Mercurial > repos > public > sbplib

comparison diracDiscr1D.m @ 1129:b29892853daf feature/laplace_curvilinear_test

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
author Martin Almquist <malmquist@stanford.edu>
date Tue, 21 May 2019 18:10:06 -0700
parents
children
comparison
equal deleted inserted replaced
1128:3a9262c045d0 1129:b29892853daf
1 % Generates discrete 1D delta function
2 function ret = diracDiscr1D(x_0in , x , m_order, s_order, H)
3
4 m = length(x);
5
6 % Return zeros if x0 is outside grid
7 if(x_0in < x(1) || x_0in > x(end) )
8
9 ret = zeros(size(x));
10
11 else
12
13 fnorm = diag(H);
14 eta = abs(x-x_0in);
15 tot = m_order+s_order;
16 S = [];
17 M = [];
18
19 % Get interior grid spacing
20 middle = floor(m/2);
21 h = x(middle+1) - x(middle);
22
23 poss = find(tot*h/2 >= eta);
24
25 % Ensure that poss is not too long
26 if length(poss) == (tot + 2)
27 poss = poss(2:end-1);
28 elseif length(poss) == (tot + 1)
29 poss = poss(1:end-1);
30 end
31
32 % Use first tot grid points
33 if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
34 index=1:tot;
35 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
36 x_0=(x_0in-x(1))/(x(tot)-x(1));
37 norm=fnorm(1:tot)/h;
38
39 % Use last tot grid points
40 elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
41 index = length(x)-tot+1:length(x);
42 pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
43 norm = fnorm(end-tot+1:end)/h;
44 x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));
45
46 % Interior, compensate for round-off errors.
47 elseif length(poss) < tot
48 if poss(end)<m
49 poss = [poss; poss(end)+1];
50 else
51 poss = [poss(1)-1; poss];
52 end
53 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
54 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
55 norm = fnorm(poss)/h;
56 index = poss;
57
58 % Interior
59 else
60 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
61 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
62 norm = fnorm(poss)/h;
63 index = poss;
64 end
65
66 h_pol = pol(2)-pol(1);
67 b = zeros(m_order+s_order,1);
68
69 for i = 1:m_order
70 b(i,1) = x_0^(i-1);
71 end
72
73 for i = 1:(m_order+s_order)
74 for j = 1:m_order
75 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
76 end
77 end
78
79 for i = 1:(m_order+s_order)
80 for j = 1:s_order
81 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
82 end
83 end
84
85 A = [M;S];
86
87 d = A\b;
88 ret = x*0;
89 ret(index) = d/h*h_pol;
90 end
91
92 end