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annotate diracDiscr.m @ 647:46c40711830f feature/d1_staggered

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Add test for diracDiscr.m
author Martin Almquist <malmquist@stanford.edu>
date Tue, 14 Nov 2017 15:35:28 -0800
parents 0990765e3e4d
children 9e5dd0d3cf60
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a5307adc6177 Add diracDiscr.m. Noticed bug if source is on grid point.
Martin Almquist <malmquist@stanford.edu>
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1 function ret = diracDiscr(x_0in , x , m_order, s_order, H)
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2
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3 fnorm = diag(H);
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4 eta = abs(x-x_0in);
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5 h = x(2)-x(1);
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6 tot = m_order+s_order;
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7 S = [];
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8 M = [];
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9 poss = find(tot*h/2 >= eta);
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10
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11 % Ensure that poss is not too long
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12 if length(poss) == (tot + 2)
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13 poss = poss(2:end-1);
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14 elseif length(poss) == (tot + 1)
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15 poss = poss(1:end-1);
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16 end
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17
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18 % Use first tot grid points
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19 if length(poss)<tot && eta(end)>eta(1)
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20 index=1:tot;
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21 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
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22 x_0=(x_0in-x(1))/(x(tot)-x(1));
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23 norm=fnorm(1:tot)/h;
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24
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25 % Use last tot grid points
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26 elseif length(poss)<tot && eta(end)<eta(1)
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27 index = length(x)-tot:tot;
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28 pol = (x(end-tot:end)-x(end-tot))/(x(end)-x(end-tot));
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29 norm = fnorm(end-tot:end)/h;
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30 x_0 = (x_0in-x(end-tot))/(x(end)-x(end-tot));
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31
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32 % Interior
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33 else
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34 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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35 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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36 norm = fnorm(poss)/h;
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37 index = poss;
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38 end
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39
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40 h_pol = pol(2)-pol(1);
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41 b = zeros(m_order+s_order,1);
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42
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43 for i = 1:m_order
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44 b(i,1) = x_0^(i-1);
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45 end
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47 for i = 1:(m_order+s_order)
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48 for j = 1:m_order
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49 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
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50 end
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51 end
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53 for i = 1:(m_order+s_order)
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54 for j = 1:s_order
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55 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
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56 end
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57 end
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58
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59 A = [M;S];
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60
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61 d = A\b;
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62 ret = x*0;
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63 ret(index) = d/h*h_pol;
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64 end
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