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annotate diracDiscr.m @ 1232:52d774e69b1f feature/dirac_discr

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Clean up diracDiscr, remove obsolete tests.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 19 Nov 2019 13:54:41 -0800
parents 86ee5648e384
children f1806475498b 48c9a83260c8
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rev   line source
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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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35
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36 m = length(x);
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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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40
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41 ret = zeros(size(x));
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42
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43 else
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44
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45 fnorm = diag(H);
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46 tot_order = m_order+s_order; %This is equiv. to the number of equations solved for
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47 S = [];
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48 M = [];
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50 % Get interior grid spacing
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51 middle = floor(m/2);
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52 h = x(middle+1) - x(middle);
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53
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54 % Find the indices that are within range of of the point source location
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55 ind_delta = find(tot_order*h/2 >= abs(x-x_s));
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56
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57 % Ensure that ind_delta is not too long
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58 if length(ind_delta) == (tot_order + 2)
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59 ind_delta = ind_delta(2:end-1);
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60 elseif length(ind_delta) == (tot_order + 1)
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61 ind_delta = ind_delta(1:end-1);
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62 end
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64 % Use first tot_order grid points
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65 if length(ind_delta)<tot_order && x_s < x(1) + ceil(tot_order/2)*h;
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66 index=1:tot_order;
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67 polynomial=(x(1:tot_order)-x(1))/(x(tot_order)-x(1));
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68 x_0=(x_s-x(1))/(x(tot_order)-x(1));
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69 norm=fnorm(1:tot_order)/h;
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71 % Use last tot_order grid points
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72 elseif length(ind_delta)<tot_order && x_s > x(end) - ceil(tot_order/2)*h;
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73 index = length(x)-tot_order+1:length(x);
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74 polynomial = (x(end-tot_order+1:end)-x(end-tot_order+1))/(x(end)-x(end-tot_order+1));
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75 norm = fnorm(end-tot_order+1:end)/h;
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76 x_0 = (x_s-x(end-tot_order+1))/(x(end)-x(end-tot_order+1));
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77
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78 % Interior, compensate for round-off errors.
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79 elseif length(ind_delta) < tot_order
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80 if ind_delta(end)<m
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81 ind_delta = [ind_delta; ind_delta(end)+1];
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82 else
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83 ind_delta = [ind_delta(1)-1; ind_delta];
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84 end
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85 polynomial = (x(ind_delta)-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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86 x_0 = (x_s-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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87 norm = fnorm(ind_delta)/h;
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88 index = ind_delta;
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89
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90 % Interior
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91 else
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92 polynomial = (x(ind_delta)-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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93 x_0 = (x_s-x(ind_delta(1)))/(x(ind_delta(end))-x(ind_delta(1)));
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94 norm = fnorm(ind_delta)/h;
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95 index = ind_delta;
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96 end
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97
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98 h_polynomial = polynomial(2)-polynomial(1);
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99 b = zeros(m_order+s_order,1);
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100
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101 for i = 1:m_order
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102 b(i,1) = x_0^(i-1);
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103 end
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104
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105 for i = 1:(m_order+s_order)
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106 for j = 1:m_order
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107 M(j,i) = polynomial(i)^(j-1)*h_polynomial*norm(i);
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108 end
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109 end
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110
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111 for i = 1:(m_order+s_order)
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112 for j = 1:s_order
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113 S(j,i) = (-1)^(i-1)*polynomial(i)^(j-1);
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114 end
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115 end
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116
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117 A = [M;S];
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118
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119 d = A\b;
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120 ret = x*0;
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121 ret(index) = d/h*h_polynomial;
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122 end
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Martin Almquist <malmquist@stanford.edu>
parents:
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86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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