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annotate +sbp/+implementations/d2_4.m @ 261:6009f2712d13 operator_remake

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Moved and renamned all implementations.
author Martin Almquist <martin.almquist@it.uu.se>
date Thu, 08 Sep 2016 15:35:45 +0200
parents
children bfa130b7abf6
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261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
1 function [H, HI, D1, D2, e_1, e_m, M, Q, S_1, S_m] = d2_4(m,h)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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2 e_1=zeros(m,1);e_1(1)=1;
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Martin Almquist <martin.almquist@it.uu.se>
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3 e_m=zeros(m,1);e_m(m)=1;
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4
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Martin Almquist <martin.almquist@it.uu.se>
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5 e=ones(m,1);
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Martin Almquist <martin.almquist@it.uu.se>
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6 H=spdiags(e,0,m,m);
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Martin Almquist <martin.almquist@it.uu.se>
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7 %H=diag(ones(m,1),0);
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Martin Almquist <martin.almquist@it.uu.se>
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8
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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9 H(1:4,1:4)=diag([17/48 59/48 43/48 49/48]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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10 H(m-3:m,m-3:m)=rot90(diag([17/48 59/48 43/48 49/48]),2);
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Martin Almquist <martin.almquist@it.uu.se>
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11 H=H*h;
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Martin Almquist <martin.almquist@it.uu.se>
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12 HI=inv(H);
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Martin Almquist <martin.almquist@it.uu.se>
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13
6009f2712d13 Moved and renamned all implementations.
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14
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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15 Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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16 %Q=(-1/12*diag(ones(m-2,1),2)+8/12*diag(ones(m-1,1),1)-8/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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17 Q_U = [0 0.59e2 / 0.96e2 -0.1e1 / 0.12e2 -0.1e1 / 0.32e2; -0.59e2 / 0.96e2 0 0.59e2 / 0.96e2 0; 0.1e1 / 0.12e2 -0.59e2 / 0.96e2 0 0.59e2 / 0.96e2; 0.1e1 / 0.32e2 0 -0.59e2 / 0.96e2 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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18 Q(1:4,1:4)=Q_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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19 Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
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Martin Almquist <martin.almquist@it.uu.se>
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20
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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21 D1=HI*(Q-1/2*e_1*e_1'+1/2*e_m*e_m') ;
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Martin Almquist <martin.almquist@it.uu.se>
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22
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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23 M=-spdiags([-e 16*e -30*e 16*e -e], -2:2, m, m)/12;
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24
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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25 %M=-(-1/12*diag(ones(m-2,1),2)+16/12*diag(ones(m-1,1),1)+16/12*diag(ones(m-1,1),-1)-1/12*diag(ones(m-2,1),-2)-30/12*diag(ones(m,1),0));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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26
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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27 M_U=[0.9e1 / 0.8e1 -0.59e2 / 0.48e2 0.1e1 / 0.12e2 0.1e1 / 0.48e2; -0.59e2 / 0.48e2 0.59e2 / 0.24e2 -0.59e2 / 0.48e2 0; 0.1e1 / 0.12e2 -0.59e2 / 0.48e2 0.55e2 / 0.24e2 -0.59e2 / 0.48e2; 0.1e1 / 0.48e2 0 -0.59e2 / 0.48e2 0.59e2 / 0.24e2;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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28 M(1:4,1:4)=M_U;
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29
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30 M(m-3:m,m-3:m)=rot90( M_U ,2 );
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Martin Almquist <martin.almquist@it.uu.se>
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31 M=M/h;
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Martin Almquist <martin.almquist@it.uu.se>
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32
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Martin Almquist <martin.almquist@it.uu.se>
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33 S_U=[-0.11e2 / 0.6e1 3 -0.3e1 / 0.2e1 0.1e1 / 0.3e1;]/h;
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Martin Almquist <martin.almquist@it.uu.se>
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34 S_1=sparse(zeros(1,m));
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Martin Almquist <martin.almquist@it.uu.se>
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35 S_1(1:4)=S_U;
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Martin Almquist <martin.almquist@it.uu.se>
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36 S_m=sparse(zeros(1,m));
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Martin Almquist <martin.almquist@it.uu.se>
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37 S_m(m-3:m)=fliplr(-S_U);
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Martin Almquist <martin.almquist@it.uu.se>
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38
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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39
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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40 D2=HI*(-M-e_1*S_1+e_m*S_m);
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Martin Almquist <martin.almquist@it.uu.se>
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41 S_1 = S_1';
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Martin Almquist <martin.almquist@it.uu.se>
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42 S_m = S_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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43 end