[476] | 1 | %'filter_tps': find the thin plate spline coefficients for interpolation-smoothing |
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[382] | 2 | %------------------------------------------------------------------------ |
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[896] | 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) |
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[476] | 4 | % |
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[382] | 5 | % OUTPUT: |
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| 6 | % SubRange(NbCoord,NbSubdomain,2): range (min, max) of the coordiantes x and y respectively, for each subdomain |
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[651] | 7 | % NbCentre(NbSubdomain): number of source points for each subdomain |
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[382] | 8 | % FF: false flags |
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| 9 | % U_smooth, V_smooth: filtered velocity components at the positions of the initial data |
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[651] | 10 | % Coord_tps(NbCentre,NbCoord,NbSubdomain): positions of the tps centres |
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[382] | 11 | % U_tps,V_tps: weight of the tps for each subdomain |
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[494] | 12 | % to get the interpolated field values, use the function calc_field.m |
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[382] | 13 | % |
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| 14 | % INPUT: |
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[476] | 15 | % coord=[X Y]: matrix whose first column is the x coordinates of the initial data, the second column the y coordiantes |
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[382] | 16 | % U,V: set of velocity components of the initial data |
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| 17 | % Rho: smoothing parameter |
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| 18 | % Threshold: max diff accepted between smoothed and initial data |
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| 19 | % Subdomain: estimated number of data points in each subdomain |
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| 20 | |
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[809] | 21 | %======================================================================= |
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[977] | 22 | % Copyright 2008-2017, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France |
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[809] | 23 | % http://www.legi.grenoble-inp.fr |
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| 24 | % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr |
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| 25 | % |
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| 26 | % This file is part of the toolbox UVMAT. |
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| 27 | % |
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| 28 | % UVMAT is free software; you can redistribute it and/or modify |
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| 29 | % it under the terms of the GNU General Public License as published |
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| 30 | % by the Free Software Foundation; either version 2 of the license, |
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| 31 | % or (at your option) any later version. |
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| 32 | % |
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| 33 | % UVMAT is distributed in the hope that it will be useful, |
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| 34 | % but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 35 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 36 | % GNU General Public License (see LICENSE.txt) for more details. |
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| 37 | %======================================================================= |
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| 38 | |
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[896] | 39 | function [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) |
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[581] | 40 | |
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| 41 | %% adjust subdomain decomposition |
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[382] | 42 | warning off |
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[896] | 43 | NbVec=size(Coord,1);% nbre of vectors in the field to interpolate |
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| 44 | NbCoord=size(Coord,2);% space dimension |
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[581] | 45 | MinCoord=min(Coord,[],1);%lower coordinate bounds |
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| 46 | MaxCoord=max(Coord,[],1);%upper coordinate bounds |
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[382] | 47 | Range=MaxCoord-MinCoord; |
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| 48 | AspectRatio=Range(2)/Range(1); |
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[896] | 49 | NbSubDomain=NbVec/SubDomainSize;% estimated number of subdomains |
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| 50 | NbSubDomainX=max(floor(sqrt(NbSubDomain/AspectRatio)),1);% estimated number of subdomains in x |
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| 51 | NbSubDomainY=max(floor(sqrt(NbSubDomain*AspectRatio)),1);% estimated number of subdomains in y |
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| 52 | NbSubDomain=NbSubDomainX*NbSubDomainY;% new estimated number of subdomains in a matrix shape partition in subdomains |
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[382] | 53 | Siz(1)=Range(1)/NbSubDomainX;%width of subdomains |
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| 54 | Siz(2)=Range(2)/NbSubDomainY;%height of subdomains |
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[896] | 55 | CentreX=linspace(MinCoord(1)+Siz(1)/2,MaxCoord(1)-Siz(1)/2,NbSubDomainX);% X positions of subdomain centres |
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| 56 | CentreY=linspace(MinCoord(2)+Siz(2)/2,MaxCoord(2)-Siz(2)/2,NbSubDomainY);% Y positions of subdomain centres |
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[382] | 57 | [CentreX,CentreY]=meshgrid(CentreX,CentreY); |
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[896] | 58 | CentreX=reshape(CentreX,1,[]);% X positions of subdomain centres |
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[382] | 59 | CentreY=reshape(CentreY,1,[]);% Y positions of subdomain centres |
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[581] | 60 | |
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| 61 | %% smoothing parameter |
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| 62 | rho=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) |
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| 63 | |
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| 64 | %% default output |
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[896] | 65 | SubRange=zeros(NbCoord,2,NbSubDomain);%initialise the boundaries of subdomains |
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| 66 | Coord_tps=zeros(1,NbCoord,NbSubDomain);% initialize coordinates of interpolated data |
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| 67 | U_tps=zeros(1,NbSubDomain);% initialize interpolated u component |
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| 68 | V_tps=zeros(1,NbSubDomain);% initialize interpolated v component |
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| 69 | NbCentre=zeros(1,NbSubDomain);%number of interpolated field values per subdomain, =0 by default |
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[581] | 70 | W_tps=[];%default (2 component case) |
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| 71 | U_smooth=zeros(NbVec,1); % smoothed velocity U at the initial positions |
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| 72 | V_smooth=zeros(NbVec,1);% smoothed velocity V at the initial positions |
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| 73 | W_smooth=[];%default (2 component case) |
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| 74 | FF=zeros(NbVec,1); |
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| 75 | nb_select=zeros(NbVec,1); |
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[382] | 76 | check_empty=zeros(1,NbSubDomain); |
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[581] | 77 | |
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[896] | 78 | |
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[581] | 79 | %% calculate tps coeff in each subdomain |
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[382] | 80 | for isub=1:NbSubDomain |
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[896] | 81 | SubRange(1,:,isub)=[CentreX(isub)-0.55*Siz(1) CentreX(isub)+0.55*Siz(1)];%bounds of subdomain #isub in x coordinate |
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| 82 | SubRange(2,:,isub)=[CentreY(isub)-0.55*Siz(2) CentreY(isub)+0.55*Siz(2)];%bounds of subdomain #isub in y coordinate |
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[382] | 83 | ind_sel_previous=[]; |
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[896] | 84 | ind_sel=0;%initialize set of vector indices in the subdomain |
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[581] | 85 | %increase iteratively the subdomain if it contains less than SubDomainNbVec/4 source vectors |
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| 86 | while numel(ind_sel)>numel(ind_sel_previous) |
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[896] | 87 | ind_sel_previous=ind_sel;% record the set of selected vector indices for next iteration |
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[382] | 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)); |
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[896] | 89 | % if no vector in the subdomain #isub, skip the subdomain |
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[382] | 90 | if isempty(ind_sel) |
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[581] | 91 | check_empty(isub)=1; |
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[896] | 92 | break % go to next subdomain |
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| 93 | % if too few selected vectors, increase the subrange for next iteration |
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| 94 | elseif numel(ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous); |
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[387] | 95 | SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4; |
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| 96 | SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4; |
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[896] | 97 | % subdomain includes enough vectors, perform tps interpolation |
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[581] | 98 | else |
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[382] | 99 | [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel,:),U(ind_sel),rho); |
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| 100 | [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel,:),V(ind_sel),rho); |
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[896] | 101 | UDiff=U_smooth_sub-U(ind_sel);% difference between interpolated U component and initial value |
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| 102 | VDiff=V_smooth_sub-V(ind_sel);% difference between interpolated V component and initial value |
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| 103 | NormDiff=UDiff.*UDiff+VDiff.*VDiff;% Square of difference norm |
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[382] | 104 | ind_ind_sel=1:numel(ind_sel);%default |
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[772] | 105 | if exist('Threshold','var')&&~isempty(Threshold) |
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[581] | 106 | FF(ind_sel)=20*(NormDiff>Threshold);%put FF value to 20 to identify the criterium of elimmination |
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| 107 | ind_ind_sel=find(FF(ind_sel)==0); % select the indices of ind_sel corresponding to the remaining vectors |
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[382] | 108 | end |
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[387] | 109 | % if no value exceeds threshold, the result is recorded |
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[382] | 110 | if isequal(numel(ind_ind_sel),numel(ind_sel)) |
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| 111 | U_smooth(ind_sel)=U_smooth(ind_sel)+U_smooth_sub; |
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| 112 | V_smooth(ind_sel)=V_smooth(ind_sel)+V_smooth_sub; |
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[651] | 113 | NbCentre(isub)=numel(ind_sel); |
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| 114 | Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel,:); |
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| 115 | U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub; |
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| 116 | V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub; |
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[382] | 117 | nb_select(ind_sel)=nb_select(ind_sel)+1; |
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[896] | 118 | display(['tps done in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)]) |
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[382] | 119 | break |
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[896] | 120 | % if too few selected vectors, increase the subrange for next iteration |
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| 121 | elseif numel(ind_ind_sel)<SubDomainSize/4 && ~isequal( ind_sel,ind_sel_previous); |
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[387] | 122 | SubRange(:,1,isub)=SubRange(:,1,isub)-Siz'/4; |
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| 123 | SubRange(:,2,isub)=SubRange(:,2,isub)+Siz'/4; |
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[896] | 124 | % else interpolation-smoothing is done again with the selected vectors |
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[382] | 125 | else |
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[387] | 126 | [U_smooth_sub,U_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),U(ind_sel(ind_ind_sel)),rho); |
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| 127 | [V_smooth_sub,V_tps_sub]=tps_coeff(Coord(ind_sel(ind_ind_sel),:),V(ind_sel(ind_ind_sel)),rho); |
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[382] | 128 | U_smooth(ind_sel(ind_ind_sel))=U_smooth(ind_sel(ind_ind_sel))+U_smooth_sub; |
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[581] | 129 | V_smooth(ind_sel(ind_ind_sel))=V_smooth(ind_sel(ind_ind_sel))+V_smooth_sub; |
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[651] | 130 | NbCentre(isub)=numel(ind_ind_sel); |
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| 131 | Coord_tps(1:NbCentre(isub),:,isub)=Coord(ind_sel(ind_ind_sel),:); |
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| 132 | U_tps(1:NbCentre(isub)+3,isub)=U_tps_sub; |
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| 133 | V_tps(1:NbCentre(isub)+3,isub)=V_tps_sub; |
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[382] | 134 | nb_select(ind_sel(ind_ind_sel))=nb_select(ind_sel(ind_ind_sel))+1; |
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[896] | 135 | display(['tps redone after elimination of erratic vectors in subdomain # ' num2str(isub) ' among ' num2str(NbSubDomain)]) |
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[382] | 136 | break |
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| 137 | end |
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| 138 | end |
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| 139 | end |
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| 140 | end |
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[581] | 141 | |
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| 142 | %% remove empty subdomains |
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[382] | 143 | ind_empty=find(check_empty); |
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| 144 | if ~isempty(ind_empty) |
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| 145 | SubRange(:,:,ind_empty)=[]; |
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| 146 | Coord_tps(:,:,ind_empty)=[]; |
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| 147 | U_tps(:,ind_empty)=[]; |
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| 148 | V_tps(:,ind_empty)=[]; |
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[896] | 149 | NbCentre(ind_empty)=[]; |
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[382] | 150 | end |
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[581] | 151 | |
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| 152 | %% final adjustments |
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| 153 | nb_select(nb_select==0)=1; |
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| 154 | U_smooth=U_smooth./nb_select;% take the average at the intersection of several subdomains |
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[382] | 155 | V_smooth=V_smooth./nb_select; |
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[949] | 156 | U_smooth(FF==20)=U(FF==20);% set to the initial values the eliminated vectors (flagged as false) |
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| 157 | V_smooth(FF==20)=V(FF==20); |
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[494] | 158 | fill=zeros(NbCoord+1,NbCoord,size(SubRange,3)); %matrix of zeros to complement the matrix Data.Civ1_Coord_tps (conveninent for file storage) |
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| 159 | Coord_tps=cat(1,Coord_tps,fill); |
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| 160 | |
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