1 | #!/usr/bin/env python |
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2 | |
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3 | #TEST |
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4 | import sys |
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5 | import unittest |
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6 | from math import sqrt |
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7 | |
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8 | |
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9 | from interpolate import * |
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10 | from Numeric import allclose, array, transpose |
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11 | |
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12 | from coordinate_transforms.geo_reference import Geo_reference |
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13 | |
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14 | def distance(x, y): |
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15 | return sqrt( sum( (array(x)-array(y))**2 )) |
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16 | |
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17 | def linear_function(point): |
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18 | point = array(point) |
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19 | return point[:,0]+point[:,1] |
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20 | |
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21 | |
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22 | class Test_Interpolate(unittest.TestCase): |
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23 | |
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24 | def setUp(self): |
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25 | pass |
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26 | |
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27 | def tearDown(self): |
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28 | pass |
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29 | |
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30 | def test_datapoint_at_centroid(self): |
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31 | a = [0.0, 0.0] |
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32 | b = [0.0, 2.0] |
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33 | c = [2.0,0.0] |
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34 | points = [a, b, c] |
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35 | vertices = [ [1,0,2] ] #bac |
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36 | |
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37 | data = [ [2.0/3, 2.0/3] ] #Use centroid as one data point |
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38 | |
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39 | interp = Interpolate(points, vertices) |
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40 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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41 | [[1./3, 1./3, 1./3]]) |
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42 | |
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43 | |
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44 | def test_quad_tree(self): |
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45 | p0 = [-10.0, -10.0] |
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46 | p1 = [20.0, -10.0] |
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47 | p2 = [-10.0, 20.0] |
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48 | p3 = [10.0, 50.0] |
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49 | p4 = [30.0, 30.0] |
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50 | p5 = [50.0, 10.0] |
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51 | p6 = [40.0, 60.0] |
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52 | p7 = [60.0, 40.0] |
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53 | p8 = [-66.0, 20.0] |
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54 | p9 = [10.0, -66.0] |
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55 | |
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56 | points = [p0, p1, p2, p3, p4, p5, p6, p7, p8, p9] |
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57 | triangles = [ [0, 1, 2], |
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58 | [3, 2, 4], |
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59 | [4, 2, 1], |
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60 | [4, 1, 5], |
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61 | [3, 4, 6], |
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62 | [6, 4, 7], |
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63 | [7, 4, 5], |
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64 | [8, 0, 2], |
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65 | [0, 9, 1]] |
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66 | |
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67 | data = [ [4,4] ] |
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68 | interp = Interpolate(points, triangles, |
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69 | max_vertices_per_cell = 4) |
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70 | #print "PDSG - interp.get_A()", interp.get_A() |
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71 | answer = [ [ 0.06666667, 0.46666667, 0.46666667, 0., |
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72 | 0., 0. , 0., 0., 0., 0.]] |
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73 | |
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74 | |
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75 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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76 | answer) |
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77 | #interp.set_point_coordinates([[-30, -30]]) #point outside of mesh |
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78 | #print "PDSG - interp.get_A()", interp.get_A() |
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79 | data = [[-30, -30]] |
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80 | answer = [ [ 0.0, 0.0, 0.0, 0., |
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81 | 0., 0. , 0., 0., 0., 0.]] |
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82 | |
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83 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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84 | answer) |
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85 | |
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86 | |
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87 | #point outside of quad tree root cell |
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88 | #interp.set_point_coordinates([[-70, -70]]) |
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89 | #print "PDSG - interp.get_A()", interp.get_A() |
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90 | data = [[-70, -70]] |
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91 | answer = [ [ 0.0, 0.0, 0.0, 0., |
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92 | 0., 0. , 0., 0., 0., 0.]] |
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93 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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94 | answer) |
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95 | |
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96 | def test_datapoints_at_vertices(self): |
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97 | """Test that data points coinciding with vertices yield a diagonal matrix |
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98 | """ |
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99 | |
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100 | a = [0.0, 0.0] |
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101 | b = [0.0, 2.0] |
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102 | c = [2.0,0.0] |
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103 | points = [a, b, c] |
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104 | vertices = [ [1,0,2] ] #bac |
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105 | |
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106 | data = points #Use data at vertices |
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107 | |
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108 | interp = Interpolate(points, vertices) |
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109 | answer = [[1., 0., 0.], |
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110 | [0., 1., 0.], |
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111 | [0., 0., 1.]] |
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112 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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113 | answer) |
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114 | |
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115 | |
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116 | def test_datapoints_on_edge_midpoints(self): |
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117 | """Try datapoints midway on edges - |
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118 | each point should affect two matrix entries equally |
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119 | """ |
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120 | |
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121 | a = [0.0, 0.0] |
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122 | b = [0.0, 2.0] |
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123 | c = [2.0,0.0] |
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124 | points = [a, b, c] |
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125 | vertices = [ [1,0,2] ] #bac |
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126 | |
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127 | data = [ [0., 1.], [1., 0.], [1., 1.] ] |
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128 | answer = [[0.5, 0.5, 0.0], #Affects vertex 1 and 0 |
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129 | [0.5, 0.0, 0.5], #Affects vertex 0 and 2 |
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130 | [0.0, 0.5, 0.5]] |
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131 | interp = Interpolate(points, vertices, data) |
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132 | |
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133 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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134 | answer) |
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135 | |
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136 | def test_datapoints_on_edges(self): |
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137 | """Try datapoints on edges - |
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138 | each point should affect two matrix entries in proportion |
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139 | """ |
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140 | |
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141 | a = [0.0, 0.0] |
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142 | b = [0.0, 2.0] |
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143 | c = [2.0,0.0] |
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144 | points = [a, b, c] |
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145 | vertices = [ [1,0,2] ] #bac |
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146 | |
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147 | data = [ [0., 1.5], [1.5, 0.], [1.5, 0.5] ] |
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148 | answer = [[0.25, 0.75, 0.0], #Affects vertex 1 and 0 |
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149 | [0.25, 0.0, 0.75], #Affects vertex 0 and 2 |
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150 | [0.0, 0.25, 0.75]] |
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151 | |
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152 | interp = Interpolate(points, vertices, data) |
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153 | |
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154 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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155 | answer) |
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156 | |
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157 | |
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158 | def test_arbitrary_datapoints(self): |
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159 | """Try arbitrary datapoints |
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160 | """ |
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161 | |
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162 | from Numeric import sum |
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163 | |
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164 | a = [0.0, 0.0] |
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165 | b = [0.0, 2.0] |
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166 | c = [2.0,0.0] |
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167 | points = [a, b, c] |
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168 | vertices = [ [1,0,2] ] #bac |
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169 | |
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170 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44] ] |
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171 | |
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172 | interp = Interpolate(points, vertices, data) |
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173 | #print "interp.get_A()", interp.get_A() |
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174 | results = interp._build_interpolation_matrix_A(data).todense() |
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175 | assert allclose(sum(results, axis=1), 1.0) |
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176 | |
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177 | #FIXME - have to change this test to check default info |
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178 | def NO_test_arbitrary_datapoints_some_outside(self): |
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179 | """Try arbitrary datapoints one outside the triangle. |
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180 | That one should be ignored |
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181 | """ |
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182 | |
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183 | from Numeric import sum |
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184 | |
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185 | a = [0.0, 0.0] |
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186 | b = [0.0, 2.0] |
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187 | c = [2.0,0.0] |
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188 | points = [a, b, c] |
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189 | vertices = [ [1,0,2] ] #bac |
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190 | |
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191 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44], [5.0, 7.0]] |
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192 | |
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193 | |
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194 | interp = Interpolate(points, vertices, data, precrop = True) |
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195 | |
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196 | results = interp._build_interpolation_matrix_A(data).todense() |
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197 | assert allclose(sum(results, axis=1), 1.0) |
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198 | |
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199 | interp = Interpolate(points, vertices, data, precrop = False) |
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200 | results = interp._build_interpolation_matrix_A(data).todense() |
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201 | assert allclose(sum(results, axis=1), [1,1,1,0]) |
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202 | |
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203 | |
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204 | |
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205 | # this causes a memory error in scipy.sparse |
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206 | def test_more_triangles(self): |
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207 | |
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208 | a = [-1.0, 0.0] |
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209 | b = [3.0, 4.0] |
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210 | c = [4.0,1.0] |
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211 | d = [-3.0, 2.0] #3 |
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212 | e = [-1.0,-2.0] |
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213 | f = [1.0, -2.0] #5 |
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214 | |
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215 | points = [a, b, c, d,e,f] |
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216 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
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217 | |
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218 | #Data points |
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219 | data = [ [-3., 2.0], [-2, 1], [0.0, 1], [0, 3], [2, 3], [-1.0/3,-4./3] ] |
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220 | interp = Interpolate(points, triangles) |
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221 | |
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222 | answer = [[0.0, 0.0, 0.0, 1.0, 0.0, 0.0], #Affects point d |
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223 | [0.5, 0.0, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
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224 | [0.75, 0.25, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
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225 | [0.0, 0.5, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
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226 | [0.25, 0.75, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
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227 | [1./3, 0.0, 0.0, 0.0, 1./3, 1./3]] #Affects points a, e and f |
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228 | |
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229 | |
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230 | A = interp._build_interpolation_matrix_A(data).todense() |
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231 | for i in range(A.shape[0]): |
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232 | for j in range(A.shape[1]): |
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233 | if not allclose(A[i,j], answer[i][j]): |
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234 | print i,j,':',A[i,j], answer[i][j] |
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235 | |
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236 | |
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237 | #results = interp._build_interpolation_matrix_A(data).todense() |
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238 | |
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239 | assert allclose(A, answer) |
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240 | |
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241 | |
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242 | def test_interpolate_attributes_to_points(self): |
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243 | v0 = [0.0, 0.0] |
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244 | v1 = [0.0, 5.0] |
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245 | v2 = [5.0, 0.0] |
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246 | |
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247 | vertices = [v0, v1, v2] |
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248 | triangles = [ [1,0,2] ] #bac |
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249 | |
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250 | d0 = [1.0, 1.0] |
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251 | d1 = [1.0, 2.0] |
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252 | d2 = [3.0, 1.0] |
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253 | point_coords = [ d0, d1, d2] |
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254 | |
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255 | interp = Interpolate(vertices, triangles, point_coords) |
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256 | f = linear_function(vertices) |
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257 | z = interp.interpolate(f, point_coords) |
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258 | answer = linear_function(point_coords) |
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259 | |
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260 | |
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261 | assert allclose(z, answer) |
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262 | |
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263 | |
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264 | |
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265 | def test_interpolate_attributes_to_pointsII(self): |
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266 | a = [-1.0, 0.0] |
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267 | b = [3.0, 4.0] |
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268 | c = [4.0, 1.0] |
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269 | d = [-3.0, 2.0] #3 |
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270 | e = [-1.0, -2.0] |
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271 | f = [1.0, -2.0] #5 |
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272 | |
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273 | vertices = [a, b, c, d,e,f] |
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274 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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275 | |
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276 | |
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277 | point_coords = [[-2.0, 2.0], |
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278 | [-1.0, 1.0], |
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279 | [0.0, 2.0], |
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280 | [1.0, 1.0], |
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281 | [2.0, 1.0], |
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282 | [0.0, 0.0], |
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283 | [1.0, 0.0], |
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284 | [0.0, -1.0], |
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285 | [-0.2, -0.5], |
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286 | [-0.9, -1.5], |
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287 | [0.5, -1.9], |
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288 | [3.0, 1.0]] |
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289 | |
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290 | interp = Interpolate(vertices, triangles) |
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291 | f = linear_function(vertices) |
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292 | z = interp.interpolate(f, point_coords) |
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293 | answer = linear_function(point_coords) |
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294 | #print "z",z |
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295 | #print "answer",answer |
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296 | assert allclose(z, answer) |
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297 | |
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298 | def test_interpolate_attributes_to_pointsIII(self): |
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299 | """Test linear interpolation of known values at vertices to |
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300 | new points inside a triangle |
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301 | """ |
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302 | a = [0.0, 0.0] |
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303 | b = [0.0, 5.0] |
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304 | c = [5.0, 0.0] |
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305 | d = [5.0, 5.0] |
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306 | |
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307 | vertices = [a, b, c, d] |
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308 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
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309 | |
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310 | #Points within triangle 1 |
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311 | d0 = [1.0, 1.0] |
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312 | d1 = [1.0, 2.0] |
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313 | d2 = [3.0, 1.0] |
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314 | |
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315 | #Point within triangle 2 |
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316 | d3 = [4.0, 3.0] |
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317 | |
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318 | #Points on common edge |
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319 | d4 = [2.5, 2.5] |
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320 | d5 = [4.0, 1.0] |
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321 | |
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322 | #Point on common vertex |
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323 | d6 = [0., 5.] |
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324 | |
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325 | point_coords = [d0, d1, d2, d3, d4, d5, d6] |
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326 | |
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327 | interp = Interpolate(vertices, triangles) |
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328 | |
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329 | #Known values at vertices |
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330 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
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331 | f = [ [0., 0., 0., -5.], # (0,0) |
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332 | [5., 10., 5., -10.], # (0,5) |
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333 | [5., 5., 10.0, 0.], # (5,0) |
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334 | [10., 15., 15., -5.]] # (5,5) |
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335 | |
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336 | z = interp.interpolate(f, point_coords) |
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337 | answer = [ [2., 3., 3., -5.], # (1,1) |
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338 | [3., 5., 4., -6.], # (1,2) |
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339 | [4., 5., 7., -3.], # (3,1) |
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340 | [7., 10., 11., -4.], # (4,3) |
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341 | [5., 7.5, 7.5, -5.], # (2.5, 2.5) |
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342 | [5., 6., 9., -2.], # (4,1) |
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343 | [5., 10., 5., -10.]] # (0,5) |
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344 | |
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345 | #print "***********" |
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346 | #print "z",z |
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347 | #print "answer",answer |
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348 | #print "***********" |
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349 | |
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350 | #Should an error message be returned if points are outside |
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351 | # of the mesh? Not currently. |
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352 | |
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353 | assert allclose(z, answer) |
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354 | |
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355 | |
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356 | def test_interpolate_point_outside_of_mesh(self): |
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357 | """Test linear interpolation of known values at vertices to |
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358 | new points inside a triangle |
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359 | """ |
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360 | a = [0.0, 0.0] |
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361 | b = [0.0, 5.0] |
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362 | c = [5.0, 0.0] |
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363 | d = [5.0, 5.0] |
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364 | |
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365 | vertices = [a, b, c, d] |
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366 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
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367 | |
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368 | #Far away point |
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369 | d7 = [-1., -1.] |
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370 | |
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371 | point_coords = [ d7] |
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372 | interp = Interpolate(vertices, triangles) |
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373 | |
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374 | #Known values at vertices |
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375 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
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376 | f = [ [0., 0., 0., -5.], # (0,0) |
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377 | [5., 10., 5., -10.], # (0,5) |
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378 | [5., 5., 10.0, 0.], # (5,0) |
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379 | [10., 15., 15., -5.]] # (5,5) |
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380 | |
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381 | z = interp.interpolate(f, point_coords) |
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382 | answer = [ [0., 0., 0., 0.]] # (-1,-1) |
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383 | |
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384 | #print "***********" |
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385 | #print "z",z |
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386 | #print "answer",answer |
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387 | #print "***********" |
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388 | |
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389 | #Should an error message be returned if points are outside |
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390 | # of the mesh? Not currently. |
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391 | |
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392 | assert allclose(z, answer) |
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393 | |
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394 | def test_interpolate_attributes_to_pointsIV(self): |
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395 | a = [-1.0, 0.0] |
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396 | b = [3.0, 4.0] |
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397 | c = [4.0, 1.0] |
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398 | d = [-3.0, 2.0] #3 |
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399 | e = [-1.0, -2.0] |
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400 | f = [1.0, -2.0] #5 |
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401 | |
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402 | vertices = [a, b, c, d,e,f] |
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403 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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404 | |
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405 | |
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406 | point_coords = [[-2.0, 2.0], |
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407 | [-1.0, 1.0], |
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408 | [0.0, 2.0], |
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409 | [1.0, 1.0], |
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410 | [2.0, 1.0], |
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411 | [0.0, 0.0], |
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412 | [1.0, 0.0], |
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413 | [0.0, -1.0], |
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414 | [-0.2, -0.5], |
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415 | [-0.9, -1.5], |
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416 | [0.5, -1.9], |
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417 | [3.0, 1.0]] |
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418 | |
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419 | interp = Interpolate(vertices, triangles) |
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420 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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421 | f = transpose(f) |
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422 | #print "f",f |
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423 | z = interp.interpolate(f, point_coords) |
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424 | answer = [linear_function(point_coords), |
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425 | 2*linear_function(point_coords) ] |
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426 | answer = transpose(answer) |
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427 | #print "z",z |
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428 | #print "answer",answer |
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429 | assert allclose(z, answer) |
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430 | |
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431 | |
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432 | def test_interpolate_blocking(self): |
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433 | a = [-1.0, 0.0] |
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434 | b = [3.0, 4.0] |
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435 | c = [4.0, 1.0] |
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436 | d = [-3.0, 2.0] #3 |
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437 | e = [-1.0, -2.0] |
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438 | f = [1.0, -2.0] #5 |
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439 | |
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440 | vertices = [a, b, c, d,e,f] |
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441 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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442 | |
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443 | |
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444 | point_coords = [[-2.0, 2.0], |
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445 | [-1.0, 1.0], |
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446 | [0.0, 2.0], |
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447 | [1.0, 1.0], |
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448 | [2.0, 1.0], |
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449 | [0.0, 0.0], |
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450 | [1.0, 0.0], |
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451 | [0.0, -1.0], |
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452 | [-0.2, -0.5], |
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453 | [-0.9, -1.5], |
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454 | [0.5, -1.9], |
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455 | [3.0, 1.0]] |
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456 | |
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457 | interp = Interpolate(vertices, triangles) |
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458 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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459 | f = transpose(f) |
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460 | #print "f",f |
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461 | for blocking_max in range(len(point_coords)+2): |
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462 | #if True: |
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463 | # blocking_max = 5 |
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464 | z = interp.interpolate(f, point_coords, |
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465 | start_blocking_len=blocking_max) |
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466 | answer = [linear_function(point_coords), |
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467 | 2*linear_function(point_coords) ] |
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468 | answer = transpose(answer) |
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469 | #print "z",z |
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470 | #print "answer",answer |
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471 | assert allclose(z, answer) |
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472 | |
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473 | def test_interpolate_reuse(self): |
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474 | a = [-1.0, 0.0] |
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475 | b = [3.0, 4.0] |
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476 | c = [4.0, 1.0] |
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477 | d = [-3.0, 2.0] #3 |
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478 | e = [-1.0, -2.0] |
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479 | f = [1.0, -2.0] #5 |
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480 | |
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481 | vertices = [a, b, c, d,e,f] |
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482 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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483 | |
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484 | |
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485 | point_coords = [[-2.0, 2.0], |
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486 | [-1.0, 1.0], |
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487 | [0.0, 2.0], |
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488 | [1.0, 1.0], |
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489 | [2.0, 1.0], |
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490 | [0.0, 0.0], |
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491 | [1.0, 0.0], |
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492 | [0.0, -1.0], |
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493 | [-0.2, -0.5], |
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494 | [-0.9, -1.5], |
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495 | [0.5, -1.9], |
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496 | [3.0, 1.0]] |
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497 | |
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498 | interp = Interpolate(vertices, triangles) |
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499 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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500 | f = transpose(f) |
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501 | z = interp.interpolate(f, point_coords, |
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502 | start_blocking_len=20) |
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503 | answer = [linear_function(point_coords), |
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504 | 2*linear_function(point_coords) ] |
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505 | answer = transpose(answer) |
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506 | #print "z",z |
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507 | #print "answer",answer |
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508 | assert allclose(z, answer) |
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509 | assert allclose(interp._A_can_be_reused, True) |
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510 | |
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511 | z = interp.interpolate(f) |
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512 | assert allclose(z, answer) |
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513 | |
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514 | # This causes blocking to occur. |
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515 | z = interp.interpolate(f, start_blocking_len=10) |
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516 | assert allclose(z, answer) |
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517 | assert allclose(interp._A_can_be_reused, False) |
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518 | |
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519 | #A is recalculated |
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520 | z = interp.interpolate(f) |
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521 | assert allclose(z, answer) |
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522 | assert allclose(interp._A_can_be_reused, True) |
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523 | |
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524 | interp = Interpolate(vertices, triangles) |
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525 | #Must raise an exception, no points specified |
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526 | try: |
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527 | z = interp.interpolate(f) |
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528 | except: |
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529 | pass |
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530 | |
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531 | |
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532 | #------------------------------------------------------------- |
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533 | if __name__ == "__main__": |
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534 | suite = unittest.makeSuite(Test_Interpolate,'test') |
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535 | runner = unittest.TextTestRunner(verbosity=1) |
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536 | runner.run(suite) |
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537 | |
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538 | |
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539 | |
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540 | |
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541 | |
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