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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 % GETJACOBIAN Calculate Jacobian of a given model function.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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6 % Calculate Jacobian of a given model function for the given set of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % coefficients. Jacobian is approximated with finite difference method.
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % CALL:
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % J = getjacobian(coeff,model,X)
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12 %
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13 % INPUT:
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14 %
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15 % J - fit coefficients
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16 % model - model function
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17 % X - x vactor (abscissa)
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18 %
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19 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % OUTPUT:
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21 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % J - Jacobian
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23 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % Note: Look at nlinfit.m of the stats toolbox. Model should be a matlab
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % function calculating Model values as a function of X and of coefficients
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26 % NOTE: The function prefer to work with column objects. Therefore it is
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % good practise to directly input coeff and X as column objects
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28 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % Examples:
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30 %
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31 % Use @ to specify MODELFUN:
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32 % load reaction;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % J = getjacobian(coeff,@mymodel,X);
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34 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % where MYMODEL is a MATLAB function such as:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % function yhat = mymodel(beta, X)
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37 % yhat = (beta(1)*X(:,2) - X(:,3)/beta(5)) ./ ...
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38 % (1+beta(2)*X(:,1)+beta(3)*X(:,2)+beta(4)*X(:,3));
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39 % or
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40 %
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41 % mymodel = @(beta,X)(beta(1).*X(:,1)+beta(2).*X(:,2)+...)
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42 %
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43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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44 % VERSION: $Id: getjacobian.m,v 1.1 2009/03/26 16:26:05 luigi Exp $
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45 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % HISTORY: 26-03-2009 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % Creation
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48 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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49
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50 function J = getjacobian(coeff,model,X)
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51 % checking size, willing to work with columns
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52 [a,b] = size(coeff);
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53 if a<b
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54 coeff = coeff.';
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55 end
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56 [a,b] = size(X);
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57 if a<b
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58 X = X.';
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59 end
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60
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61 % finite difference relative step
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62 fdiffstep = eps^(1/3);
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63 % evaluate model on the input coefficients
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64 yfit = model(coeff,X);
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65 % check for NaNs
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66 nans = isnan(yfit(:));
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67
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68 % initialization
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69 p = numel(coeff);
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70 delta = zeros(size(coeff));
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71 J = zeros(numel(yfit),p);
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72 for k = 1:p
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73 if (coeff(k) == 0)
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74 nb = sqrt(norm(coeff));
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75 delta(k) = fdiffstep * (nb + (nb==0));
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76 else
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77 delta(k) = fdiffstep*coeff(k);
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78 end
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79 yplus = model(coeff+delta,X);
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80 dy = yplus(:) - yfit(:);
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81 dy(nans) = [];
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82 J(:,k) = dy/delta(k);
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83 delta(k) = 0;
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84 end
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85 end