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annotate m-toolbox/classes/+utils/@math/linfitsvd.m @ 52:daf4eab1a51e database-connection-manager tip

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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
children
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rev   line source
0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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1 % Linear fit 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 % INPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % - exps: is a N dimensional struct whose fields are fitdata
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % (experimental data), fitbasis (basis for the fit) and params (cell
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % array with the names of the parameters used in the experiment).
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % - groundexps: a M dim struct containing results from on ground experiments.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % Fuields are: pos (parameter position number), value (on ground measurement
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % result) and err (experimental error on the on ground measurement).
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % - 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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11 % number, typically 1. It will remove singular values larger
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % than sThreshold which corresponds to removing svd parameters estimated
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % with an error larger than sThreshold.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % OUTPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % a: params values
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % Ca: fit covariance matrix for A
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % Corra: fit correlation matrix for A
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % Vu: is the complete conversion matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % Cbu: is the new variables covariance matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % Fbu: is the information matrix for the new variable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % mse: is the fit Mean Square Error
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % dof: degrees of freedom for the global estimation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % ppm: number of svd parameters per measurements, provides also the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % number of independent combinations of parameters per each singular
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % measurement. The coefficients of the combinations are then stored in Vu
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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 % 21-07-2009 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % CREATION
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % $Id: linfitsvd.m,v 1.8 2010/10/29 12:40:47 ingo Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 function [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = linfitsvd(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % get inputs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 if nargin == 1 % no ground experiment
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 exps = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 groundexps = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 remerr = false;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 elseif nargin == 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 exps = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 if isnumeric(varargin{2})
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 sThreshold = varargin{2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 remerr = true;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 groundexps = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 groundexps = varargin{2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 remerr = false;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 elseif nargin == 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 exps = varargin{1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 groundexps = varargin{2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 sThreshold = varargin{3}; % admitted threshold for singular values
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 remerr = true;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 if ~isnumeric(sThreshold)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 sThreshold = inf;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 % init collect results struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 % init union matrices
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 Vu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 Fbu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 wFbu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 bu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 % eCbu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 Cbu = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 ppm = []; % number of svd parameters per measurements
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 N = numel(exps);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 % run over input experiments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 for ii=1:N
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 % get data of the experiments out of the input struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 y = exps(ii).fitdata;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 X = exps(ii).fitbasis;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 % willing to work with columns
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 if size(y,1)<size(y,2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 y = y.';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 if size(X,1)<size(X,2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 X = X.';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 % get svd of X
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 [U,W,V] = svd(X,0);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 % removing zero singular values
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 svals = diag(W);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 idx = svals==0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 svals(idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 % removing columns of U and V corresponding to zero svalues
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 U(:,idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 V(:,idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 if remerr
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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101 % Find params combinations with error larger than 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 idx = svals<sThreshold;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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103 svals(idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105 % removing columns of U and V corresponding to params combinations with
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 % error larger than 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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107 U(:,idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108 V(:,idx) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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109 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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110
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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111 % Sanity check
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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112 % if svals is empty you are going to gain no information from the
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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113 % current data series
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 if ~isempty(svals) % go with the fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 % rebuild W
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 W = diag(svals);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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117
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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118 % update ppm with the number of parameters for the given experiment
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 ppm = [ppm; numel(svals)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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120
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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121 % get new basis for the fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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122 K = U*W;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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124 % get expected covariance matrix for b, assuming white noise
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 Fb = W*W; % information matrix for parameters b
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127 % get b params with errors, mse is the mean square error, Cb is the
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 % covariance matrix of fitted b. It should be equal to eCb.*mse
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 [b,stdxb,mseb,Cb] = lscov(K,y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 % information matrix weighted for fit results Cb = inv(wFb)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 wFb = Fb./mseb;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134 % add params from present experiment
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 % get union matrices
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136 Vu = [Vu;V.'];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 Fbu = blkdiag(Fbu,Fb);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 wFbu = blkdiag(wFbu,wFb);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 Cbu = blkdiag(Cbu,Cb);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140 bu = [bu;b];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 else % no information, no fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 % update ppm with the number of parameters for the given experiment
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 ppm = [ppm; 0];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 % insert values from on-ground measured parameters if applicable
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152 if nargin == 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 for jj = 1:numel(groundexps)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 % get values
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 pos = groundexps(jj).pos;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 val = groundexps(jj).value;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 err = groundexps(jj).err;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 tV = zeros(1,size(Vu,2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 tV(1,pos) = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163 Vu = [Vu;tV];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 bu = [bu;val];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 Cbu = blkdiag(Cbu,err^2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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166 Fbu = blkdiag(Fbu,1/(err^2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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167 wFbu = blkdiag(wFbu,1/(err^2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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168 ppm = [ppm; 1];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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169
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Daniele Nicolodi <nicolodi@science.unitn.it>
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170 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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171
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Daniele Nicolodi <nicolodi@science.unitn.it>
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172 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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173
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Daniele Nicolodi <nicolodi@science.unitn.it>
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174 % get results on physical parameters, solve the system with proper weights
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Daniele Nicolodi <nicolodi@science.unitn.it>
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175 a = lscov(Vu,bu,1./diag(Cbu));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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176
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Daniele Nicolodi <nicolodi@science.unitn.it>
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177 % get params covariance
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Daniele Nicolodi <nicolodi@science.unitn.it>
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178 Ca = inv(Vu'*wFbu*Vu);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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179
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Daniele Nicolodi <nicolodi@science.unitn.it>
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180 % get params correlation matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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181 Corra = Ca;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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182 for tt=1:size(Corra,1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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183 for hh=1:size(Corra,2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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184 Corra(tt,hh) = Ca(tt,hh)/(sqrt(Ca(tt,tt))*sqrt(Ca(hh,hh)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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185 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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186 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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187
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Daniele Nicolodi <nicolodi@science.unitn.it>
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188 % get chi square assuming unitary variance white noise
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Daniele Nicolodi <nicolodi@science.unitn.it>
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189 N = numel(exps);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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190 mse = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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191 tL = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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192 % run over input experiments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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193 for ii=1:N
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Daniele Nicolodi <nicolodi@science.unitn.it>
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194 % get data of the experiments out of the input struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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195 y = exps(ii).fitdata;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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196 X = exps(ii).fitbasis;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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197
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Daniele Nicolodi <nicolodi@science.unitn.it>
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198 mse = mse + sum((y - X*a).^2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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199 tL = tL + numel(y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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200 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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201 dof = tL-numel(a);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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202 mse = mse./dof;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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203
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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204 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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205
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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206
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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207
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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208
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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209
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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210
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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211
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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212
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213