source: trunk/src/filter_tps.m @ 941

Last change on this file since 941 was 924, checked in by g7moreau, 5 years ago
  • Update Copyright Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
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1%'filter_tps': find the thin plate spline coefficients for interpolation-smoothing
2%------------------------------------------------------------------------
3% [SubRange,NbCentre,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomainSize,Rho,Threshold)
4%
5% OUTPUT:
6% SubRange(NbCoord,NbSubdomain,2): range (min, max) of the coordiantes x and y respectively, for each subdomain
7% NbCentre(NbSubdomain): number of source points for each subdomain
8% FF: false flags
9% U_smooth, V_smooth: filtered velocity components at the positions of the initial data
10% Coord_tps(NbCentre,NbCoord,NbSubdomain): positions of the tps centres
11% U_tps,V_tps: weight of the tps for each subdomain
12% to get the interpolated field values, use the function calc_field.m
13%
14% INPUT:
15% coord=[X Y]: matrix whose first column is the x coordinates of the initial data, the second column the y coordiantes
16% U,V: set of velocity components of the initial data
17% Rho: smoothing parameter
18% Threshold: max diff accepted between smoothed and initial data
19% Subdomain: estimated number of data points in each subdomain
20
21%=======================================================================
22% Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
23%   http://www.legi.grenoble-inp.fr
24%   Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr
25%
26%     This file is part of the toolbox UVMAT.
27%
28%     UVMAT is free software; you can redistribute it and/or modify
29%     it under the terms of the GNU General Public License as published
30%     by the Free Software Foundation; either version 2 of the license,
31%     or (at your option) any later version.
32%
33%     UVMAT is distributed in the hope that it will be useful,
34%     but WITHOUT ANY WARRANTY; without even the implied warranty of
35%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
36%     GNU General Public License (see LICENSE.txt) for more details.
37%=======================================================================
38
39function [SubRange,NbCentre,Coord_tps,U_tps,V_tps,W_tps,U_smooth,V_smooth,W_smooth,FF] =filter_tps(Coord,U,V,W,SubDomainSize,Rho,Threshold)
40
41%% adjust subdomain decomposition
42warning off
43NbVec=size(Coord,1);% nbre of vectors in the field to interpolate
44NbCoord=size(Coord,2);% space dimension
45MinCoord=min(Coord,[],1);%lower coordinate bounds
46MaxCoord=max(Coord,[],1);%upper coordinate bounds
47Range=MaxCoord-MinCoord;
48AspectRatio=Range(2)/Range(1);
49NbSubDomain=NbVec/SubDomainSize;% estimated number of subdomains
50NbSubDomainX=max(floor(sqrt(NbSubDomain/AspectRatio)),1);% estimated number of subdomains in x
51NbSubDomainY=max(floor(sqrt(NbSubDomain*AspectRatio)),1);% estimated number of subdomains in y
52NbSubDomain=NbSubDomainX*NbSubDomainY;% new estimated number of subdomains in a matrix shape partition in subdomains
53Siz(1)=Range(1)/NbSubDomainX;%width of subdomains
54Siz(2)=Range(2)/NbSubDomainY;%height of subdomains
55CentreX=linspace(MinCoord(1)+Siz(1)/2,MaxCoord(1)-Siz(1)/2,NbSubDomainX);% X positions of subdomain centres
56CentreY=linspace(MinCoord(2)+Siz(2)/2,MaxCoord(2)-Siz(2)/2,NbSubDomainY);% Y positions of subdomain centres
57[CentreX,CentreY]=meshgrid(CentreX,CentreY);
58CentreX=reshape(CentreX,1,[]);% X positions of subdomain centres
59CentreY=reshape(CentreY,1,[]);% Y positions of subdomain centres
60
61%% smoothing parameter
62rho=Siz(1)*Siz(2)*Rho/1000;%optimum rho increase as the area of the subdomain (division by 1000 to reach good values with the default GUI input)
63
64%% default output
65SubRange=zeros(NbCoord,2,NbSubDomain);%initialise the boundaries of subdomains
66Coord_tps=zeros(1,NbCoord,NbSubDomain);% initialize coordinates of interpolated data
67U_tps=zeros(1,NbSubDomain);% initialize  interpolated u component
68V_tps=zeros(1,NbSubDomain);% initialize interpolated v component
69NbCentre=zeros(1,NbSubDomain);%number of interpolated field values per subdomain, =0 by default
70W_tps=[];%default (2 component case)
71U_smooth=zeros(NbVec,1); % smoothed velocity U at the initial positions
72V_smooth=zeros(NbVec,1);% smoothed velocity V at the initial positions
73W_smooth=[];%default (2 component case)
74FF=zeros(NbVec,1);
75nb_select=zeros(NbVec,1);
76check_empty=zeros(1,NbSubDomain);
77
78
79%% calculate tps coeff in each subdomain
80for isub=1:NbSubDomain
81    SubRange(1,:,isub)=[CentreX(isub)-0.55*Siz(1) CentreX(isub)+0.55*Siz(1)];%bounds of subdomain #isub in x coordinate
82    SubRange(2,:,isub)=[CentreY(isub)-0.55*Siz(2) CentreY(isub)+0.55*Siz(2)];%bounds of subdomain #isub in y coordinate
83    ind_sel_previous=[];
84    ind_sel=0;%initialize set of vector indices in the subdomain
85    %increase iteratively the subdomain if it contains less than SubDomainNbVec/4 source vectors
86    while numel(ind_sel)>numel(ind_sel_previous)
87        ind_sel_previous=ind_sel;% record the set of selected vector indices for next iteration
88        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));
89        % if no vector in the subdomain  #isub, skip the subdomain
90        if isempty(ind_sel)
91            check_empty(isub)=1;
92            break %  go to next subdomain
93        % if too few selected vectors, increase the subrange for next iteration
94        elseif numel(ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous);
95            SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4;
96            SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4;
97        % subdomain includes enough vectors, perform tps interpolation
98        else
99            [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel,:),U(ind_sel),rho);
100            [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel,:),V(ind_sel),rho);
101            UDiff=U_smooth_sub-U(ind_sel);% difference between interpolated U component and initial value
102            VDiff=V_smooth_sub-V(ind_sel);% difference between interpolated V component and initial value
103            NormDiff=UDiff.*UDiff+VDiff.*VDiff;% Square of difference norm
104            ind_ind_sel=1:numel(ind_sel);%default
105            if exist('Threshold','var')&&~isempty(Threshold)
106                FF(ind_sel)=20*(NormDiff>Threshold);%put FF value to 20 to identify the criterium of elimmination
107                ind_ind_sel=find(FF(ind_sel)==0); % select the indices of ind_sel corresponding to the remaining vectors
108            end
109            % if no value exceeds threshold, the result is recorded
110            if isequal(numel(ind_ind_sel),numel(ind_sel))
111                U_smooth(ind_sel)=U_smooth(ind_sel)+U_smooth_sub;
112                V_smooth(ind_sel)=V_smooth(ind_sel)+V_smooth_sub;
113                NbCentre(isub)=numel(ind_sel);
114                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel,:);
115                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
116                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
117                nb_select(ind_sel)=nb_select(ind_sel)+1;
118                display(['tps done in subdomain # ' num2str(isub)  ' among ' num2str(NbSubDomain)])
119                break
120            % if too few selected vectors, increase the subrange for next iteration
121            elseif numel(ind_ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous);
122                SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4;
123                SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4;
124            % else interpolation-smoothing is done again with the selected vectors
125            else
126                [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),U(ind_sel(ind_ind_sel)),rho);
127                [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),V(ind_sel(ind_ind_sel)),rho);
128                U_smooth(ind_sel(ind_ind_sel))=U_smooth(ind_sel(ind_ind_sel))+U_smooth_sub;
129                V_smooth(ind_sel(ind_ind_sel))=V_smooth(ind_sel(ind_ind_sel))+V_smooth_sub;
130                NbCentre(isub)=numel(ind_ind_sel);
131                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel(ind_ind_sel),:);
132                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
133                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
134                nb_select(ind_sel(ind_ind_sel))=nb_select(ind_sel(ind_ind_sel))+1;
135                display(['tps redone after elimination of erratic vectors in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)])
136                break
137            end
138        end
139    end
140end
141
142%% remove empty subdomains
143ind_empty=find(check_empty);
144if ~isempty(ind_empty)
145    SubRange(:,:,ind_empty)=[];
146    Coord_tps(:,:,ind_empty)=[];
147    U_tps(:,ind_empty)=[];
148    V_tps(:,ind_empty)=[];
149    NbCentre(ind_empty)=[];
150end
151
152%% final adjustments
153nb_select(nb_select==0)=1;
154U_smooth=U_smooth./nb_select;% take the average at the intersection of several subdomains
155V_smooth=V_smooth./nb_select;
156fill=zeros(NbCoord+1,NbCoord,size(SubRange,3)); %matrix of zeros to complement the matrix Data.Civ1_Coord_tps (conveninent for file storage)
157Coord_tps=cat(1,Coord_tps,fill);
158
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