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comparison m-toolbox/classes/+utils/@math/linfitsvd.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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1 % Linear fit with singular value decomposition
2 %
3 % INPUT:
4 % - exps: is a N dimensional struct whose fields are fitdata
5 % (experimental data), fitbasis (basis for the fit) and params (cell
6 % array with the names of the parameters used in the experiment).
7 % - groundexps: a M dim struct containing results from on ground experiments.
8 % Fuields are: pos (parameter position number), value (on ground measurement
9 % result) and err (experimental error on the on ground measurement).
10 % - sThreshold it's a threshold for singular values. It is a
11 % number, typically 1. It will remove singular values larger
12 % than sThreshold which corresponds to removing svd parameters estimated
13 % with an error larger than sThreshold.
14 %
15 % OUTPUT:
16 % a: params values
17 % Ca: fit covariance matrix for A
18 % Corra: fit correlation matrix for A
19 % Vu: is the complete conversion matrix
20 % Cbu: is the new variables covariance matrix
21 % Fbu: is the information matrix for the new variable
22 % mse: is the fit Mean Square Error
23 % dof: degrees of freedom for the global estimation
24 % ppm: number of svd parameters per measurements, provides also the
25 % number of independent combinations of parameters per each singular
26 % measurement. The coefficients of the combinations are then stored in Vu
27 %
28 % 21-07-2009 L Ferraioli
29 % CREATION
30 %
31 %
32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
33 % $Id: linfitsvd.m,v 1.8 2010/10/29 12:40:47 ingo Exp $
34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
35 function [a,Ca,Corra,Vu,bu,Cbu,Fbu,mse,dof,ppm] = linfitsvd(varargin)
36
37 % get inputs
38 if nargin == 1 % no ground experiment
39 exps = varargin{1};
40 groundexps = [];
41 remerr = false;
42 elseif nargin == 2
43 exps = varargin{1};
44 if isnumeric(varargin{2})
45 sThreshold = varargin{2};
46 remerr = true;
47 groundexps = [];
48 else
49 groundexps = varargin{2};
50 remerr = false;
51 end
52 elseif nargin == 3
53 exps = varargin{1};
54 groundexps = varargin{2};
55 sThreshold = varargin{3}; % admitted threshold for singular values
56 remerr = true;
57 if ~isnumeric(sThreshold)
58 sThreshold = inf;
59 end
60 end
61
62 % init collect results struct
63
64 % init union matrices
65 Vu = [];
66 Fbu = [];
67 wFbu = [];
68 bu = [];
69 % eCbu = [];
70 Cbu = [];
71 ppm = []; % number of svd parameters per measurements
72
73 N = numel(exps);
74 % run over input experiments
75 for ii=1:N
76 % get data of the experiments out of the input struct
77 y = exps(ii).fitdata;
78 X = exps(ii).fitbasis;
79
80 % willing to work with columns
81 if size(y,1)<size(y,2)
82 y = y.';
83 end
84 if size(X,1)<size(X,2)
85 X = X.';
86 end
87
88 % get svd of X
89 [U,W,V] = svd(X,0);
90
91 % removing zero singular values
92 svals = diag(W);
93 idx = svals==0;
94 svals(idx) = [];
95
96 % removing columns of U and V corresponding to zero svalues
97 U(:,idx) = [];
98 V(:,idx) = [];
99
100 if remerr
101 % Find params combinations with error larger than 1
102 idx = svals<sThreshold;
103 svals(idx) = [];
104
105 % removing columns of U and V corresponding to params combinations with
106 % error larger than 1
107 U(:,idx) = [];
108 V(:,idx) = [];
109 end
110
111 % Sanity check
112 % if svals is empty you are going to gain no information from the
113 % current data series
114 if ~isempty(svals) % go with the fit
115 % rebuild W
116 W = diag(svals);
117
118 % update ppm with the number of parameters for the given experiment
119 ppm = [ppm; numel(svals)];
120
121 % get new basis for the fit
122 K = U*W;
123
124 % get expected covariance matrix for b, assuming white noise
125 Fb = W*W; % information matrix for parameters b
126
127 % get b params with errors, mse is the mean square error, Cb is the
128 % covariance matrix of fitted b. It should be equal to eCb.*mse
129 [b,stdxb,mseb,Cb] = lscov(K,y);
130
131 % information matrix weighted for fit results Cb = inv(wFb)
132 wFb = Fb./mseb;
133
134 % add params from present experiment
135 % get union matrices
136 Vu = [Vu;V.'];
137 Fbu = blkdiag(Fbu,Fb);
138 wFbu = blkdiag(wFbu,wFb);
139 Cbu = blkdiag(Cbu,Cb);
140 bu = [bu;b];
141
142 else % no information, no fit
143 % update ppm with the number of parameters for the given experiment
144 ppm = [ppm; 0];
145 end
146
147
148
149 end
150
151 % insert values from on-ground measured parameters if applicable
152 if nargin == 2
153
154 for jj = 1:numel(groundexps)
155
156 % get values
157 pos = groundexps(jj).pos;
158 val = groundexps(jj).value;
159 err = groundexps(jj).err;
160
161 tV = zeros(1,size(Vu,2));
162 tV(1,pos) = 1;
163 Vu = [Vu;tV];
164 bu = [bu;val];
165 Cbu = blkdiag(Cbu,err^2);
166 Fbu = blkdiag(Fbu,1/(err^2));
167 wFbu = blkdiag(wFbu,1/(err^2));
168 ppm = [ppm; 1];
169
170 end
171
172 end
173
174 % get results on physical parameters, solve the system with proper weights
175 a = lscov(Vu,bu,1./diag(Cbu));
176
177 % get params covariance
178 Ca = inv(Vu'*wFbu*Vu);
179
180 % get params correlation matrix
181 Corra = Ca;
182 for tt=1:size(Corra,1)
183 for hh=1:size(Corra,2)
184 Corra(tt,hh) = Ca(tt,hh)/(sqrt(Ca(tt,tt))*sqrt(Ca(hh,hh)));
185 end
186 end
187
188 % get chi square assuming unitary variance white noise
189 N = numel(exps);
190 mse = 0;
191 tL = 0;
192 % run over input experiments
193 for ii=1:N
194 % get data of the experiments out of the input struct
195 y = exps(ii).fitdata;
196 X = exps(ii).fitbasis;
197
198 mse = mse + sum((y - X*a).^2);
199 tL = tL + numel(y);
200 end
201 dof = tL-numel(a);
202 mse = mse./dof;
203
204 end
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