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annotate m-toolbox/classes/+utils/@math/jr2cov.m @ 33:5e7477b94d94 database-connection-manager

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % JR2COV Calculates coefficients covariance matrix from Jacobian and Residuals.
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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
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5 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % Calculates coefficients covariance matrix from Jacobian and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % Residuals. The algorithm uses the QR factorization of J to perform
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % the calculation inv(J'J)*s wehre J is the Jacobian matrix and s is
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % the mean squared error.
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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 % CALL:
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12 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % covmat = jr2cov(J,resid)
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % INPUT:
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16 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % J - Jacobian of the function with respect to the given coefficients
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18 % resid - Fit residuals
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19 %
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20 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % OUTPUT:
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22 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % covmat - covariance matrix of the fit coefficients
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24 %
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25 % Note: Resid should be a column vector, Number of rows of J must be equal
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % to the number of rows of Resid. The number of columns of J defines the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % number of corresponding fit parameters for which we want to calculate the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % covariance matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % Estimate covariance from J and residuals. Look at the nlparci.m function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % of the stats toolbox for further details
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31 %
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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33 % VERSION: $Id: jr2cov.m,v 1.2 2009/03/27 14:48:54 luigi Exp $
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34 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % HISTORY: 26-03-2009 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % Creation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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38
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 function covmat = jr2cov(J,resid)
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40
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41 missing = isnan(resid);
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42 if ~isempty(missing)
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43 resid(missing) = [];
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44 end
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45
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46 n = length(resid);
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47
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48 J(missing,:) = [];
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49
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50 if size(J,1)~=n
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51 error('The number of rows of J does not match the number of rows of RESID.');
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52 end
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53 [n,p] = size(J);
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54 v = n-p; % degrees of freedom of the parameters estimation
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55
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56 % Approximation when a column is zero vector
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57 temp = find(max(abs(J)) == 0);
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58 if ~isempty(temp)
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59 J(temp,:) = J(temp,:) + sqrt(eps(class(J)));
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60 end
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61
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62 % Calculate covariance matrix
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63 [Q,R] = qr(J,0);
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64 Rinv = R\eye(size(R));
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65
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66 mse = norm(resid)^2 / v; % mean square error
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67 covmat = mse * Rinv*Rinv';
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68
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69 end