source: inundation/ga/storm_surge/pyvolution/quantity.py @ 269

"""Class Quantity - Implements values at each triangular element

To create:

   Quantity(domain, vertex_values)

   domain: Associated domain structure. Required.
   
   vertex_values: N x 3 array of values at each vertex for each element.
                  Default None

   If vertex_values are None Create array of zeros compatible with domain.
   Otherwise check that it is compatible with dimenions of domain.
   Otherwise raise an exception
"""


class Quantity:

    def __init__(self, domain, vertex_values=None):

        from mesh import Mesh
        from Numeric import array, zeros, Float

        msg = 'First argument in Quantity.__init__ '
        msg += 'must be of class Mesh (or a subclass thereof)'
        assert isinstance(domain, Mesh), msg

        if vertex_values is None:
            N = domain.number_of_elements            
            self.vertex_values = zeros((N, 3), Float)
        else:    
            self.vertex_values = array(vertex_values).astype(Float)

            N, V = self.vertex_values.shape
            assert V == 3,\
                   'Three vertex values per element must be specified'
            

            msg = 'Number of vertex values (%d) must be consistent with'\
                  %N
            msg += 'number of elements in specified domain (%d).'\
                   %domain.number_of_elements
            
            assert N == domain.number_of_elements, msg

        self.domain = domain    

        #Allocate space for other quantities
        self.centroid_values = zeros(N, Float)
        self.edge_values = zeros((N, 3), Float)        

        #Intialise centroid and edge_values
        self.interpolate()


    def interpolate(self):
        """Compute interpolated values at edges and centroid
        Pre-condition: vertex_values have been set
        """

        N = self.vertex_values.shape[0]        
        for i in range(N):
            v0 = self.vertex_values[i, 0]
            v1 = self.vertex_values[i, 1]
            v2 = self.vertex_values[i, 2]
            
            self.centroid_values[i] = (v0 + v1 + v2)/3

        self.interpolate_from_vertices_to_edges()


    def interpolate_from_vertices_to_edges(self):
        #Call correct module function
        #(either from this module or C-extension)
        interpolate_from_vertices_to_edges(self)
            
            
    def set_values(self, X, location='vertices'):
        """Set values for quantity

        X: Compatible list, Numeric array (see below), constant or function
        location: Where values are to be stored.
                  Permissible options are: vertices, edges, centroid
                  Default is "vertices"

        In case of location == 'centroid' the dimension values must
        be a list of a Numerical array of length N, N being the number
        of elements in the mesh. Otherwise it must be of dimension Nx3

        The values will be stored in elements following their
        internal ordering.

        If values are described a function, it will be evaluated at specified points

        If selected location is vertices, values for centroid and edges
        will be assigned interpolated values.
        In any other case, only values for the specified locations
        will be assigned and the others will be left undefined.
        """

        if location not in ['vertices', 'centroids', 'edges']:
            msg = 'Invalid location: %s' %location
            raise msg

        if X is None:
            msg = 'Given values are None'
            raise msg            
        
        import types
        
        if callable(X):
            #Use function specific method
            self.set_function_values(X, location)            
        elif type(X) in [types.FloatType, types.IntType, types.LongType]:
            if location == 'centroids':
                self.centroid_values[:] = X
            elif location == 'edges':
                self.edge_values[:] = X
            else:
                self.vertex_values[:] = X                

        else:
            #Use array specific method
            self.set_array_values(X, location)

        if location == 'vertices':
            #Intialise centroid and edge_values
            self.interpolate()
            


    def set_function_values(self, f, location='vertices'):
        """Set values for quantity using specified function

        f: x, y -> z Function where x, y and z are arrays
        location: Where values are to be stored.
                  Permissible options are: vertices, edges, centroid
                  Default is "vertices"
        """

        if location == 'centroids':
            P = self.domain.centroids
            self.set_values(f(P[:,0], P[:,1]), location)
        elif location == 'edges':
            raise 'Not implemented: %s' %location
        else:
            #Vertices
            P = self.domain.get_vertex_coordinates()
            for i in range(3):
                self.vertex_values[:,i] = f(P[:,2*i], P[:,2*i+1])

            
    def set_array_values(self, values, location='vertices'):
        """Set values for quantity

        values: Numeric array
        location: Where values are to be stored.
                  Permissible options are: vertices, edges, centroid
                  Default is "vertices"

        In case of location == 'centroid' the dimension values must
        be a list of a Numerical array of length N, N being the number
        of elements in the mesh. Otherwise it must be of dimension Nx3

        The values will be stored in elements following their
        internal ordering.

        If selected location is vertices, values for centroid and edges
        will be assigned interpolated values.
        In any other case, only values for the specified locations
        will be assigned and the others will be left undefined.
        """

        from Numeric import array, Float

        values = array(values).astype(Float)

        N = self.centroid_values.shape[0]
        
        msg = 'Number of values must match number of elements'
        assert values.shape[0] == N, msg
        
        if location == 'centroids':
            assert len(values.shape) == 1, 'Values array must be 1d'
            self.centroid_values = values                        
        elif location == 'edges':
            assert len(values.shape) == 2, 'Values array must be 2d'
            msg = 'Array must be N x 3'            
            assert values.shape[1] == 3, msg
            
            self.edge_values = values
        else:
            assert len(values.shape) == 2, 'Values array must be 2d'
            msg = 'Array must be N x 3'            
            assert values.shape[1] == 3, msg
            
            self.vertex_values = values



class Conserved_quantity(Quantity):
    """Class conserved quantity adds to Quantity:

    boundary values, storage and method for updating, and
    methods for extrapolation from centropid to vertices inluding
    gradients and limiters
    """

    def __init__(self, domain, vertex_values=None):
        Quantity.__init__(self, domain, vertex_values)
        
        from Numeric import zeros, Float

        #Allocate space for boundary values
        L = len(domain.boundary)
        self.boundary_values = zeros(L, Float)

        #Allocate space for updates of conserved quantities by
        #flux calculations and forcing functions

        N = domain.number_of_elements
        self.explicit_update = zeros(N, Float )
        self.semi_implicit_update = zeros(N, Float )
                

    def update(self, timestep):
        """Update centroid values based on values stored in
        explicit_update and semi_implicit_update as well as given timestep
        """

        from Numeric import sum, equal, ones, Float
        
        N = self.centroid_values.shape[0]
        
        #Explicit updates
        self.centroid_values += timestep*self.explicit_update
            
        #Semi implicit updates
        denominator = ones(N, Float)-timestep*self.semi_implicit_update

        if sum(equal(denominator, 0.0)) > 0.0:
            msg = 'Zero division in semi implicit update. Call Stephen :-)'
            raise msg
        else:
            #Update conserved_quantities from semi implicit updates
            self.centroid_values /= denominator


    def compute_gradients(self):
        #Call correct module function
        #(either from this module or C-extension)
        return compute_gradients(self)
            

    def limit(self):
        #Call correct module function
        #(either from this module or C-extension)
        limit(self)
        
        
    def extrapolate_first_order(self):
        """Extrapolate conserved quantities from centroid to
        vertices for each volume using
        first order scheme.
        """
        
        qc = self.centroid_values
        qv = self.vertex_values

        for i in range(3):
            qv[:,i] = qc
            
            
    def extrapolate_second_order(self):
        #Call correct module function
        #(either from this module or C-extension)
        extrapolate_second_order(self)



def interpolate_from_vertices_to_edges(quantity):
    """Compute edge values from vertex values using linear interpolation
    """

    for k in range(quantity.vertex_values.shape[0]):
        q0 = quantity.vertex_values[k, 0]
        q1 = quantity.vertex_values[k, 1]
        q2 = quantity.vertex_values[k, 2]
            
        quantity.edge_values[k, 0] = 0.5*(q1+q2)
        quantity.edge_values[k, 1] = 0.5*(q0+q2)  
        quantity.edge_values[k, 2] = 0.5*(q0+q1)



def extrapolate_second_order(quantity):        
    """Extrapolate conserved quantities from centroid to
    vertices for each volume using
    second order scheme.
    """
        
    a, b = quantity.compute_gradients()

    X = quantity.domain.get_vertex_coordinates()
    qc = quantity.centroid_values
    qv = quantity.vertex_values
    
    #Check each triangle
    for k in range(quantity.domain.number_of_elements):
        #Centroid coordinates            
        x, y = quantity.domain.centroids[k]
        
        #vertex coordinates
        x0, y0, x1, y1, x2, y2 = X[k,:]
        
        #Extrapolate
        qv[k,0] = qc[k] + a[k]*(x0-x) + b[k]*(y0-y)
        qv[k,1] = qc[k] + a[k]*(x1-x) + b[k]*(y1-y)
        qv[k,2] = qc[k] + a[k]*(x2-x) + b[k]*(y2-y)            


def compute_gradients(quantity):                    
    """Compute gradients of triangle surfaces defined by centroids of
    neighbouring volumes.
    If one edge is on the boundary, use own centroid as neighbour centroid.
    If two or more are on the boundary, fall back to first order scheme.
    """

    from Numeric import zeros, Float
    from util import gradient
    
    centroids = quantity.domain.centroids
    surrogate_neighbours = quantity.domain.surrogate_neighbours    
    centroid_values = quantity.centroid_values    
    number_of_boundaries = quantity.domain.number_of_boundaries     
    
    N = centroid_values.shape[0]

    a = zeros(N, Float)
    b = zeros(N, Float)
    
    for k in range(N):
        if number_of_boundaries[k] < 2:
            #Two or three true neighbours

            #Get indices of neighbours (or self when used as surrogate)     
            k0, k1, k2 = surrogate_neighbours[k,:]

            #Get data       
            q0 = centroid_values[k0]
            q1 = centroid_values[k1]
            q2 = centroid_values[k2]                    

            x0, y0 = centroids[k0] #V0 centroid
            x1, y1 = centroids[k1] #V1 centroid
            x2, y2 = centroids[k2] #V2 centroid

            #Gradient
            a[k], b[k] = gradient(x0, y0, x1, y1, x2, y2, q0, q1, q2)
        
        elif number_of_boundaries[k] == 2:
            #One true neighbour

            #Get index of the one neighbour
            for k0 in surrogate_neighbours[k,:]:
                if k0 != k: break
            assert k0 != k

            k1 = k  #self

            #Get data
            q0 = centroid_values[k0]
            q1 = centroid_values[k1]

            x0, y0 = centroids[k0] #V0 centroid
            x1, y1 = centroids[k1] #V1 centroid        

            #Gradient
            det = x0*y1 - x1*y0
            if det != 0.0:
                a[k] = (y1*q0 - y0*q1)/det
                b[k] = (x0*q1 - x1*q0)/det

        else:
            #No true neighbours -       
            #Fall back to first order scheme
            pass
        
    
    return a, b
        
                    

def limit(quantity):        
    """Limit slopes for each volume to eliminate artificial variance
    introduced by e.g. second order extrapolator
    
    This is an unsophisticated limiter as it does not take into
    account dependencies among quantities.
    
    precondition:
    vertex values are estimated from gradient
    postcondition:
    vertex values are updated
    """

    from Numeric import zeros, Float

    N = quantity.domain.number_of_elements
    
    beta = quantity.domain.beta
        
    qc = quantity.centroid_values
    qv = quantity.vertex_values
        
    #Find min and max of this and neighbour's centroid values
    qmax = zeros(qc.shape, Float)
    qmin = zeros(qc.shape, Float)        
    
    for k in range(N):
        qmax[k] = qmin[k] = qc[k]
        for i in range(3):
            n = quantity.domain.neighbours[k,i]
            if n >= 0:
                qn = qc[n] #Neighbour's centroid value
                
                qmin[k] = min(qmin[k], qn)
                qmax[k] = max(qmax[k], qn)
      
    
    #Diffences between centroids and maxima/minima
    dqmax = qmax - qc 
    dqmin = qmin - qc
        
    #Deltas between vertex and centroid values
    dq = zeros(qv.shape, Float)
    for i in range(3):
        dq[:,i] = qv[:,i] - qc

    #Phi limiter    
    for k in range(N):
        
        #Find the gradient limiter (phi) across vertices
        phi = 1.0
        for i in range(3):
            r = 1.0
            if (dq[k,i] > 0): r = dqmax[k]/dq[k,i]
            if (dq[k,i] < 0): r = dqmin[k]/dq[k,i]
            
            phi = min( min(r*beta, 1), phi )    

        #Then update using phi limiter
        for i in range(3):            
            qv[k,i] = qc[k] + phi*dq[k,i]



import compile
if compile.can_use_C_extension('quantity_ext.c'):
    #Replace python version with c implementations
        
    from quantity_ext import limit, compute_gradients,\
    extrapolate_second_order, interpolate_from_vertices_to_edges