--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/@ssm/steadyState.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,195 @@
+% STEADYSTATE returns a possible value for the steady state of an ssm.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% DESCRIPTION: STEADYSTATE returns a possible value for the steady state
+%              of the state space of an ssm with given inputs.
+%
+% CALL: [pl_out] = steadyState(sys, pl)
+%
+% INPUTS:
+%         - sys, an ssm object
+%
+% OUTPUTS:
+%         _ pl_out contains 'state', the random state position
+%
+% <a href="matlab:utils.helper.displayMethodInfo('ssm', 'steadyState')">Parameters Description</a>
+%
+% VERSION: $Id: steadyState.m,v 1.11 2011/04/08 08:56:23 hewitson Exp $
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% TO DO: Check input aos for the timestep, tsdata, and ssm.timestep
+% options to be defined (NL case)
+% add check if one input mach no ssm input variable
+% allow use of other LTPDA functions to generate white noise
+
+
+function varargout = steadyState(varargin)
+  
+  %% starting initial checks
+  
+  % Check if this is a call for parameters
+  if utils.helper.isinfocall(varargin{:})
+    varargout{1} = getInfo(varargin{3});
+    return
+  end
+  
+  utils.helper.msg(utils.const.msg.MNAME, ['running ', mfilename]);
+  
+  % Collect input variable names
+  in_names = cell(size(varargin));
+  for ii = 1:nargin,in_names{ii} = inputname(ii);end
+  
+  % Collect all SSMs and plists
+  [sys, ssm_invars, rest] = utils.helper.collect_objects(varargin(:), 'ssm', in_names);
+  [pl, invars2, rest]  = utils.helper.collect_objects(rest(:), 'plist');
+  if ~isempty(rest)
+    pl = combine(pl, plist(rest{:}));
+  end
+  pl = combine(pl, getDefaultPlist());
+  
+  %% begin function body
+  
+  if numel(sys)~=1
+    error('simulate needs exactly one ssm as an input')
+  end
+  if ~sys.isnumerical
+    error(['error because system ',sys.name,' is not numerical']);
+  end
+  timestep  = sys.timestep;
+  if timestep==0
+    error('timestep should not be 0 in steadyState!!')
+  end
+  if pl.isparam('noise variable names')
+    error('The noise option used must be split between "covariance" and "cpsd". "noise variable names" does not exist anymore!')
+  end
+  sssizes = sys.sssizes;
+  %% collecting simulation i/o data
+  
+  constants_in = find(pl, 'constants');
+  cov_in = find(pl, 'covariance');
+  cpsd_in = find(pl, 'CPSD');
+  noise_in = blkdiag(cov_in, cpsd_in/(timestep*2));
+  [U1,S1,V1] = svd(noise_in.');
+  if (sum(S1<0)>0)
+    error('Covariance matrix is not positive definite')
+  end
+  noise_mat = U1*sqrt(S1);
+  
+  %% modifying system's ordering
+  if find(pl, 'reorganize')
+    sys = reorganize(sys, pl, 'set', 'for simulate', 'internal', 'internal');
+  end
+  
+  %% getting system's i/o sizes
+  inputSizes = sys.inputsizes;
+  
+  Nnoise = inputSizes(2);
+  Nconstants = inputSizes(3);
+  
+  if numel(diag(noise_in))~=Nnoise
+    error(['There are ' num2str(numel(diag(noise_in))) ' input noise variances and ' num2str(Nnoise) ' corresponding inputs indexed.' ])
+  elseif numel(constants_in)~=Nconstants
+    error(['There are ' num2str(numel(constants_in)) ' input constants and ' num2str(Nconstants) ' corresponding inputs indexed.' ])
+  end
+  
+  A = sys.amats{1,1};
+  Bnoise   = sys.bmats{1,2} * noise_mat;
+  Bcst     = sys.bmats{1,3} * reshape(constants_in, Nconstants, 1);
+  
+  %% counting powers of 2 to use for initilization
+  nSteps = 500;
+  tSteady =  find(pl, 'tSteady');
+  nPow2 = nextpow2(tSteady/(nSteps*timestep));
+  
+  %% simulation loop
+  A_pow2=cell(1,nPow2);
+  G_pow2=cell(1,nPow2);
+  
+  A_pow2{1} = A;
+  G_pow2{1} = Bcst;
+  
+  %% method 1 :  iterate equations with growing time-step for a very long time
+  E_pow2=cell(1,nPow2);
+  E_pow2{1} = Bnoise;
+  for i_pow2 = 2:nPow2
+    G_pow2{i_pow2} = G_pow2{i_pow2-1} + A_pow2{i_pow2-1}*G_pow2{i_pow2-1};
+    E_pow2{i_pow2} = E_pow2{i_pow2-1} + A_pow2{i_pow2-1}*E_pow2{i_pow2-1};
+    A_pow2{i_pow2} = A_pow2{i_pow2-1}^2;
+  end
+  lastX = zeros(size(A,1),1);
+  for i_pow2 = fliplr(1:nPow2)
+    A = A_pow2{i_pow2};
+    G = G_pow2{i_pow2};
+    E = E_pow2{i_pow2};
+    noise_array = randn(size(E,2), nSteps);
+    for i_steps = 1:nSteps
+      lastX  = A*lastX +  G + E*noise_array(:,i_steps) ;
+    end
+  end
+  
+  %% method 2 : compute the limit state-mean and covariance as i_pow2 tends to infinity
+  %   P_pow2=cell(1,nPow2);
+  %   P_pow2{1} = Bnoise*Bnoise.';
+  %   for i_pow2 = 2:nPow2
+  %     G_pow2{i_pow2} = G_pow2{i_pow2-1} + A_pow2{i_pow2-1}*G_pow2{i_pow2-1}; % taking step response to 2 longer time;
+  %     P_pow2{i_pow2} = P_pow2{i_pow2-1} + A_pow2{i_pow2-1}*P_pow2{i_pow2-1}*(A_pow2{i_pow2-1}.');% taking state covariance to 2 longer time;
+  %     A_pow2{i_pow2} = A_pow2{i_pow2-1}^2;
+  %   end
+  %   [U1,S1,V1] = svd(P_pow2{nPow2});
+  %   lastX = U1*sqrt(S1)*randn(size(A,1),1) + G_pow2{nPow2};
+  
+  %% construct output analysis object
+  plist_out = plist('state', ssm.blockMatRecut(lastX,sssizes,1) );
+  varargout  = {plist_out};
+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: steadyState.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({'cpsd variable names', 'A cell-array of strings specifying the desired input variable names.'}, {} );
+  pl.append(p);
+  
+  p = param({'cpsd', 'The covariance of this noise between input ports for the <i>time-continuous</i> noise model.'}, []);
+  pl.append(p);
+  
+  p = param({'covariance variable names', 'A cell-array of strings specifying the desired input variable names.'}, {} );
+  pl.append(p);
+  
+  p = param({'covariance', 'The covariance of this noise between input ports for the <i>time-continuous</i> noise model.'}, []);
+  pl.append(p);
+  
+  p = param({'constant variable names', 'A cell-array of strings of the desired input variable names.'}, {});
+  pl.append(p);
+  
+  p = param({'constants', 'Array of DC values for the different corresponding inputs.'}, paramValue.DOUBLE_VALUE(zeros(0,1)));
+  pl.append(p);
+  
+  p = param({'tSteady', 'The settling time used in the calculation, in the same unit as the ssm''s timestep'}, paramValue.DOUBLE_VALUE(10^6) );
+  pl.append(p);
+  
+  p = param({'reorganize', 'When set to 0, this means the ssm does not need be modified to match the requested i/o. Faster but dangerous!'}, paramValue.TRUE_FALSE);
+  pl.append(p);
+  
+end
+