## Copyright (C) 2006, 2007 Arno Onken <asnelt@asnelt.org>
## Copyright (C) 2023 Andreas Bertsatos <abertsatos@biol.uoa.gr>
##
## This file is part of the statistics 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/>.

## -*- texinfo -*-
## @deftypefn  {statistics} @var{vpath} = hmmviterbi (@var{sequence}, @var{transprob}, @var{outprob})
## @deftypefnx {statistics} @var{vpath} = hmmviterbi (@dots{}, "symbols", @var{symbols})
## @deftypefnx {statistics} @var{vpath} = hmmviterbi (@dots{}, "statenames", @var{statenames})
##
## Viterbi path of a hidden Markov model.
##
## Use the Viterbi algorithm to find the Viterbi path of a hidden Markov
## model given a sequence of outputs. The model assumes that the generation
## starts in state @code{1} at step @code{0} but does not include step
## @code{0} in the generated states and sequence.
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{sequence} is the vector of length @var{len} of given outputs. The
## outputs must be integers ranging from @code{1} to
## @code{columns (outprob)}.
##
## @item
## @var{transprob} is the matrix of transition probabilities of the states.
## @code{transprob(i, j)} is the probability of a transition to state
## @code{j} given state @code{i}.
##
## @item
## @var{outprob} is the matrix of output probabilities.
## @code{outprob(i, j)} is the probability of generating output @code{j}
## given state @code{i}.
## @end itemize
##
## @subheading Return values
##
## @itemize @bullet
## @item
## @var{vpath} is the vector of the same length as @var{sequence} of the
## estimated hidden states. The states are integers ranging from @code{1} to
## @code{columns (transprob)}.
## @end itemize
##
## If @code{"symbols"} is specified, then @var{sequence} is expected to be a
## sequence of the elements of @var{symbols} instead of integers ranging
## from @code{1} to @code{columns (outprob)}. @var{symbols} can be a cell array.
##
## If @code{"statenames"} is specified, then the elements of
## @var{statenames} are used for the states in @var{vpath} instead of
## integers ranging from @code{1} to @code{columns (transprob)}.
## @var{statenames} can be a cell array.
##
## @subheading Examples
##
## @example
## @group
## transprob = [0.8, 0.2; 0.4, 0.6];
## outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
## [sequence, states] = hmmgenerate (25, transprob, outprob);
## vpath = hmmviterbi (sequence, transprob, outprob);
## @end group
##
## @group
## symbols = @{"A", "B", "C"@};
## statenames = @{"One", "Two"@};
## [sequence, states] = hmmgenerate (25, transprob, outprob, ...
##                      "symbols", symbols, "statenames", statenames);
## vpath = hmmviterbi (sequence, transprob, outprob, ...
##         "symbols", symbols, "statenames", statenames);
## @end group
## @end example
##
## @subheading References
##
## @enumerate
## @item
## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC,
## 2001.
##
## @item
## Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected
## Applications in Speech Recognition. @cite{Proceedings of the IEEE},
## 77(2), pages 257-286, February 1989.
## @end enumerate
## @end deftypefn

function vpath = hmmviterbi (sequence, transprob, outprob, varargin)

  # Check arguments
  if (nargin < 3 || mod (length (varargin), 2) != 0)
    print_usage ();
  endif

  if (! ismatrix (transprob))
    error ("hmmviterbi: transprob must be a non-empty numeric matrix");
  endif
  if (! ismatrix (outprob))
    error ("hmmviterbi: outprob must be a non-empty numeric matrix");
  endif

  len = length (sequence);
  # nstate is the number of states of the hidden Markov model
  nstate = rows (transprob);
  # noutput is the number of different outputs that the hidden Markov model
  # can generate
  noutput = columns (outprob);

  # Check whether transprob and outprob are feasible for a hidden Markov model
  if (columns (transprob) != nstate)
    error ("hmmviterbi: transprob must be a square matrix");
  endif
  if (rows (outprob) != nstate)
    error (strcat (["hmmviterbi: outprob must have the same number of"], ...
                   [" rows as transprob"]));
  endif

  # Flag for symbols
  usesym = false;
  # Flag for statenames
  usesn = false;

  # Process varargin
  for i = 1:2:length (varargin)
    # There must be an identifier: 'symbols' or 'statenames'
    if (! ischar (varargin{i}))
      print_usage ();
    endif
    # Upper case is also fine
    lowerarg = lower (varargin{i});
    if (strcmp (lowerarg, 'symbols'))
      if (length (varargin{i + 1}) != noutput)
        error (strcat (["hmmviterbi: number of symbols does not match"], ...
                       [" number of possible outputs"]));
      endif
      usesym = true;
      # Use the following argument as symbols
      symbols = varargin{i + 1};
    # The same for statenames
    elseif (strcmp (lowerarg, 'statenames'))
      if (length (varargin{i + 1}) != nstate)
        error (strcat (["hmmviterbi: number of statenames does not match"], ...
                       [" number of states"]));
      endif
      usesn = true;
      # Use the following argument as statenames
      statenames = varargin{i + 1};
    else
      error (strcat (["hmmviterbi: expected 'symbols' or 'statenames'"], ...
                     sprintf (" but found '%s'", varargin{i})));
    endif
  endfor

  # Transform sequence from symbols to integers if necessary
  if (usesym)
    # sequenceint is used to build the transformed sequence
    sequenceint = zeros (1, len);
    for i = 1:noutput
      # Search for symbols(i) in the sequence, isequal will have 1 at
      # corresponding indices; i is the right integer for that symbol
      isequal = ismember (sequence, symbols(i));
      # We do not want to change sequenceint if the symbol appears a second
      # time in symbols
      if (any ((sequenceint == 0) & (isequal == 1)))
        isequal *= i;
        sequenceint += isequal;
      endif
    endfor
    if (! all (sequenceint))
      index = max ((sequenceint == 0) .* (1:len));
      error (["hmmviterbi: sequence(" int2str (index) ") not in symbols"]);
    endif
    sequence = sequenceint;
  else
    if (! isvector (sequence) && ! isempty (sequence))
      error ("hmmviterbi: sequence must be a vector");
    endif
    if (! all (ismember (sequence, 1:noutput)))
      index = max ((ismember (sequence, 1:noutput) == 0) .* (1:len));
      error (["hmmviterbi: sequence(" int2str (index) ") out of range"]);
    endif
  endif

  # Each row in transprob and outprob should contain log probabilities
  # => scale so that the sum is 1 and convert to log space
  # - for transprob
  s = sum (transprob, 2);
  s(s == 0) = 1;
  transprob = log (transprob ./ (s * ones (1, columns (transprob))));
  # - for outprob
  s = sum (outprob, 2);
  s(s == 0) = 1;
  outprob = log (outprob ./ (s * ones (1, columns (outprob))));

  # Store the path starting from i in spath(i, :)
  spath = ones (nstate, len + 1);
  # Set the first state for each path
  spath(:, 1) = (1:nstate)';
  # Store the probability of path i in spathprob(i)
  spathprob = transprob(1, :);

  # Find the most likely paths for the given output sequence
  for i = 1:len
    # Calculate the new probabilities of the continuation with each state
    nextpathprob = ((spathprob' + outprob(:, sequence(i))) * ...
                    ones (1, nstate)) + transprob;
    # Find the paths with the highest probabilities
    [spathprob, mindex] = max (nextpathprob);
    # Update spath and spathprob with the new paths
    spath = spath(mindex, :);
    spath(:, i + 1) = (1:nstate)';
  endfor

  # Set vpath to the most likely path
  # We do not want the last state because we do not have an output for it
  [m, mindex] = max (spathprob);
  vpath = spath(mindex, 1:len);

  # Transform vpath into statenames if requested
  if (usesn)
    vpath = reshape (statenames(vpath), 1, len);
  endif

endfunction

%!test
%! sequence = [1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 3, ...
%!             3, 2, 3, 1, 1, 1, 1, 3, 3, 2, 3, 1, 3];
%! transprob = [0.8, 0.2; 0.4, 0.6];
%! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
%! vpath = hmmviterbi (sequence, transprob, outprob);
%! expected = [1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, ...
%!             1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1];
%! assert (vpath, expected);

%!test
%! sequence = {"A", "B", "A", "A", "A", "B", "B", "A", "B", "C", "C", "C", ...
%!             "C", "B", "C", "A", "A", "A", "A", "C", "C", "B", "C", "A", "C"};
%! transprob = [0.8, 0.2; 0.4, 0.6];
%! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
%! symbols = {"A", "B", "C"};
%! statenames = {"One", "Two"};
%! vpath = hmmviterbi (sequence, transprob, outprob, "symbols", symbols, ...
%!                                                   "statenames", statenames);
%! expected = {"One", "One", "Two", "Two", "Two", "One", "One", "One", ...
%!             "One", "One", "One", "One", "One", "One", "One", "Two", ...
%!             "Two", "Two", "Two", "One", "One", "One", "One", "One", "One"};
%! assert (vpath, expected);
