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annotate diracDiscr.m @ 1234:f1806475498b feature/dirac_discr

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- Pass grids to diracDiscr and adjust tests. - Minor edits in diracDiscr
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 19 Nov 2019 15:16:08 -0800
parents 52d774e69b1f
children dea852e85b77
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1
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2 function d = diracDiscr(g, x_s, m_order, s_order, H)
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3 % n-dimensional delta function
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4 % g: cartesian grid
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5 % x_s: source point coordinate vector, e.g. [x, y] or [x, y, z].
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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 assertType(g, 'grid.Cartesian');
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10 dim = g.d;
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11 d_1D = cell(dim,1);
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12
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13 % Allow for non-cell input in 1D
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14 if dim == 1
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15 H = {H};
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16 end
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17 % Create 1D dirac discr for each coordinate dir.
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18 for i = 1:dim
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19 d_1D{i} = diracDiscr1D(x_s(i), g.x{i}, m_order, s_order, H{i});
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20 end
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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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29 end
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32 % Helper function for 1D delta functions
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33 function ret = diracDiscr1D(x_s , x , m_order, s_order, H)
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34
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35 m = length(x);
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36
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37 % Return zeros if x0 is outside grid
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38 if x_s < x(1) || x_s > x(end)
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39 ret = zeros(size(x));
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40 return
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41 else
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43 fnorm = diag(H);
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44 tot_order = m_order+s_order; %This is equiv. to the number of equations solved for
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45 S = [];
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46 M = [];
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47
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48 % Get interior grid spacing
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49 middle = floor(m/2);
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50 h = x(middle+1) - x(middle); % Use middle point to allow for staggerd grids.
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52 % Find the indices that are within range of of the point source location
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53 ind_delta = find(tot_order*h/2 >= abs(x-x_s));
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54
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55 % Ensure that ind_delta is not too long
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56 if length(ind_delta) == (tot_order + 2)
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57 ind_delta = ind_delta(2:end-1);
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58 elseif length(ind_delta) == (tot_order + 1)
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59 ind_delta = ind_delta(1:end-1);
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60 end
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62 % Use first tot_order grid points
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63 if length(ind_delta)<tot_order && x_s < x(1) + ceil(tot_order/2)*h
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64 index=1:tot_order;
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65 polynomial=(x(1:tot_order)-x(1))/(x(tot_order)-x(1));
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66 x_0=(x_s-x(1))/(x(tot_order)-x(1));
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67 norm=fnorm(1:tot_order)/h;
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68
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69 % Use last tot_order grid points
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70 elseif length(ind_delta)<tot_order && x_s > x(end) - ceil(tot_order/2)*h
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71 index = length(x)-tot_order+1:length(x);
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72 polynomial = (x(end-tot_order+1:end)-x(end-tot_order+1))/(x(end)-x(end-tot_order+1));
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73 norm = fnorm(end-tot_order+1:end)/h;
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74 x_0 = (x_s-x(end-tot_order+1))/(x(end)-x(end-tot_order+1));
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75
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76 % Interior, compensate for round-off errors.
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77 elseif length(ind_delta) < tot_order
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78 if ind_delta(end)<m
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79 ind_delta = [ind_delta; ind_delta(end)+1];
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80 else
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81 ind_delta = [ind_delta(1)-1; ind_delta];
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82 end
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83 polynomial = (x(ind_delta)-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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84 x_0 = (x_s-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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85 norm = fnorm(ind_delta)/h;
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86 index = ind_delta;
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87
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88 % Interior
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89 else
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90 polynomial = (x(ind_delta)-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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91 x_0 = (x_s-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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92 norm = fnorm(ind_delta)/h;
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93 index = ind_delta;
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94 end
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95
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96 h_polynomial = polynomial(2)-polynomial(1);
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97 b = zeros(m_order+s_order,1);
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98
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99 for i = 1:m_order
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100 b(i,1) = x_0^(i-1);
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101 end
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102
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103 for i = 1:(m_order+s_order)
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104 for j = 1:m_order
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105 M(j,i) = polynomial(i)^(j-1)*h_polynomial*norm(i);
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106 end
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107 end
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108
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109 for i = 1:(m_order+s_order)
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110 for j = 1:s_order
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111 S(j,i) = (-1)^(i-1)*polynomial(i)^(j-1);
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112 end
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113 end
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114
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115 A = [M;S];
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116
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117 d = A\b;
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118 ret = x*0;
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119 ret(index) = d/h*h_polynomial;
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120 end
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
121
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
122 end