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annotate m-toolbox/classes/+utils/@math/linlsqsvd.m @ 0:f0afece42f48

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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % LINLSQSVD Linear least squares with singular value decomposition
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % DESCRIPTION: Linear least square problem with singular value
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % decomposition
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % ALGORITHM: % It solves the problem
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % Y = HX
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % where X are the parameters, Y the measurements, and H the linear
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % equations relating the two.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % It is able to perform linear identification of the parameters of a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % multichannel systems. The results of different experiments on the same
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % system can be passed as input. The algorithm, thanks to the singular
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % value decomposition, extract the maximum amount of information from each
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % single channel and for each experiment. Total information is then
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % combined to get the final result.
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19 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % CALL: [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y);
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21 % [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y,errthres);
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22 % [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linlsqsvd(H1,...,HN,Y,errthres,knwpars);
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23 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % If the experiment is 1 then H1,...,HN and Y are aos.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % If the experiments are M, then H1,...,HN and Y are Mx1 matrix objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % with the aos relating to the given experiment in the proper position.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % INPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % - Hi represent the columns of H
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % - Y represent the measurement set
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % - sThreshold it's a threshold for singular values. It is a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % number, typically 1. It will remove singular values larger
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % than sThreshold which corresponds to removing svd parameters estimated
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % with an error larger than sThreshold.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % - knwpars A struct array with the fields:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % pos - a number indicating the corresponding position of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % the parameter (corresponding column of H)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 % value - the value for the parameter
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 % err - the uncertainty associated to the parameter
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % OUTPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 % a: params values
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43 % Ca: fit covariance matrix for A
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44 % Corra: fit correlation matrix for A
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45 % Vu: is the complete conversion matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % Cbu: is the new variables covariance matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % Fbu: is the information matrix for the new variable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 % mse: is the fit Mean Square Error
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % dof: degrees of freedom for the global estimation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 % ppm: number of svd parameters per measurements, provides also the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 % number of independent combinations of parameters per each singular
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 % measurement. The coefficients of the combinations are then stored in Vu
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53 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 % 09-11-2010 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 % CREATION
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 % <a href="matlab:utils.helper.displayMethodInfo('matrix', 'linfitsvd')">Parameter Sets</a>
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58 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 % VERSION: $Id: linlsqsvd.m,v 1.2 2011/03/11 09:28:26 luigi Exp $
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60 %
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61 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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62
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 function [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = linlsqsvd(varargin)
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64
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65
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66
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 %%% get input params
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 if isstruct(varargin{end})
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 kwnpars = varargin{end};
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70 if isnumeric(varargin{end-1})
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71 sThreshold = varargin{end-1};
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72 A = varargin{1:end-2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 else
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74 A = varargin{1:end-1};
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75 sThreshold = [];
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76 end
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77 else
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78 kwnpars = [];
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79 if isnumeric(varargin{end})
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 sThreshold = varargin{end};
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81 A = varargin{1:end-1};
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82 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 A = varargin{:};
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84 sThreshold = [];
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85 end
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86 end
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87
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88
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 %%% sort between one or multiple experiments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 exps = struct;
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91
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92 if isa(A(1),'ao') % one experiment
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 % Build matrices for lscov
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 C = A(1:end-1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 Y = A(end);
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96
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 H = C(:).y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 y = Y.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 exps.fitbasis = H;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 exps.fitdata = y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 elseif isa(A(1),'matrix') % multiple experiments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 % run over input objects and experiments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 for jj=1:numel(A(1).objs)
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104 C = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 for ii=1:numel(A)-1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 D = A(ii).objs(jj).y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 % willing to work with columns
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108 if size(D,1)<size(D,2)
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109 D = D.';
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110 end
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111 C = [C D];
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112 end
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113 y = A(end).objs(jj).y;
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114 exps(jj).fitbasis = C;
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115 exps(jj).fitdata = y;
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116 end
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117 else
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118 error('Unknown input data type!')
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119 end
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120
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121 %%% do fit
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122 if ~isempty(kwnpars) && isfield(kwnpars,'pos')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 if ~isempty(sThreshold)
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124 [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,kwnpars,sThreshold);
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125 else
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126 [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,kwnpars);
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127 end
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128 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 if ~isempty(sThreshold)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps,sThreshold);
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131 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = utils.math.linfitsvd(exps);
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133 end
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134 end
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135
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136
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137
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138
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139 end
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140