1 | """Least squares smooting and interpolation. |
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2 | |
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3 | Implements a penalised least-squares fit and associated interpolations. |
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4 | |
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5 | The penalty term (or smoothing term) is controlled by the smoothing |
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6 | parameter alpha. |
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7 | With a value of alpha=0, the fit function will attempt |
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8 | to interpolate as closely as possible in the least-squares sense. |
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9 | With values alpha > 0, a certain amount of smoothing will be applied. |
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10 | A positive alpha is essential in cases where there are too few |
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11 | data points. |
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12 | A negative alpha is not allowed. |
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13 | A typical value of alpha is 1.0e-6 |
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14 | |
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15 | |
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16 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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17 | Geoscience Australia, 2004. |
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18 | """ |
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19 | |
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20 | import exceptions |
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21 | class ShapeError(exceptions.Exception): pass |
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22 | class FittingError(exceptions.Exception): pass |
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23 | |
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24 | |
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25 | #from general_mesh import General_mesh |
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26 | from Numeric import zeros, array, Float, Int, transpose, concatenate, ArrayType, NewAxis |
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27 | from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh |
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28 | |
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29 | from Numeric import dot, zeros, take, compress, array, Float, Int, transpose, concatenate, ArrayType |
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30 | from anuga.utilities.sparse import Sparse, Sparse_CSR |
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31 | from anuga.utilities.cg_solve import conjugate_gradient, VectorShapeError |
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32 | from anuga.utilities.numerical_tools import ensure_numeric, mean, gradient |
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33 | |
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34 | |
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35 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
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36 | |
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37 | import time |
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38 | |
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39 | DEFAULT_ALPHA = 0.001 |
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40 | |
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41 | def fit_to_mesh_file(mesh_file, point_file, mesh_output_file, |
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42 | alpha=DEFAULT_ALPHA, verbose= False, |
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43 | expand_search = False, |
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44 | data_origin = None, |
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45 | mesh_origin = None, |
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46 | precrop = False, |
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47 | display_errors = True): |
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48 | """ |
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49 | Given a mesh file (tsh) and a point attribute file (xya), fit |
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50 | point attributes to the mesh and write a mesh file with the |
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51 | results. |
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52 | |
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53 | |
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54 | If data_origin is not None it is assumed to be |
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55 | a 3-tuple with geo referenced |
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56 | UTM coordinates (zone, easting, northing) |
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57 | |
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58 | NOTE: Throws IOErrors, for a variety of file problems. |
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59 | |
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60 | mesh_origin is the same but refers to the input tsh file. |
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61 | FIXME: When the tsh format contains it own origin, these parameters can go. |
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62 | FIXME: And both origins should be obtained from the specified files. |
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63 | """ |
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64 | |
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65 | from load_mesh.loadASCII import import_mesh_file, \ |
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66 | import_points_file, export_mesh_file, \ |
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67 | concatinate_attributelist |
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68 | |
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69 | |
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70 | try: |
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71 | mesh_dict = import_mesh_file(mesh_file) |
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72 | except IOError,e: |
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73 | if display_errors: |
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74 | print "Could not load bad file. ", e |
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75 | raise IOError #Re-raise exception |
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76 | |
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77 | vertex_coordinates = mesh_dict['vertices'] |
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78 | triangles = mesh_dict['triangles'] |
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79 | if type(mesh_dict['vertex_attributes']) == ArrayType: |
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80 | old_point_attributes = mesh_dict['vertex_attributes'].tolist() |
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81 | else: |
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82 | old_point_attributes = mesh_dict['vertex_attributes'] |
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83 | |
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84 | if type(mesh_dict['vertex_attribute_titles']) == ArrayType: |
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85 | old_title_list = mesh_dict['vertex_attribute_titles'].tolist() |
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86 | else: |
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87 | old_title_list = mesh_dict['vertex_attribute_titles'] |
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88 | |
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89 | if verbose: print 'tsh file %s loaded' %mesh_file |
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90 | |
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91 | # load in the .pts file |
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92 | try: |
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93 | point_dict = import_points_file(point_file, verbose=verbose) |
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94 | except IOError,e: |
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95 | if display_errors: |
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96 | print "Could not load bad file. ", e |
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97 | raise IOError #Re-raise exception |
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98 | |
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99 | point_coordinates = point_dict['pointlist'] |
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100 | title_list,point_attributes = concatinate_attributelist(point_dict['attributelist']) |
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101 | |
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102 | if point_dict.has_key('geo_reference') and not point_dict['geo_reference'] is None: |
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103 | data_origin = point_dict['geo_reference'].get_origin() |
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104 | else: |
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105 | data_origin = (56, 0, 0) #FIXME(DSG-DSG) |
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106 | |
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107 | if mesh_dict.has_key('geo_reference') and not mesh_dict['geo_reference'] is None: |
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108 | mesh_origin = mesh_dict['geo_reference'].get_origin() |
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109 | else: |
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110 | mesh_origin = (56, 0, 0) #FIXME(DSG-DSG) |
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111 | |
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112 | if verbose: print "points file loaded" |
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113 | if verbose: print "fitting to mesh" |
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114 | f = fit_to_mesh(vertex_coordinates, |
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115 | triangles, |
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116 | point_coordinates, |
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117 | point_attributes, |
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118 | alpha = alpha, |
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119 | verbose = verbose, |
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120 | expand_search = expand_search, |
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121 | data_origin = data_origin, |
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122 | mesh_origin = mesh_origin, |
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123 | precrop = precrop) |
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124 | if verbose: print "finished fitting to mesh" |
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125 | |
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126 | # convert array to list of lists |
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127 | new_point_attributes = f.tolist() |
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128 | #FIXME have this overwrite attributes with the same title - DSG |
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129 | #Put the newer attributes last |
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130 | if old_title_list <> []: |
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131 | old_title_list.extend(title_list) |
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132 | #FIXME can this be done a faster way? - DSG |
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133 | for i in range(len(old_point_attributes)): |
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134 | old_point_attributes[i].extend(new_point_attributes[i]) |
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135 | mesh_dict['vertex_attributes'] = old_point_attributes |
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136 | mesh_dict['vertex_attribute_titles'] = old_title_list |
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137 | else: |
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138 | mesh_dict['vertex_attributes'] = new_point_attributes |
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139 | mesh_dict['vertex_attribute_titles'] = title_list |
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140 | |
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141 | #FIXME (Ole): Remember to output mesh_origin as well |
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142 | if verbose: print "exporting to file ", mesh_output_file |
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143 | |
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144 | try: |
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145 | export_mesh_file(mesh_output_file, mesh_dict) |
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146 | except IOError,e: |
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147 | if display_errors: |
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148 | print "Could not write file. ", e |
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149 | raise IOError |
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150 | |
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151 | def fit_to_mesh(vertex_coordinates, |
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152 | triangles, |
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153 | point_coordinates, |
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154 | point_attributes, |
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155 | alpha = DEFAULT_ALPHA, |
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156 | verbose = False, |
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157 | acceptable_overshoot = 1.01, |
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158 | expand_search = False, |
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159 | data_origin = None, |
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160 | mesh_origin = None, |
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161 | precrop = False, |
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162 | use_cache = False): |
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163 | """ |
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164 | Fit a smooth surface to a triangulation, |
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165 | given data points with attributes. |
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166 | |
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167 | |
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168 | Inputs: |
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169 | |
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170 | vertex_coordinates: List of coordinate pairs [xi, eta] of points |
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171 | constituting mesh (or a an m x 2 Numeric array) |
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172 | |
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173 | triangles: List of 3-tuples (or a Numeric array) of |
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174 | integers representing indices of all vertices in the mesh. |
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175 | |
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176 | point_coordinates: List of coordinate pairs [x, y] of data points |
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177 | (or an nx2 Numeric array) |
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178 | |
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179 | alpha: Smoothing parameter. |
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180 | |
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181 | acceptable overshoot: controls the allowed factor by which fitted values |
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182 | may exceed the value of input data. The lower limit is defined |
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183 | as min(z) - acceptable_overshoot*delta z and upper limit |
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184 | as max(z) + acceptable_overshoot*delta z |
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185 | |
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186 | |
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187 | point_attributes: Vector or array of data at the point_coordinates. |
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188 | |
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189 | data_origin and mesh_origin are 3-tuples consisting of |
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190 | UTM zone, easting and northing. If specified |
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191 | point coordinates and vertex coordinates are assumed to be |
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192 | relative to their respective origins. |
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193 | |
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194 | """ |
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195 | if use_cache is True: |
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196 | from anuga.caching.caching import cache |
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197 | interp = cache(_interpolation, |
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198 | (vertex_coordinates, |
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199 | triangles, |
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200 | point_coordinates), |
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201 | {'alpha': alpha, |
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202 | 'verbose': verbose, |
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203 | 'expand_search': expand_search, |
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204 | 'data_origin': data_origin, |
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205 | 'mesh_origin': mesh_origin, |
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206 | 'precrop': precrop}, |
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207 | verbose = verbose) |
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208 | |
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209 | else: |
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210 | interp = Interpolation(vertex_coordinates, |
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211 | triangles, |
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212 | point_coordinates, |
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213 | alpha = alpha, |
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214 | verbose = verbose, |
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215 | expand_search = expand_search, |
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216 | data_origin = data_origin, |
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217 | mesh_origin = mesh_origin, |
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218 | precrop = precrop) |
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219 | |
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220 | vertex_attributes = interp.fit_points(point_attributes, verbose = verbose) |
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221 | |
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222 | |
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223 | #Sanity check |
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224 | point_coordinates = ensure_numeric(point_coordinates) |
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225 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
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226 | |
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227 | #Data points |
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228 | X = point_coordinates[:,0] |
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229 | Y = point_coordinates[:,1] |
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230 | Z = ensure_numeric(point_attributes) |
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231 | if len(Z.shape) == 1: |
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232 | Z = Z[:, NewAxis] |
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233 | |
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234 | |
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235 | #Data points inside mesh boundary |
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236 | indices = interp.point_indices |
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237 | if indices is not None: |
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238 | Xc = take(X, indices) |
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239 | Yc = take(Y, indices) |
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240 | Zc = take(Z, indices) |
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241 | else: |
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242 | Xc = X |
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243 | Yc = Y |
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244 | Zc = Z |
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245 | |
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246 | #Vertex coordinates |
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247 | Xi = vertex_coordinates[:,0] |
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248 | Eta = vertex_coordinates[:,1] |
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249 | Zeta = ensure_numeric(vertex_attributes) |
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250 | if len(Zeta.shape) == 1: |
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251 | Zeta = Zeta[:, NewAxis] |
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252 | |
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253 | for i in range(Zeta.shape[1]): #For each attribute |
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254 | zeta = Zeta[:,i] |
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255 | z = Z[:,i] |
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256 | zc = Zc[:,i] |
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257 | |
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258 | max_zc = max(zc) |
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259 | min_zc = min(zc) |
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260 | delta_zc = max_zc-min_zc |
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261 | upper_limit = max_zc + delta_zc*acceptable_overshoot |
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262 | lower_limit = min_zc - delta_zc*acceptable_overshoot |
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263 | |
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264 | |
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265 | if max(zeta) > upper_limit or min(zeta) < lower_limit: |
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266 | msg = 'Least sqares produced values outside the allowed ' |
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267 | msg += 'range [%f, %f].\n' %(lower_limit, upper_limit) |
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268 | msg += 'z in [%f, %f], zeta in [%f, %f].\n' %(min_zc, max_zc, |
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269 | min(zeta), max(zeta)) |
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270 | msg += 'If greater range is needed, increase the value of ' |
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271 | msg += 'acceptable_fit_overshoot (currently %.2f).\n' %(acceptable_overshoot) |
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272 | |
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273 | |
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274 | offending_vertices = (zeta > upper_limit or zeta < lower_limit) |
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275 | Xi_c = compress(offending_vertices, Xi) |
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276 | Eta_c = compress(offending_vertices, Eta) |
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277 | offending_coordinates = concatenate((Xi_c[:, NewAxis], |
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278 | Eta_c[:, NewAxis]), |
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279 | axis=1) |
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280 | |
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281 | msg += 'Offending locations:\n %s' %(offending_coordinates) |
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282 | |
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283 | raise FittingError, msg |
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284 | |
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285 | |
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286 | |
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287 | if verbose: |
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288 | print '+------------------------------------------------' |
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289 | print 'Least squares statistics' |
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290 | print '+------------------------------------------------' |
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291 | print 'points: %d points' %(len(z)) |
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292 | print ' x in [%f, %f]'%(min(X), max(X)) |
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293 | print ' y in [%f, %f]'%(min(Y), max(Y)) |
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294 | print ' z in [%f, %f]'%(min(z), max(z)) |
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295 | print |
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296 | |
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297 | if indices is not None: |
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298 | print 'Cropped points: %d points' %(len(zc)) |
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299 | print ' x in [%f, %f]'%(min(Xc), max(Xc)) |
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300 | print ' y in [%f, %f]'%(min(Yc), max(Yc)) |
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301 | print ' z in [%f, %f]'%(min(zc), max(zc)) |
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302 | print |
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303 | |
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304 | |
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305 | print 'Mesh: %d vertices' %(len(zeta)) |
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306 | print ' xi in [%f, %f]'%(min(Xi), max(Xi)) |
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307 | print ' eta in [%f, %f]'%(min(Eta), max(Eta)) |
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308 | print ' zeta in [%f, %f]'%(min(zeta), max(zeta)) |
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309 | print '+------------------------------------------------' |
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310 | |
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311 | return vertex_attributes |
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312 | |
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313 | |
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314 | |
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315 | def pts2rectangular(pts_name, M, N, alpha = DEFAULT_ALPHA, |
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316 | verbose = False, reduction = 1): |
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317 | """Fits attributes from pts file to MxN rectangular mesh |
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318 | |
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319 | Read pts file and create rectangular mesh of resolution MxN such that |
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320 | it covers all points specified in pts file. |
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321 | |
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322 | FIXME: This may be a temporary function until we decide on |
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323 | netcdf formats etc |
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324 | |
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325 | FIXME: Uses elevation hardwired |
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326 | """ |
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327 | |
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328 | import mesh_factory |
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329 | from load_mesh.loadASCII import import_points_file |
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330 | |
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331 | if verbose: print 'Read pts' |
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332 | points_dict = import_points_file(pts_name) |
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333 | #points, attributes = util.read_xya(pts_name) |
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334 | |
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335 | #Reduce number of points a bit |
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336 | points = points_dict['pointlist'][::reduction] |
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337 | elevation = points_dict['attributelist']['elevation'] #Must be elevation |
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338 | elevation = elevation[::reduction] |
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339 | |
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340 | if verbose: print 'Got %d data points' %len(points) |
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341 | |
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342 | if verbose: print 'Create mesh' |
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343 | #Find extent |
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344 | max_x = min_x = points[0][0] |
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345 | max_y = min_y = points[0][1] |
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346 | for point in points[1:]: |
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347 | x = point[0] |
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348 | if x > max_x: max_x = x |
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349 | if x < min_x: min_x = x |
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350 | y = point[1] |
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351 | if y > max_y: max_y = y |
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352 | if y < min_y: min_y = y |
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353 | |
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354 | #Create appropriate mesh |
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355 | vertex_coordinates, triangles, boundary =\ |
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356 | mesh_factory.rectangular(M, N, max_x-min_x, max_y-min_y, |
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357 | (min_x, min_y)) |
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358 | |
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359 | #Fit attributes to mesh |
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360 | vertex_attributes = fit_to_mesh(vertex_coordinates, |
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361 | triangles, |
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362 | points, |
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363 | elevation, alpha=alpha, verbose=verbose) |
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364 | |
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365 | |
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366 | |
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367 | return vertex_coordinates, triangles, boundary, vertex_attributes |
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368 | |
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369 | |
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370 | def _interpolation(*args, **kwargs): |
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371 | """Private function for use with caching. Reason is that classes |
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372 | may change their byte code between runs which is annoying. |
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373 | """ |
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374 | |
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375 | return Interpolation(*args, **kwargs) |
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376 | |
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377 | |
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378 | class Interpolation: |
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379 | |
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380 | def __init__(self, |
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381 | vertex_coordinates, |
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382 | triangles, |
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383 | point_coordinates = None, |
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384 | alpha = None, |
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385 | verbose = False, |
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386 | expand_search = True, |
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387 | interp_only = False, |
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388 | max_points_per_cell = 30, |
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389 | mesh_origin = None, |
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390 | data_origin = None, |
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391 | precrop = False): |
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392 | |
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393 | |
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394 | """ Build interpolation matrix mapping from |
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395 | function values at vertices to function values at data points |
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396 | |
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397 | Inputs: |
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398 | |
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399 | vertex_coordinates: List of coordinate pairs [xi, eta] of |
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400 | points constituting mesh (or a an m x 2 Numeric array) |
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401 | Points may appear multiple times |
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402 | (e.g. if vertices have discontinuities) |
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403 | |
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404 | triangles: List of 3-tuples (or a Numeric array) of |
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405 | integers representing indices of all vertices in the mesh. |
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406 | |
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407 | point_coordinates: List of coordinate pairs [x, y] of |
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408 | data points (or an nx2 Numeric array) |
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409 | If point_coordinates is absent, only smoothing matrix will |
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410 | be built |
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411 | |
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412 | alpha: Smoothing parameter |
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413 | |
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414 | data_origin and mesh_origin are 3-tuples consisting of |
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415 | UTM zone, easting and northing. If specified |
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416 | point coordinates and vertex coordinates are assumed to be |
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417 | relative to their respective origins. |
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418 | |
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419 | """ |
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420 | #Convert input to Numeric arrays |
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421 | triangles = ensure_numeric(triangles, Int) |
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422 | vertex_coordinates = ensure_numeric(vertex_coordinates, Float) |
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423 | |
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424 | #Build underlying mesh |
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425 | if verbose: print 'Building mesh' |
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426 | #self.mesh = General_mesh(vertex_coordinates, triangles, |
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427 | #FIXME: Trying the normal mesh while testing precrop, |
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428 | # The functionality of boundary_polygon is needed for that |
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429 | |
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430 | #FIXME - geo ref does not have to go into mesh. |
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431 | # Change the point co-ords to conform to the |
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432 | # mesh co-ords early in the code |
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433 | if mesh_origin is None: |
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434 | geo = None |
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435 | else: |
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436 | geo = Geo_reference(mesh_origin[0],mesh_origin[1],mesh_origin[2]) |
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437 | |
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438 | |
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439 | self.mesh = Mesh(vertex_coordinates, triangles, |
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440 | geo_reference = geo) |
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441 | |
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442 | if verbose: print 'Checking mesh integrity' |
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443 | self.mesh.check_integrity() |
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444 | |
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445 | if verbose: print 'Mesh integrity checked' |
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446 | |
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447 | self.data_origin = data_origin |
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448 | |
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449 | self.point_indices = None |
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450 | |
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451 | #Smoothing parameter |
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452 | if alpha is None: |
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453 | self.alpha = DEFAULT_ALPHA |
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454 | else: |
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455 | self.alpha = alpha |
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456 | |
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457 | |
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458 | if point_coordinates is not None: |
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459 | if verbose: print 'Building interpolation matrix' |
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460 | self.build_interpolation_matrix_A(point_coordinates, |
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461 | verbose = verbose, |
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462 | expand_search = expand_search, |
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463 | interp_only = interp_only, |
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464 | max_points_per_cell =\ |
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465 | max_points_per_cell, |
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466 | data_origin = data_origin, |
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467 | precrop = precrop) |
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468 | #Build coefficient matrices |
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469 | if interp_only == False: |
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470 | self.build_coefficient_matrix_B(point_coordinates, |
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471 | verbose = verbose, |
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472 | expand_search = expand_search, |
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473 | max_points_per_cell =\ |
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474 | max_points_per_cell, |
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475 | data_origin = data_origin, |
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476 | precrop = precrop) |
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477 | if verbose: print 'Finished interpolation' |
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478 | |
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479 | def set_point_coordinates(self, point_coordinates, |
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480 | data_origin = None, |
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481 | verbose = False, |
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482 | precrop = True): |
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483 | """ |
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484 | A public interface to setting the point co-ordinates. |
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485 | """ |
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486 | if point_coordinates is not None: |
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487 | if verbose: print 'Building interpolation matrix' |
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488 | self.build_interpolation_matrix_A(point_coordinates, |
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489 | verbose = verbose, |
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490 | data_origin = data_origin, |
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491 | precrop = precrop) |
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492 | self.build_coefficient_matrix_B(point_coordinates, data_origin) |
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493 | |
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494 | def build_coefficient_matrix_B(self, point_coordinates=None, |
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495 | verbose = False, expand_search = True, |
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496 | max_points_per_cell=30, |
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497 | data_origin = None, |
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498 | precrop = False): |
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499 | """Build final coefficient matrix""" |
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500 | |
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501 | |
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502 | if self.alpha <> 0: |
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503 | if verbose: print 'Building smoothing matrix' |
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504 | self.build_smoothing_matrix_D() |
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505 | |
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506 | if point_coordinates is not None: |
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507 | if self.alpha <> 0: |
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508 | self.B = self.AtA + self.alpha*self.D |
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509 | else: |
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510 | self.B = self.AtA |
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511 | |
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512 | #Convert self.B matrix to CSR format for faster matrix vector |
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513 | self.B = Sparse_CSR(self.B) |
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514 | |
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515 | def build_interpolation_matrix_A(self, point_coordinates, |
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516 | verbose = False, expand_search = True, |
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517 | max_points_per_cell=30, |
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518 | data_origin = None, |
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519 | precrop = False, |
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520 | interp_only = False): |
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521 | """Build n x m interpolation matrix, where |
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522 | n is the number of data points and |
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523 | m is the number of basis functions phi_k (one per vertex) |
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524 | |
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525 | This algorithm uses a quad tree data structure for fast binning of data points |
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526 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
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527 | If specified coordinates are assumed to be relative to this origin. |
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528 | |
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529 | This one will override any data_origin that may be specified in |
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530 | interpolation instance |
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531 | |
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532 | """ |
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533 | |
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534 | |
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535 | |
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536 | #FIXME (Ole): Check that this function is memeory efficient. |
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537 | #6 million datapoints and 300000 basis functions |
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538 | #causes out-of-memory situation |
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539 | #First thing to check is whether there is room for self.A and self.AtA |
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540 | # |
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541 | #Maybe we need some sort of blocking |
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542 | |
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543 | from anuga.abstract_2d_finite_volumes.quad import build_quadtree |
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544 | from anuga.utilities.polygon import inside_polygon |
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545 | |
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546 | |
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547 | if data_origin is None: |
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548 | data_origin = self.data_origin #Use the one from |
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549 | #interpolation instance |
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550 | |
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551 | #Convert input to Numeric arrays just in case. |
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552 | point_coordinates = ensure_numeric(point_coordinates, Float) |
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553 | |
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554 | #Keep track of discarded points (if any). |
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555 | #This is only registered if precrop is True |
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556 | self.cropped_points = False |
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557 | |
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558 | #Shift data points to same origin as mesh (if specified) |
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559 | |
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560 | #FIXME this will shift if there was no geo_ref. |
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561 | #But all this should be removed anyhow. |
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562 | #change coords before this point |
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563 | mesh_origin = self.mesh.geo_reference.get_origin() |
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564 | if point_coordinates is not None: |
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565 | if data_origin is not None: |
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566 | if mesh_origin is not None: |
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567 | |
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568 | #Transformation: |
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569 | # |
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570 | #Let x_0 be the reference point of the point coordinates |
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571 | #and xi_0 the reference point of the mesh. |
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572 | # |
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573 | #A point coordinate (x + x_0) is then made relative |
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574 | #to xi_0 by |
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575 | # |
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576 | # x_new = x + x_0 - xi_0 |
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577 | # |
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578 | #and similarly for eta |
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579 | |
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580 | x_offset = data_origin[1] - mesh_origin[1] |
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581 | y_offset = data_origin[2] - mesh_origin[2] |
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582 | else: #Shift back to a zero origin |
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583 | x_offset = data_origin[1] |
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584 | y_offset = data_origin[2] |
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585 | |
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586 | point_coordinates[:,0] += x_offset |
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587 | point_coordinates[:,1] += y_offset |
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588 | else: |
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589 | if mesh_origin is not None: |
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590 | #Use mesh origin for data points |
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591 | point_coordinates[:,0] -= mesh_origin[1] |
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592 | point_coordinates[:,1] -= mesh_origin[2] |
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593 | |
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594 | |
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595 | |
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596 | #Remove points falling outside mesh boundary |
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597 | #This reduced one example from 1356 seconds to 825 seconds |
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598 | |
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599 | |
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600 | if precrop is True: |
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601 | from Numeric import take |
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602 | |
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603 | if verbose: print 'Getting boundary polygon' |
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604 | P = self.mesh.get_boundary_polygon() |
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605 | |
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606 | if verbose: print 'Getting indices inside mesh boundary' |
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607 | indices = inside_polygon(point_coordinates, P, verbose = verbose) |
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608 | |
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609 | |
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610 | if len(indices) != point_coordinates.shape[0]: |
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611 | self.cropped_points = True |
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612 | if verbose: |
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613 | print 'Done - %d points outside mesh have been cropped.'\ |
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614 | %(point_coordinates.shape[0] - len(indices)) |
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615 | |
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616 | point_coordinates = take(point_coordinates, indices) |
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617 | self.point_indices = indices |
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618 | |
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619 | |
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620 | |
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621 | |
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622 | #Build n x m interpolation matrix |
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623 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
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624 | n = point_coordinates.shape[0] #Nbr of data points |
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625 | |
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626 | if verbose: print 'Number of datapoints: %d' %n |
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627 | if verbose: print 'Number of basis functions: %d' %m |
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628 | |
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629 | #FIXME (Ole): We should use CSR here since mat-mat mult is now OK. |
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630 | #However, Sparse_CSR does not have the same methods as Sparse yet |
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631 | #The tests will reveal what needs to be done |
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632 | |
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633 | # |
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634 | #self.A = Sparse_CSR(Sparse(n,m)) |
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635 | #self.AtA = Sparse_CSR(Sparse(m,m)) |
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636 | self.A = Sparse(n,m) |
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637 | self.AtA = Sparse(m,m) |
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638 | |
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639 | #Build quad tree of vertices (FIXME: Is this the right spot for that?) |
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640 | root = build_quadtree(self.mesh, |
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641 | max_points_per_cell = max_points_per_cell) |
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642 | #root.show() |
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643 | self.expanded_quad_searches = [] |
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644 | #Compute matrix elements |
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645 | for i in range(n): |
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646 | #For each data_coordinate point |
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647 | |
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648 | if verbose and i%((n+10)/10)==0: print 'Doing %d of %d' %(i, n) |
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649 | x = point_coordinates[i] |
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650 | |
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651 | #Find vertices near x |
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652 | candidate_vertices = root.search(x[0], x[1]) |
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653 | is_more_elements = True |
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654 | |
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655 | |
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656 | element_found, sigma0, sigma1, sigma2, k = \ |
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657 | self.search_triangles_of_vertices(candidate_vertices, x) |
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658 | first_expansion = True |
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659 | while not element_found and is_more_elements and expand_search: |
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660 | #if verbose: print 'Expanding search' |
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661 | if first_expansion == True: |
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662 | self.expanded_quad_searches.append(1) |
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663 | first_expansion = False |
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664 | else: |
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665 | end = len(self.expanded_quad_searches) - 1 |
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666 | assert end >= 0 |
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667 | self.expanded_quad_searches[end] += 1 |
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668 | candidate_vertices, branch = root.expand_search() |
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669 | if branch == []: |
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670 | # Searching all the verts from the root cell that haven't |
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671 | # been searched. This is the last try |
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672 | element_found, sigma0, sigma1, sigma2, k = \ |
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673 | self.search_triangles_of_vertices(candidate_vertices, x) |
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674 | is_more_elements = False |
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675 | else: |
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676 | element_found, sigma0, sigma1, sigma2, k = \ |
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677 | self.search_triangles_of_vertices(candidate_vertices, x) |
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678 | |
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679 | |
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680 | #Update interpolation matrix A if necessary |
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681 | if element_found is True: |
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682 | #Assign values to matrix A |
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683 | |
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684 | j0 = self.mesh.triangles[k,0] #Global vertex id for sigma0 |
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685 | j1 = self.mesh.triangles[k,1] #Global vertex id for sigma1 |
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686 | j2 = self.mesh.triangles[k,2] #Global vertex id for sigma2 |
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687 | |
---|
688 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
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689 | js = [j0,j1,j2] |
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690 | |
---|
691 | for j in js: |
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692 | self.A[i,j] = sigmas[j] |
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693 | for k in js: |
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694 | if interp_only == False: |
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695 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
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696 | else: |
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697 | pass |
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698 | #Ok if there is no triangle for datapoint |
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699 | #(as in brute force version) |
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700 | #raise 'Could not find triangle for point', x |
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701 | |
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702 | |
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703 | |
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704 | def search_triangles_of_vertices(self, candidate_vertices, x): |
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705 | |
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706 | |
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707 | #Find triangle containing x: |
---|
708 | element_found = False |
---|
709 | |
---|
710 | # This will be returned if element_found = False |
---|
711 | sigma2 = -10.0 |
---|
712 | sigma0 = -10.0 |
---|
713 | sigma1 = -10.0 |
---|
714 | k = -10.0 |
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715 | #print "*$* candidate_vertices", candidate_vertices |
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716 | #For all vertices in same cell as point x |
---|
717 | for v in candidate_vertices: |
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718 | #FIXME (DSG-DSG): this catches verts with no triangle. |
---|
719 | #Currently pmesh is producing these. |
---|
720 | #this should be stopped, |
---|
721 | if self.mesh.vertexlist[v] is None: |
---|
722 | continue |
---|
723 | #for each triangle id (k) which has v as a vertex |
---|
724 | for k, _ in self.mesh.vertexlist[v]: |
---|
725 | |
---|
726 | #Get the three vertex_points of candidate triangle |
---|
727 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
728 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
729 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
730 | |
---|
731 | #print "PDSG - k", k |
---|
732 | #print "PDSG - xi0", xi0 |
---|
733 | #print "PDSG - xi1", xi1 |
---|
734 | #print "PDSG - xi2", xi2 |
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735 | #print "PDSG element %i verts((%f, %f),(%f, %f),(%f, %f))"\ |
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736 | # % (k, xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1]) |
---|
737 | |
---|
738 | #Get the three normals |
---|
739 | n0 = self.mesh.get_normal(k, 0) |
---|
740 | n1 = self.mesh.get_normal(k, 1) |
---|
741 | n2 = self.mesh.get_normal(k, 2) |
---|
742 | |
---|
743 | |
---|
744 | #Compute interpolation |
---|
745 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
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746 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
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747 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
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748 | |
---|
749 | #print "PDSG - sigma0", sigma0 |
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750 | #print "PDSG - sigma1", sigma1 |
---|
751 | #print "PDSG - sigma2", sigma2 |
---|
752 | |
---|
753 | #FIXME: Maybe move out to test or something |
---|
754 | epsilon = 1.0e-6 |
---|
755 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
756 | |
---|
757 | #Check that this triangle contains the data point |
---|
758 | |
---|
759 | #Sigmas can get negative within |
---|
760 | #machine precision on some machines (e.g nautilus) |
---|
761 | #Hence the small eps |
---|
762 | eps = 1.0e-15 |
---|
763 | if sigma0 >= -eps and sigma1 >= -eps and sigma2 >= -eps: |
---|
764 | element_found = True |
---|
765 | break |
---|
766 | |
---|
767 | if element_found is True: |
---|
768 | #Don't look for any other triangle |
---|
769 | break |
---|
770 | return element_found, sigma0, sigma1, sigma2, k |
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771 | |
---|
772 | |
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773 | |
---|
774 | def build_interpolation_matrix_A_brute(self, point_coordinates): |
---|
775 | """Build n x m interpolation matrix, where |
---|
776 | n is the number of data points and |
---|
777 | m is the number of basis functions phi_k (one per vertex) |
---|
778 | |
---|
779 | This is the brute force which is too slow for large problems, |
---|
780 | but could be used for testing |
---|
781 | """ |
---|
782 | |
---|
783 | |
---|
784 | #Convert input to Numeric arrays |
---|
785 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
786 | |
---|
787 | #Build n x m interpolation matrix |
---|
788 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
789 | n = point_coordinates.shape[0] #Nbr of data points |
---|
790 | |
---|
791 | self.A = Sparse(n,m) |
---|
792 | self.AtA = Sparse(m,m) |
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793 | |
---|
794 | #Compute matrix elements |
---|
795 | for i in range(n): |
---|
796 | #For each data_coordinate point |
---|
797 | |
---|
798 | x = point_coordinates[i] |
---|
799 | element_found = False |
---|
800 | k = 0 |
---|
801 | while not element_found and k < len(self.mesh): |
---|
802 | #For each triangle (brute force) |
---|
803 | #FIXME: Real algorithm should only visit relevant triangles |
---|
804 | |
---|
805 | #Get the three vertex_points |
---|
806 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
807 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
808 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
809 | |
---|
810 | #Get the three normals |
---|
811 | n0 = self.mesh.get_normal(k, 0) |
---|
812 | n1 = self.mesh.get_normal(k, 1) |
---|
813 | n2 = self.mesh.get_normal(k, 2) |
---|
814 | |
---|
815 | #Compute interpolation |
---|
816 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
817 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
818 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
819 | |
---|
820 | #FIXME: Maybe move out to test or something |
---|
821 | epsilon = 1.0e-6 |
---|
822 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
823 | |
---|
824 | #Check that this triangle contains data point |
---|
825 | if sigma0 >= 0 and sigma1 >= 0 and sigma2 >= 0: |
---|
826 | element_found = True |
---|
827 | #Assign values to matrix A |
---|
828 | |
---|
829 | j0 = self.mesh.triangles[k,0] #Global vertex id |
---|
830 | #self.A[i, j0] = sigma0 |
---|
831 | |
---|
832 | j1 = self.mesh.triangles[k,1] #Global vertex id |
---|
833 | #self.A[i, j1] = sigma1 |
---|
834 | |
---|
835 | j2 = self.mesh.triangles[k,2] #Global vertex id |
---|
836 | #self.A[i, j2] = sigma2 |
---|
837 | |
---|
838 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
839 | js = [j0,j1,j2] |
---|
840 | |
---|
841 | for j in js: |
---|
842 | self.A[i,j] = sigmas[j] |
---|
843 | for k in js: |
---|
844 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
845 | k = k+1 |
---|
846 | |
---|
847 | |
---|
848 | |
---|
849 | def get_A(self): |
---|
850 | return self.A.todense() |
---|
851 | |
---|
852 | def get_B(self): |
---|
853 | return self.B.todense() |
---|
854 | |
---|
855 | def get_D(self): |
---|
856 | return self.D.todense() |
---|
857 | |
---|
858 | #FIXME: Remember to re-introduce the 1/n factor in the |
---|
859 | #interpolation term |
---|
860 | |
---|
861 | def build_smoothing_matrix_D(self): |
---|
862 | """Build m x m smoothing matrix, where |
---|
863 | m is the number of basis functions phi_k (one per vertex) |
---|
864 | |
---|
865 | The smoothing matrix is defined as |
---|
866 | |
---|
867 | D = D1 + D2 |
---|
868 | |
---|
869 | where |
---|
870 | |
---|
871 | [D1]_{k,l} = \int_\Omega |
---|
872 | \frac{\partial \phi_k}{\partial x} |
---|
873 | \frac{\partial \phi_l}{\partial x}\, |
---|
874 | dx dy |
---|
875 | |
---|
876 | [D2]_{k,l} = \int_\Omega |
---|
877 | \frac{\partial \phi_k}{\partial y} |
---|
878 | \frac{\partial \phi_l}{\partial y}\, |
---|
879 | dx dy |
---|
880 | |
---|
881 | |
---|
882 | The derivatives \frac{\partial \phi_k}{\partial x}, |
---|
883 | \frac{\partial \phi_k}{\partial x} for a particular triangle |
---|
884 | are obtained by computing the gradient a_k, b_k for basis function k |
---|
885 | """ |
---|
886 | |
---|
887 | #FIXME: algorithm might be optimised by computing local 9x9 |
---|
888 | #"element stiffness matrices: |
---|
889 | |
---|
890 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
891 | |
---|
892 | self.D = Sparse(m,m) |
---|
893 | |
---|
894 | #For each triangle compute contributions to D = D1+D2 |
---|
895 | for i in range(len(self.mesh)): |
---|
896 | |
---|
897 | #Get area |
---|
898 | area = self.mesh.areas[i] |
---|
899 | |
---|
900 | #Get global vertex indices |
---|
901 | v0 = self.mesh.triangles[i,0] |
---|
902 | v1 = self.mesh.triangles[i,1] |
---|
903 | v2 = self.mesh.triangles[i,2] |
---|
904 | |
---|
905 | #Get the three vertex_points |
---|
906 | xi0 = self.mesh.get_vertex_coordinate(i, 0) |
---|
907 | xi1 = self.mesh.get_vertex_coordinate(i, 1) |
---|
908 | xi2 = self.mesh.get_vertex_coordinate(i, 2) |
---|
909 | |
---|
910 | #Compute gradients for each vertex |
---|
911 | a0, b0 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
912 | 1, 0, 0) |
---|
913 | |
---|
914 | a1, b1 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
915 | 0, 1, 0) |
---|
916 | |
---|
917 | a2, b2 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
918 | 0, 0, 1) |
---|
919 | |
---|
920 | #Compute diagonal contributions |
---|
921 | self.D[v0,v0] += (a0*a0 + b0*b0)*area |
---|
922 | self.D[v1,v1] += (a1*a1 + b1*b1)*area |
---|
923 | self.D[v2,v2] += (a2*a2 + b2*b2)*area |
---|
924 | |
---|
925 | #Compute contributions for basis functions sharing edges |
---|
926 | e01 = (a0*a1 + b0*b1)*area |
---|
927 | self.D[v0,v1] += e01 |
---|
928 | self.D[v1,v0] += e01 |
---|
929 | |
---|
930 | e12 = (a1*a2 + b1*b2)*area |
---|
931 | self.D[v1,v2] += e12 |
---|
932 | self.D[v2,v1] += e12 |
---|
933 | |
---|
934 | e20 = (a2*a0 + b2*b0)*area |
---|
935 | self.D[v2,v0] += e20 |
---|
936 | self.D[v0,v2] += e20 |
---|
937 | |
---|
938 | |
---|
939 | def fit(self, z): |
---|
940 | """Fit a smooth surface to given 1d array of data points z. |
---|
941 | |
---|
942 | The smooth surface is computed at each vertex in the underlying |
---|
943 | mesh using the formula given in the module doc string. |
---|
944 | |
---|
945 | Pre Condition: |
---|
946 | self.A, self.AtA and self.B have been initialised |
---|
947 | |
---|
948 | Inputs: |
---|
949 | z: Single 1d vector or array of data at the point_coordinates. |
---|
950 | """ |
---|
951 | |
---|
952 | #Convert input to Numeric arrays |
---|
953 | z = ensure_numeric(z, Float) |
---|
954 | |
---|
955 | if len(z.shape) > 1 : |
---|
956 | raise VectorShapeError, 'Can only deal with 1d data vector' |
---|
957 | |
---|
958 | if self.point_indices is not None: |
---|
959 | #Remove values for any points that were outside mesh |
---|
960 | z = take(z, self.point_indices) |
---|
961 | |
---|
962 | #Compute right hand side based on data |
---|
963 | #FIXME (DSG-DsG): could Sparse_CSR be used here? Use this format |
---|
964 | # after a matrix is built, before calcs. |
---|
965 | Atz = self.A.trans_mult(z) |
---|
966 | |
---|
967 | |
---|
968 | #Check sanity |
---|
969 | n, m = self.A.shape |
---|
970 | if n<m and self.alpha == 0.0: |
---|
971 | msg = 'ERROR (least_squares): Too few data points\n' |
---|
972 | msg += 'There are only %d data points and alpha == 0. ' %n |
---|
973 | msg += 'Need at least %d\n' %m |
---|
974 | msg += 'Alternatively, set smoothing parameter alpha to a small ' |
---|
975 | msg += 'positive value,\ne.g. 1.0e-3.' |
---|
976 | raise Exception(msg) |
---|
977 | |
---|
978 | |
---|
979 | |
---|
980 | return conjugate_gradient(self.B, Atz, Atz, imax=2*len(Atz) ) |
---|
981 | #FIXME: Should we store the result here for later use? (ON) |
---|
982 | |
---|
983 | |
---|
984 | def fit_points(self, z, verbose=False): |
---|
985 | """Like fit, but more robust when each point has two or more attributes |
---|
986 | FIXME (Ole): The name fit_points doesn't carry any meaning |
---|
987 | for me. How about something like fit_multiple or fit_columns? |
---|
988 | """ |
---|
989 | |
---|
990 | try: |
---|
991 | if verbose: print 'Solving penalised least_squares problem' |
---|
992 | return self.fit(z) |
---|
993 | except VectorShapeError, e: |
---|
994 | # broadcasting is not supported. |
---|
995 | |
---|
996 | #Convert input to Numeric arrays |
---|
997 | z = ensure_numeric(z, Float) |
---|
998 | |
---|
999 | #Build n x m interpolation matrix |
---|
1000 | m = self.mesh.coordinates.shape[0] #Number of vertices |
---|
1001 | n = z.shape[1] #Number of data points |
---|
1002 | |
---|
1003 | f = zeros((m,n), Float) #Resulting columns |
---|
1004 | |
---|
1005 | for i in range(z.shape[1]): |
---|
1006 | f[:,i] = self.fit(z[:,i]) |
---|
1007 | |
---|
1008 | return f |
---|
1009 | |
---|
1010 | |
---|
1011 | def interpolate(self, f): |
---|
1012 | """Evaluate smooth surface f at data points implied in self.A. |
---|
1013 | |
---|
1014 | The mesh values representing a smooth surface are |
---|
1015 | assumed to be specified in f. This argument could, |
---|
1016 | for example have been obtained from the method self.fit() |
---|
1017 | |
---|
1018 | Pre Condition: |
---|
1019 | self.A has been initialised |
---|
1020 | |
---|
1021 | Inputs: |
---|
1022 | f: Vector or array of data at the mesh vertices. |
---|
1023 | If f is an array, interpolation will be done for each column as |
---|
1024 | per underlying matrix-matrix multiplication |
---|
1025 | |
---|
1026 | Output: |
---|
1027 | Interpolated values at data points implied in self.A |
---|
1028 | |
---|
1029 | """ |
---|
1030 | print "obsolete in least_squares, use fit_interpolate.interpolate" |
---|
1031 | return self.A * f |
---|
1032 | |
---|
1033 | def cull_outsiders(self, f): |
---|
1034 | pass |
---|
1035 | |
---|
1036 | |
---|
1037 | |
---|
1038 | |
---|
1039 | class Interpolation_function: |
---|
1040 | """Interpolation_function - creates callable object f(t, id) or f(t,x,y) |
---|
1041 | which is interpolated from time series defined at vertices of |
---|
1042 | triangular mesh (such as those stored in sww files) |
---|
1043 | |
---|
1044 | Let m be the number of vertices, n the number of triangles |
---|
1045 | and p the number of timesteps. |
---|
1046 | |
---|
1047 | Mandatory input |
---|
1048 | time: px1 array of monotonously increasing times (Float) |
---|
1049 | quantities: Dictionary of arrays or 1 array (Float) |
---|
1050 | The arrays must either have dimensions pxm or mx1. |
---|
1051 | The resulting function will be time dependent in |
---|
1052 | the former case while it will be constant with |
---|
1053 | respect to time in the latter case. |
---|
1054 | |
---|
1055 | Optional input: |
---|
1056 | quantity_names: List of keys into the quantities dictionary |
---|
1057 | vertex_coordinates: mx2 array of coordinates (Float) |
---|
1058 | triangles: nx3 array of indices into vertex_coordinates (Int) |
---|
1059 | interpolation_points: Nx2 array of coordinates to be interpolated to |
---|
1060 | verbose: Level of reporting |
---|
1061 | |
---|
1062 | |
---|
1063 | The quantities returned by the callable object are specified by |
---|
1064 | the list quantities which must contain the names of the |
---|
1065 | quantities to be returned and also reflect the order, e.g. for |
---|
1066 | the shallow water wave equation, on would have |
---|
1067 | quantities = ['stage', 'xmomentum', 'ymomentum'] |
---|
1068 | |
---|
1069 | The parameter interpolation_points decides at which points interpolated |
---|
1070 | quantities are to be computed whenever object is called. |
---|
1071 | If None, return average value |
---|
1072 | """ |
---|
1073 | |
---|
1074 | |
---|
1075 | |
---|
1076 | def __init__(self, |
---|
1077 | time, |
---|
1078 | quantities, |
---|
1079 | quantity_names = None, |
---|
1080 | vertex_coordinates = None, |
---|
1081 | triangles = None, |
---|
1082 | interpolation_points = None, |
---|
1083 | verbose = False): |
---|
1084 | """Initialise object and build spatial interpolation if required |
---|
1085 | """ |
---|
1086 | |
---|
1087 | from Numeric import array, zeros, Float, alltrue, concatenate,\ |
---|
1088 | reshape, ArrayType |
---|
1089 | |
---|
1090 | |
---|
1091 | from anuga.config import time_format |
---|
1092 | import types |
---|
1093 | |
---|
1094 | |
---|
1095 | |
---|
1096 | #Check temporal info |
---|
1097 | time = ensure_numeric(time) |
---|
1098 | msg = 'Time must be a monotonuosly ' |
---|
1099 | msg += 'increasing sequence %s' %time |
---|
1100 | assert alltrue(time[1:] - time[:-1] >= 0 ), msg |
---|
1101 | |
---|
1102 | |
---|
1103 | #Check if quantities is a single array only |
---|
1104 | if type(quantities) != types.DictType: |
---|
1105 | quantities = ensure_numeric(quantities) |
---|
1106 | quantity_names = ['Attribute'] |
---|
1107 | |
---|
1108 | #Make it a dictionary |
---|
1109 | quantities = {quantity_names[0]: quantities} |
---|
1110 | |
---|
1111 | |
---|
1112 | #Use keys if no names are specified |
---|
1113 | if quantity_names is None: |
---|
1114 | quantity_names = quantities.keys() |
---|
1115 | |
---|
1116 | |
---|
1117 | #Check spatial info |
---|
1118 | if vertex_coordinates is None: |
---|
1119 | self.spatial = False |
---|
1120 | else: |
---|
1121 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
---|
1122 | |
---|
1123 | assert triangles is not None, 'Triangles array must be specified' |
---|
1124 | triangles = ensure_numeric(triangles) |
---|
1125 | self.spatial = True |
---|
1126 | |
---|
1127 | |
---|
1128 | |
---|
1129 | #Save for use with statistics |
---|
1130 | self.quantity_names = quantity_names |
---|
1131 | self.quantities = quantities |
---|
1132 | self.vertex_coordinates = vertex_coordinates |
---|
1133 | self.interpolation_points = interpolation_points |
---|
1134 | self.time = time[:] # Time assumed to be relative to starttime |
---|
1135 | self.index = 0 # Initial time index |
---|
1136 | self.precomputed_values = {} |
---|
1137 | |
---|
1138 | |
---|
1139 | |
---|
1140 | #Precomputed spatial interpolation if requested |
---|
1141 | if interpolation_points is not None: |
---|
1142 | if self.spatial is False: |
---|
1143 | raise 'Triangles and vertex_coordinates must be specified' |
---|
1144 | |
---|
1145 | try: |
---|
1146 | self.interpolation_points = ensure_numeric(interpolation_points) |
---|
1147 | except: |
---|
1148 | msg = 'Interpolation points must be an N x 2 Numeric array '+\ |
---|
1149 | 'or a list of points\n' |
---|
1150 | msg += 'I got: %s.' %(str(self.interpolation_points)[:60] +\ |
---|
1151 | '...') |
---|
1152 | raise msg |
---|
1153 | |
---|
1154 | |
---|
1155 | m = len(self.interpolation_points) |
---|
1156 | p = len(self.time) |
---|
1157 | |
---|
1158 | for name in quantity_names: |
---|
1159 | self.precomputed_values[name] = zeros((p, m), Float) |
---|
1160 | |
---|
1161 | #Build interpolator |
---|
1162 | interpol = Interpolation(vertex_coordinates, |
---|
1163 | triangles, |
---|
1164 | point_coordinates = \ |
---|
1165 | self.interpolation_points, |
---|
1166 | alpha = 0, |
---|
1167 | precrop = False, |
---|
1168 | verbose = verbose) |
---|
1169 | |
---|
1170 | if verbose: print 'Interpolate' |
---|
1171 | for i, t in enumerate(self.time): |
---|
1172 | #Interpolate quantities at this timestep |
---|
1173 | if verbose and i%((p+10)/10)==0: |
---|
1174 | print ' time step %d of %d' %(i, p) |
---|
1175 | |
---|
1176 | for name in quantity_names: |
---|
1177 | if len(quantities[name].shape) == 2: |
---|
1178 | result = interpol.interpolate(quantities[name][i,:]) |
---|
1179 | else: |
---|
1180 | #Assume no time dependency |
---|
1181 | result = interpol.interpolate(quantities[name][:]) |
---|
1182 | |
---|
1183 | self.precomputed_values[name][i, :] = result |
---|
1184 | |
---|
1185 | |
---|
1186 | |
---|
1187 | #Report |
---|
1188 | if verbose: |
---|
1189 | print self.statistics() |
---|
1190 | #self.print_statistics() |
---|
1191 | |
---|
1192 | else: |
---|
1193 | #Store quantitites as is |
---|
1194 | for name in quantity_names: |
---|
1195 | self.precomputed_values[name] = quantities[name] |
---|
1196 | |
---|
1197 | |
---|
1198 | #else: |
---|
1199 | # #Return an average, making this a time series |
---|
1200 | # for name in quantity_names: |
---|
1201 | # self.values[name] = zeros(len(self.time), Float) |
---|
1202 | # |
---|
1203 | # if verbose: print 'Compute mean values' |
---|
1204 | # for i, t in enumerate(self.time): |
---|
1205 | # if verbose: print ' time step %d of %d' %(i, len(self.time)) |
---|
1206 | # for name in quantity_names: |
---|
1207 | # self.values[name][i] = mean(quantities[name][i,:]) |
---|
1208 | |
---|
1209 | |
---|
1210 | |
---|
1211 | |
---|
1212 | def __repr__(self): |
---|
1213 | #return 'Interpolation function (spatio-temporal)' |
---|
1214 | return self.statistics() |
---|
1215 | |
---|
1216 | |
---|
1217 | def __call__(self, t, point_id = None, x = None, y = None): |
---|
1218 | """Evaluate f(t), f(t, point_id) or f(t, x, y) |
---|
1219 | |
---|
1220 | Inputs: |
---|
1221 | t: time - Model time. Must lie within existing timesteps |
---|
1222 | point_id: index of one of the preprocessed points. |
---|
1223 | x, y: Overrides location, point_id ignored |
---|
1224 | |
---|
1225 | If spatial info is present and all of x,y,point_id |
---|
1226 | are None an exception is raised |
---|
1227 | |
---|
1228 | If no spatial info is present, point_id and x,y arguments are ignored |
---|
1229 | making f a function of time only. |
---|
1230 | |
---|
1231 | |
---|
1232 | FIXME: point_id could also be a slice |
---|
1233 | FIXME: What if x and y are vectors? |
---|
1234 | FIXME: What about f(x,y) without t? |
---|
1235 | """ |
---|
1236 | |
---|
1237 | from math import pi, cos, sin, sqrt |
---|
1238 | from Numeric import zeros, Float |
---|
1239 | from anuga.utilities.numerical_tools import mean |
---|
1240 | |
---|
1241 | if self.spatial is True: |
---|
1242 | if point_id is None: |
---|
1243 | if x is None or y is None: |
---|
1244 | msg = 'Either point_id or x and y must be specified' |
---|
1245 | raise Exception(msg) |
---|
1246 | else: |
---|
1247 | if self.interpolation_points is None: |
---|
1248 | msg = 'Interpolation_function must be instantiated ' +\ |
---|
1249 | 'with a list of interpolation points before parameter ' +\ |
---|
1250 | 'point_id can be used' |
---|
1251 | raise Exception(msg) |
---|
1252 | |
---|
1253 | |
---|
1254 | msg = 'Time interval [%s:%s]' %(self.time[0], self.time[-1]) |
---|
1255 | msg += ' does not match model time: %s\n' %t |
---|
1256 | if t < self.time[0]: raise Exception(msg) |
---|
1257 | if t > self.time[-1]: raise Exception(msg) |
---|
1258 | |
---|
1259 | oldindex = self.index #Time index |
---|
1260 | |
---|
1261 | #Find current time slot |
---|
1262 | while t > self.time[self.index]: self.index += 1 |
---|
1263 | while t < self.time[self.index]: self.index -= 1 |
---|
1264 | |
---|
1265 | if t == self.time[self.index]: |
---|
1266 | #Protect against case where t == T[-1] (last time) |
---|
1267 | # - also works in general when t == T[i] |
---|
1268 | ratio = 0 |
---|
1269 | else: |
---|
1270 | #t is now between index and index+1 |
---|
1271 | ratio = (t - self.time[self.index])/\ |
---|
1272 | (self.time[self.index+1] - self.time[self.index]) |
---|
1273 | |
---|
1274 | #Compute interpolated values |
---|
1275 | q = zeros(len(self.quantity_names), Float) |
---|
1276 | |
---|
1277 | for i, name in enumerate(self.quantity_names): |
---|
1278 | Q = self.precomputed_values[name] |
---|
1279 | |
---|
1280 | if self.spatial is False: |
---|
1281 | #If there is no spatial info |
---|
1282 | assert len(Q.shape) == 1 |
---|
1283 | |
---|
1284 | Q0 = Q[self.index] |
---|
1285 | if ratio > 0: Q1 = Q[self.index+1] |
---|
1286 | |
---|
1287 | else: |
---|
1288 | if x is not None and y is not None: |
---|
1289 | #Interpolate to x, y |
---|
1290 | |
---|
1291 | raise 'x,y interpolation not yet implemented' |
---|
1292 | else: |
---|
1293 | #Use precomputed point |
---|
1294 | Q0 = Q[self.index, point_id] |
---|
1295 | if ratio > 0: Q1 = Q[self.index+1, point_id] |
---|
1296 | |
---|
1297 | #Linear temporal interpolation |
---|
1298 | if ratio > 0: |
---|
1299 | q[i] = Q0 + ratio*(Q1 - Q0) |
---|
1300 | else: |
---|
1301 | q[i] = Q0 |
---|
1302 | |
---|
1303 | |
---|
1304 | #Return vector of interpolated values |
---|
1305 | #if len(q) == 1: |
---|
1306 | # return q[0] |
---|
1307 | #else: |
---|
1308 | # return q |
---|
1309 | |
---|
1310 | |
---|
1311 | #Return vector of interpolated values |
---|
1312 | #FIXME: |
---|
1313 | if self.spatial is True: |
---|
1314 | return q |
---|
1315 | else: |
---|
1316 | #Replicate q according to x and y |
---|
1317 | #This is e.g used for Wind_stress |
---|
1318 | if x is None or y is None: |
---|
1319 | return q |
---|
1320 | else: |
---|
1321 | try: |
---|
1322 | N = len(x) |
---|
1323 | except: |
---|
1324 | return q |
---|
1325 | else: |
---|
1326 | from Numeric import ones, Float |
---|
1327 | #x is a vector - Create one constant column for each value |
---|
1328 | N = len(x) |
---|
1329 | assert len(y) == N, 'x and y must have same length' |
---|
1330 | res = [] |
---|
1331 | for col in q: |
---|
1332 | res.append(col*ones(N, Float)) |
---|
1333 | |
---|
1334 | return res |
---|
1335 | |
---|
1336 | def get_time(self): |
---|
1337 | """Return model time as a vector of timesteps |
---|
1338 | """ |
---|
1339 | return self.time |
---|
1340 | |
---|
1341 | |
---|
1342 | def statistics(self): |
---|
1343 | """Output statistics about interpolation_function |
---|
1344 | """ |
---|
1345 | |
---|
1346 | vertex_coordinates = self.vertex_coordinates |
---|
1347 | interpolation_points = self.interpolation_points |
---|
1348 | quantity_names = self.quantity_names |
---|
1349 | quantities = self.quantities |
---|
1350 | precomputed_values = self.precomputed_values |
---|
1351 | |
---|
1352 | x = vertex_coordinates[:,0] |
---|
1353 | y = vertex_coordinates[:,1] |
---|
1354 | |
---|
1355 | str = '------------------------------------------------\n' |
---|
1356 | str += 'Interpolation_function (spatio-temporal) statistics:\n' |
---|
1357 | str += ' Extent:\n' |
---|
1358 | str += ' x in [%f, %f], len(x) == %d\n'\ |
---|
1359 | %(min(x), max(x), len(x)) |
---|
1360 | str += ' y in [%f, %f], len(y) == %d\n'\ |
---|
1361 | %(min(y), max(y), len(y)) |
---|
1362 | str += ' t in [%f, %f], len(t) == %d\n'\ |
---|
1363 | %(min(self.time), max(self.time), len(self.time)) |
---|
1364 | str += ' Quantities:\n' |
---|
1365 | for name in quantity_names: |
---|
1366 | q = quantities[name][:].flat |
---|
1367 | str += ' %s in [%f, %f]\n' %(name, min(q), max(q)) |
---|
1368 | |
---|
1369 | if interpolation_points is not None: |
---|
1370 | str += ' Interpolation points (xi, eta):'\ |
---|
1371 | ' number of points == %d\n' %interpolation_points.shape[0] |
---|
1372 | str += ' xi in [%f, %f]\n' %(min(interpolation_points[:,0]), |
---|
1373 | max(interpolation_points[:,0])) |
---|
1374 | str += ' eta in [%f, %f]\n' %(min(interpolation_points[:,1]), |
---|
1375 | max(interpolation_points[:,1])) |
---|
1376 | str += ' Interpolated quantities (over all timesteps):\n' |
---|
1377 | |
---|
1378 | for name in quantity_names: |
---|
1379 | q = precomputed_values[name][:].flat |
---|
1380 | str += ' %s at interpolation points in [%f, %f]\n'\ |
---|
1381 | %(name, min(q), max(q)) |
---|
1382 | str += '------------------------------------------------\n' |
---|
1383 | |
---|
1384 | return str |
---|
1385 | |
---|
1386 | #FIXME: Delete |
---|
1387 | #print '------------------------------------------------' |
---|
1388 | #print 'Interpolation_function statistics:' |
---|
1389 | #print ' Extent:' |
---|
1390 | #print ' x in [%f, %f], len(x) == %d'\ |
---|
1391 | # %(min(x), max(x), len(x)) |
---|
1392 | #print ' y in [%f, %f], len(y) == %d'\ |
---|
1393 | # %(min(y), max(y), len(y)) |
---|
1394 | #print ' t in [%f, %f], len(t) == %d'\ |
---|
1395 | # %(min(self.time), max(self.time), len(self.time)) |
---|
1396 | #print ' Quantities:' |
---|
1397 | #for name in quantity_names: |
---|
1398 | # q = quantities[name][:].flat |
---|
1399 | # print ' %s in [%f, %f]' %(name, min(q), max(q)) |
---|
1400 | #print ' Interpolation points (xi, eta):'\ |
---|
1401 | # ' number of points == %d ' %interpolation_points.shape[0] |
---|
1402 | #print ' xi in [%f, %f]' %(min(interpolation_points[:,0]), |
---|
1403 | # max(interpolation_points[:,0])) |
---|
1404 | #print ' eta in [%f, %f]' %(min(interpolation_points[:,1]), |
---|
1405 | # max(interpolation_points[:,1])) |
---|
1406 | #print ' Interpolated quantities (over all timesteps):' |
---|
1407 | # |
---|
1408 | #for name in quantity_names: |
---|
1409 | # q = precomputed_values[name][:].flat |
---|
1410 | # print ' %s at interpolation points in [%f, %f]'\ |
---|
1411 | # %(name, min(q), max(q)) |
---|
1412 | #print '------------------------------------------------' |
---|
1413 | |
---|
1414 | |
---|
1415 | #------------------------------------------------------------- |
---|
1416 | if __name__ == "__main__": |
---|
1417 | """ |
---|
1418 | Load in a mesh and data points with attributes. |
---|
1419 | Fit the attributes to the mesh. |
---|
1420 | Save a new mesh file. |
---|
1421 | """ |
---|
1422 | import os, sys |
---|
1423 | usage = "usage: %s mesh_input.tsh point.xya mesh_output.tsh [expand|no_expand][vervose|non_verbose] [alpha] [display_errors|no_display_errors]"\ |
---|
1424 | %os.path.basename(sys.argv[0]) |
---|
1425 | |
---|
1426 | if len(sys.argv) < 4: |
---|
1427 | print usage |
---|
1428 | else: |
---|
1429 | mesh_file = sys.argv[1] |
---|
1430 | point_file = sys.argv[2] |
---|
1431 | mesh_output_file = sys.argv[3] |
---|
1432 | |
---|
1433 | expand_search = False |
---|
1434 | if len(sys.argv) > 4: |
---|
1435 | if sys.argv[4][0] == "e" or sys.argv[4][0] == "E": |
---|
1436 | expand_search = True |
---|
1437 | else: |
---|
1438 | expand_search = False |
---|
1439 | |
---|
1440 | verbose = False |
---|
1441 | if len(sys.argv) > 5: |
---|
1442 | if sys.argv[5][0] == "n" or sys.argv[5][0] == "N": |
---|
1443 | verbose = False |
---|
1444 | else: |
---|
1445 | verbose = True |
---|
1446 | |
---|
1447 | if len(sys.argv) > 6: |
---|
1448 | alpha = sys.argv[6] |
---|
1449 | else: |
---|
1450 | alpha = DEFAULT_ALPHA |
---|
1451 | |
---|
1452 | # This is used more for testing |
---|
1453 | if len(sys.argv) > 7: |
---|
1454 | if sys.argv[7][0] == "n" or sys.argv[5][0] == "N": |
---|
1455 | display_errors = False |
---|
1456 | else: |
---|
1457 | display_errors = True |
---|
1458 | |
---|
1459 | t0 = time.time() |
---|
1460 | try: |
---|
1461 | fit_to_mesh_file(mesh_file, |
---|
1462 | point_file, |
---|
1463 | mesh_output_file, |
---|
1464 | alpha, |
---|
1465 | verbose= verbose, |
---|
1466 | expand_search = expand_search, |
---|
1467 | display_errors = display_errors) |
---|
1468 | except IOError,e: |
---|
1469 | import sys; sys.exit(1) |
---|
1470 | |
---|
1471 | print 'That took %.2f seconds' %(time.time()-t0) |
---|
1472 | |
---|