[1] | 1 | function h = smoothgrid(h,maskr,hmin,hmax_coast,rmax,n_filter_deep_topo,n_filter_final) |
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| 2 | % |
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| 3 | % Smooth the topography to get a maximum r factor = rmax |
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| 4 | % |
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| 5 | % n_filter_deep_topo: |
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| 6 | % Number of pass of a selective filter to reduce the isolated |
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| 7 | % seamounts on the deep ocean. |
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| 8 | % |
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| 9 | % n_filter_final: |
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| 10 | % Number of pass of a single hanning filter at the end of the |
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| 11 | % procedure to ensure that there is no 2DX noise in the |
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| 12 | % topography. |
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| 13 | % |
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| 14 | % Further Information: |
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| 15 | % http://www.brest.ird.fr/Roms_tools/ |
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| 16 | % |
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| 17 | % This file is part of ROMSTOOLS |
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| 18 | % |
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| 19 | % ROMSTOOLS is free software; you can redistribute it and/or modify |
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| 20 | % it under the terms of the GNU General Public License as published |
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| 21 | % by the Free Software Foundation; either version 2 of the License, |
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| 22 | % or (at your option) any later version. |
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| 23 | % |
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| 24 | % ROMSTOOLS is distributed in the hope that it will be useful, but |
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| 25 | % WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 26 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 27 | % GNU General Public License for more details. |
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| 28 | % |
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| 29 | % You should have received a copy of the GNU General Public License |
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| 30 | % along with this program; if not, write to the Free Software |
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| 31 | % Foundation, Inc., 59 Temple Place, Suite 330, Boston, |
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| 32 | % MA 02111-1307 USA |
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| 33 | % |
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| 34 | % Copyright (c) 2005-2006 by Pierrick Penven |
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| 35 | % e-mail:Pierrick.Penven@ird.fr |
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| 36 | % |
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| 37 | % Contributions of A. Shchepetkin (UCLA), P. Marchesiello (IRD) |
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| 38 | % and X. Capet (UCLA) |
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| 39 | % |
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| 40 | % Updated Aug-2006 by Pierrick Penven |
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| 41 | % |
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| 42 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 43 | |
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| 44 | % |
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| 45 | % Cut the topography |
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| 46 | % |
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| 47 | h(h<hmin)=hmin; |
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| 48 | h(h>5000)=5000; |
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| 49 | % |
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| 50 | % |
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| 51 | % 1: Deep Ocean Filter |
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| 52 | % |
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| 53 | if n_filter_deep_topo>=1 |
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| 54 | disp(' Apply a filter on the Deep Ocean to remove the isolated seamounts :') |
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| 55 | disp([' ',num2str(n_filter_deep_topo),' pass of a selective filter.']) |
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| 56 | % |
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| 57 | % Build a smoothing coefficient that is a linear function |
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| 58 | % of a smooth topography. |
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| 59 | % |
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| 60 | coef=h; |
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| 61 | for i=1:8 |
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| 62 | coef=hanning_smoother(coef); % coef is a smoothed bathy |
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| 63 | end |
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| 64 | coef=0.125*(coef./max(max(coef))); % rescale the smoothed bathy |
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| 65 | % |
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| 66 | for i=1:n_filter_deep_topo; |
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| 67 | h=hanning_smoother_coef2d(h,coef); % smooth with avariable coef |
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| 68 | h(maskr==0 & h>hmax_coast)=hmax_coast; |
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| 69 | end |
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| 70 | end |
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| 71 | % |
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| 72 | % Apply a selective filter on log(h) to reduce grad(h)/h. |
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| 73 | % |
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| 74 | disp(' Apply a selective filter on log(h) to reduce grad(h)/h :') |
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| 75 | h=rotfilter(h,maskr,hmax_coast,rmax); |
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| 76 | % |
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| 77 | % Smooth the topography again to prevent 2D noise |
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| 78 | % |
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| 79 | if n_filter_final>1 |
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| 80 | disp(' Smooth the topography a last time to prevent 2DX noise:') |
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| 81 | disp([' ',num2str(n_filter_final),' pass of a hanning smoother.']) |
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| 82 | for i=1:n_filter_final |
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| 83 | h=hanning_smoother(h); |
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| 84 | h(maskr==0 & h>hmax_coast)=hmax_coast; |
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| 85 | end |
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| 86 | end |
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| 87 | % |
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| 88 | h(h<hmin)=hmin; |
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| 89 | % |
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| 90 | return |
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| 91 | % |
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| 92 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 93 | function h=rotfilter(h,maskr,hmax_coast,rmax) |
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| 94 | % |
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| 95 | % Apply a selective filter on log(h) to reduce grad(h)/h. |
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| 96 | % |
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| 97 | [M,L]=size(h); |
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| 98 | Mm=M-1; |
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| 99 | Mmm=M-2; |
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| 100 | Lm=L-1; |
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| 101 | Lmm=L-2; |
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| 102 | cff=0.8; |
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| 103 | nu=3/16; |
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| 104 | [rx,ry]=rfact(h); |
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| 105 | r=max(max(max(rx)),max(max(ry))); |
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| 106 | h=log(h); |
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| 107 | hmax_coast=log(hmax_coast); |
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| 108 | i=0; |
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| 109 | while r>rmax |
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| 110 | i=i+1; |
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| 111 | cx=double(rx>cff*rmax); |
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| 112 | cx=hanning_smoother(cx); |
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| 113 | cy=double(ry>cff*rmax); |
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| 114 | cy=hanning_smoother(cy); |
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| 115 | fx=cx.*FX(h); |
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| 116 | fy=cy.*FY(h); |
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| 117 | h(2:Mm,2:Lm)=h(2:Mm,2:Lm)+nu*... |
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| 118 | ((fx(2:Mm,2:Lm)-fx(2:Mm,1:Lmm))+... |
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| 119 | (fy(2:Mm,2:Lm)-fy(1:Mmm,2:Lm))); |
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| 120 | h(1,:)=h(2,:); |
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| 121 | h(M,:)=h(Mm,:); |
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| 122 | h(:,1)=h(:,2); |
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| 123 | h(:,L)=h(:,Lm); |
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| 124 | h(maskr==0 & h>hmax_coast)=hmax_coast; |
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| 125 | [rx,ry]=rfact(exp(h)); |
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| 126 | r=max(max(max(rx)),max(max(ry))); |
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| 127 | end |
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| 128 | |
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| 129 | disp([' ',num2str(i),' iterations - rmax = ',num2str(r)]) |
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| 130 | h=exp(h); |
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| 131 | |
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| 132 | return |
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| 133 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 134 | function [rx,ry]=rfact(h); |
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| 135 | [M,L]=size(h); |
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| 136 | Mm=M-1; |
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| 137 | Mmm=M-2; |
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| 138 | Lm=L-1; |
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| 139 | Lmm=L-2; |
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| 140 | rx=abs(h(1:M,2:L)-h(1:M,1:Lm))./(h(1:M,2:L)+h(1:M,1:Lm)); |
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| 141 | ry=abs(h(2:M,1:L)-h(1:Mm,1:L))./(h(2:M,1:L)+h(1:Mm,1:L)); |
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| 142 | |
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| 143 | return |
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| 144 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 145 | function h=hanning_smoother(h); |
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| 146 | [M,L]=size(h); |
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| 147 | Mm=M-1; |
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| 148 | Mmm=M-2; |
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| 149 | Lm=L-1; |
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| 150 | Lmm=L-2; |
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| 151 | |
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| 152 | h(2:Mm,2:Lm)=0.125*(h(1:Mmm,2:Lm)+h(3:M,2:Lm)+... |
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| 153 | h(2:Mm,1:Lmm)+h(2:Mm,3:L)+... |
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| 154 | 4*h(2:Mm,2:Lm)); |
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| 155 | |
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| 156 | h(1,:)=h(2,:); |
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| 157 | h(M,:)=h(Mm,:); |
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| 158 | h(:,1)=h(:,2); |
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| 159 | h(:,L)=h(:,Lm); |
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| 160 | |
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| 161 | return |
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| 162 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 163 | function h=hanning_smoother_coef2d(h,coef); |
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| 164 | [M,L]=size(h); |
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| 165 | Mm=M-1; |
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| 166 | Mmm=M-2; |
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| 167 | Lm=L-1; |
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| 168 | Lmm=L-2; |
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| 169 | h(2:Mm,2:Lm)=coef(2:Mm,2:Lm).*(h(1:Mmm,2:Lm)+h(3:M,2:Lm)+... |
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| 170 | h(2:Mm,1:Lmm)+h(2:Mm,3:L))... |
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| 171 | +(1-4.*coef(2:Mm,2:Lm)).*h(2:Mm,2:Lm); |
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| 172 | h(1,:)=h(2,:); |
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| 173 | h(M,:)=h(Mm,:); |
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| 174 | h(:,1)=h(:,2); |
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| 175 | h(:,L)=h(:,Lm); |
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| 176 | |
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| 177 | return |
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| 178 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 179 | function fx=FX(h); |
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| 180 | [M,L]=size(h); |
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| 181 | Mm=M-1; |
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| 182 | Mmm=M-2; |
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| 183 | Lm=L-1; |
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| 184 | Lmm=L-2; |
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| 185 | |
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| 186 | fx(2:Mm,:)=(h(2:Mm,2:L)-h(2:Mm,1:Lm))*5/6 +... |
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| 187 | (h(1:Mmm,2:L)-h(1:Mmm,1:Lm)+h(3:M,2:L)-h(3:M,1:Lm))/12; |
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| 188 | |
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| 189 | fx(1,:)=fx(2,:); |
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| 190 | fx(M,:)=fx(Mm,:); |
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| 191 | |
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| 192 | return |
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| 193 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 194 | function fy=FY(h); |
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| 195 | [M,L]=size(h); |
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| 196 | Mm=M-1; |
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| 197 | Mmm=M-2; |
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| 198 | Lm=L-1; |
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| 199 | Lmm=L-2; |
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| 200 | |
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| 201 | fy(:,2:Lm)=(h(2:M,2:Lm)-h(1:Mm,2:Lm))*5/6 +... |
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| 202 | (h(2:M,1:Lmm)-h(1:Mm,1:Lmm)+h(2:M,3:L)-h(1:Mm,3:L))/12; |
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| 203 | |
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| 204 | fy(:,1)=fy(:,2); |
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| 205 | fy(:,L)=fy(:,Lm); |
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| 206 | |
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| 207 | return |
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| 208 | |
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