--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/+utils/@math/diffStepFish.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,113 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  Look for differentiation step for a given parameter and
+%
+%  Parameters are:
+
+%
+% $Id: diffStepFish.m,v 1.2 2011/09/19 06:17:45 miquel Exp $
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function best = diffStepFish(i1,i2,S11,S12,S21,S22,N,meval,params,ngrid,ranges,freqs,inNames,outNames)
+
+% remove aux file if existing
+if exist('diffStepFish.txt') == 2
+    ! rm diffStepFish.txt
+end
+
+step = ones(ngrid,numel(params));
+% build matrix of steps
+% for ii = 1:length(params)
+%       step(:,ii) = [] logspace(ranges(1,ii),ranges(2,ii),ngrid);
+% end
+for ii = 1:ngrid
+    step(ii,:) = ranges(1,:);
+end
+
+% step(:,1) = logspace(ranges(1,1),ranges(2,1),ngrid);
+
+for kk = 1:length(params)
+    step(:,kk) = logspace(log10(ranges(1,kk)),log10(ranges(2,kk)),ngrid);
+    Rmat = [];
+    for jj = 1:ngrid
+        for ii = 1:length(params)
+            tic
+            % differentiate numerically
+            dH = meval.parameterDiff(plist('names', params(ii),'values',step(jj,ii)));
+            % create plist with correct outNames (since parameterDiff change them)
+            out1 = strrep(outNames{1},'.', sprintf('_DIFF_%s.',params{ii})); % 2x2 case
+            out2 =strrep(outNames{2},'.', sprintf('_DIFF_%s.',params{ii}));
+            spl = plist('set', 'for bode', ...
+                'outputs', {out1,out2}, ...
+                'inputs', inNames, ...
+                'reorganize', true,...
+                'f', freqs);
+            % do bode
+            d  = bode(dH, spl);
+            % assign according matlab's matrix notation:
+            % H(1,1)->h(1)  H(2,1)->h(2)  H(1,2)->h(3)  H(2,2)->h(4)
+            d11(ii) = d.objs(1);
+            d21(ii) = d.objs(2);
+            d12(ii) = d.objs(3);
+            d22(ii) = d.objs(4);
+            
+        end
+        
+        fs = S11.fs;
+        % scaling of PSD
+        % PSD = 2/(N*fs) * FFT *conj(FFT)
+        C11 = N*fs/2.*S11.y;
+        C22 = N*fs/2.*S22.y;
+        C12 = N*fs/2.*S12.y;
+        C21 = N*fs/2.*S21.y;
+        
+        % compute elements of inverse cross-spectrum matrix
+        InvS11 = (C22./(C11.*C22 - C12.*C21));
+        InvS22 = (C11./(C11.*C22 - C12.*C21));
+        InvS12 = (C21./(C11.*C22 - C12.*C21));
+        InvS21 = (C12./(C11.*C22 - C12.*C21));
+        
+        
+        % compute Fisher Matrix
+        for i =1:length(params)
+            for j =1:length(params)
+                
+                v1v1 = conj(d11(i).y.*i1.y + d12(i).y.*i2.y).*(d11(j).y.*i1.y + d12(j).y.*i2.y);
+                v2v2 = conj(d21(i).y.*i1.y + d22(i).y.*i2.y).*(d21(j).y.*i1.y + d22(j).y.*i2.y);
+                v1v2 = conj(d11(i).y.*i1.y + d12(i).y.*i2.y).*(d21(j).y.*i1.y + d22(j).y.*i2.y);
+                v2v1 = conj(d21(i).y.*i1.y + d22(i).y.*i2.y).*(d11(j).y.*i1.y + d12(j).y.*i2.y);
+                
+                FisMat(i,j) = sum(real(InvS11.*v1v1 + InvS22.*v2v2 - InvS12.*v1v2 - InvS21.*v2v1));
+            end
+        end
+        
+        detFisMat = det(FisMat);
+        R = [step(jj,:) detFisMat];
+        save('diffStepFish.txt','R','-ascii','-append');
+        Rmat = [Rmat; R];
+        
+        toc
+    end
+    
+    % look for the stable step: compute diff and
+    % look for the smallest one in absolute value
+    % The smallest slope marks the plateau
+    diffDetFisMat = abs(diff(Rmat(:,end)));
+    lowdet = diffDetFisMat(1);
+    ind = 2;
+    for k = 1:numel(diffDetFisMat) 
+        if diffDetFisMat(k) < lowdet
+            lowdet = diffDetFisMat(k);
+            ind = k+1; % index give by diff = x(2) - x(1). We take the step corresponding to x(2)
+        end
+    end
+    
+    step(:,kk) = step(jj,kk)*ones(ngrid,1);
+    
+end
+
+step(:,end) = logspace(log10(ranges(1,end)),log10(ranges(2,end)),ngrid);
+best = step(1,:);
+
+end
+