1 | """Class Quantity - Implements values at each triangular element |
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2 | |
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3 | To create: |
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4 | |
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5 | Quantity(domain, vertex_values) |
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6 | |
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7 | domain: Associated domain structure. Required. |
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8 | |
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9 | vertex_values: N x 3 array of values at each vertex for each element. |
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10 | Default None |
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11 | |
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12 | If vertex_values are None Create array of zeros compatible with domain. |
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13 | Otherwise check that it is compatible with dimenions of domain. |
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14 | Otherwise raise an exception |
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15 | """ |
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16 | |
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17 | from Numeric import array, zeros, Float, less, concatenate, NewAxis,\ |
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18 | argmax, allclose, take, reshape |
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19 | |
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20 | from anuga.utilities.numerical_tools import ensure_numeric, is_scalar |
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21 | from anuga.utilities.polygon import inside_polygon |
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22 | |
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23 | from anuga.geospatial_data.geospatial_data import Geospatial_data |
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24 | from anuga.fit_interpolate.fit import fit_to_mesh |
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25 | from anuga.config import points_file_block_line_size as default_block_line_size |
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26 | |
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27 | class Quantity: |
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28 | |
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29 | def __init__(self, domain, vertex_values=None): |
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30 | |
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31 | from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh |
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32 | |
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33 | msg = 'First argument in Quantity.__init__ ' |
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34 | msg += 'must be of class Mesh (or a subclass thereof)' |
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35 | assert isinstance(domain, Mesh), msg |
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36 | |
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37 | if vertex_values is None: |
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38 | N = len(domain) # number_of_elements |
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39 | self.vertex_values = zeros((N, 3), Float) |
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40 | else: |
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41 | self.vertex_values = array(vertex_values).astype(Float) |
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42 | |
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43 | N, V = self.vertex_values.shape |
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44 | assert V == 3,\ |
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45 | 'Three vertex values per element must be specified' |
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46 | |
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47 | |
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48 | msg = 'Number of vertex values (%d) must be consistent with'\ |
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49 | %N |
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50 | msg += 'number of elements in specified domain (%d).'\ |
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51 | %len(domain) |
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52 | |
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53 | assert N == len(domain), msg |
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54 | |
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55 | self.domain = domain |
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56 | |
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57 | #Allocate space for other quantities |
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58 | self.centroid_values = zeros(N, Float) |
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59 | self.edge_values = zeros((N, 3), Float) |
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60 | |
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61 | #Intialise centroid and edge_values |
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62 | self.interpolate() |
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63 | |
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64 | |
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65 | |
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66 | #Methods for operator overloading |
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67 | def __len__(self): |
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68 | return self.centroid_values.shape[0] |
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69 | |
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70 | |
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71 | def __neg__(self): |
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72 | """Negate all values in this quantity giving meaning to the |
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73 | expression -Q where Q is an instance of class Quantity |
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74 | """ |
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75 | |
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76 | Q = Quantity(self.domain) |
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77 | Q.set_values(-self.vertex_values) |
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78 | return Q |
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79 | |
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80 | |
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81 | def __add__(self, other): |
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82 | """Add to self anything that could populate a quantity |
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83 | |
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84 | E.g other can be a constant, an array, a function, another quantity |
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85 | (except for a filename or points, attributes (for now)) |
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86 | - see set_values for details |
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87 | """ |
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88 | |
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89 | Q = Quantity(self.domain) |
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90 | Q.set_values(other) |
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91 | |
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92 | result = Quantity(self.domain) |
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93 | result.set_values(self.vertex_values + Q.vertex_values) |
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94 | return result |
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95 | |
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96 | def __radd__(self, other): |
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97 | """Handle cases like 7+Q, where Q is an instance of class Quantity |
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98 | """ |
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99 | return self + other |
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100 | |
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101 | |
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102 | def __sub__(self, other): |
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103 | return self + -other #Invoke __neg__ |
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104 | |
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105 | def __mul__(self, other): |
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106 | """Multiply self with anything that could populate a quantity |
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107 | |
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108 | E.g other can be a constant, an array, a function, another quantity |
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109 | (except for a filename or points, attributes (for now)) |
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110 | - see set_values for details |
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111 | |
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112 | Note that if two quantitites q1 and q2 are multiplied, |
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113 | vertex values are multiplied entry by entry |
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114 | while centroid and edge values are re-interpolated. |
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115 | Hence they won't be the product of centroid or edge values |
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116 | from q1 and q2. |
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117 | """ |
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118 | |
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119 | Q = Quantity(self.domain) |
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120 | Q.set_values(other) |
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121 | |
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122 | result = Quantity(self.domain) |
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123 | result.set_values(self.vertex_values * Q.vertex_values) |
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124 | return result |
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125 | |
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126 | def __rmul__(self, other): |
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127 | """Handle cases like 3*Q, where Q is an instance of class Quantity |
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128 | """ |
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129 | return self * other |
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130 | |
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131 | def __pow__(self, other): |
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132 | """Raise quantity to (numerical) power |
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133 | |
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134 | As with __mul__ vertex values are processed entry by entry |
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135 | while centroid and edge values are re-interpolated. |
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136 | |
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137 | Example using __pow__: |
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138 | Q = (Q1**2 + Q2**2)**0.5 |
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139 | |
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140 | """ |
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141 | |
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142 | result = Quantity(self.domain) |
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143 | result.set_values(self.vertex_values**other) |
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144 | return result |
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145 | |
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146 | |
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147 | |
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148 | def interpolate(self): |
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149 | """Compute interpolated values at edges and centroid |
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150 | Pre-condition: vertex_values have been set |
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151 | """ |
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152 | |
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153 | N = self.vertex_values.shape[0] |
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154 | for i in range(N): |
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155 | v0 = self.vertex_values[i, 0] |
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156 | v1 = self.vertex_values[i, 1] |
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157 | v2 = self.vertex_values[i, 2] |
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158 | |
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159 | self.centroid_values[i] = (v0 + v1 + v2)/3 |
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160 | |
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161 | self.interpolate_from_vertices_to_edges() |
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162 | |
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163 | |
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164 | def interpolate_from_vertices_to_edges(self): |
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165 | #Call correct module function |
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166 | #(either from this module or C-extension) |
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167 | interpolate_from_vertices_to_edges(self) |
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168 | |
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169 | |
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170 | |
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171 | |
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172 | #New leaner interface to setting values |
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173 | def set_values(self, |
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174 | numeric = None, # List, numeric array or constant |
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175 | quantity = None, # Another quantity |
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176 | function = None, # Callable object: f(x,y) |
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177 | geospatial_data = None, # Arbitrary dataset |
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178 | points = None, values = None, data_georef = None, #Input |
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179 | # for fit (obsoleted by use of geo_spatial object) |
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180 | filename = None, attribute_name = None, #Input from file |
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181 | alpha = None, |
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182 | location = 'vertices', |
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183 | polygon = None, |
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184 | indices = None, |
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185 | verbose = False, |
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186 | use_cache = False): |
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187 | |
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188 | """Set values for quantity based on different sources. |
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189 | |
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190 | numeric: |
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191 | Compatible list, Numeric array (see below) or constant. |
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192 | If callable it will treated as a function (see below) |
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193 | If instance of another Quantity it will be treated as such. |
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194 | If geo_spatial object it will be treated as such |
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195 | |
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196 | quantity: |
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197 | Another quantity (compatible quantity, e.g. obtained as a |
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198 | linear combination of quantities) |
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199 | |
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200 | function: |
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201 | Any callable object that takes two 1d arrays x and y |
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202 | each of length N and returns an array also of length N. |
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203 | The function will be evaluated at points determined by |
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204 | location and indices in the underlying mesh. |
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205 | |
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206 | geospatial_data: |
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207 | Arbitrary geo spatial dataset in the form of the class |
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208 | Geospatial_data. Mesh points are populated using |
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209 | fit_interpolate.fit fitting |
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210 | |
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211 | points: |
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212 | Nx2 array of data points for use with fit_interpolate.fit |
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213 | If points are present, an N array of attribute |
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214 | values corresponding to |
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215 | each data point must be present. |
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216 | (Obsoleted by geospatial_data) |
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217 | |
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218 | values: |
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219 | If points is specified, values is an array of length N containing |
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220 | attribute values for each point. |
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221 | (Obsoleted by geospatial_data) |
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222 | |
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223 | data_georef: |
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224 | If points is specified, geo_reference applies to each point. |
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225 | (Obsoleted by geospatial_data) |
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226 | |
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227 | filename: |
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228 | Name of a points file containing data points and attributes for |
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229 | use with fit_interpolate.fit. |
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230 | |
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231 | attribute_name: |
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232 | If specified, any array matching that name |
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233 | will be used. from file or geospatial_data. |
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234 | Otherwise a default will be used. |
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235 | |
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236 | alpha: |
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237 | Smoothing parameter to be used with fit_interpolate.fit. |
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238 | See module fit_interpolate.fit for further details about alpha. |
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239 | Alpha will only be used with points, values or filename. |
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240 | Otherwise it will be ignored. |
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241 | |
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242 | |
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243 | location: Where values are to be stored. |
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244 | Permissible options are: vertices, edges, centroids |
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245 | Default is 'vertices' |
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246 | |
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247 | In case of location == 'centroids' the dimension values must |
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248 | be a list of a Numerical array of length N, |
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249 | N being the number of elements. |
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250 | Otherwise it must be of dimension Nx3 |
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251 | |
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252 | |
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253 | The values will be stored in elements following their |
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254 | internal ordering. |
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255 | |
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256 | If location is not 'unique vertices' Indices is the |
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257 | set of element ids that the operation applies to. |
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258 | If location is 'unique vertices' Indices is the set |
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259 | of vertex ids that the operation applies to. |
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260 | |
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261 | If selected location is vertices, values for |
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262 | centroid and edges will be assigned interpolated |
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263 | values. In any other case, only values for the |
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264 | specified locations will be assigned and the others |
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265 | will be left undefined. |
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266 | |
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267 | |
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268 | polygon: Restrict update of quantity to locations that fall |
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269 | inside polygon. Polygon works by selecting indices |
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270 | and calling set_values recursively. |
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271 | Polygon mode has only been implemented for |
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272 | constant values so far. |
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273 | |
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274 | indices: Restrict update of quantity to locations that are |
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275 | identified by indices (e.g. node ids if location |
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276 | is 'vertices') |
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277 | |
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278 | verbose: True means that output to stdout is generated |
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279 | |
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280 | use_cache: True means that caching of intermediate results is |
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281 | attempted for fit_interpolate.fit. |
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282 | |
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283 | |
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284 | |
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285 | |
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286 | Exactly one of the arguments |
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287 | numeric, quantity, function, points, filename |
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288 | must be present. |
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289 | """ |
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290 | |
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291 | from anuga.geospatial_data.geospatial_data import Geospatial_data |
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292 | from types import FloatType, IntType, LongType, ListType, NoneType |
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293 | from Numeric import ArrayType |
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294 | |
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295 | |
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296 | # Treat special case: Polygon situation |
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297 | # Location will be ignored and set to 'centroids' |
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298 | # FIXME (Ole): This needs to be generalised and |
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299 | # perhaps the notion of location and indices simplified |
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300 | |
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301 | if polygon is not None: |
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302 | if indices is not None: |
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303 | msg = 'Only one of polygon and indices can be specified' |
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304 | raise Exception, msg |
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305 | |
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306 | msg = 'With polygon selected, set_quantity must provide ' |
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307 | msg += 'the keyword numeric and it must (currently) be ' |
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308 | msg += 'a constant.' |
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309 | if numeric is None: |
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310 | raise Exception, msg |
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311 | else: |
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312 | # Check that numeric is as constant |
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313 | assert type(numeric) in [FloatType, IntType, LongType], msg |
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314 | |
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315 | |
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316 | location = 'centroids' |
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317 | |
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318 | |
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319 | points = self.domain.get_centroid_coordinates(absolute=True) |
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320 | indices = inside_polygon(points, polygon) |
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321 | |
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322 | self.set_values_from_constant(numeric, |
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323 | location, indices, verbose) |
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324 | |
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325 | self.extrapolate_first_order() |
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326 | return |
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327 | |
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328 | |
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329 | |
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330 | |
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331 | |
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332 | |
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333 | #General input checks |
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334 | L = [numeric, quantity, function, geospatial_data, points, filename] |
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335 | msg = 'Exactly one of the arguments '+\ |
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336 | 'numeric, quantity, function, geospatial_data, points, '+\ |
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337 | 'or filename must be present.' |
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338 | assert L.count(None) == len(L)-1, msg |
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339 | |
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340 | |
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341 | if location not in ['vertices', 'centroids', 'edges', |
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342 | 'unique vertices']: |
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343 | msg = 'Invalid location: %s' %location |
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344 | raise Exception, msg |
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345 | |
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346 | |
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347 | msg = 'Indices must be a list or None' |
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348 | assert type(indices) in [ListType, NoneType, ArrayType], msg |
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349 | |
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350 | |
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351 | if not(points is None and values is None and data_georef is None): |
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352 | from warnings import warn |
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353 | |
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354 | msg = 'Using points, values or data_georef with set_quantity ' |
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355 | msg += 'is obsolete. Please use a Geospatial_data object instead.' |
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356 | warn(msg, DeprecationWarning) |
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357 | |
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358 | |
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359 | |
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360 | #Determine which 'set_values_from_...' to use |
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361 | |
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362 | if numeric is not None: |
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363 | if type(numeric) in [FloatType, IntType, LongType]: |
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364 | self.set_values_from_constant(numeric, |
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365 | location, indices, verbose) |
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366 | elif type(numeric) in [ArrayType, ListType]: |
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367 | self.set_values_from_array(numeric, |
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368 | location, indices, verbose) |
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369 | elif callable(numeric): |
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370 | self.set_values_from_function(numeric, |
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371 | location, indices, verbose) |
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372 | elif isinstance(numeric, Quantity): |
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373 | self.set_values_from_quantity(numeric, |
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374 | location, indices, verbose) |
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375 | elif isinstance(numeric, Geospatial_data): |
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376 | self.set_values_from_geospatial_data(numeric, |
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377 | alpha, |
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378 | location, indices, |
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379 | verbose = verbose, |
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380 | use_cache = use_cache) |
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381 | else: |
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382 | msg = 'Illegal type for argument numeric: %s' %str(numeric) |
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383 | raise msg |
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384 | |
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385 | elif quantity is not None: |
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386 | self.set_values_from_quantity(quantity, |
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387 | location, indices, verbose) |
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388 | elif function is not None: |
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389 | msg = 'Argument function must be callable' |
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390 | assert callable(function), msg |
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391 | self.set_values_from_function(function, |
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392 | location, indices, verbose) |
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393 | elif geospatial_data is not None: |
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394 | self.set_values_from_geospatial_data(geospatial_data, |
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395 | alpha, |
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396 | location, indices, |
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397 | verbose = verbose, |
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398 | use_cache = use_cache) |
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399 | elif points is not None: |
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400 | print 'The usage of points in set_values will be deprecated.' +\ |
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401 | 'Please use the geospatial_data object.' |
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402 | |
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403 | msg = 'When points are specified, associated values must also be.' |
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404 | assert values is not None, msg |
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405 | self.set_values_from_points(points, values, alpha, |
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406 | location, indices, |
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407 | data_georef = data_georef, |
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408 | verbose = verbose, |
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409 | use_cache = use_cache) |
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410 | elif filename is not None: |
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411 | if hasattr(self.domain, 'points_file_block_line_size'): |
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412 | max_read_lines = self.domain.points_file_block_line_size |
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413 | else: |
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414 | max_read_lines = default_block_line_size |
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415 | self.set_values_from_file(filename, attribute_name, alpha, |
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416 | location, indices, |
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417 | verbose = verbose, |
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418 | max_read_lines=max_read_lines, |
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419 | use_cache = use_cache) |
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420 | else: |
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421 | raise Exception, 'This can\'t happen :-)' |
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422 | |
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423 | |
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424 | |
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425 | # Update all locations in triangles |
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426 | if location == 'vertices' or location == 'unique vertices': |
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427 | # Intialise centroid and edge_values |
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428 | self.interpolate() |
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429 | |
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430 | if location == 'centroids': |
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431 | # Extrapolate 1st order - to capture notion of area being specified |
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432 | self.extrapolate_first_order() |
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433 | |
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434 | |
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435 | |
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436 | #Specific functions for setting values |
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437 | def set_values_from_constant(self, X, |
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438 | location, indices, verbose): |
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439 | """Set quantity values from specified constant X |
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440 | """ |
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441 | |
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442 | # FIXME (Ole): Somehow indices refer to centroids |
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443 | # rather than vertices as default. See unit test |
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444 | # test_set_vertex_values_using_general_interface_with_subset(self): |
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445 | |
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446 | |
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447 | if location == 'centroids': |
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448 | if indices is None: |
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449 | self.centroid_values[:] = X |
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450 | else: |
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451 | #Brute force |
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452 | for i in indices: |
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453 | self.centroid_values[i] = X |
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454 | |
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455 | elif location == 'edges': |
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456 | if indices is None: |
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457 | self.edge_values[:] = X |
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458 | else: |
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459 | #Brute force |
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460 | for i in indices: |
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461 | self.edge_values[i] = X |
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462 | |
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463 | elif location == 'unique vertices': |
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464 | if indices is None: |
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465 | self.edge_values[:] = X #FIXME (Ole): Shouldn't this be vertex_values? |
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466 | else: |
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467 | |
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468 | #Go through list of unique vertices |
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469 | for unique_vert_id in indices: |
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470 | |
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471 | triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id) |
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472 | |
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473 | #In case there are unused points |
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474 | if len(triangles) == 0: |
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475 | continue |
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476 | |
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477 | #Go through all triangle, vertex pairs |
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478 | #and set corresponding vertex value |
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479 | for triangle_id, vertex_id in triangles: |
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480 | self.vertex_values[triangle_id, vertex_id] = X |
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481 | |
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482 | #Intialise centroid and edge_values |
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483 | self.interpolate() |
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484 | else: |
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485 | if indices is None: |
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486 | self.vertex_values[:] = X |
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487 | else: |
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488 | #Brute force |
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489 | for i_vertex in indices: |
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490 | self.vertex_values[i_vertex] = X |
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491 | |
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492 | |
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493 | |
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494 | |
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495 | def set_values_from_array(self, values, |
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496 | location='vertices', |
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497 | indices=None, |
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498 | verbose=False): |
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499 | """Set values for quantity |
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500 | |
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501 | values: Numeric array |
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502 | location: Where values are to be stored. |
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503 | Permissible options are: vertices, edges, centroid, unique vertices |
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504 | Default is 'vertices' |
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505 | |
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506 | indices - if this action is carried out on a subset of |
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507 | elements or unique vertices |
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508 | The element/unique vertex indices are specified here. |
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509 | |
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510 | In case of location == 'centroid' the dimension values must |
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511 | be a list of a Numerical array of length N, N being the number |
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512 | of elements. |
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513 | |
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514 | Otherwise it must be of dimension Nx3 |
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515 | |
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516 | The values will be stored in elements following their |
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517 | internal ordering. |
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518 | |
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519 | If selected location is vertices, values for centroid and edges |
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520 | will be assigned interpolated values. |
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521 | In any other case, only values for the specified locations |
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522 | will be assigned and the others will be left undefined. |
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523 | """ |
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524 | |
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525 | from Numeric import array, Float, Int, allclose |
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526 | |
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527 | values = array(values).astype(Float) |
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528 | |
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529 | if indices is not None: |
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530 | indices = array(indices).astype(Int) |
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531 | msg = 'Number of values must match number of indices' |
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532 | assert values.shape[0] == indices.shape[0], msg |
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533 | |
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534 | N = self.centroid_values.shape[0] |
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535 | |
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536 | if location == 'centroids': |
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537 | assert len(values.shape) == 1, 'Values array must be 1d' |
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538 | |
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539 | if indices is None: |
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540 | msg = 'Number of values must match number of elements' |
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541 | assert values.shape[0] == N, msg |
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542 | |
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543 | self.centroid_values = values |
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544 | else: |
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545 | msg = 'Number of values must match number of indices' |
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546 | assert values.shape[0] == indices.shape[0], msg |
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547 | |
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548 | #Brute force |
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549 | for i in range(len(indices)): |
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550 | self.centroid_values[indices[i]] = values[i] |
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551 | |
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552 | elif location == 'edges': |
---|
553 | # FIXME (Ole): No mention of indices here. However, I don't |
---|
554 | # think we ever need to set values at edges anyway |
---|
555 | assert len(values.shape) == 2, 'Values array must be 2d' |
---|
556 | |
---|
557 | msg = 'Number of values must match number of elements' |
---|
558 | assert values.shape[0] == N, msg |
---|
559 | |
---|
560 | msg = 'Array must be N x 3' |
---|
561 | assert values.shape[1] == 3, msg |
---|
562 | |
---|
563 | self.edge_values = values |
---|
564 | |
---|
565 | elif location == 'unique vertices': |
---|
566 | assert len(values.shape) == 1 or allclose(values.shape[1:], 1),\ |
---|
567 | 'Values array must be 1d' |
---|
568 | |
---|
569 | self.set_vertex_values(values.flat, indices=indices) |
---|
570 | |
---|
571 | else: |
---|
572 | # Location vertices |
---|
573 | if len(values.shape) == 1: |
---|
574 | self.set_vertex_values(values, indices=indices) |
---|
575 | |
---|
576 | elif len(values.shape) == 2: |
---|
577 | #Vertex values are given as a triplet for each triangle |
---|
578 | |
---|
579 | msg = 'Array must be N x 3' |
---|
580 | assert values.shape[1] == 3, msg |
---|
581 | |
---|
582 | if indices is None: |
---|
583 | self.vertex_values = values |
---|
584 | else: |
---|
585 | for element_index, value in map(None, indices, values): |
---|
586 | self.vertex_values[element_index] = value |
---|
587 | else: |
---|
588 | msg = 'Values array must be 1d or 2d' |
---|
589 | raise msg |
---|
590 | |
---|
591 | |
---|
592 | def set_values_from_quantity(self, q, |
---|
593 | location, indices, verbose): |
---|
594 | """Set quantity values from specified quantity instance q |
---|
595 | |
---|
596 | Location is ignored - vertices will always be used here. |
---|
597 | """ |
---|
598 | |
---|
599 | |
---|
600 | A = q.vertex_values |
---|
601 | |
---|
602 | from Numeric import allclose |
---|
603 | msg = 'Quantities are defined on different meshes. '+\ |
---|
604 | 'This might be a case for implementing interpolation '+\ |
---|
605 | 'between different meshes.' |
---|
606 | assert allclose(A.shape, self.vertex_values.shape), msg |
---|
607 | |
---|
608 | self.set_values(A, location='vertices', |
---|
609 | indices=indices, |
---|
610 | verbose=verbose) |
---|
611 | |
---|
612 | |
---|
613 | def set_values_from_function(self, f, |
---|
614 | location='vertices', |
---|
615 | indices=None, |
---|
616 | verbose=False): |
---|
617 | """Set values for quantity using specified function |
---|
618 | |
---|
619 | Input |
---|
620 | |
---|
621 | f: x, y -> z Function where x, y and z are arrays |
---|
622 | location: Where values are to be stored. |
---|
623 | Permissible options are: vertices, centroid, edges, |
---|
624 | unique vertices |
---|
625 | Default is "vertices" |
---|
626 | indices: |
---|
627 | |
---|
628 | |
---|
629 | """ |
---|
630 | |
---|
631 | #FIXME: Should check that function returns something sensible and |
---|
632 | #raise a meaningfull exception if it returns None for example |
---|
633 | |
---|
634 | #FIXME: Should supply absolute coordinates |
---|
635 | |
---|
636 | |
---|
637 | # Compute the function values and call set_values again |
---|
638 | if location == 'centroids': |
---|
639 | if indices is None: |
---|
640 | indices = range(len(self)) |
---|
641 | |
---|
642 | V = take(self.domain.get_centroid_coordinates(), indices) |
---|
643 | self.set_values(f(V[:,0], V[:,1]), |
---|
644 | location=location, |
---|
645 | indices=indices) |
---|
646 | |
---|
647 | elif location == 'vertices': |
---|
648 | |
---|
649 | M = self.domain.number_of_triangles |
---|
650 | V = self.domain.get_vertex_coordinates() |
---|
651 | |
---|
652 | x = V[:,0]; y = V[:,1]; |
---|
653 | values = f(x, y) |
---|
654 | |
---|
655 | |
---|
656 | # FIXME (Ole): This code should replace all the |
---|
657 | # rest of this function and it would work, except |
---|
658 | # one unit test in test_region fails. |
---|
659 | # If that could be resolved this one will be |
---|
660 | # more robust and simple. |
---|
661 | |
---|
662 | #values = reshape(values, (M,3)) |
---|
663 | #self.set_values(values, |
---|
664 | # location='vertices', |
---|
665 | # indices=indices) |
---|
666 | |
---|
667 | |
---|
668 | # This should be removed |
---|
669 | if is_scalar(values): |
---|
670 | # Function returned a constant value |
---|
671 | self.set_values_from_constant(values, |
---|
672 | location, indices, verbose) |
---|
673 | return |
---|
674 | |
---|
675 | # This should be removed |
---|
676 | if indices is None: |
---|
677 | for j in range(3): |
---|
678 | self.vertex_values[:,j] = values[j::3] |
---|
679 | else: |
---|
680 | #Brute force |
---|
681 | for i in indices: |
---|
682 | for j in range(3): |
---|
683 | self.vertex_values[i,j] = values[3*i+j] |
---|
684 | |
---|
685 | |
---|
686 | else: |
---|
687 | raise 'Not implemented: %s' %location |
---|
688 | |
---|
689 | |
---|
690 | |
---|
691 | def set_values_from_geospatial_data(self, geospatial_data, alpha, |
---|
692 | location, indices, |
---|
693 | verbose = False, |
---|
694 | use_cache = False): |
---|
695 | |
---|
696 | #FIXME: Use this function for the time being. Later move code in here |
---|
697 | |
---|
698 | points = geospatial_data.get_data_points(absolute = False) |
---|
699 | values = geospatial_data.get_attributes() |
---|
700 | data_georef = geospatial_data.get_geo_reference() |
---|
701 | |
---|
702 | |
---|
703 | |
---|
704 | self.set_values_from_points(points, values, alpha, |
---|
705 | location, indices, |
---|
706 | data_georef = data_georef, |
---|
707 | verbose = verbose, |
---|
708 | use_cache = use_cache) |
---|
709 | |
---|
710 | |
---|
711 | |
---|
712 | def set_values_from_points(self, points, values, alpha, |
---|
713 | location, indices, |
---|
714 | data_georef = None, |
---|
715 | verbose = False, |
---|
716 | use_cache = False): |
---|
717 | """ |
---|
718 | Set quantity values from arbitray data points using |
---|
719 | fit_interpolate.fit |
---|
720 | """ |
---|
721 | |
---|
722 | |
---|
723 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
---|
724 | |
---|
725 | |
---|
726 | points = ensure_numeric(points, Float) |
---|
727 | values = ensure_numeric(values, Float) |
---|
728 | |
---|
729 | if location != 'vertices': |
---|
730 | msg = 'set_values_from_points is only defined for '+\ |
---|
731 | 'location=\'vertices\'' |
---|
732 | raise ms |
---|
733 | |
---|
734 | coordinates = self.domain.get_nodes() |
---|
735 | triangles = self.domain.triangles #FIXME |
---|
736 | |
---|
737 | |
---|
738 | #Take care of georeferencing |
---|
739 | if data_georef is None: |
---|
740 | data_georef = Geo_reference() |
---|
741 | |
---|
742 | |
---|
743 | mesh_georef = self.domain.geo_reference |
---|
744 | |
---|
745 | #print mesh_georef |
---|
746 | #print data_georef |
---|
747 | #print points |
---|
748 | |
---|
749 | |
---|
750 | # Call fit_interpolate.fit function |
---|
751 | args = (coordinates, triangles, points, values) |
---|
752 | kwargs = {'data_origin': data_georef.get_origin(), |
---|
753 | 'mesh_origin': mesh_georef.get_origin(), |
---|
754 | 'alpha': alpha, |
---|
755 | 'verbose': verbose} |
---|
756 | |
---|
757 | vertex_attributes = apply(fit_to_mesh, |
---|
758 | args, kwargs) |
---|
759 | |
---|
760 | # Call underlying method using array values |
---|
761 | self.set_values_from_array(vertex_attributes, |
---|
762 | location, indices, verbose) |
---|
763 | |
---|
764 | def set_values_from_file(self, filename, attribute_name, alpha, |
---|
765 | location, indices, |
---|
766 | verbose = False, |
---|
767 | use_cache = False, |
---|
768 | max_read_lines=None): |
---|
769 | """Set quantity based on arbitrary points in a points file |
---|
770 | using attribute_name selects name of attribute |
---|
771 | present in file. |
---|
772 | If attribute_name is not specified, use first available attribute |
---|
773 | as defined in geospatial_data. |
---|
774 | """ |
---|
775 | |
---|
776 | from types import StringType |
---|
777 | msg = 'Filename must be a text string' |
---|
778 | assert type(filename) == StringType, msg |
---|
779 | |
---|
780 | |
---|
781 | if location != 'vertices': |
---|
782 | msg = 'set_values_from_points is only defined for '+\ |
---|
783 | 'location=\'vertices\'' |
---|
784 | raise msg |
---|
785 | |
---|
786 | coordinates = self.domain.get_nodes(absolute=True) |
---|
787 | triangles = self.domain.triangles #FIXME |
---|
788 | |
---|
789 | vertex_attributes = fit_to_mesh(coordinates, triangles, filename, |
---|
790 | alpha=alpha, |
---|
791 | attribute_name=attribute_name, |
---|
792 | use_cache=use_cache, |
---|
793 | verbose=verbose, |
---|
794 | max_read_lines=max_read_lines) |
---|
795 | |
---|
796 | # Call underlying method using array values |
---|
797 | self.set_values_from_array(vertex_attributes, |
---|
798 | location, indices, verbose) |
---|
799 | |
---|
800 | |
---|
801 | def get_maximum_index(self, indices=None): |
---|
802 | """Return index for maximum value of quantity (on centroids) |
---|
803 | |
---|
804 | Optional argument: |
---|
805 | indices is the set of element ids that the operation applies to. |
---|
806 | |
---|
807 | Usage: |
---|
808 | i = get_maximum_index() |
---|
809 | |
---|
810 | Notes: |
---|
811 | We do not seek the maximum at vertices as each vertex can |
---|
812 | have multiple values - one for each triangle sharing it. |
---|
813 | |
---|
814 | If there are multiple cells with same maximum value, the |
---|
815 | first cell encountered in the triangle array is returned. |
---|
816 | """ |
---|
817 | |
---|
818 | V = self.get_values(location='centroids', indices=indices) |
---|
819 | |
---|
820 | # Always return absolute indices |
---|
821 | i = argmax(V) |
---|
822 | |
---|
823 | if indices is None: |
---|
824 | return i |
---|
825 | else: |
---|
826 | return indices[i] |
---|
827 | |
---|
828 | |
---|
829 | def get_maximum_value(self, indices=None): |
---|
830 | """Return maximum value of quantity (on centroids) |
---|
831 | |
---|
832 | Optional argument: |
---|
833 | indices is the set of element ids that the operation applies to. |
---|
834 | |
---|
835 | Usage: |
---|
836 | v = get_maximum_value() |
---|
837 | |
---|
838 | Note, we do not seek the maximum at vertices as each vertex can |
---|
839 | have multiple values - one for each triangle sharing it |
---|
840 | """ |
---|
841 | |
---|
842 | |
---|
843 | i = self.get_maximum_index(indices) |
---|
844 | V = self.get_values(location='centroids') #, indices=indices) |
---|
845 | |
---|
846 | return V[i] |
---|
847 | |
---|
848 | |
---|
849 | def get_maximum_location(self, indices=None): |
---|
850 | """Return location of maximum value of quantity (on centroids) |
---|
851 | |
---|
852 | Optional argument: |
---|
853 | indices is the set of element ids that the operation applies to. |
---|
854 | |
---|
855 | Usage: |
---|
856 | x, y = get_maximum_location() |
---|
857 | |
---|
858 | |
---|
859 | Notes: |
---|
860 | We do not seek the maximum at vertices as each vertex can |
---|
861 | have multiple values - one for each triangle sharing it. |
---|
862 | |
---|
863 | If there are multiple cells with same maximum value, the |
---|
864 | first cell encountered in the triangle array is returned. |
---|
865 | """ |
---|
866 | |
---|
867 | i = self.get_maximum_index(indices) |
---|
868 | x, y = self.domain.get_centroid_coordinates()[i] |
---|
869 | |
---|
870 | return x, y |
---|
871 | |
---|
872 | |
---|
873 | |
---|
874 | |
---|
875 | def get_interpolated_values(self, interpolation_points): |
---|
876 | |
---|
877 | # Interpolation object based on internal (discontinuous triangles) |
---|
878 | x, y, vertex_values, triangles = self.get_vertex_values(xy=True, |
---|
879 | smooth=False) |
---|
880 | # FIXME: This concat should roll into get_vertex_values |
---|
881 | vertex_coordinates = concatenate((x[:, NewAxis], y[:, NewAxis]), |
---|
882 | axis=1) |
---|
883 | |
---|
884 | can_reuse = False |
---|
885 | if hasattr(self, 'interpolation_object'): |
---|
886 | # Reuse to save time |
---|
887 | I = self.interpolation_object |
---|
888 | |
---|
889 | if allclose(interpolation_points, I._point_coordinates): |
---|
890 | can_reuse = True |
---|
891 | |
---|
892 | |
---|
893 | if can_reuse is True: |
---|
894 | # Use absence of points to indicate reuse in I.interpolate |
---|
895 | result = I.interpolate(vertex_values) |
---|
896 | else: |
---|
897 | from anuga.fit_interpolate.interpolate import Interpolate |
---|
898 | |
---|
899 | # Create interpolation object with matrix |
---|
900 | I = Interpolate(vertex_coordinates, triangles) |
---|
901 | self.interpolation_object = I |
---|
902 | |
---|
903 | # Call interpolate with points the first time |
---|
904 | interpolation_points = ensure_numeric(interpolation_points, Float) |
---|
905 | result = I.interpolate(vertex_values, interpolation_points) |
---|
906 | |
---|
907 | return result |
---|
908 | |
---|
909 | |
---|
910 | def get_values(self, interpolation_points=None, |
---|
911 | location='vertices', |
---|
912 | indices = None): |
---|
913 | """get values for quantity |
---|
914 | |
---|
915 | return X, Compatible list, Numeric array (see below) |
---|
916 | interpolation_points: List of x, y coordinates where value is |
---|
917 | sought (using interpolation). If points are given, values of |
---|
918 | location and indices are ignored |
---|
919 | |
---|
920 | location: Where values are to be stored. |
---|
921 | Permissible options are: vertices, edges, centroid |
---|
922 | and unique vertices. Default is 'vertices' |
---|
923 | |
---|
924 | |
---|
925 | The returned values with be a list the length of indices |
---|
926 | (N if indices = None). |
---|
927 | |
---|
928 | In case of location == 'centroids' the dimension of returned |
---|
929 | values will be a list or a Numerical array of length N, N being |
---|
930 | the number of elements. |
---|
931 | |
---|
932 | In case of location == 'vertices' or 'edges' the dimension of |
---|
933 | returned values will be of dimension Nx3 |
---|
934 | |
---|
935 | In case of location == 'unique vertices' the average value at |
---|
936 | each vertex will be returned and the dimension of returned values |
---|
937 | will be a 1d array of length "number of vertices" |
---|
938 | |
---|
939 | Indices is the set of element ids that the operation applies to. |
---|
940 | |
---|
941 | The values will be stored in elements following their |
---|
942 | internal ordering. |
---|
943 | |
---|
944 | """ |
---|
945 | from Numeric import take |
---|
946 | |
---|
947 | if interpolation_points is not None: |
---|
948 | return self.get_interpolated_values(interpolation_points) |
---|
949 | |
---|
950 | |
---|
951 | |
---|
952 | if location not in ['vertices', 'centroids', 'edges', |
---|
953 | 'unique vertices']: |
---|
954 | msg = 'Invalid location: %s' %location |
---|
955 | raise msg |
---|
956 | |
---|
957 | import types, Numeric |
---|
958 | assert type(indices) in [types.ListType, types.NoneType, |
---|
959 | Numeric.ArrayType],\ |
---|
960 | 'Indices must be a list or None' |
---|
961 | |
---|
962 | if location == 'centroids': |
---|
963 | if (indices == None): |
---|
964 | indices = range(len(self)) |
---|
965 | return take(self.centroid_values,indices) |
---|
966 | elif location == 'edges': |
---|
967 | if (indices == None): |
---|
968 | indices = range(len(self)) |
---|
969 | return take(self.edge_values,indices) |
---|
970 | elif location == 'unique vertices': |
---|
971 | if (indices == None): |
---|
972 | indices=range(self.domain.number_of_nodes) |
---|
973 | vert_values = [] |
---|
974 | #Go through list of unique vertices |
---|
975 | for unique_vert_id in indices: |
---|
976 | triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id) |
---|
977 | |
---|
978 | #In case there are unused points |
---|
979 | if len(triangles) == 0: |
---|
980 | msg = 'Unique vertex not associated with triangles' |
---|
981 | raise msg |
---|
982 | |
---|
983 | # Go through all triangle, vertex pairs |
---|
984 | # Average the values |
---|
985 | |
---|
986 | # FIXME (Ole): Should we merge this with get_vertex_values |
---|
987 | sum = 0 |
---|
988 | for triangle_id, vertex_id in triangles: |
---|
989 | sum += self.vertex_values[triangle_id, vertex_id] |
---|
990 | vert_values.append(sum/len(triangles)) |
---|
991 | return Numeric.array(vert_values) |
---|
992 | else: |
---|
993 | if (indices == None): |
---|
994 | indices = range(len(self)) |
---|
995 | return take(self.vertex_values,indices) |
---|
996 | |
---|
997 | |
---|
998 | |
---|
999 | def set_vertex_values(self, A, indices = None): |
---|
1000 | """Set vertex values for all unique vertices based on input array A |
---|
1001 | which has one entry per unique vertex, i.e. |
---|
1002 | one value for each row in array self.domain.nodes. |
---|
1003 | |
---|
1004 | indices is the list of vertex_id's that will be set. |
---|
1005 | |
---|
1006 | This function is used by set_values_from_array |
---|
1007 | """ |
---|
1008 | |
---|
1009 | from Numeric import array, Float |
---|
1010 | |
---|
1011 | #Assert that A can be converted to a Numeric array of appropriate dim |
---|
1012 | A = array(A, Float) |
---|
1013 | |
---|
1014 | #print 'SHAPE A', A.shape |
---|
1015 | assert len(A.shape) == 1 |
---|
1016 | |
---|
1017 | if indices is None: |
---|
1018 | assert A.shape[0] == self.domain.get_nodes().shape[0] |
---|
1019 | vertex_list = range(A.shape[0]) |
---|
1020 | else: |
---|
1021 | assert A.shape[0] == len(indices) |
---|
1022 | vertex_list = indices |
---|
1023 | |
---|
1024 | #Go through list of unique vertices |
---|
1025 | |
---|
1026 | for i_index, unique_vert_id in enumerate(vertex_list): |
---|
1027 | |
---|
1028 | |
---|
1029 | triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id) |
---|
1030 | |
---|
1031 | #In case there are unused points |
---|
1032 | if len(triangles) == 0: continue |
---|
1033 | |
---|
1034 | #Go through all triangle, vertex pairs |
---|
1035 | #touching vertex unique_vert_id and set corresponding vertex value |
---|
1036 | for triangle_id, vertex_id in triangles: |
---|
1037 | self.vertex_values[triangle_id, vertex_id] = A[i_index] |
---|
1038 | |
---|
1039 | #Intialise centroid and edge_values |
---|
1040 | self.interpolate() |
---|
1041 | |
---|
1042 | |
---|
1043 | def smooth_vertex_values(self, value_array='field_values', |
---|
1044 | precision = None): |
---|
1045 | """ Smooths field_values or conserved_quantities data. |
---|
1046 | TODO: be able to smooth individual fields |
---|
1047 | NOTE: This function does not have a test. |
---|
1048 | FIXME: NOT DONE - do we need it? |
---|
1049 | FIXME: this function isn't called by anything. |
---|
1050 | Maybe it should be removed..-DSG |
---|
1051 | """ |
---|
1052 | |
---|
1053 | from Numeric import concatenate, zeros, Float, Int, array, reshape |
---|
1054 | |
---|
1055 | |
---|
1056 | A,V = self.get_vertex_values(xy=False, |
---|
1057 | value_array=value_array, |
---|
1058 | smooth = True, |
---|
1059 | precision = precision) |
---|
1060 | |
---|
1061 | #Set some field values |
---|
1062 | for volume in self: |
---|
1063 | for i,v in enumerate(volume.vertices): |
---|
1064 | if value_array == 'field_values': |
---|
1065 | volume.set_field_values('vertex', i, A[v,:]) |
---|
1066 | elif value_array == 'conserved_quantities': |
---|
1067 | volume.set_conserved_quantities('vertex', i, A[v,:]) |
---|
1068 | |
---|
1069 | if value_array == 'field_values': |
---|
1070 | self.precompute() |
---|
1071 | elif value_array == 'conserved_quantities': |
---|
1072 | Volume.interpolate_conserved_quantities() |
---|
1073 | |
---|
1074 | |
---|
1075 | # Methods for outputting model results |
---|
1076 | def get_vertex_values(self, |
---|
1077 | xy=True, |
---|
1078 | smooth=None, |
---|
1079 | precision=None): |
---|
1080 | """Return vertex values like an OBJ format i.e. one value per node. |
---|
1081 | |
---|
1082 | The vertex values are returned as one sequence in the 1D float array A. |
---|
1083 | If requested the coordinates will be returned in 1D arrays X and Y. |
---|
1084 | |
---|
1085 | The connectivity is represented as an integer array, V, of dimension |
---|
1086 | Mx3, where M is the number of triangles. Each row has three indices |
---|
1087 | defining the triangle and they correspond to elements in the arrays |
---|
1088 | X, Y and A. |
---|
1089 | |
---|
1090 | if smooth is True, vertex values corresponding to one common |
---|
1091 | coordinate set will be smoothed by taking the average of vertex values for each node. |
---|
1092 | In this case vertex coordinates will be |
---|
1093 | de-duplicated corresponding to the original nodes as obtained from |
---|
1094 | the method general_mesh.get_nodes() |
---|
1095 | |
---|
1096 | If no smoothings is required, vertex coordinates and values will |
---|
1097 | be aggregated as a concatenation of values at |
---|
1098 | vertices 0, vertices 1 and vertices 2. This corresponds to |
---|
1099 | the node coordinates obtained from the method |
---|
1100 | general_mesh.get_vertex_coordinates() |
---|
1101 | |
---|
1102 | |
---|
1103 | Calling convention |
---|
1104 | if xy is True: |
---|
1105 | X,Y,A,V = get_vertex_values |
---|
1106 | else: |
---|
1107 | A,V = get_vertex_values |
---|
1108 | |
---|
1109 | """ |
---|
1110 | |
---|
1111 | from Numeric import concatenate, zeros, Float, Int, array, reshape |
---|
1112 | |
---|
1113 | |
---|
1114 | if smooth is None: |
---|
1115 | # Take default from domain |
---|
1116 | smooth = self.domain.smooth |
---|
1117 | |
---|
1118 | if precision is None: |
---|
1119 | precision = Float |
---|
1120 | |
---|
1121 | |
---|
1122 | if smooth is True: |
---|
1123 | # Ensure continuous vertex values by averaging |
---|
1124 | # values at each node |
---|
1125 | |
---|
1126 | V = self.domain.get_triangles() |
---|
1127 | N = self.domain.number_of_full_nodes # Ignore ghost nodes if any |
---|
1128 | A = zeros(N, Float) |
---|
1129 | points = self.domain.get_nodes() |
---|
1130 | |
---|
1131 | if 1: |
---|
1132 | # Fast C version |
---|
1133 | average_vertex_values(ensure_numeric(self.domain.vertex_value_indices), |
---|
1134 | ensure_numeric(self.domain.number_of_triangles_per_node), |
---|
1135 | ensure_numeric(self.vertex_values), |
---|
1136 | A) |
---|
1137 | A = A.astype(precision) |
---|
1138 | else: |
---|
1139 | |
---|
1140 | # Slow Python version |
---|
1141 | |
---|
1142 | current_node = 0 |
---|
1143 | k = 0 # Track triangles touching on node |
---|
1144 | total = 0.0 |
---|
1145 | for index in self.domain.vertex_value_indices: |
---|
1146 | if current_node == N: |
---|
1147 | msg = 'Current node exceeding number of nodes (%d) ' %(N) |
---|
1148 | raise msg |
---|
1149 | |
---|
1150 | |
---|
1151 | |
---|
1152 | k += 1 |
---|
1153 | |
---|
1154 | volume_id = index / 3 |
---|
1155 | vertex_id = index % 3 |
---|
1156 | |
---|
1157 | #assert V[volume_id, vertex_id] == current_node |
---|
1158 | |
---|
1159 | v = self.vertex_values[volume_id, vertex_id] |
---|
1160 | total += v |
---|
1161 | |
---|
1162 | #print 'current_node=%d, index=%d, k=%d, total=%f' %(current_node, index, k, total) |
---|
1163 | if self.domain.number_of_triangles_per_node[current_node] == k: |
---|
1164 | A[current_node] = total/k |
---|
1165 | |
---|
1166 | |
---|
1167 | # Move on to next node |
---|
1168 | total = 0.0 |
---|
1169 | k = 0 |
---|
1170 | current_node += 1 |
---|
1171 | |
---|
1172 | |
---|
1173 | |
---|
1174 | else: |
---|
1175 | # Allow discontinuous vertex values |
---|
1176 | V = self.domain.get_disconnected_triangles() |
---|
1177 | points = self.domain.get_vertex_coordinates() |
---|
1178 | A = self.vertex_values.flat.astype(precision) |
---|
1179 | |
---|
1180 | |
---|
1181 | # Return |
---|
1182 | if xy is True: |
---|
1183 | X = points[:,0].astype(precision) |
---|
1184 | Y = points[:,1].astype(precision) |
---|
1185 | |
---|
1186 | return X, Y, A, V |
---|
1187 | else: |
---|
1188 | return A, V |
---|
1189 | |
---|
1190 | |
---|
1191 | |
---|
1192 | def extrapolate_first_order(self): |
---|
1193 | """Extrapolate conserved quantities from centroid to |
---|
1194 | vertices for each volume using |
---|
1195 | first order scheme. |
---|
1196 | """ |
---|
1197 | |
---|
1198 | qc = self.centroid_values |
---|
1199 | qv = self.vertex_values |
---|
1200 | |
---|
1201 | for i in range(3): |
---|
1202 | qv[:,i] = qc |
---|
1203 | |
---|
1204 | |
---|
1205 | def get_integral(self): |
---|
1206 | """Compute the integral of quantity across entire domain |
---|
1207 | """ |
---|
1208 | integral = 0 |
---|
1209 | for k in range(len(self.domain)): |
---|
1210 | area = self.domain.areas[k] |
---|
1211 | qc = self.centroid_values[k] |
---|
1212 | integral += qc*area |
---|
1213 | |
---|
1214 | return integral |
---|
1215 | |
---|
1216 | |
---|
1217 | |
---|
1218 | |
---|
1219 | class Conserved_quantity(Quantity): |
---|
1220 | """Class conserved quantity adds to Quantity: |
---|
1221 | |
---|
1222 | boundary values, storage and method for updating, and |
---|
1223 | methods for (second order) extrapolation from centroid to vertices inluding |
---|
1224 | gradients and limiters |
---|
1225 | """ |
---|
1226 | |
---|
1227 | def __init__(self, domain, vertex_values=None): |
---|
1228 | Quantity.__init__(self, domain, vertex_values) |
---|
1229 | |
---|
1230 | from Numeric import zeros, Float |
---|
1231 | |
---|
1232 | #Allocate space for boundary values |
---|
1233 | L = len(domain.boundary) |
---|
1234 | self.boundary_values = zeros(L, Float) |
---|
1235 | |
---|
1236 | #Allocate space for updates of conserved quantities by |
---|
1237 | #flux calculations and forcing functions |
---|
1238 | |
---|
1239 | N = len(domain) # number_of_triangles |
---|
1240 | self.explicit_update = zeros(N, Float ) |
---|
1241 | self.semi_implicit_update = zeros(N, Float ) |
---|
1242 | |
---|
1243 | |
---|
1244 | def update(self, timestep): |
---|
1245 | #Call correct module function |
---|
1246 | #(either from this module or C-extension) |
---|
1247 | return update(self, timestep) |
---|
1248 | |
---|
1249 | |
---|
1250 | def compute_gradients(self): |
---|
1251 | #Call correct module function |
---|
1252 | #(either from this module or C-extension) |
---|
1253 | return compute_gradients(self) |
---|
1254 | |
---|
1255 | |
---|
1256 | def limit(self): |
---|
1257 | #Call correct module function |
---|
1258 | #(either from this module or C-extension) |
---|
1259 | limit(self) |
---|
1260 | |
---|
1261 | |
---|
1262 | def extrapolate_second_order(self): |
---|
1263 | #Call correct module function |
---|
1264 | #(either from this module or C-extension) |
---|
1265 | extrapolate_second_order(self) |
---|
1266 | |
---|
1267 | |
---|
1268 | def update(quantity, timestep): |
---|
1269 | """Update centroid values based on values stored in |
---|
1270 | explicit_update and semi_implicit_update as well as given timestep |
---|
1271 | |
---|
1272 | Function implementing forcing terms must take on argument |
---|
1273 | which is the domain and they must update either explicit |
---|
1274 | or implicit updates, e,g,: |
---|
1275 | |
---|
1276 | def gravity(domain): |
---|
1277 | .... |
---|
1278 | domain.quantities['xmomentum'].explicit_update = ... |
---|
1279 | domain.quantities['ymomentum'].explicit_update = ... |
---|
1280 | |
---|
1281 | |
---|
1282 | |
---|
1283 | Explicit terms must have the form |
---|
1284 | |
---|
1285 | G(q, t) |
---|
1286 | |
---|
1287 | and explicit scheme is |
---|
1288 | |
---|
1289 | q^{(n+1}) = q^{(n)} + delta_t G(q^{n}, n delta_t) |
---|
1290 | |
---|
1291 | |
---|
1292 | Semi implicit forcing terms are assumed to have the form |
---|
1293 | |
---|
1294 | G(q, t) = H(q, t) q |
---|
1295 | |
---|
1296 | and the semi implicit scheme will then be |
---|
1297 | |
---|
1298 | q^{(n+1}) = q^{(n)} + delta_t H(q^{n}, n delta_t) q^{(n+1}) |
---|
1299 | |
---|
1300 | |
---|
1301 | """ |
---|
1302 | |
---|
1303 | from Numeric import sum, equal, ones, exp, Float |
---|
1304 | |
---|
1305 | N = quantity.centroid_values.shape[0] |
---|
1306 | |
---|
1307 | |
---|
1308 | #Divide H by conserved quantity to obtain G (see docstring above) |
---|
1309 | |
---|
1310 | |
---|
1311 | for k in range(N): |
---|
1312 | x = quantity.centroid_values[k] |
---|
1313 | if x == 0.0: |
---|
1314 | #FIXME: Is this right |
---|
1315 | quantity.semi_implicit_update[k] = 0.0 |
---|
1316 | else: |
---|
1317 | quantity.semi_implicit_update[k] /= x |
---|
1318 | |
---|
1319 | |
---|
1320 | #Semi implicit updates |
---|
1321 | denominator = ones(N, Float)-timestep*quantity.semi_implicit_update |
---|
1322 | |
---|
1323 | if sum(less(denominator, 1.0)) > 0.0: |
---|
1324 | msg = 'denominator < 1.0 in semi implicit update. Call Stephen :-)' |
---|
1325 | raise msg |
---|
1326 | |
---|
1327 | if sum(equal(denominator, 0.0)) > 0.0: |
---|
1328 | msg = 'Zero division in semi implicit update. Call Stephen :-)' |
---|
1329 | raise msg |
---|
1330 | else: |
---|
1331 | #Update conserved_quantities from semi implicit updates |
---|
1332 | quantity.centroid_values /= denominator |
---|
1333 | |
---|
1334 | # quantity.centroid_values = exp(timestep*quantity.semi_implicit_update)*quantity.centroid_values |
---|
1335 | |
---|
1336 | #Explicit updates |
---|
1337 | quantity.centroid_values += timestep*quantity.explicit_update |
---|
1338 | |
---|
1339 | def interpolate_from_vertices_to_edges(quantity): |
---|
1340 | """Compute edge values from vertex values using linear interpolation |
---|
1341 | """ |
---|
1342 | |
---|
1343 | for k in range(quantity.vertex_values.shape[0]): |
---|
1344 | q0 = quantity.vertex_values[k, 0] |
---|
1345 | q1 = quantity.vertex_values[k, 1] |
---|
1346 | q2 = quantity.vertex_values[k, 2] |
---|
1347 | |
---|
1348 | quantity.edge_values[k, 0] = 0.5*(q1+q2) |
---|
1349 | quantity.edge_values[k, 1] = 0.5*(q0+q2) |
---|
1350 | quantity.edge_values[k, 2] = 0.5*(q0+q1) |
---|
1351 | |
---|
1352 | |
---|
1353 | |
---|
1354 | def extrapolate_second_order(quantity): |
---|
1355 | """Extrapolate conserved quantities from centroid to |
---|
1356 | vertices for each volume using |
---|
1357 | second order scheme. |
---|
1358 | """ |
---|
1359 | |
---|
1360 | a, b = quantity.compute_gradients() |
---|
1361 | |
---|
1362 | X = quantity.domain.get_vertex_coordinates() |
---|
1363 | qc = quantity.centroid_values |
---|
1364 | qv = quantity.vertex_values |
---|
1365 | |
---|
1366 | #Check each triangle |
---|
1367 | for k in range(len(quantity.domain)): |
---|
1368 | #Centroid coordinates |
---|
1369 | x, y = quantity.domain.centroid_coordinates[k] |
---|
1370 | |
---|
1371 | #vertex coordinates |
---|
1372 | x0, y0, x1, y1, x2, y2 = X[k,:] |
---|
1373 | |
---|
1374 | #Extrapolate |
---|
1375 | qv[k,0] = qc[k] + a[k]*(x0-x) + b[k]*(y0-y) |
---|
1376 | qv[k,1] = qc[k] + a[k]*(x1-x) + b[k]*(y1-y) |
---|
1377 | qv[k,2] = qc[k] + a[k]*(x2-x) + b[k]*(y2-y) |
---|
1378 | |
---|
1379 | |
---|
1380 | def compute_gradients(quantity): |
---|
1381 | """Compute gradients of triangle surfaces defined by centroids of |
---|
1382 | neighbouring volumes. |
---|
1383 | If one edge is on the boundary, use own centroid as neighbour centroid. |
---|
1384 | If two or more are on the boundary, fall back to first order scheme. |
---|
1385 | """ |
---|
1386 | |
---|
1387 | from Numeric import zeros, Float |
---|
1388 | from utilitites.numerical_tools import gradient |
---|
1389 | |
---|
1390 | centroid_coordinates = quantity.domain.centroid_coordinates |
---|
1391 | surrogate_neighbours = quantity.domain.surrogate_neighbours |
---|
1392 | centroid_values = quantity.centroid_values |
---|
1393 | number_of_boundaries = quantity.domain.number_of_boundaries |
---|
1394 | |
---|
1395 | N = centroid_values.shape[0] |
---|
1396 | |
---|
1397 | a = zeros(N, Float) |
---|
1398 | b = zeros(N, Float) |
---|
1399 | |
---|
1400 | for k in range(N): |
---|
1401 | if number_of_boundaries[k] < 2: |
---|
1402 | #Two or three true neighbours |
---|
1403 | |
---|
1404 | #Get indices of neighbours (or self when used as surrogate) |
---|
1405 | k0, k1, k2 = surrogate_neighbours[k,:] |
---|
1406 | |
---|
1407 | #Get data |
---|
1408 | q0 = centroid_values[k0] |
---|
1409 | q1 = centroid_values[k1] |
---|
1410 | q2 = centroid_values[k2] |
---|
1411 | |
---|
1412 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
---|
1413 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
---|
1414 | x2, y2 = centroid_coordinates[k2] #V2 centroid |
---|
1415 | |
---|
1416 | #Gradient |
---|
1417 | a[k], b[k] = gradient(x0, y0, x1, y1, x2, y2, q0, q1, q2) |
---|
1418 | |
---|
1419 | elif number_of_boundaries[k] == 2: |
---|
1420 | #One true neighbour |
---|
1421 | |
---|
1422 | #Get index of the one neighbour |
---|
1423 | for k0 in surrogate_neighbours[k,:]: |
---|
1424 | if k0 != k: break |
---|
1425 | assert k0 != k |
---|
1426 | |
---|
1427 | k1 = k #self |
---|
1428 | |
---|
1429 | #Get data |
---|
1430 | q0 = centroid_values[k0] |
---|
1431 | q1 = centroid_values[k1] |
---|
1432 | |
---|
1433 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
---|
1434 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
---|
1435 | |
---|
1436 | #Gradient |
---|
1437 | a[k], b[k] = gradient2(x0, y0, x1, y1, q0, q1) |
---|
1438 | else: |
---|
1439 | #No true neighbours - |
---|
1440 | #Fall back to first order scheme |
---|
1441 | pass |
---|
1442 | |
---|
1443 | |
---|
1444 | return a, b |
---|
1445 | |
---|
1446 | |
---|
1447 | |
---|
1448 | def limit(quantity): |
---|
1449 | """Limit slopes for each volume to eliminate artificial variance |
---|
1450 | introduced by e.g. second order extrapolator |
---|
1451 | |
---|
1452 | This is an unsophisticated limiter as it does not take into |
---|
1453 | account dependencies among quantities. |
---|
1454 | |
---|
1455 | precondition: |
---|
1456 | vertex values are estimated from gradient |
---|
1457 | postcondition: |
---|
1458 | vertex values are updated |
---|
1459 | """ |
---|
1460 | |
---|
1461 | from Numeric import zeros, Float |
---|
1462 | |
---|
1463 | N = quantity.domain.number_of_nodes |
---|
1464 | |
---|
1465 | beta_w = quantity.domain.beta_w |
---|
1466 | |
---|
1467 | qc = quantity.centroid_values |
---|
1468 | qv = quantity.vertex_values |
---|
1469 | |
---|
1470 | #Find min and max of this and neighbour's centroid values |
---|
1471 | qmax = zeros(qc.shape, Float) |
---|
1472 | qmin = zeros(qc.shape, Float) |
---|
1473 | |
---|
1474 | for k in range(N): |
---|
1475 | qmax[k] = qc[k] |
---|
1476 | qmin[k] = qc[k] |
---|
1477 | for i in range(3): |
---|
1478 | n = quantity.domain.neighbours[k,i] |
---|
1479 | if n >= 0: |
---|
1480 | qn = qc[n] #Neighbour's centroid value |
---|
1481 | |
---|
1482 | qmin[k] = min(qmin[k], qn) |
---|
1483 | qmax[k] = max(qmax[k], qn) |
---|
1484 | qmax[k] = min(qmax[k], 2.0*qc[k]) |
---|
1485 | qmin[k] = max(qmin[k], 0.5*qc[k]) |
---|
1486 | |
---|
1487 | |
---|
1488 | #Diffences between centroids and maxima/minima |
---|
1489 | dqmax = qmax - qc |
---|
1490 | dqmin = qmin - qc |
---|
1491 | |
---|
1492 | #Deltas between vertex and centroid values |
---|
1493 | dq = zeros(qv.shape, Float) |
---|
1494 | for i in range(3): |
---|
1495 | dq[:,i] = qv[:,i] - qc |
---|
1496 | |
---|
1497 | #Phi limiter |
---|
1498 | for k in range(N): |
---|
1499 | |
---|
1500 | #Find the gradient limiter (phi) across vertices |
---|
1501 | phi = 1.0 |
---|
1502 | for i in range(3): |
---|
1503 | r = 1.0 |
---|
1504 | if (dq[k,i] > 0): r = dqmax[k]/dq[k,i] |
---|
1505 | if (dq[k,i] < 0): r = dqmin[k]/dq[k,i] |
---|
1506 | |
---|
1507 | phi = min( min(r*beta_w, 1), phi ) |
---|
1508 | |
---|
1509 | #Then update using phi limiter |
---|
1510 | for i in range(3): |
---|
1511 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
1512 | |
---|
1513 | |
---|
1514 | |
---|
1515 | from anuga.utilities import compile |
---|
1516 | if compile.can_use_C_extension('quantity_ext.c'): |
---|
1517 | #Replace python version with c implementations |
---|
1518 | |
---|
1519 | from quantity_ext import average_vertex_values |
---|
1520 | |
---|
1521 | from quantity_ext import compute_gradients, limit,\ |
---|
1522 | extrapolate_second_order, interpolate_from_vertices_to_edges, update |
---|