[2526] | 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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[2608] | 17 | from numpy import concatenate, zeros, Float, Int, array, reshape, ArrayType, allclose, take, sum, equal |
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[2526] | 18 | |
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[2608] | 19 | |
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[2526] | 20 | class Quantity: |
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| 21 | |
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| 22 | def __init__(self, domain, vertex_values=None): |
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| 23 | |
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| 24 | from mesh import Mesh |
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[2608] | 25 | #from Numeric import array, zeros, Float |
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[2526] | 26 | |
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| 27 | msg = 'First argument in Quantity.__init__ ' |
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| 28 | msg += 'must be of class Mesh (or a subclass thereof)' |
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| 29 | assert isinstance(domain, Mesh), msg |
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| 30 | |
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| 31 | if vertex_values is None: |
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| 32 | N = domain.number_of_elements |
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| 33 | self.vertex_values = zeros((N, 3), Float) |
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| 34 | else: |
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| 35 | self.vertex_values = array(vertex_values).astype(Float) |
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| 36 | |
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| 37 | N, V = self.vertex_values.shape |
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| 38 | assert V == 3,\ |
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| 39 | 'Three vertex values per element must be specified' |
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| 40 | |
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| 41 | |
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| 42 | msg = 'Number of vertex values (%d) must be consistent with'\ |
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| 43 | %N |
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| 44 | msg += 'number of elements in specified domain (%d).'\ |
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| 45 | %domain.number_of_elements |
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| 46 | |
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| 47 | assert N == domain.number_of_elements, msg |
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| 48 | |
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| 49 | self.domain = domain |
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| 50 | |
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| 51 | #Allocate space for other quantities |
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| 52 | self.centroid_values = zeros(N, Float) |
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| 53 | self.edge_values = zeros((N, 3), Float) |
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| 54 | |
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| 55 | #Intialise centroid and edge_values |
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| 56 | self.interpolate() |
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| 57 | |
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| 58 | |
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| 59 | |
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| 60 | #Methods for operator overloading |
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| 61 | def __len__(self): |
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| 62 | return self.centroid_values.shape[0] |
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| 63 | |
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| 64 | |
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| 65 | def __neg__(self): |
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| 66 | """Negate all values in this quantity giving meaning to the |
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| 67 | expression -Q where Q is an instance of class Quantity |
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| 68 | """ |
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| 69 | |
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| 70 | Q = Quantity(self.domain) |
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| 71 | Q.set_values(-self.vertex_values) |
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| 72 | return Q |
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| 73 | |
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| 74 | |
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| 75 | def __add__(self, other): |
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| 76 | """Add to self anything that could populate a quantity |
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| 77 | |
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| 78 | E.g other can be a constant, an array, a function, another quantity |
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| 79 | (except for a filename or points, attributes (for now)) |
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| 80 | - see set_values for details |
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| 81 | """ |
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| 82 | |
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| 83 | Q = Quantity(self.domain) |
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| 84 | Q.set_values(other) |
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| 85 | |
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| 86 | result = Quantity(self.domain) |
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| 87 | result.set_values(self.vertex_values + Q.vertex_values) |
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| 88 | return result |
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| 89 | |
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| 90 | def __radd__(self, other): |
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| 91 | """Handle cases like 7+Q, where Q is an instance of class Quantity |
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| 92 | """ |
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| 93 | return self + other |
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| 94 | |
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| 95 | |
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| 96 | def __sub__(self, other): |
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| 97 | return self + -other #Invoke __neg__ |
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| 98 | |
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| 99 | def __mul__(self, other): |
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| 100 | """Multiply self with anything that could populate a quantity |
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| 101 | |
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| 102 | E.g other can be a constant, an array, a function, another quantity |
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| 103 | (except for a filename or points, attributes (for now)) |
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| 104 | - see set_values for details |
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| 105 | |
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| 106 | Note that if two quantitites q1 and q2 are multiplied, |
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| 107 | vertex values are multiplied entry by entry |
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| 108 | while centroid and edge values are re-interpolated. |
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| 109 | Hence they won't be the product of centroid or edge values |
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| 110 | from q1 and q2. |
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| 111 | """ |
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| 112 | |
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| 113 | Q = Quantity(self.domain) |
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| 114 | Q.set_values(other) |
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| 115 | |
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| 116 | result = Quantity(self.domain) |
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| 117 | result.set_values(self.vertex_values * Q.vertex_values) |
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| 118 | return result |
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| 119 | |
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| 120 | def __rmul__(self, other): |
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| 121 | """Handle cases like 3*Q, where Q is an instance of class Quantity |
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| 122 | """ |
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| 123 | return self * other |
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| 124 | |
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| 125 | def __pow__(self, other): |
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| 126 | """Raise quantity to (numerical) power |
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| 127 | |
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| 128 | As with __mul__ vertex values are processed entry by entry |
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| 129 | while centroid and edge values are re-interpolated. |
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| 130 | |
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| 131 | Example using __pow__: |
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| 132 | Q = (Q1**2 + Q2**2)**0.5 |
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| 133 | |
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| 134 | """ |
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| 135 | |
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| 136 | result = Quantity(self.domain) |
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| 137 | result.set_values(self.vertex_values**other) |
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| 138 | return result |
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| 139 | |
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| 140 | |
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| 141 | |
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| 142 | def interpolate(self): |
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| 143 | """Compute interpolated values at edges and centroid |
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| 144 | Pre-condition: vertex_values have been set |
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| 145 | """ |
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| 146 | |
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| 147 | N = self.vertex_values.shape[0] |
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| 148 | for i in range(N): |
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| 149 | v0 = self.vertex_values[i, 0] |
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| 150 | v1 = self.vertex_values[i, 1] |
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| 151 | v2 = self.vertex_values[i, 2] |
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| 152 | |
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| 153 | self.centroid_values[i] = (v0 + v1 + v2)/3 |
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| 154 | |
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| 155 | self.interpolate_from_vertices_to_edges() |
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| 156 | |
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| 157 | |
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| 158 | def interpolate_from_vertices_to_edges(self): |
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| 159 | #Call correct module function |
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| 160 | #(either from this module or C-extension) |
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| 161 | interpolate_from_vertices_to_edges(self) |
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| 162 | |
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| 163 | |
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| 164 | |
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| 165 | |
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| 166 | #New leaner interface to setting values |
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| 167 | def set_values(self, |
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| 168 | numeric = None, # List, numeric array or constant |
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| 169 | quantity = None, # Another quantity |
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| 170 | function = None, # Callable object: f(x,y) |
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| 171 | geospatial_data = None, #Arbitrary dataset |
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| 172 | points = None, values = None, data_georef = None, #Input for least squares (obsoleted by use of geo_spatial object) |
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| 173 | filename = None, attribute_name = None, #Input from file |
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| 174 | alpha = None, |
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| 175 | location = 'vertices', |
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| 176 | indices = None, |
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| 177 | verbose = False, |
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| 178 | use_cache = False): |
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| 179 | |
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| 180 | """Set values for quantity based on different sources. |
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| 181 | |
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| 182 | numeric: |
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| 183 | Compatible list, Numeric array (see below) or constant. |
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| 184 | If callable it will treated as a function (see below) |
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| 185 | If instance of another Quantity it will be treated as such. |
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| 186 | If geo_spatial object it will be treated as such |
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| 187 | |
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| 188 | quantity: |
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| 189 | Another quantity (compatible quantity, e.g. obtained as a |
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| 190 | linear combination of quantities) |
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| 191 | |
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| 192 | function: |
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| 193 | Any callable object that takes two 1d arrays x and y |
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| 194 | each of length N and returns an array also of length N. |
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| 195 | The function will be evaluated at points determined by |
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| 196 | location and indices in the underlying mesh. |
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| 197 | |
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| 198 | geospatial_data: |
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| 199 | Arbitrary geo spatial dataset in the form of the class |
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| 200 | Geospatial_data. Mesh points are populated using least squares |
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| 201 | fitting |
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| 202 | |
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| 203 | points: |
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| 204 | Nx2 array of data points for use with least squares fit |
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| 205 | If points are present, an N array of attribute |
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| 206 | values corresponding to |
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| 207 | each data point must be present. |
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| 208 | |
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| 209 | values: |
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| 210 | If points is specified, values is an array of length N containing |
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| 211 | attribute values for each point. |
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| 212 | |
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| 213 | data_georef: |
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| 214 | If points is specified, geo_reference applies to each point. |
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| 215 | |
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| 216 | filename: |
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| 217 | Name of a .pts file containing data points and attributes for |
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| 218 | use with least squares. |
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| 219 | |
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| 220 | attribute_name: |
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| 221 | If specified, any array matching that name |
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| 222 | will be used. from file or geospatial_data. |
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| 223 | Otherwise a default will be used. |
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| 224 | |
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| 225 | alpha: |
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| 226 | Smoothing parameter to be used with least squares fits. |
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| 227 | See module least_squares for further details about alpha. |
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| 228 | Alpha will only be used with points, values or filename. |
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| 229 | Otherwise it will be ignored. |
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| 230 | |
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| 231 | |
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| 232 | location: Where values are to be stored. |
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| 233 | Permissible options are: vertices, edges, centroids |
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| 234 | Default is 'vertices' |
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| 235 | |
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| 236 | In case of location == 'centroids' the dimension values must |
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| 237 | be a list of a Numerical array of length N, |
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| 238 | N being the number of elements. |
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| 239 | Otherwise it must be of dimension Nx3 |
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| 240 | |
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| 241 | |
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| 242 | The values will be stored in elements following their |
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| 243 | internal ordering. |
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| 244 | |
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| 245 | If location is not 'unique vertices' Indices is the |
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| 246 | set of element ids that the operation applies to. |
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| 247 | If location is 'unique vertices' Indices is the set |
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| 248 | of vertex ids that the operation applies to. |
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| 249 | |
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| 250 | If selected location is vertices, values for |
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| 251 | centroid and edges will be assigned interpolated |
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| 252 | values. In any other case, only values for the |
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| 253 | specified locations will be assigned and the others |
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| 254 | will be left undefined. |
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| 255 | |
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| 256 | verbose: True means that output to stdout is generated |
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| 257 | |
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| 258 | use_cache: True means that caching of intermediate results is |
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| 259 | attempted for least squares fit. |
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| 260 | |
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| 261 | |
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| 262 | |
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| 263 | |
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| 264 | Exactly one of the arguments |
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| 265 | numeric, quantity, function, points, filename |
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| 266 | must be present. |
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| 267 | """ |
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| 268 | |
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| 269 | from geospatial_data.geospatial_data import Geospatial_data |
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| 270 | from types import FloatType, IntType, LongType, ListType, NoneType |
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| 271 | |
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| 272 | #General input checks |
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| 273 | L = [numeric, quantity, function, geospatial_data, points, filename] |
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| 274 | msg = 'Exactly one of the arguments '+\ |
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| 275 | 'numeric, quantity, function, geospatial_data, points, or filename '+\ |
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| 276 | 'must be present.' |
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| 277 | assert L.count(None) == len(L)-1, msg |
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| 278 | |
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| 279 | |
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| 280 | if location not in ['vertices', 'centroids', 'edges', |
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| 281 | 'unique vertices']: |
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| 282 | msg = 'Invalid location: %s' %location |
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| 283 | raise msg |
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| 284 | |
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| 285 | |
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| 286 | msg = 'Indices must be a list or None' |
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| 287 | assert type(indices) in [ListType, NoneType, ArrayType], msg |
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| 288 | |
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| 289 | |
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| 290 | if not(points is None and values is None and data_georef is None): |
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| 291 | from warnings import warn |
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| 292 | |
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| 293 | msg = 'Using points, values or data_georef with set_quantity ' |
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| 294 | msg += 'is obsolete. Please use a Geospatial_data object instead.' |
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| 295 | warn(msg, DeprecationWarning) |
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| 296 | |
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| 297 | |
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| 298 | |
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| 299 | #Determine which 'set_values_from_...' to use |
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| 300 | |
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| 301 | if numeric is not None: |
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| 302 | if type(numeric) in [FloatType, IntType, LongType]: |
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| 303 | self.set_values_from_constant(numeric, |
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| 304 | location, indices, verbose) |
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| 305 | elif type(numeric) in [ArrayType, ListType]: |
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| 306 | self.set_values_from_array(numeric, |
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| 307 | location, indices, verbose) |
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| 308 | elif callable(numeric): |
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| 309 | self.set_values_from_function(numeric, |
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| 310 | location, indices, verbose) |
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| 311 | elif isinstance(numeric, Quantity): |
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| 312 | self.set_values_from_quantity(numeric, |
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| 313 | location, indices, verbose) |
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| 314 | elif isinstance(numeric, Geospatial_data): |
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| 315 | self.set_values_from_geospatial_data(numeric, |
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| 316 | alpha, |
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| 317 | location, indices, |
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| 318 | verbose = verbose, |
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| 319 | use_cache = use_cache) |
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| 320 | else: |
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| 321 | msg = 'Illegal type for argument numeric: %s' %str(numeric) |
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| 322 | raise msg |
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| 323 | |
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| 324 | elif quantity is not None: |
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| 325 | self.set_values_from_quantity(quantity, |
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| 326 | location, indices, verbose) |
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| 327 | elif function is not None: |
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| 328 | msg = 'Argument function must be callable' |
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| 329 | assert callable(function), msg |
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| 330 | self.set_values_from_function(function, |
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| 331 | location, indices, verbose) |
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| 332 | elif geospatial_data is not None: |
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| 333 | self.set_values_from_geospatial_data(geospatial_data, |
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| 334 | alpha, |
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| 335 | location, indices, |
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| 336 | verbose = verbose, |
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| 337 | use_cache = use_cache) |
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| 338 | elif points is not None: |
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| 339 | print 'The usage of points in set_values will be deprecated.' +\ |
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| 340 | 'Please use the geospatial_data object.' |
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| 341 | |
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| 342 | msg = 'When points are specified, associated values must also be.' |
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| 343 | assert values is not None, msg |
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| 344 | self.set_values_from_points(points, values, alpha, |
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| 345 | location, indices, |
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| 346 | data_georef = data_georef, |
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| 347 | verbose = verbose, |
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| 348 | use_cache = use_cache) |
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| 349 | elif filename is not None: |
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| 350 | self.set_values_from_file(filename, attribute_name, alpha, |
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| 351 | location, indices, |
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| 352 | verbose = verbose, |
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| 353 | use_cache = use_cache) |
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| 354 | else: |
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| 355 | raise 'This can\'t happen :-)' |
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| 356 | |
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| 357 | |
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| 358 | #Update all locations in triangles |
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| 359 | if location == 'vertices' or location == 'unique vertices': |
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| 360 | #Intialise centroid and edge_values |
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| 361 | self.interpolate() |
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| 362 | |
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| 363 | if location == 'centroids': |
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| 364 | #Extrapolate 1st order - to capture notion of area being specified |
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| 365 | self.extrapolate_first_order() |
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| 366 | |
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| 367 | |
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| 368 | |
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| 369 | #Specific functions for setting values |
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| 370 | def set_values_from_constant(self, X, |
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| 371 | location, indices, verbose): |
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| 372 | """Set quantity values from specified constant X |
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| 373 | """ |
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| 374 | |
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| 375 | |
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| 376 | if location == 'centroids': |
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| 377 | if (indices == None): |
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| 378 | self.centroid_values[:] = X |
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| 379 | else: |
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| 380 | #Brute force |
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| 381 | for i in indices: |
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| 382 | self.centroid_values[i,:] = X |
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| 383 | |
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| 384 | elif location == 'edges': |
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| 385 | if (indices == None): |
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| 386 | self.edge_values[:] = X |
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| 387 | else: |
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| 388 | #Brute force |
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| 389 | for i in indices: |
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| 390 | self.edge_values[i,:] = X |
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| 391 | |
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| 392 | elif location == 'unique vertices': |
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| 393 | if (indices == None): |
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| 394 | self.edge_values[:] = X |
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| 395 | else: |
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| 396 | |
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| 397 | #Go through list of unique vertices |
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| 398 | for unique_vert_id in indices: |
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| 399 | triangles = self.domain.vertexlist[unique_vert_id] |
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| 400 | |
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| 401 | #In case there are unused points |
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| 402 | if triangles is None: continue |
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| 403 | |
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| 404 | #Go through all triangle, vertex pairs |
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| 405 | #and set corresponding vertex value |
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| 406 | for triangle_id, vertex_id in triangles: |
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| 407 | self.vertex_values[triangle_id, vertex_id] = X |
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| 408 | |
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| 409 | #Intialise centroid and edge_values |
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| 410 | self.interpolate() |
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| 411 | else: |
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| 412 | if (indices == None): |
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| 413 | self.vertex_values[:] = X |
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| 414 | else: |
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| 415 | #Brute force |
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| 416 | for i_vertex in indices: |
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| 417 | self.vertex_values[i_vertex,:] = X |
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| 418 | |
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| 419 | |
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| 420 | |
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| 421 | |
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| 422 | |
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| 423 | |
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| 424 | def set_values_from_array(self, values, |
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| 425 | location, indices, verbose): |
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| 426 | """Set values for quantity |
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| 427 | |
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| 428 | values: Numeric array |
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| 429 | location: Where values are to be stored. |
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| 430 | Permissible options are: vertices, edges, centroid, unique vertices |
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| 431 | Default is 'vertices' |
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| 432 | |
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| 433 | indices - if this action is carried out on a subset of |
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| 434 | elements or unique vertices |
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| 435 | The element/unique vertex indices are specified here. |
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| 436 | |
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| 437 | In case of location == 'centroid' the dimension values must |
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| 438 | be a list of a Numerical array of length N, N being the number |
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| 439 | of elements. |
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| 440 | |
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| 441 | Otherwise it must be of dimension Nx3 |
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| 442 | |
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| 443 | The values will be stored in elements following their |
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| 444 | internal ordering. |
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| 445 | |
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| 446 | If selected location is vertices, values for centroid and edges |
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| 447 | will be assigned interpolated values. |
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| 448 | In any other case, only values for the specified locations |
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| 449 | will be assigned and the others will be left undefined. |
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| 450 | """ |
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| 451 | |
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| 452 | values = array(values).astype(Float) |
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| 453 | |
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| 454 | if indices is not None: |
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| 455 | indices = array(indices).astype(Int) |
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| 456 | msg = 'Number of values must match number of indices' |
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| 457 | assert values.shape[0] == indices.shape[0], msg |
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| 458 | |
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| 459 | N = self.centroid_values.shape[0] |
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| 460 | |
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| 461 | if location == 'centroids': |
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| 462 | assert len(values.shape) == 1, 'Values array must be 1d' |
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| 463 | |
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| 464 | if indices is None: |
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| 465 | msg = 'Number of values must match number of elements' |
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| 466 | assert values.shape[0] == N, msg |
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| 467 | |
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| 468 | self.centroid_values = values |
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| 469 | else: |
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| 470 | msg = 'Number of values must match number of indices' |
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| 471 | assert values.shape[0] == indices.shape[0], msg |
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| 472 | |
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| 473 | #Brute force |
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| 474 | for i in range(len(indices)): |
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| 475 | self.centroid_values[indices[i]] = values[i] |
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| 476 | |
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| 477 | elif location == 'edges': |
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| 478 | assert len(values.shape) == 2, 'Values array must be 2d' |
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| 479 | |
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| 480 | msg = 'Number of values must match number of elements' |
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| 481 | assert values.shape[0] == N, msg |
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| 482 | |
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| 483 | msg = 'Array must be N x 3' |
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| 484 | assert values.shape[1] == 3, msg |
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| 485 | |
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| 486 | self.edge_values = values |
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| 487 | |
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| 488 | elif location == 'unique vertices': |
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| 489 | assert len(values.shape) == 1 or allclose(values.shape[1:], 1),\ |
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| 490 | 'Values array must be 1d' |
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| 491 | |
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| 492 | self.set_vertex_values(values.flat, indices = indices) |
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| 493 | else: |
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| 494 | if len(values.shape) == 1: |
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| 495 | self.set_vertex_values(values, indices = indices) |
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| 496 | #if indices == None: |
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| 497 | #Values are being specified once for each unique vertex |
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| 498 | # msg = 'Number of values must match number of vertices' |
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| 499 | # assert values.shape[0] == self.domain.coordinates.shape[0], msg |
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| 500 | # self.set_vertex_values(values) |
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| 501 | #else: |
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| 502 | # for element_index, value in map(None, indices, values): |
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| 503 | # self.vertex_values[element_index, :] = value |
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| 504 | |
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| 505 | elif len(values.shape) == 2: |
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| 506 | #Vertex values are given as a triplet for each triangle |
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| 507 | |
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| 508 | msg = 'Array must be N x 3' |
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| 509 | assert values.shape[1] == 3, msg |
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| 510 | |
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| 511 | if indices == None: |
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| 512 | self.vertex_values = values |
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| 513 | else: |
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| 514 | for element_index, value in map(None, indices, values): |
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| 515 | self.vertex_values[element_index] = value |
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| 516 | else: |
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| 517 | msg = 'Values array must be 1d or 2d' |
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| 518 | raise msg |
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| 519 | |
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| 520 | def set_values_from_quantity(self, q, |
---|
| 521 | location, indices, verbose): |
---|
| 522 | """Set quantity values from specified quantity instance q |
---|
| 523 | |
---|
| 524 | Location is ignored |
---|
| 525 | """ |
---|
| 526 | |
---|
| 527 | |
---|
| 528 | A = q.vertex_values |
---|
| 529 | |
---|
| 530 | msg = 'Quantities are defined on different meshes. '+\ |
---|
| 531 | 'This might be a case for implementing interpolation '+\ |
---|
| 532 | 'between different meshes.' |
---|
| 533 | assert allclose(A.shape, self.vertex_values.shape), msg |
---|
| 534 | |
---|
| 535 | self.set_values(A, location='vertices', |
---|
| 536 | indices=indices, |
---|
| 537 | verbose=verbose) |
---|
| 538 | |
---|
| 539 | |
---|
| 540 | def set_values_from_function(self, f, |
---|
| 541 | location, indices, verbose): |
---|
| 542 | """Set values for quantity using specified function |
---|
| 543 | |
---|
| 544 | f: x, y -> z Function where x, y and z are arrays |
---|
| 545 | location: Where values are to be stored. |
---|
| 546 | Permissible options are: vertices, centroid, edges, |
---|
| 547 | unique vertices |
---|
| 548 | Default is "vertices" |
---|
| 549 | """ |
---|
| 550 | |
---|
| 551 | #FIXME: Should check that function returns something sensible and |
---|
| 552 | #raise a meaningfull exception if it returns None for example |
---|
| 553 | |
---|
| 554 | #FIXME: Should supply absolute coordinates |
---|
| 555 | |
---|
| 556 | if (indices is None): |
---|
| 557 | indices = range(len(self)) |
---|
| 558 | is_subset = False |
---|
| 559 | else: |
---|
| 560 | is_subset = True |
---|
| 561 | |
---|
| 562 | if location == 'centroids': |
---|
| 563 | P = take(self.domain.centroid_coordinates, indices) |
---|
| 564 | if is_subset: |
---|
| 565 | self.set_values(f(P[:,0], P[:,1]), |
---|
| 566 | location = location, |
---|
| 567 | indices = indices) |
---|
| 568 | else: |
---|
| 569 | self.set_values(f(P[:,0], P[:,1]), location = location) |
---|
| 570 | elif location == 'vertices': |
---|
| 571 | P = self.domain.vertex_coordinates |
---|
| 572 | if is_subset: |
---|
| 573 | #Brute force |
---|
| 574 | for e in indices: |
---|
| 575 | for i in range(3): |
---|
| 576 | self.vertex_values[e,i] = f(P[e,2*i], P[e,2*i+1]) |
---|
| 577 | else: |
---|
| 578 | for i in range(3): |
---|
| 579 | self.vertex_values[:,i] = f(P[:,2*i], P[:,2*i+1]) |
---|
| 580 | else: |
---|
| 581 | raise 'Not implemented: %s' %location |
---|
| 582 | |
---|
| 583 | |
---|
| 584 | |
---|
| 585 | def set_values_from_geospatial_data(self, geospatial_data, alpha, |
---|
| 586 | location, indices, |
---|
| 587 | verbose = False, |
---|
| 588 | use_cache = False): |
---|
| 589 | |
---|
| 590 | #FIXME: Use this function for the time being. Later move code in here |
---|
| 591 | |
---|
| 592 | points = geospatial_data.get_data_points(absolute = False) |
---|
| 593 | values = geospatial_data.get_attributes() |
---|
| 594 | data_georef = geospatial_data.get_geo_reference() |
---|
| 595 | |
---|
| 596 | |
---|
| 597 | |
---|
| 598 | self.set_values_from_points(points, values, alpha, |
---|
| 599 | location, indices, |
---|
| 600 | data_georef = data_georef, |
---|
| 601 | verbose = verbose, |
---|
| 602 | use_cache = use_cache) |
---|
| 603 | |
---|
| 604 | |
---|
| 605 | |
---|
| 606 | def set_values_from_points(self, points, values, alpha, |
---|
| 607 | location, indices, |
---|
| 608 | data_georef = None, |
---|
| 609 | verbose = False, |
---|
| 610 | use_cache = False): |
---|
| 611 | """Set quantity values from arbitray data points using least squares |
---|
| 612 | """ |
---|
| 613 | |
---|
| 614 | |
---|
| 615 | from utilities.numerical_tools import ensure_numeric |
---|
| 616 | from least_squares import fit_to_mesh |
---|
| 617 | from coordinate_transforms.geo_reference import Geo_reference |
---|
| 618 | |
---|
| 619 | |
---|
| 620 | points = ensure_numeric(points, Float) |
---|
| 621 | values = ensure_numeric(values, Float) |
---|
| 622 | |
---|
| 623 | if location != 'vertices': |
---|
| 624 | msg = 'set_values_from_points is only defined for '+\ |
---|
| 625 | 'location=\'vertices\'' |
---|
| 626 | raise msg |
---|
| 627 | |
---|
| 628 | coordinates = self.domain.coordinates |
---|
| 629 | triangles = self.domain.triangles |
---|
| 630 | |
---|
| 631 | |
---|
| 632 | #Take care of georeferencing |
---|
| 633 | if data_georef is None: |
---|
| 634 | data_georef = Geo_reference() |
---|
| 635 | |
---|
| 636 | |
---|
| 637 | mesh_georef = self.domain.geo_reference |
---|
| 638 | |
---|
| 639 | #print mesh_georef |
---|
| 640 | #print data_georef |
---|
| 641 | #print points |
---|
| 642 | |
---|
| 643 | |
---|
| 644 | #Call least squares method |
---|
| 645 | args = (coordinates, triangles, points, values) |
---|
| 646 | kwargs = {'data_origin': data_georef.get_origin(), |
---|
| 647 | 'mesh_origin': mesh_georef.get_origin(), |
---|
| 648 | 'alpha': alpha, |
---|
| 649 | 'precrop': True, |
---|
| 650 | 'verbose': verbose} |
---|
| 651 | |
---|
| 652 | #print kwargs |
---|
| 653 | |
---|
| 654 | if use_cache is True: |
---|
| 655 | try: |
---|
| 656 | from caching import cache |
---|
| 657 | except: |
---|
| 658 | msg = 'Caching was requested, but caching module'+\ |
---|
| 659 | 'could not be imported' |
---|
| 660 | raise msg |
---|
| 661 | |
---|
| 662 | vertex_attributes = cache(fit_to_mesh, |
---|
| 663 | args, kwargs, |
---|
| 664 | verbose = verbose) |
---|
| 665 | else: |
---|
| 666 | |
---|
| 667 | vertex_attributes = apply(fit_to_mesh, |
---|
| 668 | args, kwargs) |
---|
| 669 | |
---|
| 670 | #Call underlying method using array values |
---|
| 671 | self.set_values_from_array(vertex_attributes, |
---|
| 672 | location, indices, verbose) |
---|
| 673 | |
---|
| 674 | |
---|
| 675 | |
---|
| 676 | def set_values_from_file(self, filename, attribute_name, alpha, |
---|
| 677 | location, indices, |
---|
| 678 | verbose = False, |
---|
| 679 | use_cache = False): |
---|
| 680 | """Set quantity based on arbitrary points in .pts file |
---|
| 681 | using least_squares attribute_name selects name of attribute |
---|
| 682 | present in file. |
---|
| 683 | If not specified try to use whatever is available in file. |
---|
| 684 | """ |
---|
| 685 | |
---|
| 686 | from load_mesh.loadASCII import import_points_file |
---|
| 687 | from geospatial_data.geospatial_data import points_dictionary2geospatial_data |
---|
| 688 | |
---|
| 689 | from types import StringType |
---|
| 690 | msg = 'Filename must be a text string' |
---|
| 691 | assert type(filename) == StringType, msg |
---|
| 692 | |
---|
| 693 | |
---|
| 694 | #Read from (NetCDF) file |
---|
| 695 | #FIXME (Ole): This function should really return a Geospatial_data object. |
---|
| 696 | points_dict = import_points_file(filename) |
---|
| 697 | points = points_dict['pointlist'] |
---|
| 698 | attributes = points_dict['attributelist'] |
---|
| 699 | |
---|
| 700 | if attribute_name is None: |
---|
| 701 | names = attributes.keys() |
---|
| 702 | attribute_name = names[0] |
---|
| 703 | |
---|
| 704 | msg = 'Attribute_name must be a text string' |
---|
| 705 | assert type(attribute_name) == StringType, msg |
---|
| 706 | |
---|
| 707 | |
---|
| 708 | if verbose: |
---|
| 709 | print 'Using attribute %s from file %s' %(attribute_name, filename) |
---|
| 710 | print 'Available attributes: %s' %(names) |
---|
| 711 | |
---|
| 712 | #try: |
---|
| 713 | # z = attributes[attribute_name] |
---|
| 714 | #except: |
---|
| 715 | # msg = 'Could not extract attribute %s from file %s'\ |
---|
| 716 | # %(attribute_name, filename) |
---|
| 717 | # raise msg |
---|
| 718 | |
---|
| 719 | |
---|
| 720 | #Take care of georeferencing |
---|
| 721 | if points_dict.has_key('geo_reference') and \ |
---|
| 722 | points_dict['geo_reference'] is not None: |
---|
| 723 | data_georef = points_dict['geo_reference'] |
---|
| 724 | else: |
---|
| 725 | data_georef = None |
---|
| 726 | |
---|
| 727 | |
---|
| 728 | |
---|
| 729 | #Call underlying method for geospatial data |
---|
| 730 | geospatial_data = points_dictionary2geospatial_data(points_dict) |
---|
| 731 | geospatial_data.set_default_attribute_name(attribute_name) |
---|
| 732 | |
---|
| 733 | self.set_values_from_geospatial_data(geospatial_data, |
---|
| 734 | alpha, |
---|
| 735 | location, indices, |
---|
| 736 | verbose = verbose, |
---|
| 737 | use_cache = use_cache) |
---|
| 738 | |
---|
| 739 | #Call underlying method for points |
---|
| 740 | #self.set_values_from_points(points, z, alpha, |
---|
| 741 | # location, indices, |
---|
| 742 | # data_georef = data_georef, |
---|
| 743 | # verbose = verbose, |
---|
| 744 | # use_cache = use_cache) |
---|
| 745 | |
---|
| 746 | |
---|
| 747 | |
---|
| 748 | def get_values(self, location='vertices', indices = None): |
---|
| 749 | """get values for quantity |
---|
| 750 | |
---|
| 751 | return X, Compatible list, Numeric array (see below) |
---|
| 752 | location: Where values are to be stored. |
---|
| 753 | Permissible options are: vertices, edges, centroid |
---|
| 754 | and unique vertices. Default is 'vertices' |
---|
| 755 | |
---|
| 756 | In case of location == 'centroids' the dimension values must |
---|
| 757 | be a list of a Numerical array of length N, N being the number |
---|
| 758 | of elements. Otherwise it must be of dimension Nx3 |
---|
| 759 | |
---|
| 760 | The returned values with be a list the length of indices |
---|
| 761 | (N if indices = None). Each value will be a list of the three |
---|
| 762 | vertex values for this quantity. |
---|
| 763 | |
---|
| 764 | Indices is the set of element ids that the operation applies to. |
---|
| 765 | |
---|
| 766 | The values will be stored in elements following their |
---|
| 767 | internal ordering. |
---|
| 768 | |
---|
| 769 | """ |
---|
| 770 | |
---|
| 771 | if location not in ['vertices', 'centroids', 'edges', 'unique vertices']: |
---|
| 772 | msg = 'Invalid location: %s' %location |
---|
| 773 | raise msg |
---|
| 774 | |
---|
[2608] | 775 | import types |
---|
[2526] | 776 | assert type(indices) in [types.ListType, types.NoneType, |
---|
[2608] | 777 | ArrayType],\ |
---|
[2526] | 778 | 'Indices must be a list or None' |
---|
| 779 | |
---|
| 780 | if location == 'centroids': |
---|
| 781 | if (indices == None): |
---|
| 782 | indices = range(len(self)) |
---|
| 783 | return take(self.centroid_values,indices) |
---|
| 784 | elif location == 'edges': |
---|
| 785 | if (indices == None): |
---|
| 786 | indices = range(len(self)) |
---|
| 787 | return take(self.edge_values,indices) |
---|
| 788 | elif location == 'unique vertices': |
---|
| 789 | if (indices == None): |
---|
| 790 | indices=range(self.domain.coordinates.shape[0]) |
---|
| 791 | vert_values = [] |
---|
| 792 | #Go through list of unique vertices |
---|
| 793 | for unique_vert_id in indices: |
---|
| 794 | triangles = self.domain.vertexlist[unique_vert_id] |
---|
| 795 | |
---|
| 796 | #In case there are unused points |
---|
| 797 | if triangles is None: |
---|
| 798 | msg = 'Unique vertex not associated with triangles' |
---|
| 799 | raise msg |
---|
| 800 | |
---|
| 801 | # Go through all triangle, vertex pairs |
---|
| 802 | # Average the values |
---|
| 803 | sum = 0 |
---|
| 804 | for triangle_id, vertex_id in triangles: |
---|
| 805 | sum += self.vertex_values[triangle_id, vertex_id] |
---|
| 806 | vert_values.append(sum/len(triangles)) |
---|
[2608] | 807 | return array(vert_values) |
---|
[2526] | 808 | else: |
---|
| 809 | if (indices == None): |
---|
| 810 | indices = range(len(self)) |
---|
| 811 | return take(self.vertex_values,indices) |
---|
| 812 | |
---|
| 813 | |
---|
| 814 | |
---|
| 815 | def set_vertex_values(self, A, indices = None): |
---|
| 816 | """Set vertex values for all unique vertices based on input array A |
---|
| 817 | which has one entry per unique vertex, i.e. |
---|
| 818 | one value for each row in array self.domain.coordinates or |
---|
| 819 | one value for each row in vertexlist. |
---|
| 820 | |
---|
| 821 | indices is the list of vertex_id's that will be set. |
---|
| 822 | |
---|
| 823 | This function is used by set_values_from_array |
---|
| 824 | """ |
---|
| 825 | |
---|
| 826 | #Assert that A can be converted to a Numeric array of appropriate dim |
---|
| 827 | A = array(A, Float) |
---|
| 828 | |
---|
| 829 | #print 'SHAPE A', A.shape |
---|
| 830 | assert len(A.shape) == 1 |
---|
| 831 | |
---|
| 832 | if indices == None: |
---|
| 833 | assert A.shape[0] == self.domain.coordinates.shape[0] |
---|
| 834 | vertex_list = range(A.shape[0]) |
---|
| 835 | else: |
---|
| 836 | assert A.shape[0] == len(indices) |
---|
| 837 | vertex_list = indices |
---|
| 838 | |
---|
| 839 | #Go through list of unique vertices |
---|
| 840 | for i_index, unique_vert_id in enumerate(vertex_list): |
---|
| 841 | triangles = self.domain.vertexlist[unique_vert_id] |
---|
| 842 | |
---|
| 843 | if triangles is None: continue #In case there are unused points |
---|
| 844 | |
---|
| 845 | #Go through all triangle, vertex pairs |
---|
| 846 | #touching vertex unique_vert_id and set corresponding vertex value |
---|
| 847 | for triangle_id, vertex_id in triangles: |
---|
| 848 | self.vertex_values[triangle_id, vertex_id] = A[i_index] |
---|
| 849 | |
---|
| 850 | #Intialise centroid and edge_values |
---|
| 851 | self.interpolate() |
---|
| 852 | |
---|
| 853 | |
---|
| 854 | def smooth_vertex_values(self, value_array='field_values', |
---|
| 855 | precision = None): |
---|
| 856 | """ Smooths field_values or conserved_quantities data. |
---|
| 857 | TODO: be able to smooth individual fields |
---|
| 858 | NOTE: This function does not have a test. |
---|
| 859 | FIXME: NOT DONE - do we need it? |
---|
| 860 | FIXME: this function isn't called by anything. |
---|
| 861 | Maybe it should be removed..-DSG |
---|
| 862 | """ |
---|
| 863 | |
---|
| 864 | |
---|
| 865 | A,V = self.get_vertex_values(xy=False, |
---|
| 866 | value_array=value_array, |
---|
| 867 | smooth = True, |
---|
| 868 | precision = precision) |
---|
| 869 | |
---|
| 870 | #Set some field values |
---|
| 871 | for volume in self: |
---|
| 872 | for i,v in enumerate(volume.vertices): |
---|
| 873 | if value_array == 'field_values': |
---|
| 874 | volume.set_field_values('vertex', i, A[v,:]) |
---|
| 875 | elif value_array == 'conserved_quantities': |
---|
| 876 | volume.set_conserved_quantities('vertex', i, A[v,:]) |
---|
| 877 | |
---|
| 878 | if value_array == 'field_values': |
---|
| 879 | self.precompute() |
---|
| 880 | elif value_array == 'conserved_quantities': |
---|
| 881 | Volume.interpolate_conserved_quantities() |
---|
| 882 | |
---|
| 883 | |
---|
| 884 | #Method for outputting model results |
---|
| 885 | #FIXME: Split up into geometric and numeric stuff. |
---|
| 886 | #FIXME: Geometric (X,Y,V) should live in mesh.py |
---|
| 887 | #FIXME: STill remember to move XY to mesh |
---|
| 888 | def get_vertex_values(self, |
---|
| 889 | xy=True, |
---|
| 890 | smooth = None, |
---|
| 891 | precision = None, |
---|
| 892 | reduction = None): |
---|
| 893 | """Return vertex values like an OBJ format |
---|
| 894 | |
---|
| 895 | The vertex values are returned as one sequence in the 1D float array A. |
---|
| 896 | If requested the coordinates will be returned in 1D arrays X and Y. |
---|
| 897 | |
---|
| 898 | The connectivity is represented as an integer array, V, of dimension |
---|
| 899 | M x 3, where M is the number of volumes. Each row has three indices |
---|
| 900 | into the X, Y, A arrays defining the triangle. |
---|
| 901 | |
---|
| 902 | if smooth is True, vertex values corresponding to one common |
---|
| 903 | coordinate set will be smoothed according to the given |
---|
| 904 | reduction operator. In this case vertex coordinates will be |
---|
| 905 | de-duplicated. |
---|
| 906 | |
---|
| 907 | If no smoothings is required, vertex coordinates and values will |
---|
| 908 | be aggregated as a concatenation of values at |
---|
| 909 | vertices 0, vertices 1 and vertices 2 |
---|
| 910 | |
---|
| 911 | |
---|
| 912 | Calling convention |
---|
| 913 | if xy is True: |
---|
| 914 | X,Y,A,V = get_vertex_values |
---|
| 915 | else: |
---|
| 916 | A,V = get_vertex_values |
---|
| 917 | |
---|
| 918 | """ |
---|
| 919 | |
---|
| 920 | if smooth is None: |
---|
| 921 | smooth = self.domain.smooth |
---|
| 922 | |
---|
| 923 | if precision is None: |
---|
| 924 | precision = Float |
---|
| 925 | |
---|
| 926 | if reduction is None: |
---|
| 927 | reduction = self.domain.reduction |
---|
| 928 | |
---|
| 929 | #Create connectivity |
---|
| 930 | |
---|
| 931 | if smooth == True: |
---|
| 932 | |
---|
| 933 | V = self.domain.get_vertices() |
---|
| 934 | N = len(self.domain.vertexlist) |
---|
| 935 | A = zeros(N, precision) |
---|
| 936 | |
---|
| 937 | #Smoothing loop |
---|
| 938 | for k in range(N): |
---|
| 939 | L = self.domain.vertexlist[k] |
---|
| 940 | |
---|
| 941 | #Go through all triangle, vertex pairs |
---|
| 942 | #contributing to vertex k and register vertex value |
---|
| 943 | |
---|
| 944 | if L is None: continue #In case there are unused points |
---|
| 945 | |
---|
| 946 | contributions = [] |
---|
| 947 | for volume_id, vertex_id in L: |
---|
| 948 | v = self.vertex_values[volume_id, vertex_id] |
---|
| 949 | contributions.append(v) |
---|
| 950 | |
---|
| 951 | A[k] = reduction(contributions) |
---|
| 952 | |
---|
| 953 | |
---|
| 954 | if xy is True: |
---|
| 955 | X = self.domain.coordinates[:,0].astype(precision) |
---|
| 956 | Y = self.domain.coordinates[:,1].astype(precision) |
---|
| 957 | |
---|
| 958 | return X, Y, A, V |
---|
| 959 | else: |
---|
| 960 | return A, V |
---|
| 961 | else: |
---|
| 962 | #Don't smooth |
---|
| 963 | #obj machinery moved to general_mesh |
---|
| 964 | |
---|
| 965 | # Create a V like [[0 1 2], [3 4 5]....[3*m-2 3*m-1 3*m]] |
---|
| 966 | # These vert_id's will relate to the verts created below |
---|
| 967 | #m = len(self.domain) #Number of volumes |
---|
| 968 | #M = 3*m #Total number of unique vertices |
---|
| 969 | #V = reshape(array(range(M)).astype(Int), (m,3)) |
---|
| 970 | |
---|
| 971 | V = self.domain.get_triangles(obj=True) |
---|
| 972 | #FIXME use get_vertices, when ready |
---|
| 973 | |
---|
| 974 | A = self.vertex_values.flat |
---|
| 975 | |
---|
| 976 | #Do vertex coordinates |
---|
| 977 | if xy is True: |
---|
| 978 | C = self.domain.get_vertex_coordinates() |
---|
| 979 | |
---|
| 980 | X = C[:,0:6:2].copy() |
---|
| 981 | Y = C[:,1:6:2].copy() |
---|
| 982 | |
---|
| 983 | return X.flat, Y.flat, A, V |
---|
| 984 | else: |
---|
| 985 | return A, V |
---|
| 986 | |
---|
| 987 | |
---|
| 988 | def extrapolate_first_order(self): |
---|
| 989 | """Extrapolate conserved quantities from centroid to |
---|
| 990 | vertices for each volume using |
---|
| 991 | first order scheme. |
---|
| 992 | """ |
---|
| 993 | |
---|
| 994 | qc = self.centroid_values |
---|
| 995 | qv = self.vertex_values |
---|
| 996 | |
---|
| 997 | for i in range(3): |
---|
| 998 | qv[:,i] = qc |
---|
| 999 | |
---|
| 1000 | |
---|
| 1001 | def get_integral(self): |
---|
| 1002 | """Compute the integral of quantity across entire domain |
---|
| 1003 | """ |
---|
| 1004 | integral = 0 |
---|
| 1005 | for k in range(self.domain.number_of_elements): |
---|
| 1006 | area = self.domain.areas[k] |
---|
| 1007 | qc = self.centroid_values[k] |
---|
| 1008 | integral += qc*area |
---|
| 1009 | |
---|
| 1010 | return integral |
---|
| 1011 | |
---|
| 1012 | |
---|
| 1013 | |
---|
| 1014 | |
---|
| 1015 | class Conserved_quantity(Quantity): |
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| 1016 | """Class conserved quantity adds to Quantity: |
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| 1017 | |
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| 1018 | boundary values, storage and method for updating, and |
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| 1019 | methods for (second order) extrapolation from centroid to vertices inluding |
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| 1020 | gradients and limiters |
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| 1021 | """ |
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| 1022 | |
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| 1023 | def __init__(self, domain, vertex_values=None): |
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| 1024 | Quantity.__init__(self, domain, vertex_values) |
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| 1025 | |
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| 1026 | |
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| 1027 | #Allocate space for boundary values |
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| 1028 | L = len(domain.boundary) |
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| 1029 | self.boundary_values = zeros(L, Float) |
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| 1030 | |
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| 1031 | #Allocate space for updates of conserved quantities by |
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| 1032 | #flux calculations and forcing functions |
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| 1033 | |
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| 1034 | N = domain.number_of_elements |
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| 1035 | self.explicit_update = zeros(N, Float ) |
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| 1036 | self.semi_implicit_update = zeros(N, Float ) |
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| 1037 | |
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| 1038 | |
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| 1039 | def update(self, timestep): |
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| 1040 | #Call correct module function |
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| 1041 | #(either from this module or C-extension) |
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| 1042 | return update(self, timestep) |
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| 1043 | |
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| 1044 | |
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| 1045 | def compute_gradients(self): |
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| 1046 | #Call correct module function |
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| 1047 | #(either from this module or C-extension) |
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| 1048 | return compute_gradients(self) |
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| 1049 | |
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| 1050 | |
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| 1051 | def limit(self): |
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| 1052 | #Call correct module function |
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| 1053 | #(either from this module or C-extension) |
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| 1054 | limit(self) |
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| 1055 | |
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| 1056 | |
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| 1057 | def extrapolate_second_order(self): |
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| 1058 | #Call correct module function |
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| 1059 | #(either from this module or C-extension) |
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| 1060 | extrapolate_second_order(self) |
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| 1061 | |
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| 1062 | |
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| 1063 | def update(quantity, timestep): |
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| 1064 | """Update centroid values based on values stored in |
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| 1065 | explicit_update and semi_implicit_update as well as given timestep |
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| 1066 | |
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| 1067 | Function implementing forcing terms must take on argument |
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| 1068 | which is the domain and they must update either explicit |
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| 1069 | or implicit updates, e,g,: |
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| 1070 | |
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| 1071 | def gravity(domain): |
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| 1072 | .... |
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| 1073 | domain.quantities['xmomentum'].explicit_update = ... |
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| 1074 | domain.quantities['ymomentum'].explicit_update = ... |
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| 1075 | |
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| 1076 | |
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| 1077 | |
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| 1078 | Explicit terms must have the form |
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| 1079 | |
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| 1080 | G(q, t) |
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| 1081 | |
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| 1082 | and explicit scheme is |
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| 1083 | |
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| 1084 | q^{(n+1}) = q^{(n)} + delta_t G(q^{n}, n delta_t) |
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| 1085 | |
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| 1086 | |
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| 1087 | Semi implicit forcing terms are assumed to have the form |
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| 1088 | |
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| 1089 | G(q, t) = H(q, t) q |
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| 1090 | |
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| 1091 | and the semi implicit scheme will then be |
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| 1092 | |
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| 1093 | q^{(n+1}) = q^{(n)} + delta_t H(q^{n}, n delta_t) q^{(n+1}) |
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| 1094 | |
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| 1095 | |
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| 1096 | """ |
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| 1097 | |
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[2608] | 1098 | #from Numeric import sum, equal, ones, Float |
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[2526] | 1099 | |
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| 1100 | N = quantity.centroid_values.shape[0] |
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| 1101 | |
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| 1102 | |
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| 1103 | #Divide H by conserved quantity to obtain G (see docstring above) |
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| 1104 | |
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| 1105 | |
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| 1106 | for k in range(N): |
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| 1107 | x = quantity.centroid_values[k] |
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| 1108 | if x == 0.0: |
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| 1109 | #FIXME: Is this right |
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| 1110 | quantity.semi_implicit_update[k] = 0.0 |
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| 1111 | else: |
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| 1112 | quantity.semi_implicit_update[k] /= x |
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| 1113 | |
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| 1114 | #Explicit updates |
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| 1115 | quantity.centroid_values += timestep*quantity.explicit_update |
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| 1116 | |
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| 1117 | #Semi implicit updates |
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| 1118 | denominator = ones(N, Float)-timestep*quantity.semi_implicit_update |
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| 1119 | |
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| 1120 | if sum(equal(denominator, 0.0)) > 0.0: |
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| 1121 | msg = 'Zero division in semi implicit update. Call Stephen :-)' |
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| 1122 | raise msg |
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| 1123 | else: |
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| 1124 | #Update conserved_quantities from semi implicit updates |
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| 1125 | quantity.centroid_values /= denominator |
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| 1126 | |
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| 1127 | |
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| 1128 | def interpolate_from_vertices_to_edges(quantity): |
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| 1129 | """Compute edge values from vertex values using linear interpolation |
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| 1130 | """ |
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| 1131 | |
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| 1132 | for k in range(quantity.vertex_values.shape[0]): |
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| 1133 | q0 = quantity.vertex_values[k, 0] |
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| 1134 | q1 = quantity.vertex_values[k, 1] |
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| 1135 | q2 = quantity.vertex_values[k, 2] |
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| 1136 | |
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| 1137 | quantity.edge_values[k, 0] = 0.5*(q1+q2) |
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| 1138 | quantity.edge_values[k, 1] = 0.5*(q0+q2) |
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| 1139 | quantity.edge_values[k, 2] = 0.5*(q0+q1) |
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| 1140 | |
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| 1141 | |
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| 1142 | |
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| 1143 | def extrapolate_second_order(quantity): |
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| 1144 | """Extrapolate conserved quantities from centroid to |
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| 1145 | vertices for each volume using |
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| 1146 | second order scheme. |
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| 1147 | """ |
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| 1148 | |
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| 1149 | a, b = quantity.compute_gradients() |
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| 1150 | |
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| 1151 | X = quantity.domain.get_vertex_coordinates() |
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| 1152 | qc = quantity.centroid_values |
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| 1153 | qv = quantity.vertex_values |
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| 1154 | |
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| 1155 | #Check each triangle |
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| 1156 | for k in range(quantity.domain.number_of_elements): |
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| 1157 | #Centroid coordinates |
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| 1158 | x, y = quantity.domain.centroid_coordinates[k] |
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| 1159 | |
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| 1160 | #vertex coordinates |
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| 1161 | x0, y0, x1, y1, x2, y2 = X[k,:] |
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| 1162 | |
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| 1163 | #Extrapolate |
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| 1164 | qv[k,0] = qc[k] + a[k]*(x0-x) + b[k]*(y0-y) |
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| 1165 | qv[k,1] = qc[k] + a[k]*(x1-x) + b[k]*(y1-y) |
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| 1166 | qv[k,2] = qc[k] + a[k]*(x2-x) + b[k]*(y2-y) |
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| 1167 | |
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| 1168 | |
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| 1169 | def compute_gradients(quantity): |
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| 1170 | """Compute gradients of triangle surfaces defined by centroids of |
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| 1171 | neighbouring volumes. |
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| 1172 | If one edge is on the boundary, use own centroid as neighbour centroid. |
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| 1173 | If two or more are on the boundary, fall back to first order scheme. |
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| 1174 | """ |
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| 1175 | |
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| 1176 | from utilitites.numerical_tools import gradient |
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| 1177 | |
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| 1178 | centroid_coordinates = quantity.domain.centroid_coordinates |
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| 1179 | surrogate_neighbours = quantity.domain.surrogate_neighbours |
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| 1180 | centroid_values = quantity.centroid_values |
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| 1181 | number_of_boundaries = quantity.domain.number_of_boundaries |
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| 1182 | |
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| 1183 | N = centroid_values.shape[0] |
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| 1184 | |
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| 1185 | a = zeros(N, Float) |
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| 1186 | b = zeros(N, Float) |
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| 1187 | |
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| 1188 | for k in range(N): |
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| 1189 | if number_of_boundaries[k] < 2: |
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| 1190 | #Two or three true neighbours |
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| 1191 | |
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| 1192 | #Get indices of neighbours (or self when used as surrogate) |
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| 1193 | k0, k1, k2 = surrogate_neighbours[k,:] |
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| 1194 | |
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| 1195 | #Get data |
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| 1196 | q0 = centroid_values[k0] |
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| 1197 | q1 = centroid_values[k1] |
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| 1198 | q2 = centroid_values[k2] |
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| 1199 | |
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| 1200 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
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| 1201 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
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| 1202 | x2, y2 = centroid_coordinates[k2] #V2 centroid |
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| 1203 | |
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| 1204 | #Gradient |
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| 1205 | a[k], b[k] = gradient(x0, y0, x1, y1, x2, y2, q0, q1, q2) |
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| 1206 | |
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| 1207 | elif number_of_boundaries[k] == 2: |
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| 1208 | #One true neighbour |
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| 1209 | |
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| 1210 | #Get index of the one neighbour |
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| 1211 | for k0 in surrogate_neighbours[k,:]: |
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| 1212 | if k0 != k: break |
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| 1213 | assert k0 != k |
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| 1214 | |
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| 1215 | k1 = k #self |
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| 1216 | |
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| 1217 | #Get data |
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| 1218 | q0 = centroid_values[k0] |
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| 1219 | q1 = centroid_values[k1] |
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| 1220 | |
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| 1221 | x0, y0 = centroid_coordinates[k0] #V0 centroid |
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| 1222 | x1, y1 = centroid_coordinates[k1] #V1 centroid |
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| 1223 | |
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| 1224 | #Gradient |
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| 1225 | a[k], b[k] = gradient2(x0, y0, x1, y1, q0, q1) |
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| 1226 | else: |
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| 1227 | #No true neighbours - |
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| 1228 | #Fall back to first order scheme |
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| 1229 | pass |
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| 1230 | |
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| 1231 | |
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| 1232 | return a, b |
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| 1233 | |
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| 1234 | |
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| 1235 | |
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| 1236 | def limit(quantity): |
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| 1237 | """Limit slopes for each volume to eliminate artificial variance |
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| 1238 | introduced by e.g. second order extrapolator |
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| 1239 | |
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| 1240 | This is an unsophisticated limiter as it does not take into |
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| 1241 | account dependencies among quantities. |
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| 1242 | |
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| 1243 | precondition: |
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| 1244 | vertex values are estimated from gradient |
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| 1245 | postcondition: |
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| 1246 | vertex values are updated |
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| 1247 | """ |
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| 1248 | |
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| 1249 | N = quantity.domain.number_of_elements |
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| 1250 | |
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| 1251 | beta_w = quantity.domain.beta_w |
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| 1252 | |
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| 1253 | qc = quantity.centroid_values |
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| 1254 | qv = quantity.vertex_values |
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| 1255 | |
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| 1256 | #Find min and max of this and neighbour's centroid values |
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| 1257 | qmax = zeros(qc.shape, Float) |
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| 1258 | qmin = zeros(qc.shape, Float) |
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| 1259 | |
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| 1260 | for k in range(N): |
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| 1261 | qmax[k] = qmin[k] = qc[k] |
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| 1262 | for i in range(3): |
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| 1263 | n = quantity.domain.neighbours[k,i] |
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| 1264 | if n >= 0: |
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| 1265 | qn = qc[n] #Neighbour's centroid value |
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| 1266 | |
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| 1267 | qmin[k] = min(qmin[k], qn) |
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| 1268 | qmax[k] = max(qmax[k], qn) |
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| 1269 | |
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| 1270 | |
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| 1271 | #Diffences between centroids and maxima/minima |
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| 1272 | dqmax = qmax - qc |
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| 1273 | dqmin = qmin - qc |
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| 1274 | |
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| 1275 | #Deltas between vertex and centroid values |
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| 1276 | dq = zeros(qv.shape, Float) |
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| 1277 | for i in range(3): |
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| 1278 | dq[:,i] = qv[:,i] - qc |
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| 1279 | |
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| 1280 | #Phi limiter |
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| 1281 | for k in range(N): |
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| 1282 | |
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| 1283 | #Find the gradient limiter (phi) across vertices |
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| 1284 | phi = 1.0 |
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| 1285 | for i in range(3): |
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| 1286 | r = 1.0 |
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| 1287 | if (dq[k,i] > 0): r = dqmax[k]/dq[k,i] |
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| 1288 | if (dq[k,i] < 0): r = dqmin[k]/dq[k,i] |
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| 1289 | |
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| 1290 | phi = min( min(r*beta_w, 1), phi ) |
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| 1291 | |
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| 1292 | #Then update using phi limiter |
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| 1293 | for i in range(3): |
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| 1294 | qv[k,i] = qc[k] + phi*dq[k,i] |
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| 1295 | |
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| 1296 | |
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| 1297 | |
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| 1298 | from utilities import compile |
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| 1299 | if compile.can_use_C_extension('quantity_ext.c'): |
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| 1300 | #Replace python version with c implementations |
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| 1301 | |
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| 1302 | from quantity_ext import limit, compute_gradients,\ |
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| 1303 | extrapolate_second_order, interpolate_from_vertices_to_edges, update |
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