source: trunk/src/filter_tps.m @ 1135

Last change on this file since 1135 was 1135, checked in by sommeria, 12 days ago

fct for python added
File size: 8.9 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                U_smooth(ind_sel)=U_smooth(ind_sel)+U_smooth_sub;
115                V_smooth(ind_sel)=V_smooth(ind_sel)+V_smooth_sub;
116                NbCentre(isub)=numel(ind_sel);
117                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel,:);
118                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
119                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
120                nb_select(ind_sel)=nb_select(ind_sel)+1;
121                display(['tps done in subdomain # ' num2str(isub)  ' among ' num2str(NbSubDomain)])
122                break
123            % if too few selected vectors, increase the subrange for next iteration
124            elseif numel(ind_ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous);
125                SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4;
126                SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4;
127            % else interpolation-smoothing is done again with the selected vectors
128            else
129                [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),U(ind_sel(ind_ind_sel)),rho);
130                [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),V(ind_sel(ind_ind_sel)),rho);
131                U_smooth(ind_sel(ind_ind_sel))=U_smooth(ind_sel(ind_ind_sel))+U_smooth_sub;
132                V_smooth(ind_sel(ind_ind_sel))=V_smooth(ind_sel(ind_ind_sel))+V_smooth_sub;
133                NbCentre(isub)=numel(ind_ind_sel);
134                Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel(ind_ind_sel),:);
135                U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub;
136                V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub;
137                nb_select(ind_sel(ind_ind_sel))=nb_select(ind_sel(ind_ind_sel))+1;
138                display(['tps redone after elimination of erratic vectors in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)])
139                break
140            end
141        end
142    end
143end
144
145%% remove empty subdomains
146ind_empty=find(check_empty);
147if ~isempty(ind_empty)
148    SubRange(:,:,ind_empty)=[];
149    Coord_tps(:,:,ind_empty)=[];
150    U_tps(:,ind_empty)=[];
151    V_tps(:,ind_empty)=[];
152    NbCentre(ind_empty)=[];
153end
154
155%% final adjustments
156nb_select(nb_select==0)=1;
157U_smooth=U_smooth./nb_select;% take the average at the intersection of several subdomains
158V_smooth=V_smooth./nb_select;
159U_smooth(FF==20)=U(FF==20);% set to the initial values the eliminated vectors (flagged as false)
160V_smooth(FF==20)=V(FF==20);
161fill=zeros(NbCoord+1,NbCoord,size(SubRange,3)); %matrix of zeros to complement the matrix Data.Civ1_Coord_tps (conveninent for file storage)
162Coord_tps=cat(1,Coord_tps,fill);
163
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