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annotate diracDiscrTest.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
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1 function tests = diracDiscrTest()
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2 tests = functiontests(localfunctions);
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3 end
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4
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5 %TODO: Test discretizing with smoothness conditions.
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6 % Only discretization with moment conditions currently tested.
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7
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8 function testLeftRandom(testCase)
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9
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10 orders = [2, 4, 6];
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11 mom_conds = orders;
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12 rng(0xDABBAD00) % Set seed. Jabba-dabba-doooo!
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13
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14 for o = 1:length(orders)
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15 order = orders(o);
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16 mom_cond = mom_conds(o);
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17 [xl, ~, h, x, H, fs] = setup1D(order, mom_cond);
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18
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19 % Test random points near left boundary
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20 x0s = xl + 2*h*rand(1,10);
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21
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22 for j = 1:length(fs)
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23 f = fs{j};
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24 fx = f(x);
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25 for i = 1:length(x0s)
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26 x0 = x0s(i);
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27 delta = diracDiscr(x0, x, mom_cond, 0, H);
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28 integral = delta'*H*fx;
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29 err = abs(integral - f(x0));
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30 testCase.verifyLessThan(err, 1e-12);
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31 end
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32 end
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33 end
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34 end
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35
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36 function testRightRandom(testCase)
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37
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38 orders = [2, 4, 6];
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39 mom_conds = orders;
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40 rng(0xDABBAD00) % Set seed. Jabba-dabba-doooo!
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41
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42 for o = 1:length(orders)
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43 order = orders(o);
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44 mom_cond = mom_conds(o);
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45 [~, xr, h, x, H, fs] = setup1D(order, mom_cond);
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46
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47 % Test random points near right boundary
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48 x0s = xr - 2*h*rand(1,10);
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49
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50 for j = 1:length(fs)
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51 f = fs{j};
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52 fx = f(x);
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53 for i = 1:length(x0s)
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54 x0 = x0s(i);
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55 delta = diracDiscr(x0, x, mom_cond, 0, H);
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56 integral = delta'*H*fx;
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57 err = abs(integral - f(x0));
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58 testCase.verifyLessThan(err, 1e-12);
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59 end
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60 end
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61 end
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62 end
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63
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64 function testInteriorRandom(testCase)
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65
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66 orders = [2, 4, 6];
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67 mom_conds = orders;
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68 rng(0xDABBAD00) % Set seed. Jabba-dabba-doooo!
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69
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70 for o = 1:length(orders)
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71 order = orders(o);
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72 mom_cond = mom_conds(o);
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73 [xl, xr, h, x, H, fs] = setup1D(order, mom_cond);
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74
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75 % Test random points in interior
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76 x0s = (xl+2*h) + (xr-xl-4*h)*rand(1,20);
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77
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78 for j = 1:length(fs)
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79 f = fs{j};
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80 fx = f(x);
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81 for i = 1:length(x0s)
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82 x0 = x0s(i);
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83 delta = diracDiscr(x0, x, mom_cond, 0, H);
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84 integral = delta'*H*fx;
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85 err = abs(integral - f(x0));
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86 testCase.verifyLessThan(err, 1e-12);
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87 end
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88 end
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89 end
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90 end
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91
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92 % x0 outside grid should yield 0 integral!
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93 function testX0OutsideGrid(testCase)
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94
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95 orders = [2, 4, 6];
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96 mom_conds = orders;
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97
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98 for o = 1:length(orders)
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99 order = orders(o);
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100 mom_cond = mom_conds(o);
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101 [xl, xr, h, x, H, fs] = setup1D(order, mom_cond);
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102
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103 % Test points outisde grid
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104 x0s = [xl-1.1*h, xr+1.1*h];
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105
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106 for j = 1:length(fs)
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107 f = fs{j};
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108 fx = f(x);
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109 for i = 1:length(x0s)
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110 x0 = x0s(i);
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111 delta = diracDiscr(x0, x, mom_cond, 0, H);
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112 integral = delta'*H*fx;
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113 err = abs(integral - 0);
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114 testCase.verifyLessThan(err, 1e-12);
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115 end
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116 end
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117 end
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118 end
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119
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120 function testAllGP(testCase)
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121
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122 orders = [2, 4, 6];
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123 mom_conds = orders;
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124
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125 for o = 1:length(orders)
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126 order = orders(o);
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127 mom_cond = mom_conds(o);
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128 [~, ~, ~, x, H, fs] = setup1D(order, mom_cond);
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129
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130 % Test all grid points
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131 x0s = x;
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132
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133 for j = 1:length(fs)
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134 f = fs{j};
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135 fx = f(x);
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136 for i = 1:length(x0s)
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137 x0 = x0s(i);
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138 delta = diracDiscr(x0, x, mom_cond, 0, H);
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139 integral = delta'*H*fx;
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140 err = abs(integral - f(x0));
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141 testCase.verifyLessThan(err, 1e-12);
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142 end
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143 end
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144 end
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145 end
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 function testHalfGP(testCase)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 orders = [2, 4, 6];
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 mom_conds = orders;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 for o = 1:length(orders)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 mom_cond = mom_conds(o);
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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diff changeset
155 [~, ~, ~, x, H, fs] = setup1D(order, mom_cond);
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 % Test halfway between all grid points
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 x0s = 1/2*( x(2:end)+x(1:end-1) );
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 fx = f(x);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 x0 = x0s(i);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 integral = delta'*H*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 err = abs(integral - f(x0));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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173
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 %=============== 2D tests ==============================
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 function testAllGP2D(testCase)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 orders = [2, 4, 6];
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 mom_conds = orders;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 for o = 1:length(orders)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 mom_cond = mom_conds(o);
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
183 [~, ~, x, X, ~, H, fs] = setup2D(order, mom_cond);
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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184 H_global = kron(H{1}, H{2});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 % Test all grid points
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 x0s = X;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 fx = f(X(:,1), X(:,2));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195 integral = delta'*H_global*fx;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 err = abs(integral - f(x0(1), x0(2)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 function testAllRandom2D(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 mom_conds = orders;
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
207 rng(0xDABBAD00) % Set seed. Jabba-dabba-doooo!
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 mom_cond = mom_conds(o);
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
212 [xlims, ylims, x, X, h, H, fs] = setup2D(order, mom_cond);
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 H_global = kron(H{1}, H{2});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 xl = xlims{1};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 xr = xlims{2};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 yl = ylims{1};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 yr = ylims{2};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 % Test random points, even outside grid
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 Npoints = 100;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 x0s = [(xl-3*h{1}) + (xr-xl+6*h{1})*rand(Npoints,1), ...
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 (yl-3*h{2}) + (yr-yl+6*h{2})*rand(Npoints,1) ];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 fx = f(X(:,1), X(:,2));
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 x0 = x0s(i,:);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 % Integral should be 0 if point is outside grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 if x0(1) < xl || x0(1) > xr || x0(2) < yl || x0(2) > yr
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 err = abs(integral - 0);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 else
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 err = abs(integral - f(x0(1), x0(2)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 %=============== 3D tests ==============================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 function testAllGP3D(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 mom_cond = mom_conds(o);
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
254 [~, ~, ~, x, X, ~, H, fs] = setup3D(order, mom_cond);
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 H_global = kron(kron(H{1}, H{2}), H{3});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 % Test all grid points
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 x0s = X;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 fx = f(X(:,1), X(:,2), X(:,3));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 err = abs(integral - f(x0(1), x0(2), x0(3)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 function testAllRandom3D(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277 mom_conds = orders;
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
278 rng(0xDABBAD00) % Set seed. Jabba-dabba-doooo!
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
279
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
280 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
282 mom_cond = mom_conds(o);
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
283 [xlims, ylims, zlims, x, X, h, H, fs] = setup3D(order, mom_cond);
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 H_global = kron(kron(H{1}, H{2}), H{3});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
285
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
286 xl = xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287 xr = xlims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 yl = ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
289 yr = ylims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
290 zl = zlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291 zr = zlims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
292
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
293 % Test random points, even outside grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294 Npoints = 200;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
295 x0s = [(xl-3*h{1}) + (xr-xl+6*h{1})*rand(Npoints,1), ...
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296 (yl-3*h{2}) + (yr-yl+6*h{2})*rand(Npoints,1), ...
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297 (zl-3*h{3}) + (zr-zl+6*h{3})*rand(Npoints,1) ];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301 fx = f(X(:,1), X(:,2), X(:,3));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307 % Integral should be 0 if point is outside grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 if x0(1) < xl || x0(1) > xr || x0(2) < yl || x0(2) > yr || x0(3) < zl || x0(3) > zr
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 err = abs(integral - 0);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310 else
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311 err = abs(integral - f(x0(1), x0(2), x0(3)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320 % ======================================================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 % ============== Setup functions =======================
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 % ======================================================
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
323 function [xl, xr, h, x, H, fs] = setup1D(order, mom_cond)
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 % Grid
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 xl = -3;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327 xr = 900;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 L = xr-xl;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 m = 101;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330 h = (xr-xl)/(m-1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 g = grid.equidistant(m, {xl, xr});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
332 x = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 ops = sbp.D2Standard(m, {xl, xr}, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 H = ops.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
338 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
339 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 fs{p+1} = @(x) (x/L).^p;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
346 function [xlims, ylims, x, X, h, H, fs] = setup2D(order, mom_cond)
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 xlims = {-3, 20};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350 ylims = {-11,5};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 Lx = xlims{2} - xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 Ly = ylims{2} - ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 m = [15, 16];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 g = grid.equidistant(m, xlims, ylims);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 X = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 x = g.x;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 opsx = sbp.D2Standard(m(1), xlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 opsy = sbp.D2Standard(m(2), ylims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 Hx = opsx.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 Hy = opsy.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 H = {Hx, Hy};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
369 fs{p+1} = @(x,y) (x/Lx + y/Ly).^p;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 % Grid spacing in interior
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373 mm = round(m/2);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374 hx = x{1}(mm(1)+1) - x{1}(mm(1));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375 hy = x{2}(mm(2)+1) - x{2}(mm(2));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376 h = {hx, hy};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
378 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
379
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
380 function [xlims, ylims, zlims, x, X, h, H, fs] = setup3D(order, mom_cond)
1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
382 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 xlims = {-3, 20};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384 ylims = {-11,5};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385 zlims = {2,4};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
386 Lx = xlims{2} - xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
387 Ly = ylims{2} - ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
388 Lz = zlims{2} - zlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
389
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
390 m = [13, 14, 15];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
391 g = grid.equidistant(m, xlims, ylims, zlims);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
392 X = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
393 x = g.x;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
394
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
395 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
396 opsx = sbp.D2Standard(m(1), xlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397 opsy = sbp.D2Standard(m(2), ylims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398 opsz = sbp.D2Standard(m(3), zlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 Hx = opsx.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
400 Hy = opsy.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
401 Hz = opsz.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
402 H = {Hx, Hy, Hz};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
403
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
404 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
405 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
406 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
407 fs{p+1} = @(x,y,z) (x/Lx + y/Ly + z/Lz).^p;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
408 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
409
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
410 % Grid spacing in interior
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411 mm = round(m/2);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
412 hx = x{1}(mm(1)+1) - x{1}(mm(1));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
413 hy = x{2}(mm(2)+1) - x{2}(mm(2));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
414 hz = x{3}(mm(3)+1) - x{3}(mm(3));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
415 h = {hx, hy, hz};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
416
1232
52d774e69b1f Clean up diracDiscr, remove obsolete tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1229
diff changeset
417 end