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Attempt to factor out a function for finding indecies of the source
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 20 Nov 2019 00:10:30 +0100
parents 48c9a83260c8
children 6e4cc4b66de0
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1
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2 function d = diracDiscr(x_s, x, m_order, s_order, H)
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3 % n-dimensional delta function
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4 % x_s: source point coordinate vector, e.g. [x, y] or [x, y, z].
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5 % x: cell array of grid point column vectors for each dimension.
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6 % m_order: Number of moment conditions
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7 % s_order: Number of smoothness conditions
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8 % H: cell array of 1D norm matrices
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9
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10 dim = length(x_s);
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11 d_1D = cell(dim,1);
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12
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13 % If 1D, non-cell input is accepted
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14 if dim == 1 && ~iscell(x)
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15 d = diracDiscr1D(x_s, x, m_order, s_order, H);
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16
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17 else
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18 for i = 1:dim
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19 d_1D{i} = diracDiscr1D(x_s(i), x{i}, m_order, s_order, H{i});
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20 end
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21
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22 d = d_1D{dim};
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23 for i = dim-1: -1: 1
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24 % Perform outer product, transpose, and then turn into column vector
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25 d = (d_1D{i}*d')';
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26 d = d(:);
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27 end
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28 end
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30 end
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33 % Helper function for 1D delta functions
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34 function ret = diracDiscr1D(x_s , x , m_order, s_order, H)
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36 m = length(x);
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37
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38 % Return zeros if x0 is outside grid
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39 if(x_s < x(1) || x_s > x(end) )
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41 ret = zeros(size(x));
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43 else
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44 fnorm = diag(H);
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45 tot_order = m_order+s_order; %This is equiv. to the number of equations solved for
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46 S = [];
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47 M = [];
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49 % Get interior grid spacing
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50 middle = floor(m/2);
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51 h = x(middle+1) - x(middle);
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52
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53 index = sourceIndecies(x_s, x, tot_order, h)
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54
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55 polynomial = (x(index)-x(index(1)))/(x(index(end))-x(index(1)));
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56 x_0 = (x_s-x(index(1)))/(x(index(end))-x(index(1)));
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57 norm = fnorm(index)/h;
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58
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59 h_polynomial = polynomial(2)-polynomial(1);
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60 b = zeros(tot_order,1);
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61
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62 for i = 1:m_order
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63 b(i,1) = x_0^(i-1);
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64 end
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66 for i = 1:tot_order
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67 for j = 1:m_order
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68 M(j,i) = polynomial(i)^(j-1)*h_polynomial*norm(i);
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69 end
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70 end
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72 for i = 1:tot_order
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73 for j = 1:s_order
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74 S(j,i) = (-1)^(i-1)*polynomial(i)^(j-1);
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75 end
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76 end
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77
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78 A = [M;S];
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79
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80 d = A\b;
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81 ret = x*0;
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82 ret(index) = d/h*h_polynomial;
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83 end
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84
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85 end
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86
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88 function I = sourceIndecies(x_s, x, tot_order, h)
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89 % Find the indices that are within range of of the point source location
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90 I = find(tot_order*h/2 >= abs(x-x_s));
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91
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92 if length(I) > tot_order
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93 if length(I) == tot_order + 2
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94 I = I(2:end-1);
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95 elseif length(I) == tot_order + 1
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96 I = I(1:end-1);
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97 end
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98 elseif length(I) < tot_order
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99 if x_s < x(1) + ceil(tot_order/2)*h;
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100 I = 1:tot_order;
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101 elseif x_s > x(end) - ceil(tot_order/2)*h;
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102 I = length(x)-tot_order+1:length(x);
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103 else
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104 if I(end) < length(x)
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105 I = [I; I(end)+1];
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106 else
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107 I = [I(1)-1; I];
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108 end
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109 end
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110 end
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111 end