[7827] | 1 | """ |
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| 2 | Class Quantity - Implements values at each 1d element |
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| 3 | |
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| 4 | To create: |
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| 5 | |
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| 6 | Quantity(domain, vertex_values) |
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| 7 | |
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| 8 | domain: Associated domain structure. Required. |
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| 9 | |
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| 10 | vertex_values: N x 2 array of values at each vertex for each element. |
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| 11 | Default None |
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| 12 | |
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| 13 | If vertex_values are None Create array of zeros compatible with domain. |
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| 14 | Otherwise check that it is compatible with dimenions of domain. |
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| 15 | Otherwise raise an exception |
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| 16 | """ |
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| 17 | |
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| 18 | import numpy |
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| 19 | |
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| 20 | |
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| 21 | |
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| 22 | class Quantity: |
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| 23 | |
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| 24 | |
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| 25 | def __init__(self, domain, vertex_values=None): |
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| 26 | #Initialise Quantity using optional vertex values. |
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| 27 | |
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| 28 | from generic_domain import Generic_domain |
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| 29 | |
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| 30 | msg = 'First argument in Quantity.__init__ ' |
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| 31 | msg += 'must be of class Domain (or a subclass thereof)' |
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| 32 | assert isinstance(domain, Generic_domain), msg |
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| 33 | |
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| 34 | if vertex_values is None: |
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| 35 | N = domain.number_of_elements |
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| 36 | self.vertex_values = numpy.zeros((N, 2), numpy.float) |
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| 37 | else: |
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| 38 | self.vertex_values = numpy.array(vertex_values, numpy.float) |
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| 39 | |
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| 40 | N, V = self.vertex_values.shape |
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| 41 | assert V == 2,\ |
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| 42 | 'Two vertex values per element must be specified' |
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| 43 | |
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| 44 | |
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| 45 | msg = 'Number of vertex values (%d) must be consistent with'\ |
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| 46 | %N |
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| 47 | msg += 'number of elements in specified domain (%d).'\ |
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| 48 | %domain.number_of_elements |
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| 49 | |
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| 50 | assert N == domain.number_of_elements, msg |
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| 51 | |
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| 52 | self.domain = domain |
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| 53 | |
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| 54 | #Allocate space for other quantities |
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| 55 | self.centroid_values = numpy.zeros(N, numpy.float) |
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| 56 | self.centroid_backup_values = numpy.zeros(N, numpy.float) |
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| 57 | #self.edge_values = numpy.zeros((N, 2), numpy.float) |
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| 58 | #edge values are values of the ends of each interval |
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| 59 | |
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| 60 | #Intialise centroid values |
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| 61 | self.interpolate() |
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| 62 | |
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| 63 | |
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| 64 | |
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| 65 | #Allocate space for boundary values |
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| 66 | #L = len(domain.boundary) |
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| 67 | self.boundary_values = numpy.zeros(2, numpy.float) #assumes no parrellism |
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| 68 | |
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| 69 | #Allocate space for updates of conserved quantities by |
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| 70 | #flux calculations and forcing functions |
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| 71 | |
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| 72 | N = domain.number_of_elements |
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| 73 | self.explicit_update = numpy.zeros(N, numpy.float ) |
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| 74 | self.semi_implicit_update = numpy.zeros(N, numpy.float ) |
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| 75 | |
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| 76 | self.gradients = numpy.zeros(N, numpy.float) |
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| 77 | self.qmax = numpy.zeros(self.centroid_values.shape, numpy.float) |
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| 78 | self.qmin = numpy.zeros(self.centroid_values.shape, numpy.float) |
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| 79 | |
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| 80 | self.beta = domain.beta |
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| 81 | |
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| 82 | |
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| 83 | def __len__(self): |
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| 84 | """ |
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| 85 | Returns number of intervals. |
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| 86 | """ |
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| 87 | return self.centroid_values.shape[0] |
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| 88 | |
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| 89 | def __neg__(self): |
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| 90 | """Negate all values in this quantity giving meaning to the |
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| 91 | expression -Q where Q is an instance of class Quantity |
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| 92 | """ |
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| 93 | |
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| 94 | Q = Quantity(self.domain) |
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| 95 | Q.set_values_from_numeric(-self.vertex_values) |
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| 96 | return Q |
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| 97 | |
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| 98 | |
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| 99 | |
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| 100 | def __add__(self, other): |
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| 101 | """Add to self anything that could populate a quantity |
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| 102 | |
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| 103 | E.g other can be a constant, an array, a function, another quantity |
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| 104 | (except for a filename or points, attributes (for now)) |
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| 105 | - see set_values_from_numeric for details |
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| 106 | """ |
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| 107 | |
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| 108 | Q = Quantity(self.domain) |
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| 109 | Q.set_values_from_numeric(other) |
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| 110 | |
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| 111 | result = Quantity(self.domain) |
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| 112 | result.set_values_from_numeric(self.vertex_values + Q.vertex_values) |
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| 113 | return result |
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| 114 | |
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| 115 | def __radd__(self, other): |
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| 116 | """Handle cases like 7+Q, where Q is an instance of class Quantity |
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| 117 | """ |
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| 118 | |
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| 119 | return self + other |
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| 120 | |
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| 121 | def __sub__(self, other): |
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| 122 | return self + -other # Invoke self.__neg__() |
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| 123 | |
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| 124 | def __mul__(self, other): |
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| 125 | """Multiply self with anything that could populate a quantity |
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| 126 | |
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| 127 | E.g other can be a constant, an array, a function, another quantity |
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| 128 | (except for a filename or points, attributes (for now)) |
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| 129 | - see set_values_from_numeric for details |
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| 130 | """ |
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| 131 | |
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| 132 | if isinstance(other, Quantity): |
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| 133 | Q = other |
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| 134 | else: |
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| 135 | Q = Quantity(self.domain) |
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| 136 | Q.set_values_from_numeric(other) |
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| 137 | |
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| 138 | result = Quantity(self.domain) |
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| 139 | |
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| 140 | # The product of vertex_values, edge_values and centroid_values |
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| 141 | # are calculated and assigned directly without using |
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| 142 | # set_values_from_numeric (which calls interpolate). Otherwise |
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| 143 | # centroid values wouldn't be products from q1 and q2 |
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| 144 | result.vertex_values = self.vertex_values * Q.vertex_values |
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| 145 | result.centroid_values = self.centroid_values * Q.centroid_values |
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| 146 | |
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| 147 | return result |
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| 148 | |
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| 149 | def __rmul__(self, other): |
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| 150 | """Handle cases like 3*Q, where Q is an instance of class Quantity |
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| 151 | """ |
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| 152 | |
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| 153 | return self * other |
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| 154 | |
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| 155 | def __div__(self, other): |
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| 156 | """Divide self with anything that could populate a quantity |
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| 157 | |
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| 158 | E.g other can be a constant, an array, a function, another quantity |
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| 159 | (except for a filename or points, attributes (for now)) |
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| 160 | - see set_values_from_numeric for details |
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| 161 | |
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| 162 | Zero division is dealt with by adding an epsilon to the divisore |
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| 163 | FIXME (Ole): Replace this with native INF once we migrate to NumPy |
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| 164 | """ |
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| 165 | |
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| 166 | if isinstance(other, Quantity): |
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| 167 | Q = other |
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| 168 | else: |
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| 169 | Q = Quantity(self.domain) |
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| 170 | Q.set_values_from_numeric(other) |
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| 171 | |
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| 172 | result = Quantity(self.domain) |
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| 173 | |
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| 174 | # The quotient of vertex_values, edge_values and centroid_values |
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| 175 | # are calculated and assigned directly without using |
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| 176 | # set_values_from_numeric (which calls interpolate). Otherwise |
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| 177 | # centroid values wouldn't be quotient of q1 and q2 |
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| 178 | result.vertex_values = self.vertex_values/(Q.vertex_values + epsilon) |
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| 179 | result.centroid_values = self.centroid_values/(Q.centroid_values + epsilon) |
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| 180 | |
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| 181 | return result |
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| 182 | |
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| 183 | def __rdiv__(self, other): |
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| 184 | """Handle cases like 3/Q, where Q is an instance of class Quantity |
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| 185 | """ |
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| 186 | |
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| 187 | return self / other |
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| 188 | |
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| 189 | def __pow__(self, other): |
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| 190 | """Raise quantity to (numerical) power |
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| 191 | |
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| 192 | As with __mul__ vertex values are processed entry by entry |
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| 193 | while centroid and edge values are re-interpolated. |
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| 194 | |
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| 195 | Example using __pow__: |
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| 196 | Q = (Q1**2 + Q2**2)**0.5 |
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| 197 | """ |
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| 198 | |
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| 199 | if isinstance(other, Quantity): |
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| 200 | Q = other |
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| 201 | else: |
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| 202 | Q = Quantity(self.domain) |
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| 203 | Q.set_values_from_numeric(other) |
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| 204 | |
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| 205 | result = Quantity(self.domain) |
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| 206 | |
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| 207 | # The power of vertex_values, edge_values and centroid_values |
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| 208 | # are calculated and assigned directly without using |
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| 209 | # set_values_from_numeric (which calls interpolate). Otherwise |
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| 210 | # centroid values wouldn't be correct |
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| 211 | result.vertex_values = self.vertex_values ** other |
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| 212 | result.centroid_values = self.centroid_values ** other |
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| 213 | |
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| 214 | return result |
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| 215 | |
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| 216 | def set_values_from_numeric(self, numeric): |
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| 217 | |
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| 218 | x = numpy.array([1.0,2.0]) |
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| 219 | y = [1.0,2.0] |
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| 220 | |
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| 221 | if type(numeric) == type(y): |
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| 222 | self.set_values_from_array(numeric) |
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| 223 | elif type(numeric) == type(x): |
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| 224 | self.set_values_from_array(numeric) |
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| 225 | elif callable(numeric): |
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| 226 | self.set_values_from_function(numeric) |
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| 227 | elif isinstance(numeric, Quantity): |
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| 228 | self.set_values_from_quantity(numeric) |
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| 229 | else: # see if it's coercible to a float (float, int or long, etc) |
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| 230 | try: |
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| 231 | numeric = float(numeric) |
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| 232 | except ValueError: |
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| 233 | msg = ("Illegal type for variable 'numeric': %s" % type(numeric)) |
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| 234 | raise Exception(msg) |
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| 235 | self.set_values_from_constant(numeric) |
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| 236 | |
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| 237 | def set_values_from_constant(self,numeric): |
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| 238 | |
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| 239 | self.vertex_values[:,:] = numeric |
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| 240 | self.centroid_values[:,] = numeric |
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| 241 | |
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| 242 | |
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| 243 | def set_values_from_array(self,numeric): |
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| 244 | |
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| 245 | self.vertex_values[:,:] = numeric |
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| 246 | self.interpolate() |
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| 247 | |
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| 248 | |
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| 249 | def set_values_from_quantity(self,quantity): |
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| 250 | |
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| 251 | self.vertex_values[:,:] = quantity.vertex_values |
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| 252 | self.centroid_values[:,] = quantity.centroid_values |
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| 253 | |
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| 254 | def set_values_from_function(self,function): |
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| 255 | |
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| 256 | self.vertex_values[:,:] = map(function, self.domain.vertices) |
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| 257 | self.centroid_values[:,] = map(function, self.domain.centroids) |
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| 258 | |
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| 259 | |
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| 260 | def interpolate(self): |
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| 261 | """ |
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| 262 | Compute interpolated values at centroid |
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| 263 | Pre-condition: vertex_values have been set |
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| 264 | """ |
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| 265 | |
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| 266 | N = self.vertex_values.shape[0] |
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| 267 | for i in range(N): |
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| 268 | v0 = self.vertex_values[i, 0] |
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| 269 | v1 = self.vertex_values[i, 1] |
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| 270 | |
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| 271 | self.centroid_values[i] = (v0 + v1)/2.0 |
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| 272 | |
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| 273 | |
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| 274 | |
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| 275 | |
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| 276 | def set_values(self, X, location='vertices'): |
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| 277 | """Set values for quantity |
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| 278 | |
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| 279 | X: Compatible list, Numeric array (see below), constant or function |
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| 280 | location: Where values are to be stored. |
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| 281 | Permissible options are: vertices, centroid |
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| 282 | Default is "vertices" |
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| 283 | |
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| 284 | In case of location == 'centroid' the dimension values must |
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| 285 | be a list of a Numerical array of length N, N being the number |
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| 286 | of elements in the mesh. Otherwise it must be of dimension Nx2 |
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| 287 | |
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| 288 | The values will be stored in elements following their |
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| 289 | internal ordering. |
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| 290 | |
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| 291 | If values are described a function, it will be evaluated at specified points |
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| 292 | |
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| 293 | If selected location is vertices, values for centroid and edges |
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| 294 | will be assigned interpolated values. |
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| 295 | In any other case, only values for the specified locations |
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| 296 | will be assigned and the others will be left undefined. |
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| 297 | """ |
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| 298 | |
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| 299 | if location not in ['vertices', 'centroids', 'unique_vertices']: |
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| 300 | msg = 'Invalid location: %s, (possible choices vertices, centroids, unique_vertices)' %location |
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| 301 | raise Exception(msg) |
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| 302 | |
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| 303 | if X is None: |
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| 304 | msg = 'Given values are None' |
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| 305 | raise Exception(msg) |
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| 306 | |
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| 307 | import types |
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| 308 | |
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| 309 | if callable(X): |
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| 310 | #Use function specific method |
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| 311 | self.set_function_values(X, location) |
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| 312 | |
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| 313 | elif type(X) in [types.FloatType, types.IntType, types.LongType]: |
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| 314 | |
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| 315 | self.centroid_values[:,] = float(X) |
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| 316 | self.vertex_values[:,:] = float(X) |
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| 317 | |
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| 318 | elif isinstance(X, Quantity): |
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| 319 | self.set_array_values(X.vertex_values, location) |
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| 320 | |
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| 321 | else: |
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| 322 | #Use array specific method |
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| 323 | self.set_array_values(X, location) |
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| 324 | |
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| 325 | if location == 'vertices' or location == 'unique_vertices': |
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| 326 | #Intialise centroid |
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| 327 | self.interpolate() |
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| 328 | |
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| 329 | if location == 'centroid': |
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| 330 | self.extrapolate_first_order() |
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| 331 | |
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| 332 | |
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| 333 | |
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| 334 | |
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| 335 | |
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| 336 | def set_function_values(self, f, location='vertices'): |
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| 337 | """Set values for quantity using specified function |
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| 338 | |
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| 339 | f: x -> z Function where x and z are arrays |
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| 340 | location: Where values are to be stored. |
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| 341 | Permissible options are: vertices, centroid |
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| 342 | Default is "vertices" |
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| 343 | """ |
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| 344 | |
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| 345 | if location == 'centroids': |
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| 346 | |
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| 347 | P = self.domain.centroids |
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| 348 | self.set_values(f(P), location) |
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| 349 | else: |
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| 350 | #Vertices |
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| 351 | |
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| 352 | P = self.domain.get_vertices() |
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| 353 | |
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| 354 | for i in range(2): |
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| 355 | |
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| 356 | self.vertex_values[:,i] = f(P[:,i]) |
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| 357 | |
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| 358 | def set_array_values(self, values, location='vertices'): |
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| 359 | """Set values for quantity |
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| 360 | |
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| 361 | values: Numeric array |
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| 362 | location: Where values are to be stored. |
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| 363 | Permissible options are: vertices, centroid, unique_vertices |
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| 364 | Default is "vertices" |
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| 365 | |
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| 366 | In case of location == 'centroid' the dimension values must |
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| 367 | be a list of a Numerical array of length N, N being the number |
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| 368 | of elements in the mesh. If location == 'unique_vertices' the |
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| 369 | dimension values must be a list or a Numeric array of length N+1. |
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| 370 | Otherwise it must be of dimension Nx2 |
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| 371 | |
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| 372 | The values will be stored in elements following their |
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| 373 | internal ordering. |
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| 374 | |
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| 375 | If selected location is vertices, values for centroid |
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| 376 | will be assigned interpolated values. |
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| 377 | In any other case, only values for the specified locations |
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| 378 | will be assigned and the others will be left undefined. |
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| 379 | """ |
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| 380 | |
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| 381 | |
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| 382 | values = numpy.array(values).astype(numpy.float) |
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| 383 | |
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| 384 | N = self.centroid_values.shape[0] |
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| 385 | |
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| 386 | |
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| 387 | if location == 'centroids': |
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| 388 | msg = 'Number of values must match number of elements' |
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| 389 | assert values.shape[0] == N, msg |
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| 390 | assert len(values.shape) == 1, 'Values array must be 1d' |
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| 391 | |
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| 392 | for i in range(N): |
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| 393 | self.centroid_values[i] = values[i] |
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| 394 | |
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| 395 | self.vertex_values[:,0] = values |
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| 396 | self.vertex_values[:,1] = values |
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| 397 | |
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| 398 | if location == 'vertices': |
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| 399 | msg = 'Number of values must match number of elements' |
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| 400 | assert values.shape[0] == N, msg |
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| 401 | assert len(values.shape) == 2, 'Values array must be 2d' |
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| 402 | msg = 'Array must be N x 2' |
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| 403 | assert values.shape[1] == 2, msg |
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| 404 | |
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| 405 | self.vertex_values[:,:] = values[:,:] |
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| 406 | |
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| 407 | if location == 'unique_vertices': |
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| 408 | msg = 'Number of values must match number of elements +1' |
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| 409 | assert values.shape[0] == N+1, msg |
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| 410 | assert len(values.shape) == 1, 'Values array must be 1d' |
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| 411 | |
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| 412 | self.vertex_values[:,0] = values[0:-1] |
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| 413 | self.vertex_values[:,1] = values[1:N+1] |
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| 414 | |
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| 415 | |
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| 416 | |
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| 417 | |
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| 418 | |
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| 419 | def get_values(self, location='vertices', indices = None): |
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| 420 | """get values for quantity |
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| 421 | |
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| 422 | return X, Compatible list, Numeric array (see below) |
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| 423 | location: Where values are to be stored. |
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| 424 | Permissible options are: vertices, centroid |
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| 425 | and unique vertices. Default is 'vertices' |
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| 426 | |
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| 427 | In case of location == 'centroids' the dimension values must |
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| 428 | be a list of a Numerical array of length N, N being the number |
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| 429 | of elements. Otherwise it must be of dimension Nx3 |
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| 430 | |
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| 431 | The returned values with be a list the length of indices |
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| 432 | (N if indices = None). Each value will be a list of the three |
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| 433 | vertex values for this quantity. |
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| 434 | |
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| 435 | Indices is the set of element ids that the operation applies to. |
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| 436 | |
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| 437 | """ |
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| 438 | |
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| 439 | |
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| 440 | if location not in ['vertices', 'centroids', 'unique vertices']: |
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| 441 | msg = 'Invalid location: %s' %location |
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| 442 | raise Exception(msg) |
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| 443 | |
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| 444 | import types, numpy |
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| 445 | assert type(indices) in [types.ListType, types.NoneType, |
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| 446 | numpy.ArrayType],\ |
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| 447 | 'Indices must be a list or None' |
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| 448 | |
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| 449 | if location == 'centroids': |
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| 450 | if (indices == None): |
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| 451 | indices = range(len(self)) |
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| 452 | return take(self.centroid_values,indices) |
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| 453 | elif location == 'unique vertices': |
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| 454 | if (indices == None): |
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| 455 | indices=range(self.domain.coordinates.shape[0]) |
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| 456 | vert_values = [] |
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| 457 | #Go through list of unique vertices |
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| 458 | for unique_vert_id in indices: |
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| 459 | cells = self.domain.vertexlist[unique_vert_id] |
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| 460 | |
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| 461 | #In case there are unused points |
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| 462 | if cells is None: |
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| 463 | msg = 'Unique vertex not associated with cells' |
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| 464 | raise Exception(msg) |
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| 465 | |
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| 466 | # Go through all cells, vertex pairs |
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| 467 | # Average the values |
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| 468 | sum = 0 |
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| 469 | for cell_id, vertex_id in cells: |
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| 470 | sum += self.vertex_values[cell_id, vertex_id] |
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| 471 | vert_values.append(sum/len(cells)) |
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| 472 | return numpy.array(vert_values) |
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| 473 | else: |
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| 474 | if (indices == None): |
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| 475 | indices = range(len(self)) |
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| 476 | return take(self.vertex_values,indices) |
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| 477 | |
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| 478 | |
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| 479 | def get_vertex_values(self, |
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| 480 | x=True, |
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| 481 | smooth = None, |
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| 482 | precision = None, |
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| 483 | reduction = None): |
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| 484 | """Return vertex values like an OBJ format |
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| 485 | |
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| 486 | The vertex values are returned as one sequence in the 1D float array A. |
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| 487 | If requested the coordinates will be returned in 1D arrays X. |
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| 488 | |
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| 489 | The connectivity is represented as an integer array, V, of dimension |
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| 490 | M x 2, where M is the number of volumes. Each row has two indices |
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| 491 | into the X, A arrays defining the element. |
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| 492 | |
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| 493 | if smooth is True, vertex values corresponding to one common |
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| 494 | coordinate set will be smoothed according to the given |
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| 495 | reduction operator. In this case vertex coordinates will be |
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| 496 | de-duplicated. |
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| 497 | |
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| 498 | If no smoothings is required, vertex coordinates and values will |
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| 499 | be aggregated as a concatenation of values at |
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| 500 | vertices 0, vertices 1 |
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| 501 | |
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| 502 | |
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| 503 | Calling convention |
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| 504 | if x is True: |
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| 505 | X,A,V = get_vertex_values |
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| 506 | else: |
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| 507 | A,V = get_vertex_values |
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| 508 | |
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| 509 | """ |
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| 510 | |
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| 511 | |
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| 512 | |
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| 513 | |
---|
| 514 | if smooth is None: |
---|
| 515 | smooth = self.domain.smooth |
---|
| 516 | |
---|
| 517 | if precision is None: |
---|
| 518 | precision = numpy.float |
---|
| 519 | |
---|
| 520 | if reduction is None: |
---|
| 521 | reduction = self.domain.reduction |
---|
| 522 | |
---|
| 523 | #Create connectivity |
---|
| 524 | |
---|
| 525 | if smooth == True: |
---|
| 526 | |
---|
| 527 | V = self.domain.get_vertices() |
---|
| 528 | N = len(self.domain.vertexlist) |
---|
| 529 | #N = len(self.domain.vertices) |
---|
| 530 | A = numpy.zeros(N, precision) |
---|
| 531 | |
---|
| 532 | #Smoothing loop |
---|
| 533 | for k in range(N): |
---|
| 534 | L = self.domain.vertexlist[k] |
---|
| 535 | #L = self.domain.vertices[k] |
---|
| 536 | |
---|
| 537 | #Go through all triangle, vertex pairs |
---|
| 538 | #contributing to vertex k and register vertex value |
---|
| 539 | |
---|
| 540 | if L is None: continue #In case there are unused points |
---|
| 541 | |
---|
| 542 | contributions = [] |
---|
| 543 | for volume_id, vertex_id in L: |
---|
| 544 | v = self.vertex_values[volume_id, vertex_id] |
---|
| 545 | contributions.append(v) |
---|
| 546 | |
---|
| 547 | A[k] = reduction(contributions) |
---|
| 548 | |
---|
| 549 | if x is True: |
---|
| 550 | #X = self.domain.coordinates[:,0].astype(precision) |
---|
| 551 | X = self.domain.coordinates[:].astype(precision) |
---|
| 552 | #Y = self.domain.coordinates[:,1].astype(precision) |
---|
| 553 | |
---|
| 554 | #return X, Y, A, V |
---|
| 555 | return X, A, V |
---|
| 556 | |
---|
| 557 | #else: |
---|
| 558 | return A, V |
---|
| 559 | else: |
---|
| 560 | #Don't smooth |
---|
| 561 | #obj machinery moved to general_mesh |
---|
| 562 | |
---|
| 563 | # Create a V like [[0 1 2], [3 4 5]....[3*m-2 3*m-1 3*m]] |
---|
| 564 | # These vert_id's will relate to the verts created below |
---|
| 565 | #m = len(self.domain) #Number of volumes |
---|
| 566 | #M = 3*m #Total number of unique vertices |
---|
| 567 | #V = reshape(array(range(M)).astype(Int), (m,3)) |
---|
| 568 | |
---|
| 569 | #V = self.domain.get_triangles(obj=True) |
---|
| 570 | V = self.domain.get_vertices |
---|
| 571 | #FIXME use get_vertices, when ready |
---|
| 572 | |
---|
| 573 | A = self.vertex_values.flat |
---|
| 574 | |
---|
| 575 | #Do vertex coordinates |
---|
| 576 | if x is True: |
---|
| 577 | X = self.domain.get_vertex_coordinates() |
---|
| 578 | |
---|
| 579 | #X = C[:,0:6:2].copy() |
---|
| 580 | #Y = C[:,1:6:2].copy() |
---|
| 581 | |
---|
| 582 | return X.flat, A, V |
---|
| 583 | else: |
---|
| 584 | return A, V |
---|
| 585 | |
---|
| 586 | def get_integral(self): |
---|
| 587 | """Compute the integral of quantity across entire domain |
---|
| 588 | """ |
---|
| 589 | integral = 0 |
---|
| 590 | for k in range(self.domain.number_of_elements): |
---|
| 591 | area = self.domain.areas[k] |
---|
| 592 | qc = self.centroid_values[k] |
---|
| 593 | integral += qc*area |
---|
| 594 | |
---|
| 595 | return integral |
---|
| 596 | |
---|
| 597 | |
---|
| 598 | def update(self, timestep): |
---|
| 599 | """Update centroid values based on values stored in |
---|
| 600 | explicit_update and semi_implicit_update as well as given timestep |
---|
| 601 | """ |
---|
| 602 | |
---|
| 603 | |
---|
| 604 | |
---|
| 605 | N = self.centroid_values.shape[0] |
---|
| 606 | |
---|
| 607 | #Explicit updates |
---|
| 608 | self.centroid_values += timestep*self.explicit_update |
---|
| 609 | |
---|
| 610 | #Semi implicit updates |
---|
| 611 | denominator = numpy.ones(N, numpy.float)-timestep*self.semi_implicit_update |
---|
| 612 | |
---|
| 613 | if sum(numpy.equal(denominator, 0.0)) > 0.0: |
---|
| 614 | msg = 'Zero division in semi implicit update. Call Stephen :-)' |
---|
| 615 | raise Exception(msg) |
---|
| 616 | else: |
---|
| 617 | #Update conserved_quantities from semi implicit updates |
---|
| 618 | self.centroid_values /= denominator |
---|
| 619 | |
---|
| 620 | |
---|
| 621 | def compute_gradients(self): |
---|
| 622 | """Compute gradients of piecewise linear function defined by centroids of |
---|
| 623 | neighbouring volumes. |
---|
| 624 | """ |
---|
| 625 | |
---|
| 626 | |
---|
| 627 | |
---|
| 628 | |
---|
| 629 | N = self.centroid_values.shape[0] |
---|
| 630 | |
---|
| 631 | |
---|
| 632 | G = self.gradients |
---|
| 633 | Q = self.centroid_values |
---|
| 634 | X = self.domain.centroids |
---|
| 635 | |
---|
| 636 | for k in range(N): |
---|
| 637 | |
---|
| 638 | # first and last elements have boundaries |
---|
| 639 | |
---|
| 640 | if k == 0: |
---|
| 641 | |
---|
| 642 | #Get data |
---|
| 643 | k0 = k |
---|
| 644 | k1 = k+1 |
---|
| 645 | k2 = k+2 |
---|
| 646 | |
---|
| 647 | q0 = Q[k0] |
---|
| 648 | q1 = Q[k1] |
---|
| 649 | q2 = Q[k2] |
---|
| 650 | |
---|
| 651 | x0 = X[k0] #V0 centroid |
---|
| 652 | x1 = X[k1] #V1 centroid |
---|
| 653 | x2 = X[k2] |
---|
| 654 | |
---|
| 655 | #Gradient |
---|
| 656 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 657 | |
---|
| 658 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 659 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 660 | |
---|
| 661 | elif k == N-1: |
---|
| 662 | |
---|
| 663 | #Get data |
---|
| 664 | k0 = k |
---|
| 665 | k1 = k-1 |
---|
| 666 | k2 = k-2 |
---|
| 667 | |
---|
| 668 | q0 = Q[k0] |
---|
| 669 | q1 = Q[k1] |
---|
| 670 | q2 = Q[k2] |
---|
| 671 | |
---|
| 672 | x0 = X[k0] #V0 centroid |
---|
| 673 | x1 = X[k1] #V1 centroid |
---|
| 674 | x2 = X[k2] |
---|
| 675 | |
---|
| 676 | #Gradient |
---|
| 677 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 678 | |
---|
| 679 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 680 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 681 | |
---|
| 682 | ## q0 = Q[k0] |
---|
| 683 | ## q1 = Q[k1] |
---|
| 684 | ## |
---|
| 685 | ## x0 = X[k0] #V0 centroid |
---|
| 686 | ## x1 = X[k1] #V1 centroid |
---|
| 687 | ## |
---|
| 688 | ## #Gradient |
---|
| 689 | ## G[k] = (q1 - q0)/(x1 - x0) |
---|
| 690 | |
---|
| 691 | else: |
---|
| 692 | #Interior Volume (2 neighbours) |
---|
| 693 | |
---|
| 694 | #Get data |
---|
| 695 | k0 = k-1 |
---|
| 696 | k2 = k+1 |
---|
| 697 | |
---|
| 698 | q0 = Q[k0] |
---|
| 699 | q1 = Q[k] |
---|
| 700 | q2 = Q[k2] |
---|
| 701 | |
---|
| 702 | x0 = X[k0] #V0 centroid |
---|
| 703 | x1 = X[k] #V1 centroid (Self) |
---|
| 704 | x2 = X[k2] #V2 centroid |
---|
| 705 | |
---|
| 706 | #Gradient |
---|
| 707 | #G[k] = (q2-q0)/(x2-x0) |
---|
| 708 | G[k] = ((q0-q1)/(x0-x1)*(x2-x1) - (q2-q1)/(x2-x1)*(x0-x1))/(x2-x0) |
---|
| 709 | |
---|
| 710 | |
---|
| 711 | def compute_minmod_gradients(self): |
---|
| 712 | """Compute gradients of piecewise linear function defined by centroids of |
---|
| 713 | neighbouring volumes. |
---|
| 714 | """ |
---|
| 715 | |
---|
| 716 | #print 'compute_minmod_gradients' |
---|
| 717 | from numpy import sign |
---|
| 718 | |
---|
| 719 | |
---|
| 720 | def xmin(a,b): |
---|
| 721 | return 0.5*(sign(a)+sign(b))*min(abs(a),abs(b)) |
---|
| 722 | |
---|
| 723 | def xmic(t,a,b): |
---|
| 724 | return xmin(t*xmin(a,b), 0.50*(a+b) ) |
---|
| 725 | |
---|
| 726 | |
---|
| 727 | |
---|
| 728 | N = self.centroid_values.shape[0] |
---|
| 729 | |
---|
| 730 | |
---|
| 731 | G = self.gradients |
---|
| 732 | Q = self.centroid_values |
---|
| 733 | X = self.domain.centroids |
---|
| 734 | |
---|
| 735 | for k in range(N): |
---|
| 736 | |
---|
| 737 | # first and last elements have boundaries |
---|
| 738 | |
---|
| 739 | if k == 0: |
---|
| 740 | |
---|
| 741 | #Get data |
---|
| 742 | k0 = k |
---|
| 743 | k1 = k+1 |
---|
| 744 | k2 = k+2 |
---|
| 745 | |
---|
| 746 | q0 = Q[k0] |
---|
| 747 | q1 = Q[k1] |
---|
| 748 | q2 = Q[k2] |
---|
| 749 | |
---|
| 750 | x0 = X[k0] #V0 centroid |
---|
| 751 | x1 = X[k1] #V1 centroid |
---|
| 752 | x2 = X[k2] |
---|
| 753 | |
---|
| 754 | #Gradient |
---|
| 755 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 756 | |
---|
| 757 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 758 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 759 | |
---|
| 760 | elif k == N-1: |
---|
| 761 | |
---|
| 762 | #Get data |
---|
| 763 | k0 = k |
---|
| 764 | k1 = k-1 |
---|
| 765 | k2 = k-2 |
---|
| 766 | |
---|
| 767 | q0 = Q[k0] |
---|
| 768 | q1 = Q[k1] |
---|
| 769 | q2 = Q[k2] |
---|
| 770 | |
---|
| 771 | x0 = X[k0] #V0 centroid |
---|
| 772 | x1 = X[k1] #V1 centroid |
---|
| 773 | x2 = X[k2] |
---|
| 774 | |
---|
| 775 | #Gradient |
---|
| 776 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 777 | |
---|
| 778 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 779 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 780 | |
---|
| 781 | ## #Get data |
---|
| 782 | ## k0 = k |
---|
| 783 | ## k1 = k-1 |
---|
| 784 | ## |
---|
| 785 | ## q0 = Q[k0] |
---|
| 786 | ## q1 = Q[k1] |
---|
| 787 | ## |
---|
| 788 | ## x0 = X[k0] #V0 centroid |
---|
| 789 | ## x1 = X[k1] #V1 centroid |
---|
| 790 | ## |
---|
| 791 | ## #Gradient |
---|
| 792 | ## G[k] = (q1 - q0)/(x1 - x0) |
---|
| 793 | |
---|
| 794 | elif (self.domain.wet_nodes[k,0] == 2) & (self.domain.wet_nodes[k,1] == 2): |
---|
| 795 | G[k] = 0.0 |
---|
| 796 | |
---|
| 797 | else: |
---|
| 798 | #Interior Volume (2 neighbours) |
---|
| 799 | |
---|
| 800 | #Get data |
---|
| 801 | k0 = k-1 |
---|
| 802 | k2 = k+1 |
---|
| 803 | |
---|
| 804 | q0 = Q[k0] |
---|
| 805 | q1 = Q[k] |
---|
| 806 | q2 = Q[k2] |
---|
| 807 | |
---|
| 808 | x0 = X[k0] #V0 centroid |
---|
| 809 | x1 = X[k] #V1 centroid (Self) |
---|
| 810 | x2 = X[k2] #V2 centroid |
---|
| 811 | |
---|
| 812 | # assuming uniform grid |
---|
| 813 | d1 = (q1 - q0)/(x1-x0) |
---|
| 814 | d2 = (q2 - q1)/(x2-x1) |
---|
| 815 | |
---|
| 816 | #Gradient |
---|
| 817 | #G[k] = (d1+d2)*0.5 |
---|
| 818 | #G[k] = (d1*(x2-x1) - d2*(x0-x1))/(x2-x0) |
---|
| 819 | G[k] = xmic( self.domain.beta, d1, d2 ) |
---|
| 820 | |
---|
| 821 | |
---|
| 822 | def extrapolate_first_order(self): |
---|
| 823 | """Extrapolate conserved quantities from centroid to |
---|
| 824 | vertices for each volume using |
---|
| 825 | first order scheme. |
---|
| 826 | """ |
---|
| 827 | |
---|
| 828 | qc = self.centroid_values |
---|
| 829 | qv = self.vertex_values |
---|
| 830 | |
---|
| 831 | for i in range(2): |
---|
| 832 | qv[:,i] = qc |
---|
| 833 | |
---|
| 834 | |
---|
| 835 | def extrapolate_second_order(self): |
---|
| 836 | """Extrapolate conserved quantities from centroid to |
---|
| 837 | vertices for each volume using |
---|
| 838 | second order scheme. |
---|
| 839 | """ |
---|
| 840 | if self.domain.limiter == "pyvolution": |
---|
| 841 | #Z = self.gradients |
---|
| 842 | #print "gradients 1",Z |
---|
| 843 | self.compute_gradients() |
---|
| 844 | #print "gradients 2",Z |
---|
| 845 | |
---|
| 846 | #Z = self.gradients |
---|
| 847 | #print "gradients 1",Z |
---|
| 848 | #self.compute_minmod_gradients() |
---|
| 849 | #print "gradients 2", Z |
---|
| 850 | |
---|
| 851 | G = self.gradients |
---|
| 852 | V = self.domain.vertices |
---|
| 853 | qc = self.centroid_values |
---|
| 854 | qv = self.vertex_values |
---|
| 855 | |
---|
| 856 | #Check each triangle |
---|
| 857 | for k in range(self.domain.number_of_elements): |
---|
| 858 | #Centroid coordinates |
---|
| 859 | x = self.domain.centroids[k] |
---|
| 860 | |
---|
| 861 | #vertex coordinates |
---|
| 862 | x0, x1 = V[k,:] |
---|
| 863 | |
---|
| 864 | #Extrapolate |
---|
| 865 | qv[k,0] = qc[k] + G[k]*(x0-x) |
---|
| 866 | qv[k,1] = qc[k] + G[k]*(x1-x) |
---|
| 867 | self.limit_pyvolution() |
---|
| 868 | elif self.domain.limiter == "minmod_steve": |
---|
| 869 | self.limit_minmod() |
---|
| 870 | else: |
---|
| 871 | self.limit_range() |
---|
| 872 | |
---|
| 873 | |
---|
| 874 | |
---|
| 875 | def limit_minmod(self): |
---|
| 876 | #Z = self.gradients |
---|
| 877 | #print "gradients 1",Z |
---|
| 878 | self.compute_minmod_gradients() |
---|
| 879 | #print "gradients 2", Z |
---|
| 880 | |
---|
| 881 | G = self.gradients |
---|
| 882 | V = self.domain.vertices |
---|
| 883 | qc = self.centroid_values |
---|
| 884 | qv = self.vertex_values |
---|
| 885 | |
---|
| 886 | #Check each triangle |
---|
| 887 | for k in range(self.domain.number_of_elements): |
---|
| 888 | #Centroid coordinates |
---|
| 889 | x = self.domain.centroids[k] |
---|
| 890 | |
---|
| 891 | #vertex coordinates |
---|
| 892 | x0, x1 = V[k,:] |
---|
| 893 | |
---|
| 894 | #Extrapolate |
---|
| 895 | qv[k,0] = qc[k] + G[k]*(x0-x) |
---|
| 896 | qv[k,1] = qc[k] + G[k]*(x1-x) |
---|
| 897 | |
---|
| 898 | |
---|
| 899 | def limit_pyvolution(self): |
---|
| 900 | """ |
---|
| 901 | Limit slopes for each volume to eliminate artificial variance |
---|
| 902 | introduced by e.g. second order extrapolator |
---|
| 903 | |
---|
| 904 | This is an unsophisticated limiter as it does not take into |
---|
| 905 | account dependencies among quantities. |
---|
| 906 | |
---|
| 907 | precondition: |
---|
| 908 | vertex values are estimated from gradient |
---|
| 909 | postcondition: |
---|
| 910 | vertex values are updated |
---|
| 911 | """ |
---|
| 912 | |
---|
| 913 | |
---|
| 914 | N = self.domain.number_of_elements |
---|
| 915 | beta = self.domain.beta |
---|
| 916 | #beta = 0.8 |
---|
| 917 | |
---|
| 918 | qc = self.centroid_values |
---|
| 919 | qv = self.vertex_values |
---|
| 920 | |
---|
| 921 | #Find min and max of this and neighbour's centroid values |
---|
| 922 | qmax = self.qmax |
---|
| 923 | qmin = self.qmin |
---|
| 924 | |
---|
| 925 | for k in range(N): |
---|
| 926 | qmax[k] = qmin[k] = qc[k] |
---|
| 927 | for i in range(2): |
---|
| 928 | n = self.domain.neighbours[k,i] |
---|
| 929 | if n >= 0: |
---|
| 930 | qn = qc[n] #Neighbour's centroid value |
---|
| 931 | |
---|
| 932 | qmin[k] = min(qmin[k], qn) |
---|
| 933 | qmax[k] = max(qmax[k], qn) |
---|
| 934 | |
---|
| 935 | |
---|
| 936 | #Diffences between centroids and maxima/minima |
---|
| 937 | dqmax = qmax - qc |
---|
| 938 | dqmin = qmin - qc |
---|
| 939 | |
---|
| 940 | #Deltas between vertex and centroid values |
---|
| 941 | dq = numpy.zeros(qv.shape, numpy.float) |
---|
| 942 | for i in range(2): |
---|
| 943 | dq[:,i] = qv[:,i] - qc |
---|
| 944 | |
---|
| 945 | #Phi limiter |
---|
| 946 | for k in range(N): |
---|
| 947 | |
---|
| 948 | #Find the gradient limiter (phi) across vertices |
---|
| 949 | phi = 1.0 |
---|
| 950 | for i in range(2): |
---|
| 951 | r = 1.0 |
---|
| 952 | if (dq[k,i] > 0): r = dqmax[k]/dq[k,i] |
---|
| 953 | if (dq[k,i] < 0): r = dqmin[k]/dq[k,i] |
---|
| 954 | |
---|
| 955 | phi = min( min(r*beta, 1), phi ) |
---|
| 956 | |
---|
| 957 | #Then update using phi limiter |
---|
| 958 | for i in range(2): |
---|
| 959 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
| 960 | |
---|
| 961 | def limit_range(self): |
---|
| 962 | import sys |
---|
| 963 | |
---|
| 964 | from util import minmod, minmod_kurganov, maxmod, vanleer, vanalbada |
---|
| 965 | |
---|
| 966 | limiter = self.domain.limiter |
---|
| 967 | #print limiter |
---|
| 968 | |
---|
| 969 | #print 'limit_range' |
---|
| 970 | N = self.domain.number_of_elements |
---|
| 971 | qc = self.centroid_values |
---|
| 972 | qv = self.vertex_values |
---|
| 973 | C = self.domain.centroids |
---|
| 974 | X = self.domain.vertices |
---|
| 975 | beta_p = numpy.zeros(N,numpy.float) |
---|
| 976 | beta_m = numpy.zeros(N,numpy.float) |
---|
| 977 | beta_x = numpy.zeros(N,numpy.float) |
---|
| 978 | |
---|
| 979 | for k in range(N): |
---|
| 980 | |
---|
| 981 | n0 = self.domain.neighbours[k,0] |
---|
| 982 | n1 = self.domain.neighbours[k,1] |
---|
| 983 | |
---|
| 984 | if ( n0 >= 0) & (n1 >= 0): |
---|
| 985 | #SLOPE DERIVATIVE LIMIT |
---|
| 986 | beta_p[k] = (qc[k]-qc[k-1])/(C[k]-C[k-1]) |
---|
| 987 | beta_m[k] = (qc[k+1]-qc[k])/(C[k+1]-C[k]) |
---|
| 988 | beta_x[k] = (qc[k+1]-qc[k-1])/(C[k+1]-C[k-1]) |
---|
| 989 | |
---|
| 990 | dq = numpy.zeros(qv.shape, numpy.float) |
---|
| 991 | for i in range(2): |
---|
| 992 | dq[:,i] =self.domain.vertices[:,i]-self.domain.centroids |
---|
| 993 | |
---|
| 994 | #Phi limiter |
---|
| 995 | for k in range(N): |
---|
| 996 | n0 = self.domain.neighbours[k,0] |
---|
| 997 | n1 = self.domain.neighbours[k,1] |
---|
| 998 | if n0 < 0: |
---|
| 999 | phi = (qc[k+1] - qc[k])/(C[k+1] - C[k]) |
---|
| 1000 | elif n1 < 0: |
---|
| 1001 | phi = (qc[k] - qc[k-1])/(C[k] - C[k-1]) |
---|
| 1002 | #elif (self.domain.wet_nodes[k,0] == 2) & (self.domain.wet_nodes[k,1] == 2): |
---|
| 1003 | # phi = 0.0 |
---|
| 1004 | else: |
---|
| 1005 | if limiter == "minmod": |
---|
| 1006 | phi = minmod(beta_p[k],beta_m[k]) |
---|
| 1007 | |
---|
| 1008 | elif limiter == "minmod_kurganov":#Change this |
---|
| 1009 | # Also known as monotonized central difference limiter |
---|
| 1010 | # if theta = 2.0 |
---|
| 1011 | theta = 2.0 |
---|
| 1012 | phi = minmod_kurganov(theta*beta_p[k],theta*beta_m[k],beta_x[k]) |
---|
| 1013 | elif limiter == "superbee": |
---|
| 1014 | slope1 = minmod(beta_m[k],2.0*beta_p[k]) |
---|
| 1015 | slope2 = minmod(2.0*beta_m[k],beta_p[k]) |
---|
| 1016 | phi = maxmod(slope1,slope2) |
---|
| 1017 | |
---|
| 1018 | elif limiter == "vanleer": |
---|
| 1019 | phi = vanleer(beta_p[k],beta_m[k]) |
---|
| 1020 | |
---|
| 1021 | elif limiter == "vanalbada": |
---|
| 1022 | phi = vanalbada(beta_m[k],beta_p[k]) |
---|
| 1023 | |
---|
| 1024 | for i in range(2): |
---|
| 1025 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
| 1026 | |
---|
| 1027 | def limit_steve_slope(self): |
---|
| 1028 | |
---|
| 1029 | import sys |
---|
| 1030 | |
---|
| 1031 | from util import minmod, minmod_kurganov, maxmod, vanleer |
---|
| 1032 | |
---|
| 1033 | N = self.domain.number_of_elements |
---|
| 1034 | limiter = self.domain.limiter |
---|
| 1035 | limiter_type = self.domain.limiter_type |
---|
| 1036 | |
---|
| 1037 | qc = self.centroid_values |
---|
| 1038 | qv = self.vertex_values |
---|
| 1039 | |
---|
| 1040 | #Find min and max of this and neighbour's centroid values |
---|
| 1041 | beta_p = numpy.zeros(N,numpy.float) |
---|
| 1042 | beta_m = numpy.zeros(N,numpy.float) |
---|
| 1043 | beta_x = numpy.zeros(N,numpy.float) |
---|
| 1044 | C = self.domain.centroids |
---|
| 1045 | X = self.domain.vertices |
---|
| 1046 | |
---|
| 1047 | for k in range(N): |
---|
| 1048 | |
---|
| 1049 | n0 = self.domain.neighbours[k,0] |
---|
| 1050 | n1 = self.domain.neighbours[k,1] |
---|
| 1051 | |
---|
| 1052 | if (n0 >= 0) & (n1 >= 0): |
---|
| 1053 | # Check denominator not zero |
---|
| 1054 | if (qc[k+1]-qc[k]) == 0.0: |
---|
| 1055 | beta_p[k] = float(sys.maxint) |
---|
| 1056 | beta_m[k] = float(sys.maxint) |
---|
| 1057 | else: |
---|
| 1058 | #STEVE LIMIT |
---|
| 1059 | beta_p[k] = (qc[k]-qc[k-1])/(qc[k+1]-qc[k]) |
---|
| 1060 | beta_m[k] = (qc[k+2]-qc[k+1])/(qc[k+1]-qc[k]) |
---|
| 1061 | |
---|
| 1062 | #Deltas between vertex and centroid values |
---|
| 1063 | dq = numpy.zeros(qv.shape, numpy.float) |
---|
| 1064 | for i in range(2): |
---|
| 1065 | dq[:,i] =self.domain.vertices[:,i]-self.domain.centroids |
---|
| 1066 | |
---|
| 1067 | #Phi limiter |
---|
| 1068 | for k in range(N): |
---|
| 1069 | |
---|
| 1070 | phi = 0.0 |
---|
| 1071 | if limiter == "flux_minmod": |
---|
| 1072 | #FLUX MINMOD |
---|
| 1073 | phi = minmod_kurganov(1.0,beta_m[k],beta_p[k]) |
---|
| 1074 | elif limiter == "flux_superbee": |
---|
| 1075 | #FLUX SUPERBEE |
---|
| 1076 | phi = max(0.0,min(1.0,2.0*beta_m[k]),min(2.0,beta_m[k]))+max(0.0,min(1.0,2.0*beta_p[k]),min(2.0,beta_p[k]))-1.0 |
---|
| 1077 | elif limiter == "flux_muscl": |
---|
| 1078 | #FLUX MUSCL |
---|
| 1079 | phi = max(0.0,min(2.0,2.0*beta_m[k],2.0*beta_p[k],0.5*(beta_m[k]+beta_p[k]))) |
---|
| 1080 | elif limiter == "flux_vanleer": |
---|
| 1081 | #FLUX VAN LEER |
---|
| 1082 | phi = (beta_m[k]+abs(beta_m[k]))/(1.0+abs(beta_m[k]))+(beta_p[k]+abs(beta_p[k]))/(1.0+abs(beta_p[k]))-1.0 |
---|
| 1083 | |
---|
| 1084 | #Then update using phi limiter |
---|
| 1085 | n = self.domain.neighbours[k,1] |
---|
| 1086 | if n>=0: |
---|
| 1087 | #qv[k,0] = qc[k] - 0.5*phi*(qc[k+1]-qc[k]) |
---|
| 1088 | #qv[k,1] = qc[k] + 0.5*phi*(qc[k+1]-qc[k]) |
---|
| 1089 | qv[k,0] = qc[k] + 0.5*phi*(qv[k,0]-qc[k]) |
---|
| 1090 | qv[k,1] = qc[k] + 0.5*phi*(qv[k,1]-qc[k]) |
---|
| 1091 | else: |
---|
| 1092 | qv[k,i] = qc[k] |
---|
| 1093 | |
---|
| 1094 | def backup_centroid_values(self): |
---|
| 1095 | # Call correct module function |
---|
| 1096 | # (either from this module or C-extension) |
---|
| 1097 | #backup_centroid_values(self) |
---|
| 1098 | |
---|
| 1099 | self.centroid_backup_values[:,] = (self.centroid_values).astype('f') |
---|
| 1100 | |
---|
| 1101 | def saxpy_centroid_values(self,a,b): |
---|
| 1102 | # Call correct module function |
---|
| 1103 | # (either from this module or C-extension) |
---|
| 1104 | self.centroid_values[:,] = (a*self.centroid_values + b*self.centroid_backup_values).astype('f') |
---|
| 1105 | |
---|
| 1106 | |
---|
| 1107 | |
---|
| 1108 | def newLinePlot(title='Simple Plot'): |
---|
| 1109 | import pylab as g |
---|
| 1110 | g.ion() |
---|
| 1111 | g.hold(False) |
---|
| 1112 | g.title(title) |
---|
| 1113 | g.xlabel('x') |
---|
| 1114 | g.ylabel('y') |
---|
| 1115 | |
---|
| 1116 | |
---|
| 1117 | def linePlot(x,y): |
---|
| 1118 | import pylab as g |
---|
| 1119 | g.plot(x.flat,y.flat) |
---|
| 1120 | |
---|
| 1121 | |
---|
| 1122 | def closePlots(): |
---|
| 1123 | import pylab as g |
---|
| 1124 | g.close('all') |
---|
| 1125 | |
---|
| 1126 | if __name__ == "__main__": |
---|
| 1127 | #from domain import Domain |
---|
[7830] | 1128 | from generic_domain import Generic_domain as Domain |
---|
[7827] | 1129 | |
---|
| 1130 | points1 = [0.0, 1.0, 2.0, 3.0] |
---|
| 1131 | vertex_values = [[1.0,2.0],[4.0,5.0],[-1.0,2.0]] |
---|
| 1132 | |
---|
| 1133 | D1 = Domain(points1) |
---|
| 1134 | |
---|
| 1135 | Q1 = Quantity(D1, vertex_values) |
---|
| 1136 | |
---|
| 1137 | print Q1.vertex_values |
---|
| 1138 | print Q1.centroid_values |
---|
| 1139 | |
---|
| 1140 | new_vertex_values = [[2.0,1.0],[3.0,4.0],[-2.0,4.0]] |
---|
| 1141 | |
---|
| 1142 | Q1.set_values(new_vertex_values) |
---|
| 1143 | |
---|
| 1144 | print Q1.vertex_values |
---|
| 1145 | print Q1.centroid_values |
---|
| 1146 | |
---|
| 1147 | new_centroid_values = [20,30,40] |
---|
| 1148 | Q1.set_values(new_centroid_values,'centroids') |
---|
| 1149 | |
---|
| 1150 | print Q1.vertex_values |
---|
| 1151 | print Q1.centroid_values |
---|
| 1152 | |
---|
| 1153 | class FunClass: |
---|
| 1154 | def __init__(self,value): |
---|
| 1155 | self.value = value |
---|
| 1156 | |
---|
| 1157 | def __call__(self,x): |
---|
| 1158 | return self.value*(x**2) |
---|
| 1159 | |
---|
| 1160 | |
---|
| 1161 | fun = FunClass(1.0) |
---|
| 1162 | Q1.set_values(fun,'vertices') |
---|
| 1163 | |
---|
| 1164 | print Q1.vertex_values |
---|
| 1165 | print Q1.centroid_values |
---|
| 1166 | |
---|
| 1167 | Xc = Q1.domain.vertices |
---|
| 1168 | Qc = Q1.vertex_values |
---|
| 1169 | print Xc |
---|
| 1170 | print Qc |
---|
| 1171 | |
---|
| 1172 | Qc[1,0] = 3 |
---|
| 1173 | |
---|
| 1174 | Q1.extrapolate_second_order() |
---|
| 1175 | #Q1.limit_minmod() |
---|
| 1176 | |
---|
| 1177 | newLinePlot('plots') |
---|
| 1178 | linePlot(Xc,Qc) |
---|
| 1179 | raw_input('press return') |
---|
| 1180 | |
---|
| 1181 | points2 = numpy.arange(10) |
---|
| 1182 | D2 = Domain(points2) |
---|
| 1183 | |
---|
| 1184 | Q2 = Quantity(D2) |
---|
| 1185 | Q2.set_values(fun,'vertices') |
---|
| 1186 | Xc = Q2.domain.vertices |
---|
| 1187 | Qc = Q2.vertex_values |
---|
| 1188 | linePlot(Xc,Qc) |
---|
| 1189 | raw_input('press return') |
---|
| 1190 | |
---|
| 1191 | |
---|
| 1192 | Q2.extrapolate_second_order() |
---|
| 1193 | #Q2.limit_minmod() |
---|
| 1194 | Xc = Q2.domain.vertices |
---|
| 1195 | Qc = Q2.vertex_values |
---|
| 1196 | print Q2.centroid_values |
---|
| 1197 | print Qc |
---|
| 1198 | linePlot(Xc,Qc) |
---|
| 1199 | raw_input('press return') |
---|
| 1200 | |
---|
| 1201 | |
---|
| 1202 | for i in range(10): |
---|
| 1203 | import pylab as g |
---|
| 1204 | g.hold(True) |
---|
| 1205 | fun = FunClass(i/10.0) |
---|
| 1206 | Q2.set_values(fun,'centroids') |
---|
| 1207 | Q2.extrapolate_second_order() |
---|
| 1208 | #Q2.limit_minmod() |
---|
| 1209 | Qc = Q2.vertex_values |
---|
| 1210 | linePlot(Xc,Qc) |
---|
| 1211 | raw_input('press return') |
---|
| 1212 | |
---|
| 1213 | raw_input('press return to quit') |
---|
| 1214 | closePlots() |
---|