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annotate diracDiscrTest.m @ 1229:86ee5648e384 feature/dirac_discr

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Add multi-d dirac discretization with tests
author Martin Almquist <malmquist@stanford.edu>
date Tue, 19 Nov 2019 10:56:57 -0800
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children 52d774e69b1f
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1229
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
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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 function testLeftGP(testCase)
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6
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7 orders = [2, 4, 6];
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8 mom_conds = orders;
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9
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10 for o = 1:length(orders)
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11 order = orders(o);
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12 mom_cond = mom_conds(o);
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13 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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14
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15 % Test left boundary grid points
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16 x0s = xl + [0, h, 2*h];
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17
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18 for j = 1:length(fs)
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19 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
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20 fx = f(x);
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21 for i = 1:length(x0s)
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22 x0 = x0s(i);
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23 delta = diracDiscr(x0, x, mom_cond, 0, H);
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24 integral = delta'*H*fx;
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25 err = abs(integral - f(x0));
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26 testCase.verifyLessThan(err, 1e-12);
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27 end
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28 end
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29 end
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30 end
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31
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32 function testLeftRandom(testCase)
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33
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34 orders = [2, 4, 6];
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35 mom_conds = orders;
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36
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37 for o = 1:length(orders)
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38 order = orders(o);
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39 mom_cond = mom_conds(o);
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40 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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41
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42 % Test random points near left boundary
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43 x0s = xl + 2*h*rand(1,10);
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44
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45 for j = 1:length(fs)
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46 f = fs{j};
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47 fx = f(x);
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48 for i = 1:length(x0s)
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49 x0 = x0s(i);
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50 delta = diracDiscr(x0, x, mom_cond, 0, H);
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51 integral = delta'*H*fx;
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52 err = abs(integral - f(x0));
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53 testCase.verifyLessThan(err, 1e-12);
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54 end
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55 end
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56 end
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57 end
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58
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59 function testRightGP(testCase)
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60
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61 orders = [2, 4, 6];
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62 mom_conds = orders;
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63
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64 for o = 1:length(orders)
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65 order = orders(o);
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66 mom_cond = mom_conds(o);
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67 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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68
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69 % Test right boundary grid points
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70 x0s = xr-[0, h, 2*h];
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71
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72 for j = 1:length(fs)
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73 f = fs{j};
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74 fx = f(x);
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75 for i = 1:length(x0s)
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76 x0 = x0s(i);
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77 delta = diracDiscr(x0, x, mom_cond, 0, H);
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78 integral = delta'*H*fx;
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79 err = abs(integral - f(x0));
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80 testCase.verifyLessThan(err, 1e-12);
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81 end
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82 end
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83 end
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84 end
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85
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86 function testRightRandom(testCase)
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87
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88 orders = [2, 4, 6];
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89 mom_conds = orders;
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90
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91 for o = 1:length(orders)
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92 order = orders(o);
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93 mom_cond = mom_conds(o);
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94 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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95
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96 % Test random points near right boundary
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97 x0s = xr - 2*h*rand(1,10);
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98
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99 for j = 1:length(fs)
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100 f = fs{j};
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101 fx = f(x);
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102 for i = 1:length(x0s)
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103 x0 = x0s(i);
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104 delta = diracDiscr(x0, x, mom_cond, 0, H);
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105 integral = delta'*H*fx;
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106 err = abs(integral - f(x0));
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107 testCase.verifyLessThan(err, 1e-12);
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108 end
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109 end
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110 end
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111 end
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112
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113 function testInteriorGP(testCase)
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114
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115 orders = [2, 4, 6];
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116 mom_conds = orders;
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117
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118 for o = 1:length(orders)
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119 order = orders(o);
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120 mom_cond = mom_conds(o);
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121 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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122
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123 % Test interior grid points
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124 m_half = round(m/2);
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125 x0s = xl + (m_half-1:m_half+1)*h;
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126
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127 for j = 1:length(fs)
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128 f = fs{j};
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129 fx = f(x);
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130 for i = 1:length(x0s)
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131 x0 = x0s(i);
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132 delta = diracDiscr(x0, x, mom_cond, 0, H);
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133 integral = delta'*H*fx;
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134 err = abs(integral - f(x0));
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135 testCase.verifyLessThan(err, 1e-12);
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136 end
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137 end
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138 end
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139 end
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140
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141 function testInteriorRandom(testCase)
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142
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143 orders = [2, 4, 6];
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144 mom_conds = orders;
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145
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146 for o = 1:length(orders)
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147 order = orders(o);
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148 mom_cond = mom_conds(o);
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149 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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150
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diff changeset
151 % Test random points in interior
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Martin Almquist <malmquist@stanford.edu>
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152 x0s = (xl+2*h) + (xr-xl-4*h)*rand(1,20);
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parents:
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153
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
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diff changeset
154 for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 fx = f(x);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 x0 = x0s(i);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 delta = diracDiscr(x0, x, mom_cond, 0, H);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 err = abs(integral - f(x0));
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 testCase.verifyLessThan(err, 1e-12);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 end
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Martin Almquist <malmquist@stanford.edu>
parents:
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165 end
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Martin Almquist <malmquist@stanford.edu>
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166 end
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Martin Almquist <malmquist@stanford.edu>
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167
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Martin Almquist <malmquist@stanford.edu>
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168 % x0 outside grid should yield 0 integral!
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Martin Almquist <malmquist@stanford.edu>
parents:
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169 function testX0OutsideGrid(testCase)
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Martin Almquist <malmquist@stanford.edu>
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170
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Martin Almquist <malmquist@stanford.edu>
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171 orders = [2, 4, 6];
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Martin Almquist <malmquist@stanford.edu>
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172 mom_conds = orders;
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Martin Almquist <malmquist@stanford.edu>
parents:
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173
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Martin Almquist <malmquist@stanford.edu>
parents:
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174 for o = 1:length(orders)
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Martin Almquist <malmquist@stanford.edu>
parents:
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175 order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
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176 mom_cond = mom_conds(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
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177 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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178
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Martin Almquist <malmquist@stanford.edu>
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179 % Test points outisde grid
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Martin Almquist <malmquist@stanford.edu>
parents:
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180 x0s = [xl-1.1*h, xr+1.1*h];
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parents:
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181
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182 for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
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183 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
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184 fx = f(x);
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Martin Almquist <malmquist@stanford.edu>
parents:
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185 for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
parents:
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186 x0 = x0s(i);
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Martin Almquist <malmquist@stanford.edu>
parents:
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187 delta = diracDiscr(x0, x, mom_cond, 0, H);
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Martin Almquist <malmquist@stanford.edu>
parents:
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188 integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
parents:
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189 err = abs(integral - 0);
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Martin Almquist <malmquist@stanford.edu>
parents:
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190 testCase.verifyLessThan(err, 1e-12);
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Martin Almquist <malmquist@stanford.edu>
parents:
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191 end
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Martin Almquist <malmquist@stanford.edu>
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192 end
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Martin Almquist <malmquist@stanford.edu>
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193 end
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Martin Almquist <malmquist@stanford.edu>
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194 end
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Martin Almquist <malmquist@stanford.edu>
parents:
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195
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Martin Almquist <malmquist@stanford.edu>
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196 function testAllGP(testCase)
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Martin Almquist <malmquist@stanford.edu>
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197
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198 orders = [2, 4, 6];
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Martin Almquist <malmquist@stanford.edu>
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199 mom_conds = orders;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200
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Martin Almquist <malmquist@stanford.edu>
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201 for o = 1:length(orders)
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Martin Almquist <malmquist@stanford.edu>
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202 order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
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203 mom_cond = mom_conds(o);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 % Test all grid points
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Martin Almquist <malmquist@stanford.edu>
parents:
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207 x0s = x;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
209 for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
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210 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 fx = f(x);
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Martin Almquist <malmquist@stanford.edu>
parents:
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212 for i = 1:length(x0s)
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213 x0 = x0s(i);
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Martin Almquist <malmquist@stanford.edu>
parents:
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214 delta = diracDiscr(x0, x, mom_cond, 0, H);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
parents:
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216 err = abs(integral - f(x0));
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Martin Almquist <malmquist@stanford.edu>
parents:
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217 testCase.verifyLessThan(err, 1e-12);
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Martin Almquist <malmquist@stanford.edu>
parents:
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218 end
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219 end
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220 end
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221 end
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222
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Martin Almquist <malmquist@stanford.edu>
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223 function testHalfGP(testCase)
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224
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225 orders = [2, 4, 6];
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226 mom_conds = orders;
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227
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228 for o = 1:length(orders)
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229 order = orders(o);
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230 mom_cond = mom_conds(o);
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parents:
diff changeset
231 [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond);
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232
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233 % Test halfway between all grid points
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Martin Almquist <malmquist@stanford.edu>
parents:
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234 x0s = 1/2*( x(2:end)+x(1:end-1) );
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235
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236 for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
237 f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
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238 fx = f(x);
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Martin Almquist <malmquist@stanford.edu>
parents:
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239 for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
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240 x0 = x0s(i);
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Martin Almquist <malmquist@stanford.edu>
parents:
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241 delta = diracDiscr(x0, x, mom_cond, 0, H);
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Martin Almquist <malmquist@stanford.edu>
parents:
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242 integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
parents:
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243 err = abs(integral - f(x0));
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 testCase.verifyLessThan(err, 1e-12);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 end
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Martin Almquist <malmquist@stanford.edu>
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246 end
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247 end
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248 end
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249
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
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250 % function testAllGPStaggered(testCase)
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251
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Martin Almquist <malmquist@stanford.edu>
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252 % orders = [2, 4, 6];
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253 % mom_conds = orders;
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254
86ee5648e384 Add multi-d dirac discretization with tests
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255 % for o = 1:length(orders)
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256 % order = orders(o);
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257 % mom_cond = mom_conds(o);
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parents:
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258 % [xl, xr, m, h, x, H, fs] = setupStaggered(order, mom_cond);
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diff changeset
259
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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260 % % Test all grid points
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Martin Almquist <malmquist@stanford.edu>
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261 % x0s = x;
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262
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Martin Almquist <malmquist@stanford.edu>
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263 % for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
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264 % f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
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265 % fx = f(x);
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parents:
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266 % for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
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267 % x0 = x0s(i);
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parents:
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268 % delta = diracDiscr(x0, x, mom_cond, 0, H);
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Martin Almquist <malmquist@stanford.edu>
parents:
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269 % integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
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270 % err = abs(integral - f(x0));
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Martin Almquist <malmquist@stanford.edu>
parents:
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271 % testCase.verifyLessThan(err, 1e-12);
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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 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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275 % end
86ee5648e384 Add multi-d dirac discretization with tests
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parents:
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276
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Martin Almquist <malmquist@stanford.edu>
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277 % function testHalfGPStaggered(testCase)
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278
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279 % orders = [2, 4, 6];
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280 % mom_conds = orders;
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281
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Martin Almquist <malmquist@stanford.edu>
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282 % for o = 1:length(orders)
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Martin Almquist <malmquist@stanford.edu>
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283 % order = orders(o);
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Martin Almquist <malmquist@stanford.edu>
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284 % mom_cond = mom_conds(o);
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parents:
diff changeset
285 % [xl, xr, m, h, x, H, fs] = setupStaggered(order, mom_cond);
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parents:
diff changeset
286
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287 % % Test halfway between all grid points
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288 % x0s = 1/2*( x(2:end)+x(1:end-1) );
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parents:
diff changeset
289
86ee5648e384 Add multi-d dirac discretization with tests
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diff changeset
290 % for j = 1:length(fs)
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
291 % f = fs{j};
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Martin Almquist <malmquist@stanford.edu>
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292 % fx = f(x);
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Martin Almquist <malmquist@stanford.edu>
parents:
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293 % for i = 1:length(x0s)
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Martin Almquist <malmquist@stanford.edu>
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294 % x0 = x0s(i);
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295 % delta = diracDiscr(x0, x, mom_cond, 0, H);
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parents:
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296 % integral = delta'*H*fx;
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Martin Almquist <malmquist@stanford.edu>
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297 % err = abs(integral - f(x0));
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298 % testCase.verifyLessThan(err, 1e-12);
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299 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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300 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
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301 % end
86ee5648e384 Add multi-d dirac discretization with tests
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parents:
diff changeset
302 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 % function testRandomStaggered(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 % orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307 % mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 % for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310 % order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311 % mom_cond = mom_conds(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 % [xl, xr, m, h, x, H, fs] = setupStaggered(order, mom_cond);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314 % % Test random points within grid boundaries
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315 % x0s = xl + (xr-xl)*rand(1,300);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317 % for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318 % f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 % fx = f(x);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320 % for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321 % x0 = x0s(i);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 % delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323 % integral = delta'*H*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 % err = abs(integral - f(x0));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 % testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 % end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 %=============== 2D tests ==============================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
332 function testAllGP2D(testCase)
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 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
338 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
339 mom_cond = mom_conds(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 [xlims, ylims, m, x, X, ~, H, fs] = setup2D(order, mom_cond);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 H_global = kron(H{1}, H{2});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343 % Test all grid points
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 x0s = X;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 fx = f(X(:,1), X(:,2));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 err = abs(integral - f(x0(1), x0(2)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 function testAllRandom2D(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367 mom_cond = mom_conds(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368 [xlims, ylims, m, x, X, h, H, fs] = setup2D(order, mom_cond);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
369 H_global = kron(H{1}, H{2});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371 xl = xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 xr = xlims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373 yl = ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374 yr = ylims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376 % Test random points, even outside grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377 Npoints = 100;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
378 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
379 (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
380
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
382 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 fx = f(X(:,1), X(:,2));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
386 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
387 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
388
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
389 % 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
390 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
391 err = abs(integral - 0);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
392 else
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
393 err = abs(integral - f(x0(1), x0(2)));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
394 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
395 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
396 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
397 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
398 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
399 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
400
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
401 %=============== 3D tests ==============================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
402 function testAllGP3D(testCase)
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 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
405 mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
406
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
407 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
408 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
409 mom_cond = mom_conds(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
410 [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
411 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
412
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
413 % Test all grid points
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
414 x0s = X;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
415
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
416 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
417 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
418 fx = f(X(:,1), X(:,2), X(:,3));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
419 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
420 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
421 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
422 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
423 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
424 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
425 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
426 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
427 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
428 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
429
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
430 function testAllRandom3D(testCase)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
431
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
432 orders = [2, 4, 6];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
433 mom_conds = orders;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
434
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
435 for o = 1:length(orders)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
436 order = orders(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
437 mom_cond = mom_conds(o);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
438 [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
439 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
440
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
441 xl = xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
442 xr = xlims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
443 yl = ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
444 yr = ylims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
445 zl = zlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
446 zr = zlims{2};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
447
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
448 % Test random points, even outside grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
449 Npoints = 200;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
450 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
451 (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
452 (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
453
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
454 for j = 1:length(fs)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
455 f = fs{j};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
456 fx = f(X(:,1), X(:,2), X(:,3));
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
457 for i = 1:length(x0s)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
458 x0 = x0s(i,:);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
459 delta = diracDiscr(x0, x, mom_cond, 0, H);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
460 integral = delta'*H_global*fx;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
461
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
462 % 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
463 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
464 err = abs(integral - 0);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
465 else
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
466 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
467 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
468 testCase.verifyLessThan(err, 1e-12);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
469 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
470 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
471 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
472 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
473
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
474
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
475 % ======================================================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
476 % ============== Setup functions =======================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
477 % ======================================================
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
478 function [xl, xr, m, h, x, H, fs] = setup1D(order, mom_cond)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
479
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
480 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
481 xl = -3;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
482 xr = 900;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
483 L = xr-xl;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
484 m = 101;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
485 h = (xr-xl)/(m-1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
486 g = grid.equidistant(m, {xl, xr});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
487 x = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
488
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
489 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
490 ops = sbp.D2Standard(m, {xl, xr}, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
491 H = ops.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
492
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
493 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
494 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
495 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
496 fs{p+1} = @(x) (x/L).^p;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
497 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
498
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
499 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
500
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
501 function [xlims, ylims, m, x, X, h, H, fs] = setup2D(order, mom_cond)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
502
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
503 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
504 xlims = {-3, 20};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
505 ylims = {-11,5};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
506 Lx = xlims{2} - xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
507 Ly = ylims{2} - ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
508
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
509 m = [15, 16];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
510 g = grid.equidistant(m, xlims, ylims);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
511 X = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
512 x = g.x;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
513
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
514 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
515 opsx = sbp.D2Standard(m(1), xlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
516 opsy = sbp.D2Standard(m(2), ylims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
517 Hx = opsx.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
518 Hy = opsy.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
519 H = {Hx, Hy};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
520
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
521 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
522 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
523 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
524 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
525 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
526
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
527 % Grid spacing in interior
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
528 mm = round(m/2);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
529 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
530 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
531 h = {hx, hy};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
532
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
533 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
534
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
535 function [xlims, ylims, zlims, m, x, X, h, H, fs] = setup3D(order, mom_cond)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
536
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
537 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
538 xlims = {-3, 20};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
539 ylims = {-11,5};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
540 zlims = {2,4};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
541 Lx = xlims{2} - xlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
542 Ly = ylims{2} - ylims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
543 Lz = zlims{2} - zlims{1};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
544
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
545 m = [13, 14, 15];
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
546 g = grid.equidistant(m, xlims, ylims, zlims);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
547 X = g.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
548 x = g.x;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
549
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
550 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
551 opsx = sbp.D2Standard(m(1), xlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
552 opsy = sbp.D2Standard(m(2), ylims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
553 opsz = sbp.D2Standard(m(3), zlims, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
554 Hx = opsx.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
555 Hy = opsy.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
556 Hz = opsz.H;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
557 H = {Hx, Hy, Hz};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
558
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
559 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
560 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
561 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
562 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
563 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
564
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
565 % Grid spacing in interior
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
566 mm = round(m/2);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
567 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
568 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
569 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
570 h = {hx, hy, hz};
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
571
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
572 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
573
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
574 function [xl, xr, m, h, x, H, fs] = setupStaggered(order, mom_cond)
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
575
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
576 % Grid
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
577 xl = -3;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
578 xr = 900;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
579 L = xr-xl;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
580 m = 101;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
581 [~, g_dual] = grid.primalDual1D(m, {xl, xr});
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
582 x = g_dual.points();
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
583 h = g_dual.h;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
584
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
585 % Quadrature
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
586 ops = sbp.D1Staggered(m, {xl, xr}, order);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
587 H = ops.H_dual;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
588
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
589 % Moment conditions
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
590 fs = cell(mom_cond,1);
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
591 for p = 0:mom_cond-1
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
592 fs{p+1} = @(x) (x/L).^p;
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
593 end
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
594
86ee5648e384 Add multi-d dirac discretization with tests
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
595 end