source: trunk/src/filter_tps.m @ 1137

Last change on this file since 1137 was 1137, checked in by sommeria, 11 days ago

tps improved by a cosine window in each subdomain. Default size of subdomains reduced for faster computation in the civ interface
File size: 9.8 KB
Line 
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,2,NbSubdomain): range (min, max) of the coordinates 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, possibly W: set of velocity components of the initial data
17% SubdomainSize: estimated number of data points in each subdomain
18% Rho: smoothing parameter
19% Threshold: max diff accepted between smoothed and initial data
20
21
22%=======================================================================
23% Copyright 2008-2024, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
24%   http://www.legi.grenoble-inp.fr
25%   Joel.Sommeria - Joel.Sommeria (A) univ-grenoble-alpes.fr
26%
27%     This file is part of the toolbox UVMAT.
28%
29%     UVMAT is free software; you can redistribute it and/or modify
30%     it under the terms of the GNU General Public License as published
31%     by the Free Software Foundation; either version 2 of the license,
32%     or (at your option) any later version.
33%
34%     UVMAT is distributed in the hope that it will be useful,
35%     but WITHOUT ANY WARRANTY; without even the implied warranty of
36%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
37%     GNU General Public License (see LICENSE.txt) for more details.
38%=======================================================================
39
40function [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)
41
42%% adjust subdomain decomposition
43warning off
44NbVec=size(Coord,1);% nbre of vectors in the field to interpolate
45NbCoord=size(Coord,2);% space dimension
46MinCoord=min(Coord,[],1);%lower coordinate bounds
47MaxCoord=max(Coord,[],1);%upper coordinate bounds
48Range=MaxCoord-MinCoord;
49AspectRatio=Range(2)/Range(1);
50NbSubDomain=NbVec/SubDomainSize;% estimated number of subdomains
51NbSubDomainX=max(floor(sqrt(NbSubDomain/AspectRatio)),1);% estimated number of subdomains in x
52NbSubDomainY=max(floor(sqrt(NbSubDomain*AspectRatio)),1);% estimated number of subdomains in y
53NbSubDomain=NbSubDomainX*NbSubDomainY;% new estimated number of subdomains in a matrix shape partition in subdomains
54Siz(1)=Range(1)/NbSubDomainX;%width of subdomains
55Siz(2)=Range(2)/NbSubDomainY;%height of subdomains
56CentreX=linspace(MinCoord(1)+Siz(1)/2,MaxCoord(1)-Siz(1)/2,NbSubDomainX);% X positions of subdomain centres
57CentreY=linspace(MinCoord(2)+Siz(2)/2,MaxCoord(2)-Siz(2)/2,NbSubDomainY);% Y positions of subdomain centres
58[CentreX,CentreY]=meshgrid(CentreX,CentreY);
59CentreX=reshape(CentreX,1,[]);% X positions of subdomain centres
60CentreY=reshape(CentreY,1,[]);% Y positions of subdomain centres
61
62%% smoothing parameter
63rho=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)
64
65%% default output
66SubRange=zeros(NbCoord,2,NbSubDomain);%initialise the boundaries of subdomains
67Coord_tps=zeros(1,NbCoord,NbSubDomain);% initialize coordinates of interpolated data
68U_tps=zeros(1,NbSubDomain);% initialize  interpolated u component
69V_tps=zeros(1,NbSubDomain);% initialize interpolated v component
70NbCentre=zeros(1,NbSubDomain);%number of interpolated field values per subdomain, =0 by default
71W_tps=[];%default (2 component case)
72U_smooth=zeros(NbVec,1); % smoothed velocity U at the initial positions
73V_smooth=zeros(NbVec,1);% smoothed velocity V at the initial positions
74W_smooth=[];%default (2 component case)
75FF=zeros(NbVec,1);
76nb_select=zeros(NbVec,1);
77check_empty=zeros(1,NbSubDomain);
78
79
80%% calculate tps coeff in each subdomain
81for isub=1:NbSubDomain
82    isub
83    SubRange(1,:,isub)=[CentreX(isub)-0.55*Siz(1) CentreX(isub)+0.55*Siz(1)];%bounds of subdomain #isub in x coordinate
84    SubRange(2,:,isub)=[CentreY(isub)-0.55*Siz(2) CentreY(isub)+0.55*Siz(2)];%bounds of subdomain #isub in y coordinate
85    ind_sel_previous=[];
86    ind_sel=0;%initialize set of vector indices in the subdomain
87    %increase iteratively the subdomain if it contains less than SubDomainNbVec/4 source vectors
88    while numel(ind_sel)>numel(ind_sel_previous)
89        ind_sel_previous=ind_sel;% record the set of selected vector indices for next iteration
90        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));
91        numel(ind_sel)
92        % if no vector in the subdomain  #isub, skip the subdomain
93        if isempty(ind_sel)
94            check_empty(isub)=1;
95            break %  go to next subdomain
96        % if too few selected vectors, increase the subrange for next iteration
97        elseif numel(ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous)
98            SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4;
99            SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4;
100        % subdomain includes enough vectors, perform tps interpolation
101        else
102            [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel,:),U(ind_sel),rho);
103            [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel,:),V(ind_sel),rho);
104            UDiff=U_smooth_sub-U(ind_sel);% difference between interpolated U component and initial value
105            VDiff=V_smooth_sub-V(ind_sel);% difference between interpolated V component and initial value
106            NormDiff=UDiff.*UDiff+VDiff.*VDiff;% Square of difference norm
107            ind_ind_sel=1:numel(ind_sel);%default
108            if exist('Threshold','var')&&~isempty(Threshold)
109                FF(ind_sel)=20*(NormDiff>Threshold);%put FF value to 20 to identify the criterium of elimmination
110                ind_ind_sel=find(FF(ind_sel)==0); % select the indices of ind_sel corresponding to the remaining vectors
111            end
112            % if no value exceeds threshold, the result is recorded
113            if isequal(numel(ind_ind_sel),numel(ind_sel))
114                x_width=(SubRange(1,2,isub)-SubRange(1,1,isub))/pi;
115                y_width=(SubRange(2,2,isub)-SubRange(2,1,isub))/pi;
116                x_dist=(Coord(ind_sel,1)-CentreX(isub))/x_width;% relative x distance to the retangle centre
117                y_dist=(Coord(ind_sel,2)-CentreY(isub))/y_width;% relative ydistance to the retangle centre
118                weight=cos(x_dist).*cos(y_dist);%weighting fct =1 at the rectangle center and 0 at edge
119                U_smooth(ind_sel)=U_smooth(ind_sel)+weight.*U_smooth_sub;
120                V_smooth(ind_sel)=V_smooth(ind_sel)+weight.*V_smooth_sub;
121                NbCentre(isub)=numel(ind_sel);
122                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel,:);
123                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
124                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
125                nb_select(ind_sel)=nb_select(ind_sel)+weight;
126                display(['tps done in subdomain # ' num2str(isub)  ' among ' num2str(NbSubDomain)])
127                break
128            % if too few selected vectors, increase the subrange for next iteration
129            elseif numel(ind_ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous)
130                SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4;
131                SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4;
132            % else interpolation-smoothing is done again with the selected vectors
133            else
134                [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),U(ind_sel(ind_ind_sel)),rho);
135                [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),V(ind_sel(ind_ind_sel)),rho);
136                x_width=(SubRange(1,2,isub)-SubRange(1,1,isub))/pi;
137                y_width=(SubRange(2,2,isub)-SubRange(2,1,isub))/pi;
138                x_dist=(Coord(ind_sel(ind_ind_sel),1)-CentreX(isub))/x_width;% relative x distance to the retangle centre
139                y_dist=(Coord(ind_sel(ind_ind_sel),2)-CentreY(isub))/y_width;% relative ydistance to the retangle centre
140                weight=cos(x_dist).*cos(y_dist);%weighting fct =1 at the rectangle center and 0 at edge
141                U_smooth(ind_sel(ind_ind_sel))=U_smooth(ind_sel(ind_ind_sel))+weight.*U_smooth_sub;
142                V_smooth(ind_sel(ind_ind_sel))=V_smooth(ind_sel(ind_ind_sel))+weight.*V_smooth_sub;
143                NbCentre(isub)=numel(ind_ind_sel);
144                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel(ind_ind_sel),:);
145                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
146                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
147                nb_select(ind_sel(ind_ind_sel))=nb_select(ind_sel(ind_ind_sel))+weight;
148                display(['tps redone after elimination of erratic vectors in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)])
149                break
150            end
151        end
152    end
153end
154
155%% remove empty subdomains
156ind_empty=find(check_empty);
157if ~isempty(ind_empty)
158    SubRange(:,:,ind_empty)=[];
159    Coord_tps(:,:,ind_empty)=[];
160    U_tps(:,ind_empty)=[];
161    V_tps(:,ind_empty)=[];
162    NbCentre(ind_empty)=[];
163end
164
165%% final adjustments
166nb_select(nb_select==0)=1;
167U_smooth=U_smooth./nb_select;% take the average at the intersection of several subdomains
168V_smooth=V_smooth./nb_select;
169U_smooth(FF==20)=U(FF==20);% set to the initial values the eliminated vectors (flagged as false)
170V_smooth(FF==20)=V(FF==20);
171fill=zeros(NbCoord+1,NbCoord,size(SubRange,3)); %matrix of zeros to complement the matrix Data.Civ1_Coord_tps (conveninent for file storage)
172Coord_tps=cat(1,Coord_tps,fill);
173
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