source: anuga_core/source/anuga/abstract_2d_finite_volumes/quantity.py @ 6166

"""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
"""

from anuga.utilities.numerical_tools import ensure_numeric, is_scalar
from anuga.utilities.polygon import inside_polygon

from anuga.geospatial_data.geospatial_data import Geospatial_data
from anuga.fit_interpolate.fit import fit_to_mesh
from anuga.config import points_file_block_line_size as default_block_line_size
from anuga.config import epsilon

import Numeric as num


class Quantity:

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

        from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh

        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 = len(domain) # number_of_elements
            self.vertex_values = num.zeros((N, 3), num.Float)
        else:
            self.vertex_values = num.array(vertex_values, num.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).'\
                   %len(domain)

            assert N == len(domain), msg

        self.domain = domain

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

        # Allocate space for Gradient
        self.x_gradient = num.zeros(N, num.Float)
        self.y_gradient = num.zeros(N, num.Float)

        # Allocate space for Limiter Phi
        self.phi = num.zeros(N, num.Float)        

        # Intialise centroid and edge_values
        self.interpolate()

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

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

        # Allocate space for update fields
        self.explicit_update = num.zeros(N, num.Float )
        self.semi_implicit_update = num.zeros(N, num.Float )
        self.centroid_backup_values = num.zeros(N, num.Float)

        self.set_beta(1.0)



    # Methods for operator overloading
    def __len__(self):
        return self.centroid_values.shape[0]


    def __neg__(self):
        """Negate all values in this quantity giving meaning to the
        expression -Q where Q is an instance of class Quantity
        """

        Q = Quantity(self.domain)
        Q.set_values(-self.vertex_values)
        return Q


    def __add__(self, other):
        """Add to self anything that could populate a quantity

        E.g other can be a constant, an array, a function, another quantity
        (except for a filename or points, attributes (for now))
        - see set_values for details
        """

        Q = Quantity(self.domain)
        Q.set_values(other)

        result = Quantity(self.domain)
        result.set_values(self.vertex_values + Q.vertex_values)
        return result

    def __radd__(self, other):
        """Handle cases like 7+Q, where Q is an instance of class Quantity
        """
        return self + other


    def __sub__(self, other):
        return self + -other  #Invoke __neg__

    def __mul__(self, other):
        """Multiply self with anything that could populate a quantity

        E.g other can be a constant, an array, a function, another quantity
        (except for a filename or points, attributes (for now))
        - see set_values for details
        """

        if isinstance(other, Quantity):
            Q = other
        else:    
            Q = Quantity(self.domain)
            Q.set_values(other)

        result = Quantity(self.domain)

        # The product of vertex_values, edge_values and centroid_values
        # are calculated and assigned directly without using
        # set_values (which calls interpolate). Otherwise
        # edge and centroid values wouldn't be products from q1 and q2
        result.vertex_values = self.vertex_values * Q.vertex_values
        result.edge_values = self.edge_values * Q.edge_values
        result.centroid_values = self.centroid_values * Q.centroid_values
        
        return result

    def __rmul__(self, other):
        """Handle cases like 3*Q, where Q is an instance of class Quantity
        """
        return self * other

    def __div__(self, other):
        """Divide self with anything that could populate a quantity

        E.g other can be a constant, an array, a function, another quantity
        (except for a filename or points, attributes (for now))
        - see set_values for details

        Zero division is dealt with by adding an epsilon to the divisore
        FIXME (Ole): Replace this with native INF once we migrate to NumPy
        """

        if isinstance(other, Quantity):
            Q = other
        else:    
            Q = Quantity(self.domain)
            Q.set_values(other)

        result = Quantity(self.domain)

        # The quotient of vertex_values, edge_values and centroid_values
        # are calculated and assigned directly without using
        # set_values (which calls interpolate). Otherwise
        # edge and centroid values wouldn't be quotient of q1 and q2
        result.vertex_values = self.vertex_values/(Q.vertex_values + epsilon)
        result.edge_values = self.edge_values/(Q.edge_values + epsilon)
        result.centroid_values = self.centroid_values/(Q.centroid_values + epsilon)

        return result

    def __rdiv__(self, other):
        """Handle cases like 3/Q, where Q is an instance of class Quantity
        """
        return self / other

    def __pow__(self, other):
        """Raise quantity to (numerical) power

        As with __mul__ vertex values are processed entry by entry
        while centroid and edge values are re-interpolated.

        Example using __pow__:
          Q = (Q1**2 + Q2**2)**0.5

        """

        if isinstance(other, Quantity):
            Q = other
        else:    
            Q = Quantity(self.domain)
            Q.set_values(other)

        result = Quantity(self.domain)

        # The power of vertex_values, edge_values and centroid_values
        # are calculated and assigned directly without using
        # set_values (which calls interpolate). Otherwise
        # edge and centroid values wouldn't be correct
        result.vertex_values = self.vertex_values ** other
        result.edge_values = self.edge_values ** other
        result.centroid_values = self.centroid_values ** other

        return result

    #def __sqrt__(self, other):
    #    """Define in terms of x**0.5
    #    """
    #    pass

    def set_beta(self,beta):
        """Set default beta value for limiting
        """

        if beta < 0.0:
            print 'WARNING: setting beta < 0.0'
        if beta > 2.0:
            print 'WARNING: setting beta > 2.0'
            
        self.beta = beta

    def get_beta(self):
        """Get default beta value for limiting
        """

        return self.beta

    def interpolate(self):
        """Compute interpolated values at edges and centroid
        Pre-condition: vertex_values have been set
        """
        
        # FIXME (Ole): Maybe this function
        # should move to the C-interface?
        # However, it isn't called by validate_all.py, so it
        # may not be that important to optimise it?
        
        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 interpolate_from_edges_to_vertices(self):
        # Call correct module function
        # (either from this module or C-extension)
        interpolate_from_edges_to_vertices(self)




    #---------------------------------------------
    # Public interface for setting quantity values
    #---------------------------------------------
    def set_values(self,
                   numeric=None,    # List, numeric array or constant
                   quantity=None,   # Another quantity
                   function=None,   # Callable object: f(x,y)
                   geospatial_data=None, # Arbitrary dataset
                   filename=None, attribute_name=None, # Input from file
                   alpha=None,
                   location='vertices',
                   polygon=None,
                   indices=None,
                   smooth=False,
                   verbose=False,
                   use_cache=False):

        """Set values for quantity based on different sources.

        numeric:
          Compatible list, Numeric array (see below) or constant.
          If callable it will treated as a function (see below)
          If instance of another Quantity it will be treated as such.
          If geo_spatial object it will be treated as such

        quantity:
          Another quantity (compatible quantity, e.g. obtained as a
          linear combination of quantities)

        function:
          Any callable object that takes two 1d arrays x and y
          each of length N and returns an array also of length N.
          The function will be evaluated at points determined by
          location and indices in the underlying mesh.

        geospatial_data:
          Arbitrary geo spatial dataset in the form of the class
          Geospatial_data. Mesh points are populated using
          fit_interpolate.fit fitting

        filename:
          Name of a points file containing data points and attributes for
          use with fit_interpolate.fit.

        attribute_name:
          If specified, any array matching that name
          will be used. from file or geospatial_data.
          Otherwise a default will be used.

        alpha:
          Smoothing parameter to be used with fit_interpolate.fit.
          See module fit_interpolate.fit for further details about alpha.
          Alpha will only be used with points, values or filename.
          Otherwise it will be ignored.


        location: Where values are to be stored.
                  Permissible options are: vertices, edges, centroids
                  Default is 'vertices'

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


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

                  If location is 'unique vertices' indices refers the set
                  of node ids that the operation applies to.
                  If location is not 'unique vertices' indices refers the
                  set of triangle ids that the operation applies to.


                  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.


        polygon: Restrict update of quantity to locations that fall
                 inside polygon. Polygon works by selecting indices
                 and calling set_values recursively.
                 Polygon mode has only been implemented for
                 constant values so far.

        indices: Restrict update of quantity to locations that are 
                 identified by indices (e.g. node ids if location
                 is 'unique vertices' or triangle ids otherwise).
        
        verbose: True means that output to stdout is generated

        use_cache: True means that caching of intermediate results is
                   attempted for fit_interpolate.fit.




        Exactly one of the arguments
          numeric, quantity, function, filename
        must be present.
        """

        from anuga.geospatial_data.geospatial_data import Geospatial_data
        from types import FloatType, IntType, LongType, ListType, NoneType

        # Treat special case: Polygon situation
        # Location will be ignored and set to 'centroids'
        # FIXME (Ole): This needs to be generalised and
        # perhaps the notion of location and indices simplified

        # FIXME (Ole): Need to compute indices based on polygon 
        # (and location) and use existing code after that.
        
        # See ticket:275, ticket:250, ticeket:254 for refactoring plan
        
        if polygon is not None:
            if indices is not None:
                msg = 'Only one of polygon and indices can be specified'
                raise Exception, msg

            msg = 'With polygon selected, set_quantity must provide '
            msg += 'the keyword numeric and it must (currently) be '
            msg += 'a constant.'
            if numeric is None:
                raise Exception, msg            
            else:
                # Check that numeric is as constant
                assert type(numeric) in [FloatType, IntType, LongType], msg


            location = 'centroids'


            points = self.domain.get_centroid_coordinates(absolute=True)
            indices = inside_polygon(points, polygon)
            
            self.set_values_from_constant(numeric,
                                          location, indices, verbose)


            self.extrapolate_first_order()

            if smooth:
                self.smooth_vertex_values()

                
            return
        
        




        # General input checks
        L = [numeric, quantity, function, geospatial_data, filename]
        msg = 'Exactly one of the arguments '+\
              'numeric, quantity, function, geospatial_data, '+\
              'or filename must be present.'
        assert L.count(None) == len(L)-1, msg


        if location == 'edges':
            msg = 'edges has been deprecated as valid location'
            raise Exception, msg
            
        if location not in ['vertices', 'centroids', 'unique vertices']:
            msg = 'Invalid location: %s' %location
            raise Exception, msg


        msg = 'Indices must be a list or None'
        assert type(indices) in [ListType, NoneType, num.ArrayType], msg



        # Determine which 'set_values_from_...' to use

        if numeric is not None:
            if type(numeric) in [FloatType, IntType, LongType]:
                self.set_values_from_constant(numeric,
                                              location, indices, verbose)
            elif type(numeric) in [num.ArrayType, ListType]:
                self.set_values_from_array(numeric,
                                           location, indices, verbose)
            elif callable(numeric):
                self.set_values_from_function(numeric,
                                              location, indices, verbose)
            elif isinstance(numeric, Quantity):
                self.set_values_from_quantity(numeric,
                                              location, indices, verbose)
            elif isinstance(numeric, Geospatial_data):
                self.set_values_from_geospatial_data(numeric,
                                                     alpha,
                                                     location, indices,
                                                     verbose=verbose,
                                                     use_cache=use_cache)
            else:
                msg = 'Illegal type for argument numeric: %s' %str(numeric)
                raise msg

        elif quantity is not None:
            self.set_values_from_quantity(quantity,
                                          location, indices, verbose)
        elif function is not None:
            msg = 'Argument function must be callable'
            assert callable(function), msg
            self.set_values_from_function(function,
                                          location, indices, verbose)
        elif geospatial_data is not None:
                self.set_values_from_geospatial_data(geospatial_data,
                                                     alpha,
                                                     location, indices,
                                                     verbose=verbose,
                                                     use_cache=use_cache)
            
        elif filename is not None:
            if hasattr(self.domain, 'points_file_block_line_size'):
                max_read_lines = self.domain.points_file_block_line_size
            else:
                max_read_lines = default_block_line_size
            self.set_values_from_file(filename, attribute_name, alpha,
                                      location, indices,
                                      verbose=verbose,
                                      max_read_lines=max_read_lines,
                                      use_cache=use_cache)
        else:
            raise Exception, 'This can\'t happen :-)'



        # Update all locations in triangles
        if location == 'vertices' or location == 'unique vertices':
            # Intialise centroid and edge_values
            self.interpolate()

        if location == 'centroids':
            # Extrapolate 1st order - to capture notion of area being specified
            self.extrapolate_first_order()



    #-------------------------------------------------------------        
    # Specific internal functions for setting values based on type
    #-------------------------------------------------------------            
    
    def set_values_from_constant(self, X,
                                 location, indices, verbose):
        """Set quantity values from specified constant X
        """

        # FIXME (Ole): Somehow indices refer to centroids
        # rather than vertices as default. See unit test
        # test_set_vertex_values_using_general_interface_with_subset(self):
        

        if location == 'centroids':
            if indices is None:
                self.centroid_values[:] = X
            else:
                # Brute force
                for i in indices:
                    self.centroid_values[i] = X

        #elif location == 'edges':
        #    if indices is None:
        #        self.edge_values[:] = X
        #    else:
        #        # Brute force
        #        for i in indices:
        #            self.edge_values[i] = X

        elif location == 'unique vertices':
            if indices is None:
                self.edge_values[:] = X  #FIXME (Ole): Shouldn't this be vertex_values?
            else:

                # Go through list of unique vertices
                for unique_vert_id in indices:

                    triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id)
                    
                    # In case there are unused points
                    if len(triangles) == 0:
                        continue
                    
                    # Go through all triangle, vertex pairs
                    # and set corresponding vertex value
                    for triangle_id, vertex_id in triangles:
                        self.vertex_values[triangle_id, vertex_id] = X

                    # Intialise centroid and edge_values
                    self.interpolate()
        else:
            if indices is None:
                self.vertex_values[:] = X
            else:
                # Brute force
                for i_vertex in indices:
                    self.vertex_values[i_vertex] = X




    def set_values_from_array(self, values,
                              location='vertices',
                              indices=None,
                              verbose=False):
        """Set values for quantity

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

        indices - if this action is carried out on a subset of
        elements or unique vertices
        The element/unique vertex indices are specified here.

        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.

        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.
        """

        values = num.array(values, num.Float)

        if indices is not None:
            indices = num.array(indices, num.Int)
            msg = 'Number of values must match number of indices:'
            msg += ' You specified %d values and %d indices'\
                   %(values.shape[0], indices.shape[0])
            assert values.shape[0] == indices.shape[0], msg

        N = self.centroid_values.shape[0]

        if location == 'centroids':
            assert len(values.shape) == 1, 'Values array must be 1d'

            if indices is None:
                msg = 'Number of values must match number of elements'
                assert values.shape[0] == N, msg

                self.centroid_values = values
            else:
                msg = 'Number of values must match number of indices'
                assert values.shape[0] == indices.shape[0], msg

                # Brute force
                for i in range(len(indices)):
                    self.centroid_values[indices[i]] = values[i]

        elif location == 'unique vertices':
            assert len(values.shape) == 1 or num.allclose(values.shape[1:], 1),\
                   'Values array must be 1d'

            self.set_vertex_values(values.flat, indices=indices)
            
        else:
            # Location vertices
            if len(values.shape) == 1:
                self.set_vertex_values(values, indices=indices)

            elif len(values.shape) == 2:
                # Vertex values are given as a triplet for each triangle

                msg = 'Array must be N x 3'
                assert values.shape[1] == 3, msg

                if indices is None:
                    self.vertex_values = values
                else:
                    for element_index, value in map(None, indices, values):
                        self.vertex_values[element_index] = value
            else:
                msg = 'Values array must be 1d or 2d'
                raise msg
            

    def set_values_from_quantity(self, q,
                                 location, indices, verbose):
        """Set quantity values from specified quantity instance q

        Location is ignored - vertices will always be used here.
        """


        A = q.vertex_values

        msg = 'Quantities are defined on different meshes. '+\
              'This might be a case for implementing interpolation '+\
              'between different meshes.'
        assert num.allclose(A.shape, self.vertex_values.shape), msg

        self.set_values(A, location='vertices',
                        indices=indices,
                        verbose=verbose)


    def set_values_from_function(self, f,
                                 location='vertices',
                                 indices=None,
                                 verbose=False):
        """Set values for quantity using specified function

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

                  
        """

        # FIXME: Should check that function returns something sensible and
        # raise a meaningfull exception if it returns None for example

        # FIXME: Should supply absolute coordinates


        # Compute the function values and call set_values again
        if location == 'centroids':
            if indices is None:
                indices = range(len(self))
                
            V = num.take(self.domain.get_centroid_coordinates(), indices)
            self.set_values(f(V[:,0], V[:,1]),
                            location=location,
                            indices=indices)
            
        elif location == 'vertices':

            M = self.domain.number_of_triangles
            V = self.domain.get_vertex_coordinates()

            x = V[:,0]; y = V[:,1];                     
            values = f(x, y)


            # FIXME (Ole): This code should replace all the
            # rest of this function and it would work, except
            # one unit test in test_region fails.
            # If that could be resolved this one will be
            # more robust and simple.
            
            #values = num.reshape(values, (M,3))
            #self.set_values(values,
            #                location='vertices',
            #                indices=indices)


            # This should be removed
            if is_scalar(values):
                # Function returned a constant value
                self.set_values_from_constant(values,
                                              location, indices, verbose)
                return

            # This should be removed            
            if indices is None:
                for j in range(3):
                    self.vertex_values[:,j] = values[j::3]                 
            else:    
                # Brute force
                for i in indices:
                    for j in range(3):
                        self.vertex_values[i,j] = values[3*i+j]


        else:
            raise 'Not implemented: %s' %location



    def set_values_from_geospatial_data(self, geospatial_data, alpha,
                                        location, indices,
                                        verbose=False,
                                        use_cache=False):
        """ Set values based on geo referenced geospatial data object.
        """

        points = geospatial_data.get_data_points(absolute=False)
        values = geospatial_data.get_attributes()
        data_georef = geospatial_data.get_geo_reference()


        from anuga.coordinate_transforms.geo_reference import Geo_reference


        points = ensure_numeric(points, num.Float)
        values = ensure_numeric(values, num.Float)

        if location != 'vertices':
            msg = 'set_values_from_points is only defined for '+\
                  'location=\'vertices\''
            raise ms

        coordinates = self.domain.get_nodes()
        triangles = self.domain.triangles      #FIXME


        # Take care of georeferencing
        if data_georef is None:
            data_georef = Geo_reference()


        mesh_georef = self.domain.geo_reference


        # Call fit_interpolate.fit function
        # args = (coordinates, triangles, points, values)
        args = (points, )
        kwargs = {'vertex_coordinates': coordinates,
                  'triangles': triangles,
                  'mesh': None,
                  'point_attributes': values,
                  'data_origin': data_georef.get_origin(),
                  'mesh_origin': mesh_georef.get_origin(),
                  'alpha': alpha,
                  'verbose': verbose}

        vertex_attributes = apply(fit_to_mesh,
                                  args, kwargs)        

        # Call underlying method using array values
        self.set_values_from_array(vertex_attributes,
                                   location, indices, verbose)



    def set_values_from_points(self, points, values, alpha,
                               location, indices,
                               data_georef=None,
                               verbose=False,
                               use_cache=False):
        """
        Set quantity values from arbitray data points using
        fit_interpolate.fit
        """

        raise Exception, 'set_values_from_points is obsolete, use geospatial data object instead'
        

    def set_values_from_file(self, filename, attribute_name, alpha,
                             location, indices,
                             verbose=False,
                             use_cache=False,
                             max_read_lines=None):
        """Set quantity based on arbitrary points in a points file
        using attribute_name selects name of attribute
        present in file.
        If attribute_name is not specified, use first available attribute
        as defined in geospatial_data.
        """

        from types import StringType
        msg = 'Filename must be a text string'
        assert type(filename) == StringType, msg


        if location != 'vertices':
            msg = 'set_values_from_file is only defined for '+\
                  'location=\'vertices\''
            raise msg

        if False:  
            # FIXME (Ole)
            # Use mesh as defined by domain
            # This causes problems for caching 
            # due to quantities changing, but
            # it would work if we only passed in
            # the appropriate Mesh object.
            vertex_attributes = fit_to_mesh(filename,
                                            mesh=self.domain,  
                                            alpha=alpha,
                                            attribute_name=attribute_name,
                                            use_cache=use_cache,
                                            verbose=verbose,
                                            max_read_lines=max_read_lines)
        else:
            # This variant will cause Mesh object to be recreated
            # in fit_to_mesh thus doubling up on the neighbour structure 
            nodes = self.domain.get_nodes(absolute=True)
            triangles = self.domain.triangles      
            vertex_attributes = fit_to_mesh(filename,
                                            nodes, triangles, 
                                            mesh=None,
                                            alpha=alpha,
                                            attribute_name=attribute_name,
                                            use_cache=use_cache,
                                            verbose=verbose,
                                            max_read_lines=max_read_lines)
                                            
        # Call underlying method using array values
        self.set_values_from_array(vertex_attributes,
                                   location, indices, verbose)

    
    
    #-----------------------------------------------------    
    def get_extremum_index(self, mode=None, indices=None):
        """Return index for maximum or minimum value of quantity (on centroids)

        Optional arguments:
            mode is either 'max'(default) or 'min'.
            indices is the set of element ids that the operation applies to.

        Usage:
            i = get_extreme_index()

        Notes:
            We do not seek the extremum at vertices as each vertex can
            have multiple values - one for each triangle sharing it.

            If there are multiple cells with same maximum value, the
            first cell encountered in the triangle array is returned.
        """

        V = self.get_values(location='centroids', indices=indices)

        # Always return absolute indices
        if mode is None or mode == 'max':
            i = num.argmax(V)
        elif mode == 'min':    
            i = num.argmin(V)

            
        if indices is None:
            return i
        else:
            return indices[i]


    def get_maximum_index(self, indices=None):
        """See get extreme index for details
        """

        return self.get_extremum_index(mode='max',
                                       indices=indices)


        
    def get_maximum_value(self, indices=None):
        """Return maximum value of quantity (on centroids)

        Optional argument:
            indices is the set of element ids that the operation applies to.

        Usage:
            v = get_maximum_value()

        Note, we do not seek the maximum at vertices as each vertex can
        have multiple values - one for each triangle sharing it            
        """


        i = self.get_maximum_index(indices)
        V = self.get_values(location='centroids') #, indices=indices)
        
        return V[i]
        

    def get_maximum_location(self, indices=None):
        """Return location of maximum value of quantity (on centroids)

        Optional argument:
            indices is the set of element ids that the operation applies to.

        Usage:
            x, y = get_maximum_location()


        Notes:
            We do not seek the maximum at vertices as each vertex can
            have multiple values - one for each triangle sharing it.

            If there are multiple cells with same maximum value, the
            first cell encountered in the triangle array is returned.       
        """

        i = self.get_maximum_index(indices)
        x, y = self.domain.get_centroid_coordinates()[i]

        return x, y


    def get_minimum_index(self, indices=None):
        """See get extreme index for details
        """        

        return self.get_extremum_index(mode='min',
                                       indices=indices)


    def get_minimum_value(self, indices=None):
        """Return minimum value of quantity (on centroids)

        Optional argument:
            indices is the set of element ids that the operation applies to.

        Usage:
            v = get_minimum_value()

        See get_maximum_value for more details.    
        """


        i = self.get_minimum_index(indices)
        V = self.get_values(location='centroids')
        
        return V[i]
        

    def get_minimum_location(self, indices=None):
        """Return location of minimum value of quantity (on centroids)

        Optional argument:
            indices is the set of element ids that the operation applies to.

        Usage:
            x, y = get_minimum_location()


        Notes:
            We do not seek the maximum at vertices as each vertex can
            have multiple values - one for each triangle sharing it.

            If there are multiple cells with same maximum value, the
            first cell encountered in the triangle array is returned.       
        """

        i = self.get_minimum_index(indices)
        x, y = self.domain.get_centroid_coordinates()[i]

        return x, y



    def get_interpolated_values(self, interpolation_points,
                                use_cache=False,
                                verbose=False):
        """ Get values at interpolation points
        
        The argument interpolation points must be given as either a 
        list of absolute UTM coordinates or a geospatial data object.
        """
        

        # FIXME (Ole): Points might be converted to coordinates relative to mesh origin
        # This could all be refactored using the 
        # 'change_points_geo_ref' method of Class geo_reference. 
        # The purpose is to make interpolation points relative
        # to the mesh origin.
        #
        # Speed is also a consideration here.
        
        
        # Ensure that interpolation points is either a list of 
        # points, Nx2 array, or geospatial and convert to Numeric array
        if isinstance(interpolation_points, Geospatial_data):        
            # Ensure interpolation points are in absolute UTM coordinates
            interpolation_points = interpolation_points.get_data_points(absolute=True)
                
        # Reconcile interpolation points with georeference of domain
        interpolation_points = self.domain.geo_reference.get_relative(interpolation_points) 
        interpolation_points = ensure_numeric(interpolation_points)

        
        # Get internal representation (disconnected) of vertex values
        vertex_values, triangles = self.get_vertex_values(xy=False,
                                                          smooth=False)                
    
        # Get possibly precomputed interpolation object
        I = self.domain.get_interpolation_object()

        # Call interpolate method with interpolation points                
        result = I.interpolate_block(vertex_values, interpolation_points,
                                     use_cache=use_cache,
                                     verbose=verbose)
                               
        return result
        
        


    def get_values(self, 
                   interpolation_points=None,
                   location='vertices',
                   indices=None,
                   use_cache=False,
                   verbose=False):
        """get values for quantity

        Extract values for quantity as a Numeric array.        
        
        Inputs:
           interpolation_points: List of x, y coordinates where value is
                                 sought (using interpolation). If points 
                                 are given, values of location and indices 
                                 are ignored. Assume either absolute UTM
                                 coordinates or geospatial data object.
        
           location: Where values are to be stored.
                     Permissible options are: vertices, edges, centroids
                     and unique vertices. Default is 'vertices'


        The returned values will have the leading dimension equal to length of the indices list or
        N (all values) if indices is None.

        In case of location == 'centroids' the dimension of returned
        values will be a list or a Numerical array of length N, N being
        the number of elements.
        
        In case of location == 'vertices' or 'edges' the dimension of
        returned values will be of dimension Nx3

        In case of location == 'unique vertices' the average value at
        each vertex will be returned and the dimension of returned values
        will be a 1d array of length "number of vertices" 
        
        Indices is the set of element ids that the operation applies to.

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

        # FIXME (Ole): I reckon we should have the option of passing a
        #              polygon into get_values. The question becomes how
        #              resulting values should be ordered.
        
        if verbose is True:
            print 'Getting values from %s' %location

        if interpolation_points is not None:
            return self.get_interpolated_values(interpolation_points,
                                                use_cache=use_cache,
                                                verbose=verbose)
        
        
        # FIXME (Ole): Consider deprecating 'edges' - but not if it is used
        # elsewhere in ANUGA. 
        # Edges have already been deprecated in set_values, see changeset:5521,
        # but *might* be useful in get_values. Any thoughts anyone?
        
        if location not in ['vertices', 'centroids', 'edges',
                            'unique vertices']:
            msg = 'Invalid location: %s' %location
            raise msg

        import types
        assert type(indices) in [types.ListType, types.NoneType,
                                 num.ArrayType],\
                                 'Indices must be a list or None'

        if location == 'centroids':
            if (indices ==  None):
                indices = range(len(self))
            return num.take(self.centroid_values,indices)
        elif location == 'edges':
            if (indices ==  None):
                indices = range(len(self))
            return num.take(self.edge_values,indices)
        elif location == 'unique vertices':
            if (indices ==  None):
                indices=range(self.domain.number_of_nodes)
            vert_values = []

            # Go through list of unique vertices
            for unique_vert_id in indices:
                triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id)
                    
                # In case there are unused points
                if len(triangles) == 0:
                    msg = 'Unique vertex not associated with triangles'
                    raise msg

                # Go through all triangle, vertex pairs
                # Average the values
                
                # FIXME (Ole): Should we merge this with get_vertex_values
                sum = 0
                for triangle_id, vertex_id in triangles:
                    sum += self.vertex_values[triangle_id, vertex_id]
                vert_values.append(sum/len(triangles))
            return num.array(vert_values)
        else:
            if (indices is None):
                indices = range(len(self))
            return num.take(self.vertex_values, indices)



    def set_vertex_values(self, A, indices = None):
        """Set vertex values for all unique vertices based on input array A
        which has one entry per unique vertex, i.e.
        one value for each row in array self.domain.nodes.

        indices is the list of vertex_id's that will be set.

        This function is used by set_values_from_array
        """


        # Assert that A can be converted to a Numeric array of appropriate dim
        A = ensure_numeric(A, num.Float)

        # print 'SHAPE A', A.shape
        assert len(A.shape) == 1

        if indices is None:
            assert A.shape[0] == self.domain.get_nodes().shape[0]
            vertex_list = range(A.shape[0])
        else:
            assert A.shape[0] == len(indices)
            vertex_list = indices

        # Go through list of unique vertices
        for i_index, unique_vert_id in enumerate(vertex_list):


            triangles = self.domain.get_triangles_and_vertices_per_node(node=unique_vert_id)
                    
            # In case there are unused points
            if len(triangles) == 0: continue

            # Go through all triangle, vertex pairs
            # touching vertex unique_vert_id and set corresponding vertex value
            for triangle_id, vertex_id in triangles:
                self.vertex_values[triangle_id, vertex_id] = A[i_index]

        # Intialise centroid and edge_values
        self.interpolate()


    def smooth_vertex_values(self):
        """ Smooths vertex values.
        """

        A,V = self.get_vertex_values(xy=False, smooth=True)
        self.set_vertex_values(A)


    # Methods for outputting model results
    def get_vertex_values(self,
                          xy=True,
                          smooth=None,
                          precision=None):
        """Return vertex values like an OBJ format i.e. one value per node.

        The vertex values are returned as one sequence in the 1D float array A.
        If requested the coordinates will be returned in 1D arrays X and Y.

        The connectivity is represented as an integer array, V, of dimension
        Mx3, where M is the number of triangles. Each row has three indices
        defining the triangle and they correspond to elements in the arrays
        X, Y and A. 

        if smooth is True, vertex values corresponding to one common
        coordinate set will be smoothed by taking the average of vertex values for each node.
        In this case vertex coordinates will be
        de-duplicated corresponding to the original nodes as obtained from
        the method general_mesh.get_nodes()

        If no smoothings is required, vertex coordinates and values will
        be aggregated as a concatenation of values at
        vertices 0, vertices 1 and vertices 2. This corresponds to
        the node coordinates obtained from the method
        general_mesh.get_vertex_coordinates()


        Calling convention
        if xy is True:
           X,Y,A,V = get_vertex_values
        else:
           A,V = get_vertex_values

        """


        if smooth is None:
            # Take default from domain
            try:
                smooth = self.domain.smooth
            except:
                smooth = False

        if precision is None:
            precision = num.Float
            

        if smooth is True:
            # Ensure continuous vertex values by averaging
            # values at each node
            
            V = self.domain.get_triangles()
            N = self.domain.number_of_full_nodes # Ignore ghost nodes if any
            A = num.zeros(N, num.Float)
            points = self.domain.get_nodes()            
            
            if 1:
                # Fast C version
                average_vertex_values(ensure_numeric(self.domain.vertex_value_indices),
                                      ensure_numeric(self.domain.number_of_triangles_per_node),
                                      ensure_numeric(self.vertex_values),
                                      A)
                A = A.astype(precision)
            else:    

                # Slow Python version
                
                current_node = 0
                k = 0 # Track triangles touching on node
                total = 0.0
                for index in self.domain.vertex_value_indices:
                    if current_node == N:
                        msg = 'Current node exceeding number of nodes (%d) ' %(N)
                        raise msg
                    

                    
                    k += 1
                    
                    volume_id = index / 3
                    vertex_id = index % 3
                 
                    #assert V[volume_id, vertex_id] == current_node
                
                    v = self.vertex_values[volume_id, vertex_id]
                    total += v

                    #print 'current_node=%d, index=%d, k=%d, total=%f' %(current_node, index, k, total)
                    if self.domain.number_of_triangles_per_node[current_node] == k:
                        A[current_node] = total/k
                
                    
                        # Move on to next node
                        total = 0.0
                        k = 0
                        current_node += 1



        else:
            # Return disconnected internal vertex values 
            V = self.domain.get_disconnected_triangles()
            points = self.domain.get_vertex_coordinates()
            A = self.vertex_values.flat.astype(precision)


        # Return    
        if xy is True:
            X = points[:,0].astype(precision)
            Y = points[:,1].astype(precision)
            
            return X, Y, A, V
        else:
            return A, V            



    def extrapolate_first_order(self):
        """Extrapolate conserved quantities from centroid to
        vertices and edges for each volume using
        first order scheme.
        """

        qc = self.centroid_values
        qv = self.vertex_values
        qe = self.edge_values

        for i in range(3):
            qv[:,i] = qc
            qe[:,i] = qc

        self.x_gradient *= 0.0
        self.y_gradient *= 0.0


    def get_integral(self):
        """Compute the integral of quantity across entire domain
        """
        integral = 0
        for k in range(len(self.domain)):
            area = self.domain.areas[k]
            qc = self.centroid_values[k]
            integral += qc*area

        return integral

    def get_gradients(self):
        """Provide gradients. Use compute_gradients first
        """

        return self.x_gradient, self.y_gradient


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

    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 depending on whether
        # basing limit calculations on edges or vertices
        limit_old(self)

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

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

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

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

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

    def bound_vertices_below_by_constant(self, bound):
        # Call correct module function
        # (either from this module or C-extension)
        bound_vertices_below_by_constant(self, bound)

    def bound_vertices_below_by_quantity(self, quantity):
        # Call correct module function
        # (either from this module or C-extension)

        # check consistency
        assert self.domain == quantity.domain
        bound_vertices_below_by_quantity(self, quantity)                        

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

    def saxpy_centroid_values(self,a,b):
        # Call correct module function
        # (either from this module or C-extension)
        saxpy_centroid_values(self,a,b)
    
#Conserved_quantity = Quantity

class Conserved_quantity(Quantity):
    """Class conserved quantity being removed, use Quantity

    """

    def __init__(self, domain, vertex_values=None):
        #Quantity.__init__(self, domain, vertex_values)

        msg = 'ERROR: Use Quantity instead of Conserved_quantity'

        raise Exception, msg



from anuga.utilities import compile
if compile.can_use_C_extension('quantity_ext.c'):    
    # Underlying C implementations can be accessed 

    from quantity_ext import \
         average_vertex_values,\
         backup_centroid_values,\
         saxpy_centroid_values,\
         compute_gradients,\
         limit_old,\
         limit_vertices_by_all_neighbours,\
         limit_edges_by_all_neighbours,\
         limit_edges_by_neighbour,\
         limit_gradient_by_neighbour,\
         extrapolate_from_gradient,\
         extrapolate_second_order_and_limit_by_edge,\
         extrapolate_second_order_and_limit_by_vertex,\
         bound_vertices_below_by_constant,\
         bound_vertices_below_by_quantity,\
         interpolate_from_vertices_to_edges,\
         interpolate_from_edges_to_vertices,\
         update    
else:
    msg = 'C implementations could not be accessed by %s.\n ' %__file__
    msg += 'Make sure compile_all.py has been run as described in '
    msg += 'the ANUGA installation guide.'
    raise Exception, msg