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annotate spdiagsPeriodic.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents bbf303c1f0cf
children
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1 function A = spdiagsPeriodic(vals,diags)
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2 % Creates an m x m periodic discretization matrix.
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3 % vals - m x ndiags matrix of values
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4 % diags - 1 x ndiags vector of the 'center diagonals' that vals end up on
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5 % vals that are not on main diagonal are going to spill over to
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6 % off-diagonal corners.
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7
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8 default_arg('diags',0);
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9
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10 [m, ~] = size(vals);
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11
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12 A = sparse(m,m);
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13
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14 for i = 1:length(diags)
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15
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16 d = diags(i);
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17 a = vals(:,i);
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18
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19 % Sub-diagonals
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20 if d < 0
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21 a_bulk = a(1+abs(d):end);
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22 a_corner = a(1:1+abs(d)-1);
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23 corner_diag = m-abs(d);
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24 A = A + spdiagVariable(a_bulk, d);
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25 A = A + spdiagVariable(a_corner, corner_diag);
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26
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27 % Super-diagonals
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28 elseif d > 0
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29 a_bulk = a(1:end-d);
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30 a_corner = a(end-d+1:end);
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31 corner_diag = -m + d;
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32 A = A + spdiagVariable(a_bulk, d);
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33 A = A + spdiagVariable(a_corner, corner_diag);
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34
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35 % Main diagonal
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36 else
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37 A = A + spdiagVariable(a, 0);
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38 end
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39
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40 end
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41
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42 end
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43
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44 function A = spdiagVariable(a,i)
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45 default_arg('i',0);
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46
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47 if isrow(a)
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48 a = a';
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49 end
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50
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51 n = length(a)+abs(i);
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52
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53 if i > 0
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54 a = [sparse(i,1); a];
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55 elseif i < 0
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56 a = [a; sparse(abs(i),1)];
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57 end
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58
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59 A = spdiags(a,i,n,n);
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60 end