%'filter_tps': find the thin plate spline coefficients for interpolation-smoothing %------------------------------------------------------------------------ % [SubRange,NbSites,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomain,Rho,Threshold) % % OUTPUT: % SubRange(NbCoord,NbSubdomain,2): range (min, max) of the coordiantes x and y respectively, for each subdomain % NbSites(NbSubdomain): number of source points for each subdomain % FF: false flags % U_smooth, V_smooth: filtered velocity components at the positions of the initial data % Coord_tps(NbSites,NbCoord,NbSubdomain): positions of the tps centres % U_tps,V_tps: weight of the tps for each subdomain % to get the interpolated field values, use the function calc_field.m % % INPUT: % coord=[X Y]: matrix whose first column is the x coordinates of the initial data, the second column the y coordiantes % U,V: set of velocity components of the initial data % Rho: smoothing parameter % Threshold: max diff accepted between smoothed and initial data % Subdomain: estimated number of data points in each subdomain function [SubRange,NbSites,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomain,Rho,Threshold) %subdomain decomposition warning off nbvec=size(Coord,1); W_tps=[];%default W_smooth=[]; NbCoord=size(Coord,2); NbSubDomain=nbvec/SubDomain; MinCoord=min(Coord,[],1); MaxCoord=max(Coord,[],1); Range=MaxCoord-MinCoord; AspectRatio=Range(2)/Range(1); NbSubDomainX=max(floor(sqrt(NbSubDomain/AspectRatio)),1); NbSubDomainY=max(floor(sqrt(NbSubDomain*AspectRatio)),1); NbSubDomain=NbSubDomainX*NbSubDomainY; Siz(1)=Range(1)/NbSubDomainX;%width of subdomains Siz(2)=Range(2)/NbSubDomainY;%height of subdomains CentreX=linspace(MinCoord(1)+Siz(1)/2,MaxCoord(1)-Siz(1)/2,NbSubDomainX); CentreY=linspace(MinCoord(2)+Siz(2)/2,MaxCoord(2)-Siz(2)/2,NbSubDomainY); [CentreX,CentreY]=meshgrid(CentreX,CentreY); CentreY=reshape(CentreY,1,[]);% Y positions of subdomain centres CentreX=reshape(CentreX,1,[]);% X positions of subdomain centres rho=Siz(1)*Siz(2)*Rho/1000;%optimum rho increase as the area of the subdomain (division by 10^6 to reach good values with the default GUI input) U_tps_sub=zeros(nbvec,NbSubDomain);%default spline V_tps_sub=zeros(nbvec,NbSubDomain);%default spline Indices_tps=zeros(nbvec,NbSubDomain);%default indices U_smooth=zeros(nbvec,1); V_smooth=zeros(nbvec,1); nb_select=zeros(nbvec,1); FF=zeros(nbvec,1); check_empty=zeros(1,NbSubDomain); SubRange=zeros(NbCoord,2,NbSubDomain);%initialise the positions of subdomains % SubRangy=zeros(NbSubDomain,2); for isub=1:NbSubDomain SubRange(1,:,isub)=[CentreX(isub)-0.55*Siz(1) CentreX(isub)+0.55*Siz(1)]; SubRange(2,:,isub)=[CentreY(isub)-0.55*Siz(2) CentreY(isub)+0.55*Siz(2)]; ind_sel_previous=[]; ind_sel=0; while numel(ind_sel)>numel(ind_sel_previous) %increase the subdomain during four iterations at most ind_sel_previous=ind_sel; ind_sel=find(Coord(:,1)>=SubRange(1,1,isub) & Coord(:,1)<=SubRange(1,2,isub) & Coord(:,2)>=SubRange(2,1,isub) & Coord(:,2)<=SubRange(2,2,isub)); % if no vector in the subdomain, skip the subdomain if isempty(ind_sel) check_empty(isub)=1; U_tps(1,isub)=0;%define U_tps and V_tps by default V_tps(1,isub)=0; break % if too few selected vectors, increase the subrange for next iteration elseif numel(ind_sel)Threshold);%put FF value to 20 to identify the criterium of elimmination ind_ind_sel=find(FF(ind_sel)==0); % select the indices of ind_sel corresponding to the remaining vectors end % if no value exceeds threshold, the result is recorded if isequal(numel(ind_ind_sel),numel(ind_sel)) U_smooth(ind_sel)=U_smooth(ind_sel)+U_smooth_sub; V_smooth(ind_sel)=V_smooth(ind_sel)+V_smooth_sub; NbSites(isub)=numel(ind_sel); Coord_tps(1:NbSites(isub),:,isub)=Coord(ind_sel,:); U_tps(1:NbSites(isub)+3,isub)=U_tps_sub; V_tps(1:NbSites(isub)+3,isub)=V_tps_sub; nb_select(ind_sel)=nb_select(ind_sel)+1; display('good') break % if too few selected vectors, increase the subrange for next iteration elseif numel(ind_ind_sel)