--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/@ssm/modifyTimeStep.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,231 @@
+% MODIFYTIMESTEP modifies the timestep of a ssm object
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% DESCRIPTION: MODIFYTIMESTEP modifies the timestep of a ssm object, and updates
+%              the A and B matrices supposing there is no aliasing.
+%
+% CALL: sys = modifyTimeStep(sys,pl)
+%
+% INPUTS:
+%           sys - (array of) ssm objects
+%            pl - A plist or numeric value giving new timestep value (param name 'newtimestep')
+%
+% OUTPUTS: 
+%           sys - (array of) ssm
+%
+% <a href="matlab:utils.helper.displayMethodInfo('ssm', 'modifyTimeStep')">Parameters Description</a>
+%
+% VERSION: $Id: modifyTimeStep.m,v 1.11 2011/04/08 08:56:23 hewitson Exp $
+% 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function varargout = modifyTimeStep(varargin)
+  
+  %% Check if this is a call for parameters
+  if utils.helper.isinfocall(varargin{:})
+    varargout{1} = getInfo(varargin{3});
+    return
+  end
+  
+  %% send starting message
+  import utils.const.*
+  utils.helper.msg(msg.PROC3, 'running %s/%s', mfilename('class'), mfilename);
+  
+  %% collecting input
+  in_names = cell(size(varargin));
+  for ii = 1:nargin,in_names{ii} = inputname(ii);end
+  
+  [sys, ssm_invars, rest] = utils.helper.collect_objects(varargin(:), 'ssm', in_names);
+  [pl, invars2, rest]  = utils.helper.collect_objects(rest(:), 'plist');
+  % override with a numeric input value
+  if ~isempty(rest)
+    % if the user inputs a single numerical value, we use it
+    if isnumeric(rest{1}) && numel(rest{1}) == 1
+      if ~isa(pl, 'plist') % perhaps we dont' have a plist yet
+        pl = plist();
+      end
+      pl.pset('newtimestep', rest{1}); % set newtimestep
+    else
+      pl = combine(pl, plist(rest{:}));
+    end
+  end
+  pl = combine(pl, getDefaultPlist());
+  
+  %%% Internal call: Only one object + don't look for a plist
+  internal = strcmp(varargin{end}, 'internal');
+  
+  %% dealing with user custom inputs
+  
+  Nsys     = numel(sys);
+  
+  %% begin function body
+  
+  %% building output depending on options
+  sys = copy(sys,nargout);
+  newtimestep = find(pl,'newtimestep');
+  outputAntiAlias = find(pl, 'outputAntiAlias');
+  if numel(newtimestep)~=1
+    error('parameter "newtimestep" should be of size 1x1')
+  end
+  
+  for i = 1:Nsys
+    if ~sys(i).isnumerical
+      error(['error in modifTimeStep because system "',sys(i).name, '" should be numerical to be modified' ]);
+    end
+    
+    %% retrieving input data
+    timestep    = sys(i).timestep;
+    sssizes     = sys(i).sssizes;
+    inputsizes  = sys(i).inputsizes;
+
+    amat       = ssm.blockMatFusion(sys(i).amats, sssizes, sssizes);   
+    bmat       = ssm.blockMatFusion(sys(i).bmats, sssizes, inputsizes);
+    if outputAntiAlias
+      outputsizes = sys(i).outputsizes;
+      cmat        = ssm.blockMatFusion(sys(i).cmats, outputsizes, sssizes);
+      dmat        = ssm.blockMatFusion(sys(i).dmats, outputsizes, inputsizes);
+    end
+
+    %% take different actions depending on old and new timestep
+    if timestep == newtimestep
+      action = 'DoNothing';
+    elseif newtimestep == 0
+      action = 'MakeContinuous';
+      str = 'warning because system is sent back to continuous time';
+      utils.helper.msg(utils.const.msg.MNAME, str);
+    elseif timestep == 0
+      action = 'Discretize';
+    elseif floor(newtimestep/timestep) == newtimestep/timestep
+      action = 'TakeMultiple';
+    elseif newtimestep > timestep
+      action = 'MakeLonger';
+    else
+      action = 'MakeShorter';
+      str = 'warning because system is sent back to shorter time step';
+      utils.helper.msg(utils.const.msg.MNAME, str);
+    end
+    
+    %% proceed with matrix modifications
+    
+    amat_input = zeros(size(amat));
+    if isequal(action,'DoNothing')
+      %% same timestep : do nothing
+      amat_2 = amat;
+      bmat_2 = bmat;
+    elseif isequal(action,'Discretize')
+      %% from continuous to discrete
+      amat_2 = expm(amat * newtimestep);
+      amat_input = ExpInt(amat, newtimestep);
+      bmat_2 = real(amat_input * bmat);
+      if outputAntiAlias
+        cmat_2 = cmat * 0.5*(eye(size(amat_2)) + amat_2);
+        dmat_2 = dmat + cmat*0.5*bmat_2;
+        sys(i).cmats = ssm.blockMatRecut(real(cmat_2), outputsizes, sssizes);
+        sys(i).dmats = ssm.blockMatRecut(real(dmat_2), outputsizes, inputsizes);
+      end
+    elseif isequal(action,'MakeContinuous')
+      %% for discrete to continuous
+      [V, E] = eig(amat);
+      amat_2 = real(V * (diag(log(diag(E)))/timestep) * V^(-1));
+      amat_input = ExpInt(amat_2, timestep);
+      amat_input_inv = (amat_input)^(-1);
+      bmat_2 = real(amat_input_inv * bmat);
+      if outputAntiAlias
+        cmat_2 = cmat * (0.5*(eye(size(amat)) + amat))^-1;
+        dmat_2 = dmat - cmat_2*0.5*bmat;
+        sys(i).cmats = ssm.blockMatRecut(real(cmat_2), outputsizes, sssizes);
+        sys(i).dmats = ssm.blockMatRecut(real(dmat_2), outputsizes, inputsizes);
+      end
+    elseif isequal(action,'TakeMultiple')
+      %% discrete to discrete with a multiple
+      multiple = newtimestep/timestep;
+      amat_2 = amat^multiple;
+      for i_step = 1:multiple
+        amat_input = amat_input + amat^(i_step-1);
+      end
+      bmat_2 = real(amat_input * bmat);
+      if outputAntiAlias
+        cmat_0 = cmat * (0.5*(eye(size(amat)) + amat))^-1;
+        cmat_2 = cmat_0 * 0.5*(eye(size(amat_2)) + amat_2);
+        dmat_2 = dmat + cmat_0*0.5*bmat_2 - cmat_0*0.5*bmat;
+        sys(i).cmats = ssm.blockMatRecut(real(cmat_2), outputsizes, sssizes);
+        sys(i).dmats = ssm.blockMatRecut(real(dmat_2), outputsizes, inputsizes);
+      end
+    elseif isequal(action,'MakeLonger')||isequal(action,'MakeShorter')
+      %% discrete to discrete with no multiple relationship
+      [V, E] = eig(amat);
+      amat_c = real(V * (diag(log(diag(E)))/timestep) * V^(-1));
+      amat_2 = expm( amat * newtimestep/timestep);
+      amat_input_1 = ExpInt(amat_c, timestep);
+      amat_input_2 = ExpInt(amat_c, newtimestep);
+      bmat_2 = real(amat_input_2 * (amat_input_1)^(-1) * bmat);
+      if outputAntiAlias
+        cmat_0 = cmat * (0.5*(eye(size(amat)) + amat))^-1;
+        cmat_2 = cmat_0 * 0.5*(eye(size(amat_2)) + amat_2);
+        dmat_2 = dmat + cmat_0*0.5*bmat_2 - cmat_0*0.5*bmat;
+        sys(i).cmats = ssm.blockMatRecut(real(cmat_2), outputsizes, sssizes);
+        sys(i).dmats = ssm.blockMatRecut(real(dmat_2), outputsizes, inputsizes);
+      end
+    end
+    amat_2 = real(amat_2);
+    bmat_2 = real(bmat_2);
+    %% Save Matrix modifications
+    sys(i).amats = ssm.blockMatRecut(amat_2, sssizes, sssizes);
+    sys(i).bmats = ssm.blockMatRecut(bmat_2, sssizes, inputsizes);
+    sys(i).timestep = newtimestep;
+    if ~internal
+      sys(i).addHistory(getInfo('None'), pl, ssm_invars(i), sys(i).hist );
+    end
+  end
+  if nargout == numel(sys)
+    for ii = 1:numel(sys)
+      varargout{ii} = sys(ii);
+    end
+  else
+    varargout{1} = sys;
+  end
+end
+
+function A_int = ExpInt(A, t)
+  niter = 35;
+  A1 = A*t;
+  A2 = eye(size(A))*t;
+  A_int = zeros(size(A));
+  for i=1:niter
+    A_int = A_int + A2;
+    A2 = A1*A2/(i+1);
+  end
+end
+
+
+%--------------------------------------------------------------------------
+% Get Info Object
+%--------------------------------------------------------------------------
+function ii = getInfo(varargin)
+  
+  if nargin == 1 && strcmpi(varargin{1}, 'None')
+    sets = {};
+    pl   = [];
+  else
+    sets = {'Default'};
+    pl   = getDefaultPlist;
+  end
+  % Build info object
+  ii = minfo(mfilename, 'ssm', 'ltpda', utils.const.categories.op, '$Id: modifyTimeStep.m,v 1.11 2011/04/08 08:56:23 hewitson Exp $', sets, pl);
+end
+
+%--------------------------------------------------------------------------
+% Get Default Plist
+%--------------------------------------------------------------------------
+function pl = getDefaultPlist()
+  pl = plist();
+  
+  p = param({'newtimestep', 'Specify the desired new timestep.'}, paramValue.EMPTY_DOUBLE);
+  pl.append(p);
+  
+  p = param({'outputAntiAlias', 'Uses a linear averaging method to compute the systems output.'}, paramValue.TRUE_FALSE);
+  pl.append(p);
+  
+end
+
+