% 'check_peaklocking': estimte peaklocking error in a civ field series TODO: UPDATE %------------------------------------------------------------------------ % function ParamOut=check_peaklocking(Param) % %%%%%%%%%%% GENERAL TO ALL SERIES ACTION FCTS %%%%%%%%%%%%%%%%%%%%%%%%%%% % % This function is used in four modes by the GUI series: % 1) config GUI: with no input argument, the function determine the suitable GUI configuration % 2) interactive input: the function is used to interactively introduce input parameters, and then stops % 3) RUN: the function itself runs, when an appropriate input structure Param has been introduced. % 4) BATCH: the function itself proceeds in BATCH mode, using an xml file 'Param' as input. % % This function is used in four modes by the GUI series: % 1) config GUI: with no input argument, the function determine the suitable GUI configuration % 2) interactive input: the function is used to interactively introduce input parameters, and then stops % 3) RUN: the function itself runs, when an appropriate input structure Param has been introduced. % 4) BATCH: the function itself proceeds in BATCH mode, using an xml file 'Param' as input. % %OUTPUT % GUI_input=list of options in the GUI series.fig needed for the function % %INPUT: % In run mode, the input parameters are given as a Matlab structure Param copied from the GUI series. % In batch mode, Param is the name of the corresponding xml file containing the same information % In the absence of input (as activated when the current Action is selected % in series), the function ouput GUI_input set the activation of the needed GUI elements % % Param contains the elements:(use the menu bar command 'export/GUI config' in series to see the current structure Param) % .InputTable: cell of input file names, (several lines for multiple input) % each line decomposed as {RootPath,SubDir,Rootfile,NomType,Extension} % .OutputSubDir: name of the subdirectory for data outputs % .OutputDirExt: directory extension for data outputs % .Action: .ActionName: name of the current activated function % .ActionPath: path of the current activated function % .IndexRange: set the file or frame indices on which the action must be performed % .FieldTransform: .TransformName: name of the selected transform function % .TransformPath: path of the selected transform function % .TransformHandle: corresponding function handle % .InputFields: sub structure describing the input fields withfields % .FieldName: name of the field % .VelType: velocity type % .FieldName_1: name of the second field in case of two input series % .VelType_1: velocity type of the second field in case of two input series % .ProjObject: %sub structure describing a projection object (read from ancillary GUI set_object) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %======================================================================= % Copyright 2008-2022, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France % http://www.legi.grenoble-inp.fr % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr % % This file is part of the toolbox UVMAT. % % UVMAT is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation; either version 2 of the license, % or (at your option) any later version. % % UVMAT is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License (see LICENSE.txt) for more details. %======================================================================= function ParamOut=check_peaklocking(Param) %% set the input elements needed on the GUI series when the action is selected in the menu ActionName if ~exist('Param','var') % case with no input parameter ParamOut={'AllowInputSort';'off';...% allow alphabetic sorting of the list of input files (options 'off'/'on', 'off' by default) 'WholeIndexRange';'off';...% prescribes the file index ranges from min to max (options 'off'/'on', 'off' by default) 'NbSlice';'on'; ...%nbre of slices ('off' by default) 'VelType';'two';...% menu for selecting the velocity type (options 'off'/'one'/'two', 'off' by default) 'FieldName';'off';...% menu for selecting the field (s) in the input file(options 'off'/'one'/'two', 'off' by default) 'FieldTransform'; 'off';...%can use a transform function 'ProjObject';'on';...%can use projection object(option 'off'/'on', 'Mask';'off';...%can use mask option (option 'off'/'on', 'off' by default) 'OutputDirExt';'.pklock';...%set the output dir extension ''}; return end %%%%%%%%%%%% STANDARD PART %%%%%%%%%%%% %% select different modes, RUN, parameter input, BATCH % BATCH case: read the xml file for batch case if ischar(Param) Param=xml2struct(Param); checkrun=0; % RUN case: parameters introduced as the input structure Param else hseries=guidata(Param.hseries);%handles of the GUI series if isfield(Param,'Specific')&& strcmp(Param.Specific,'?') checkrun=1;% will only search interactive input parameters (preparation of BATCH mode) else checkrun=2; % indicate the RUN option is used end end ParamOut=Param; %default output OutputDir=[Param.OutputSubDir Param.OutputDirExt]; %% root input file(s) and type RootPath=Param.InputTable(:,1); RootFile=Param.InputTable(:,3); SubDir=Param.InputTable(:,2); NomType=Param.InputTable(:,4); FileExt=Param.InputTable(:,5); [filecell,i1_series,i2_series,j1_series,j2_series]=get_file_series(Param); %%%%%%%%%%%% % The cell array filecell is the list of input file names, while % filecell{iview,fileindex}: % iview: line in the table corresponding to a given file series % fileindex: file index within the file series, % i1_series(iview,ref_j,ref_i)... are the corresponding arrays of indices i1,i2,j1,j2, depending on the input line iview and the two reference indices ref_i,ref_j % i1_series(iview,fileindex) expresses the same indices as a 1D array in file indices %%%%%%%%%%%% NbSlice=1;%default if isfield(Param.IndexRange,'NbSlice')&&~isempty(Param.IndexRange.NbSlice) NbSlice=Param.IndexRange.NbSlice; end nbview=1;%number of input file series (lines in InputTable) nbfield_j=size(i1_series{1},1); %nb of fields for the j index (bursts or volume slices) nbfield_i=size(i1_series{1},2); %nb of fields for the i index nbfield=nbfield_j*nbfield_i; %total number of fields nbfield_i=floor(nbfield/NbSlice);%total number of indexes in a slice (adjusted to an integer number of slices) nbfield=nbfield_i*NbSlice; %total number of fields after adjustement %determine the file type on each line from the first input file NcTypeOptions={'netcdf','civx','civdata'}; for iview=1:nbview if ~exist(filecell{iview,1}','file') disp_uvmat('ERROR',['the first input file ' filecell{iview,1} ' does not exist'],checkrun) return end [FileInfo{iview},MovieObject{iview}]=get_file_info(filecell{iview,1}); FileType{iview}=FileInfo{iview}.FileType; CheckImage{iview}=strcmp(FileInfo{iview}.FieldType,'image');% =1 for images CheckNc{iview}=~isempty(find(strcmp(FileType{iview},NcTypeOptions)));% =1 for netcdf files if ~isempty(j1_series{iview}) frame_index{iview}=j1_series{iview}; else frame_index{iview}=i1_series{iview}; end end %% calibration data and timing: read the ImaDoc files %none %% coordinate transform or other user defined transform % none %%%%%%%%%%%% END STANDARD PART %%%%%%%%%%%% % EDIT FROM HERE %% check the validity of ctinput file types %none %% Set field names and velocity types InputFields{1}=[];%default (case of images) if isfield(Param,'InputFields') InputFields{1}=Param.InputFields; end % only one input fieldseries %% Initiate output fields %initiate the output structure as a copy of the first input one (reproduce fields) [DataOut,tild,errormsg] = read_field(filecell{1,1},FileType{1},InputFields{1},1); if ~isempty(errormsg) disp_uvmat('ERROR',['error reading ' filecell{1,1} ': ' errormsg],checkrun) return end time_1=[]; if isfield(DataOut,'Time') time_1=DataOut.Time(1); end if CheckNc{iview} if isempty(strcmp('Conventions',DataOut.ListGlobalAttribute)) DataOut.ListGlobalAttribute=['Conventions' DataOut.ListGlobalAttribute]; end DataOut.Conventions='uvmat'; DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {Param.Action}]; ActionKey='Action'; while isfield(DataOut,ActionKey) ActionKey=[ActionKey '_1']; end DataOut.(ActionKey)=Param.Action; DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {ActionKey}]; if isfield(DataOut,'Time') DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {'Time','Time_end'}]; end end %%%%%%%%%%%%%%%% loop on field indices %%%%%%%%%%%%%%%% index_slice=1:nbfield;% select the file indices for index=index_slice if checkrun update_waitbar(hseries.Waitbar,index/(nbfield)) stopstate=get(hseries.RUN,'BusyAction'); else stopstate='queue'; end if isequal(stopstate,'queue')% enable STOP command Data=cell(1,nbview);%initiate the set Data; nbtime=0; dt=[]; %%%%%%%%%%%%%%%% loop on views (input lines) %%%%%%%%%%%%%%%% for iview=1:nbview % reading input file(s) [Data{iview},tild,errormsg] = read_field(filecell{iview,index},FileType{iview},InputFields{iview},frame_index{iview}(index)); if ~isempty(errormsg) errormsg=['time_series / read_field / ' errormsg]; display(errormsg) break end end if isempty(errormsg) Field=Data{1}; % default input field structure % coordinate transform (or other user defined transform) % none %field projection on an object if Param.CheckObject [Field,errormsg]=proj_field(Field,Param.ProjObject); if ~isempty(errormsg) msgbox_uvmat('ERROR',['time_series / proj_field / ' errormsg]) return end end % initiate the time series at the first iteration if index==1 % stop program if the first field reading is in error if ~isempty(errormsg) disp_uvmat('ERROR',['time_series / sub_field / ' errormsg],checkrun) return end DataOut=Field;%default DataOut.NbDim=Field.NbDim+1; %add the time dimension for plots nbvar=length(Field.ListVarName); if nbvar==0 disp_uvmat('ERROR','no input variable selected',checkrun) return end testsum=2*ones(1,nbvar);%initiate flag for action on each variable if isfield(Field,'VarAttribute') % look for coordinate and flag variables for ivar=1:nbvar if length(Field.VarAttribute)>=ivar && isfield(Field.VarAttribute{ivar},'Role') var_role=Field.VarAttribute{ivar}.Role;%'role' of the variable if isequal(var_role,'errorflag') disp_uvmat('ERROR','do not handle error flags in time series',checkrun) return end if isequal(var_role,'warnflag') testsum(ivar)=0; % not recorded variable eval(['DataOut=rmfield(DataOut,''' Field.ListVarName{ivar} ''');']);%remove variable end if isequal(var_role,'coord_x')| isequal(var_role,'coord_y')|... isequal(var_role,'coord_z')|isequal(var_role,'coord') testsum(ivar)=1; %constant coordinates, record without time evolution end end % check whether the variable ivar is a dimension variable DimCell=Field.VarDimName{ivar}; if ischar(DimCell) DimCell={DimCell}; end if numel(DimCell)==1 && isequal(Field.ListVarName{ivar},DimCell{1})%detect dimension variables testsum(ivar)=1; end end end for ivar=1:nbvar if testsum(ivar)==2 eval(['DataOut.' Field.ListVarName{ivar} '=[];']) end end DataOut.ListVarName=[{'Time'} DataOut.ListVarName]; end % add data to the current field for ivar=1:length(Field.ListVarName) VarName=Field.ListVarName{ivar}; VarVal=Field.(VarName); if testsum(ivar)==2% test for recorded variable if isempty(errormsg) if isequal(Param.ProjObject.ProjMode,'inside')% take the average in the domain for 'inside' mode if isempty(VarVal) disp_uvmat('ERROR',['empty result at frame index ' num2str(i1_series{iview}(index))],checkrun) return end VarVal=mean(VarVal,1); end VarVal=shiftdim(VarVal,-1); %shift dimension DataOut.(VarName)=cat(1,DataOut.(VarName),VarVal);%concanete the current field to the time series else DataOut.(VarName)=cat(1,DataOut.(VarName),0);% put each variable to 0 in case of input reading error end elseif testsum(ivar)==1% variable representing fixed coordinates VarInit=DataOut.(VarName); if isempty(errormsg) && ~isequal(VarVal,VarInit) disp_uvmat('ERROR',['time series requires constant coordinates ' VarName],checkrun) return end end end end end end %%%%%%% END OF LOOP WITHIN A SLICE %remove time for global attributes if exists Time_index=find(strcmp('Time',DataOut.ListGlobalAttribute)); if ~isempty(Time_index) DataOut.ListGlobalAttribute(Time_index)=[]; end DataOut.Conventions='uvmat'; for ivar=1:numel(DataOut.ListVarName) VarName=DataOut.ListVarName{ivar}; eval(['DataOut.' VarName '=squeeze(DataOut.' VarName ');']) %remove singletons end % add time dimension for ivar=1:length(Field.ListVarName) DimCell=Field.VarDimName(ivar); if testsum(ivar)==2%variable used as time series DataOut.VarDimName{ivar}=[{'Time'} DimCell]; elseif testsum(ivar)==1 DataOut.VarDimName{ivar}=DimCell; end end indexremove=find(~testsum); if ~isempty(indexremove) DataOut.ListVarName(1+indexremove)=[]; DataOut.VarDimName(indexremove)=[]; if isfield(DataOut,'Role') && ~isempty(DataOut.Role{1})%generaliser aus autres attributs DataOut.Role(1+indexremove)=[]; end end %shift variable attributes if isfield(DataOut,'VarAttribute') DataOut.VarAttribute=[{[]} DataOut.VarAttribute]; end DataOut.VarDimName=[{'Time'} DataOut.VarDimName]; DataOut.Action=Param.Action;%name of the processing programme test_time=diff(DataOut.Time)>0;% test that the readed time is increasing (not constant) if ~test_time DataOut.Time=1:filecounter; end % display nbmissing if ~isequal(nbmissing,0) disp_uvmat('WARNING',[num2str(nbmissing) ' files skipped: missing files or bad input, see command window display'],checkrun) end %name of result file OutputFile=fullfile_uvmat(RootPath{1},OutputDir,RootFile{1},FileExtOut,NomTypeOut,i1_series{1}(1),i1_series{1}(end),i_slice,[]); errormsg=struct2nc(OutputFile,DataOut); %save result file if isempty(errormsg) display([OutputFile ' written']) else disp_uvmat('ERROR',['error in Series/struct2nc: ' errormsg],checkrun) end return %%%%%%%%%%%%%%%%%% END%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %evaluation of peacklocking errors %use splinhist: give spline coeff cc for a smooth histo (call spline4) %use histsmooth(x,cc): calculate the smooth histo for any value x %use histder(x,cc): calculate the derivative of the smooth histo global hfig1 hfig2 hfig3 global nbb Uval Vval Uhist Vhist % nbb resolution of the histogram nbb=10: 10 values in unity interval global xval xerror yval yerror set(handles.vector_y,'Value',1)% trigger the option Uhist on the interface set(handles.Vhist_input,'Value',1) set(handles.cm_switch,'Value',0) % put the switch to 'pixel' %adjust the extremal values of the histogram in U with respect to integer %values minimU=round(min(Uval)-0.5)+0.5; %first value of the histogram with integer bins maximU=round(max(Uval)-0.5)+0.5; minim_fin=(minimU-0.5+1/(2*nbb)); % first bin valueat the beginning of an integer interval maxim_fin=(maximU+0.5-1/(2*nbb)); % last integer value nb_bin_min= round(-(minim_fin - min(Uval))*nbb); % nbre of bins added below nb_bin_max=round((maxim_fin -max(Uval))*nbb); %nbre of bins added above Uval=[minim_fin:(1/nbb):maxim_fin]; histu_min=zeros(nb_bin_min,1); histu_max=zeros(nb_bin_max,1); Uhist=[histu_min; Uhist ;histu_max]; % column vector %adjust the extremal values of the histogram in V minimV=round(min(Vval-0.5)+0.5); maximV=round(max(Vval-0.5)+0.5); minim_fin=minimV-0.5+1/(2*nbb); % first bin valueat the beginning of an integer interval maxim_fin=maximV+0.5-1/(2*nbb); % last integer value nb_bin_min=round((min(Vval) - minim_fin)*nbb); % nbre of bins added below nb_bin_max=round((maxim_fin -max(Vval))*nbb); Vval=[minim_fin:(1/nbb):maxim_fin]; histu_min=zeros(nb_bin_min,1); histu_max=zeros(nb_bin_max,1); Vhist=[histu_min; Vhist ;histu_max]; % column vector % RUN_histo_Callback(hObject, eventdata, handles) % %adjust the histogram to integer values: %histoU and V [Uhistinter,xval,xerror]=peaklock(nbb,minimU,maximU,Uhist); [Vhistinter,yval,yerror]=peaklock(nbb,minimV,maximV,Vhist); % selection of value ranges such that histo>=10 (enough statistics) Uval_ind=find(Uhist>=10); ind_min=min(Uval_ind); ind_max=max(Uval_ind); U_min=Uval(ind_min);% minimum allowed value U_max=Uval(ind_max);%maximum allowed value % selection of value ranges such that histo>=10 (enough statistics) Vval_ind=find(Vhist>=10); ind_min=min(Vval_ind); ind_max=max(Vval_ind); V_min=Vval(ind_min);% minimum allowed value V_max=Vval(ind_max);%maximum allowed value figure(4)% plot U histogram with smoothed one plot(Uval,Uhist,'b') grid on hold on plot(Uval,Uhistinter,'r'); hold off figure(5)% plot V histogram with smoothed one plot(Vval,Vhist,'b') grid on hold on plot(Vval,Vhistinter,'r'); hold off figure(6)% plot pixel error in two subplots hfig4=subplot(2,1,1); hfig5=subplot(2,1,2); axes(hfig4) plot(xval,xerror) axis([U_min U_max -0.4 0.4]) xlabel('velocity u (pix)') ylabel('peaklocking error (pix)') grid on axes(hfig5) plot(yval,yerror) axis([V_min V_max -0.4 0.4]); xlabel('velocity v (pix)') ylabel('peaklocking error (pix)') grid on %'peaklock': determines peacklocking errors from velocity histograms. %------------------------------------------------------- %first smooth the input histogram 'histu' in such a way that the integral over %n-n+1 is preserved, then deduce the peaklocking 'error' function of the pixcel displacement 'x'. % % [histinter,x,error]=peaklock(nbb,minim,maxim,histu) %OUTPUT: %histinter: smoothed interpolated histogram % x: vector of displacement values. % error: vector of estimated errors corresponding to x %INPUT: %histu=vector representing the values of histogram of measured velocity ; %minim, maxim: extremal values of the measured velocity (absica for histu) %nbb: number of bins inside each integer interval for the histograms %SUBROUTINES INCLUDED: %spline4.m% spline interpolation at 4th order %splinhist.m: give spline coeff cc for a smooth histo (call spline4) %histsmooth.m(x,cc): calculate the smooth histo for any value x %histder.m(x,cc): calculate the derivative of the smooth histo function [histinter,x,error]=peaklock(nbb,minim,maxim,histu) nint=maxim-minim+1 xfin=[minim-0.5+1/(2*nbb):(1/nbb):maxim+0.5-(1/(2*nbb))]; histo=(reshape(histu,nbb,nint));%extract values with x between integer -1/2 integer +1/2 Integ=sum(histo)/nbb; %integral of the pdf on each integer bin [histinter,cc]=splinhist(Integ,minim,nbb); histx=reshape(histinter,nbb,nint); xint=[minim:1:maxim]; x=zeros(nbb,nint); %determination of the displacement x(j,:) %j=1 delx=histo(1,:)./histsmooth(-0.5*ones(1,nint),cc)/nbb; %del(1,:)=delx; x(1,:)=-0.5+delx-(delx.*delx/2).*histder(-0.5*ones(1,nint),cc); %histx(1,:)=histsmooth(x(j-1,:),cc); for j=2:nbb delx=histo(j,:)./histsmooth(x(j-1,:),cc)/nbb; %delx=delx.*(delx<3*ones(1,nint)/nbb)+3*ones(1,nint)/nbb.*~(delx <3*ones(1,nint)/nbb) x(j,:)=x(j-1,:)+delx-(delx.*delx/2).*histder(x(j-1,:),cc); end %reshape xint=ones(nbb,1)*xint; x=x+xint; x=reshape(x,1,nbb*nint); error=xfin+1/(2*nbb)-x; %------------------------------------------------------- % --- determine the spline coefficients cc for the interpolated histogram. %------------------------------------------------- function [histsmooth,cc]= splinhist(Integ,mini,nbb) % provides a smooth histogramm histmooth, which remains always positive, % and is such that its sum over each integer bin [i-1/2 i+1/2] is equal to % Integ(i). The function determines histmooth as the exponential of a 4th % order spline function and adjust the cefficients by a Newton method to % fit the integral conditions Integ % histmooth is determined at the abscissa % xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))] (maxi=mini+size(aa)-1) %cc(1-5,i) provides the spline coefficients % order 0 siz=size(Integ); nint=siz(2); izero=find(Integ==0); %indices of zero elements inonzero=find(Integ); Integ(izero)=min(Integ(inonzero)); aa=log(Integ);%initial guess for a coeff spli=spline4(aa,mini,nbb); %appel � la fonction spline4 histsmooth=exp(spli); S=(sum(reshape(histsmooth,nbb,nint)))/nbb;% integral of the fit histsmooth on ]i-1/2 i+1/2[ epsilon=max(abs(Integ-S)); iter=0; while epsilon > 0.000001 & iter<10 ident=eye(nint); dSda=ones(nint); for j=1:nint% determination of the jacobian matrix dSda dhistda=spline4(ident(j,:),mini,nbb); expdhistda=dhistda.*histsmooth; dSda(j,:)=(sum(reshape(expdhistda,nbb,nint)))/nbb; end aa=aa+(Integ-S)*inv(dSda);%new estimate of coefficients aa by linear interpolation [spli,bb]=spline4(aa,mini,nbb);% new fit histsmooth histsmooth=exp(spli); S=(sum(reshape(histsmooth,nbb,nint)))/nbb;% integral of the fit histsmooth on ]i-1/2 i+1/2[ epsilon=max(abs(Integ-S)); iter=iter+1; end if iter==10, errordlg('splinhist did not converge after 10 iterations'),end cc(1,:)=aa; cc(2,:)=bb(1,:); cc(3,:)=bb(2,:); cc(4,:)=bb(3,:); cc(5,:)=bb(4,:); %------------------------------------------------------- % --- determine the 4th order spline coefficients from the function values aa. %------------------------------------------------- function [histsmooth,bb]= spline4(aa,mini,n) % spline interpolation at 4th order %aa=vector of values of a function at integer abscissa, starting at mini %n=number of subdivisions for the interpolated function % histmooth =interpolated values at absissa % xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))] (maxi=mini+size(aa)-1) %bb=[b(i);c(i);d(i); e(i)] matrix of spline coeff L1=[1/2 1/4 1/8 1/16;1 1 3/4 1/2;0 2 3 3;0 0 6 12]; L2=[-1/2 1/4 -1/8 1/16;1 -1 3/4 -1/2;0 2 -3 3;0 0 6 -12]; M=inv(L2)*L1; [V,D]=eig(M); F=-inv(V)*inv(L2)*[1 ;0 ;0;0]; a1rev=[1 -1/D(1,1)]; b1rev=[F(1)/D(1,1)]; a2rev=[1 -1/D(2,2)]; b2rev=[F(2)/D(2,2)]; a3=[1 -D(3,3)]; b3=[F(3)]; a4=[1 -D(4,4)]; b4=[F(4)]; %data % n=10;% r�solution de la pdf: nbre de points par unite de u % mini=-10.0;%general mini=uint16(min(values)-1 CHOOSE maxi-mini+1 EVEN % maxi=9.0; % general maxi=uint16(max(values))+1 %nint=double(maxi-mini+1); % nombre d'intervals entiers EVEN! siz=size(aa); nint=siz(2); maxi=mini+nint-1; npdf=nint*n;% nbre total d'intervals � introduire dans la pdf: hist(u,npdf) %simulation de pdf xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))];% valeurs d'interpolation: we take n values in each integer interval %histolin=exp(-(xfin-1).*(xfin-1)).*(2+cos(10*(xfin-1)));% simulation d'une pdf %histo=log(histolin); %histo=sin(2*pi*xfin); %histextract=(reshape(histo,n,nint)); %aa=sum(histextract)/n %integral of the pdf on each integer bin IP=[0 diff(aa)]; Irev=zeros(size(aa)); for i=1:nint Irev(i)=aa(end-i+1); end IPrev=[0 diff(Irev)]; %get the spline coelfficients a_d, using filter on the eigen vectors A,B,C Arev=filter(b1rev,a1rev,IPrev); Brev=filter(b2rev,a2rev,IPrev); C=filter(b3,a3,IP); D=filter(b4,a4,IP); A=zeros(size(Arev)); B=zeros(size(Brev)); for i=1:nint A(i)=Arev(end-i+1); B(i)=Brev(end-i+1); end %Matr=V*[A;B;C;D]; bb=V*[A;B;C;D]; %b=Matr(1,:); %c=Matr(2,:); %d=Matr(3,:); %e=Matr(4,:); %a=aa; %calculate the interpolation using the spline coefficients a-d %xextract=(reshape(xfin,n,nint));% chi=xfin+1/(2*n)-min(xfin)-double(int16(xfin+(1/(2*n))-min(xfin)))-0.5;% decimal part chi2=chi.*chi; chi3=chi2.*chi; chi4=chi3.*chi; avec=reshape(ones(n,1)*aa,1,n*nint); bvec=reshape(ones(n,1)*bb(1,:),1,n*nint); cvec=reshape(ones(n,1)*bb(2,:),1,n*nint); dvec=reshape(ones(n,1)*bb(3,:),1,n*nint); evec=reshape(ones(n,1)*bb(4,:),1,n*nint); histsmooth=avec+bvec.*chi+cvec.*chi2+dvec.*chi3+evec.*chi4; %------------------------------------------------------- % --- determine the interpolated histogram at points chi from the spline ceff cc. %------------------------------------------------- function histx= histsmooth(chi,cc) % provides the value of the interpolated histogram at values chi=x-i %(difference with the mnearest integer) % cc(5,size(chi)) is the set of spline coefficients obtained by splinhist chi2=chi.*chi; chi3=chi2.*chi; chi4=chi3.*chi; histx=exp(cc(1,:)+cc(2,:).*chi+cc(3,:).*chi2+cc(4,:).*chi3+cc(5,:).*chi4); %------------------------------------------------------- % --- determine the derivative p'/p of the interpolated histogram at points chi from the spline ceff cc. %------------------------------------------------- function histder= histder(chi,cc) % provides the logarithmique derivative p'/p of the interpolated histogram %at values chi=x-i %(difference with the nearest integer) % cc(5,size(chi)) is the set of spline coefficients obtained by splinhist chi2=chi.*chi; chi3=chi2.*chi; chi4=chi3.*chi; histder=cc(2,:)+2*cc(3,:).*chi+3*cc(4,:).*chi2+4*cc(5,:).*chi3;