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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%
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−%  Look for differentiation step for a given parameter and
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−%
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−%  Parameters are:
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−
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−%
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−% $Id: diffStepFish_1x1.m,v 1.1 2011/10/07 08:17:52 miquel Exp $
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−%
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−function best = diffStepFish_1x1(i1,S11,N,meval,params,numparams,ngrid,ranges,freqs,inNames,outNames)
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−
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−import utils.const.*
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−
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−% remove aux file if existing
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−if exist('diffStepFish.txt') == 2
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−    ! rm diffStepFish.txt
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−end
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−
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−step = ones(ngrid,numel(params));
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−
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−% initialize matrix of steps
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−for ii = 1:numel(params)
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−    step(:,ii) = ranges(1)*numparams(ii);
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−end
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−
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−% step(:,1) = logspace(ranges(1,1),ranges(2,1),ngrid);
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−
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−for kk = 1:length(params)
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−    step(:,kk) = numparams(kk)*logspace(log10(ranges(1)),log10(ranges(2)),ngrid);
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−    Rmat = [];
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−    for jj = 1:ngrid
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−        for ii = 1:length(params)
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−            % differentiate numerically
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−            dH = meval.parameterDiff(plist('names', params(ii),'values',step(jj,ii)));
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−            % create plist with correct outNames (since parameterDiff change them)
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−            out1 = strrep(outNames{1},'.', sprintf('_DIFF_%s.',params{ii})); % 2x2 case
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−            spl = plist('set', 'for bode', ...
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−                'outputs', {out1}, ...
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−                'inputs', inNames, ...
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−                'reorganize', true,...
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−                'f', freqs);
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−            % do bode
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−            d  = bode(dH, spl);
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−            % assign according matlab's matrix notation:
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−            % H(1,1)->h(1)  H(2,1)->h(2)  H(1,2)->h(3)  H(2,2)->h(4)
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−            d11(ii) = d.objs(1);
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−        end
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−        
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−        fs = S11.fs;
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−        % scaling of PSD
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−        % PSD = 2/(N*fs) * FFT *conj(FFT)
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−        C11 = N*fs/2.*S11.y;
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−        
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−        % compute elements of inverse cross-spectrum matrix
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−        InvS11 = 1./C11;
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−        
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−        % compute Fisher Matrix
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−        for i =1:length(params)
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−            for j =1:length(params)
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−                
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−                v1v1 = conj(d11(i).y.*i1.y).*(d11(j).y.*i1.y);
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−                FisMat(i,j) = sum(real(InvS11.*v1v1));
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−            end
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−        end
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−        
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−        detFisMat = det(FisMat);
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−        R = [step(jj,:) detFisMat];
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−        % only file diffStepFish.txt stores all iterations. Rmat is
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−        % initialized for each loop
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−        save('diffStepFish.txt','R','-ascii','-append');
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−        Rmat = [Rmat; R];
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−    end
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−    
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−    % look for the stable step: compute diff and
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−    % look for the smallest one in absolute value
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−    % The smallest slope marks the plateau
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−    diffDetFisMat = abs(diff(Rmat(:,end)));
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−    lowdet = diffDetFisMat(1);
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−    ind = 2;
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−    for k = 1:numel(diffDetFisMat)
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−        if diffDetFisMat(k) < lowdet
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−            lowdet = diffDetFisMat(k);
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−            ind = k+1; % index give by diff = x(2) - x(1). We take the step corresponding to x(2)
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−        end
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−    end
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−    % display message
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−    utils.helper.msg(msg.IMPORTANT, ...
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−        sprintf('Best numerical diff. step with respect %s: %d',params{kk}, step(ind,kk)), mfilename('class'), mfilename);
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−    % reassing all current column to the best step
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−    step(:,kk) = step(ind,kk)*ones(ngrid,1);
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−    
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−    figure
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−    diffDetFisMat(diffDetFisMat == 0) = 1e-20; % to avoid zeros in loglog plot
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−    loglog(Rmat(1:end-1,kk)/numparams(kk),diffDetFisMat,'--ks','LineWidth',2,'MarkerSize',10)
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−    title(sprintf('Parameter: %s',params{kk}))
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−    ylabel('\Delta FisMat / \Delta\theta')
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−    xlabel('Normalised \Delta\theta')
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−    
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−end
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−best = step(1,:);
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−end
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−