+
−% cpsdForCorrelatedInputs computes the output theoretical CPSD shape with given inputs.
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%
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−% DESCRIPTION: cpsdForCorrelatedInputs computes the output theoretical CPSD
+
−%              or PSD shape with given inputs.
+
−%              It returns summed and contributions only and takes
+
−%              input arrays of objects (instead of vectors) 
+
−%
+
−% CALL: [mat_out] = CPSD(sys, pl)
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−%
+
−% INPUTS:
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−%         - sys, (array of) ssm object
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−%
+
−% OUTPUTS:
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−%          _ mat_out contains specified returned aos
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−%
+
−% <a href="matlab:utils.helper.displayMethodInfo('ssm', 'cpsdForCorrelatedInputs')">Parameters Description</a>
+
−% 
+
−% VERSION: $Id: cpsdForCorrelatedInputs.m,v 1.2 2011/05/23 14:18:20 adrien Exp $
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−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
+
−function varargout = cpsdForCorrelatedInputs(varargin)
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−  
+
−  %% starting initial checks
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−  
+
−  % use the caller is method flag
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−  callerIsMethod = utils.helper.callerIsMethod;
+
−  
+
−  % Check if this is a call for parameters
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−  if utils.helper.isinfocall(varargin{:})
+
−    varargout{1} = getInfo(varargin{3});
+
−    return
+
−  end
+
−  
+
−  utils.helper.msg(utils.const.msg.MNAME, ['running ', mfilename]);
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−  
+
−  % Collect input variable names
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−  in_names = cell(size(varargin));
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−  for ii = 1:nargin,in_names{ii} = inputname(ii);end
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−  
+
−  % Collect all SSMs and plists
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−  [sys, ssm_invars, rest] = utils.helper.collect_objects(varargin(:), 'ssm', in_names);
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−  [pl, invars2, rest]  = utils.helper.collect_objects(rest(:), 'plist'); 
+
−  if ~isempty(rest)
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−    pl = combine(pl, plist(rest{:}));
+
−  end
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−  pl = combine(pl, getDefaultPlist());
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−  
+
−  %%% Internal call: Only one object + don't look for a plist
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−  internal = strcmp(varargin{end}, 'internal');
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−  
+
−  %% begin function body
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−  
+
−  %% retrieve system infos
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−  
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−  if numel(sys)~=1
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−    error('noisespectrum needs exactly one ssm as an input')
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−  end
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−  if ~sys.isnumerical
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−    error(['error because system ',sys.name,' is not numerical']);
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−  end
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−  if ~sys.isStable
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−    error('input ssm is not stable!')
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−  end
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−  if sys.timestep==0
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−   timestep = 1;
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−  else
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−    timestep = sys.timestep;
+
−  end
+
−  if ~internal
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−    inhist  = sys.hist;
+
−  end
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−  
+
−  %% modifying system's ordering
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−  if find(pl, 'reorganize')
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−    sys = reorganize(sys, pl, 'set', 'for cpsdForCorrelatedInputs', 'internal', 'internal');
+
−  end
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−  
+
−  %% collecting functions i/o data
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−  aos_in = find(pl, 'aos');
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−  PZ_in = find(pl, 'PZmodels');
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−  cov_in = find(pl, 'covariance');
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−  cpsd_in = find(pl, 'CPSD');
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−  noise_in = blkdiag(cov_in, cpsd_in/(timestep*2));
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−  powWhiteNoise = noise_in;
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−  [U1,S1,V1] = svd(noise_in.'); % testing hermitian symmetry and definite positiveness
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−  if (sum(S1<0)>0)
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−    error('covariance/cpsd matrix is not positive')
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−  elseif norm(U1-V1')>1e-15*sqrt(numel(U1))
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−    error('covariance/cpsd matrix is not hermitian symmetric')
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−  end
+
−    
+
−  %% getting system's i/o sizes
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−  inputSizes = sys.inputsizes;
+
−  outputSizes = sys.outputsizes; %#ok<NASGU>
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−  
+
−  Naos_in = inputSizes(1);
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−  NPZmodels = inputSizes(3);
+
−  
+
−  %% retrieving frequency vector
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−  if isempty(Naos_in)==0
+
−    f1 = find(pl,'f1');
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−    f2 = find(pl,'f2');
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−    NFreqs = find(pl,'nf');
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−    if isempty(f1) || isempty(f2)|| isempty(NFreqs)
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−      error('### Please specify frequency vector a start and stop frequency .');
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−    else
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−      freqs = 10.^linspace(log10(f1), log10(f2), NFreqs);
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−    end
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−  else
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−    freqs = aos_in(1).x;
+
−  end
+
−  
+
−  %% checking frequency vector
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−  for i=2:numel(aos_in)
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−    if ~isequal(freqs,aos_in(i).x)
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−      error('there exist different frequency vectors');
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−    end
+
−  end
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−  
+
−  %% reshape pzmodels and aos for input cross-spectra
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−  if size(PZ_in,1)==NPZmodels
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−    PZdata = zeros(Npzmodels,Npzmodels,NFreqs);
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−    for i=1:NPZmodels
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−      for j=1:Npzmodels
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−        a = resp(PZ_in(i,j), freqs);
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−        PZdata(i,j,:) = reshape(a.y,[1,NFreqs]) ;
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−      end
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−    end
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−  else
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−    error('Wrong size for field PZ_in')
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−  end
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−  
+
−  if size(aos_in,1)==Naos_in && size(aos_in,2)==Naos_in
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−    AOdata = zeros(Naos_in,Naos_in,NFreqs);
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−    for i=1:Naos_in
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−      for j=1:Naos_in
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−        AOdata(i,j,:) = reshape(aos_in(i,j).y,[1,NFreqs]) ;
+
−      end
+
−    end
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−  else
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−    error('Wrong size for field aos_in')
+
−  end
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−    
+
−  %% SSM Transfer function
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−  [a, b, c, d, Ts, InputName, StateName, OutputName,...
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−    inputvarunits, ssvarunits, outputvarunits] = double(sys);      %#ok<ASGLU>
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−  resps    = ssm.doBode(a, b, c, d, 2*pi*freqs, Ts);
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−  Noutputs = numel(OutputName);
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−
+
−  %% power for each frequency with SVD computation
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−  diagOnly = pl.find('DIAGONAL ONLY');
+
−  if diagOnly
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−    Result = zeros(Noutputs,NFreqs);
+
−  else
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−    Result = zeros(Noutputs,Noutputs,NFreqs);
+
−  end
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−  
+
−  for i_freq=1:NFreqs
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−    %% contribution from aos, testing positiveness
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−    powAO = squeeze(AOdata(:,:,i_freq));
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−    [U1,S1,V1] = svd(powAO.'); % testing hermitian symmetry and definite positiveness
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−    if (sum(S1<0)>0)
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−      error('AO covariance matrix is not positive')
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−    elseif norm(U1-V1')>1e-15*sqrt(numel(U1))
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−      error('AO covariance matrix is not hermitian symmetric')
+
−    end
+
−    %% contribution from PZmodels, testing positiveness
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−    tfPZ = squeeze(PZdata(:,:,i_freq));
+
−    powPZ = tfPZ * tfPZ';
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−    %% summing all three contributions sources, computing CPSD
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−    pow = blkdiag(powAO, powWhiteNoise, powPZ);
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−    RespLoc = squeeze(resps(:,:,i_freq));
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−    noise = RespLoc * pow * RespLoc' * (2*timestep) ;
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−    if diagOnly
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−      Result(:,i_freq) = real(diag(noise)) ;
+
−    else
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−      Result(:,:,i_freq) = noise ;
+
−    end
+
−  end
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−  
+
−  %% saving in aos
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−  if diagOnly    % making a psd only
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−    ao_out = ao.initObjectWithSize(Noutputs, 1);
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−    for io=1:Noutputs
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−        ao_out(io).setData(fsdata(freqs, squeeze(Result(io,:)) ));
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−        ao_out(io).setName( ['PSD of ' , OutputName{io}]);
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−        ao_out(io).setXunits('Hz');
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−        ao_out(io).setYunits(outputvarunits(io)*outputvarunits(io)/unit('Hz'));
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−        ao_out(io).setDescription( ['PSD of ' , OutputName{io}]);
+
−    end
+
−  else    % making a cpsd matrix
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−    ao_out = ao.initObjectWithSize(Noutputs, Noutputs);
+
−    for io=1:Noutputs
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−      for jo=1:Noutputs
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−        ao_out(io,jo).setData(fsdata(freqs, squeeze(Result(jo,io,:)) ));
+
−        ao_out(io,jo).setXunits('Hz');
+
−        ao_out(io,jo).setYunits(outputvarunits(io)*outputvarunits(jo)/unit('Hz'));
+
−        if io~=jo
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−          ao_out(io,jo).setName( ['Cross PSD of ', OutputName{jo}, ' and ', OutputName{io}]);
+
−          ao_out(io,jo).setDescription( ['Cross PSD of ', OutputName{jo}, ' and ', OutputName{io}]);
+
−        else
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−          ao_out(io,jo).setName( ['PSD of ' , OutputName{jo}]);
+
−          ao_out(io,jo).setDescription( ['PSD of ' , OutputName{jo}]);
+
−        end
+
−      end
+
−    end
+
−  end
+
−  
+
−  %% construct output matrix object
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−  out = matrix(ao_out);
+
−  if callerIsMethod
+
−    % do nothing
+
−  else
+
−    myinfo = getInfo('None');
+
−    out.addHistory(myinfo, pl , ssm_invars(1), inhist );
+
−  end
+
−  
+
−  %% Set output depending on nargout
+
−  if nargout == 1;
+
−    varargout = {out};
+
−  elseif nargout == 0;
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−    iplot(ao_out);
+
−  else
+
−    error('Wrong number of outputs')
+
−  end
+
−end
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−
+
−
+
−%--------------------------------------------------------------------------
+
−% 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: cpsdForCorrelatedInputs.m,v 1.2 2011/05/23 14:18:20 adrien Exp $', sets, pl);
+
−  
+
−end
+
−
+
−%--------------------------------------------------------------------------
+
−% Get Default Plist
+
−%--------------------------------------------------------------------------
+
−function pl = getDefaultPlist()
+
−  pl = ssm.getInfo('reorganize', 'for cpsdForCorrelatedInputs').plists;
+
−  pl.remove('set');
+
−  
+
−  p = param({'covariance', 'The covariance matrix of this noise between input ports for the <i>time-discrete</i> noise model.'}, []);
+
−  pl.append(p);
+
−  
+
−  p = param({'CPSD', 'The one sided cpsd matrix of the white noise between input ports.'}, []);
+
−  pl.append(p);
+
−  
+
−  p = param({'aos', 'An array of input AOs, provides the cpsd of the input noise.'}, ao.initObjectWithSize(1,0));
+
−  pl.append(p);
+
−  
+
−  p = param({'PZmodels', 'An array of input pzmodels, used to filter the input noise.'}, paramValue.DOUBLE_VALUE(zeros(0,1))); 
+
−  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);
+
−
+
−  p = param({'f2', 'The maximum frequency. Default is Nyquist or 1Hz.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  p = param({'f1', 'The minimum frequency. Default is f2*1e-5.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  p = param({'nf', 'The number of frequency bins. Frequencies are scale logarithmically'}, paramValue.DOUBLE_VALUE(200));
+
−  pl.append(p);
+
−  
+
−  p = param({'diagonal only', 'Set to true if you want the PSD instead of the CPSD'}, paramValue.TRUE_FALSE);
+
−  pl.append(p);
+
−
+
−end
+
−