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−% LINLSQSVD Linear least squares with singular value decomposition
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%
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−% DESCRIPTION: Linear least square problem with singular value
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−% decomposition
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−%
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−% ALGORITHM: % It solves the problem
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−%
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−%        Y = HX
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−%
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−% where X are the parameters, Y the measurements, and H the linear
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−% equations relating the two.
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−% It is able to perform linear identification of the parameters of a
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−% multichannel systems. The results of different experiments on the same
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−% system can be passed as input. The algorithm, thanks to the singular
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−% value decomposition, extract the maximum amount of information from each
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−% single channel and for each experiment. Total information is then
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−% combined to get the final result.
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−%            
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−% CALL: [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y);
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−%       [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y,errthres);
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−%       [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y,errthres,knwpars);
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−% 
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−% If the experiment is 1 then H1,...,HN and Y are aos.
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−% If the experiments are M, then H1,...,HN and Y are Mx1 matrix objects
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−% with the aos relating to the given experiment in the proper position.
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−% 
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−% INPUT:
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−%               - Hi represent the columns of H
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−%               - Y represent the measurement set
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−%               - sThreshold it's a threshold for singular values. It is a
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−%               number, typically 1. It will remove singular values larger
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−%               than sThreshold which corresponds to removing svd parameters estimated
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−%               with an error larger than sThreshold.
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−%               - knwpars A struct array with the fields:
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−%                   pos - a number indicating the corresponding position of
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−%                     the parameter (corresponding column of H)
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−%                   value - the value for the parameter
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−%                   err - the uncertainty associated to the parameter
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−% 
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−% OUTPUT:
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−%   a:      params values
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−%   Ca:     fit covariance matrix for A
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−%   Corra:  fit correlation matrix for A
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−%   Vu:     is the complete conversion matrix
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−%   Cbu:    is the new variables covariance matrix
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−%   Fbu:    is the information matrix for the new variable
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−%   mse:    is the fit Mean Square Error
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−%   dof:    degrees of freedom for the global estimation
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−%   ppm:    number of svd parameters per measurements, provides also the
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−%   number of independent combinations of parameters per each singular
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−%   measurement. The coefficients of the combinations are then stored in Vu
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−% 
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−% 09-11-2010 L Ferraioli
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−%       CREATION
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−%
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−% <a href="matlab:utils.helper.displayMethodInfo('matrix', 'linfitsvd')">Parameter Sets</a>
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−%
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−% VERSION:     $Id: linlsqsvd.m,v 1.2 2011/03/11 09:28:26 luigi Exp $
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−%
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−function  [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = linlsqsvd(varargin)
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−  
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−  
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−  
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−  %%% get input params
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−  if isstruct(varargin{end})
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−    kwnpars   = varargin{end};
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−    if isnumeric(varargin{end-1})
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−      sThreshold = varargin{end-1};
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−      A = varargin{1:end-2};
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−    else
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−      A = varargin{1:end-1};
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−      sThreshold = [];
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−    end
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−  else
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−    kwnpars = [];
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−    if isnumeric(varargin{end})
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−      sThreshold = varargin{end};
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−      A = varargin{1:end-1};
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−    else
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−      A = varargin{:};
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−      sThreshold = [];
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−    end
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−  end
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−  
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− 
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−  %%% sort between one or multiple experiments
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−  exps = struct;
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−  
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−  if isa(A(1),'ao') % one experiment
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−    % Build matrices for lscov
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−    C = A(1:end-1);
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−    Y = A(end);
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−
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−    H = C(:).y;
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−    y = Y.y;
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−    exps.fitbasis = H;
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−    exps.fitdata = y;
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−  elseif isa(A(1),'matrix') % multiple experiments
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−    % run over input objects and experiments
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−    for jj=1:numel(A(1).objs)
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−      C = [];
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−      for ii=1:numel(A)-1
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−        D = A(ii).objs(jj).y;
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−        % willing to work with columns
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−        if size(D,1)<size(D,2)
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−          D = D.';
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−        end
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−        C = [C D];
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−      end
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−      y = A(end).objs(jj).y;
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−      exps(jj).fitbasis = C;
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−      exps(jj).fitdata = y;
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−    end
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−  else
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−    error('Unknown input data type!')
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−  end
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−  
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−  %%% do fit
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−  if ~isempty(kwnpars) && isfield(kwnpars,'pos')
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−    if ~isempty(sThreshold)
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−      [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,kwnpars,sThreshold);
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−    else
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−      [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,kwnpars);
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−    end
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−  else
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−    if ~isempty(sThreshold)
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−      [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,sThreshold);
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−    else
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−      [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps);
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−    end
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−  end
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−  
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−  
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−  
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−  
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−end
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−