1 | """Least squares interpolation. |
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2 | |
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3 | Implements a least-squares interpolation. |
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4 | Putting mesh data onto points. |
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5 | |
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6 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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7 | Geoscience Australia, 2004. |
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8 | |
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9 | DESIGN ISSUES |
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10 | * what variables should be global? |
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11 | - if there are no global vars functions can be moved around alot easier |
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12 | |
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13 | * The public interface to Interpolate |
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14 | __init__ |
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15 | interpolate |
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16 | interpolate_block |
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17 | |
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18 | """ |
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19 | |
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20 | import time |
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21 | import os |
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22 | from warnings import warn |
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23 | from math import sqrt |
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24 | from csv import writer, DictWriter |
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25 | |
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26 | from Numeric import zeros, array, Float, Int, dot, transpose, concatenate, \ |
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27 | ArrayType, allclose, take, NewAxis, arange |
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28 | |
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29 | from anuga.caching.caching import cache |
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30 | from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh |
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31 | from anuga.utilities.sparse import Sparse, Sparse_CSR |
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32 | from anuga.utilities.cg_solve import conjugate_gradient, VectorShapeError |
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33 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
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34 | from anuga.utilities.numerical_tools import ensure_numeric, mean, NAN |
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35 | from anuga.utilities.polygon import in_and_outside_polygon |
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36 | from anuga.geospatial_data.geospatial_data import Geospatial_data |
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37 | from anuga.geospatial_data.geospatial_data import ensure_absolute |
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38 | from anuga.fit_interpolate.search_functions import search_tree_of_vertices |
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39 | from anuga.fit_interpolate.general_fit_interpolate import FitInterpolate |
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40 | from anuga.abstract_2d_finite_volumes.util import file_function |
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41 | |
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42 | |
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43 | class Interpolate (FitInterpolate): |
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44 | |
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45 | def __init__(self, |
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46 | vertex_coordinates, |
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47 | triangles, |
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48 | mesh_origin=None, |
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49 | verbose=False, |
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50 | max_vertices_per_cell=None): |
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51 | |
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52 | |
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53 | """ Build interpolation matrix mapping from |
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54 | function values at vertices to function values at data points |
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55 | |
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56 | Inputs: |
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57 | |
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58 | vertex_coordinates: List of coordinate pairs [xi, eta] of |
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59 | points constituting a mesh (or an m x 2 Numeric array or |
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60 | a geospatial object) |
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61 | Points may appear multiple times |
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62 | (e.g. if vertices have discontinuities) |
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63 | |
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64 | triangles: List of 3-tuples (or a Numeric array) of |
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65 | integers representing indices of all vertices in the mesh. |
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66 | |
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67 | mesh_origin: A geo_reference object or 3-tuples consisting of |
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68 | UTM zone, easting and northing. |
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69 | If specified vertex coordinates are assumed to be |
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70 | relative to their respective origins. |
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71 | |
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72 | max_vertices_per_cell: Number of vertices in a quad tree cell |
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73 | at which the cell is split into 4. |
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74 | |
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75 | Note: Don't supply a vertex coords as a geospatial object and |
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76 | a mesh origin, since geospatial has its own mesh origin. |
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77 | """ |
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78 | |
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79 | # FIXME (Ole): Need an input check |
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80 | |
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81 | # Initialise variabels |
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82 | self._A_can_be_reused = False |
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83 | self._point_coordinates = None |
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84 | |
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85 | FitInterpolate.__init__(self, |
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86 | vertex_coordinates=vertex_coordinates, |
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87 | triangles=triangles, |
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88 | mesh_origin=mesh_origin, |
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89 | verbose=verbose, |
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90 | max_vertices_per_cell=max_vertices_per_cell) |
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91 | |
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92 | def interpolate_polyline(self, |
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93 | f, |
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94 | vertex_coordinates, |
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95 | gauge_neighbour_id, |
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96 | point_coordinates=None, |
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97 | verbose=False): |
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98 | """Interpolate linearly between values f on nodes (vertex coordinates) of a polyline to midpoints of triangles |
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99 | of boundary. |
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100 | |
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101 | f is the data on the polyline nodes. |
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102 | |
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103 | The mesh values representing a smooth surface are |
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104 | assumed to be specified in f. |
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105 | |
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106 | Inputs: |
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107 | f: Vector or array of data at the polyline nodes. |
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108 | If f is an array, interpolation will be done for each column as |
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109 | per underlying matrix-matrix multiplication |
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110 | point_coordinates: Interpolate polyline data to these positions. |
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111 | List of coordinate pairs [x, y] of |
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112 | data points or an nx2 Numeric array or a Geospatial_data object |
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113 | |
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114 | Output: |
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115 | Interpolated values at inputted points (z). |
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116 | """ |
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117 | |
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118 | |
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119 | # FIXME: There is an option of passing a tolerance into this |
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120 | |
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121 | if isinstance(point_coordinates, Geospatial_data): |
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122 | point_coordinates = point_coordinates.get_data_points( \ |
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123 | absolute = True) |
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124 | |
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125 | from utilities.polygon import point_on_line |
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126 | from Numeric import ones |
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127 | z=ones(len(point_coordinates),Float) |
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128 | |
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129 | msg='point coordinates are not given (interpolate.py)' |
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130 | assert point_coordinates is not None, msg |
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131 | msg='function value must be specified at every interpolation node' |
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132 | assert f.shape[0]==vertex_coordinates.shape[0], msg |
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133 | msg='Must define function value at one or more nodes' |
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134 | assert f.shape[0]>0, msg |
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135 | |
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136 | n=f.shape[0] |
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137 | if n==1: |
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138 | z=f*z |
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139 | msg = 'Polyline contained only one point. I need more. ', str(f) |
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140 | raise Exception, msg |
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141 | |
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142 | # FIXME (John): add unit test for only One vertex point. Exception should be thrown. |
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143 | |
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144 | |
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145 | elif n>1: |
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146 | for i in range(len(point_coordinates)): |
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147 | found = False |
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148 | for j in range(n): |
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149 | if gauge_neighbour_id[j]>=0: |
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150 | if point_on_line(point_coordinates[i], |
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151 | [vertex_coordinates[j], vertex_coordinates[gauge_neighbour_id[j]]], |
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152 | rtol=1.0e-6): |
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153 | found=True |
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154 | x0=vertex_coordinates[j][0] |
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155 | y0=vertex_coordinates[j][1] |
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156 | x1=vertex_coordinates[gauge_neighbour_id[j]][0] |
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157 | y1=vertex_coordinates[gauge_neighbour_id[j]][1] |
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158 | x2=point_coordinates[i][0] |
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159 | y2=point_coordinates[i][1] |
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160 | |
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161 | segment_len=sqrt((x1-x0)**2+(y1-y0)**2) |
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162 | dist=sqrt((x2-x0)**2+(y2-y0)**2) |
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163 | z[i]=(f[gauge_neighbour_id[j]]-f[j])/segment_len*dist+f[j] |
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164 | #print 'element found on segment' |
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165 | break |
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166 | |
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167 | if not found: |
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168 | z[i]=0.0 |
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169 | #print 'point not on urs boundary' |
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170 | return z |
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171 | |
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172 | # FIXME: What is a good start_blocking_len value? |
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173 | def interpolate(self, |
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174 | f, |
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175 | point_coordinates=None, |
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176 | start_blocking_len=500000, |
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177 | verbose=False): |
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178 | """Interpolate mesh data f to determine values, z, at points. |
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179 | |
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180 | f is the data on the mesh vertices. |
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181 | |
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182 | The mesh values representing a smooth surface are |
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183 | assumed to be specified in f. |
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184 | |
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185 | Inputs: |
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186 | f: Vector or array of data at the mesh vertices. |
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187 | If f is an array, interpolation will be done for each column as |
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188 | per underlying matrix-matrix multiplication |
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189 | point_coordinates: Interpolate mesh data to these positions. |
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190 | List of coordinate pairs [x, y] of |
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191 | data points or an nx2 Numeric array or a Geospatial_data object |
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192 | |
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193 | If point_coordinates is absent, the points inputted last time |
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194 | this method was called are used, if possible. |
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195 | start_blocking_len: If the # of points is more or greater than this, |
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196 | start blocking |
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197 | |
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198 | Output: |
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199 | Interpolated values at inputted points (z). |
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200 | """ |
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201 | |
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202 | # FIXME (Ole): Why is the interpolation matrix rebuilt everytime the |
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203 | # method is called even if interpolation points are unchanged. |
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204 | |
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205 | #print "point_coordinates interpolate.interpolate", point_coordinates |
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206 | if verbose: print 'Build intepolation object' |
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207 | if isinstance(point_coordinates, Geospatial_data): |
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208 | point_coordinates = point_coordinates.get_data_points( \ |
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209 | absolute = True) |
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210 | |
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211 | # Can I interpolate, based on previous point_coordinates? |
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212 | if point_coordinates is None: |
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213 | if self._A_can_be_reused is True and \ |
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214 | len(self._point_coordinates) < start_blocking_len: |
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215 | z = self._get_point_data_z(f, |
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216 | verbose=verbose) |
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217 | elif self._point_coordinates is not None: |
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218 | # if verbose, give warning |
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219 | if verbose: |
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220 | print 'WARNING: Recalculating A matrix, due to blocking.' |
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221 | point_coordinates = self._point_coordinates |
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222 | else: |
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223 | #There are no good point_coordinates. import sys; sys.exit() |
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224 | msg = 'ERROR (interpolate.py): No point_coordinates inputted' |
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225 | raise Exception(msg) |
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226 | |
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227 | if point_coordinates is not None: |
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228 | self._point_coordinates = point_coordinates |
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229 | if len(point_coordinates) < start_blocking_len or \ |
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230 | start_blocking_len == 0: |
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231 | self._A_can_be_reused = True |
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232 | z = self.interpolate_block(f, point_coordinates, |
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233 | verbose=verbose) |
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234 | else: |
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235 | #print 'BLOCKING' |
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236 | #Handle blocking |
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237 | self._A_can_be_reused = False |
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238 | start = 0 |
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239 | # creating a dummy array to concatenate to. |
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240 | |
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241 | f = ensure_numeric(f, Float) |
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242 | #print "f.shape",f.shape |
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243 | if len(f.shape) > 1: |
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244 | z = zeros((0,f.shape[1])) |
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245 | else: |
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246 | z = zeros((0,)) |
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247 | |
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248 | for end in range(start_blocking_len, |
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249 | len(point_coordinates), |
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250 | start_blocking_len): |
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251 | |
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252 | t = self.interpolate_block(f, point_coordinates[start:end], |
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253 | verbose=verbose) |
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254 | #print "t", t |
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255 | #print "z", z |
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256 | z = concatenate((z,t)) |
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257 | start = end |
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258 | |
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259 | end = len(point_coordinates) |
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260 | t = self.interpolate_block(f, point_coordinates[start:end], |
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261 | verbose=verbose) |
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262 | z = concatenate((z,t)) |
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263 | return z |
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264 | |
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265 | |
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266 | def interpolate_block(self, f, point_coordinates, verbose=False): |
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267 | """ |
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268 | Call this if you want to control the blocking or make sure blocking |
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269 | doesn't occur. |
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270 | |
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271 | Return the point data, z. |
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272 | |
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273 | See interpolate for doc info. |
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274 | """ |
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275 | if isinstance(point_coordinates,Geospatial_data): |
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276 | point_coordinates = point_coordinates.get_data_points(\ |
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277 | absolute=True) |
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278 | |
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279 | # Convert lists to Numeric arrays if necessary |
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280 | point_coordinates = ensure_numeric(point_coordinates, Float) |
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281 | f = ensure_numeric(f, Float) |
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282 | |
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283 | self._A = self._build_interpolation_matrix_A(point_coordinates, |
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284 | verbose=verbose) |
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285 | |
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286 | |
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287 | # Check that input dimensions are compatible |
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288 | msg = 'Two colums must be specified in point coordinates. I got shape=%s'\ |
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289 | %(str(point_coordinates.shape)) |
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290 | assert point_coordinates.shape[1] == 2, msg |
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291 | |
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292 | msg = 'The number of rows in matrix A must be the same as the number of points supplied.' |
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293 | msg += ' I got %d points and %d matrix rows.'\ |
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294 | %(point_coordinates.shape[0], self._A.shape[0]) |
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295 | assert point_coordinates.shape[0] == self._A.shape[0], msg |
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296 | |
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297 | msg = 'The number of columns in matrix A must be the same as the number of mesh vertices.' |
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298 | msg += ' I got %d vertices and %d matrix columns.'\ |
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299 | %(f.shape[0], self._A.shape[1]) |
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300 | assert self._A.shape[1] == f.shape[0], msg |
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301 | |
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302 | # Compute Matrix vector product and return |
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303 | return self._get_point_data_z(f) |
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304 | |
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305 | |
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306 | def _get_point_data_z(self, f, verbose=False): |
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307 | """ |
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308 | Return the point data, z. |
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309 | |
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310 | Precondition, |
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311 | The _A matrix has been created |
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312 | """ |
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313 | |
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314 | z = self._A * f |
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315 | # Taking into account points outside the mesh. |
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316 | #print "self.outside_poly_indices", self.outside_poly_indices |
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317 | #print "self.inside_poly_indices", self.inside_poly_indices |
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318 | #print "z", z |
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319 | for i in self.outside_poly_indices: |
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320 | z[i] = NAN |
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321 | return z |
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322 | |
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323 | def _build_interpolation_matrix_A(self, |
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324 | point_coordinates, |
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325 | verbose=False): |
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326 | """Build n x m interpolation matrix, where |
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327 | n is the number of data points and |
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328 | m is the number of basis functions phi_k (one per vertex) |
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329 | |
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330 | This algorithm uses a quad tree data structure for fast binning |
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331 | of data points |
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332 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
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333 | If specified coordinates are assumed to be relative to this origin. |
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334 | |
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335 | This one will override any data_origin that may be specified in |
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336 | instance interpolation |
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337 | |
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338 | Preconditions |
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339 | Point_coordindates and mesh vertices have the same origin. |
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340 | """ |
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341 | |
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342 | if verbose: print 'Building interpolation matrix' |
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343 | |
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344 | # Convert point_coordinates to Numeric arrays, in case it was a list. |
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345 | point_coordinates = ensure_numeric(point_coordinates, Float) |
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346 | |
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347 | |
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348 | if verbose: print 'Getting indices inside mesh boundary' |
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349 | self.inside_poly_indices, self.outside_poly_indices = \ |
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350 | in_and_outside_polygon(point_coordinates, |
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351 | self.mesh.get_boundary_polygon(), |
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352 | closed = True, verbose = verbose) |
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353 | |
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354 | #Build n x m interpolation matrix |
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355 | if verbose and len(self.outside_poly_indices) > 0: |
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356 | print '\n WARNING: Points outside mesh boundary. \n' |
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357 | # Since you can block, throw a warning, not an error. |
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358 | if verbose and 0 == len(self.inside_poly_indices): |
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359 | print '\n WARNING: No points within the mesh! \n' |
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360 | |
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361 | m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex) |
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362 | n = point_coordinates.shape[0] # Nbr of data points |
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363 | |
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364 | if verbose: print 'Number of datapoints: %d' %n |
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365 | if verbose: print 'Number of basis functions: %d' %m |
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366 | |
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367 | A = Sparse(n,m) |
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368 | |
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369 | n = len(self.inside_poly_indices) |
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370 | #Compute matrix elements for points inside the mesh |
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371 | if verbose: print 'Building interpolation matrix from %d points' %n |
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372 | for d, i in enumerate(self.inside_poly_indices): |
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373 | # For each data_coordinate point |
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374 | if verbose and d%((n+10)/10)==0: print 'Doing %d of %d' %(d, n) |
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375 | x = point_coordinates[i] |
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376 | element_found, sigma0, sigma1, sigma2, k = \ |
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377 | search_tree_of_vertices(self.root, self.mesh, x) |
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378 | |
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379 | # Update interpolation matrix A if necessary |
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380 | if element_found is True: |
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381 | # Assign values to matrix A |
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382 | |
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383 | j0 = self.mesh.triangles[k,0] # Global vertex id for sigma0 |
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384 | j1 = self.mesh.triangles[k,1] # Global vertex id for sigma1 |
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385 | j2 = self.mesh.triangles[k,2] # Global vertex id for sigma2 |
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386 | |
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387 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
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388 | js = [j0,j1,j2] |
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389 | |
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390 | for j in js: |
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391 | A[i,j] = sigmas[j] |
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392 | else: |
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393 | msg = 'Could not find triangle for point', x |
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394 | raise Exception(msg) |
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395 | return A |
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396 | |
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397 | def benchmark_interpolate(vertices, |
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398 | vertex_attributes, |
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399 | triangles, points, |
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400 | max_points_per_cell=None, |
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401 | start_blocking_len=500000, |
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402 | mesh_origin=None): |
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403 | """ |
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404 | points: Interpolate mesh data to these positions. |
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405 | List of coordinate pairs [x, y] of |
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406 | data points or an nx2 Numeric array or a Geospatial_data object |
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407 | |
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408 | No test for this yet. |
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409 | Note, this has no time the input data has no time dimension. Which is |
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410 | different from most of the data we interpolate, eg sww info. |
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411 | |
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412 | Output: |
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413 | Interpolated values at inputted points. |
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414 | """ |
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415 | interp = Interpolate(vertices, |
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416 | triangles, |
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417 | max_vertices_per_cell=max_points_per_cell, |
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418 | mesh_origin=mesh_origin) |
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419 | |
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420 | calc = interp.interpolate(vertex_attributes |
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421 | ,points |
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422 | ,start_blocking_len=start_blocking_len) |
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423 | #print "calc", calc |
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424 | |
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425 | def interpolate_sww2csv(sww_file, |
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426 | points, |
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427 | depth_file, |
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428 | velocity_x_file, |
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429 | velocity_y_file, |
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430 | stage_file=None, |
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431 | froude_file=None, |
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432 | #quantities = ['depth', 'velocity'], |
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433 | time_thinning=1, |
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434 | verbose=True, |
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435 | use_cache = True): |
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436 | """ |
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437 | Interpolate the quantities at a given set of locations, given |
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438 | an sww file. |
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439 | The results are written to csv files. |
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440 | |
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441 | sww_file is the input sww file. |
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442 | points is a list of the 'gauges' x,y location. |
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443 | depth_file is the name of the output depth file |
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444 | velocity_x_file is the name of the output x velocity file. |
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445 | velocity_y_file is the name of the output y velocity file. |
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446 | stage_file is the name of the output stage file. |
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447 | |
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448 | In the csv files columns represents the gauges and each row is a |
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449 | time slice. |
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450 | |
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451 | |
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452 | Time_thinning_number controls how many timesteps to use. Only |
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453 | timesteps with index%time_thinning_number == 0 will used, or |
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454 | in other words a value of 3, say, will cause the algorithm to |
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455 | use every third time step. |
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456 | |
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457 | In the future let points be a points file. |
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458 | And let the user choose the quantities. |
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459 | |
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460 | This is currently quite specific. |
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461 | If it is need to be more general, change things. |
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462 | |
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463 | """ |
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464 | quantities = ['stage', 'elevation', 'xmomentum', 'ymomentum'] |
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465 | #print "points",points |
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466 | points = ensure_absolute(points) |
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467 | point_count = len(points) |
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468 | callable_sww = file_function(sww_file, |
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469 | quantities=quantities, |
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470 | interpolation_points=points, |
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471 | verbose=verbose, |
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472 | time_thinning=time_thinning, |
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473 | use_cache=use_cache) |
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474 | |
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475 | depth_writer = writer(file(depth_file, "wb")) |
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476 | velocity_x_writer = writer(file(velocity_x_file, "wb")) |
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477 | velocity_y_writer = writer(file(velocity_y_file, "wb")) |
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478 | if stage_file is not None: |
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479 | stage_writer = writer(file(stage_file, "wb")) |
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480 | if froude_file is not None: |
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481 | froude_writer = writer(file(froude_file, "wb")) |
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482 | # Write heading |
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483 | heading = [str(x[0])+ ':' + str(x[1]) for x in points] |
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484 | heading.insert(0, "time") |
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485 | depth_writer.writerow(heading) |
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486 | velocity_x_writer.writerow(heading) |
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487 | velocity_y_writer.writerow(heading) |
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488 | if stage_file is not None: |
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489 | stage_writer.writerow(heading) |
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490 | if froude_file is not None: |
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491 | froude_writer.writerow(heading) |
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492 | |
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493 | for time in callable_sww.get_time(): |
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494 | depths = [time] |
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495 | velocity_xs = [time] |
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496 | velocity_ys = [time] |
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497 | if stage_file is not None: |
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498 | stages = [time] |
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499 | if froude_file is not None: |
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500 | froudes = [time] |
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501 | for point_i, point in enumerate(points): |
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502 | quantities = callable_sww(time,point_i) |
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503 | #print "quantities", quantities |
---|
504 | |
---|
505 | w = quantities[0] |
---|
506 | z = quantities[1] |
---|
507 | momentum_x = quantities[2] |
---|
508 | momentum_y = quantities[3] |
---|
509 | depth = w - z |
---|
510 | |
---|
511 | if w == NAN or z == NAN or momentum_x == NAN: |
---|
512 | velocity_x = NAN |
---|
513 | else: |
---|
514 | if depth > 1.e-30: # use epsilon |
---|
515 | velocity_x = momentum_x / depth #Absolute velocity |
---|
516 | else: |
---|
517 | velocity_x = 0 |
---|
518 | if w == NAN or z == NAN or momentum_y == NAN: |
---|
519 | velocity_y = NAN |
---|
520 | else: |
---|
521 | if depth > 1.e-30: # use epsilon |
---|
522 | velocity_y = momentum_y / depth #Absolute velocity |
---|
523 | else: |
---|
524 | velocity_y = 0 |
---|
525 | if depth < 1.e-30: # use epsilon |
---|
526 | froude = NAN |
---|
527 | else: |
---|
528 | froude = sqrt(velocity_x*velocity_x + velocity_y*velocity_y)/ \ |
---|
529 | sqrt(depth * 9.8066) # gravity m/s/s |
---|
530 | depths.append(depth) |
---|
531 | velocity_xs.append(velocity_x) |
---|
532 | velocity_ys.append(velocity_y) |
---|
533 | if stage_file is not None: |
---|
534 | stages.append(w) |
---|
535 | if froude_file is not None: |
---|
536 | froudes.append(froude) |
---|
537 | depth_writer.writerow(depths) |
---|
538 | velocity_x_writer.writerow(velocity_xs) |
---|
539 | velocity_y_writer.writerow(velocity_ys) |
---|
540 | if stage_file is not None: |
---|
541 | stage_writer.writerow(stages) |
---|
542 | if froude_file is not None: |
---|
543 | froude_writer.writerow(froudes) |
---|
544 | |
---|
545 | |
---|
546 | class Interpolation_function: |
---|
547 | """Interpolation_interface - creates callable object f(t, id) or f(t,x,y) |
---|
548 | which is interpolated from time series defined at vertices of |
---|
549 | triangular mesh (such as those stored in sww files) |
---|
550 | |
---|
551 | Let m be the number of vertices, n the number of triangles |
---|
552 | and p the number of timesteps. |
---|
553 | Also, let N be the number of interpolation points. |
---|
554 | |
---|
555 | Mandatory input |
---|
556 | time: px1 array of monotonously increasing times (Float) |
---|
557 | quantities: Dictionary of arrays or 1 array (Float) |
---|
558 | The arrays must either have dimensions pxm or mx1. |
---|
559 | The resulting function will be time dependent in |
---|
560 | the former case while it will be constant with |
---|
561 | respect to time in the latter case. |
---|
562 | |
---|
563 | Optional input: |
---|
564 | quantity_names: List of keys into the quantities dictionary for |
---|
565 | imposing a particular order on the output vector. |
---|
566 | vertex_coordinates: mx2 array of coordinates (Float) |
---|
567 | triangles: nx3 array of indices into vertex_coordinates (Int) |
---|
568 | interpolation_points: Nx2 array of coordinates to be interpolated to |
---|
569 | verbose: Level of reporting |
---|
570 | |
---|
571 | |
---|
572 | The quantities returned by the callable object are specified by |
---|
573 | the list quantities which must contain the names of the |
---|
574 | quantities to be returned and also reflect the order, e.g. for |
---|
575 | the shallow water wave equation, on would have |
---|
576 | quantities = ['stage', 'xmomentum', 'ymomentum'] |
---|
577 | |
---|
578 | The parameter interpolation_points decides at which points interpolated |
---|
579 | quantities are to be computed whenever object is called. |
---|
580 | If None, return average value |
---|
581 | |
---|
582 | FIXME (Ole): Need to allow vertex coordinates and interpolation points to be |
---|
583 | geospatial data objects |
---|
584 | |
---|
585 | Time assumed to be relative to starttime (FIXME (Ole): This comment should be removed) |
---|
586 | All coordinates assume origin of (0,0) - e.g. georeferencing must be taken care of |
---|
587 | outside this function |
---|
588 | """ |
---|
589 | |
---|
590 | |
---|
591 | def __init__(self, |
---|
592 | time, |
---|
593 | quantities, |
---|
594 | quantity_names=None, |
---|
595 | vertex_coordinates=None, |
---|
596 | triangles=None, |
---|
597 | interpolation_points=None, |
---|
598 | time_thinning=1, |
---|
599 | verbose=False, |
---|
600 | gauge_neighbour_id=None): |
---|
601 | """Initialise object and build spatial interpolation if required |
---|
602 | |
---|
603 | Time_thinning_number controls how many timesteps to use. Only timesteps with |
---|
604 | index%time_thinning_number == 0 will used, or in other words a value of 3, say, |
---|
605 | will cause the algorithm to use every third time step. |
---|
606 | """ |
---|
607 | |
---|
608 | from Numeric import array, zeros, Float, alltrue, concatenate,\ |
---|
609 | reshape, ArrayType |
---|
610 | |
---|
611 | |
---|
612 | from anuga.config import time_format |
---|
613 | import types |
---|
614 | |
---|
615 | |
---|
616 | # Check temporal info |
---|
617 | time = ensure_numeric(time) |
---|
618 | msg = 'Time must be a monotonuosly ' |
---|
619 | msg += 'increasing sequence %s' %time |
---|
620 | assert alltrue(time[1:] - time[:-1] >= 0 ), msg |
---|
621 | |
---|
622 | |
---|
623 | # Check if quantities is a single array only |
---|
624 | if type(quantities) != types.DictType: |
---|
625 | quantities = ensure_numeric(quantities) |
---|
626 | quantity_names = ['Attribute'] |
---|
627 | |
---|
628 | # Make it a dictionary |
---|
629 | quantities = {quantity_names[0]: quantities} |
---|
630 | |
---|
631 | |
---|
632 | # Use keys if no names are specified |
---|
633 | if quantity_names is None: |
---|
634 | quantity_names = quantities.keys() |
---|
635 | |
---|
636 | |
---|
637 | # Check spatial info |
---|
638 | if vertex_coordinates is None: |
---|
639 | self.spatial = False |
---|
640 | else: |
---|
641 | # FIXME (Ole): Try ensure_numeric here - |
---|
642 | #this function knows nothing about georefering. |
---|
643 | vertex_coordinates = ensure_absolute(vertex_coordinates) |
---|
644 | |
---|
645 | if triangles is not None: |
---|
646 | triangles = ensure_numeric(triangles) |
---|
647 | self.spatial = True |
---|
648 | |
---|
649 | # Thin timesteps if needed |
---|
650 | # Note array() is used to make the thinned arrays contiguous in memory |
---|
651 | self.time = array(time[::time_thinning]) |
---|
652 | for name in quantity_names: |
---|
653 | if len(quantities[name].shape) == 2: |
---|
654 | quantities[name] = array(quantities[name][::time_thinning,:]) |
---|
655 | |
---|
656 | # Save for use with statistics |
---|
657 | self.quantities_range = {} |
---|
658 | for name in quantity_names: |
---|
659 | q = quantities[name][:].flat |
---|
660 | self.quantities_range[name] = [min(q), max(q)] |
---|
661 | |
---|
662 | self.quantity_names = quantity_names |
---|
663 | self.vertex_coordinates = vertex_coordinates |
---|
664 | self.interpolation_points = interpolation_points |
---|
665 | |
---|
666 | |
---|
667 | self.index = 0 # Initial time index |
---|
668 | self.precomputed_values = {} |
---|
669 | |
---|
670 | |
---|
671 | # Precomputed spatial interpolation if requested |
---|
672 | if interpolation_points is not None: |
---|
673 | #no longer true. sts files have spatial = True but |
---|
674 | #if self.spatial is False: |
---|
675 | # raise 'Triangles and vertex_coordinates must be specified' |
---|
676 | # |
---|
677 | try: |
---|
678 | self.interpolation_points = interpolation_points = ensure_numeric(interpolation_points) |
---|
679 | except: |
---|
680 | msg = 'Interpolation points must be an N x 2 Numeric array '+\ |
---|
681 | 'or a list of points\n' |
---|
682 | msg += 'I got: %s.' %(str(self.interpolation_points)[:60] +\ |
---|
683 | '...') |
---|
684 | raise msg |
---|
685 | |
---|
686 | if triangles is not None and vertex_coordinates is not None: |
---|
687 | # Check that all interpolation points fall within |
---|
688 | # mesh boundary as defined by triangles and vertex_coordinates. |
---|
689 | from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh |
---|
690 | from anuga.utilities.polygon import outside_polygon |
---|
691 | |
---|
692 | # Create temporary mesh object from mesh info passed |
---|
693 | # into this function. |
---|
694 | mesh = Mesh(vertex_coordinates, triangles) |
---|
695 | mesh_boundary_polygon = mesh.get_boundary_polygon() |
---|
696 | |
---|
697 | |
---|
698 | indices = outside_polygon(interpolation_points, |
---|
699 | mesh_boundary_polygon) |
---|
700 | |
---|
701 | # Record result |
---|
702 | #self.mesh_boundary_polygon = mesh_boundary_polygon |
---|
703 | self.indices_outside_mesh = indices |
---|
704 | |
---|
705 | # Report |
---|
706 | if len(indices) > 0: |
---|
707 | msg = 'Interpolation points in Interpolation function fall ' |
---|
708 | msg += 'outside specified mesh. ' |
---|
709 | msg += 'Offending points:\n' |
---|
710 | out_interp_pts = [] |
---|
711 | for i in indices: |
---|
712 | msg += '%d: %s\n' %(i, interpolation_points[i]) |
---|
713 | out_interp_pts.append(ensure_numeric(interpolation_points[i])) |
---|
714 | |
---|
715 | if verbose is True: |
---|
716 | import sys |
---|
717 | if sys.platform == 'win32': |
---|
718 | from anuga.utilities.polygon import plot_polygons |
---|
719 | #out_interp_pts = take(interpolation_points,[indices]) |
---|
720 | title = 'Interpolation points fall outside specified mesh' |
---|
721 | plot_polygons([mesh_boundary_polygon,interpolation_points,out_interp_pts], |
---|
722 | ['line','point','outside'],figname='points_boundary_out',label=title,verbose=verbose) |
---|
723 | |
---|
724 | # Joaquim Luis suggested this as an Exception, so |
---|
725 | # that the user can now what the problem is rather than |
---|
726 | # looking for NaN's. However, NANs are handy as they can |
---|
727 | # be ignored leaving good points for continued processing. |
---|
728 | if verbose: |
---|
729 | print msg |
---|
730 | #raise Exception(msg) |
---|
731 | elif triangles is None and vertex_coordinates is not None:#jj |
---|
732 | #Dealing with sts file |
---|
733 | pass |
---|
734 | else: |
---|
735 | msg = 'Sww file function requires both triangles and vertex_coordinates. sts file file function requires the later.' |
---|
736 | raise Exception(msg) |
---|
737 | |
---|
738 | # Plot boundary and interpolation points |
---|
739 | if verbose is True: |
---|
740 | import sys |
---|
741 | if sys.platform == 'win32': |
---|
742 | from anuga.utilities.polygon import plot_polygons |
---|
743 | title = 'Interpolation function: Polygon and interpolation points' |
---|
744 | plot_polygons([mesh_boundary_polygon,interpolation_points], |
---|
745 | ['line','point'],figname='points_boundary',label=title,verbose=verbose) |
---|
746 | |
---|
747 | m = len(self.interpolation_points) |
---|
748 | p = len(self.time) |
---|
749 | |
---|
750 | for name in quantity_names: |
---|
751 | self.precomputed_values[name] = zeros((p, m), Float) |
---|
752 | |
---|
753 | # Build interpolator |
---|
754 | if verbose: |
---|
755 | if triangles is not None and vertex_coordinates is not None: |
---|
756 | msg = 'Building interpolation matrix from source mesh ' |
---|
757 | msg += '(%d vertices, %d triangles)' %(vertex_coordinates.shape[0], |
---|
758 | triangles.shape[0]) |
---|
759 | elif triangles is None and vertex_coordinates is not None: |
---|
760 | msg = 'Building interpolation matrix from source points' |
---|
761 | |
---|
762 | print msg |
---|
763 | |
---|
764 | |
---|
765 | interpol = Interpolate(vertex_coordinates, |
---|
766 | triangles, |
---|
767 | verbose=verbose) |
---|
768 | |
---|
769 | if verbose: |
---|
770 | print 'Interpolating (%d interpolation points, %d timesteps).'\ |
---|
771 | %(self.interpolation_points.shape[0], self.time.shape[0]), |
---|
772 | |
---|
773 | if time_thinning > 1: |
---|
774 | print 'Timesteps were thinned by a factor of %d' %time_thinning |
---|
775 | else: |
---|
776 | print |
---|
777 | |
---|
778 | for i, t in enumerate(self.time): |
---|
779 | # Interpolate quantities at this timestep |
---|
780 | if verbose and i%((p+10)/10)==0: |
---|
781 | print ' time step %d of %d' %(i, p) |
---|
782 | |
---|
783 | for name in quantity_names: |
---|
784 | if len(quantities[name].shape) == 2: |
---|
785 | Q = quantities[name][i,:] # Quantities at timestep i |
---|
786 | else: |
---|
787 | Q = quantities[name][:] # No time dependency |
---|
788 | |
---|
789 | if verbose and i%((p+10)/10)==0: |
---|
790 | print ' quantity %s, size=%d' %(name, len(Q)) |
---|
791 | |
---|
792 | # Interpolate |
---|
793 | if triangles is not None and vertex_coordinates is not None: |
---|
794 | result = interpol.interpolate(Q, |
---|
795 | point_coordinates=\ |
---|
796 | self.interpolation_points, |
---|
797 | verbose=False) # Don't clutter |
---|
798 | elif triangles is None and vertex_coordinates is not None: |
---|
799 | result=interpol.interpolate_polyline(Q,vertex_coordinates,gauge_neighbour_id,point_coordinates=self.interpolation_points) |
---|
800 | |
---|
801 | #assert len(result), len(interpolation_points) |
---|
802 | self.precomputed_values[name][i, :] = result |
---|
803 | |
---|
804 | |
---|
805 | # Report |
---|
806 | if verbose: |
---|
807 | print self.statistics() |
---|
808 | #self.print_statistics() |
---|
809 | |
---|
810 | else: |
---|
811 | # Store quantitites as is |
---|
812 | for name in quantity_names: |
---|
813 | self.precomputed_values[name] = quantities[name] |
---|
814 | |
---|
815 | def __repr__(self): |
---|
816 | # return 'Interpolation function (spatio-temporal)' |
---|
817 | return self.statistics() |
---|
818 | |
---|
819 | def __call__(self, t, point_id=None, x=None, y=None): |
---|
820 | """Evaluate f(t) or f(t, point_id) |
---|
821 | |
---|
822 | Inputs: |
---|
823 | t: time - Model time. Must lie within existing timesteps |
---|
824 | point_id: index of one of the preprocessed points. |
---|
825 | |
---|
826 | |
---|
827 | If spatial info is present and all of point_id |
---|
828 | are None an exception is raised |
---|
829 | |
---|
830 | If no spatial info is present, point_id arguments are ignored |
---|
831 | making f a function of time only. |
---|
832 | |
---|
833 | |
---|
834 | FIXME: f(t, x, y) x, y could overrided location, point_id ignored |
---|
835 | FIXME: point_id could also be a slice |
---|
836 | FIXME: What if x and y are vectors? |
---|
837 | FIXME: What about f(x,y) without t? |
---|
838 | """ |
---|
839 | |
---|
840 | from math import pi, cos, sin, sqrt |
---|
841 | from Numeric import zeros, Float |
---|
842 | from anuga.abstract_2d_finite_volumes.util import mean |
---|
843 | |
---|
844 | if self.spatial is True: |
---|
845 | if point_id is None: |
---|
846 | if x is None or y is None: |
---|
847 | msg = 'Either point_id or x and y must be specified' |
---|
848 | raise Exception(msg) |
---|
849 | else: |
---|
850 | if self.interpolation_points is None: |
---|
851 | msg = 'Interpolation_function must be instantiated ' +\ |
---|
852 | 'with a list of interpolation points before parameter ' +\ |
---|
853 | 'point_id can be used' |
---|
854 | raise Exception(msg) |
---|
855 | |
---|
856 | msg = 'Time interval [%.16f:%.16f]' %(self.time[0], self.time[-1]) |
---|
857 | msg += ' does not match model time: %.16f\n' %t |
---|
858 | if t < self.time[0]: raise Exception(msg) |
---|
859 | if t > self.time[-1]: raise Exception(msg) |
---|
860 | |
---|
861 | oldindex = self.index #Time index |
---|
862 | |
---|
863 | # Find current time slot |
---|
864 | while t > self.time[self.index]: self.index += 1 |
---|
865 | while t < self.time[self.index]: self.index -= 1 |
---|
866 | |
---|
867 | if t == self.time[self.index]: |
---|
868 | # Protect against case where t == T[-1] (last time) |
---|
869 | # - also works in general when t == T[i] |
---|
870 | ratio = 0 |
---|
871 | else: |
---|
872 | # t is now between index and index+1 |
---|
873 | ratio = (t - self.time[self.index])/\ |
---|
874 | (self.time[self.index+1] - self.time[self.index]) |
---|
875 | |
---|
876 | # Compute interpolated values |
---|
877 | q = zeros(len(self.quantity_names), Float) |
---|
878 | # print "self.precomputed_values", self.precomputed_values |
---|
879 | for i, name in enumerate(self.quantity_names): |
---|
880 | Q = self.precomputed_values[name] |
---|
881 | |
---|
882 | if self.spatial is False: |
---|
883 | # If there is no spatial info |
---|
884 | assert len(Q.shape) == 1 |
---|
885 | |
---|
886 | Q0 = Q[self.index] |
---|
887 | if ratio > 0: Q1 = Q[self.index+1] |
---|
888 | |
---|
889 | else: |
---|
890 | if x is not None and y is not None: |
---|
891 | # Interpolate to x, y |
---|
892 | |
---|
893 | raise 'x,y interpolation not yet implemented' |
---|
894 | else: |
---|
895 | # Use precomputed point |
---|
896 | Q0 = Q[self.index, point_id] |
---|
897 | if ratio > 0: |
---|
898 | Q1 = Q[self.index+1, point_id] |
---|
899 | |
---|
900 | # Linear temporal interpolation |
---|
901 | if ratio > 0: |
---|
902 | if Q0 == NAN and Q1 == NAN: |
---|
903 | q[i] = Q0 |
---|
904 | else: |
---|
905 | q[i] = Q0 + ratio*(Q1 - Q0) |
---|
906 | else: |
---|
907 | q[i] = Q0 |
---|
908 | |
---|
909 | |
---|
910 | # Return vector of interpolated values |
---|
911 | # if len(q) == 1: |
---|
912 | # return q[0] |
---|
913 | # else: |
---|
914 | # return q |
---|
915 | |
---|
916 | |
---|
917 | # Return vector of interpolated values |
---|
918 | # FIXME: |
---|
919 | if self.spatial is True: |
---|
920 | return q |
---|
921 | else: |
---|
922 | # Replicate q according to x and y |
---|
923 | # This is e.g used for Wind_stress |
---|
924 | if x is None or y is None: |
---|
925 | return q |
---|
926 | else: |
---|
927 | try: |
---|
928 | N = len(x) |
---|
929 | except: |
---|
930 | return q |
---|
931 | else: |
---|
932 | from Numeric import ones, Float |
---|
933 | # x is a vector - Create one constant column for each value |
---|
934 | N = len(x) |
---|
935 | assert len(y) == N, 'x and y must have same length' |
---|
936 | res = [] |
---|
937 | for col in q: |
---|
938 | res.append(col*ones(N, Float)) |
---|
939 | |
---|
940 | return res |
---|
941 | |
---|
942 | |
---|
943 | def get_time(self): |
---|
944 | """Return model time as a vector of timesteps |
---|
945 | """ |
---|
946 | return self.time |
---|
947 | |
---|
948 | |
---|
949 | def statistics(self): |
---|
950 | """Output statistics about interpolation_function |
---|
951 | """ |
---|
952 | |
---|
953 | vertex_coordinates = self.vertex_coordinates |
---|
954 | interpolation_points = self.interpolation_points |
---|
955 | quantity_names = self.quantity_names |
---|
956 | #quantities = self.quantities |
---|
957 | precomputed_values = self.precomputed_values |
---|
958 | |
---|
959 | x = vertex_coordinates[:,0] |
---|
960 | y = vertex_coordinates[:,1] |
---|
961 | |
---|
962 | str = '------------------------------------------------\n' |
---|
963 | str += 'Interpolation_function (spatio-temporal) statistics:\n' |
---|
964 | str += ' Extent:\n' |
---|
965 | str += ' x in [%f, %f], len(x) == %d\n'\ |
---|
966 | %(min(x), max(x), len(x)) |
---|
967 | str += ' y in [%f, %f], len(y) == %d\n'\ |
---|
968 | %(min(y), max(y), len(y)) |
---|
969 | str += ' t in [%f, %f], len(t) == %d\n'\ |
---|
970 | %(min(self.time), max(self.time), len(self.time)) |
---|
971 | str += ' Quantities:\n' |
---|
972 | for name in quantity_names: |
---|
973 | minq, maxq = self.quantities_range[name] |
---|
974 | str += ' %s in [%f, %f]\n' %(name, minq, maxq) |
---|
975 | #q = quantities[name][:].flat |
---|
976 | #str += ' %s in [%f, %f]\n' %(name, min(q), max(q)) |
---|
977 | |
---|
978 | if interpolation_points is not None: |
---|
979 | str += ' Interpolation points (xi, eta):'\ |
---|
980 | ' number of points == %d\n' %interpolation_points.shape[0] |
---|
981 | str += ' xi in [%f, %f]\n' %(min(interpolation_points[:,0]), |
---|
982 | max(interpolation_points[:,0])) |
---|
983 | str += ' eta in [%f, %f]\n' %(min(interpolation_points[:,1]), |
---|
984 | max(interpolation_points[:,1])) |
---|
985 | str += ' Interpolated quantities (over all timesteps):\n' |
---|
986 | |
---|
987 | for name in quantity_names: |
---|
988 | q = precomputed_values[name][:].flat |
---|
989 | str += ' %s at interpolation points in [%f, %f]\n'\ |
---|
990 | %(name, min(q), max(q)) |
---|
991 | str += '------------------------------------------------\n' |
---|
992 | |
---|
993 | return str |
---|
994 | |
---|
995 | |
---|
996 | def interpolate_sww(sww_file, time, interpolation_points, |
---|
997 | quantity_names=None, verbose=False): |
---|
998 | """ |
---|
999 | obsolete. |
---|
1000 | use file_function in utils |
---|
1001 | """ |
---|
1002 | #open sww file |
---|
1003 | x, y, volumes, time, quantities = read_sww(sww_file) |
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1004 | print "x",x |
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1005 | print "y",y |
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1006 | |
---|
1007 | print "time", time |
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1008 | print "quantities", quantities |
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1009 | |
---|
1010 | #Add the x and y together |
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1011 | vertex_coordinates = concatenate((x[:,NewAxis], y[:,NewAxis]),axis=1) |
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1012 | |
---|
1013 | #Will return the quantity values at the specified times and locations |
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1014 | interp = Interpolation_interface(time, |
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1015 | quantities, |
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1016 | quantity_names=quantity_names, |
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1017 | vertex_coordinates=vertex_coordinates, |
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1018 | triangles=volumes, |
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1019 | interpolation_points=interpolation_points, |
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1020 | verbose=verbose) |
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1021 | |
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1022 | |
---|
1023 | def read_sww(file_name): |
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1024 | """ |
---|
1025 | obsolete - Nothing should be calling this |
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1026 | |
---|
1027 | Read in an sww file. |
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1028 | |
---|
1029 | Input; |
---|
1030 | file_name - the sww file |
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1031 | |
---|
1032 | Output; |
---|
1033 | x - Vector of x values |
---|
1034 | y - Vector of y values |
---|
1035 | z - Vector of bed elevation |
---|
1036 | volumes - Array. Each row has 3 values, representing |
---|
1037 | the vertices that define the volume |
---|
1038 | time - Vector of the times where there is stage information |
---|
1039 | stage - array with respect to time and vertices (x,y) |
---|
1040 | """ |
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1041 | |
---|
1042 | msg = 'Function read_sww in interpolat.py is obsolete' |
---|
1043 | raise Exception, msg |
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1044 | |
---|
1045 | #FIXME Have this reader as part of data_manager? |
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1046 | |
---|
1047 | from Scientific.IO.NetCDF import NetCDFFile |
---|
1048 | import tempfile |
---|
1049 | import sys |
---|
1050 | import os |
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1051 | |
---|
1052 | #Check contents |
---|
1053 | #Get NetCDF |
---|
1054 | |
---|
1055 | # see if the file is there. Throw a QUIET IO error if it isn't |
---|
1056 | # I don't think I could implement the above |
---|
1057 | |
---|
1058 | #throws prints to screen if file not present |
---|
1059 | junk = tempfile.mktemp(".txt") |
---|
1060 | fd = open(junk,'w') |
---|
1061 | stdout = sys.stdout |
---|
1062 | sys.stdout = fd |
---|
1063 | fid = NetCDFFile(file_name, 'r') |
---|
1064 | sys.stdout = stdout |
---|
1065 | fd.close() |
---|
1066 | #clean up |
---|
1067 | os.remove(junk) |
---|
1068 | |
---|
1069 | # Get the variables |
---|
1070 | x = fid.variables['x'][:] |
---|
1071 | y = fid.variables['y'][:] |
---|
1072 | volumes = fid.variables['volumes'][:] |
---|
1073 | time = fid.variables['time'][:] |
---|
1074 | |
---|
1075 | keys = fid.variables.keys() |
---|
1076 | keys.remove("x") |
---|
1077 | keys.remove("y") |
---|
1078 | keys.remove("volumes") |
---|
1079 | keys.remove("time") |
---|
1080 | #Turn NetCDF objects into Numeric arrays |
---|
1081 | quantities = {} |
---|
1082 | for name in keys: |
---|
1083 | quantities[name] = fid.variables[name][:] |
---|
1084 | |
---|
1085 | fid.close() |
---|
1086 | return x, y, volumes, time, quantities |
---|
1087 | |
---|
1088 | |
---|
1089 | #------------------------------------------------------------- |
---|
1090 | if __name__ == "__main__": |
---|
1091 | names = ["x","y"] |
---|
1092 | someiterable = [[1,2],[3,4]] |
---|
1093 | csvwriter = writer(file("some.csv", "wb")) |
---|
1094 | csvwriter.writerow(names) |
---|
1095 | for row in someiterable: |
---|
1096 | csvwriter.writerow(row) |
---|