif
            ## Calculate remaining duration in seconds
            x = x - h * 3600;
            ## Calculate remaining minutes
            tmp = x / 60;
            m = fix (tmp);
            ## Fix round-off errors with threshold scaled by minutes
            if (abs (tmp - m - 1) < 1e-13 * (1 + m))
              m++;
            endif
            ## Calculate remaining seconds
            x = x - m * 60;
            s = fix (x);
            ## Fix round-off errors with threshold scaled by seconds
            if (abs (x - s - 1) < 1e-12 * (1 + s))
              s++;
            endif
            str = [str, sprintf('%02d:%02d:%02d', h, m, s)];
            if (fracSec)
              fs = x - s; # fraction of a second
              ## Round to nearest nanosecond
              fs = round (fs * 1e+9) * 1e-9;
              ## Promote to integer value according to requested digits
              ms = floor (fs * 10 ^ fdigits);
              str = [str, sprintf(pat, ms)];
            endif
          elseif (strcmp (fmt, 'dd:hh:mm:ss'))
            ## Calculate days
            tmp = fix (d);
            ## Fix round-off errors with threshold scaled by days
            if (abs (d - tmp - 1) < 1e-15 * (1 + d))
              tmp++;
            endif
            x = d - tmp;
            d = tmp;
            ## Calculate remaining duration in seconds
            x = x * 86400;
            ## Calculate hours
            tmp = x / 3600;
            h = fix (tmp);
            ## Fix round-off errors with threshold scaled by hours
            if (abs (tmp - h - 1) < 1e-13 * (1 + h))
              h++;
            endif
            ## Calculate remaining duration in seconds
            x = x - h * 3600;
            ## Calculate remaining minutes
            tmp = x / 60;
            m = fix (tmp);
            ## Fix round-off errors with threshold scaled by minutes
            if (abs (tmp - m - 1) < 1e-13 * (1 + m))
              m++;
            endif
            ## Calculate remaining seconds
            x = x - m * 60;
            s = fix (x);
            ## Fix round-off errors with threshold scaled by seconds
            if (abs (x - s - 1) < 1e-12 * (1 + s))
              s++;
            endif
            if (fix (d) > 0)
              str = [str, sprintf('%02d:%02d:%02d:%02d', d, h, m, s)];
            else
              str = [str, sprintf('%02d:%02d:%02d', h, m, s)];
            endif
            if (fracSec)
              fs = x - s; # fraction of a second
              ## Round to nearest nanosecond
              fs = round (fs * 1e+9) * 1e-9;
              ## Promote to integer value according to requested digits
              ms = floor (fs * 10 ^ fdigits);
              str = [str, sprintf(pat, ms)];
            endif
          endif
          cstr{i} = str;
        endif
      endfor
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{cstr} =} cellstr (@var{D})
    ## @deftypefnx {duration} {@var{cstr} =} cellstr (@var{D}, @var{Format})
    ##
    ## Convert duration array to a cell array of character vectors.
    ##
    ## @code{@var{cstr} = cellstr (@var{D})} returns a cellstr array of
    ## character vectors, @var{cstr}, which has the same size as the input
    ## duration @var{D}.
    ##
    ## @end deftypefn
    function cstr = cellstr (this, Format = '')
      if (! isempty (Format))
        ## Convert string to character vector if necessary
        if (isstring (Format))
          if (! isscalar (Format))
            error (strcat ("duration.cellstr: FORMAT must be a", ...
                           " character vector or a string scalar."));
          endif
          Format = char (Format);
        elseif (! (ischar (Format) && isrow (Format)))
          error (strcat ("duration.cellstr: FORMAT must be a", ...
                         " character vector or a string scalar."));
        endif
        errmsg = checkFormatString (Format);
        if (! isempty (errmsg))
          error ("duration.cellstr: %s", errmsg);
        endif
        this.Format = Format;
      endif
      cstr = dispstrings (this);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{cmat} =} char (@var{D})
    ##
    ## Convert duration array to a character matrix.
    ##
    ## @code{@var{cmat} = char (@var{D})} returns a character matrix with one
    ## row per element in @var{D}, taken in column-major order.
    ##
    ## Rows shorter than the widest are padded on the @emph{left}, so the
    ## character matrix is right-justified, as MATLAB returns it and as the
    ## array itself is displayed.
    ##
    ## @end deftypefn
    function cmat = char (this, Format = '')
      if (! isempty (Format))
        ## Convert string to character vector if necessary
        if (isstring (Format))
          if (! isscalar (Format))
            error (strcat ("duration.char: FORMAT must be a", ...
                           " character vector or a string scalar."));
          endif
          Format = char (Format);
        elseif (! (ischar (Format) && isrow (Format)))
          error (strcat ("duration.char: FORMAT must be a", ...
                         " character vector or a string scalar."));
        endif
        errmsg = checkFormatString (Format);
        if (! isempty (errmsg))
          error ("duration.char: %s", errmsg);
        endif
        this.Format = Format;
      endif
      cmat = strjust (char (dispstrings (this)), 'right');
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{DV} =} datevec (@var{DT})
    ## @deftypefnx {duration} {[@var{Y}, @var{MO}, @var{D}, @var{h}, @var{mi}, @var{s}] =} datevec (@var{DT})
    ##
    ## Convert duration array to date vectors.
    ##
    ## @code{@var{DV} = datevec (@var{DT})} returns an @math{N*6} numeric matrix
    ## whose rows represent each element in @var{DT} and each column corresponds
    ## to years, months, days, hours, minutes, and seconds, respectively.  Since
    ## months cannot be represented as a fixed length of time, the second column
    ## of @var{DV} is always zero.  @var{DV} represents a length of time split
    ## across different fixed-length elapsed time units.  The number of rows in
    ## @var{DV} equals to the number of elements in the duration array @var{DT}.
    ##
    ## @code{[@var{Y}, @var{MO}, @var{D}, @var{h}, @var{mi}, @var{s}] = datevec
    ## (@var{DT})} returns the components of @var{DT} as individual variables,
    ## but unlike @var{DV} in the previous syntax, each variable has the same
    ## size as the duration array @var{DT}.
    ##
    ## Values containing a fractional portion less than 1 picosecond are rounded
    ## to the nearest picosecond.
    ##
    ## @end deftypefn
    function varargout = datevec (this)
      d = this.Millis / 86400000;
      tmp = d / 365.2425;
      y = fix (tmp);
      ## Fix round-off errors with threshold scaled by years
      idx = abs (tmp - y - 1) < 1e-15 * y;
      y(idx) += 1;
      x = rem (d, 365.2425);
      d = fix (x);
      x = x - d;
      ## Get remaining duration in seconds
      x = x * 86400;
      tmp = x / 3600;
      h = fix (tmp);
      idx = abs (tmp - h - 1) < 1e-15 * h;
      h(idx) += 1;
      x = x - h * 3600;
      tmp = x / 60;
      m = fix (tmp);
      idx = abs (tmp - m - 1) < 1e-15 * m;
      m(idx) += 1;
      s = x - m * 60;
      ## Fix floating point precision to nearest picosecond
      s = round (s * 1e+12) * 1e-12;
      ## Add months column
      mo = zeros (size (s));
      mo(isnan (d)) = NaN;
      ## Transform to matrix
      DV = [y(:), mo(:), d(:), h(:), m(:), s(:)];
      if (nargout == 0 || nargout == 1)
        varargout{1} = DV;
      elseif (nargout <= 6)
        for i = 1:nargout
          ## Multiple outputs are reshaped to original input size
          varargout{i} = reshape (DV(:,i), size (this));
        endfor
      else
        error ("duration.datevec: too many output arguments.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{N} =} datenum (@var{D})
    ##
    ## Convert a duration array to numbers of days.
    ##
    ## @code{@var{N} = datenum (@var{D})} returns a @code{double} array of the
    ## same size as @var{D} holding the length of each duration in days,
    ## including any fractional part.  @code{NaN} durations give @code{NaN}.
    ##
    ## A duration measures elapsed time rather than naming a point in it, so the
    ## result is a count of days and not a serial date number: adding it to a
    ## serial date number shifts that date by the duration.  This is the same
    ## value @code{days} returns, under the name the older date functions use.
    ##
    ## @end deftypefn
    function N = datenum (D)
      N = D.Millis / 86400000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{H} =} hms (@var{D})
    ## @deftypefnx {duration} {[@var{H}, @var{M}] =} hms (@var{D})
    ## @deftypefnx {duration} {[@var{H}, @var{M}, @var{S}] =} hms (@var{D})
    ##
    ## Split duration array into separate time unit values.
    ##
    ## @code{[@var{H}, @var{M}, @var{S}] = hms (@var{D})} splits the duration
    ## array @var{D} into separate numeric arrays @var{H}, @var{M}, and @var{S},
    ## which correspond to hours, minutes, and seconds, respectively.  Hours and
    ## minutes are returned as whole numbers, while seconds may also have a
    ## fractional part.
    ##
    ## Each component is what truncating division leaves, so every one of them
    ## carries the sign of the duration as a whole and a span a hair under an
    ## hour reports 59 minutes rather than a whole one.  Nothing is snapped to a
    ## whole unit and nothing is rounded to a fixed precision.
    ##
    ## A duration that is not finite has no components to divide between: all
    ## three take that same infinity, or @code{NaN}.
    ##
    ## @end deftypefn
    function varargout = hms (this)
      ## Each component is what truncating division leaves, exactly as MATLAB
      ## computes it.  Nothing is snapped to a whole unit and nothing is rounded
      ## to a fixed precision: a span a hair under an hour must report 59
      ## minutes, and a fraction of a second must survive whichever side of zero
      ## it falls.  Truncation towards zero also gives every component the sign
      ## of the whole, down to the negative zeros MATLAB returns.
      x = this.Millis / 1000;
      h = fix (x / 3600);
      x = x - h * 3600;
      m = fix (x / 60);
      s = x - m * 60;
      ## A non-finite duration has no components to divide between: each of
      ## them is that same infinity, or NaN, as MATLAB returns.  Subtracting
      ## the hours off an infinite count of seconds otherwise leaves NaN
      ## behind in the minutes and seconds.
      nf = ! isfinite (this.Millis);
      if (any (nf, 'all'))
        h(nf) = this.Millis(nf);
        m(nf) = this.Millis(nf);
        s(nf) = this.Millis(nf);
      endif
      if (nargout == 0 || nargout == 1)
        varargout{1} = h;
      elseif (nargout == 2)
        varargout{1} = h;
        varargout{2} = m;
      elseif (nargout == 3)
        varargout{1} = h;
        varargout{2} = m;
        varargout{3} = s;
      else
        error ("duration.hms: too many output arguments.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} years (@var{D})
    ##
    ## Duration equivalent numeric values in fixed-length years.
    ##
    ## @code{@var{X} = years (@var{D})} converts durations in @var{D} to the
    ## equivalent number of fixed-length years (1 year equals 365.2425 days).
    ## @var{X} is a double array of the same size as @var{D}.
    ##
    ## @end deftypefn
    function out = years (this)
      out = this.Millis / 31556952000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} days (@var{D})
    ##
    ## Duration equivalent numeric values in fixed-length days.
    ##
    ## @code{@var{X} = days (@var{D})} converts durations in @var{D} to the
    ## equivalent number of fixed-length days (1 day equals 24 hours).  @var{X}
    ## is a double array of the same size as @var{D}.
    ##
    ## @end deftypefn
    function out = days (this)
      out = this.Millis / 86400000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} hours (@var{D})
    ##
    ## Duration equivalent numeric values in hours.
    ##
    ## @code{@var{X} = hours (@var{D})} converts durations in @var{D} to the
    ## equivalent number of hours.  @var{X} is a double array of the same size
    ## as @var{D}.
    ##
    ## @end deftypefn
    function out = hours (this)
      out = this.Millis / 3600000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} minutes (@var{D})
    ##
    ## Duration equivalent numeric values in minutes.
    ##
    ## @code{@var{X} = minutes (@var{D})} converts durations in @var{D} to the
    ## equivalent number of minutes.  @var{X} is a double array of the same size
    ## as @var{D}.
    ##
    ## @end deftypefn
    function out = minutes (this)
      out = this.Millis / 60000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} seconds (@var{D})
    ##
    ## Duration equivalent numeric values in seconds.
    ##
    ## @code{@var{X} = seconds (@var{D})} converts durations in @var{D} to the
    ## equivalent number of seconds.  @var{X} is a double array of the same size
    ## as @var{D}.
    ##
    ## @end deftypefn
    function out = seconds (this)
      out = this.Millis / 1000;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{X} =} milliseconds (@var{D})
    ##
    ## Duration equivalent numeric values in milliseconds.
    ##
    ## @code{@var{X} = milliseconds (@var{D})} converts durations in @var{D} to
    ## the equivalent number of milliseconds.  @var{X} is a double array of the
    ## same size as @var{D}.
    ##
    ## @end deftypefn
    function out = milliseconds (this)
      out = this.Millis;
    endfunction

  endmethods

################################################################################
##                         ** Summary Information **                          ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'size'             'ndims'            'numel'            'nnz'             ##
## 'length'           'keyHash'                                               ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{sz} =} size (@var{D})
    ## @deftypefnx {duration} {@var{dim_sz} =} size (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{dim_sz} =} size (@var{D}, @var{d1}, @var{d2}, @dots{})
    ## @deftypefnx {duration} {[@var{rows}, @var{columns}, @dots{}, @var{dim_n_sz}] =} size (@dots{})
    ##
    ## Return the size of a duration array.
    ##
    ## @code{@var{sz} = size (@var{D})} returns a row vector with the size
    ## (number of elements) of each dimension for the duration array @var{D}.
    ##
    ## @code{@var{dim_sz} = size (@var{D}, @var{dim})} returns the size of
    ## the corresponding dimension specified in @var{dim}.  If @var{dim} is a
    ## vector, then @var{dim_sz} is a vector of the same length and with each
    ## element corresponding to a specified dimension.  Multiple dimensions may
    ## also be specified as separate arguments.
    ##
    ## With a single output argument, @code{size} returns a row vector.  With
    ## several, the size of dimension N is returned in the Nth argument.
    ## Asking for fewer output arguments than the array has dimensions folds
    ## the trailing dimensions into the last one, so @code{[r, c] = size
    ## (@var{D})} on a 2-by-2-by-2 array returns 2 and 4; asking for more pads
    ## with ones.  When a dimension is named, however, the number of output
    ## arguments must equal the number of dimensions requested.
    ##
    ## @end deftypefn
    function varargout = size (this, varargin)
      if (! isempty (varargin))
        ## A named dimension fixes how many outputs there may be.
        sz = size (this.Millis, varargin{:});
        if (nargout > 1 && numel (sz) != nargout)
          error (strcat ("duration.size: nargout does not match the",
                         " number of requested dimensions."));
        endif
      else
        sz = size (this.Millis);
        ## With no dimension named, asking for more outputs than the array has
        ## dimensions pads with ones, and asking for fewer folds the trailing
        ## dimensions into the last output, as core Octave and MATLAB both do.
        if (nargout > numel (sz))
          sz = [sz, ones(1, nargout - numel (sz))];
        elseif (nargout > 1 && nargout < numel (sz))
          sz = [sz(1:nargout-1), prod(sz(nargout:end))];
        endif
      endif
      if (nargout == 0 || nargout == 1)
        varargout{1} = sz;
      else
        for i = 1:nargout
          varargout{i} = sz(i);
        endfor
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{out} =} ndims (@var{D})
    ##
    ## Number of dimensions in a duration array.
    ##
    ## @code{@var{out} = ndims (@var{D})} returns the number of dimensions of
    ## the duration array @var{D}.
    ##
    ## @end deftypefn
    function out = ndims (this)
      out = ndims (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{out} =} numel (@var{D})
    ##
    ## Total number of elements in a duration array.
    ##
    ## @code{@var{out} = numel (@var{D})} returns the number of elements in the
    ## duration array @var{D}.
    ##
    ## @end deftypefn
    function out = numel (this, varargin)
      out = numel (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{out} =} nnz (@var{D})
    ##
    ## Number of nonzero elements in duration array.
    ##
    ## @code{@var{out} = nnz (@var{D})} returns the number of nonzero
    ## elements in the duration array @var{D}.
    ##
    ## @end deftypefn
    function out = nnz (this)
      d = this.Millis(:);
      out = numel (d) - sum (d == 0);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{N} =} length (@var{D})
    ##
    ## Length of a duration vector.
    ##
    ## @code{@var{N} = length (@var{D})} returns the size of the longest
    ## dimension of the duration array @var{D}, unless any of its dimensions has
    ## zero length, in which case @code{length (@var{D})} returns 0.
    ##
    ## @end deftypefn
    function N = length (this)
      if (isempty (this.Millis))
        N = 0;
      else
        N = max (size (this.Millis));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{key} =} keyHash (@var{D})
    ## @deftypefnx {duration} {@var{key} =} keyHash (@var{D}, @var{base})
    ##
    ## Generate a hash code for duration array.
    ##
    ## @code{@var{key} = keyHash (@var{D})} generates a @qcode{uint64} scalar
    ## that represents the input array @var{D}.  @code{keyHash} utilizes the
    ## 64-bit FNV-1a variant of the Fowler-Noll-Vo non-cryptographic hash
    ## function.
    ##
    ## @code{@var{key} = keyHash (@var{D}, @var{base})} also generates a 64-bit
    ## hash code using @var{base} as the offset basis for the FNV-1a hash
    ## algorithm.  @var{base} must be a @qcode{uint64} integer type scalar.  Use
    ## this syntax to cascade @code{keyHash} on multiple objects for which a
    ## single hash code is required.
    ##
    ## A duration array is keyed on its length in milliseconds, so the unit it
    ## was written in is not part of the key and @code{seconds (1)} hashes as
    ## @code{milliseconds (1000)}.  A missing duration is keyed alike whatever
    ## produced its @qcode{NaN}.  The @qcode{Format} property is display only
    ## and is not part of the key.  Two arrays that @code{keyMatch} reports as
    ## the same key always hash alike.
    ##
    ## Note that unlike MATLAB, this implementation does not use any random
    ## seed.  As a result, @code{keyHash} will always generate the exact same
    ## hash key for any particular input across different workers and Octave
    ## sessions.
    ##
    ## @end deftypefn
    function key = keyHash (this, base = [])
      ## Initialize string with size and class name
      size_str = sprintf ('%dx', size (this.Millis))(1:end-1);
      init_str = [size_str class(this)];
      if (! isempty (base))
        if (! (isscalar (base) && isa (base, 'uint64')))
          error ("duration.keyHash: BASE must be a UINT64 scalar.");
        endif
        key = __ckeyHash__(init_str, base);
      else
        key = __ckeyHash__(init_str);
      endif
      if (! isempty (this.Millis))
        key = __nkeyHash__(this.Millis(:), key);
      endif
    endfunction

  endmethods

################################################################################
##                          ** Query Operations **                            ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'isbetween'        'iscolumn'         'isempty'          'isequal'         ##
## 'isequaln'         'isfinite'         'isinf'            'ismatrix'        ##
## 'ismember'         'ismissing'        'isnan'            'isregular'       ##
## 'isrow'            'isscalar'         'issorted'         'issortedrows'    ##
## 'isvector'                                                                 ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} isbetween (@var{D}, @var{lower}, @var{upper})
    ## @deftypefnx {duration} {@var{TF} =} isbetween (@var{D}, @var{lower}, @var{upper}, @var{intervalType})
    ##
    ## Find duration elements within specified range.
    ##
    ## @code{@var{TF} = isbetween (@var{D}, @var{lower}, @var{upper})} returns a
    ## logical array, @var{TF}, which is the same size as the input duration
    ## array @var{D} and it contains @qcode{true} for each corresponding element
    ## which is within the range specified by @var{lower} and @var{upper} and
    ## @qcode{false} otherwise.  @var{lower} and @var{upper} must be duration
    ## arrays of compatible size with @var{D} or alternatively they can be
    ## specified as a character vector, a cell array of character vectors or a
    ## string array containing valid text duration representations.
    ##
    ## @code{@var{TF} = isbetween (@var{D}, @var{lower}, @var{upper},
    ## @var{intervalType})} specifies the type of interval for the @var{lower}
    ## and @var{upper} bounds and it can be one of the following values.
    ##
    ## @itemize
    ## @item @qcode{'closed'} (default) includes lower and upper bounds.
    ##
    ## @item @qcode{'open'} excludes lower and upper bounds.
    ##
    ## @item @qcode{'openleft'} or @qcode{'closedright'} exclude the lower and
    ## include the upper bound.  They have identical behavior.
    ##
    ## @item @qcode{'closedleft'} or @qcode{'openright'} include the lower and
    ## exclude the upper bound.  They have identical behavior.
    ## @end itemize
    ##
    ## @var{intervalType} can be specified either as a character vector or a
    ## string scalar.
    ##
    ## @end deftypefn
    function TF = isbetween (this, lower, upper, varargin)
      if (nargin < 3)
        error ("duration.isbetween: too few input arguments.");
      elseif (nargin == 3)
        intervaltype = 'closed';
      elseif (nargin == 4)
        intervaltype = varargin{1};
      elseif (nargin > 4)
        error (strcat ("duration.isbetween: optional paired arguments", ...
                       " are not supported for duration arrays."));
      endif
      if (isnumeric (lower) || isnumeric (upper))
        error ("duration.isbetween: LOWER and UPPER cannot be numeric.");
      endif
      if (strcmpi (intervaltype, 'closed'))
        TF = lower <= this & this <= upper;
      elseif (strcmpi (intervaltype, 'open'))
        TF = lower < this & this < upper;
      elseif (any (strcmpi (intervaltype, {'openleft', 'closedright'})))
        TF = lower < this & this <= upper;
      elseif (any (strcmpi (intervaltype, {'openright', 'closedleft'})))
        TF = lower <= this & this < upper;
      else
        error ("duration.isbetween: invalid INTERVALTYPE option.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} iscolumn (@var{D})
    ##
    ## Return true if duration array is a column vector.
    ##
    ## @code{@var{TF} = iscolumn (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is a column vector
    ## and @qcode{false} otherwise.  A column vector is a 2-D array for which
    ## @code{size (@var{D})} returns @code{[@var{N}, 1]} with non-negative
    ## @var{N}.  By definition, a scalar is also a column vector.
    ##
    ## @end deftypefn
    function TF = iscolumn (this)
      TF = iscolumn (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isempty (@var{D})
    ##
    ## Return true if duration array is empty.
    ##
    ## @code{@var{TF} = isempty (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is empty and
    ## @qcode{false} otherwise.
    ##
    ## @end deftypefn
    function TF = isempty (this)
      TF = isempty (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} isequal (@var{D1}, @var{D2})
    ## @deftypefnx {duration} {@var{TF} =} isequal (@var{D1}, @var{D2}, @dots{})
    ##
    ## Return true if duration arrays are equal.
    ##
    ## @code{@var{TF} = isequal (@var{D1}, @var{D2})} returns a logical scalar
    ## @var{TF}, which is @qcode{true}, if the duration arrays @var{D1} and
    ## @var{D2} contain the same values, and @qcode{false} otherwise.  Either
    ## @var{D1} or @var{D2} can also be specified as a character vector, a cell
    ## array of character vectors or a string array containing valid text
    ## duration representations.
    ##
    ## @code{@var{TF} = isequal (@var{D1}, @var{D2}, @dots{})} returns a logical
    ## scalar @var{TF}, which is @qcode{true}, if all input arguments are equal,
    ## and @qcode{false} otherwise.
    ##
    ## @end deftypefn
    function TF = isequal (varargin)
      args = varargin;
      [args{:}] = promote (varargin{:});
      mils = cellfun (@(obj) obj.Millis, args, 'UniformOutput', false);
      TF = isequal (mils{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} isequaln (@var{D1}, @var{D2})
    ## @deftypefnx {duration} {@var{TF} =} isequaln (@var{D1}, @var{D2}, @dots{})
    ##
    ## Return true if duration arrays are equal under the assumption that
    ## missing elements are equal.
    ##
    ## @code{@var{TF} = isequaln (@var{D1}, @var{D2})} returns a logical scalar
    ## @var{TF}, which is @qcode{true}, if the duration arrays @var{D1} and
    ## @var{D2} contain the same values or corresponding missing elements, and
    ## @qcode{false} otherwise.  Either @var{D1} or @var{D2} can also be
    ## specified as a character vector, a cell array of character vectors or a
    ## string array containing valid text duration representations.
    ##
    ## @code{@var{TF} = isequaln (@var{D1}, @var{D2}, @dots{})} returns a
    ## logical scalar @var{TF}, which is @qcode{true}, if all input arguments
    ## are equal under the assumption that missing elements are equal, and
    ## @qcode{false} otherwise.
    ##
    ## @end deftypefn
    function TF = isequaln (varargin)
      args = varargin;
      [args{:}] = promote (varargin{:});
      mils = cellfun (@(obj) obj.Millis, args, 'UniformOutput', false);
      TF = isequaln (mils{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isfinite (@var{D})
    ##
    ## Return true for duration elements that are finite.
    ##
    ## @code{@var{TF} = isfinite (@var{D})} returns a logical array @var{TF}
    ## of the same size as @var{calD} containing @qcode{true} for each
    ## corresponding element of @var{D} that is finite and @qcode{false}
    ## otherwise.  Finite elements are those which are neither infinite nor
    ## Not-A-Number.
    ##
    ## @end deftypefn
    function TF = isfinite (this)
      TF = isfinite (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isinf (@var{D})
    ##
    ## Return true for duration elements that are infinite.
    ##
    ## @code{@var{TF} = isinf (@var{D})} returns a logical array @var{TF}
    ## of the same size as @var{D} containing @qcode{true} for each
    ## corresponding element of @var{calD} that is either @qcode{Inf} or
    ## @qcode{-Inf} and @qcode{false} otherwise.
    ##
    ## @end deftypefn
    function TF = isinf (this)
      TF = isinf (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} ismatrix (@var{D})
    ##
    ## Return true if duration array is a 2-D array.
    ##
    ## @code{@var{TF} = ismatrix (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is a matrix and
    ## @qcode{false} otherwise.  A matrix is an array of any type where
    ## @code{ndims (@var{D}) == 2}.  By definition, a scalar is also a matrix.
    ##
    ## @end deftypefn
    function TF = ismatrix (this)
      TF = ismatrix (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} ismember (@var{A}, @var{B})
    ## @deftypefnx {duration} {@var{TF} =} ismember (@var{A}, @var{B}, @qcode{'rows'})
    ## @deftypefnx {duration} {[@var{TF}, @var{index}] =} ismember (@dots{})
    ## @deftypefnx {duration} {[@var{TF}, @var{index}] =} ismember (@dots{}, @qcode{'legacy'})
    ##
    ## Find duration elements in a set.
    ##
    ## @code{@var{TF} = ismember (@var{A}, @var{B})} returns a logical array
    ## @var{TF} of the same size as @var{A} containing @qcode{true} for each
    ## corresponding element of @var{A} that is in @var{B} and @qcode{false}
    ## otherwise.  @qcode{NaN} elements are not equal with each other and always
    ## return @qcode{false}.
    ##
    ## @code{@var{TF} = ismember (@var{A}, @var{B}, @qcode{'rows'})} only
    ## applies to duration matrices with the same number of columns, in which
    ## case the logical vector @var{TF} contains @qcode{true} for each row of
    ## @var{A} that is also a row in @var{B}.  @var{TF} has the same number of
    ## rows as @var{A}.
    ##
    ## @code{[@var{TF}, @var{index}] = ismember (@var{A}, @var{B})} also returns
    ## an index array of the same size as @var{A} containing the lowest index in
    ## @var{B} for each element of @var{A} that is a member of @var{B} and 0
    ## otherwise.  If the @qcode{'rows'} optional argument is used, then the
    ## returning index is a column vector with the same rows as @var{A} and it
    ## contains the lowest index in @var{B} for each row of @var{A} that is a
    ## member of @var{B} and 0 otherwise.  If the @qcode{'legacy'} optional
    ## argument is specified, then the highest index of matched elements is
    ## returned.  Unless multiple matches exist, the @qcode{'legacy'} option has
    ## no effect on the returned @var{index}.
    ##
    ## @end deftypefn
    function varargout = ismember (A, B, varargin)
      ## Check input arguments
      if (! isa (B, 'duration'))
        B = promote (B);
      endif
      ## Check for 'rows' and 'legacy' optional arguments
      if (! isempty (varargin))
        if (! cellfun ('ischar', varargin));
          error ("duration.ismember: all options must be character vectors.");
        elseif (! all (strcmpi (varargin, 'rows') | ...
                       strcmpi (varargin, 'legacy')))
          error (strcat ("duration.ismember: only 'rows' and 'legacy'", ...
                         " are valid options."));
        endif
        do_rows = any (strcmpi ('rows', varargin));
        if (do_rows)
          if (ndims (A) != 2 || ndims (A) != ndims (B))
            error ("duration.ismember: 'rows' applies only to 2-D matrices.");
          endif
          if (size (A, 2) != size (B, 2))
            error (strcat ("duration.ismember: 'rows' requires same", ...
                           " number of columns."));
          endif
        endif
        if (nargout > 1)
          [varargout{1}, varargout{2}] = __ismember__ (A.Millis, B.Millis, ...
                                                       varargin{:});
        else
          varargout{1} = __ismember__ (A.Millis, B.Millis, varargin{:});
        endif
      else
        if (nargout > 1)
          [varargout{1}, varargout{2}] = __ismember__ (A.Millis, B.Millis);
        else
          varargout{1} = __ismember__ (A.Millis, B.Millis);
        endif
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} ismissing (@var{D})
    ## @deftypefnx {duration} {@var{TF} =} ismissing (@var{D}, @var{indicator})
    ##
    ## Find missing elements in duration array.
    ##
    ## @code{@var{TF} = ismissing (@var{D})} returns a logical array, @var{TF},
    ## with the same dimensions as @var{D}, where @code{true} values match the
    ## standard missing values in the input duration array.
    ##
    ## The optional input @var{indicator} can be a scalar or a vector duration
    ## array, specifying alternative missing values in the input data.  When
    ## specifying @var{indicator} values, the standard missing values are
    ## ignored, unless explicitly stated in the @var{indicator}.
    ##
    ## @end deftypefn
    function TF = ismissing (this, varargin)
      if (nargin > 2)
        error ("duration.ismissing: too many input arguments.");
      endif
      if (! isempty (varargin))
        indicator = varargin{1};
        TF = false (size (this));
        if (isvector (indicator))
          if (isa (indicator, 'duration'))
            for i = 1:length (indicator)
              TF(this.Millis == indicator.Millis(i)) = true;
            endfor
          else
            error ("duration.ismissing: INDICATOR must be a 'duration' array.");
          endif
        else
          error ("duration.ismissing: INDICATOR must be a vector.");
        endif
      else
        TF = isnan (this.Millis);
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isnan (@var{D})
    ##
    ## Return true for duration elements that are Not-A-Number.
    ##
    ## @code{@var{TF} = isnan (@var{D})} returns a logical array @var{TF} of
    ## the same size as @var{D} containing @qcode{true} for each corresponding
    ## element of @var{calD} that is @qcode{NaN} and @qcode{false} otherwise.
    ##
    ## @end deftypefn
    function TF = isnan (this)
      TF = isnan (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} isregular (@var{D})
    ## @deftypefnx {duration} {@var{TF} =} isregular (@var{D}, @var{COMPONENT})
    ## @deftypefnx {duration} {[@var{TF}, @var{DT}] =} isregular (@dots{})
    ##
    ## Return true if a duration vector is regularly spaced.
    ##
    ## @code{@var{TF} = isregular (@var{D})} returns true when the elements of
    ## the duration vector @var{D} are evenly spaced, that is, when every step
    ## from one element to the next is the same and is not zero.  A second
    ## output @var{DT} gives that step, and is @code{NaN} when there is none.
    ##
    ## A sequence that does not move is not regularly spaced: a step of zero
    ## describes no spacing, so @code{isregular} of a constant vector is false.
    ## A descending vector is regular, with a negative step.  A @code{NaN} or an
    ## infinite element anywhere makes the vector irregular, as does having
    ## fewer than two elements, so a scalar and an empty array are both false.
    ## @var{D} must be a vector; a matrix is an error.
    ##
    ## @code{@var{TF} = isregular (@var{D}, @var{COMPONENT})} asks about a
    ## particular component, one of @qcode{'Years'}, @qcode{'Quarters'},
    ## @qcode{'Months'}, @qcode{'Weeks'}, @qcode{'Days'} or @qcode{'Time'}.  A
    ## duration measures elapsed time and knows nothing of a calendar, so only
    ## @qcode{'Time'}, the default, can be true; every calendar component is
    ## false however the vector is spaced.  The argument exists so that a
    ## duration can be asked the same question as a @code{datetime}.
    ##
    ## Steps are compared within a few @code{eps} of the largest value present
    ## rather than exactly, because subtracting neighbouring durations rounds:
    ## even one, two and three hours have steps differing in the last bit, and
    ## an exact test would call that irregular.  MATLAB tolerates a difference
    ## of about the same size, for the same reason.
    ##
    ## @strong{Deviation from MATLAB.}  A negative step is returned there
    ## formatted in seconds whatever the vector's own format; here the step
    ## keeps @var{D}'s format whichever way the vector runs.
    ##
    ## @end deftypefn
    function [TF, DT] = isregular (this, component = 'time')
      comps = {'time', 'years', 'quarters', 'months', 'weeks', 'days'};
      if (! (ischar (component) && isrow (component)
             && any (strcmpi (component, comps))))
        error (strcat ("duration.isregular: COMPONENT must be 'Years',", ...
                       " 'Quarters', 'Months', 'Weeks', 'Days', or 'Time'."));
      endif
      DT = duration (0, 0, NaN);
      ## Only elapsed time can be regular: a duration has no calendar for a
      ## calendar component to be counted against.
      if (! strcmpi (component, 'time'))
        TF = false;
        return;
      endif
      ## Fewer than two elements have no step to be regular about.
      if (numel (this) < 2)
        TF = false;
        return;
      elseif (! isvector (this))
        error ("duration.isregular: input must be a duration vector.");
      endif
      d = diff (this);
      ds = milliseconds (d);
      ## Steps are compared within a few eps of the largest value present, not
      ## exactly.  Subtracting neighbouring durations can round in the last bit,
      ## and an exact test would then call a plainly regular vector irregular.
      ## The tolerance is taken from the values rather than the steps, since
      ## that is where the rounding comes from, and matches MATLAB's own.
      scale = max (abs (milliseconds (this)(:)));
      if (! isfinite (scale))
        scale = 0;
      endif
      tol = 4 * eps (scale);
      TF = isfinite (ds(1)) && ds(1) != 0 ...
           && all (abs (ds(:) - ds(1)) <= tol);
      if (TF)
        ## Build the scalar step by setting the value rather than by indexing:
        ## inside the class's own methods, d(1) does not go through subsref and
        ## hands back the whole array.
        DT = d;
        DT.Millis = ds(1);
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isrow (@var{D})
    ##
    ## Return true if duration array is a row vector.
    ##
    ## @code{@var{TF} = isrow (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is a row vector
    ## and @qcode{false} otherwise.  A row vector is a 2-D array for which
    ## @code{size (@var{D})} returns @code{[1, @var{N}]} with non-negative
    ## @var{N}.  By definition, a scalar is also a row vector.
    ##
    ## @end deftypefn
    function TF = isrow (this)
      TF = isrow (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isscalar (@var{D})
    ##
    ## Return true if duration array is a scalar.
    ##
    ## @code{@var{TF} = isscalar (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is also a scalar
    ## and @qcode{false} otherwise.  A scalar is a single element object for
    ## which @code{size (@var{D})} returns @code{[1, 1]}.
    ##
    ## @end deftypefn
    function TF = isscalar (this)
      TF = isscalar (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} issorted (@var{D})
    ## @deftypefnx {duration} {@var{TF} =} issorted (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{TF} =} issorted (@var{D}, @var{direction})
    ## @deftypefnx {duration} {@var{TF} =} issorted (@var{D}, @var{dim}, @var{direction})
    ## @deftypefnx {duration} {@var{TF} =} issorted (@dots{}, @qcode{'MissingPlacement'}, @var{MP})
    ## @deftypefnx {duration} {@var{TF} =} issorted (@dots{}, @qcode{'ComparisonMethod'}, @var{CM})
    ##
    ## Return true if duration array is sorted.
    ##
    ## @code{@var{TF} = issorted (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true}, if the duration array @var{D} is sorted in
    ## ascending order, and @qcode{false} otherwise.
    ##
    ## @code{@var{TF} = issorted (@var{D}, @var{dim})} returns a logical scalar
    ## @var{TF}, which is @qcode{true}, if the duration array @var{D} is
    ## sorted in ascending order along the dimension @var{dim}, and
    ## @qcode{false} otherwise.
    ##
    ## @code{@var{TF} = issorted (@var{D}, @var{direction})} returns a logical
    ## scalar @var{TF}, which is @qcode{true}, if the duration array @var{D}
    ## is sorted in the direction specified by @var{direction}, and
    ## @qcode{false} otherwise.  @var{direction} can be any of the following
    ## options:
    ##
    ## @itemize
    ## @item @qcode{'ascend'}, which is the default, checks is elements are in
    ## ascending order.
    ## @item @qcode{'descend'} checks if elements are in descending order.
    ## @item @qcode{'monotonic'} checks if elements are either in ascending or
    ## descending order.
    ## @item @qcode{'strictascend'} checks if elements are in ascending order
    ## and there are no duplicate or undefined elements.
    ## @item @qcode{'strictdescend'} checks if elements are in descending order
    ## and there are no duplicate or undefined elements.
    ## @item @qcode{'strictmonotonic'} checks if elements are either in
    ## ascending or descending order and there are no duplicate or undefined
    ## elements.
    ## @end itemize
    ##
    ## @code{@var{TF} = issorted (@dots{}, @qcode{'MissingPlacement'},
    ## @var{MP})}
    ## specifies where missing elements (@qcode{NaN}) are placed with one of the
    ## following options specified in @var{MP}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, places missing elements last
    ## for ascending sort and first for descending sort.
    ## @item @qcode{'first'} places missing elements first.
    ## @item @qcode{'last'} places missing elements last.
    ## @end itemize
    ##
    ## @code{@var{TF} = issorted (@dots{}, @qcode{'ComparisonMethod'},
    ## @var{CM})}
    ## specifies the comparison method for determining the order of elements
    ## with one of following options specified in @var{CM}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, sorts by @code{real (A)}.
    ## @item @qcode{'real'} sorts by @code{real (A)}.
    ## @item @qcode{'abs'} sorts by @code{abs (A)}.
    ## @end itemize
    ##
    ## @end deftypefn
    function TF = issorted (this, varargin)
      ## Single input argument
      if (nargin == 1)
        TF = isequaln (this, sort (this));
        return;
      endif

      ## Get operating dimension
      cid = cellfun (@isnumeric, varargin);
      if (any (cid))
        dim = varargin{cid};
      else
        sz = size (this);
        dim = find (sz != 1, 1);
        if (isempty (dim)) # scalar
          dim = 1;
        endif
      endif

      ## Force strings to character vectors
      [varargin{:}] = convertStringsToChars (varargin{:});

      ## Get direction from input argument list
      valid_direction = {'ascend', 'descend', 'monotonic', 'strictascend', ...
                         'strictdescend', 'strictmonotonic'};
      fcn = @(x) ischar (x) && ismember (x, valid_direction);
      cid = cellfun (fcn, varargin);
      if (any (cid))
        direction = lower (varargin{cid});
        switch (direction)
          case {'ascend', 'descend'}
            TF = isequaln (this, sort (this, varargin{:}));

          case 'monotonic'
            ## Check for either ascending or descending
            varargin{cid} = 'ascend';
            TF = isequaln (this, sort (this, varargin{:}));
            if (TF)
              return;
            endif
            varargin{cid} = 'descend';
            TF = isequaln (this, sort (this, varargin{:}));

          case 'strictascend'
            ## Check for missing values first (fast)
            if (any (ismissing (this), 'all'))
              TF = false;
              return;
            endif
            varargin{cid} = strrep (direction, 'strict', '');
            sorted = sort (this, varargin{:});
            if (any (diff (sorted, 1, dim) <= 0, 'all'))
              TF = false;
              return;
            endif
            TF = isequaln (this, sorted);

          case 'strictdescend'
            ## Check for missing values first (fast)
            if (any (ismissing (this), 'all'))
              TF = false;
              return;
            endif
            varargin{cid} = strrep (direction, 'strict', '');
            sorted = sort (this, varargin{:});
            if (any (diff (sorted, 1, dim) >= 0, 'all'))
              TF = false;
              return;
            endif
            TF = isequaln (this, sorted);

          case 'strictmonotonic'
            ## Check missing values first (fast)
            if (any (ismissing (this), 'all'))
              TF = false;
              return;
            endif
            ## Check for either ascending or descending
            varargin{cid} = 'ascend';
            sorted = sort (this, varargin{:});
            if (any (diff (sorted, 1, dim) <= 0, 'all'))
              TF = false;
              return;
            endif
            TF = isequaln (this, sorted);
            if (TF)
              return;
            endif
            varargin{cid} = 'descend';
            sorted = sort (this, varargin{:});
            if (any (diff (sorted, 1, dim) >= 0, 'all'))
              TF = false;
              return;
            endif
            TF = isequaln (this, sorted);
        endswitch
      else
        ## No DIRECTION input argument
        TF = isequaln (this, sort (this, varargin{:}));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{TF} =} issortedrows (@var{D})
    ## @deftypefnx {duration} {@var{TF} =} issortedrows (@var{D}, @var{col})
    ## @deftypefnx {duration} {@var{TF} =} issortedrows (@var{D}, @var{direction})
    ## @deftypefnx {duration} {@var{TF} =} issortedrows (@var{D}, @var{col}, @var{direction})
    ## @deftypefnx {duration} {@var{TF} =} issortedrows (@dots{}, @qcode{'MissingPlacement'}, @var{MP})
    ## @deftypefnx {duration} {@var{TF} =} issortedrows (@dots{}, @qcode{'ComparisonMethod'}, @var{CM})
    ##
    ## Return true if duration matrix rows are sorted.
    ##
    ## @code{@var{TF} = issortedrows (@var{D})} returns a logical scalar
    ## @var{TF}, which is @qcode{true}, if the rows in the 2-D duration array
    ## @var{D} are sorted in ascending order, and @qcode{false} otherwise.
    ##
    ## @code{@var{TF} = issortedrows (@var{D}, @var{col})} returns a logical
    ## scalar @var{TF}, which is @qcode{true}, if the duration array @var{D}
    ## is sorted according to the columns specified by the vector @var{col}, and
    ## @qcode{false} otherwise.  @var{col} must explicitly contain non-zero
    ## integers whose absolute values index existing columns in @var{D}.
    ## Positive elements sort the corresponding columns in ascending order,
    ## while negative elements sort the corresponding columns in descending
    ## order.
    ##
    ## @code{@var{TF} = issortedrows (@var{D}, @var{direction})} checks if the
    ## rows in @var{D} are sorted according to the specified direction, which
    ## can be one of the following options:
    ##
    ## @itemize
    ## @item @qcode{'ascend'}, which is the default, checks is elements are in
    ## ascending order.
    ## @item @qcode{'descend'} checks if elements are in descending order.
    ## @item @qcode{'monotonic'} checks if elements are either in ascending or
    ## descending order.
    ## @item @qcode{'strictascend'} checks if elements are in ascending order
    ## and there are no duplicate or undefined elements.
    ## @item @qcode{'strictdescend'} checks if elements are in descending order
    ## and there are no duplicate or undefined elements.
    ## @item @qcode{'strictmonotonic'} checks if elements are either in
    ## ascending or descending order and there are no duplicate or undefined
    ## elements.
    ## @end itemize
    ##
    ## Alternatively, @var{direction} can be a cell array of character
    ## vectors specifying the sorting direction for each individual column of
    ## @var{D}, in which case the number of elements in @var{direction} must
    ## equal the number of columns in @var{D}.
    ##
    ## @code{@var{TF} = issortedrows (@var{D}, @var{col}, @var{direction})}
    ## checks if the rows in the duration array @var{D} are sorted according
    ## to the columns specified in @var{col} using the corresponding sorting
    ## direction specified in @var{direction}.  In this case, the sign of the
    ## values in @var{col} is ignored.  @var{col} and @var{direction} must have
    ## the same length, but not necessarily the same number of elements as the
    ## columns in @var{D}.
    ##
    ## @code{@var{TF} = issortedrows (@dots{}, @qcode{'MissingPlacement'},
    ## @var{MP})} specifies where missing elements (@qcode{<undefined>}) are
    ## placed with one of the following options specified in @var{MP}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, places missing elements last
    ## for ascending sort and first for descending sort.
    ## @item @qcode{'first'} places missing elements first.
    ## @item @qcode{'last'} places missing elements last.
    ## @end itemize
    ##
    ## @code{@var{TF} = issortedrows (@dots{}, @qcode{'ComparisonMethod'},
    ## @var{CM})} specifies the comparison method for determining the order of
    ## elements with one of following options specified in @var{CM}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, sorts by @code{real (A)}.
    ## @item @qcode{'real'} sorts by @code{real (A)}.
    ## @item @qcode{'abs'} sorts by @code{abs (A)}.
    ## @end itemize
    ##
    ## @end deftypefn
    function TF = issortedrows (this, varargin)
      ## Single input argument
      if (nargin == 1)
        TF = isequaln (this, sortrows (this));
        return;
      endif

      ## Force strings to character vectors or cell arrays of character vectors
      [varargin{:}] = convertStringsToChars (varargin{:});

      ## Get valid direction(s) from input argument list
      valid = {'ascend', 'descend', 'monotonic', 'strictascend', ...
               'strictdescend', 'strictmonotonic'};
      fcn = @(x) (ischar (x) && ismember (x, valid)) || iscellstr (x);
      cid = cellfun (fcn, varargin);
      if (any (cid))
        direction = lower (cellstr (varargin{cid}));

        ## Check for valid type of directions in cellstring
        if (! all (cellfun (@(x) ismember (x, valid), direction)))
          error ("duration.issortedrows: invalid DIRECTION value.");
        endif

        ## Handle non-strict modes first
        if (all (cellfun (@(x) ismember (x, {'ascend', 'descend'}), direction)))
          TF = isequaln (this, sortrows (this, varargin{:}));
          return;
        endif
        simple_types = {'ascend', 'descend', 'monotonic'};
        if (all (cellfun (@(x) ismember (x, simple_types), direction)))
          idx = strcmp (direction, 'monotonic');
          direction{idx} = 'ascend';
          varargin{cid} = direction;
          TF = isequaln (this, sortrows (this, varargin{:}));
          if (TF)
            return;
          endif
          direction{idx} = 'descend';
          varargin{cid} = direction;
          TF = isequaln (this, sortrows (this, varargin{:}));
          return;
        endif

        ## Handle strict modes.  Determine the sort-key column order and the
        ## sort position holding the first strict direction, then derive the
        ## prefix (the columns sorted up to and including that position, on
        ## which the duplicate test operates) and the binding strict column
        ## (the single column on which the missing test operates).  A missing
        ## value in the binding column, or two consecutive sorted rows equal
        ## across the prefix columns, rules out a strict ordering; strict
        ## positions after the first are subsumed by it.
        strict_types = {'strictascend', 'strictdescend', 'strictmonotonic'};
        sflag = cellfun (@(x) ismember (x, strict_types), direction);

        nc = size (this, 2);
        nummask = cellfun (@isnumeric, varargin);
        if (any (nummask))
          col = varargin{nummask};
          ocols = abs (col(:)');
          if (isscalar (direction))
            sflag = repmat (sflag, 1, numel (col));
          elseif (numel (direction) != numel (col))
            error ("duration.issortedrows: COL and DIRECTION mismatch.");
          endif
        else
          ocols = 1:nc;
          if (isscalar (direction))
            sflag = repmat (sflag, 1, nc);
          endif
        endif
        K = find (sflag, 1);
        prefix = ocols(1:K);
        bindcol = ocols(K);

        ## A missing value in the binding strict column rules out strictness.
        if (any (isnan (this.Millis(:,bindcol)), 'all'))
          TF = false;
          return;
        endif

        ## Replace strict modes with their plain counterparts for the sort.
        direction = strrep (direction, 'strict', '');
        varargin{cid} = direction;

        if (all (cellfun (@(x) ismember (x, {'ascend', 'descend'}), direction)))
          sorted = sortrows (this, varargin{:});
          ## No two consecutive rows may tie across the prefix columns.
          tmpcol = sorted.Millis(:, prefix);
          if (any (all (diff (tmpcol, 1, 1) == 0, 2)))
            TF = false;
            return;
          endif
          TF = isequaln (this, sorted);

        else  # a 'monotonic' position also exists
          idx = strcmp (direction, 'monotonic');
          direction(idx) = {'ascend'};
          varargin{cid} = direction;
          sorted = sortrows (this, varargin{:});
          tmpcol = sorted.Millis(:, prefix);
          if (any (all (diff (tmpcol, 1, 1) == 0, 2)))
            TF = false;
            return;
          endif
          TF = isequaln (this, sorted);
          if (TF)
            return;
          endif
          direction(idx) = {'descend'};
          varargin{cid} = direction;
          sorted = sortrows (this, varargin{:});
          tmpcol = sorted.Millis(:, prefix);
          if (any (all (diff (tmpcol, 1, 1) == 0, 2)))
            TF = false;
            return;
          endif
          TF = isequaln (this, sorted);
        endif
      else
        ## No DIRECTION input argument
        TF = isequaln (this, sortrows (this, varargin{:}));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} isvector (@var{D})
    ##
    ## Return true if duration array is a vector.
    ##
    ## @code{@var{TF} = isvector (@var{D})} returns a logical scalar @var{TF},
    ## which is @qcode{true} if the duration array @var{D} is a vector and
    ## @qcode{false} otherwise.  A vector is a 2-D array for which one of the
    ## dimensions is equal to 1 (either @math{1*N} or @math{N*1}).  By
    ## definition, a scalar is also a vector.
    ##
    ## @end deftypefn
    function TF = isvector (this)
      TF = isvector (this.Millis);
    endfunction

  endmethods

################################################################################
##                        ** Relational Operations **                         ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'eq'               'ge'               'gt'               'le'              ##
## 'lt'               'ne'                                                    ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} eq (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = eq (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} == @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## and @var{B} are equal and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = eq (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis == B.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} ge (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = ge (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} >= @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## are greater than or equal to @var{B} and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = ge (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis >= B.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} gt (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = gt (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} > @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## are greater than @var{B} and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = gt (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis > B.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} le (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = le (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} <= @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## are less than or equal to @var{B} and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = le (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis <= B.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} lt (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = lt (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} < @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## are less than @var{B} and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = lt (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis < B.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{TF} =} ne (@var{A}, @var{B})
    ##
    ## Equality for duration arrays.
    ##
    ## @code{@var{TF} = ne (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{TF} = @var{A} != @var{B}} and returns a logical array whose
    ## elements set to @qcode{true} where the corresponding elements of @var{A}
    ## and @var{B} are not equal and set to @qcode{false} otherwise.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they can
    ## be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a character vector, a cell array
    ## of character vectors, or a string array representing duration strings or
    ## a numeric array representing days.
    ##
    ## @end deftypefn
    function TF = ne (A, B)
      [A, B] = promote (A, B);
      TF = A.Millis != B.Millis;
    endfunction

  endmethods

################################################################################
##                       ** Mathematical Operations **                        ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'abs'              'plus'             'uplus'            'minus'           ##
## 'uminus'           'times'            'mtimes'           'ldivide'         ##
## 'rdivide'          'mldivide'         'mrdivide'         'mod'             ##
## 'rem'              'eps'              'colon'            'linspace'        ##
## 'diff'                                                                     ##
## 'sum'              'cumsum'           'min'              'cummin'          ##
## 'max'              'cummax'           'floor'            'ceil'            ##
## 'round'            'sign'                                                  ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} abs (@var{A})
    ##
    ## Absolute value of the elements of a duration array.
    ##
    ## @code{@var{B} = abs (@var{A})} returns the absolute value of each element
    ## in the duration array @var{A}.  The returned duration array @var{B} has
    ## the same size as the input array @var{A}.
    ##
    ## @end deftypefn
    function this = abs (this)
      this.Millis = abs (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} plus (@var{A}, @var{B})
    ##
    ## Addition for duration arrays.
    ##
    ## @code{@var{C} = plus (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{C} = @var{A} + @var{B}} and returns the sum of @var{A} and
    ## @var{B} by adding the corresponding elements.  @var{A} and @var{B} must
    ## be size compatible, which translates to they can be the same size, one
    ## can be scalar, or for every dimension, their dimension sizes must be
    ## equal or one of them must be 1.  The size of @var{C} is determined by the
    ## size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a numeric array in which case its
    ## elements are treated as a number of 24-hour days.  If the second argument
    ## @var{B} is a calendarDuration arrays, then the returned array @var{C} is
    ## also a calendarDuration array.
    ##
    ## @end deftypefn
    function C = plus (A, B)
      ## Overload methods for certain data types
      if (isa (B, 'datetime'))
        C = B + A;
        return;
      endif
      if (isa (B, 'calendarDuration'))
        C = B + A;
        return;
      endif
      if (isa (A, 'duration') && isa (B, 'duration'))
        C = A;
        C.Millis = A.Millis + B.Millis;
      elseif (isnumeric (A))
        C = B;
        C.Millis = double (A) * 86400000 + B.Millis;
      elseif (isnumeric (B))
        C = A;
        C.Millis = A.Millis + double (B) * 86400000;
      else
        error (strcat ("duration: addition is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} uplus (@var{A})
    ##
    ## Unary plus for duration arrays.
    ##
    ## @code{@var{B} = uplus (@var{A})} is the equivalent of the syntax
    ## @code{@var{B} = + @var{A}} and returns the input array unaltered.
    ##
    ## @end deftypefn
    function this = uplus (this)

    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} minus (@var{A}, @var{B})
    ##
    ## Subtraction for duration arrays.
    ##
    ## @code{@var{C} = minus (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{C} = @var{A} - @var{B}} and returns the subtraction of @var{B}
    ## from @var{A} by subtracting the corresponding elements.  @var{A} and
    ## @var{B} must be size compatible, which translates to they can be the same
    ## size, one can be scalar, or for every dimension, their dimension sizes
    ## must be equal or one of them must be 1.  The size of @var{C} is
    ## determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## One of the input arguments can also be a numeric array in which case its
    ## elements are treated as a number of 24-hour days.  If the second argument
    ## @var{B} is a calendarDuration arrays, then the returned array @var{C} is
    ## also a calendarDuration array.
    ##
    ## @end deftypefn
    function C = minus (A, B)
      ## Overload methods for certain data types
      if (isa (B, 'calendarDuration'))
        C = -B + A;
        return;
      endif
      if (isa (A, 'duration') && isa (B, 'duration'))
        C = A;
        C.Millis = A.Millis - B.Millis;
      elseif (isnumeric (A))
        C = B;
        C.Millis = double (A) * 86400000 - B.Millis;
      elseif (isnumeric (B))
        C = A;
        C.Millis = A.Millis - double (B) * 86400000;
      else
        error (strcat ("duration: subtraction is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} uminus (@var{A})
    ##
    ## Unary minus for duration arrays.
    ##
    ## @code{@var{B} = uminus (@var{A})} is the equivalent of the syntax
    ## @code{@var{B} = - @var{A}} and returns the input array with its elements
    ## negated.
    ##
    ## @end deftypefn
    function this = uminus (this)
      this.Millis = - this.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} times (@var{A}, @var{B})
    ##
    ## Element-wise multiplication for duration arrays.
    ##
    ## @code{@var{C} = times (@var{A}, @var{B})} is the equivalent of the syntax
    ## @code{@var{C} = @var{A} .* @var{B}} and returns the element-by-element
    ## multiplication product between the corresponding elements of input arrays
    ## @var{A} and @var{B}, one of which must be a numeric array and the other a
    ## duration array.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they
    ## can be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## @end deftypefn
    function C = times (A, B)
      if (isa (A, 'duration') && isnumeric (B))
        C = A;
        C.Millis = A.Millis .* double (B);
      elseif (isnumeric (A) && isa (B, 'duration'))
        C = B;
        C.Millis = double (A) .* B.Millis;
      else
        error (strcat ("duration: multiplication is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} times (@var{A}, @var{B})
    ##
    ## Matrix multiplication for duration arrays.
    ##
    ## @code{@var{C} = mtimes (@var{A}, @var{B})} is the equivalent of the
    ## syntax @code{@var{C} = @var{A} * @var{B}} and returns the matrix
    ## multiplication product of input arrays @var{A} and @var{B}, one of which
    ## must be a numeric array and the other a duration array.
    ##
    ## The columns of @var{A} must equal the rows of @var{B} and the size of
    ## @var{C} is determined by the rows of @var{A} and the columns of @var{B}.
    ##
    ## @end deftypefn
    function C = mtimes (A, B)
      if (isa (A, 'duration') && isnumeric (B))
        C = A;
        C.Millis = A.Millis * double (B);
      elseif (isnumeric (A) && isa (B, 'duration'))
        C = B;
        C.Millis = double (A) * B.Millis;
      else
        error (strcat ("duration: matrix multiplication is not defined", ...
                       " between '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} ldivide (@var{A}, @var{B})
    ##
    ## Element-wise left division for duration arrays.
    ##
    ## @code{@var{C} = ldivide (@var{A}, @var{B})} is the equivalent of the
    ## syntax @code{@var{C} = @var{A} .\ @var{B}} and returns the element-wise
    ## division of the duration array @var{B} by the corresponding elements of
    ## input array @var{A}, which can either be a duration or a numeric array.
    ## If @var{A} is a duration array, then @var{C} is a double numeric array.
    ## If @var{A} is a numeric array, then @var{C} is a duration array.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they
    ## can be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## @end deftypefn
    function C = ldivide (A, B)
      if (! isa (B, 'duration'))
        error (strcat ("duration: right-hand side must be a duration", ...
                       " array for left division: got '%s'"), class (B));
      endif
      if (isa (A, 'duration'))
        C = A.Millis .\ B.Millis;
      elseif (isnumeric (A))
        C = B;
        C.Millis = double (A) .\ B.Millis;
      else
        error (strcat ("duration: left division is not defined", ...
                       " between '%s' and 'duration' arrays."), class (A));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} rdivide (@var{A}, @var{B})
    ##
    ## Element-wise right division for duration arrays.
    ##
    ## @code{@var{C} = rdivide (@var{A}, @var{B})} is the equivalent of the
    ## syntax @code{@var{C} = @var{A} ./ @var{B}} and returns the element-wise
    ## division of the duration array @var{A} by the corresponding elements of
    ## input array @var{B}, which can either be a duration or a numeric array.
    ## If @var{B} is a duration array, then @var{C} is a double numeric array.
    ## If @var{B} is a numeric array, then @var{C} is a duration array.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they
    ## can be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## @end deftypefn
    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} mod (@var{A}, @var{B})
    ##
    ## Remainder after division of duration arrays, with the sign of the divisor.
    ##
    ## @code{@var{C} = mod (@var{A}, @var{B})} returns the remainder left after
    ## dividing @var{A} by @var{B}, as a @code{duration} array of the size the
    ## two broadcast to.  At least one of @var{A} and @var{B} must be a
    ## @code{duration}; the other may be a @code{duration} or a numeric array,
    ## which is read as a number of days, the unit a @code{duration} counts in.
    ##
    ## The result takes its sign from @var{B} and is zero when @var{B} is, which
    ## is what distinguishes @code{mod} from @code{rem}: @code{mod} of an hour
    ## by @math{-1} day differs from @code{rem} of the same.  A remainder by a
    ## zero duration is @var{A} itself.  The display format is taken from
    ## whichever operand is a @code{duration}, or from @var{A} when both are.
    ##
    ## @end deftypefn
    function C = mod (A, B)
      if (isa (A, 'duration') && isa (B, 'duration'))
        C = A;
        C.Millis = mod (A.Millis, B.Millis);
      elseif (isa (A, 'duration') && isnumeric (B))
        C = A;
        C.Millis = mod (A.Millis, double (B) * 86400000);
      elseif (isnumeric (A) && isa (B, 'duration'))
        C = B;
        C.Millis = mod (double (A) * 86400000, B.Millis);
      else
        error (strcat ("duration: 'mod' is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} rem (@var{A}, @var{B})
    ##
    ## Remainder after division of duration arrays, with the sign of the
    ## dividend.
    ##
    ## @code{@var{C} = rem (@var{A}, @var{B})} returns the remainder left after
    ## dividing @var{A} by @var{B}, as a @code{duration} array of the size the
    ## two broadcast to.  At least one of @var{A} and @var{B} must be a
    ## @code{duration}; the other may be a @code{duration} or a numeric array,
    ## which is read as a number of days, the unit a @code{duration} counts in.
    ##
    ## The result takes its sign from @var{A}, where @code{mod} takes it from
    ## @var{B}: the two agree only where the operands share a sign.  A remainder
    ## by a zero duration is @code{NaN}, where @code{mod} gives @var{A} itself.
    ## The display format is taken from whichever operand is a @code{duration},
    ## or from @var{A} when both are.
    ##
    ## @end deftypefn
    function C = rem (A, B)
      if (isa (A, 'duration') && isa (B, 'duration'))
        C = A;
        C.Millis = rem (A.Millis, B.Millis);
      elseif (isa (A, 'duration') && isnumeric (B))
        C = A;
        C.Millis = rem (A.Millis, double (B) * 86400000);
      elseif (isnumeric (A) && isa (B, 'duration'))
        C = B;
        C.Millis = rem (double (A) * 86400000, B.Millis);
      else
        error (strcat ("duration: 'rem' is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} mldivide (@var{A}, @var{B})
    ##
    ## Left division of duration arrays, @code{@var{A} \ @var{B}}.
    ##
    ## @code{@var{C} = mldivide (@var{A}, @var{B})} divides @var{B} by @var{A}.
    ## The denominator @var{A} decides what the result means and must be a
    ## scalar.  Dividing a @code{duration} by a number scales it, giving a
    ## @code{duration}; dividing one @code{duration} by another gives how many
    ## times one goes into the other, a plain number carrying no unit.  A zero
    ## denominator gives @code{Inf}, as it does for numbers.
    ##
    ## Dividing a number by a @code{duration} is not defined, having no meaning,
    ## and neither is a non-scalar denominator.  The display format of a
    ## @code{duration} result is that of @var{B}.
    ##
    ## Unlike MATLAB, an integer denominator is accepted and converted, as it is
    ## by @code{rdivide} and @code{times} here; MATLAB requires a @code{double}
    ## while accepting a @code{logical}, which the same rule cannot explain.
    ##
    ## @end deftypefn
    function C = mldivide (A, B)
      if (isa (A, 'duration'))
        if (! isa (B, 'duration'))
          error (strcat ("duration: left division of a '%s' array by a", ...
                         " duration is not defined."), class (B));
        elseif (! isscalar (A))
          error (strcat ("duration: the denominator in left division must", ...
                         " be a scalar."));
        endif
        C = B.Millis ./ A.Millis;
      elseif (isnumeric (A) || islogical (A))
        if (! isa (B, 'duration'))
          error (strcat ("duration: left division is not defined between", ...
                         " '%s' and '%s' arrays."), class (A), class (B));
        elseif (! isscalar (A))
          error (strcat ("duration: the denominator in left division must", ...
                         " be a scalar."));
        elseif (! isreal (A))
          error (strcat ("duration: the denominator in left division must", ...
                         " be real."));
        endif
        C = B;
        C.Millis = B.Millis ./ double (A);
      else
        error (strcat ("duration: left division is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} mrdivide (@var{A}, @var{B})
    ##
    ## Right division of duration arrays, @code{@var{A} / @var{B}}.
    ##
    ## @code{@var{C} = mrdivide (@var{A}, @var{B})} divides @var{A} by @var{B}
    ## and is the mirror of @code{mldivide}: @code{@var{A} / @var{B}} is
    ## @code{@var{B} \ @var{A}}.  The denominator @var{B} decides what the
    ## result means and must be a scalar.  Dividing a @code{duration} by a
    ## number scales it, giving a @code{duration}; dividing one @code{duration}
    ## by another gives how many times one goes into the other, a plain number
    ## carrying no unit.
    ##
    ## Dividing a number by a @code{duration} is not defined, and neither is a
    ## non-scalar denominator.  For element-wise division by an array of
    ## divisors, see @code{rdivide}.
    ##
    ## @end deftypefn
    function C = mrdivide (A, B)
      if (isa (B, 'duration'))
        if (! isa (A, 'duration'))
          error (strcat ("duration: right division of a '%s' array by a", ...
                         " duration is not defined."), class (A));
        elseif (! isscalar (B))
          error (strcat ("duration: the denominator in right division must", ...
                         " be a scalar."));
        endif
        C = A.Millis ./ B.Millis;
      elseif (isnumeric (B) || islogical (B))
        if (! isa (A, 'duration'))
          error (strcat ("duration: right division is not defined between", ...
                         " '%s' and '%s' arrays."), class (A), class (B));
        elseif (! isscalar (B))
          error (strcat ("duration: the denominator in right division must", ...
                         " be a scalar."));
        elseif (! isreal (B))
          error (strcat ("duration: the denominator in right division must", ...
                         " be real."));
        endif
        C = A;
        C.Millis = A.Millis ./ double (B);
      else
        error (strcat ("duration: right division is not defined between", ...
                       " '%s' and '%s' arrays."), class (A), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{E} =} eps (@var{D})
    ##
    ## Spacing of duration values.
    ##
    ## @code{@var{E} = eps (@var{D})} returns the distance from each element of
    ## @var{D} to the next duration that can be told apart from it, as a
    ## @code{duration} array of the same size.  It is the resolution available
    ## at that magnitude: two durations closer together than this are the same
    ## value.  @code{eps} of a negative duration is that of its magnitude, and
    ## @code{eps} of @code{NaN} is @code{NaN}.
    ##
    ## The spacing is that of the milliseconds a @code{duration} is stored in,
    ## which is what MATLAB stores too, so the two agree exactly.
    ##
    ## @end deftypefn
    function E = eps (D)
      E = D;
      E.Millis = eps (D.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} rdivide (@var{A}, @var{B})
    ##
    ## Element-wise right division for duration arrays.
    ##
    ## @code{@var{C} = rdivide (@var{A}, @var{B})} is the equivalent of the
    ## syntax @code{@var{C} = @var{A} ./ @var{B}} and returns the element-wise
    ## division of the duration array @var{A} by the corresponding elements of
    ## input array @var{B}, which can either be a duration or a numeric array.
    ## If @var{B} is a duration array, then @var{C} is a double numeric array.
    ## If @var{B} is a numeric array, then @var{C} is a duration array.
    ##
    ## @var{A} and @var{B} must be size compatible, which translates to they
    ## can be the same size, one can be scalar, or for every dimension, their
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## @end deftypefn
    function C = rdivide (A, B)
      if (! isa (A, 'duration'))
        error (strcat ("duration: left-hand side must be a duration", ...
                       " array for right division: got '%s'"), class (A));
      endif
      if (isa (B, 'duration'))
        C = A.Millis ./ B.Millis;
      elseif (isnumeric (B))
        C = A;
        C.Millis = A.Millis ./ double (B);
      else
        error (strcat ("duration: right division is not defined", ...
                       " between 'duration' and '%s' arrays."), class (B));
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{R} =} colon (@var{Base}, @var{Limit})
    ## @deftypefnx {duration} {@var{R} =} colon (@var{Base}, @var{Increment}, @var{Limit})
    ##
    ## Create a range of durations in a vector.
    ##
    ## @code{@var{R} = colon (@var{Base}, @var{Limit})} is the equivalent of the
    ## syntax @code{@var{C} = @var{Base}:@var{Limit}} and returns a duration
    ## vector in the range from @var{Base} to @var{Limit} incremented by 24-hour
    ## days.
    ##
    ## @code{@var{R} = colon (@var{Base}, @var{Increment}, @var{Limit})} is
    ## equivalent to @code{@var{C} = @var{Base}:@var{Increment}:@var{Limit}}.
    ## dimension sizes must be equal or one of them must be 1.  The size of
    ## @var{C} is determined by the size compatibility of @var{A} and @var{B}.
    ##
    ## As long as one of the inputs is a duration scalar, the following types
    ## are additionally supported for the remaining input arguments:
    ##
    ## @itemize
    ## @item numeric scalar (24-hour day)
    ## @item character vector (duration string)
    ## @item cellstr scalar (duration string)
    ## @item string scalar (duration string)
    ## @end itemize
    ##
    ## @end deftypefn
    function R = colon (varargin)
      if (nargin < 2 || nargin > 3)
        error ("duration.colon: invalid number of input arguments.");
      endif
      idx = find (cellfun ('isduration', varargin), 1);
      R = varargin{idx};
      if (nargin == 2)
        [from, to] = promote (varargin{:});
        if (! isscalar (from) || ! isscalar (to))
          error ("duration.colon: input arguments must be scalars.");
        endif
        increment = days (1);
      else
        [from, increment, to] = promote (varargin{:});
        if (! isscalar (from) || ! isscalar (increment) || ! isscalar (to))
          error ("duration.colon: input arguments must be scalars.");
        endif
      endif
      R.Millis = from.Millis:increment.Millis:to.Millis;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{R} =} linspace (@var{Start}, @var{End})
    ## @deftypefnx {duration} {@var{R} =} linspace (@var{Start}, @var{End}, @var{N})
    ##
    ## Create linearly spaced duration elements.
    ##
    ## @code{@var{R} = linspace (@var{Start}, @var{End})} returns 100 linearly
    ## spaced elements between @var{Start} and @var{End}.  If @var{Start} and
    ## @var{End} are scalars, then @var{R} is a vector.  If one or both inputs
    ## are vectors, then @var{R} is a matrix where each row is an independent
    ## sequence between @code{@var{Start}(idx_N)} and @code{@var{End}(idx_N)}.
    ##
    ## @code{@var{R} = linspace (@var{Start}, @var{End}, @var{N})} specifies the
    ## number (default is 100) of equally spaced elements between @var{Start}
    ## and @var{End}.  If @var{N} is not an integer value, then it is floored
    ## to the nearest integer.  If @var{N} is zero or negative, then an empty
    ## matrix is returned.  If @var{N} is one, then @var{End} is returned.
    ## If @var{N} greater than one, then @var{Start} and @var{End} are always
    ## included in the range.
    ##
    ## Either @var{Start} or @var{End} input arguments can also be one of the
    ## following types:
    ##
    ## @itemize
    ## @item numeric scalar or vector (24-hour days)
    ## @item character vector (duration string)
    ## @item cellstr scalar or vector (duration strings)
    ## @item string scalar or vector (duration strings)
    ## @end itemize
    ##
    ## @end deftypefn
    function R = linspace (A, B, n = 100)
      if (nargin < 2)
        error ("duration.linspace: too few input arguments.");
      endif
      if (isduration (A))
        R = A;
      else
        R = B;
      endif
      [A, B] = promote (A, B);
      R.Millis = linspace (A.Millis, B.Millis, n);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{DT} =} diff (@var{D})
    ## @deftypefnx {duration} {@var{DT} =} diff (@var{D}, @var{K})
    ## @deftypefnx {duration} {@var{DT} =} diff (@var{D}, @var{K}, @var{DIM})
    ##
    ## Compute differences between adjacent elements in a duration array.
    ##
    ## This method overloads the core @code{diff} function for duration arrays.
    ## The functionality is identical to core @code{diff} function.  Type
    ## @code{help diff} for more information.
    ##
    ## @end deftypefn
    function this = diff (this, varargin)
      this.Millis = diff (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{S} =} sum (@var{D})
    ## @deftypefnx {duration} {@var{S} =} sum (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{S} =} sum (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{S} =} sum (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{S} =} sum (@dots{}, @var{nanflag})
    ##
    ## Compute the sum of the elements of a duration array.
    ##
    ## This method overloads the core @code{sum} function for duration arrays.
    ## The functionality is identical to core @code{sum} function.  Type
    ## @code{help sum} for more information.
    ##
    ## @end deftypefn
    function this = sum (this, varargin)
      ## Force strings to character vectors or cell arrays of character vectors
      if (any (cellfun ('isstring', varargin)))
        [varargin{:}] = convertStringsToChars (varargin{:});
      endif
      this.Millis = sum (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{CS} =} cumsum (@var{D})
    ## @deftypefnx {duration} {@var{CS} =} cumsum (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{CS} =} cumsum (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{CS} =} cumsum (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{CS} =} cumsum (@dots{}, @var{direction})
    ## @deftypefnx {duration} {@var{CS} =} cumsum (@dots{}, @var{nanflag})
    ##
    ## Compute the cumulative sum of the elements of a duration array.
    ##
    ## This method overloads the core @code{cumsum} function for duration
    ## arrays. The functionality is identical to core @code{cumsum} function.
    ## Type @code{help cumsum} for more information.
    ##
    ## @end deftypefn
    function this = cumsum (this, varargin)
      ## Force strings to character vectors or cell arrays of character vectors
      if (any (cellfun ('isstring', varargin)))
        [varargin{:}] = convertStringsToChars (varargin{:});
      endif
      this.Millis = cumsum (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} min (@var{D})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D}, @qcode{[]}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D}, @qcode{[]}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D}, @qcode{[]}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D}, @qcode{[]}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D}, @qcode{[]}, @dots{}, @var{nanflag})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} min (@dots{})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} min (@dots{}, @qcode{'linear'})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D1}, @var{D2})
    ## @deftypefnx {duration} {@var{M} =} min (@var{D1}, @var{D2}, @var{nanflag})
    ## @deftypefnx {duration} {@dots{} =} min (@dots{}, @qcode{'ComparisonMethod'}, @var{method})
    ##
    ## Find minimum values in duration arrays.
    ##
    ## This method overloads the core @code{min} function for duration
    ## arrays. The functionality is identical to core @code{min} function.
    ## Type @code{help min} for more information.
    ##
    ## @end deftypefn
    function varargout = min (D, varargin)
      M = D;
      if (isempty (varargin))
        if (nargout > 1)
          [M.Millis, varargout{2}] = min (D.Millis);
        else
          M.Millis = min (D.Millis);
        endif
        varargout{1} = M;
      else
        ## Force strings to character vectors or cell arrays of character
        ## vectors
        if (any (cellfun ('isstring', varargin)))
          [varargin{:}] = convertStringsToChars (varargin{:});
        endif
        ## Second argument is a duration, or a bare number, which counts
        ## days as it does everywhere else a duration meets a number.
        ## An empty second argument is the reduction form, not an operand.
        if (isduration (varargin{1})
            || (isnumeric (varargin{1}) && ! isempty (varargin{1})))
          D2 = varargin{1};
          if (! isduration (D2))
            D2 = promote (D2);
          endif
          varargin(1) = [];
          ## Make sure first argument is also a duration
          if (! isduration (D))
            D = promote (D);
            M = D2;
          endif
          M.Millis = min (D.Millis, D2.Millis, varargin{:});
          varargout{1} = M;
        else
          if (nargout > 1)
            [M.Millis, varargout{2}] = min (D.Millis, varargin{:});
          else
            M.Millis = min (D.Millis, varargin{:});
          endif
          varargout{1} = M;
        endif
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} cummin (@var{D})
    ## @deftypefnx {duration} {@var{M} =} cummin (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} cummin (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} cummin (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} cummin (@qcode{[]}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} cummin (@qcode{[]}, @var{direction})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} cummin (@dots{})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} cummin (@dots{}, @qcode{'linear'})
    ## @deftypefnx {duration} {@dots{} =} cummin (@dots{}, @qcode{'ComparisonMethod'}, @var{method})
    ##
    ## Return the cumulative minimum values in duration arrays.
    ##
    ## This method overloads the core @code{cummin} function for duration
    ## arrays. The functionality is identical to core @code{cummin} function.
    ## Type @code{help cummin} for more information.
    ##
    ## @end deftypefn
    function varargout = cummin (this, varargin)
      if (isempty (varargin))
        if (nargout > 1)
          [this.Millis, varargout{2}] = cummin (this.Millis);
        else
          this.Millis = cummin (this.Millis);
        endif
        varargout{1} = this;
      else
        ## Force strings to character vectors or cell arrays of character
        ## vectors
        if (any (cellfun ('isstring', varargin)))
          [varargin{:}] = convertStringsToChars (varargin{:});
        endif
        if (nargout > 1)
          [this.Millis, varargout{2}] = cummin (this.Millis, varargin{:});
        else
          this.Millis = cummin (this.Millis, varargin{:});
        endif
        varargout{1} = this;
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} max (@var{D})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D}, @qcode{[]}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D}, @qcode{[]}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D}, @qcode{[]}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D}, @qcode{[]}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D}, @qcode{[]}, @dots{}, @var{nanflag})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} max (@dots{})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} max (@dots{}, @qcode{'linear'})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D1}, @var{D2})
    ## @deftypefnx {duration} {@var{M} =} max (@var{D1}, @var{D2}, @var{nanflag})
    ## @deftypefnx {duration} {@dots{} =} max (@dots{}, @qcode{'ComparisonMethod'}, @var{method})
    ##
    ## Find maximum values in duration arrays.
    ##
    ## This method overloads the core @code{max} function for duration
    ## arrays. The functionality is identical to core @code{max} function.
    ## Type @code{help max} for more information.
    ##
    ## @end deftypefn
    function varargout = max (D, varargin)
      M = D;
      if (isempty (varargin))
        if (nargout > 1)
          [M.Millis, varargout{2}] = max (D.Millis);
        else
          M.Millis = max (D.Millis);
        endif
        varargout{1} = M;
      else
        ## Force strings to character vectors or cell arrays of character
        ## vectors
        if (any (cellfun ('isstring', varargin)))
          [varargin{:}] = convertStringsToChars (varargin{:});
        endif
        ## Second argument is a duration, or a bare number, which counts
        ## days as it does everywhere else a duration meets a number.
        ## An empty second argument is the reduction form, not an operand.
        if (isduration (varargin{1})
            || (isnumeric (varargin{1}) && ! isempty (varargin{1})))
          D2 = varargin{1};
          if (! isduration (D2))
            D2 = promote (D2);
          endif
          varargin(1) = [];
          ## Make sure first argument is also a duration
          if (! isduration (D))
            D = promote (D);
            M = D2;
          endif
          M.Millis = max (D.Millis, D2.Millis, varargin{:});
          varargout{1} = M;
        else
          if (nargout > 1)
            [M.Millis, varargout{2}] = max (D.Millis, varargin{:});
          else
            M.Millis = max (D.Millis, varargin{:});
          endif
          varargout{1} = M;
        endif
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} cummax (@var{D})
    ## @deftypefnx {duration} {@var{M} =} cummax (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} cummax (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} cummax (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} cummax (@qcode{[]}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} cummax (@qcode{[]}, @var{direction})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} cummax (@dots{})
    ## @deftypefnx {duration} {[@var{M}, @var{index}] =} cummax (@dots{}, @qcode{'linear'})
    ## @deftypefnx {duration} {@dots{} =} cummax (@dots{}, @qcode{'ComparisonMethod'}, @var{method})
    ##
    ## Return the cumulative maximum values in duration arrays.
    ##
    ## This method overloads the core @code{cummax} function for duration
    ## arrays. The functionality is identical to core @code{cummax} function.
    ## Type @code{help cummax} for more information.
    ##
    ## @end deftypefn
    function varargout = cummax (this, varargin)
      if (isempty (varargin))
        if (nargout > 1)
          [this.Millis, varargout{2}] = cummax (this.Millis);
        else
          this.Millis = cummax (this.Millis);
        endif
        varargout{1} = this;
      else
        ## Force strings to character vectors or cell arrays of character
        ## vectors
        if (any (cellfun ('isstring', varargin)))
          [varargin{:}] = convertStringsToChars (varargin{:});
        endif
        if (nargout > 1)
          [this.Millis, varargout{2}] = cummax (this.Millis, varargin{:});
        else
          this.Millis = cummax (this.Millis, varargin{:});
        endif
        varargout{1} = this;
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{Y} =} floor (@var{D})
    ## @deftypefnx {duration} {@var{Y} =} floor (@var{D}, @var{unit})
    ##
    ## Round toward negative infinity for duration arrays.
    ##
    ## @code{@var{Y} = floor (@var{D})} rounds each element of the duration
    ## array @var{D} to the largest integer number of seconds not greater than
    ## that element.
    ##
    ## @code{@var{Y} = floor (@var{D}, @var{unit})} rounds each element of the
    ## duration array @var{D} to the largest integer number of the specified
    ## unit of time not greater than that element.  @var{unit} must be one of
    ## the following values:
    ##
    ## @itemize
    ## @item @qcode{'seconds'} (default)
    ## @item @qcode{'minutes'}
    ## @item @qcode{'hours'}
    ## @item @qcode{'days'}
    ## @item @qcode{'years'}
    ## @end itemize
    ##
    ## @end deftypefn
    function this = floor (this, unit = 'seconds')
      if (strcmpi (unit, 'seconds'))
        this.Millis = floor (seconds (this)) * 1000;
      elseif (strcmpi (unit, 'minutes'))
        this.Millis = floor (minutes (this)) * 60000;
      elseif (strcmpi (unit, 'hours'))
        this.Millis = floor (hours (this)) * 3600000;
      elseif (strcmpi (unit, 'days'))
        this.Millis = floor (days (this)) * 86400000;
      elseif (strcmpi (unit, 'years'))
        this.Millis = floor (years (this)) * 31556952000;
      else
        error ("duration.floor: invalid UNIT.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{Y} =} ceil (@var{D})
    ## @deftypefnx {duration} {@var{Y} =} ceil (@var{D}, @var{unit})
    ##
    ## Round toward negative infinity for duration arrays.
    ##
    ## @code{@var{Y} = ceil (@var{D})} rounds each element of the duration
    ## array @var{D} to the smallest integer number of seconds not less than
    ## that element.
    ##
    ## @code{@var{Y} = ceil (@var{D}, @var{unit})} rounds each element of the
    ## duration array @var{D} to the smallest integer number of the specified
    ## unit of time not less than that element.  @var{unit} must be one of the
    ## following values:
    ##
    ## @itemize
    ## @item @qcode{'seconds'} (default)
    ## @item @qcode{'minutes'}
    ## @item @qcode{'hours'}
    ## @item @qcode{'days'}
    ## @item @qcode{'years'}
    ## @end itemize
    ##
    ## @end deftypefn
    function this = ceil (this, unit = 'seconds')
      if (strcmpi (unit, 'seconds'))
        this.Millis = ceil (seconds (this)) * 1000;
      elseif (strcmpi (unit, 'minutes'))
        this.Millis = ceil (minutes (this)) * 60000;
      elseif (strcmpi (unit, 'hours'))
        this.Millis = ceil (hours (this)) * 3600000;
      elseif (strcmpi (unit, 'days'))
        this.Millis = ceil (days (this)) * 86400000;
      elseif (strcmpi (unit, 'years'))
        this.Millis = ceil (years (this)) * 31556952000;
      else
        error ("duration.ceil: invalid UNIT.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{Y} =} round (@var{D})
    ## @deftypefnx {duration} {@var{Y} =} round (@var{D}, @var{unit})
    ##
    ## Round to the nearest integer time unit for duration arrays.
    ##
    ## @code{@var{Y} = round (@var{D})} rounds each element of the duration
    ## array @var{D} to the nearest integer number of seconds to that element.
    ## In case of a tie, return the one further away from zero.
    ##
    ## @code{@var{Y} = round (@var{D}, @var{unit})} rounds each element of the
    ## duration array @var{D} to the nearest integer number of the specified
    ## unit of time to that element.  @var{unit} must be one of the following
    ## values:
    ##
    ## @itemize
    ## @item @qcode{'seconds'} (default)
    ## @item @qcode{'minutes'}
    ## @item @qcode{'hours'}
    ## @item @qcode{'days'}
    ## @item @qcode{'years'}
    ## @end itemize
    ##
    ## @end deftypefn
    function this = round (this, unit = 'seconds')
      if (strcmpi (unit, 'seconds'))
        this.Millis = round (seconds (this)) * 1000;
      elseif (strcmpi (unit, 'minutes'))
        this.Millis = round (minutes (this)) * 60000;
      elseif (strcmpi (unit, 'hours'))
        this.Millis = round (hours (this)) * 3600000;
      elseif (strcmpi (unit, 'days'))
        this.Millis = round (days (this)) * 86400000;
      elseif (strcmpi (unit, 'years'))
        this.Millis = round (years (this)) * 31556952000;
      else
        error ("duration.round: invalid UNIT.");
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{out} =} sign (@var{D})
    ## @deftypefnx {duration} {@var{out} =} sign (@var{D}, @var{unit})
    ##
    ## Compute the signum function for duration arrays.
    ##
    ## @code{@var{out} = sign (@var{D})} returns an array of doubles, @var{out},
    ## the same size as the duration array @var{D}, where each element has one
    ## following values:
    ##
    ## @itemize
    ## @item @qcode{1} if the corresponding element of D is greater than 0.
    ## @item @qcode{0} if the corresponding element of D is equal to 0.
    ## @item @qcode{-1} if the corresponding element of D is less than 0.
    ## @item @qcode{NaN} if the corresponding element of D is a missing value.
    ## @end itemize
    ##
    ## @end deftypefn
    function out = sign (this)
      out = sign (this.Millis);
    endfunction

  endmethods

################################################################################
##                        ** Statistical Operations **                        ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'bounds'           'center'           'histc'            'iqr'             ##
## 'kurtosis'         'mad'              'mape'             'mean'            ##
## 'median'           'mode'             'prctile'          'quantile'        ##
## 'range'            'rmse'             'skewness'         'std'             ##
## 'discretize'       'histcounts'                                            ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {[@var{s}, @var{l}] =} bounds (@var{D})
    ## @deftypefnx {duration} {[@var{s}, @var{l}] =} bounds (@var{D}, @var{dim})
    ## @deftypefnx {duration} {[@var{s}, @var{l}] =} bounds (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {[@var{s}, @var{l}] =} bounds (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {[@var{s}, @var{l}] =} bounds (@dots{}, @var{nanflag})
    ##
    ## Return the smallest and largest values of a duration array.
    ##
    ## This method is a specialization of the core @code{bounds} function for
    ## duration arrays.  The functionality is identical to core @code{bounds}
    ## function.  Type @code{help bounds} for more information.
    ##
    ## @end deftypefn
    function [s, l] = bounds (this, varargin)
      if (nargin < 1 || nargin > 3)
        error ("duration.bounds: invalid number of input arguments.");
      endif
      if (isempty (varargin))
        s = min (this);
        l = max (this);
      else
        s = min (this, [], varargin{:});
        l = max (this, [], varargin{:});
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{C} =} center (@var{D})
    ## @deftypefnx {duration} {@var{C} =} center (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{C} =} center (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{C} =} center (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{C} =} center (@dots{}, @var{nanflag})
    ##
    ## Center values in a duration array.
    ##
    ## This method overloads the core @code{center} function for duration
    ## arrays.  The functionality is identical to core @code{center} function.
    ## Type @code{help center} for more information.
    ##
    ## @end deftypefn
    function this = center (this, varargin)
      this.Millis = center (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{n} =} histc (@var{D}, @var{edges})
    ## @deftypefnx {duration} {@var{n} =} histc (@var{D}, @var{edges}, @var{dim})
    ## @deftypefnx {duration} {[@var{n}, @var{idx}] =} histc (@dots{})
    ##
    ## Compute histogram counts in a duration array.
    ##
    ## This method overloads the core @code{histc} function for duration
    ## arrays.  The functionality is identical to core @code{histc} function.
    ## Type @code{help histc} for more information.
    ##
    ## @end deftypefn
    function varargout = histc (D, varargin)
      ## The edges are given as bare numbers, which count days.
      if (nargout > 1)
        [varargout{1}, varargout{2}] = histc (days (D), varargin{:});
      else
        varargout{1} = histc (days (D), varargin{:});
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{r} =} iqr (@var{D})
    ## @deftypefnx {duration} {@var{r} =} iqr (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{r} =} iqr (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{r} =} iqr (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {[@var{r}, @var{q}] =} iqr (@dots{})
    ##
    ## Compute the interquartile range of a duration array.
    ##
    ## This method overloads the core @code{iqr} function for duration arrays.
    ## The functionality is identical to core @code{iqr} function.
    ## Type @code{help iqr} for more information.
    ##
    ## @end deftypefn
    function varargout = iqr (this, varargin)
      if (nargout > 1)
        [this.Millis, varargout{2}] = iqr (this.Millis, varargin{:});
      else
        this.Millis = iqr (this.Millis, varargin{:});
      endif
      varargout{1} = this;
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{k} =} kurtosis (@var{D})
    ## @deftypefnx {duration} {@var{k} =} kurtosis (@var{D}, @var{flag})
    ## @deftypefnx {duration} {@var{k} =} kurtosis (@var{D}, @var{flag}, @var{dim})
    ## @deftypefnx {duration} {@var{k} =} kurtosis (@var{D}, @var{flag}, @var{vecdim})
    ## @deftypefnx {duration} {@var{k} =} kurtosis (@var{D}, @var{flag}, @qcode{'all'})
    ##
    ## Compute the sample kurtosis of a duration array.
    ##
    ## This method overloads the core @code{kurtosis} function for duration
    ## arrays.  The functionality is identical to core @code{kurtosis} function.
    ## Type @code{help kurtosis} for more information.
    ##
    ## Note that kurtosis is a dimensionless quantity  Thus, the returned
    ## argument is a numeric array of double type and not a duration array.
    ##
    ## @end deftypefn
    function k = kurtosis (D, varargin)
      k = kurtosis (D.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} mad (@var{D})
    ## @deftypefnx {duration} {@var{M} =} mad (@var{D}, @var{opt})
    ## @deftypefnx {duration} {@var{M} =} mad (@var{D}, @var{opt}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} mad (@var{D}, @var{opt}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} mad (@var{D}, @var{opt}, @qcode{'all'})
    ##
    ## Compute the mean or median absolute deviation of a duration array.
    ##
    ## This method overloads the core @code{mad} function for duration arrays.
    ## The functionality is identical to core @code{mad} function.
    ## Type @code{help mad} for more information.
    ##
    ## @end deftypefn
    function this = mad (this, varargin)
      this.Millis = mad (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{E} =} mape (@var{F}, @var{A})
    ## @deftypefnx {duration} {@var{E} =} mape (@var{F}, @var{A}, @var{dim})
    ## @deftypefnx {duration} {@var{E} =} mape (@var{F}, @var{A}, @var{vecdim})
    ## @deftypefnx {duration} {@var{E} =} mape (@var{F}, @var{A}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{E} =} mape (@dots{}, @var{nanflag})
    ## @deftypefnx {duration} {@var{E} =} mape (@dots{}, @var{zeroflag})
    ## @deftypefnx {duration} {@var{E} =} mape (@dots{}, @qcode{'Weights'}, @var{W})
    ##
    ## Compute the mean absolute percentage error between duration arrays.
    ##
    ## This method overloads the core @code{mape} function for duration arrays.
    ## The functionality is identical to core @code{mape} function.
    ## Type @code{help mape} for more information.
    ##
    ## Note that MAPE is expressed as a percentage.  Thus, the returned argument
    ## is a numeric array of double type and not a duration array.  However,
    ## both @var{F} and @var{A} must be duration arrays.
    ##
    ## @end deftypefn
    function E = mape (F, A, varargin)
      if (! isduration (F) || ! isduration (A))
        error ("duration.mape: both F and A must be duration arrays.");
      endif
      E = mape (F.Millis, A.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} mean (@var{D})
    ## @deftypefnx {duration} {@var{M} =} mean (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} mean (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} mean (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} mean (@dots{}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} mean (@dots{}, @var{outtype})
    ## @deftypefnx {duration} {@var{M} =} mean (@dots{}, @qcode{'Weights'}, @var{W})
    ##
    ## Compute the mean of the elements of a duration array.
    ##
    ## This method overloads the core @code{mean} function for duration arrays.
    ## The functionality is identical to core @code{mean} function.
    ## Type @code{help mean} for more information.
    ##
    ## @end deftypefn
    function this = mean (this, varargin)
      this.Millis = mean (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} median (@var{D})
    ## @deftypefnx {duration} {@var{M} =} median (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} median (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} median (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{M} =} median (@dots{}, @var{nanflag})
    ## @deftypefnx {duration} {@var{M} =} median (@dots{}, @var{outtype})
    ##
    ## Compute the median value of the elements of a duration array.
    ##
    ## This method overloads the core @code{median} function for duration
    ## arrays.  The functionality is identical to core @code{median} function.
    ## Type @code{help median} for more information.
    ##
    ## @end deftypefn
    function this = median (this, varargin)
      this.Millis = median (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{M} =} mode (@var{D})
    ## @deftypefnx {duration} {@var{M} =} mode (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{M} =} mode (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{M} =} mode (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {[@var{M}, @var{F}, @var{C}] =} mode (@dots{})
    ##
    ## Compute the most frequently occurring value in a duration array.
    ##
    ## This method overloads the core @code{mode} function for duration arrays.
    ## The functionality is identical to core @code{mode} function.
    ## Type @code{help mode} for more information.
    ##
    ## @end deftypefn
    function [this, F, C] = mode (this, varargin)
      [this.Millis, F, C] = mode (this.Millis, varargin{:});
      if (nargout == 3)
        ## C holds stored values, which are milliseconds.
        C = cellfun ('milliseconds', C, 'UniformOutput', false);
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{Q} =} prctile (@var{D})
    ## @deftypefnx {duration} {@var{q} =} prctile (@var{D}, @var{p})
    ## @deftypefnx {duration} {@var{Q} =} prctile (@var{D}, @var{p}, @var{dim})
    ## @deftypefnx {duration} {@var{Q} =} prctile (@var{D}, @var{p}, @var{vecdim})
    ## @deftypefnx {duration} {@var{Q} =} prctile (@var{D}, @var{p}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{Q} =} prctile (@var{D}, @var{p}, @dots{}, @var{method})
    ##
    ## Compute the percentiles of a duration array.
    ##
    ## This method overloads the core @code{prctile} function for duration
    ## arrays.  The functionality is identical to core @code{prctile} function.
    ## Type @code{help prctile} for more information.
    ##
    ## @end deftypefn
    function this = prctile (this, varargin)
      this.Millis = prctile (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{Q} =} quantile (@var{D})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @var{p})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @var{n})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @dots{}, @var{dim})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @dots{}, @var{vecdim})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @dots{}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @var{p}, @dots{}, @var{method})
    ## @deftypefnx {duration} {@var{Q} =} quantile (@var{D}, @var{n}, @dots{}, @var{method})
    ##
    ## Compute the quantiles of a duration array.
    ##
    ## This method overloads the core @code{quantile} function for duration
    ## arrays.  The functionality is identical to core @code{quantile} function.
    ## Type @code{help quantile} for more information.
    ##
    ## @end deftypefn
    function this = quantile (this, varargin)
      this.Millis = quantile (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{R} =} range (@var{D})
    ## @deftypefnx {duration} {@var{R} =} range (@var{D}, @var{dim})
    ## @deftypefnx {duration} {@var{R} =} range (@var{D}, @var{vecdim})
    ## @deftypefnx {duration} {@var{R} =} range (@var{D}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{R} =} range (@dots{}, @var{nanflag})
    ##
    ## Compute the range of a duration array.
    ##
    ## This method overloads the core @code{range} function for duration arrays.
    ## The functionality is identical to core @code{range} function.
    ## Type @code{help range} for more information.
    ##
    ## @end deftypefn
    function this = range (this, varargin)
      this.Millis = range (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{E} =} rmse (@var{F}, @var{A})
    ## @deftypefnx {duration} {@var{E} =} rmse (@var{F}, @var{A}, @var{dim})
    ## @deftypefnx {duration} {@var{E} =} rmse (@var{F}, @var{A}, @var{vecdim})
    ## @deftypefnx {duration} {@var{E} =} rmse (@var{F}, @var{A}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{E} =} rmse (@dots{}, @var{nanflag})
    ## @deftypefnx {duration} {@var{E} =} rmse (@dots{}, @qcode{'Weights'}, @var{W})
    ##
    ## Compute the root mean squared error between duration arrays.
    ##
    ## This method overloads the core @code{rmse} function for duration arrays.
    ## The functionality is identical to core @code{rmse} function.
    ## Type @code{help rmse} for more information.
    ##
    ## @end deftypefn
    function this = rmse (this, A, varargin)
      if (! isduration (this) || ! isduration (A))
        error ("duration.rmse: both F and A must be duration arrays.");
      endif
      this.Millis = rmse (this.Millis, A.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{y} =} skewness (@var{D})
    ## @deftypefnx {duration} {@var{y} =} skewness (@var{D}, @var{flag})
    ## @deftypefnx {duration} {@var{y} =} skewness (@var{D}, @var{flag}, @var{dim})
    ## @deftypefnx {duration} {@var{y} =} skewness (@var{D}, @var{flag}, @var{vecdim})
    ## @deftypefnx {duration} {@var{y} =} skewness (@var{D}, @var{flag}, @qcode{'all'})
    ##
    ## Compute the sample skewness of a duration array.
    ##
    ## This method overloads the core @code{skewness} function for duration
    ## arrays.  The functionality is identical to core @code{skewness} function.
    ## Type @code{help skewness} for more information.
    ##
    ## Note that skewness is a dimensionless quantity  Thus, the returned
    ## argument is a numeric array of double type and not a duration array.
    ##
    ## @end deftypefn
    function y = skewness (D, varargin)
      y = skewness (D.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{S} =} std (@var{D})
    ## @deftypefnx {duration} {@var{S} =} std (@var{D}, @var{w})
    ## @deftypefnx {duration} {@var{S} =} std (@var{D}, @var{w}, @var{dim})
    ## @deftypefnx {duration} {@var{S} =} std (@var{D}, @var{w}, @var{vecdim})
    ## @deftypefnx {duration} {@var{S} =} std (@var{D}, @var{w}, @qcode{'all'})
    ## @deftypefnx {duration} {@var{S} =} std (@dots{}, @var{nanflag})
    ## @deftypefnx {duration} {[@var{S}, @var{M}] =} std (@dots{})
    ##
    ## Compute the standard deviation of a duration array.
    ##
    ## This method overloads the core @code{std} function for duration arrays.
    ## The functionality is identical to core @code{std} function.
    ## Type @code{help std} for more information.
    ##
    ## @end deftypefn
    function varargout = std (this, varargin)
      if (nargout > 1)
        M = this;
        [this.Millis, M.Millis] = std (this.Millis, varargin{:});
        varargout{1} = this;
        varargout{2} = M;
      else
        this.Millis = std (this.Millis, varargin{:});
        varargout{1} = this;
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{bin} =} discretize (@var{D}, @var{edges})
    ## @deftypefnx {duration} {@var{bin} =} discretize (@var{D}, @var{N})
    ## @deftypefnx {duration} {@var{bin} =} discretize (@var{D}, @var{dur})
    ## @deftypefnx {duration} {@var{bin} =} discretize (@var{D}, @var{unit})
    ## @deftypefnx {duration} {@var{Y} =} discretize (@dots{}, @var{values})
    ## @deftypefnx {duration} {@var{C} =} discretize (@dots{}, 'categorical')
    ## @deftypefnx {duration} {@var{C} =} discretize (@dots{}, 'categorical', @var{names})
    ## @deftypefnx {duration} {@var{Y} =} discretize (@dots{}, 'IncludedEdge', @var{side})
    ## @deftypefnx {duration} {[@var{bin}, @var{edges}] =} discretize (@dots{})
    ##
    ## Group durations into bins.
    ##
    ## @code{@var{bin} = discretize (@var{D}, @var{edges})} returns the index of
    ## the bin each element of @var{D} falls into, given a @qcode{duration}
    ## vector of bin edges.  Bin @math{j} covers @code{[@var{edges}(j),
    ## @var{edges}(j+1))}, except the last, which is closed at both ends.
    ## Elements outside the edges, and @qcode{NaN} durations, return @qcode{NaN}.
    ##
    ## @code{@var{bin} = discretize (@var{D}, @var{N})} uses @var{N} bins of
    ## uniform width, placed on whole time units where that is possible.
    ##
    ## @code{@var{bin} = discretize (@var{D}, @var{dur})} uses bins of the fixed
    ## width @var{dur}, a scalar @qcode{duration},
    ## and @code{@var{bin} = discretize (@var{D}, @var{unit})} uses bins one
    ## @var{unit} wide, where @var{unit} is one of @qcode{'second'},
    ## @qcode{'minute'}, @qcode{'hour'}, @qcode{'day'}, @qcode{'week'},
    ## @qcode{'month'}, @qcode{'quarter'}, @qcode{'year'}, @qcode{'decade'} or
    ## @qcode{'century'}.  A month is a twelfth of the 365.2425-day year that
    ## @code{years} counts, since a @qcode{duration} has no calendar.
    ##
    ## The remaining options are as for the top-level @code{discretize}.
    ##
    ## @strong{Deviation from MATLAB, for an explicitly requested bin count
    ## only.}  Every other way of binning -- automatic, by width, by unit, or by
    ## explicit edges -- agrees with MATLAB exactly.  Asked for a bin count,
    ## MATLAB chooses between whole-unit and decimal widths in a way that is not
    ## monotonic in the data: over @code{seconds ([0 16.8])} it gives 7 bins of
    ## 2.5 s, over the wider @code{seconds ([0 17.15])} 7 bins of 3 s, and
    ## decimal widths again above that.  It also discards bins, giving
    ## @code{hours (0:24)} in 7 bins a 4-hour width that covers the data in 6.
    ## A whole time unit is used here whenever it still needs every bin
    ## requested, which is monotonic and never wastes a bin.
    ##
    ## @seealso{histcounts, discretize}
    ## @end deftypefn
    function [BIN, EDGES] = discretize (this, arg2, varargin)

      ## Input validation
      if (nargin < 2)
        error ("duration.discretize: not enough input arguments.");
      endif
      xv = this.Millis(:);
      [ev, isCount] = durbinedges (xv, arg2, 'duration.discretize');
      EDGES = milliseconds (ev);
      EDGES.Format = this.Format;
      if (isCount)
        EDGES = reshape (EDGES, 1, numel (ev));
      endif

      ## Delegate the assignment and the value mapping to the numeric function
      [BIN, ~] = discretize (reshape (xv, size (this.Millis)), ev, varargin{:});

    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{N} =} histcounts (@var{D})
    ## @deftypefnx {duration} {@var{N} =} histcounts (@var{D}, @var{nbins})
    ## @deftypefnx {duration} {@var{N} =} histcounts (@var{D}, @var{edges})
    ## @deftypefnx {duration} {@var{N} =} histcounts (@dots{}, @var{Name}, @var{Value})
    ## @deftypefnx {duration} {[@var{N}, @var{edges}] =} histcounts (@dots{})
    ## @deftypefnx {duration} {[@var{N}, @var{edges}, @var{bin}] =} histcounts (@dots{})
    ##
    ## Histogram bin counts for durations.
    ##
    ## @code{@var{N} = histcounts (@var{D})} bins the durations in @var{D},
    ## chosen automatically, and returns the number of elements in each bin.
    ## @var{D} is treated as @code{@var{D}(:)} and @qcode{NaN} durations are
    ## excluded.
    ##
    ## @code{@var{N} = histcounts (@var{D}, @var{nbins})} and
    ## @code{@var{N} = histcounts (@var{D}, @var{edges})} bin by count and by
    ## explicit @qcode{duration} edges respectively.
    ##
    ## @qcode{'BinWidth'} takes a scalar @qcode{duration},
    ## @qcode{'BinLimits'} a two-element
    ## @qcode{duration}, and @qcode{'BinEdges'} a @qcode{duration} vector.
    ## @qcode{'BinMethod'} accepts @qcode{'auto'}, @qcode{'scott'},
    ## @qcode{'fd'}, @qcode{'sturges'} and @qcode{'sqrt'}, but not
    ## @qcode{'integers'}, which has no meaning for a duration.
    ##
    ## @qcode{'Normalization'} accepts @qcode{'count'}, @qcode{'cumcount'},
    ## @qcode{'probability'}, @qcode{'percentage'} and @qcode{'cdf'}.
    ## @qcode{'countdensity'} and @qcode{'pdf'} are not accepted, since a density
    ## per unit time has no meaning here.
    ##
    ## @seealso{discretize, histcounts}
    ## @end deftypefn
    function [N, EDGES, BIN] = histcounts (this, varargin)

      xv = this.Millis(:);
      args = durhistargs (varargin, xv, 'duration.histcounts');
      if (nargout > 2)
        [N, ev, BIN] = histcounts (xv, args{:});
        BIN = reshape (BIN, size (this.Millis));
      else
        [N, ev] = histcounts (xv, args{:});
      endif
      EDGES = milliseconds (ev);
      EDGES.Format = this.Format;

    endfunction

  endmethods

################################################################################
##                   ** Sort, Filter, and Set Operations **                   ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'maxk'             'mink'             'sort'             'sortrows'        ##
## 'topkrows'         'unique'           'interp1'          'intersect'       ##
## 'setdiff'          'setxor'           'union'                              ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} maxk (@var{A}, @var{K})
    ## @deftypefnx {duration} {@var{B} =} maxk (@var{A}, @var{K}, @var{dim})
    ## @deftypefnx {duration} {[@var{B}, @var{index}] =} maxk (@var{A}, @dots{})
    ##
    ## Find the largest elements in a duration array.
    ##
    ## @code{@var{B} = maxk (@var{A}, @var{K})} returns the @var{K} largest
    ## elements of the duration array @var{A} in descending order.  If @var{A}
    ## is a vector, then @var{B} is a vector with @var{K} elements.  If @var{A}
    ## is a matrix, then @code{maxk} operates along each column of @var{A} and
    ## @var{B} has @var{K} rows.  For multidimensional arrays, @code{maxk}
    ## operates along the first non-singleton dimension.
    ##
    ## @code{@var{B} = maxk (@var{A}, @var{K}, @var{dim})} operates along the
    ## dimension specified by @var{dim}.
    ##
    ## @var{K} must be a nonnegative integer scalar.  If @var{K} is larger than
    ## the number of elements along the operating dimension, then all of them
    ## are returned.  @qcode{Inf} and @qcode{-Inf} are ranked as ordinary
    ## values.
    ##
    ## Missing elements (@qcode{NaN}) are not ranked.  They are appended after
    ## the ranked elements in their original order, and hence they only appear
    ## in @var{B} when @var{K} exceeds the number of non-missing elements along
    ## the operating dimension.  Unlike @code{sort}, @code{maxk} has no
    ## @qcode{'MissingPlacement'} option, since @qcode{NaN} elements are always
    ## placed last.  Elements comparing as equal keep their original order.
    ##
    ## @code{[@var{B}, @var{index}] = maxk (@var{A}, @dots{})} also returns an
    ## index array containing the indices of the returned elements of @var{A}
    ## along the operating dimension.
    ##
    ## @end deftypefn
    function [B, index] = maxk (A, K, varargin)
      if (nargin < 2)
        error ("duration.maxk: too few input arguments.");
      endif
      [index, lidx, errmsg] = __minmaxk__ (A.Millis, K, true, varargin);
      if (! isempty (errmsg))
        error ("duration.maxk: %s", errmsg);
      endif
      B = subset (A, lidx);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} mink (@var{A}, @var{K})
    ## @deftypefnx {duration} {@var{B} =} mink (@var{A}, @var{K}, @var{dim})
    ## @deftypefnx {duration} {[@var{B}, @var{index}] =} mink (@var{A}, @dots{})
    ##
    ## Find the smallest elements in a duration array.
    ##
    ## @code{@var{B} = mink (@var{A}, @var{K})} returns the @var{K} smallest
    ## elements of the duration array @var{A} in ascending order.  If @var{A}
    ## is a vector, then @var{B} is a vector with @var{K} elements.  If @var{A}
    ## is a matrix, then @code{mink} operates along each column of @var{A} and
    ## @var{B} has @var{K} rows.  For multidimensional arrays, @code{mink}
    ## operates along the first non-singleton dimension.
    ##
    ## @code{@var{B} = mink (@var{A}, @var{K}, @var{dim})} operates along the
    ## dimension specified by @var{dim}.
    ##
    ## @var{K} must be a nonnegative integer scalar.  If @var{K} is larger than
    ## the number of elements along the operating dimension, then all of them
    ## are returned.  @qcode{Inf} and @qcode{-Inf} are ranked as ordinary
    ## values.
    ##
    ## Missing elements (@qcode{NaN}) are not ranked.  They are appended after
    ## the ranked elements in their original order, and hence they only appear
    ## in @var{B} when @var{K} exceeds the number of non-missing elements along
    ## the operating dimension.  Unlike @code{sort}, @code{mink} has no
    ## @qcode{'MissingPlacement'} option, since @qcode{NaN} elements are always
    ## placed last.  Elements comparing as equal keep their original order.
    ##
    ## @code{[@var{B}, @var{index}] = mink (@var{A}, @dots{})} also returns an
    ## index array containing the indices of the returned elements of @var{A}
    ## along the operating dimension.
    ##
    ## @end deftypefn
    function [B, index] = mink (A, K, varargin)
      if (nargin < 2)
        error ("duration.mink: too few input arguments.");
      endif
      [index, lidx, errmsg] = __minmaxk__ (A.Millis, K, false, varargin);
      if (! isempty (errmsg))
        error ("duration.mink: %s", errmsg);
      endif
      B = subset (A, lidx);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} sort (@var{A})
    ## @deftypefnx {duration} {@var{B} =} sort (@var{A}, @var{dim})
    ## @deftypefnx {duration} {@var{B} =} sort (@var{A}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} sort (@var{A}, @var{dim}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} sort (@dots{}, @qcode{'MissingPlacement'}, @var{MP})
    ## @deftypefnx {duration} {@var{B} =} sort (@dots{}, @qcode{'ComparisonMethod'}, @var{CM})
    ## @deftypefnx {duration} {[@var{B}, @var{index}] =} sort (@var{A}, @dots{})
    ##
    ## Sort elements in a duration array.
    ##
    ## @code{@var{B} = sort (@var{A})} sorts the duration array @var{A} in
    ## ascending order.  If @var{A} is a matrix, @code{sort (@var{A})} sorts
    ## each column of @var{A} in ascending order.  For multidimensional arrays,
    ## @code{mode (@var{A})} sorts along the first non-singleton dimension.
    ##
    ## @code{@var{B} = sort (@var{A}, @var{dim})} sorts along the dimension
    ## specified by @var{dim}.
    ##
    ## @code{@var{B} = sort (@var{A}, @var{direction})} also specifies the
    ## sorting direction, which can be either @qcode{'ascend'} (default) or
    ## @qcode{'descend'}.
    ##
    ## @code{@var{B} = sort (@dots{}, @qcode{'MissingPlacement'}, @var{MP})}
    ## specifies where to place the missing elements (@qcode{<undefined>})
    ## returned in @var{B} with one of the following options specified in
    ## @var{MP}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, places missing elements last
    ## for ascending sort and first for descending sort.
    ## @item @qcode{'first'} places missing elements first.
    ## @item @qcode{'last'} places missing elements last.
    ## @end itemize
    ##
    ## @code{@var{B} = sort (@dots{}, @qcode{'ComparisonMethod'}, @var{CM})}
    ## specifies the comparison method for determining the order of elements
    ## returned in @var{B} with one of following options:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, sorts by @code{real (A)}.
    ## @item @qcode{'real'} sorts by @code{real (A)}.
    ## @item @qcode{'abs'} sorts by @code{abs (A)}.
    ## @end itemize
    ##
    ## @code{[@var{B}, @var{index}] = sort (@var{A}, @dots{})} also returns a
    ## sorting index containing the original indices of the elements in the
    ## sorted array.  @var{index} is the same size as @var{A} and it comprises
    ## indexing vectors oriented along the operating dimensions.
    ##
    ## @itemize
    ## @item If @var{A} is a vector, then @var{index} contains the original
    ## linear indices of the elements in the sorted vector @var{B} such that
    ## @code{@var{B} = @var{A}(@var{index})}.
    ## @item If @var{A} is an @math{M*N} matrix and @qcode{@var{dim} = 1}, then
    ## @var{index} contains the original row indices of the elements in the
    ## sorted vector @var{B} such that for @qcode{j = 1:N},
    ## @code{@var{B}(:,j) = @var{A}(@var{index}(:,j),j)}.
    ## @end itemize
    ##
    ## @end deftypefn
    function [B, index] = sort (A, varargin)
      ## Parse and validate optional paired arguments
      optNames = {'MissingPlacement', 'ComparisonMethod'};
      dfValues = {'auto', 'auto'};
      [MP, CM, args] = parsePairedArguments (optNames, dfValues, varargin(:));
## The values are matched without regard to case, as MATLAB does.
MP = lower (MP);
CM = lower (CM);
      if (! ismember (MP, {'auto', 'first', 'last'}))
        error ("duration.sort: invalid value for 'MissingPlacement'.");
      endif
      if (! ismember (CM, {'auto', 'real', 'abs'}))
        error ("duration.sort: invalid value for 'ComparisonMethod'.");
      endif

      ## Force strings to character vectors
      [args{:}] = convertStringsToChars (args{:});

      ## Get direction
      cid = cellfun (@ischar, args);
      if (any (cid))
        dir = lower (args{cid});
        ## Put it back, since args is forwarded to the core sort further down.
        args(cid) = {dir};
      else
        dir = 'ascend';
      endif
      ## Get operating dimension
      szA = size (A);
      cid = cellfun (@isnumeric, args);
      if (any (cid))
        dim = args{cid};
      else
        dim = find (szA != 1, 1);
        if (isempty (dim)) # scalar
          dim = 1;
        endif
      endif

      ## Apply comparison method (Octave specific)
      data = A.Millis;
      if (strcmp (CM, 'abs'))
        data = abs (data);
      endif

      ## Special handling for missing elements when missing placement overrides
      ## default behavior (only if missing data actually exist).
      is_nan = isnan (data);
      if (any (is_nan, 'all'))
        ## FIX ME: this workaround will be removed once the 'sort' function
        ## in core Octave supports 'MissingPlacement' optional argument.
        ## This implementation fails the edge case where -Inf and -realmax
        ## elements are present along the operating dimension.
        if ((strcmp (dir, 'ascend') && strcmp (MP, {'first'})) ||
            (strcmp (dir, 'descend') && strcmp (MP, {'last'})))
          ## Convert missing values to -Inf so that they are placed
          ## appropriately according to 'MissingPlacement' specification.
          ## If -Inf values already exist in data, then convert them to the
          ## next smallest possible value
          is_m_inf = data == -Inf;
          if (any (is_m_inf, 'all'))
            m_inf_rep = - realmax;
            data(is_m_inf) = m_inf_rep;
          endif
          data(is_nan) = -Inf;
        endif
      endif

      ## Sort values
      [~, index] = sort (data, args{:});

      ## Calculate linear index
      n_dims = ndims (A);
      dimarg = cell (1, n_dims);
      for i = 1:n_dims
        if (i == dim)
          dimarg{i} = index;
        else
          dim_sz = szA(i);
          tmpvec = ones (1, n_dims);
          tmpvec(i) = dim_sz;
          tmp_sz = szA;
          tmp_sz(i) = 1;
          dimarg{i} = repmat (reshape ([1:dim_sz], tmpvec), tmp_sz);
        endif
      endfor

      ## Return sorted duration array
      B = subset (A, sub2ind (szA, dimarg{:}));
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} sortrows (@var{A})
    ## @deftypefnx {duration} {@var{B} =} sortrows (@var{A}, @var{col})
    ## @deftypefnx {duration} {@var{B} =} sortrows (@var{A}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} sortrows (@var{A}, @var{col}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} sortrows (@dots{}, @qcode{'MissingPlacement'}, @var{MP})
    ## @deftypefnx {duration} {[@var{B}, @var{index}] =} sortrows (@var{A}, @dots{})
    ##
    ## Sort rows in a duration array.
    ##
    ## @code{@var{B} = sortrows (@var{A})} sorts the rows of the 2-D duration
    ## array @var{A} in ascending order.  The sorted array @var{B} has the same
    ## size as @var{A}.
    ##
    ## @code{@var{B} = sortrows (@var{A}, @var{col})} sorts @var{A} according to
    ## to the columns specified by the numeric vector @var{col}, which must
    ## explicitly contain non-zero integers whose absolute values index existing
    ## columns in @var{A}.  Positive elements sort the corresponding columns in
    ## ascending order, while negative elements sort the corresponding columns
    ## in descending order.
    ##
    ## @code{@var{B} = sortrows (@var{A}, @var{direction})} also specifies the
    ## sorting direction, which can be either @qcode{'ascend'} (default) or
    ## @qcode{'descend'} applying to all columns in @var{A}.  Alternatively,
    ## @var{direction} can be either a string array or a cell array of character
    ## vectors specifying the sorting direction for each individual column of
    ## @var{A}, in which case the number of elements in @var{direction} must
    ## equal the number of columns in @var{A}.
    ##
    ## @code{@var{B} = sortrows (@var{A}, @var{col}, @var{direction})} sorts the
    ## categorical array @var{A} according to the columns specified in @var{col}
    ## using the corresponding sorting direction specified in @var{direction}.
    ## In this case, the sign of the values in @var{col} is ignored.  @var{col}
    ## and @var{direction} must have the same number of elements, but not
    ## necessarily equal to the columns of @var{A}.
    ##
    ## @code{@var{B} = sortrows (@dots{}, @qcode{'MissingPlacement'}, @var{MP})}
    ## specifies where to place the missing elements (@qcode{NaN}) returned in
    ## @var{B} with any of the following options specified in @var{MP}:
    ##
    ## @itemize
    ## @item @qcode{'auto'}, which is the default, places missing elements last
    ## for ascending sort and first for descending sort.
    ## @item @qcode{'first'} places missing elements first.
    ## @item @qcode{'last'} places missing elements last.
    ## @end itemize
    ##
    ## @code{[@var{B}, @var{index}] = sortrows (@var{A}, @dots{})} also returns
    ## an index vector containing the original row indices of @var{A} in the
    ## sorted matrix @var{B} such that @code{@var{B} = @var{A}(@var{index},:)}.
    ##
    ## @end deftypefn
    function [B, index] = sortrows (A, varargin)
      ## Input array must be a matrix
      if (ndims (A) != 2)
        error ("duration.sortrows: A must be a 2-D matrix.");
      endif

      ## Parse and validate optional paired arguments
      optNames = {'MissingPlacement', 'ComparisonMethod'};
      dfValues = {'auto', 'auto'};
      [MP, CM, args] = parsePairedArguments (optNames, dfValues, varargin(:));
## The values are matched without regard to case, as MATLAB does.
MP = lower (MP);
CM = lower (CM);
      if (! any (strcmp (MP, {'auto', 'first', 'last'})))
        error ("duration.sortrows: invalid value for 'MissingPlacement'.");
      endif
      if (! any (strcmp (CM, {'auto', 'real', 'abs'})))
        error ("duration.sortrows: invalid value for 'ComparisonMethod'.");
      endif

      ## Parse COL / DIRECTION input
      nc = size (A, 2);
      col = [1:nc];  # default ascending direction
      dir_flag = false;
      if (numel (args) > 2)
        error ("duration.sortrows: too many input arguments.");
      endif
      if (numel (args) > 0)
        col = args{1};
        if (isnumeric (col))
          if (! isvector (col) || any (fix (col) != col) || any (col == 0))
            error (strcat ("duration.sortrows: COL must be a vector", ...
                           " of nonzero integers indexing columns in A."));
          endif
          if (max (abs (col)) > nc)
            error ("duration.sortrows: COL indexes non-existing column.");
          endif
        elseif (isvector (col) && (ischar (col) || iscellstr (col) ||
                                   isa (col, 'string')))
          direction = lower (cellstr (col));
          if (! all (ismember (direction, {'ascend', 'descend'})))
            error (strcat ("duration.sortrows: DIRECTION input must", ...
                           " contain either 'ascend' or 'descend' values."));
          endif
          ## Apply scalar expansion
          if (isscalar (direction))
            direction = repmat (direction, 1, nc);
          endif
          if (numel (direction) != nc)
            error (strcat ("duration.sortrows: DIRECTION", ...
                           " does not match the columns in A."));
          endif
          ## Assign DIRECTION to COL
          col = [1:nc];
          idx = strcmp (direction, 'descend');
          col(idx) = - col(idx);
          dir_flag = true;
        else
          error ("duration.sortrows: invalid type for COL argument.");
        endif
      endif
      if (numel (args) > 1)
        if (dir_flag)
          error ("duration.sortrows: invalid third input argument.");
        endif
        if ((isvector (args{2}) && ischar (args{2})) || isa (args{2}, 'string'))
          direction = lower (cellstr (args{2}));
        elseif (isvector (args{2}) && iscellstr (args{2}))
          direction = args{2};
        else
          error ("duration.sortrows: invalid type for DIRECTION argument.");
        endif
        if (! all (ismember (direction, {'ascend', 'descend'})))
          error (strcat ("duration.sortrows: DIRECTION input must", ...
                         " contain either 'ascend' or 'descend' values."));
        endif
        ## Assign DIRECTION to COL
        if (isscalar (direction) && strcmp (direction, 'ascend'))
          col = abs (col);
        elseif (isscalar (direction) && strcmp (direction, 'descend'))
          col = - abs (col);
        else
          if (numel (direction) != numel (col))
            error (strcat ("duration.sortrows: DIRECTION does", ...
                           " not match the elements in COL."));
          endif
          col = abs (col);
          idx = strcmp (direction, 'descend');
          col(idx) = - col(idx);
        endif
      endif

      ## Apply comparison method (Octave specific)
      data = A.Millis;
      if (strcmp (CM, 'abs'))
        data = abs (data);
      endif

      ## FIX ME: this workaround will be removed once the 'sortrows' function
      ## in core Octave supports 'MissingPlacement' optional argument.
      ## This implementation fails the edge case where -Inf and -realmax
      ## elements are present along the operating dimension.
      pos_dir = col > 0;
      neg_dir = col < 0;
      fix_pos_dir = any (pos_dir) && strcmp (MP, {'first'});
      fix_neg_dir = any (neg_dir) && strcmp (MP, {'last'});
      if (fix_pos_dir || fix_neg_dir)
        ## Apply on selected columns
        if (fix_pos_dir)
          col_idx = col(pos_dir);
        else  # must be fix_neg_dir
          col_idx = - col(neg_dir);
        endif
        cdata = data(:,col_idx);
        ## Only if missing data exist in operating columns.
        is_nan = isnan (cdata);
        if (any (is_nan, 'all'))
          ## Convert missing values to -Inf so that they are placed
          ## appropriately according to 'MissingPlacement' specification.
          ## If -Inf values already exist in data, then convert them to the
          ## next smallest possible value
          is_m_inf = cdata == -Inf;
          if (any (is_m_inf, 'all'))
            m_inf_rep = - realmax;
            cdata(is_m_inf) = m_inf_rep;
          endif
          cdata(is_nan) = -Inf;
          data(:,col_idx) = cdata;
          ## Sort values
          [~, index] = sortrows (data, col);
        else
          ## Sort values without special handling
          [~, index] = sortrows (data, col);
        endif
      else
        ## Sort values with no undefined elements
        [~, index] = sortrows (data, col);
      endif

      ## Return sorted duration array
      B = subset (A, index, ':');
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} topkrows (@var{A}, @var{K})
    ## @deftypefnx {duration} {@var{B} =} topkrows (@var{A}, @var{K}, @var{col})
    ## @deftypefnx {duration} {@var{B} =} topkrows (@var{A}, @var{K}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} topkrows (@var{A}, @var{K}, @var{col}, @var{direction})
    ## @deftypefnx {duration} {@var{B} =} topkrows (@dots{}, @qcode{'MissingPlacement'}, @var{MP})
    ## @deftypefnx {duration} {[@var{B}, @var{index}] =} topkrows (@var{A}, @dots{})
    ##
    ## Top K sorted rows of a duration array.
    ##
    ## @code{@var{B} = topkrows (@var{A}, @var{K})} returns the top @var{K} rows
    ## of the 2-D duration array @var{A} sorted in descending order as a group.
    ## @var{K} must be a nonnegative integer scalar.  If @var{K} is larger than
    ## the number of rows in @var{A}, then all of them are returned.
    ##
    ## Missing elements (@qcode{NaN}) are not ranked.  Within each sort
    ## column they are placed after the elements that are defined, whichever
    ## direction is asked for, so a row is demoted only by a missing element in
    ## a column that actually decides its position.  Rows comparing as equal
    ## keep their original order.
    ##
    ## @code{@var{B} = topkrows (@var{A}, @var{K}, @var{col})} sorts using only
    ## the columns listed in the numeric vector @var{col}, which must contain
    ## positive integers indexing existing columns in @var{A}.  Columns are used
    ## as sort keys in the order given, and those not listed are not used at
    ## all.  The direction is descending unless @var{direction} says otherwise.
    ##
    ## @code{@var{B} = topkrows (@var{A}, @var{K}, @var{direction})} sorts in
    ## the given @var{direction}, either @qcode{'descend'} (default) or
    ## @qcode{'ascend'} applying to all columns in @var{A}.  Alternatively,
    ## @var{direction} can be a cell array of character vectors specifying the
    ## sorting direction for each individual column of @var{A}.
    ##
    ## @code{@var{B} = topkrows (@var{A}, @var{K}, @var{col}, @var{direction})}
    ## combines an explicit column list with a per-column @var{direction}.
    ##
    ## @code{@var{B} = topkrows (@dots{}, @qcode{'MissingPlacement'}, @var{MP})}
    ## specifies where the missing elements are placed within each sort column,
    ## with any of the following options specified in @var{MP}:
    ##
    ## @itemize
    ## @item @qcode{'last'}, which is the default, places missing elements last
    ## whichever direction is asked for.
    ## @item @qcode{'first'} places missing elements first.
    ## @item @qcode{'auto'} places missing elements last for an ascending sort
    ## and first for a descending one, as @code{sortrows} does.
    ## @end itemize
    ##
    ## This is an Octave extension: MATLAB has no such option here and always
    ## ranks as @qcode{'last'} does.
    ##
    ## @code{[@var{B}, @var{index}] = topkrows (@var{A}, @dots{})} also returns
    ## an index vector containing the original row indices of @var{A} in
    ## @var{B}, such that @code{@var{B} = @var{A}(@var{index},:)}.
    ##
    ## @end deftypefn
    function [B, index] = topkrows (A, K, varargin)
      ## Check input arguments
      if (nargin < 2)
        error ("duration.topkrows: too few input arguments.");
      endif
      if (ndims (A) != 2)
        error ("duration.topkrows: A must be a 2-D array.");
      endif
      [col, direction, MP, errmsg] = ...
                      __topkrowsargs__ (K, columns (A), varargin);
      if (! isempty (errmsg))
        error ("duration.topkrows: %s", errmsg);
      endif
      ## Sort rows, keeping missing elements out of the ranking
      if (isempty (col))
        [B, index] = sortrows (A, direction, 'MissingPlacement', MP);
      else
        [B, index] = sortrows (A, col, direction, 'MissingPlacement', MP);
      endif
      ## Return top K rows
      if (K < numel (index))
        B = subset (B, 1:K, ':');
        index = index(1:K);
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} unique (@var{A})
    ## @deftypefnx {duration} {@var{B} =} unique (@var{A}, @var{setOrder})
    ## @deftypefnx {duration} {@var{B} =} unique (@var{A}, @var{occurrence})
    ## @deftypefnx {duration} {@var{B} =} unique (@var{A}, @var{setOrder}, @var{occurrence})
    ## @deftypefnx {duration} {@var{B} =} unique (@var{A}, @var{occurrence}, @var{setOrder})
    ## @deftypefnx {duration} {@var{B} =} unique (@var{A}, @dots{}, @qcode{'rows'})
    ## @deftypefnx {duration} {[@var{B}, @var{ixA}, @var{ixB}] =} unique (@dots{})
    ##
    ## Unique values in a duration array.
    ##
    ## @code{@var{B} = unique (@var{A})} returns the unique values of the
    ## duration array @var{A} in sorted order.
    ##
    ## @code{@var{B} = unique (@var{A}, @var{setOrder})} returns the unique
    ## values of the duration array @var{A} in an order as specified by
    ## @var{setOrder}, which can be either of the following values:
    ##
    ## @itemize
    ## @item @qcode{'sorted'} (default) returns the unique values sorted in
    ## ascending order.
    ## @item @qcode{'stable'} returns the unique values according to their order
    ## of occurrence.
    ## @end itemize
    ##
    ## @code{@var{B} = unique (@var{A}, @var{occurrence})} returns the unique
    ## values of the duration array @var{A} according to their order of
    ## occurrence.  @var{occurrence} can be either of the following values:
    ##
    ## @itemize
    ## @item @qcode{'first'} (default) returns the first occurrence of each
    ## unique value, i.e. the lowest possible indices are returned.
    ## @item @qcode{'last'} returns the last occurrence of each unique value,
    ## i.e. the highest possible indices are returned.
    ## @end itemize
    ##
    ## You can specify @var{setOrder} and @var{occurrence} arguments together.
    ##
    ## @code{@var{B} = unique (@var{A}, @dots{}, @qcode{'rows'})} returns the
    ## unique rows of @var{A} by treating each row as a single entity.  The
    ## @qcode{'rows'} option can be used alone or in any combination with the
    ## @var{setOrder} and @var{occurrence} arguments.  @qcode{'rows'} can be
    ## placed at any position in the function's argument list after the input
    ## array @var{A}.  However, this syntax is only valid for 2-dimensional
    ## duration arrays.
    ##
    ## @code{[@var{B}, @var{ixA}, @var{ixB}] = unique (@dots{})} also returns
    ## index vectors @var{ixA} and @var{ixB} using any of the previous syntaxes.
    ## @var{ixA} and @var{ixB} map the arrays @var{A} and @var{B} to one another
    ## such that @qcode{@var{B} = @var{A}(@var{ixA})} and
    ## @qcode{@var{A} = @var{B}(@var{ixB})}.  When the @qcode{'rows'} optional
    ## argument is specified, then @qcode{@var{B} = @var{A}(@var{ixA},:)} and
    ## @qcode{@var{A} = @var{B}(@var{ixB},:)}.
    ##
    ## @end deftypefn
    function [this, ixA, ixB] = unique (this, varargin)
      ## 'legacy' option is not supported
      if (any (strcmp ('legacy', varargin)))
        error ("duration.unique: 'legacy' option is not supported.");
      endif
      [this.Millis, ixA, ixB] = __unique__ (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{YI} =} interp1 (@var{X}, @var{Y}, @var{XI})
    ## @deftypefnx {duration} {@var{YI} =} interp1 (@var{Y}, @var{XI})
    ## @deftypefnx {duration} {@var{YI} =} interp1 (@dots{}, @var{method})
    ## @deftypefnx {duration} {@var{YI} =} interp1 (@dots{}, @var{method}, @var{extrapolation})
    ## @deftypefnx {duration} {@var{pp} =} interp1 (@var{X}, @var{Y}, @qcode{'pp'})
    ## @deftypefnx {duration} {@var{pp} =} interp1 (@var{X}, @var{Y}, @var{method}, @qcode{'pp'})
    ##
    ## One-dimensional interpolation for duration arrays.
    ##
    ## @code{@var{YI} = interp1 (@var{X}, @var{Y}, @var{XI})} computes the
    ## linearly interpolated values of a one-dimensional function, which is
    ## represented by sample points @var{X} and corresponding values @var{Y},
    ## at specific query points @var{XI}.  @var{X} must be a vector.  If @var{Y}
    ## is vector, then it must have the same length as @var{X}.  If @var{Y} is
    ## matrix, then each column is treated as a different set of one-dimensional
    ## sample values and the number of rows must equal the length of @var{X}.
    ## @var{XI} must be a vector and the same data type as @var{X}.  The output
    ## @var{XI} is the same data type as @var{Y} and its size depends on @var{Y}
    ## and @var{XI}.  @var{X} and @var{Y} can both be duration arrays or one of
    ## them can be a numeric array.
    ##
    ## @code{@var{YI} = interp1 (@var{Y}, @var{XI})} computes the linearly
    ## interpolated values of a one-dimensional function assuming a default set
    ## of sampling points determined by the shape of @var{Y}:
    ##
    ## @itemize
    ## @item If @var{Y} is a vector, then the default sampling points are
    ## @code{[1:length(@var{Y})}.
    ##
    ## @item If @var{Y} is an array, then the default sampling points are
    ## @code{[1:size(@var{Y})}.
    ## @end itemize
    ##
    ## @code{@var{YI} = interp1 (@dots{}, @var{method})} specifies one of the
    ## following interpolation methods to be used:
    ##
    ## @itemize
    ## @item @qcode{'linear'} (default) computes the linear interpolation from
    ## nearest neighbors.
    ##
    ## @item @qcode{'nearest'} returns the nearest neighbor.
    ##
    ## @item @qcode{'next'} returns the next neighbor.
    ##
    ## @item @qcode{'previous'} returns the previous neighbor.
    ##
    ## @item @qcode{'pchip'} computes the piecewise cubic Hermite interpolating
    ## polynomial, which corresponds to shape-preserving interpolation with
    ## smooth first derivative.
    ##
    ## @item @qcode{'cubic'} computes the cubic interpolation.
    ##
    ## @item @qcode{'spline'} computes the cubic spline interpolation, which
    ## corresponds to smooth first and second derivatives throughout the curve.
    ## @end itemize
    ##
    ## @code{@var{YI} = interp1 (@dots{}, @var{method}, @var{extrapolation})}
    ## further specifies a strategy for evaluating points that lie outside the
    ## range of the sample points in @var{X}.  Set @var{extrapolation} to
    ## @qcode{'extrap'} to use the current @var{method} to extrapolate values.
    ## Set @var{extrapolation} to a scalar value of the same data type as
    ## @var{Y} to return a constant value outside the range of @var{X}.  When
    ## unspecified, @var{extrapolation} defaults to @qcode{NaN}.
    ##
    ## @code{@var{pp} = interp1 (@var{X}, @var{Y}, @qcode{'pp'}} returns a
    ## piecewise polynomial object, using the default linear interpolation
    ## algorithm, which can be later used with @code{ppval} to evaluate the
    ## interpolation at new query points.
    ##
    ## @code{@var{pp} = interp1 (@var{X}, @var{Y}, @var{method}, @qcode{'pp'}}
    ## return a piecewise polynomial object, using the interpolation algorithm
    ## specified by @var{method}, which can be later used with @code{ppval} to
    ## evaluate the interpolation at new query points.
    ##
    ## @end deftypefn
    function YI = interp1 (X, Y, varargin)
      if (isempty (varargin))
        ## YI = interp1 (Y, XI)
        if (isduration (Y))
          Y = Y.days;
        endif
        if (isduration (X))
          YI = duration ('Format', X.Format);
          YI.Millis = interp1 (X.Millis, Y);
        else
          YI = interp1 (X, Y);
        endif
      else
        [varargin{:}] = convertStringsToChars (varargin{:});
        method = varargin{1};
        if (ischar (method))
          ## YI = interp1 (Y, XI, method)
          ## YI = interp1 (Y, XI, method, extrap)
          ## PP = interp1 (X, Y, pp)
          ## PP = interp1 (X, Y, method, pp)
          X_isDur = isa (X, 'duration');
          Y_isDur = isa (Y, 'duration');
          if (X_isDur)
            F = X.Format;
            X = X.days;
          endif
          if (Y_isDur)
            Y = Y.days;
          endif
          ## Handle numeric extrapolation input
          extrap = cellfun (@(x) isduration (x) || isnumeric (x), varargin);
          if (any (extrap))
            tmp = varargin{extrap};
            ExtDur = isduration (tmp);
            if (xor (ExtDur, X_isDur))
              error (strcat ("duration.interp1: EXTRAPOLATION scalar", ...
                             " value must match Y."));
            elseif (ExtDur)
              varargin{extrap} = days (tmp);
            endif
          endif
          YI = interp1 (X, Y, varargin{:});
          if (isnumeric (YI) && X_isDur)
            YI = days (YI);
            YI.Format = F;
          endif
        else
          XI = method;
          varargin(1) = [];
          ## YI = interp1 (X, Y, XI)
          ## YI = interp1 (X, Y, XI, method)
          ## YI = interp1 (X, Y, XI, method, extrap)
          X_isDur = isa (X, 'duration');
          Y_isDur = isa (Y, 'duration');
          XIisDur = isa (XI, 'duration');
          if (xor (X_isDur, XIisDur))
            error (strcat ("duration.interp1: if X is a duration array,", ...
                           " XI must be also."));
          endif
          ## Handle numeric extrapolation input
          extrap = cellfun (@(x) isduration (x) || isnumeric (x), varargin);
          if (any (extrap))
            tmp = varargin{extrap};
            ExtDur = isduration (tmp);
            if (xor (ExtDur, Y_isDur))
              error (strcat ("duration.interp1: EXTRAPOLATION scalar", ...
                             " value must match Y."));
            elseif (ExtDur)
              ## This branch interpolates the stored milliseconds, so the
              ## extrapolation scalar has to be given in them too.
              varargin{extrap} = milliseconds (tmp);
            endif
          endif
          if (Y_isDur)
            YI = duration ('Format', Y.Format);
            if (X_isDur)
              YI.Millis = interp1 (X.Millis, Y.Millis, XI.Millis, varargin{:});
            else
              YI.Millis = interp1 (X, Y.Millis, XI, varargin{:});
            endif
          elseif (isnumeric (Y))
            YI = interp1 (X.Millis, Y, XI.Millis, varargin{:});
          else
            error ("duration.interp1: Y must be a duration or numeric array.");
          endif
        endif
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{C} =} intersect (@var{A}, @var{B})
    ## @deftypefnx {duration} {@var{C} =} intersect (@var{A}, @var{B}, @qcode{'rows'})
    ## @deftypefnx {duration} {@var{C} =} intersect (@var{A}, @var{B}, @dots{}, @var{order})
    ## @deftypefnx {duration} {[@var{C}, @var{ixA}, @var{ixB}] =} intersect (@dots{})
    ##
    ## Set intersection of two duration arrays.
    ##
    ## @code{@var{C} = intersect (@var{A}, @var{B})} returns the unique common
    ## values of the duration arrays @var{A} and @var{B}.  Either @var{A} or
    ## @var{B} input arguments can also be a duration string specified as a
    ## character vector, a string array, or a cell array of character vectors,
    ## or a numeric array representing 24-hour days.  In such case, the input is
    ## promoted to a duration array prior to calculating the intersection.  If
    ## both @var{A} and @var{B} are row vectors, then @var{C} is also a row
    ## vector, otherwise @code{intersect} returns a column vector.
    ##
    ## @code{@var{C} = intersect (@var{A}, @var{B}, @qcode{'rows'}} returns the
    ## unique common rows of the duration matrices @var{A} and @var{B}, which
    ## must have the same number of columns.  By default, the rows in duration
    ## matrix @var{C} are in sorted order.
    ##
    ## @code{@dots{} = intersect (@var{A}, @var{B}, @dots{}, @var{order})} also
    ## specifies the order of the returned unique values.  @var{order} can be
    ## @qcode{'sorted'}, which is the default behavior, or @qcode{'stable'}, in
    ## which case the unique values are returned in order of appearance.
    ##
    ## @code{[@var{C}, @var{ixA}, @var{ixB}] = intersect (@dots{})} also returns
    ## index vectors @var{ixA} and @var{ixB} such that
    ## @code{@var{C} = @var{A}(@var{ixA})} and
    ## @code{@var{C} = @var{B}(@var{ixB})}, unless the @qcode{'rows'} optional
    ## argument is given, in which case @code{@var{C} = @var{A}(@var{ixA},:)}
    ## and @code{@var{C} = @var{B}(@var{ixB},:)}.
    ##
    ## @end deftypefn
    function [C, ixA, ixB] = intersect (A, B, varargin)
      ## 'legacy' option is not supported
      if (any (strcmp ("legacy", varargin)))
        error ("duration.intersect: 'legacy' option is not supported.");
      endif
      if (ischar (A) || isstring (A) || iscellstr (A) || isnumeric (A))
        C = duration ('Format', B.Format);
        A = promote (A);
      elseif (ischar (B) || isstring (B) || iscellstr (B) || isnumeric (B))
        C = duration ('Format', A.Format);
        B = promote (B);
      elseif (isduration (A) && isduration (B))
        C = duration ('Format', A.Format);
      else
        error (strcat ("duration.intersect: set operation not defined", ...
                       " between '%s' and '%s' arrays."), class (A), class (B));
      endif
      [C.Millis, ixA, ixB] = intersect (A.Millis, B.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{C} =} setdiff (@var{A}, @var{B})
    ## @deftypefnx {duration} {@var{C} =} setdiff (@var{A}, @var{B}, @qcode{'rows'})
    ## @deftypefnx {duration} {@var{C} =} setdiff (@var{A}, @var{B}, @dots{}, @var{order})
    ## @deftypefnx {duration} {[@var{C}, @var{ixA}] =} setdiff (@dots{})
    ##
    ## Set difference of two duration arrays.
    ##
    ## @code{@var{C} = setdiff (@var{A}, @var{B})} returns the unique common
    ## values of the duration arrays @var{A} and @var{B}.  Either @var{A} or
    ## @var{B} input arguments can also be a duration string specified as a
    ## character vector, a string array, or a cell array of character vectors,
    ## or a numeric array representing 24-hour days.  In such case, the input is
    ## promoted to a duration array prior to calculating the intersection.  If
    ## both @var{A} and @var{B} are row vectors, then @var{C} is also a row
    ## vector, otherwise @code{intersect} returns a column vector.
    ##
    ## @code{@var{C} = setdiff (@var{A}, @var{B}, @qcode{'rows'}} returns the
    ## unique common rows of the duration matrices @var{A} and @var{B}, which
    ## must have the same number of columns.  By default, the rows in duration
    ## matrix @var{C} are in sorted order.
    ##
    ## @code{@dots{} = setdiff (@var{A}, @var{B}, @dots{}, @var{order})} also
    ## specifies the order of the returned unique values.  @var{order} can be
    ## @qcode{'sorted'}, which is the default behavior, or @qcode{'stable'}, in
    ## which case the unique values are returned in order of appearance.
    ##
    ## @code{[@var{C}, @var{ixA}] = setdiff (@dots{})} also returns the index
    ## vector @var{ixA} such that @code{@var{C} = @var{A}(@var{ixA})}, unless
    ## the @qcode{'rows'} optional argument is given, in which case
    ## @code{@var{C} = @var{A}(@var{ixA},:)}.
    ##
    ## @end deftypefn
    function [C, index] = setdiff (A, B, varargin)
      ## 'legacy' option is not supported
      if (any (strcmp ("legacy", varargin)))
        error ("duration.setdiff: 'legacy' option is not supported.");
      endif
      if (ischar (A) || isstring (A) || iscellstr (A) || isnumeric (A))
        C = duration ('Format', B.Format);
        A = promote (A);
      elseif (ischar (B) || isstring (B) || iscellstr (B) || isnumeric (B))
        C = duration ('Format', A.Format);
        B = promote (B);
      elseif (isduration (A) && isduration (B))
        C = duration ('Format', A.Format);
      else
        error (strcat ("duration.setdiff: set operation not defined", ...
                       " between '%s' and '%s' arrays."), class (A), class (B));
      endif
      [C.Millis, index] = setdiff (A.Millis, B.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{C} =} setxor (@var{A}, @var{B})
    ## @deftypefnx {duration} {@var{C} =} setxor (@var{A}, @var{B}, @qcode{'rows'})
    ## @deftypefnx {duration} {@var{C} =} setxor (@var{A}, @var{B}, @dots{}, @var{order})
    ## @deftypefnx {duration} {[@var{C}, @var{ixA}, @var{ixB}] =} setxor (@dots{})
    ##
    ## Set exclusive-or of two duration arrays.
    ##
    ## @code{@var{C} = setxor (@var{A}, @var{B})} returns the unique common
    ## values of the duration arrays @var{A} and @var{B}.  Either @var{A} or
    ## @var{B} input arguments can also be a duration string specified as a
    ## character vector, a string array, or a cell array of character vectors,
    ## or a numeric array representing 24-hour days.  In such case, the input is
    ## promoted to a duration array prior to calculating the intersection.  If
    ## both @var{A} and @var{B} are row vectors, then @var{C} is also a row
    ## vector, otherwise @code{intersect} returns a column vector.
    ##
    ## @code{@var{C} = setxor (@var{A}, @var{B}, @qcode{'rows'}} returns the
    ## unique common rows of the duration matrices @var{A} and @var{B}, which
    ## must have the same number of columns.  By default, the rows in
    ## duration matrix @var{C} are in sorted order.
    ##
    ## @code{@dots{} = setxor (@var{A}, @var{B}, @dots{}, @var{order})} also
    ## specifies the order of the returned unique values.  @var{order} can be
    ## @qcode{'sorted'}, which is the default behavior, or @qcode{'stable'}, in
    ## which case the unique values are returned in order of appearance.
    ##
    ## @code{[@var{C}, @var{ixA}, @var{ixB}] = setxor (@dots{})} also returns
    ## index vectors @var{ixA} and @var{ixB} such that
    ## @code{@var{C} = @var{A}(@var{ixA})} and
    ## @code{@var{C} = @var{B}(@var{ixB})}, unless the @qcode{'rows'} optional
    ## argument is given, in which case @code{@var{C} = @var{A}(@var{ixA},:)}
    ## and @code{@var{C} = @var{B}(@var{ixB},:)}.
    ##
    ## @end deftypefn
    function [C, ixA, ixB] = setxor (A, B, varargin)
      ## 'legacy' option is not supported
      if (any (strcmp ("legacy", varargin)))
        error ("duration.setxor: 'legacy' option is not supported.");
      endif
      if (ischar (A) || isstring (A) || iscellstr (A) || isnumeric (A))
        C = duration ('Format', B.Format);
        A = promote (A);
      elseif (ischar (B) || isstring (B) || iscellstr (B) || isnumeric (B))
        C = duration ('Format', A.Format);
        B = promote (B);
      elseif (isduration (A) && isduration (B))
        C = duration ('Format', A.Format);
      else
        error (strcat ("duration.setxor: set operation not defined", ...
                       " between '%s' and '%s' arrays."), class (A), class (B));
      endif
      [C.Millis, ixA, ixB] = setxor (A.Millis, B.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{C} =} union (@var{A}, @var{B})
    ## @deftypefnx {duration} {@var{C} =} union (@var{A}, @var{B}, @qcode{'rows'})
    ## @deftypefnx {duration} {@var{C} =} union (@var{A}, @var{B}, @dots{}, @var{order})
    ## @deftypefnx {duration} {[@var{C}, @var{ixA}, @var{ixB}] =} union (@dots{})
    ##
    ## Set union of two duration arrays.
    ##
    ## @code{@var{C} = union (@var{A}, @var{B})} returns the unique common
    ## values of the duration arrays @var{A} and @var{B}.  Either @var{A} or
    ## @var{B} input arguments can also be a duration string specified as a
    ## character vector, a string array, or a cell array of character vectors,
    ## or a numeric array representing 24-hour days.  In such case, the input is
    ## promoted to a duration array prior to calculating the intersection.  If
    ## both @var{A} and @var{B} are row vectors, then @var{C} is also a row
    ## vector, otherwise @code{intersect} returns a column vector.
    ##
    ## @code{@var{C} = union (@var{A}, @var{B}, @qcode{'rows'}} returns the
    ## unique common rows of the duration matrices @var{A} and @var{B}, which
    ## must have the same number of columns.  By default, the rows in
    ## duration matrix @var{C} are in sorted order.
    ##
    ## @code{@dots{} = union (@var{A}, @var{B}, @dots{}, @var{order})} also
    ## specifies the order of the returned unique values.  @var{order} can be
    ## @qcode{'sorted'}, which is the default behavior, or @qcode{'stable'}, in
    ## which case the unique values are returned in order of appearance.
    ##
    ## @code{[@var{C}, @var{ixA}, @var{ixB}] = union (@dots{})} also returns
    ## index vectors @var{ixA} and @var{ixB} such that
    ## @code{@var{C} = @var{A}(@var{ixA})} and
    ## @code{@var{C} = @var{B}(@var{ixB})}, unless the @qcode{'rows'} optional
    ## argument is given, in which case @code{@var{C} = @var{A}(@var{ixA},:)}
    ## and @code{@var{C} = @var{B}(@var{ixB},:)}.
    ##
    ## @end deftypefn
    function [C, ixA, ixB] = union (A, B, varargin)
      ## 'legacy' option is not supported
      if (any (strcmp ("legacy", varargin)))
        error ("duration.union: 'legacy' option is not supported.");
      endif
      if (ischar (A) || isstring (A) || iscellstr (A) || isnumeric (A))
        C = duration ('Format', B.Format);
        A = promote (A);
      elseif (ischar (B) || isstring (B) || iscellstr (B) || isnumeric (B))
        C = duration ('Format', A.Format);
        B = promote (B);
      elseif (isduration (A) && isduration (B))
        C = duration ('Format', A.Format);
      else
        error (strcat ("duration.union: set operation not defined", ...
                       " between '%s' and '%s' arrays."), class (A), class (B));
      endif
      [C.Millis, ixA, ixB] = union (A.Millis, B.Millis, varargin{:});
    endfunction

  endmethods

################################################################################
##                           ** Array Operations **                           ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'cat'              'horzcat'          'vertcat'          'repmat'          ##
## 'repelem'          'repelems'         'reshape'          'circshift'       ##
## 'permute'          'ipermute'         'transpose'        'ctranspose'      ##
##                                                                            ##
################################################################################

  methods (Access = public)

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} cat (@var{dim}, @var{A}, @var{B}, @dots{})
    ##
    ## Concatenate duration arrays.
    ##
    ## @code{@var{C} = cat (@var{dim}, @var{A}, @var{B}, @dots{})} concatenates
    ## duration arrays @var{A}, @var{B}, @dots{} along dimension @var{dim}.  All
    ## input arrays must have the same size except along the operating dimension
    ## @var{dim}.  Any of the input arrays may also be string arrays or cell
    ## arrays of character vectors of compatible size.  Additionally, an input
    ## can be a numeric matrix, which when parsed to the constructor will return
    ## a duration array of compatible size.
    ##
    ## @end deftypefn
    function out = cat (dim, varargin)
      ## If any of the input arrays is a calendarDuration array, then convert
      ## the first input to calendarDuration array and call the corresponding
      ## method.
      if (any (cellfun ('iscalendarduration', varargin)))
        if (isduration (varargin{1}))
          varargin{1} = calendarDuration (0, 0, 0, varargin{1});
        elseif (isnumeric (varargin{1}))
          if (isempty (varargin{1}))
            varargout{1} = calendarDuration ([], [], []);
          else
            varargout{1} = calendarDuration (0, 0, 0, 24 * varargin{i}, 0, 0);
          endif
        else
          error ("calendarDuration: invalid input to constructor.");
        endif
        out = cat (dim, varargin{:});
      else
        args = varargin;
        [args{:}] = promote (varargin{:});
        ## Get format from first duration array argument
        idx = find (cellfun ('isduration', varargin), 1);
        fmt = varargin{idx}.Format;
        out = duration ('Format', fmt);
        mils = cellfun (@(obj) obj.Millis, args, 'UniformOutput', false);
        out.Millis = cat (dim, mils{:});
      endif
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} horzcat (@var{A}, @var{B}, @dots{})
    ##
    ## Horizontal concatenation of duration arrays.
    ##
    ## @code{@var{C} = horzcat (@var{A}, @var{B}, @dots{}} is the equivalent of
    ## the syntax @code{@var{B} = [@var{A}, @var{B}, @dots{}]} and horizontally
    ## concatenates the duration arrays @var{A}, @var{B}, @dots{}.  All input
    ## arrays must have the same size except along the second dimension.  Any of
    ## the input arrays may also be string arrays or cell arrays of character
    ## vectors of compatible size.  Additionally, an input can be a numeric
    ## matrix, which when parsed to the constructor will return a duration array
    ## of compatible size.
    ##
    ## @end deftypefn
    function out = horzcat (varargin)
      out = cat (2, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{C} =} vertcat (@var{A}, @var{B}, @dots{})
    ##
    ## Vertical concatenation of duration arrays.
    ##
    ## @code{@var{C} = vertcat (@var{A}, @var{B}, @dots{}} is the equivalent of
    ## the syntax @code{@var{B} = [@var{A}; @var{B}; @dots{}]} and vertically
    ## concatenates the duration arrays @var{A}, @var{B}, @dots{}.  All input
    ## arrays must have the same size except along the first dimension.  All of
    ## the input arrays may also be string arrays or cell arrays of character
    ## vectors of compatible size.  Additionally, an input can be a numeric
    ## matrix, which when parsed to the constructor will return a duration array
    ## of compatible size.
    ##
    ## @end deftypefn
    function out = vertcat (varargin)
      out = cat (1, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} repmat (@var{A}, @var{n})
    ## @deftypefnx {duration} {@var{B} =} repmat (@var{A}, @var{d1}, @dots{}, @var{dN})
    ## @deftypefnx {duration} {@var{B} =} repmat (@var{A}, @var{dimvec})
    ##
    ## Repeat copies of a duration array.
    ##
    ## @code{@var{B} = repmat (@var{A}, @var{n})} returns a duration array
    ## @var{B} containing @var{n} copies of the input duration array @var{A}
    ## along every dimension of @var{A}.
    ##
    ## @code{@var{B} = repmat (@var{A}, @var{d1}, @dots{}, @var{dN})} returns an
    ## array @var{B} containing copies of @var{A} along the dimensions specified
    ## by the list of scalar integer values @var{d1}, @dots{}, @var{dN}, which
    ## specify how many copies of @var{A} are made in each dimension.
    ##
    ## @code{@var{B} = repmat (@var{A}, @var{dimvec})} is equivalent to the
    ## previous syntax with @code{@var{dimvec} = [@var{d1}, @dots{}, @var{dN}]}.
    ##
    ## @end deftypefn
    function this = repmat (this, varargin)
      this.Millis = repmat (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} repelem (@var{A}, @var{n})
    ## @deftypefnx {duration} {@var{B} =} repelem (@var{A}, @var{d1}, @dots{}, @var{dN})
    ##
    ## Repeat copies of duration array elements.
    ##
    ## @code{@var{B} = repelem (@var{A}, @var{n})} returns a duration vector
    ## @var{B} containing repeated elements of the input @var{A}, which must be
    ## a duration vector.  If @var{n} is a scalar, each element of @var{A} is
    ## repeated @var{n} times along the non-singleton dimension of @var{A}.  If
    ## @var{n} is a vector, it must have the same elements as @var{A}, in which
    ## case it specifies the number of times to repeat each corresponding
    ## element of @var{A}.
    ##
    ## @code{@var{B} = repelem (@var{A}, @var{d1}, @dots{}, @var{dN})} returns
    ## an array @var{B} with each element of @var{A} repeated according to the
    ## the list of input arguments @code{@var{d1}, @dots{}, @var{dN}} each
    ## corresponding to a different dimension @code{1:ndims (@var{A})} of the
    ## input array @var{A}.  @var{d1}, @dots{}, @var{dN} must be either scalars
    ## or vectors with the same length as the corresponding dimension of
    ## @var{A} containing non-negative integer values specifying the number of
    ## repetitions of each element along the corresponding dimension.
    ##
    ## @end deftypefn
    function this = repelem (this, varargin)
      this.Millis = repelem (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} repelems (@var{A}, @var{R})
    ##
    ## Construct a vector of repeated duration array.
    ##
    ## @code{@var{B} = repelems (@var{A}, @var{R})} returns a duration vector
    ## @var{B} containing repeated elements of the input @var{A}, which must be
    ## a duration vector.  @var{R} must be a @math{2*N} matrix of integers.
    ## Entries in the first row of @var{R} correspond to the linear indexing of
    ## the elements in @var{A} to be repeated.  The corresponding entries in the
    ## second row of @var{R} specify the repeat count of each element.
    ##
    ## @end deftypefn
    function this = repelems (this, R)
      this.Millis = repelems (this.Millis, R);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} reshape (@var{A}, @var{d1}, @dots{}, @var{dN})
    ## @deftypefnx {duration} {@var{B} =} reshape (@var{A}, @dots{}, @qcode{[]}, @dots{})
    ## @deftypefnx {duration} {@var{B} =} reshape (@var{A}, @var{dimvec})
    ##
    ## Reshape duration array.
    ##
    ## @code{@var{B} = reshape (@var{A}, @var{d1}, @dots{}, @var{dN})} returns a
    ## duration array @var{B} with specified dimensions @var{d1}, @dots{},
    ## @var{dN}, whose elements are taken columnwise from the duration array
    ## @var{A}.  The product of @var{d1}, @dots{}, @var{dN} must equal the total
    ## number of elements in @var{A}.
    ##
    ## @code{@var{B} = reshape (@var{A}, @dots{}, @qcode{[]}, @dots{})} returns
    ## a duration array @var{B} with one dimension unspecified which is
    ## calculated automatically so that the product of dimensions in @var{B}
    ## matches the total elements in @var{A}, which must be divisible the
    ## product of specified dimensions.  An empty matrix @qcode{([])} is used to
    ## flag the unspecified dimension.
    ##
    ## @end deftypefn
    function this = reshape (this, varargin)
      this.Millis = reshape (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn  {duration} {@var{B} =} circshift (@var{A}, @var{n})
    ## @deftypefnx {duration} {@var{B} =} circshift (@var{A}, @var{n}, @var{dim})
    ##
    ## Circularly shift the elements in a duration array.
    ##
    ## @code{@var{B} = circshift (@var{A}, @var{n})} circularly shifts the
    ## elements of the duration array @var{A} according to @var{n}.  If @var{n}
    ## is a nonzero integer scalar, then the elements of @var{A} are shifted by
    ## @var{n} elements along the first non-singleton dimension of @var{A}.  If
    ## @var{n} is a vector, it must not be longer that the number of dimensions
    ## of @var{A} with each value of @var{n} corresponding to a dimension in
    ## @var{A}.   The sign of the value(s) in @var{n} specify the direction in
    ## the elements of @var{A} are shifted.
    ##
    ## @code{@var{B} = circshift (@var{A}, @var{n}, @var{dim})} circularly
    ## shifts the elements of the duration array @var{A} along the dimension
    ## specified by @var{dim}.  In this case, @var{n} must be a scalar integer
    ## value.
    ##
    ## @end deftypefn
    function this = circshift (this, varargin)
      this.Millis = circshift (this.Millis, varargin{:});
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} permute (@var{A}, @var{dims})
    ##
    ## Generalized transpose for a duration N-D array.
    ##
    ## @code{@var{B} = permute (@var{A}, @var{dims})} returns the generalized
    ## transpose of the duration array @var{A} by rearranging its dimensions
    ## according to the permutation vector specified in @var{dims}.
    ##
    ## @var{dims} must index all the dimensions @code{1:ndims (@var{A})} of the
    ## input array @var{A}, in any order, but only once.  The @var{N}th
    ## dimension of @var{A} gets remapped to the dimension in @var{B} specified
    ## by @code{@var{dims}(@var{N})}.
    ##
    ## @end deftypefn
    function this = permute (this, order)
      this.Millis = permute (this.Millis, order);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{A} =} ipermute (@var{B}, @var{dims})
    ##
    ## Inverse of the generalized transpose for a duration N-D array.
    ##
    ## @code{@var{A} = ipermute (@var{B}, @var{dims})} returns the inverse of
    ## the generalized transpose performed by the @code{permute} function.  The
    ## expression @code{ipermute (permute (@var{A}, @var{dims}), @var{dims})}
    ## returns the original array @var{A}.
    ##
    ## @var{dims} must index all the dimensions @code{1:ndims (@var{B})} of the
    ## input array @var{B}, in any order, but only once.  The dimension of
    ## @var{B} specified in @code{@var{dims}(@var{N})} gets remapped to the
    ## @var{N}th dimension of @var{A}.
    ##
    ## @end deftypefn
    function this = ipermute (this, order)
      this.Millis = ipermute (this.Millis, order);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} transpose (@var{A})
    ##
    ## Transpose a duration matrix.
    ##
    ## @code{@var{B} = transpose (@var{A})} is the equivalent of the syntax
    ## @code{@var{B} = @var{A}.'} and returns the transpose of the duration
    ## matrix @var{A}.
    ##
    ## @end deftypefn
    function this = transpose (this)
      this.Millis = transpose (this.Millis);
    endfunction

    ## -*- texinfo -*-
    ## @deftypefn {duration} {@var{B} =} ctranspose (@var{A})
    ##
    ## Transpose a duration matrix.
    ##
    ## @code{@var{B} = ctranspose (@var{A})} is the equivalent of the syntax
    ## @code{@var{B} = @var{A}'} and returns the transpose of the duration
    ## matrix @var{A}.  For duration arrays, @code{ctranspose} is identical to
    ## @code{transpose}.
    ##
    ## @end deftypefn
    function this = ctranspose (this)
      this.Millis = ctranspose (this.Millis);
    endfunction

  endmethods

################################################################################
##                  ** Reference and Assignment Operations **                 ##
################################################################################
##                             Available Methods                              ##
##                                                                            ##
## 'end'              'subsref'          'subsasgn'                           ##
##                                                                            ##
################################################################################

  methods (Hidden)

    ## Overload 'end' keyword
    function last_index = end (this, end_dim, ndim_obj)
      lastdim = ndims (this);
      if (end_dim == ndim_obj && ndim_obj == 1)
        last_index = prod (size (this));
      elseif (end_dim == ndim_obj && end_dim < lastdim)
        last_index = prod (size (this)(end_dim:lastdim));
      else
        last_index = size (this, end_dim);
      endif
    endfunction

    ## Class specific subscripted reference
    function varargout = subsref (this, s)

      chain_s = s(2:end);
      s = s(1);
      switch (s.type)
        case '()'
          out = this;
          out.Millis = this.Millis(s.subs{:});

        case '{}'
          error (strcat ("duration.subsref: '{}' invalid indexing", ...
                         " for referencing values. Use '()' instead."));

        case '.'
          switch (s.subs)
            case 'Format'
              out = this.Format;
            otherwise
              error ("duration.subsref: unrecognized property: '%s'", s.subs);
          endswitch
      endswitch

      ## Chained references
      if (! isempty (chain_s))
        out = subsref (out, chain_s);
      endif
      varargout{1} = out;

    endfunction

    ## Class specific subscripted assignment
    function this = subsasgn (this, s, val)

      if (numel (s) > 1)
        error ("duration.subsasgn: chained subscripts not allowed.");
      endif
      switch (s.type)
        case '()'
          if (isempty (val))
            this.Millis(s.subs{:}) = [];
          elseif (isa (val, 'missing'))
            this.Millis(s.subs{:}) = NaN;
          elseif (iscellstr (val) || ischar (val) || isstring (val))
            if (! iscellstr (val))
              val = cellstr (val);
            endif
            this.Millis(s.subs{:}) = timestrings2millis (val, []);
          elseif (isnumeric (val))
            ## A bare number counts days, as it does everywhere else a
            ## duration meets one.
            this.Millis(s.subs{:}) = double (val) * 86400000;
          elseif (isa (val, "duration"))
            this.Millis(s.subs{:}) = val.Millis;
          else
            error (strcat ("duration.subsasgn: assignment value must", ...
                           " be a duration array, a numeric array of", ...
                           " days, or a text represention of durations."));
          endif

        case '{}'
          error (strcat ("duration.subsasgn: '{}' invalid indexing", ...
                         " for assigning values. Use '()' instead."));

        case '.'
          switch (s.subs)
            case 'Format'
              ## Convert string to character vector if necessary
              if (isstring (val))
                if (! isscalar (val))
                  error (strcat ("duration.subsasgn: 'Format' must be a", ...
                                 " character vector or a string scalar."));
                endif
                val = char (val);
              elseif (! (ischar (val) && isrow (val)))
                error (strcat ("duration.subsasgn: 'Format' must be a", ...
                               " character vector or a string scalar."));
              endif
              errmsg = checkFormatString (val);
              if (! isempty (errmsg))
                error ("duration.subsasgn: %s", errmsg);
              endif
              this.Format = val;
            otherwise
              error ("duration.subsasgn: unrecognized property: '%s'", s.subs);
          endswitch
      endswitch

    endfunction

  endmethods

  methods (Access = private)

    ## Return a subset of a duration array
    function out = subset (this, varargin)
      out = this;
      out.Millis = this.Millis(varargin{:});
    endfunction


  endmethods

endclassdef

## Promote numeric and string arrays to duration objects
function varargout = promote (varargin)
  for i = 1:numel (varargin)
    x = varargin{i};
    if (isa (x, "duration"))
      varargout{i} = x;
    elseif (isa (x, "missing"))
      ## A missing value becomes an all-NaN duration of the same shape.  Only
      ## its Millis are read back by 'cat', which takes the result's format
      ## from the first real duration operand, so this filler's own format
      ## never reaches the result.
      varargout{i} = days (NaN (size (x)));
    elseif (isnumeric (x))
      varargout{i} = days (x);
    elseif (iscellstr (x) || ischar (x) || isa (x, "string"))
      varargout{i} = duration (x);
    else
      error ("duration: invalid input to constructor.");
    endif
  endfor
endfunction

## Parse H, M, S, and MS numeric inputs into days
function [err, millis] = hms2millis (H, MI, S, MS = 0)
  err = 0;
  if (! isscalar (H) || ! isscalar (MI) || ! isscalar (S) || ! isscalar (MS))
    [err, H, MI, S, MS] = common_size (H, MI, S, MS);
    if (err > 0)
      millis = NaN;
      return
    endif
  endif
  H = double (H);
  MI = double (MI);
  S = double (S);
  MS = double (MS);
  millis = H * 3600000 + MI * 60000 + S * 1000 + MS;
endfunction

## Parse TimeString inputs into days
function millis = timestrings2millis (TS, inputFormat)
  millis = NaN (size (TS));
  ## Find default format (either 'dd:hh:mm:ss' or 'hh:mm:ss') from 1st element
  if (isempty (inputFormat))
    str1 = TS{1};
    nCols = numel (find (str1 == ':'));
    nDots = numel (find (str1 == '.'));
    if (nDots > 1)
      error ("duration: could not recognize time string format of '%s'.", str1);
    endif
    if (nCols > 3 || nCols < 1)
      error ("duration: could not recognize time string format of '%s'.", str1);
    endif
    if (nCols == 1)
      error ("duration: time string format is ambiguous.");
    endif
    if (nDots)
      cstr = strsplit (str1, '.');
      if (! isempty (cstr{2}) && isnan (str2double (cstr{2})))
        error (strcat ("duration: could not recognize time string", ...
                       " format of '%s'."), str1);
      endif
      cstr = strsplit (cstr{1}, ':');
      if (numel (cstr) != nCols + 1)
        error (strcat ("duration: could not recognize time string", ...
                       " format of '%s'."), str1);
      endif
      for i = 1:nCols + 1
        if (isnan (str2double (cstr{i})))
          error (strcat ("duration: could not recognize time string", ...
                         " format of '%s'."), str1);
        endif
      endfor
    endif
  else
    nCols = numel (find (inputFormat == ':'));
    nDots = numel (find (inputFormat == '.'));
  endif
  ## Process all elements according to inputFormat (unrecognized return NaN)
  for i = 1:numel (TS)
    str1 = TS{i};
    pnd_sign = 1;
    if (numel (find (str1 == '.')))
      cstr = strsplit (str1, '.');
      if (isempty (cstr{2}))
        MS = 0;
      else
        MSnumber = str2double (cstr{2});
        MSdigits = 10 ^ (numel (cstr{2}) - 3);
        MS = MSnumber / MSdigits;
      endif
      cstr = strsplit (cstr{1}, ':');
      if (numel (cstr) != nCols + 1)
        D = H = MI = S = NaN;
      elseif (nCols == 1) # 'mm:ss' only
        D  = 0;
        H  = 0;
        MI = str2double (cstr{1});
        if (MI < 0)
          pnd_sign = -1;
          MI = -MI;
        endif
        S  = str2double (cstr{2});
        if (S >= 60)
          S = NaN;
        endif
      elseif (nCols == 2) # 'hh:mm:ss'
        D  = 0;
        H  = str2double (cstr{1});
        if (H < 0)
          pnd_sign = -1;
          H = -H;
        endif
        MI = str2double (cstr{2});
        S  = str2double (cstr{3});
        if (MI >= 60 || S >= 60)
          MI = S = NaN;
        endif
      else  # 'dd:hh:mm:ss'
        D  = str2double (cstr{1});
        if (D < 0)
          pnd_sign = -1;
          D = -D;
        endif
        H  = str2double (cstr{2});
        MI = str2double (cstr{3});
        S  = str2double (cstr{4});
        if (H >= 24 || MI >= 60 || S >= 60)
          H = MI = S = NaN;
        endif
      endif
    else
      cstr = strsplit (str1, ':');
      if (numel (cstr) != nCols + 1)
        D = H = MI = S = MS = NaN;
      elseif (nCols == 1) # either 'mm:ss' or 'hh:mm'
        if (strcmp (inputFormat, 'mm:ss'))
          D  = 0;
          H  = 0;
          MI = str2double (cstr{1});
          if (MI < 0)
            pnd_sign = -1;
            MI = -MI;
          endif
          S  = str2double (cstr{2});
          MS = 0;
        else  # 'hh:mm'
          D  = 0;
          H  = str2double (cstr{1});
          if (H < 0)
            pnd_sign = -1;
            H = -H;
          endif
          MI = str2double (cstr{2});
          if (MI >= 60)
            MI = NaN;
          endif
          S  = 0;
          MS = 0;
        endif
      elseif (nCols == 2) # 'hh:mm:ss'
        D  = 0;
        H  = str2double (cstr{1});
        if (H < 0)
          pnd_sign = -1;
          H = -H;
        endif
        MI = str2double (cstr{2});
        S  = str2double (cstr{3});
        if (MI >= 60 || S >= 60)
          MI = S = NaN;
        endif
        MS = 0;
      else  # 'dd:hh:mm:ss'
        D  = str2double (cstr{1});
        if (D < 0)
          pnd_sign = -1;
          D = -D;
        endif
        H  = str2double (cstr{2});
        MI = str2double (cstr{3});
        S  = str2double (cstr{4});
        if (H >= 24 || MI >= 60 || S >= 60)
          H = MI = S = NaN;
        endif
        MS = 0;
      endif
    endif
    millis(i) = D * 86400000 + H * 3600000 + MI * 60000 + S * 1000 + MS;
    millis(i) *= pnd_sign;
  endfor
endfunction

## Check 'Format' string
function errmsg = checkFormatString (Format)
  errmsg = "";
  Format = strsplit (Format, '.')';
  validFmt = {'y', 'd', 'h', 'm', 's', 'dd:hh:mm:ss', 'hh:mm:ss', ...
              'mm:ss', 'hh:mm'};
  foundFmt = ismember (validFmt, Format(1));
  if (! any (foundFmt) || numel (Format) > 2)
    errmsg = "invalid display format.";
  endif
  if (any (foundFmt([1:5])) && numel (Format) > 1)
    errmsg = "invalid display format.";
  endif
  if (foundFmt(9) && numel (Format) > 1)
    errmsg = "'hh:mm' display format cannot indicate fractional second digits.";
  endif
  if (numel (Format) == 2)
    if (any (char (Format(2)) != 'S'))
      errmsg = "invalid display format for fractional second digits.";
    endif
    if (numel (Format{2}) > 9)
      errmsg = "more than nine fractional second digits in display format.";
    endif
  endif
endfunction

## Check 'InputFormat' string
function errmsg = checkInputFormatString (inputFormat)
  errmsg = '';
  inputFormat = strsplit (inputFormat, '.');
  validInFmt = {'dd:hh:mm:ss','hh:mm:ss','mm:ss','hh:mm'};
  foundInFmt = ismember (validInFmt, inputFormat(1));
  if (! any (foundInFmt) || numel (inputFormat) > 2)
    errmsg = "invalid 'InputFormat'.";
  endif
  if (foundInFmt(4) && numel (inputFormat) > 1)
    errmsg = "'hh:mm' input format cannot indicate fractional second digits.";
  endif
  if (numel (inputFormat) == 2)
    if (any (char (inputFormat(2)) != 'S'))
      errmsg = "invalid 'InputFormat' for fractional second digits.";
    endif
    if (numel (inputFormat{2}) > 9)
      errmsg = "more than nine fractional second digits in 'InputFormat'.";
    endif
  endif
endfunction


## Bin edges in seconds for a duration, from a count, a width or a unit name
function [ev, isCount] = durbinedges (xv, arg2, scope)

  isCount = false;
  xf = xv(isfinite (xv));
  if (isa (arg2, 'duration'))
    dv = milliseconds (arg2);
    if (isscalar (dv))
      ev = unitbinedges (xf, dv, scope);
    else
      ev = dv(:).';
    endif
  elseif (ischar (arg2) || isa (arg2, 'string'))
    ev = unitbinedges (xf, unitseconds (char (arg2), scope), scope);
  elseif (isnumeric (arg2) && isscalar (arg2) && ! islogical (arg2))
    if (! isreal (arg2) || ! isfinite (arg2) || arg2 < 1 || fix (arg2) != arg2)
      error ("%s: N must be a real positive integer.", scope);
    endif
    isCount = true;
    ## With no finite value to bin, MATLAB places the bins as though the data
    ## were a single zero, so the constant-data rule applies at zero rather
    ## than the edges running 0, 1, ... N.
    if (isempty (xf))
      lo = 0;
      hi = 0;
    else
      lo = min (xf);
      hi = max (xf);
    endif
    ev = gridbinedges (lo, hi, double (arg2), 0.5);
  elseif (isnumeric (arg2))
    error (strcat (scope, ": numeric bin edges are not accepted for a", ...
                   " duration; give a duration vector."));
  else
    error (strcat (scope, ": the second argument must be a duration, a", ...
                   " bin count, or a unit name."));
  endif

endfunction

## Edges one UNIT wide, aligned to multiples of the unit, covering the data
function ev = unitbinedges (xf, unit, scope)

  if (! (unit > 0) || ! isfinite (unit))
    error (strcat (scope, ": a bin width must be positive and finite."));
  endif
  if (isempty (xf))
    ev = [0, unit];
    return;
  endif
  left = unit * floor (min (xf) / unit);
  nbins = max (1, ceil ((max (xf) - left) / unit));
  ev = left + (0:nbins) * unit;

endfunction

## Length in milliseconds of a named time unit.  The binning path works in the
## stored unit throughout, as MATLAB's does; computing it in seconds instead
## puts a rounding into every width that is not a whole number of seconds.
function s = unitseconds (name, scope)

  yr = 31556952000;
  switch (lower (name))
    case 'second'
      s = 1000;
    case 'minute'
      s = 60000;
    case 'hour'
      s = 3600000;
    case 'day'
      s = 86400000;
    case 'week'
      s = 604800000;
    case 'month'
      s = yr / 12;
    case 'quarter'
      s = yr / 4;
    case 'year'
      s = yr;
    case 'decade'
      s = 10 * yr;
    case 'century'
      s = 100 * yr;
    otherwise
      error (strcat (scope, ": UNIT must be one of 'second', 'minute',", ...
                     " 'hour', 'day', 'week', 'month', 'quarter', 'year',", ...
                     " 'decade', or 'century'."));
  endswitch

endfunction

## Translate duration-valued histcounts options into seconds, resolving any
## bin count or unit BinMethod into explicit edges so the grid rule is used
function args = durhistargs (args, xv, scope)

  xf = xv(isfinite (xv));

  ## BinLimits decides the range everything else is derived from
  lim = [];
  for k = 1:numel (args) - 1
    if (istextscalar (args{k}) && strcmpi (char (args{k}), 'BinLimits'))
      v = args{k+1};
      if (isa (v, 'duration'))
        v = milliseconds (v);
      endif
      if (isnumeric (v) && numel (v) == 2)
        lim = double (v(:)).';
      endif
    endif
  endfor
  if (! isempty (lim))
    xf = xf(xf >= lim(1) & xf <= lim(2));
    lo = lim(1);
    hi = lim(2);
  elseif (! isempty (xf))
    lo = min (xf);
    hi = max (xf);
  else
    lo = [];
    hi = [];
  endif

  ## A leading positional argument is a bin count or a set of edges.  Either
  ## way it is resolved here, and the option loop below starts past it.
  hasSpec = false;
  k = 1;
  if (! isempty (args) && ! istextscalar (args{1}))
    if (isa (args{1}, 'duration'))
      if (isscalar (args{1}))
        ## A lone duration reads as a bin WIDTH, which this position does not
        ## take, in MATLAB or here.  Passed on it would become a bin COUNT of
        ## however many milliseconds it holds: 'days (2)' asked for 172800000
        ## bins and the array to hold them.
        error (strcat ("%s: a bin width must be given as 'BinWidth'; the", ...
                       " second argument is a bin count or a vector of bin", ...
                       " edges."), scope);
      endif
      dv = milliseconds (args{1});
      args{1} = dv(:).';
      hasSpec = true;
      k = 2;
    elseif (isnumeric (args{1}) && isscalar (args{1}) && ! islogical (args{1}))
      args = [{'BinEdges', countbinedges(lo, hi, args{1}, scope)}, args(2:end)];
      hasSpec = true;
      k = 3;
    else
      k = 2;
    endif
  endif

  while (k < numel (args))
    if (! istextscalar (args{k}))
      k += 2;
      continue;
    endif
    switch (lower (char (args{k})))
      case 'numbins'
        args{k} = 'BinEdges';
        args{k+1} = countbinedges (lo, hi, args{k+1}, scope);
        hasSpec = true;
      case {'binwidth', 'binedges'}
        hasSpec = true;
        if (isa (args{k+1}, 'duration'))
          dv = milliseconds (args{k+1});
          args{k+1} = dv(:).';
        elseif (isnumeric (args{k+1}))
          error ("%s: '%s' must be a duration.", scope, char (args{k}));
        endif
        ## A width with no finite data to place it against: the numeric
        ## function answers [0 1] and ignores the width entirely, where MATLAB
        ## gives a single bin one width across.  Resolving it to explicit edges
        ## here is the same thing 'BinMethod' with a unit name already does.
        if (strcmpi (char (args{k}), 'BinWidth') && isempty (xf)
            && isempty (lim) && isnumeric (args{k+1}))
          args{k} = 'BinEdges';
          args{k+1} = unitbinedges (xf, args{k+1}, scope);
        endif
      case 'binlimits'
        if (isa (args{k+1}, 'duration'))
          dv = milliseconds (args{k+1});
          args{k+1} = dv(:).';
        elseif (isnumeric (args{k+1}))
          error ("%s: '%s' must be a duration.", scope, char (args{k}));
        endif
      case 'binmethod'
        if (istextscalar (args{k+1}))
          name = lower (char (args{k+1}));
          if (strcmp (name, 'integers'))
            error (strcat (scope, ": 'integers' is not a valid 'BinMethod'", ...
                           " for a duration."));
          elseif (any (strcmp (name, {'auto', 'scott', 'fd', 'sturges', 'sqrt'})))
            args{k} = 'BinEdges';
            args{k+1} = countbinedges (lo, hi, methodbins (xf, lo, hi, name), ...
                                       scope);
          else
            args{k} = 'BinEdges';
            args{k+1} = unitbinedges (xf, unitseconds (name, scope), scope);
          endif
        endif
        hasSpec = true;
      case 'normalization'
        if (istextscalar (args{k+1})
            && any (strcmpi (char (args{k+1}), {'countdensity', 'pdf'})))
          error (strcat (scope, ": '%s' is not a valid 'Normalization' for", ...
                         " a duration; a density per unit time has no", ...
                         " meaning."), lower (char (args{k+1})));
        endif
    endswitch
    k += 2;
  endwhile

  ## Nothing said how to bin: use the automatic rule, which is a bin count from
  ## Scott's rule fed through the same grid edges as every other path
  if (! hasSpec)
    args = [args, {'BinEdges', countbinedges(lo, hi, ...
                                methodbins (xf, lo, hi, 'auto'), scope)}];
  endif

endfunction

## Bin count for one of the automatic bin-selection rules
function nbins = methodbins (xf, lo, hi, method)

  n = numel (xf);
  if (n < 2 || isempty (lo) || hi == lo)
    nbins = 1;
    return;
  endif
  switch (method)
    case 'sturges'
      nbins = ceil (1 + log2 (n));
      return;
    case 'sqrt'
      nbins = ceil (sqrt (n));
      return;
    case 'fd'
      q = quantile (xf(:), [0.25, 0.75], 1, 5);
      rawWidth = 2 * (q(2) - q(1)) * n ^ (-1/3);
    otherwise
      rawWidth = 3.5 * std (xf(:)) * n ^ (-1/3);
  endswitch
  if (! (rawWidth > 0))
    nbins = 1;
  else
    nbins = max (1, ceil ((hi - lo) / rawWidth));
  endif

endfunction

## Bin edges for a requested bin count, snapped to whole time units.  LO, HI and
## the result all count seconds; NBINS is the number of bins asked for and TICK
## the half-width used when the data are constant.
##
## Taking G as a whole time unit, everything runs on INTEGER counts of G:
##
##   nLo   = floor (LO / G)
##   spanU = ceil (HI / G) - nLo            % note ceil against floor
##   w     = ceil (spanU / NBINS)
##   c     = ceil ((NBINS * w - spanU) / 2)
##   L     = G * (nLo - c)
##
## with G the largest unit for which 'spanU / NBINS > 4/3' and the width still
## needs every bin, that is 'ceil (spanU / w) == NBINS'.
##
## **The left edge is not a rounding of the centred value.**  It is the unit
## holding LO, moved down by a whole number of units.  Every attempt to write it
## as a rounding of 'LO - (NBINS*w - range)/2' fails, because two cases can
## share that value and be placed a unit apart -- 'xmin = 0.25, range = 5' and
## 'xmin = 0.75, range = 10' both give -0.25, and MATLAB answers 0 and -1.
## Sweeping XMIN through a unit settles it: the answer is constant across the
## whole interval and steps once, which is a floor and not a rounding.
##
## **The ceiling in SPANU against the floor in nLo is the load-bearing part.**
## Data ending part way through a unit claims the whole of it, so the same
## elapsed range gives a different width depending on where it starts:
## 'seconds ([0 6])' is SPANU 6 and a 2-second width, 'seconds ([0.125 6.125])'
## is SPANU 7 and a 3-second width.
##
## **The threshold is on SPANU, not on the elapsed range**, and at exactly 4/3
## the numeric rule wins.  That is what separates 'seconds ([0 4])' (SPANU 4,
## ratio 4/3, numeric) from 'seconds ([0.125 4.125])' (SPANU 5, gridded), which
## no threshold on the elapsed range can do since both have the same range.
## 'binthr_probe.m' pins it at two scales.
##
## **The ladder stops at one day.**  There is no week and no month -- a week
## grid reproduces some spans and gets others wrong, and every span that looked
## like months is reproduced by days.  There is no year either: a year rung
## makes the acceptance test vacuous at NBINS == 1, where it returned a bin one
## year wide for an hour of data.
##
## When no unit clears the threshold the plain numeric rule in '__binedges__'
## takes over.  That is the terminating case at the bottom of the ladder rather
## than a separate regime: below 4/3 seconds there is no coarser unit to snap
## to.
function ev = gridbinedges (lo, hi, nbins, tick = 0.5)

  ## Constant data: an interval of one tick centred on the value.  The offsets
  ## are formed first and added once, so only one rounding lands on LO.
  if (lo == hi)
    ev = lo + (-tick + (0:nbins) * (2 * tick / nbins));
    return;
  endif

  ## Everything is integer arithmetic on unit indices.  SPANU is the count of
  ## whole units the data touches -- note the ceiling at the top against the
  ## floor at the bottom, so data ending part way through a unit still claims
  ## the whole of it.  That asymmetry is the whole rule: 6 seconds of data
  ## starting on a second gives SPANU 6 and a 2-second width, and the same 6
  ## seconds starting an eighth of a second later gives SPANU 7 and a 3-second
  ## width.
  for u = [86400000, 3600000, 60000, 1000]
    nLo = floor (lo / u);
    spanU = ceil (hi / u) - nLo;
    if (spanU < 1)
      continue;
    endif
    ## The threshold is on SPANU, not on the elapsed range.  At exactly 4/3 the
    ## numeric rule wins, which is what separates a 4-second range starting on
    ## a second (SPANU 4, ratio 4/3, numeric) from the same range starting an
    ## eighth later (SPANU 5, ratio 5/3, gridded).
    if (spanU / nbins <= 4/3)
      continue;
    endif
    width = ceil (spanU / nbins);
    ## Keep this unit while the bins overshoot the data by less than twice one
    ## width less a unit; past that the finer decimal rule wins.  The bound
    ## rises with the width, which is why a three-unit width tolerates an
    ## excess of three and a five-unit width tolerates seven.
    ##
    ## Measured, not derived: this separates all 712 captured cases that reach
    ## a unit -- 583 gridded by R2024a and 129 sent to the decimal rule -- with
    ## no exceptions either way.  It sits one unit tighter than "the first bin
    ## still holds data" (which would be 'excess <= 2*width - 2' and wrongly
    ## grids 38 of the 129), and why that last unit is withheld is not known.
    excess = nbins * width - spanU;
    if (excess >= 2 * (width - 1))
      continue;
    endif
    ## Centre the excess, rounding a half unit outwards.
    c = ceil (excess / 2);
    ev = u * ((nLo - c) + (0:nbins) * width);
    return;
  endfor

  ## Finer than the threshold allows: the plain numeric rule takes over
  ev = __binedges__ (lo, hi, nbins);

endfunction

## Edges for a requested bin count, over a range given in seconds
function ev = countbinedges (lo, hi, nbins, scope)

  if (! isnumeric (nbins) || ! isscalar (nbins) || ! isreal (nbins)
      || ! isfinite (nbins) || nbins < 1 || fix (nbins) != nbins)
    error (strcat (scope, ": 'NumBins' must be a real, finite, positive,", ...
                   " integer value."));
  endif
  ## No finite value to bin: the bins go where they would for a single zero.
  if (isempty (lo))
    lo = 0;
    hi = 0;
  endif
  ev = gridbinedges (lo, hi, double (nbins), 0.5);

endfunction

## True for a character vector or a scalar string
function tf = istextscalar (x)
  tf = (ischar (x) && isrow (x)) || (isa (x, 'string') && isscalar (x));
endfunction
