1 | """ |
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2 | General functions used in fit and interpolate. |
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3 | |
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4 | Ole Nielsen, Stephen Roberts, Duncan Gray |
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5 | Geoscience Australia, 2006. |
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6 | |
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7 | """ |
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8 | import time |
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9 | |
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10 | from anuga.utilities.numerical_tools import get_machine_precision |
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11 | from anuga.config import max_float |
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12 | |
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13 | import Numeric as num |
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14 | |
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15 | |
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16 | initial_search_value = 'uncomment search_functions code first'#0 |
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17 | search_one_cell_time = initial_search_value |
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18 | search_more_cells_time = initial_search_value |
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19 | |
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20 | #FIXME test what happens if a |
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21 | LAST_TRIANGLE = [[-10,[(num.array([max_float,max_float]), |
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22 | num.array([max_float,max_float]), |
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23 | num.array([max_float,max_float])), |
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24 | (num.array([1,1], num.Int), #array default# |
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25 | num.array([0,0], num.Int), #array default# |
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26 | num.array([-1.1,-1.1]))]]] |
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27 | |
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28 | def search_tree_of_vertices(root, mesh, x): |
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29 | """ |
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30 | Find the triangle (element) that the point x is in. |
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31 | |
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32 | Inputs: |
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33 | root: A quad tree of the vertices |
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34 | mesh: The underlying mesh |
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35 | x: The point being placed |
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36 | |
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37 | Return: |
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38 | element_found, sigma0, sigma1, sigma2, k |
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39 | |
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40 | where |
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41 | element_found: True if a triangle containing x was found |
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42 | sigma0, sigma1, sigma2: The interpolated values |
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43 | k: Index of triangle (if found) |
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44 | |
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45 | """ |
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46 | global search_one_cell_time |
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47 | global search_more_cells_time |
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48 | |
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49 | #Find triangle containing x: |
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50 | element_found = False |
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51 | |
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52 | # This will be returned if element_found = False |
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53 | sigma2 = -10.0 |
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54 | sigma0 = -10.0 |
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55 | sigma1 = -10.0 |
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56 | k = -10.0 |
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57 | |
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58 | # Search the last triangle first |
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59 | try: |
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60 | element_found, sigma0, sigma1, sigma2, k = \ |
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61 | _search_triangles_of_vertices(mesh, last_triangle, x) |
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62 | except: |
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63 | element_found = False |
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64 | |
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65 | #print "last_triangle", last_triangle |
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66 | if element_found is True: |
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67 | #print "last_triangle", last_triangle |
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68 | return element_found, sigma0, sigma1, sigma2, k |
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69 | |
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70 | # This was only slightly faster than just checking the |
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71 | # last triangle and it significantly slowed down |
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72 | # non-gridded fitting |
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73 | # If the last element was a dud, search its neighbours |
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74 | #print "last_triangle[0][0]", last_triangle[0][0] |
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75 | #neighbours = mesh.get_triangle_neighbours(last_triangle[0][0]) |
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76 | #print "neighbours", neighbours |
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77 | #neighbours = [] |
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78 | # for k in neighbours: |
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79 | # if k >= 0: |
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80 | # tri = mesh.get_vertex_coordinates(k, |
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81 | # absolute=True) |
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82 | # n0 = mesh.get_normal(k, 0) |
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83 | # n1 = mesh.get_normal(k, 1) |
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84 | # n2 = mesh.get_normal(k, 2) |
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85 | # triangle =[[k,(tri, (n0, n1, n2))]] |
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86 | # element_found, sigma0, sigma1, sigma2, k = \ |
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87 | # _search_triangles_of_vertices(mesh, |
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88 | # triangle, x) |
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89 | # if element_found is True: |
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90 | # return element_found, sigma0, sigma1, sigma2, k |
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91 | |
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92 | #t0 = time.time() |
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93 | # Get triangles in the cell that the point is in. |
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94 | # Triangle is a list, first element triangle_id, |
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95 | # second element the triangle |
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96 | triangles = root.search(x[0], x[1]) |
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97 | is_more_elements = True |
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98 | |
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99 | element_found, sigma0, sigma1, sigma2, k = \ |
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100 | _search_triangles_of_vertices(mesh, |
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101 | triangles, x) |
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102 | #search_one_cell_time += time.time()-t0 |
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103 | #print "search_one_cell_time",search_one_cell_time |
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104 | #t0 = time.time() |
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105 | while not element_found and is_more_elements: |
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106 | triangles, branch = root.expand_search() |
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107 | if branch == []: |
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108 | # Searching all the verts from the root cell that haven't |
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109 | # been searched. This is the last try |
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110 | element_found, sigma0, sigma1, sigma2, k = \ |
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111 | _search_triangles_of_vertices(mesh, triangles, x) |
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112 | is_more_elements = False |
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113 | else: |
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114 | element_found, sigma0, sigma1, sigma2, k = \ |
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115 | _search_triangles_of_vertices(mesh, triangles, x) |
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116 | #search_more_cells_time += time.time()-t0 |
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117 | #print "search_more_cells_time", search_more_cells_time |
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118 | |
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119 | return element_found, sigma0, sigma1, sigma2, k |
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120 | |
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121 | |
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122 | def _search_triangles_of_vertices(mesh, triangles, x): |
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123 | """Search for triangle containing x amongs candidate_vertices in mesh |
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124 | |
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125 | This is called by search_tree_of_vertices once the appropriate node |
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126 | has been found from the quad tree. |
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127 | |
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128 | |
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129 | This function is responsible for most of the compute time in |
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130 | fit and interpolate. |
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131 | """ |
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132 | global last_triangle |
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133 | |
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134 | # these statments are needed if triangles is empty |
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135 | #Find triangle containing x: |
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136 | element_found = False |
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137 | |
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138 | # This will be returned if element_found = False |
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139 | sigma2 = -10.0 |
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140 | sigma0 = -10.0 |
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141 | sigma1 = -10.0 |
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142 | k = -10 |
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143 | |
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144 | #For all vertices in same cell as point x |
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145 | for k, tri_verts_norms in triangles: |
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146 | tri = tri_verts_norms[0] |
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147 | n0, n1, n2 = tri_verts_norms[1] |
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148 | # k is the triangle index |
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149 | # tri is a list of verts (x, y), representing a tringle |
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150 | # Find triangle that contains x (if any) and interpolate |
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151 | element_found, sigma0, sigma1, sigma2 =\ |
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152 | find_triangle_compute_interpolation(tri, n0, n1, n2, x) |
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153 | if element_found is True: |
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154 | # Don't look for any other triangles in the triangle list |
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155 | last_triangle = [[k,tri_verts_norms]] |
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156 | break |
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157 | return element_found, sigma0, sigma1, sigma2, k |
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158 | |
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159 | |
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160 | |
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161 | def find_triangle_compute_interpolation(triangle, n0, n1, n2, x): |
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162 | """Compute linear interpolation of point x and triangle k in mesh. |
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163 | It is assumed that x belongs to triangle k.max_float |
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164 | """ |
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165 | |
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166 | # Get the three vertex_points of candidate triangle k |
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167 | xi0, xi1, xi2 = triangle |
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168 | |
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169 | # this is where we can call some fast c code. |
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170 | |
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171 | # Integrity check - machine precision is too hard |
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172 | # so we use hardwired single precision |
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173 | epsilon = 1.0e-6 |
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174 | |
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175 | if x[0] > max(xi0[0], xi1[0], xi2[0]) + epsilon: |
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176 | # print "max(xi0[0], xi1[0], xi2[0])", max(xi0[0], xi1[0], xi2[0]) |
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177 | return False,0,0,0 |
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178 | if x[0] < min(xi0[0], xi1[0], xi2[0]) - epsilon: |
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179 | return False,0,0,0 |
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180 | if x[1] > max(xi0[1], xi1[1], xi2[1]) + epsilon: |
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181 | return False,0,0,0 |
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182 | if x[1] < min(xi0[1], xi1[1], xi2[1]) - epsilon: |
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183 | return False,0,0,0 |
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184 | |
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185 | # machine precision on some machines (e.g. nautilus) |
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186 | epsilon = get_machine_precision() * 2 |
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187 | |
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188 | # Compute interpolation - return as soon as possible |
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189 | # print "(xi0-xi1)", (xi0-xi1) |
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190 | # print "n0", n0 |
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191 | # print "dot((xi0-xi1), n0)", dot((xi0-xi1), n0) |
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192 | |
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193 | sigma0 = num.dot((x-xi1), n0)/num.dot((xi0-xi1), n0) |
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194 | if sigma0 < -epsilon: |
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195 | return False,0,0,0 |
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196 | sigma1 = num.dot((x-xi2), n1)/num.dot((xi1-xi2), n1) |
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197 | if sigma1 < -epsilon: |
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198 | return False,0,0,0 |
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199 | sigma2 = num.dot((x-xi0), n2)/num.dot((xi2-xi0), n2) |
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200 | if sigma2 < -epsilon: |
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201 | return False,0,0,0 |
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202 | |
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203 | # epsilon = 1.0e-6 |
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204 | # we want to speed this up, so don't do assertions |
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205 | #delta = abs(sigma0+sigma1+sigma2-1.0) # Should be close to zero |
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206 | #msg = 'abs(sigma0+sigma1+sigma2-1) = %.15e, eps = %.15e'\ |
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207 | # %(delta, epsilon) |
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208 | #assert delta < epsilon, msg |
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209 | |
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210 | |
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211 | # Check that this triangle contains the data point |
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212 | # Sigmas are allowed to get negative within |
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213 | # machine precision on some machines (e.g. nautilus) |
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214 | #if sigma0 >= -epsilon and sigma1 >= -epsilon and sigma2 >= -epsilon: |
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215 | # element_found = True |
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216 | #else: |
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217 | # element_found = False |
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218 | return True, sigma0, sigma1, sigma2 |
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219 | |
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220 | def set_last_triangle(): |
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221 | global last_triangle |
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222 | last_triangle = LAST_TRIANGLE |
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223 | |
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224 | def search_times(): |
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225 | |
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226 | global search_one_cell_time |
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227 | global search_more_cells_time |
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228 | |
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229 | return search_one_cell_time, search_more_cells_time |
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230 | |
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231 | def reset_search_times(): |
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232 | |
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233 | global search_one_cell_time |
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234 | global search_more_cells_time |
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235 | search_one_cell_time = initial_search_value |
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236 | search_more_cells_time = initial_search_value |
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