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 | |
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18 | class Quantity: |
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19 | |
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20 | def __init__(self, domain, vertex_values=None): |
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21 | |
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22 | from mesh import Mesh |
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23 | from Numeric import array, zeros, Float |
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24 | |
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25 | msg = 'First argument in Quantity.__init__ ' |
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26 | msg += 'must be of class Mesh (or a subclass thereof)' |
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27 | assert isinstance(domain, Mesh), msg |
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28 | |
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29 | if vertex_values is None: |
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30 | N = domain.number_of_elements |
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31 | self.vertex_values = zeros((N, 3), Float) |
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32 | else: |
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33 | self.vertex_values = array(vertex_values).astype(Float) |
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34 | |
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35 | N, V = self.vertex_values.shape |
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36 | assert V == 3,\ |
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37 | 'Three vertex values per element must be specified' |
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38 | |
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39 | |
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40 | msg = 'Number of vertex values (%d) must be consistent with'\ |
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41 | %N |
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42 | msg += 'number of elements in specified domain (%d).'\ |
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43 | %domain.number_of_elements |
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44 | |
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45 | assert N == domain.number_of_elements, msg |
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46 | |
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47 | self.domain = domain |
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48 | |
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49 | #Allocate space for other quantities |
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50 | self.centroid_values = zeros(N, Float) |
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51 | self.edge_values = zeros((N, 3), Float) |
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52 | |
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53 | #Intialise centroid and edge_values |
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54 | self.interpolate() |
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55 | |
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56 | |
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57 | |
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58 | #Methods for operator overloading |
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59 | def __len__(self): |
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60 | return self.centroid_values.shape[0] |
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61 | |
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62 | |
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63 | def __neg__(self): |
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64 | """Negate all values in this quantity giving meaning to the |
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65 | expression -Q where Q is an instance of class Quantity |
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66 | """ |
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67 | |
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68 | Q = Quantity(self.domain) |
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69 | Q.set_values(-self.vertex_values) |
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70 | return Q |
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71 | |
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72 | |
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73 | def __add__(self, other): |
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74 | """Add to self anything that could populate a quantity: |
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75 | E.g other can be a constant, an array, a function, another quantity |
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76 | (except for a filename or points, attributes (for now)) |
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77 | - see set_values for details |
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78 | """ |
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79 | |
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80 | Q = Quantity(self.domain) |
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81 | Q.set_values(other) |
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82 | |
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83 | result = Quantity(self.domain) |
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84 | result.set_values(self.vertex_values + Q.vertex_values) |
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85 | return result |
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86 | |
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87 | def __radd__(self, other): |
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88 | """Handle cases like 7+Q, where Q is an instance of class Quantity |
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89 | """ |
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90 | return self + other |
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91 | |
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92 | |
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93 | def __sub__(self, other): |
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94 | return self + -other #Invoke __neg__ |
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95 | |
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96 | def __mul__(self, other): |
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97 | """Multiply self with anything that could populate a quantity: |
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98 | E.g other can be a constant, an array, a function, another quantity |
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99 | (except for a filename or points, attributes (for now)) |
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100 | - see set_values for details |
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101 | |
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102 | Note that if two quantitites q1 and q2 are multiplied, |
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103 | vertex values are multiplied entry by entry |
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104 | while centroid and edge values are re-interpolated. |
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105 | Hence they won't be the product of centroid or edge values |
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106 | from q1 and q2. |
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107 | """ |
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108 | |
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109 | Q = Quantity(self.domain) |
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110 | Q.set_values(other) |
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111 | |
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112 | result = Quantity(self.domain) |
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113 | result.set_values(self.vertex_values * Q.vertex_values) |
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114 | return result |
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115 | |
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116 | def __rmul__(self, other): |
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117 | """Handle cases like 3*Q, where Q is an instance of class Quantity |
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118 | """ |
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119 | return self * other |
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120 | |
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121 | |
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122 | def interpolate(self): |
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123 | """Compute interpolated values at edges and centroid |
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124 | Pre-condition: vertex_values have been set |
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125 | """ |
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126 | |
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127 | N = self.vertex_values.shape[0] |
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128 | for i in range(N): |
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129 | v0 = self.vertex_values[i, 0] |
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130 | v1 = self.vertex_values[i, 1] |
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131 | v2 = self.vertex_values[i, 2] |
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132 | |
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133 | self.centroid_values[i] = (v0 + v1 + v2)/3 |
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134 | |
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135 | self.interpolate_from_vertices_to_edges() |
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136 | |
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137 | |
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138 | def interpolate_from_vertices_to_edges(self): |
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139 | #Call correct module function |
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140 | #(either from this module or C-extension) |
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141 | interpolate_from_vertices_to_edges(self) |
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142 | |
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143 | |
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144 | |
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145 | |
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146 | #New leaner interface to setting values |
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147 | def set_values(self, |
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148 | numeric = None, #List, numeric array or constant |
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149 | quantity = None, #Another quantity |
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150 | function = None, #Callable object: f(x,y) |
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151 | points = None, values = None, #Input for least squares |
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152 | filename = None, attribute_name = None, #Input from file |
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153 | alpha = None, |
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154 | location = 'vertices', |
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155 | indices = None, |
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156 | verbose = None, |
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157 | use_cache = False): |
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158 | |
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159 | """Set values for quantity based on different sources. |
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160 | |
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161 | numeric: |
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162 | Compatible list, Numeric array (see below) or constant. |
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163 | If callable it will treated as a function |
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164 | If instance of another Quantity it will be treated as such. |
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165 | |
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166 | quantity: |
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167 | Another quantity (compatible quantity, e.g. obtained as a |
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168 | linear combination of quantities) |
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169 | |
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170 | function: |
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171 | Any callable object that takes two 1d arrays x and y |
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172 | each of length N and returns an array also of length N. |
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173 | The function will be evaluated at points determined by |
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174 | location and indices. |
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175 | |
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176 | points: |
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177 | Nx2 array of data points for use with least squares fit |
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178 | If points are present, an N array of attribute |
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179 | values corresponding to |
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180 | each data point must be present. |
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181 | |
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182 | filename: |
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183 | Name of pts file containing data points and attributes for |
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184 | use with least squares. |
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185 | If attribute_name is specified, any array matching that name |
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186 | will be used. Otherwise the first available one will be used. |
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187 | |
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188 | alpha: |
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189 | Smoothing parameter to be used with least squares fits. |
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190 | See module least_squares for further details about alpha. |
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191 | Alpha will only be used with points, values or filename. |
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192 | Otherwise it will be ignored. |
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193 | |
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194 | |
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195 | location: Where values are to be stored. |
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196 | Permissible options are: vertices, edges, centroids |
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197 | Default is 'vertices' |
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198 | |
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199 | In case of location == 'centroids' the dimension values must |
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200 | be a list of a Numerical array of length N, |
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201 | N being the number of elements. |
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202 | Otherwise it must be of dimension Nx3 |
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203 | |
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204 | |
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205 | The values will be stored in elements following their |
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206 | internal ordering. |
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207 | |
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208 | If location is not 'unique vertices' Indices is the |
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209 | set of element ids that the operation applies to. |
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210 | If location is 'unique vertices' Indices is the set |
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211 | of vertex ids that the operation applies to. |
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212 | |
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213 | If selected location is vertices, values for |
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214 | centroid and edges will be assigned interpolated |
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215 | values. In any other case, only values for the |
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216 | specified locations will be assigned and the others |
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217 | will be left undefined. |
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218 | |
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219 | verbose: True means that output to stdout is generated |
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220 | |
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221 | use_cache: True means that caching of intermediate results is |
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222 | attempted for least squares fit. |
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223 | |
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224 | |
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225 | |
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226 | |
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227 | Exactly one of the arguments |
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228 | numeric, quantity, function, points, filename |
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229 | must be present. |
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230 | """ |
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231 | |
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232 | from types import FloatType, IntType, LongType, ListType, NoneType |
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233 | from Numeric import ArrayType |
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234 | |
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235 | #General input checks |
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236 | L = [numeric, quantity, function, points, filename] |
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237 | msg = 'Exactly one of the arguments '+\ |
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238 | 'numeric, quantity, function, points, or filename '+\ |
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239 | 'must be present. L = %s' %str(L) |
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240 | assert L.count(None) == len(L)-1, msg |
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241 | |
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242 | |
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243 | if location not in ['vertices', 'centroids', 'edges', |
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244 | 'unique vertices']: |
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245 | msg = 'Invalid location: %s' %location |
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246 | raise msg |
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247 | |
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248 | |
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249 | msg = 'Indices must be a list or None' |
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250 | assert type(indices) in [ListType, NoneType, ArrayType], msg |
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251 | |
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252 | |
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253 | |
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254 | #Determine which 'set_values_from_...' to use |
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255 | |
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256 | if numeric is not None: |
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257 | if type(numeric) in [FloatType, IntType, LongType]: |
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258 | self.set_values_from_constant(numeric, |
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259 | location, indices, verbose) |
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260 | elif type(numeric) in [ArrayType, ListType]: |
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261 | self.set_values_from_array(numeric, |
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262 | location, indices, verbose) |
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263 | elif callable(numeric): |
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264 | self.set_values_from_function(numeric, |
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265 | location, indices, verbose) |
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266 | elif isinstance(numeric, Quantity): |
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267 | self.set_values_from_quantity(numeric, |
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268 | location, indices, verbose) |
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269 | else: |
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270 | msg = 'Illegal type for argument numeric: %s' %str(numeric) |
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271 | raise msg |
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272 | |
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273 | elif quantity is not None: |
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274 | self.set_values_from_quantity(quantity, |
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275 | location, indices, verbose) |
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276 | elif function is not None: |
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277 | msg = 'Argument function must be callable' |
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278 | assert callable(function), msg |
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279 | self.set_values_from_function(function, |
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280 | location, indices, verbose) |
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281 | elif points is not None: |
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282 | msg = 'When points are specified, associated values must also be.' |
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283 | assert values is not None, msg |
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284 | self.set_values_from_points(points, values, alpha, |
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285 | location, indices, verbose, |
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286 | use_cache) |
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287 | elif filename is not None: |
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288 | self.set_values_from_file(filename, attribute_name, alpha, |
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289 | location, indices, verbose, |
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290 | use_cache) |
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291 | else: |
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292 | raise 'This can\'t happen :-)' |
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293 | |
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294 | |
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295 | #Update all locations in triangles |
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296 | if location == 'vertices' or location == 'unique vertices': |
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297 | #Intialise centroid and edge_values |
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298 | self.interpolate() |
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299 | |
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300 | if location == 'centroids': |
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301 | #Extrapolate 1st order - to capture notion of area being specified |
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302 | self.extrapolate_first_order() |
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303 | |
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304 | |
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305 | |
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306 | #Specific functions for setting values |
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307 | def set_values_from_constant(self, X, |
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308 | location, indices, verbose): |
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309 | """Set quantity values from specified constant X |
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310 | """ |
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311 | |
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312 | |
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313 | if location == 'centroids': |
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314 | if (indices == None): |
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315 | self.centroid_values[:] = X |
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316 | else: |
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317 | #Brute force |
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318 | for i in indices: |
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319 | self.centroid_values[i,:] = X |
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320 | |
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321 | elif location == 'edges': |
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322 | if (indices == None): |
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323 | self.edge_values[:] = X |
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324 | else: |
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325 | #Brute force |
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326 | for i in indices: |
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327 | self.edge_values[i,:] = X |
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328 | |
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329 | elif location == 'unique vertices': |
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330 | if (indices == None): |
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331 | self.edge_values[:] = X |
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332 | else: |
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333 | |
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334 | #Go through list of unique vertices |
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335 | for unique_vert_id in indices: |
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336 | triangles = self.domain.vertexlist[unique_vert_id] |
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337 | |
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338 | #In case there are unused points |
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339 | if triangles is None: continue |
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340 | |
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341 | #Go through all triangle, vertex pairs |
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342 | #and set corresponding vertex value |
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343 | for triangle_id, vertex_id in triangles: |
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344 | self.vertex_values[triangle_id, vertex_id] = X |
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345 | |
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346 | #Intialise centroid and edge_values |
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347 | self.interpolate() |
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348 | else: |
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349 | if (indices == None): |
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350 | self.vertex_values[:] = X |
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351 | else: |
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352 | #Brute force |
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353 | for i_vertex in indices: |
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354 | self.vertex_values[i_vertex,:] = X |
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355 | |
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356 | |
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357 | |
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358 | |
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359 | |
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360 | |
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361 | def set_values_from_array(self, values, |
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362 | location, indices, verbose): |
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363 | """Set values for quantity |
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364 | |
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365 | values: Numeric array |
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366 | location: Where values are to be stored. |
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367 | Permissible options are: vertices, edges, centroid, unique vertices |
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368 | Default is 'vertices' |
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369 | |
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370 | indices - if this action is carried out on a subset of |
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371 | elements or unique vertices |
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372 | The element/unique vertex indices are specified here. |
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373 | |
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374 | In case of location == 'centroid' the dimension values must |
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375 | be a list of a Numerical array of length N, N being the number |
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376 | of elements. |
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377 | |
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378 | Otherwise it must be of dimension Nx3 |
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379 | |
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380 | The values will be stored in elements following their |
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381 | internal ordering. |
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382 | |
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383 | If selected location is vertices, values for centroid and edges |
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384 | will be assigned interpolated values. |
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385 | In any other case, only values for the specified locations |
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386 | will be assigned and the others will be left undefined. |
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387 | """ |
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388 | |
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389 | from Numeric import array, Float, Int, allclose |
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390 | |
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391 | values = array(values).astype(Float) |
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392 | |
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393 | if indices is not None: |
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394 | indices = array(indices).astype(Int) |
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395 | msg = 'Number of values must match number of indices' |
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396 | assert values.shape[0] == indices.shape[0], msg |
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397 | |
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398 | N = self.centroid_values.shape[0] |
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399 | |
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400 | if location == 'centroids': |
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401 | assert len(values.shape) == 1, 'Values array must be 1d' |
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402 | |
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403 | if indices is None: |
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404 | msg = 'Number of values must match number of elements' |
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405 | assert values.shape[0] == N, msg |
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406 | |
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407 | self.centroid_values = values |
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408 | else: |
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409 | msg = 'Number of values must match number of indices' |
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410 | assert values.shape[0] == indices.shape[0], msg |
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411 | |
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412 | #Brute force |
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413 | for i in range(len(indices)): |
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414 | self.centroid_values[indices[i]] = values[i] |
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415 | |
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416 | elif location == 'edges': |
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417 | assert len(values.shape) == 2, 'Values array must be 2d' |
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418 | |
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419 | msg = 'Number of values must match number of elements' |
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420 | assert values.shape[0] == N, msg |
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421 | |
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422 | msg = 'Array must be N x 3' |
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423 | assert values.shape[1] == 3, msg |
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424 | |
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425 | self.edge_values = values |
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426 | |
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427 | elif location == 'unique vertices': |
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428 | assert len(values.shape) == 1 or allclose(values.shape[1:], 1),\ |
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429 | 'Values array must be 1d' |
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430 | |
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431 | self.set_vertex_values(values.flat, indices = indices) |
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432 | else: |
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433 | if len(values.shape) == 1: |
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434 | self.set_vertex_values(values, indices = indices) |
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435 | #if indices == None: |
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436 | #Values are being specified once for each unique vertex |
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437 | # msg = 'Number of values must match number of vertices' |
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438 | # assert values.shape[0] == self.domain.coordinates.shape[0], msg |
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439 | # self.set_vertex_values(values) |
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440 | #else: |
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441 | # for element_index, value in map(None, indices, values): |
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442 | # self.vertex_values[element_index, :] = value |
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443 | |
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444 | elif len(values.shape) == 2: |
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445 | #Vertex values are given as a triplet for each triangle |
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446 | |
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447 | msg = 'Array must be N x 3' |
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448 | assert values.shape[1] == 3, msg |
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449 | |
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450 | if indices == None: |
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451 | self.vertex_values = values |
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452 | else: |
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453 | for element_index, value in map(None, indices, values): |
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454 | self.vertex_values[element_index] = value |
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455 | else: |
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456 | msg = 'Values array must be 1d or 2d' |
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457 | raise msg |
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458 | |
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459 | def set_values_from_quantity(self, q, |
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460 | location, indices, verbose): |
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461 | """Set quantity values from specified quantity instance q |
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462 | |
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463 | Location is ignored |
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464 | """ |
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465 | |
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466 | |
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467 | A = q.vertex_values |
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468 | |
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469 | from Numeric import allclose |
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470 | msg = 'Quantities are defined on different meshes. '+\ |
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471 | 'This might be a case for implementing interpolation '+\ |
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472 | 'between different meshes.' |
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473 | assert allclose(A.shape, self.vertex_values.shape), msg |
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474 | |
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475 | self.set_values(A, location='vertices', |
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476 | indices=indices, |
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477 | verbose=verbose) |
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478 | |
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479 | |
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480 | def set_values_from_function(self, f, |
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481 | location, indices, verbose): |
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482 | """Set values for quantity using specified function |
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483 | |
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484 | f: x, y -> z Function where x, y and z are arrays |
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485 | location: Where values are to be stored. |
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486 | Permissible options are: vertices, centroid, edges, |
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487 | unique vertices |
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488 | Default is "vertices" |
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489 | """ |
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490 | |
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491 | #FIXME: Should check that function returns something sensible and |
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492 | #raise a meaningfull exception if it returns None for example |
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493 | |
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494 | from Numeric import take |
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495 | |
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496 | if (indices is None): |
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497 | indices = range(len(self)) |
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498 | is_subset = False |
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499 | else: |
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500 | is_subset = True |
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501 | |
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502 | if location == 'centroids': |
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503 | P = take(self.domain.centroid_coordinates, indices) |
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504 | if is_subset: |
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505 | self.set_values(f(P[:,0], P[:,1]), |
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506 | location = location, |
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507 | indices = indices) |
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508 | else: |
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509 | self.set_values(f(P[:,0], P[:,1]), location = location) |
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510 | elif location == 'vertices': |
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511 | P = self.domain.vertex_coordinates |
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512 | if is_subset: |
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513 | #Brute force |
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514 | for e in indices: |
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515 | for i in range(3): |
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516 | self.vertex_values[e,i] = f(P[e,2*i], P[e,2*i+1]) |
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517 | else: |
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518 | for i in range(3): |
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519 | self.vertex_values[:,i] = f(P[:,2*i], P[:,2*i+1]) |
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520 | else: |
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521 | raise 'Not implemented: %s' %location |
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522 | |
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523 | |
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524 | |
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525 | def set_values_from_points(self, points, values, alpha, |
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526 | location, indices, verbose, use_cache): |
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527 | """Set quantity values from arbitray data points using least squares |
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528 | """ |
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529 | |
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530 | from Numeric import Float |
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531 | from util import ensure_numeric |
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532 | from least_squares import fit_to_mesh |
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533 | |
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534 | points = ensure_numeric(points, Float) |
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535 | values = ensure_numeric(values, Float) |
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536 | |
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537 | if location != 'vertices': |
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538 | msg = 'set_values_from_points is only defined for'+\ |
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539 | 'location=\'vertices\'' |
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540 | raise msg |
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541 | |
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542 | coordinates = self.domain.coordinates |
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543 | triangles = self.domain.triangles |
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544 | |
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545 | if use_cache is True: |
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546 | try: |
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547 | from caching import cache |
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548 | except: |
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549 | msg = 'Caching was requested, but caching module'+\ |
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550 | 'could not be imported' |
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551 | raise msg |
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552 | |
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553 | args = (coordinates, triangles, points, values) |
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554 | kwargs = {'alpha': alpha, 'verbose': verbose} |
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555 | vertex_attributes = cache(fit_to_mesh, |
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556 | args, kwargs, |
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557 | verbose = verbose) |
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558 | else: |
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559 | vertex_attributes = fit_to_mesh(coordinates, |
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560 | triangles, |
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561 | points, |
---|
562 | values, |
---|
563 | alpha = alpha, |
---|
564 | verbose = verbose) |
---|
565 | |
---|
566 | |
---|
567 | self.set_values_from_array(vertex_attributes, |
---|
568 | location, indices, verbose) |
---|
569 | |
---|
570 | |
---|
571 | |
---|
572 | |
---|
573 | |
---|
574 | def set_values_from_file(self, filename, attribute_name, alpha, |
---|
575 | location, indices, verbose, use_cache): |
---|
576 | """Set quantity based on arbitrary points in .pts file |
---|
577 | using least_squares attribute_name selects name of attribute |
---|
578 | present in file. |
---|
579 | If not specified try to use whatever is available in file. |
---|
580 | """ |
---|
581 | |
---|
582 | |
---|
583 | from types import StringType |
---|
584 | msg = 'Filename must be a text string' |
---|
585 | assert type(filename) == StringType, msg |
---|
586 | |
---|
587 | |
---|
588 | #Read from (NetCDF) file |
---|
589 | from load_mesh.loadASCII import import_points_file |
---|
590 | points_dict = import_points_file(filename) |
---|
591 | points = points_dict['pointlist'] |
---|
592 | attributes = points_dict['attributelist'] |
---|
593 | |
---|
594 | if attribute_name is None: |
---|
595 | names = attributes.keys() |
---|
596 | attribute_name = names[0] |
---|
597 | |
---|
598 | msg = 'Attribute_name must be a text string' |
---|
599 | assert type(attribute_name) == StringType, msg |
---|
600 | |
---|
601 | |
---|
602 | if verbose: |
---|
603 | print 'Using attribute %s from file %s' %(attribute_name, filename) |
---|
604 | print 'Available attributes: %s' %(names) |
---|
605 | |
---|
606 | try: |
---|
607 | z = attributes[attribute_name] |
---|
608 | except: |
---|
609 | msg = 'Could not extract attribute %s from file %s'\ |
---|
610 | %(attribute_name, filename) |
---|
611 | raise msg |
---|
612 | |
---|
613 | |
---|
614 | #Call least squares method |
---|
615 | self.set_values_from_points(points, z, alpha, |
---|
616 | location, indices, verbose, use_cache) |
---|
617 | |
---|
618 | |
---|
619 | |
---|
620 | def get_values(self, location='vertices', indices = None): |
---|
621 | """get values for quantity |
---|
622 | |
---|
623 | return X, Compatible list, Numeric array (see below) |
---|
624 | location: Where values are to be stored. |
---|
625 | Permissible options are: vertices, edges, centroid |
---|
626 | and unique vertices. Default is 'vertices' |
---|
627 | |
---|
628 | In case of location == 'centroids' the dimension values must |
---|
629 | be a list of a Numerical array of length N, N being the number |
---|
630 | of elements. Otherwise it must be of dimension Nx3 |
---|
631 | |
---|
632 | The returned values with be a list the length of indices |
---|
633 | (N if indices = None). Each value will be a list of the three |
---|
634 | vertex values for this quantity. |
---|
635 | |
---|
636 | Indices is the set of element ids that the operation applies to. |
---|
637 | |
---|
638 | """ |
---|
639 | from Numeric import take |
---|
640 | |
---|
641 | if location not in ['vertices', 'centroids', 'edges', 'unique vertices']: |
---|
642 | msg = 'Invalid location: %s' %location |
---|
643 | raise msg |
---|
644 | |
---|
645 | import types, Numeric |
---|
646 | assert type(indices) in [types.ListType, types.NoneType, |
---|
647 | Numeric.ArrayType],\ |
---|
648 | 'Indices must be a list or None' |
---|
649 | |
---|
650 | if location == 'centroids': |
---|
651 | if (indices == None): |
---|
652 | indices = range(len(self)) |
---|
653 | return take(self.centroid_values,indices) |
---|
654 | elif location == 'edges': |
---|
655 | if (indices == None): |
---|
656 | indices = range(len(self)) |
---|
657 | return take(self.edge_values,indices) |
---|
658 | elif location == 'unique vertices': |
---|
659 | if (indices == None): |
---|
660 | indices=range(self.domain.coordinates.shape[0]) |
---|
661 | vert_values = [] |
---|
662 | #Go through list of unique vertices |
---|
663 | for unique_vert_id in indices: |
---|
664 | triangles = self.domain.vertexlist[unique_vert_id] |
---|
665 | |
---|
666 | #In case there are unused points |
---|
667 | if triangles is None: |
---|
668 | msg = 'Unique vertex not associated with triangles' |
---|
669 | raise msg |
---|
670 | |
---|
671 | # Go through all triangle, vertex pairs |
---|
672 | # Average the values |
---|
673 | sum = 0 |
---|
674 | for triangle_id, vertex_id in triangles: |
---|
675 | sum += self.vertex_values[triangle_id, vertex_id] |
---|
676 | vert_values.append(sum/len(triangles)) |
---|
677 | return Numeric.array(vert_values) |
---|
678 | else: |
---|
679 | if (indices == None): |
---|
680 | indices = range(len(self)) |
---|
681 | return take(self.vertex_values,indices) |
---|
682 | |
---|
683 | |
---|
684 | |
---|
685 | def set_vertex_values(self, A, indices = None): |
---|
686 | """Set vertex values for all unique vertices based on input array A |
---|
687 | which has one entry per unique vertex, i.e. |
---|
688 | one value for each row in array self.domain.coordinates or |
---|
689 | one value for each row in vertexlist. |
---|
690 | |
---|
691 | indices is the list of vertex_id's that will be set. |
---|
692 | |
---|
693 | This function is used by set_values_from_array |
---|
694 | """ |
---|
695 | |
---|
696 | from Numeric import array, Float |
---|
697 | |
---|
698 | #Assert that A can be converted to a Numeric array of appropriate dim |
---|
699 | A = array(A, Float) |
---|
700 | |
---|
701 | #print 'SHAPE A', A.shape |
---|
702 | assert len(A.shape) == 1 |
---|
703 | |
---|
704 | if indices == None: |
---|
705 | assert A.shape[0] == self.domain.coordinates.shape[0] |
---|
706 | vertex_list = range(A.shape[0]) |
---|
707 | else: |
---|
708 | assert A.shape[0] == len(indices) |
---|
709 | vertex_list = indices |
---|
710 | |
---|
711 | #Go through list of unique vertices |
---|
712 | for i_index, unique_vert_id in enumerate(vertex_list): |
---|
713 | triangles = self.domain.vertexlist[unique_vert_id] |
---|
714 | |
---|
715 | if triangles is None: continue #In case there are unused points |
---|
716 | |
---|
717 | #Go through all triangle, vertex pairs |
---|
718 | #touching vertex unique_vert_id and set corresponding vertex value |
---|
719 | for triangle_id, vertex_id in triangles: |
---|
720 | self.vertex_values[triangle_id, vertex_id] = A[i_index] |
---|
721 | |
---|
722 | #Intialise centroid and edge_values |
---|
723 | self.interpolate() |
---|
724 | |
---|
725 | |
---|
726 | def smooth_vertex_values(self, value_array='field_values', |
---|
727 | precision = None): |
---|
728 | """ Smooths field_values or conserved_quantities data. |
---|
729 | TODO: be able to smooth individual fields |
---|
730 | NOTE: This function does not have a test. |
---|
731 | FIXME: NOT DONE - do we need it? |
---|
732 | FIXME: this function isn't called by anything. |
---|
733 | Maybe it should be removed..-DSG |
---|
734 | """ |
---|
735 | |
---|
736 | from Numeric import concatenate, zeros, Float, Int, array, reshape |
---|
737 | |
---|
738 | |
---|
739 | A,V = self.get_vertex_values(xy=False, |
---|
740 | value_array=value_array, |
---|
741 | smooth = True, |
---|
742 | precision = precision) |
---|
743 | |
---|
744 | #Set some field values |
---|
745 | for volume in self: |
---|
746 | for i,v in enumerate(volume.vertices): |
---|
747 | if value_array == 'field_values': |
---|
748 | volume.set_field_values('vertex', i, A[v,:]) |
---|
749 | elif value_array == 'conserved_quantities': |
---|
750 | volume.set_conserved_quantities('vertex', i, A[v,:]) |
---|
751 | |
---|
752 | if value_array == 'field_values': |
---|
753 | self.precompute() |
---|
754 | elif value_array == 'conserved_quantities': |
---|
755 | Volume.interpolate_conserved_quantities() |
---|
756 | |
---|
757 | |
---|
758 | #Method for outputting model results |
---|
759 | #FIXME: Split up into geometric and numeric stuff. |
---|
760 | #FIXME: Geometric (X,Y,V) should live in mesh.py |
---|
761 | #FIXME: STill remember to move XY to mesh |
---|
762 | def get_vertex_values(self, |
---|
763 | xy=True, |
---|
764 | smooth = None, |
---|
765 | precision = None, |
---|
766 | reduction = None): |
---|
767 | """Return vertex values like an OBJ format |
---|
768 | |
---|
769 | The vertex values are returned as one sequence in the 1D float array A. |
---|
770 | If requested the coordinates will be returned in 1D arrays X and Y. |
---|
771 | |
---|
772 | The connectivity is represented as an integer array, V, of dimension |
---|
773 | M x 3, where M is the number of volumes. Each row has three indices |
---|
774 | into the X, Y, A arrays defining the triangle. |
---|
775 | |
---|
776 | if smooth is True, vertex values corresponding to one common |
---|
777 | coordinate set will be smoothed according to the given |
---|
778 | reduction operator. In this case vertex coordinates will be |
---|
779 | de-duplicated. |
---|
780 | |
---|
781 | If no smoothings is required, vertex coordinates and values will |
---|
782 | be aggregated as a concatenation of values at |
---|
783 | vertices 0, vertices 1 and vertices 2 |
---|
784 | |
---|
785 | |
---|
786 | Calling convention |
---|
787 | if xy is True: |
---|
788 | X,Y,A,V = get_vertex_values |
---|
789 | else: |
---|
790 | A,V = get_vertex_values |
---|
791 | |
---|
792 | """ |
---|
793 | |
---|
794 | from Numeric import concatenate, zeros, Float, Int, array, reshape |
---|
795 | |
---|
796 | |
---|
797 | if smooth is None: |
---|
798 | smooth = self.domain.smooth |
---|
799 | |
---|
800 | if precision is None: |
---|
801 | precision = Float |
---|
802 | |
---|
803 | if reduction is None: |
---|
804 | reduction = self.domain.reduction |
---|
805 | |
---|
806 | #Create connectivity |
---|
807 | |
---|
808 | if smooth == True: |
---|
809 | |
---|
810 | V = self.domain.get_vertices() |
---|
811 | N = len(self.domain.vertexlist) |
---|
812 | A = zeros(N, precision) |
---|
813 | |
---|
814 | #Smoothing loop |
---|
815 | for k in range(N): |
---|
816 | L = self.domain.vertexlist[k] |
---|
817 | |
---|
818 | #Go through all triangle, vertex pairs |
---|
819 | #contributing to vertex k and register vertex value |
---|
820 | |
---|
821 | if L is None: continue #In case there are unused points |
---|
822 | |
---|
823 | contributions = [] |
---|
824 | for volume_id, vertex_id in L: |
---|
825 | v = self.vertex_values[volume_id, vertex_id] |
---|
826 | contributions.append(v) |
---|
827 | |
---|
828 | A[k] = reduction(contributions) |
---|
829 | |
---|
830 | |
---|
831 | if xy is True: |
---|
832 | X = self.domain.coordinates[:,0].astype(precision) |
---|
833 | Y = self.domain.coordinates[:,1].astype(precision) |
---|
834 | |
---|
835 | return X, Y, A, V |
---|
836 | else: |
---|
837 | return A, V |
---|
838 | else: |
---|
839 | #Don't smooth |
---|
840 | #obj machinery moved to general_mesh |
---|
841 | |
---|
842 | # Create a V like [[0 1 2], [3 4 5]....[3*m-2 3*m-1 3*m]] |
---|
843 | # These vert_id's will relate to the verts created below |
---|
844 | #m = len(self.domain) #Number of volumes |
---|
845 | #M = 3*m #Total number of unique vertices |
---|
846 | #V = reshape(array(range(M)).astype(Int), (m,3)) |
---|
847 | |
---|
848 | V = self.domain.get_triangles(obj=True) |
---|
849 | #FIXME use get_vertices, when ready |
---|
850 | |
---|
851 | A = self.vertex_values.flat |
---|
852 | |
---|
853 | #Do vertex coordinates |
---|
854 | if xy is True: |
---|
855 | C = self.domain.get_vertex_coordinates() |
---|
856 | |
---|
857 | X = C[:,0:6:2].copy() |
---|
858 | Y = C[:,1:6:2].copy() |
---|
859 | |
---|
860 | return X.flat, Y.flat, A, V |
---|
861 | else: |
---|
862 | return A, V |
---|
863 | |
---|
864 | |
---|
865 | def extrapolate_first_order(self): |
---|
866 | """Extrapolate conserved quantities from centroid to |
---|
867 | vertices for each volume using |
---|
868 | first order scheme. |
---|
869 | """ |
---|
870 | |
---|
871 | qc = self.centroid_values |
---|
872 | qv = self.vertex_values |
---|
873 | |
---|
874 | for i in range(3): |
---|
875 | qv[:,i] = qc |
---|
876 | |
---|
877 | |
---|
878 | def get_integral(self): |
---|
879 | """Compute the integral of quantity across entire domain |
---|
880 | """ |
---|
881 | integral = 0 |
---|
882 | for k in range(self.domain.number_of_elements): |
---|
883 | area = self.domain.areas[k] |
---|
884 | qc = self.centroid_values[k] |
---|
885 | integral += qc*area |
---|
886 | |
---|
887 | return integral |
---|
888 | |
---|
889 | |
---|
890 | |
---|
891 | |
---|
892 | class Conserved_quantity(Quantity): |
---|
893 | """Class conserved quantity adds to Quantity: |
---|
894 | |
---|
895 | boundary values, storage and method for updating, and |
---|
896 | methods for (second order) extrapolation from centroid to vertices inluding |
---|
897 | gradients and limiters |
---|
898 | """ |
---|
899 | |
---|
900 | def __init__(self, domain, vertex_values=None): |
---|
901 | Quantity.__init__(self, domain, vertex_values) |
---|
902 | |
---|
903 | from Numeric import zeros, Float |
---|
904 | |
---|
905 | #Allocate space for boundary values |
---|
906 | L = len(domain.boundary) |
---|
907 | self.boundary_values = zeros(L, Float) |
---|
908 | |
---|
909 | #Allocate space for updates of conserved quantities by |
---|
910 | #flux calculations and forcing functions |
---|
911 | |
---|
912 | N = domain.number_of_elements |
---|
913 | self.explicit_update = zeros(N, Float ) |
---|
914 | self.semi_implicit_update = zeros(N, Float ) |
---|
915 | |
---|
916 | |
---|
917 | def update(self, timestep): |
---|
918 | #Call correct module function |
---|
919 | #(either from this module or C-extension) |
---|
920 | return update(self, timestep) |
---|
921 | |
---|
922 | |
---|
923 | def compute_gradients(self): |
---|
924 | #Call correct module function |
---|
925 | #(either from this module or C-extension) |
---|
926 | return compute_gradients(self) |
---|
927 | |
---|
928 | |
---|
929 | def limit(self): |
---|
930 | #Call correct module function |
---|
931 | #(either from this module or C-extension) |
---|
932 | limit(self) |
---|
933 | |
---|
934 | |
---|
935 | def extrapolate_second_order(self): |
---|
936 | #Call correct module function |
---|
937 | #(either from this module or C-extension) |
---|
938 | extrapolate_second_order(self) |
---|
939 | |
---|
940 | |
---|
941 | def update(quantity, timestep): |
---|
942 | """Update centroid values based on values stored in |
---|
943 | explicit_update and semi_implicit_update as well as given timestep |
---|
944 | |
---|
945 | Function implementing forcing terms must take on argument |
---|
946 | which is the domain and they must update either explicit |
---|
947 | or implicit updates, e,g,: |
---|
948 | |
---|
949 | def gravity(domain): |
---|
950 | .... |
---|
951 | domain.quantities['xmomentum'].explicit_update = ... |
---|
952 | domain.quantities['ymomentum'].explicit_update = ... |
---|
953 | |
---|
954 | |
---|
955 | |
---|
956 | Explicit terms must have the form |
---|
957 | |
---|
958 | G(q, t) |
---|
959 | |
---|
960 | and explicit scheme is |
---|
961 | |
---|
962 | q^{(n+1}) = q^{(n)} + delta_t G(q^{n}, n delta_t) |
---|
963 | |
---|
964 | |
---|
965 | Semi implicit forcing terms are assumed to have the form |
---|
966 | |
---|
967 | G(q, t) = H(q, t) q |
---|
968 | |
---|
969 | and the semi implicit scheme will then be |
---|
970 | |
---|
971 | q^{(n+1}) = q^{(n)} + delta_t H(q^{n}, n delta_t) q^{(n+1}) |
---|
972 | |
---|
973 | |
---|
974 | """ |
---|
975 | |
---|
976 | from Numeric import sum, equal, ones, Float |
---|
977 | |
---|
978 | N = quantity.centroid_values.shape[0] |
---|
979 | |
---|
980 | |
---|
981 | #Divide H by conserved quantity to obtain G (see docstring above) |
---|
982 | |
---|
983 | |
---|
984 | for k in range(N): |
---|
985 | x = quantity.centroid_values[k] |
---|
986 | if x == 0.0: |
---|
987 | #FIXME: Is this right |
---|
988 | quantity.semi_implicit_update[k] = 0.0 |
---|
989 | else: |
---|
990 | quantity.semi_implicit_update[k] /= x |
---|
991 | |
---|
992 | #Explicit updates |
---|
993 | quantity.centroid_values += timestep*quantity.explicit_update |
---|
994 | |
---|
995 | #Semi implicit updates |
---|
996 | denominator = ones(N, Float)-timestep*quantity.semi_implicit_update |
---|
997 | |
---|
998 | if sum(equal(denominator, 0.0)) > 0.0: |
---|
999 | msg = 'Zero division in semi implicit update. Call Stephen :-)' |
---|
1000 | raise msg |
---|
1001 | else: |
---|
1002 | #Update conserved_quantities from semi implicit updates |
---|
1003 | quantity.centroid_values /= denominator |
---|
1004 | |
---|
1005 | |
---|
1006 | def interpolate_from_vertices_to_edges(quantity): |
---|
1007 | """Compute edge values from vertex values using linear interpolation |
---|
1008 | """ |
---|
1009 | |
---|
1010 | for k in range(quantity.vertex_values.shape[0]): |
---|
1011 | q0 = quantity.vertex_values[k, 0] |
---|
1012 | q1 = quantity.vertex_values[k, 1] |
---|
1013 | q2 = quantity.vertex_values[k, 2] |
---|
1014 | |
---|
1015 | quantity.edge_values[k, 0] = 0.5*(q1+q2) |
---|
1016 | quantity.edge_values[k, 1] = 0.5*(q0+q2) |
---|
1017 | quantity.edge_values[k, 2] = 0.5*(q0+q1) |
---|
1018 | |
---|
1019 | |
---|
1020 | |
---|
1021 | def extrapolate_second_order(quantity): |
---|
1022 | """Extrapolate conserved quantities from centroid to |
---|
1023 | vertices for each volume using |
---|
1024 | second order scheme. |
---|
1025 | """ |
---|
1026 | |
---|
1027 | a, b = quantity.compute_gradients() |
---|
1028 | |
---|
1029 | X = quantity.domain.get_vertex_coordinates() |
---|
1030 | qc = quantity.centroid_values |
---|
1031 | qv = quantity.vertex_values |
---|
1032 | |
---|
1033 | #Check each triangle |
---|
1034 | for k in range(quantity.domain.number_of_elements): |
---|
1035 | #Centroid coordinates |
---|
1036 | x, y = quantity.domain.centroid_coordinates[k] |
---|
1037 | |
---|
1038 | #vertex coordinates |
---|
1039 | x0, y0, x1, y1, x2, y2 = X[k,:] |
---|
1040 | |
---|
1041 | #Extrapolate |
---|
1042 | qv[k,0] = qc[k] + a[k]*(x0-x) + b[k]*(y0-y) |
---|
1043 | qv[k,1] = qc[k] + a[k]*(x1-x) + b[k]*(y1-y) |
---|
1044 | qv[k,2] = qc[k] + a[k]*(x2-x) + b[k]*(y2-y) |
---|
1045 | |
---|
1046 | |
---|
1047 | def compute_gradients(quantity): |
---|
1048 | """Compute gradients of triangle surfaces defined by centroids of |
---|
1049 | neighbouring volumes. |
---|
1050 | If one edge is on the boundary, use own centroid as neighbour centroid. |
---|
1051 | If two or more are on the boundary, fall back to first order scheme. |
---|
1052 | """ |
---|
1053 | |
---|
1054 | from Numeric import zeros, Float |
---|
1055 | from util import gradient |
---|
1056 | |
---|
1057 | centroid_coordinates = quantity.domain.centroid_coordinates |
---|
1058 | surrogate_neighbours = quantity.domain.surrogate_neighbours |
---|
1059 | centroid_values = quantity.centroid_values |
---|
1060 | number_of_boundaries = quantity.domain.number_of_boundaries |
---|
1061 | |
---|
1062 | N = centroid_values.shape[0] |
---|
1063 | |
---|
1064 | a = zeros(N, Float) |
---|
1065 | b = zeros(N, Float) |
---|
1066 | |
---|
1067 | for k in range(N): |
---|
1068 | if number_of_boundaries[k] < 2: |
---|
1069 | #Two or three true neighbours |
---|
1070 | |
---|
1071 | #Get indices of neighbours (or self when used as surrogate) |
---|
1072 | k0, k1, k2 = surrogate_neighbours[k,:] |
---|
1073 | |
---|
1074 | #Get data |
---|
1075 | q0 = centroid_values[k0] |
---|
1076 | q1 = centroid_values[k1] |
---|
1077 | q2 = centroid_values[k2] |
---|
1078 | |
---|
1079 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
---|
1080 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
---|
1081 | x2, y2 = centroid_coordinates[k2] #V2 centroid |
---|
1082 | |
---|
1083 | #Gradient |
---|
1084 | a[k], b[k] = gradient(x0, y0, x1, y1, x2, y2, q0, q1, q2) |
---|
1085 | |
---|
1086 | elif number_of_boundaries[k] == 2: |
---|
1087 | #One true neighbour |
---|
1088 | |
---|
1089 | #Get index of the one neighbour |
---|
1090 | for k0 in surrogate_neighbours[k,:]: |
---|
1091 | if k0 != k: break |
---|
1092 | assert k0 != k |
---|
1093 | |
---|
1094 | k1 = k #self |
---|
1095 | |
---|
1096 | #Get data |
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1097 | q0 = centroid_values[k0] |
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1098 | q1 = centroid_values[k1] |
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1099 | |
---|
1100 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
---|
1101 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
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1102 | |
---|
1103 | #Gradient |
---|
1104 | a[k], b[k] = gradient2(x0, y0, x1, y1, q0, q1) |
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1105 | else: |
---|
1106 | #No true neighbours - |
---|
1107 | #Fall back to first order scheme |
---|
1108 | pass |
---|
1109 | |
---|
1110 | |
---|
1111 | return a, b |
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1112 | |
---|
1113 | |
---|
1114 | |
---|
1115 | def limit(quantity): |
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1116 | """Limit slopes for each volume to eliminate artificial variance |
---|
1117 | introduced by e.g. second order extrapolator |
---|
1118 | |
---|
1119 | This is an unsophisticated limiter as it does not take into |
---|
1120 | account dependencies among quantities. |
---|
1121 | |
---|
1122 | precondition: |
---|
1123 | vertex values are estimated from gradient |
---|
1124 | postcondition: |
---|
1125 | vertex values are updated |
---|
1126 | """ |
---|
1127 | |
---|
1128 | from Numeric import zeros, Float |
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1129 | |
---|
1130 | N = quantity.domain.number_of_elements |
---|
1131 | |
---|
1132 | beta_w = quantity.domain.beta_w |
---|
1133 | |
---|
1134 | qc = quantity.centroid_values |
---|
1135 | qv = quantity.vertex_values |
---|
1136 | |
---|
1137 | #Find min and max of this and neighbour's centroid values |
---|
1138 | qmax = zeros(qc.shape, Float) |
---|
1139 | qmin = zeros(qc.shape, Float) |
---|
1140 | |
---|
1141 | for k in range(N): |
---|
1142 | qmax[k] = qmin[k] = qc[k] |
---|
1143 | for i in range(3): |
---|
1144 | n = quantity.domain.neighbours[k,i] |
---|
1145 | if n >= 0: |
---|
1146 | qn = qc[n] #Neighbour's centroid value |
---|
1147 | |
---|
1148 | qmin[k] = min(qmin[k], qn) |
---|
1149 | qmax[k] = max(qmax[k], qn) |
---|
1150 | |
---|
1151 | |
---|
1152 | #Diffences between centroids and maxima/minima |
---|
1153 | dqmax = qmax - qc |
---|
1154 | dqmin = qmin - qc |
---|
1155 | |
---|
1156 | #Deltas between vertex and centroid values |
---|
1157 | dq = zeros(qv.shape, Float) |
---|
1158 | for i in range(3): |
---|
1159 | dq[:,i] = qv[:,i] - qc |
---|
1160 | |
---|
1161 | #Phi limiter |
---|
1162 | for k in range(N): |
---|
1163 | |
---|
1164 | #Find the gradient limiter (phi) across vertices |
---|
1165 | phi = 1.0 |
---|
1166 | for i in range(3): |
---|
1167 | r = 1.0 |
---|
1168 | if (dq[k,i] > 0): r = dqmax[k]/dq[k,i] |
---|
1169 | if (dq[k,i] < 0): r = dqmin[k]/dq[k,i] |
---|
1170 | |
---|
1171 | phi = min( min(r*beta_w, 1), phi ) |
---|
1172 | |
---|
1173 | #Then update using phi limiter |
---|
1174 | for i in range(3): |
---|
1175 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
1176 | |
---|
1177 | |
---|
1178 | |
---|
1179 | import compile |
---|
1180 | if compile.can_use_C_extension('quantity_ext.c'): |
---|
1181 | #Replace python version with c implementations |
---|
1182 | |
---|
1183 | from quantity_ext import limit, compute_gradients,\ |
---|
1184 | extrapolate_second_order, interpolate_from_vertices_to_edges, update |
---|