Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / sigmoid_train.m

diff --git a/octave_packages/signal-1.1.3/sigmoid_train.m b/octave_packages/signal-1.1.3/sigmoid_train.m
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+%% Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% 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 {Function File} @var{y} = sigmoid_train(@var{t}, @var{ranges}, @var{rc})
+%%
+%% Evaluates a train of sigmoid functions at @var{t}.
+%%
+%% The number and duration of each sigmoid is determined from @var{ranges}. Each
+%% row of @var{ranges} represents a real interval, e.g. if sigmod @code{i} starts
+%% at @code{t=0.1} and ends at @code{t=0.5}, then @code{@var{ranges}(i,:) = [0.1
+%% 0.5]}.
+%% The input @var{rc} is a array that defines the rising and falling time
+%% constants of each sigmoids. Its size must equal the size of @var{ranges}.
+%%
+%% Run @code{demo sigmoid_train} to some examples of the use of this function.
+%%
+%% @end deftypefn
+
+function envelope = sigmoid_train (t, range, timeconstant)
+
+  % number of sigmoids
+  nRanges = size (range, 1);
+
+  %% Parse time constants
+  if isscalar (timeconstant)
+    %% All bumps have the same time constant and are symmetric
+    timeconstant = timeconstant * ones (nRanges,2);
+
+  elseif any( size(timeconstant) != [1 1])
+
+    %% All bumps have different time constant but are symmetric
+    if length(timeconstant) ~= nRanges
+      error('signalError','Length of time constant must equal number of ranges.')
+    end
+    if isrow (timeconstant)
+      timeconstant = timeconstant';
+    end
+    timeconstant = repmat (timeconstant,1,2);
+
+  end
+
+  %% Make sure t is horizontal
+  flag_transposed = false;
+  if iscolumn (t)
+   t               = t.';
+   flag_transposed = true;
+  end
+  [ncol nrow]     = size (t);
+
+  % Compute arguments of each sigmoid
+  T    = repmat (t, nRanges, 1);
+  RC1  = repmat (timeconstant(:,1), 1, nrow);
+  RC2  = repmat (timeconstant(:,2), 1, nrow);
+  a_up = (repmat (range(:,1), 1 ,nrow) - T)./RC1;
+  a_dw = (repmat (range(:,2), 1 ,nrow) - T)./RC2;
+
+  % Evaluate the sigmoids and mix them
+  Y        = 1 ./ ( 1 + exp (a_up) ) .* (1 - 1 ./ ( 1 + exp (a_dw) ) );
+  envelope = max(Y,[],1);
+
+  if flag_transposed
+    envelope = envelope.';
+  end
+
+end
+
+%!demo
+%! % Vectorized
+%! t = linspace (0, 2, 500);
+%! range = [0.1 0.4; 0.6 0.8; 1 2];
+%! rc = [1e-2 1e-2; 1e-3 1e-3; 2e-2 2e-2];
+%! y = sigmoid_train (t, range, rc);
+%!
+%! close all
+%! for i=1:3
+%!     patch ([range(i,[2 2]) range(i,[1 1])], [0 1 1 0],...
+%!               'facecolor', [1 0.8 0.8],'edgecolor','none');
+%! end
+%! hold on; plot (t, y, 'b;Sigmoid train;','linewidth',2); hold off
+%! xlabel('time'); ylabel('S(t)')
+%! title ('Vectorized use of sigmoid train')
+%! axis tight
+%!
+%! %-------------------------------------------------------------------------
+%! % The colored regions show the limits defined in range.
+
+%!demo
+%! % On demand
+%! t = linspace(0,2,200).';
+%! ran = [0.5 1; 1.5 1.7];
+%! rc = 3e-2;
+%! dxdt = @(x_,t_) [ x_(2); sigmoid_train(t_, ran, rc) ];
+%! y = lsode(dxdt,[0 0],t);
+%!
+%! close all
+%! for i=1:2
+%!     patch ([ran(i,[2 2]) ran(i,[1 1])], [0 1 1 0],...
+%!               'facecolor', [1 0.8 0.8],'edgecolor','none');
+%! end
+%! hold on; plot (t, y(:,2), 'b;Speed;','linewidth',2); hold off
+%! xlabel('time'); ylabel('V(t)')
+%! title ('On demand use of sigmoid train')
+%! axis tight
+%!
+%! %-------------------------------------------------------------------------
+%! % The colored regions show periods when the force is active.