source: anuga_core/source/anuga/abstract_2d_finite_volumes/domain.py @ 5306

"""Class Domain - 2D triangular domains for finite-volume computations of
   conservation laws.


   Copyright 2004
   Ole Nielsen, Stephen Roberts, Duncan Gray
   Geoscience Australia
"""

from Numeric import allclose, argmax, zeros, Float
from anuga.config import epsilon
from anuga.config import beta_euler, beta_rk2

from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh
from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\
     import Boundary
from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\
     import File_boundary
from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\
     import Dirichlet_boundary
from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\
     import Time_boundary
from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\
     import Transmissive_boundary

from anuga.abstract_2d_finite_volumes.pmesh2domain import pmesh_to_domain
from anuga.abstract_2d_finite_volumes.region\
     import Set_region as region_set_region

from anuga.utilities.polygon import inside_polygon
from anuga.abstract_2d_finite_volumes.util import get_textual_float

import types



class Domain(Mesh):


    def __init__(self,
                 source=None,
                 triangles=None,
                 boundary=None,
                 conserved_quantities=None,
                 other_quantities=None,
                 tagged_elements=None,
                 geo_reference=None,
                 use_inscribed_circle=False,
                 mesh_filename=None,
                 use_cache=False,
                 verbose=False,
                 full_send_dict=None,
                 ghost_recv_dict=None,
                 processor=0,
                 numproc=1,
                 number_of_full_nodes=None,
                 number_of_full_triangles=None):


        """Instantiate generic computational Domain.

        Input:
          source:    Either a mesh filename or coordinates of mesh vertices.
                     If it is a filename values specified for triangles will
                     be overridden.
          triangles: Mesh connectivity (see mesh.py for more information)
          boundary:  See mesh.py for more information

          conserved_quantities: List of quantity names entering the
                                conservation equations
          other_quantities:     List of other quantity names

          tagged_elements:
          ...


        """

        # Determine whether source is a mesh filename or coordinates
        if type(source) == types.StringType:
            mesh_filename = source
        else:
            coordinates = source


        # In case a filename has been specified, extract content
        if mesh_filename is not None:
            coordinates, triangles, boundary, vertex_quantity_dict, \
                         tagged_elements, geo_reference = \
                         pmesh_to_domain(file_name=mesh_filename,
                                         use_cache=use_cache,
                                         verbose=verbose)


        # Initialise underlying mesh structure
        Mesh.__init__(self, coordinates, triangles,
                      boundary=boundary,
                      tagged_elements=tagged_elements,
                      geo_reference=geo_reference,
                      use_inscribed_circle=use_inscribed_circle,
                      number_of_full_nodes=number_of_full_nodes,
                      number_of_full_triangles=number_of_full_triangles,
                      verbose=verbose)

        if verbose: print 'Initialising Domain'
        from Numeric import zeros, Float, Int, ones
        from quantity import Quantity

        # List of quantity names entering
        # the conservation equations
        if conserved_quantities is None:
            self.conserved_quantities = []
        else:
            self.conserved_quantities = conserved_quantities

        # List of other quantity names
        if other_quantities is None:
            self.other_quantities = []
        else:
            self.other_quantities = other_quantities


        #Build dictionary of Quantity instances keyed by quantity names
        self.quantities = {}

        #FIXME: remove later - maybe OK, though....
        for name in self.conserved_quantities:
            self.quantities[name] = Quantity(self)
        for name in self.other_quantities:
            self.quantities[name] = Quantity(self)

        #Create an empty list for explicit forcing terms
        self.forcing_terms = []

        #Setup the ghost cell communication
        if full_send_dict is None:
            self.full_send_dict = {}
        else:
            self.full_send_dict  = full_send_dict

        # List of other quantity names
        if ghost_recv_dict is None:
            self.ghost_recv_dict = {}
        else:
            self.ghost_recv_dict = ghost_recv_dict

        self.processor = processor
        self.numproc = numproc


        # Setup Communication Buffers
        if verbose: print 'Domain: Set up communication buffers (parallel)'
        self.nsys = len(self.conserved_quantities)
        for key in self.full_send_dict:
            buffer_shape = self.full_send_dict[key][0].shape[0]
            self.full_send_dict[key].append(zeros( (buffer_shape,self.nsys) ,Float))


        for key in self.ghost_recv_dict:
            buffer_shape = self.ghost_recv_dict[key][0].shape[0]
            self.ghost_recv_dict[key].append(zeros( (buffer_shape,self.nsys) ,Float))


        # Setup cell full flag
        # =1 for full
        # =0 for ghost
        N = len(self) #number_of_elements
        self.number_of_elements = N
        self.tri_full_flag = ones(N, Int)
        for i in self.ghost_recv_dict.keys():
            for id in self.ghost_recv_dict[i][0]:
                self.tri_full_flag[id] = 0

        # Test the assumption that all full triangles are store before
        # the ghost triangles.
        if not allclose(self.tri_full_flag[:self.number_of_full_nodes],1):
            print 'WARNING:  Not all full triangles are store before ghost triangles'
                        

        # Defaults
        from anuga.config import max_smallsteps, beta_w, beta_h, epsilon
        from anuga.config import CFL
        from anuga.config import timestepping_method
        from anuga.config import protect_against_isolated_degenerate_timesteps
        self.beta_w = beta_w
        self.beta_h = beta_h
        self.epsilon = epsilon
        self.protect_against_isolated_degenerate_timesteps = protect_against_isolated_degenerate_timesteps
        
        

        # FIXME: Maybe have separate orders for h-limiter and w-limiter?
        # Or maybe get rid of order altogether and use beta_w and beta_h
        self.set_default_order(1)

        self.smallsteps = 0
        self.max_smallsteps = max_smallsteps
        self.number_of_steps = 0
        self.number_of_first_order_steps = 0
        self.CFL = CFL
        self.set_timestepping_method(timestepping_method)
        
        self.boundary_map = None  # Will be populated by set_boundary        
        

        # Model time
        self.time = 0.0
        self.finaltime = None
        self.min_timestep = self.max_timestep = 0.0
        self.starttime = 0 # Physical starttime if any
                           # (0 is 1 Jan 1970 00:00:00)
        self.timestep = 0.0
        self.flux_timestep = 0.0

        # Monitoring
        self.quantities_to_be_monitored = None
        self.monitor_polygon = None
        self.monitor_time_interval = None                
        self.monitor_indices = None

        # Checkpointing and storage
        from anuga.config import default_datadir
        self.datadir = default_datadir
        self.simulation_name = 'domain'
        self.checkpoint = False

        # To avoid calculating the flux across each edge twice,
        # keep an integer (boolean) array, to be used during the flux
        # calculation
        N = len(self) # Number_of_triangles
        self.already_computed_flux = zeros((N, 3), Int)

        # Storage for maximal speeds computed for each triangle by
        # compute_fluxes
        # This is used for diagnostics only (reset at every yieldstep)
        self.max_speed = zeros(N, Float)

        if mesh_filename is not None:
            # If the mesh file passed any quantity values
            # , initialise with these values.
            if verbose: print 'Domain: Initialising quantity values'
            self.set_quantity_vertices_dict(vertex_quantity_dict)


        if verbose: print 'Domain: Done'






    #---------------------------    
    # Public interface to Domain
    #---------------------------        
    def get_conserved_quantities(self, vol_id, vertex=None, edge=None):
        """Get conserved quantities at volume vol_id

        If vertex is specified use it as index for vertex values
        If edge is specified use it as index for edge values
        If neither are specified use centroid values
        If both are specified an exeception is raised

        Return value: Vector of length == number_of_conserved quantities

        """

        from Numeric import zeros, Float

        if not (vertex is None or edge is None):
            msg = 'Values for both vertex and edge was specified.'
            msg += 'Only one (or none) is allowed.'
            raise msg

        q = zeros( len(self.conserved_quantities), Float)

        for i, name in enumerate(self.conserved_quantities):
            Q = self.quantities[name]
            if vertex is not None:
                q[i] = Q.vertex_values[vol_id, vertex]
            elif edge is not None:
                q[i] = Q.edge_values[vol_id, edge]
            else:
                q[i] = Q.centroid_values[vol_id]

        return q

    def set_time(self, time=0.0):
        """Set the model time (seconds)"""

        self.time = time

    def get_time(self):
        """Get the model time (seconds)"""

        return self.time

    def set_default_order(self, n):
        """Set default (spatial) order to either 1 or 2
        """

        msg = 'Default order must be either 1 or 2. I got %s' %n
        assert n in [1,2], msg

        self.default_order = n
        self._order_ = self.default_order

        if self.default_order == 1:
            pass
            #self.set_timestepping_method('euler')
            #self.set_all_limiters(beta_euler)

        if self.default_order == 2:
            pass
            #self.set_timestepping_method('rk2')
            #self.set_all_limiters(beta_rk2)
        

    def set_quantity_vertices_dict(self, quantity_dict):
        """Set values for named quantities.
        The index is the quantity

        name: Name of quantity
        X: Compatible list, Numeric array, const or function (see below)

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

        """
        
        # FIXME: Could we name this a bit more intuitively
        # E.g. set_quantities_from_dictionary
        for key in quantity_dict.keys():
            self.set_quantity(key, quantity_dict[key], location='vertices')


    def set_quantity(self, name, *args, **kwargs):
        """Set values for named quantity


        One keyword argument is documented here:
        expression = None, # Arbitrary expression

        expression:
          Arbitrary expression involving quantity names

        See Quantity.set_values for further documentation.
        """

        # Do the expression stuff
        if kwargs.has_key('expression'):
            expression = kwargs['expression']
            del kwargs['expression']

            Q = self.create_quantity_from_expression(expression)
            kwargs['quantity'] = Q

        # Assign values
        self.quantities[name].set_values(*args, **kwargs)


    def get_quantity_names(self):
        """Get a list of all the quantity names that this domain is aware of.
        Any value in the result should be a valid input to get_quantity.
        """
        return self.quantities.keys()

    def get_quantity(self, name, location='vertices', indices = None):
        """Get quantity object.

        name: Name of quantity

        See methods inside the quantity object for more options

        FIXME: clean input args
        """

        return self.quantities[name] #.get_values( location, indices = indices)



    def create_quantity_from_expression(self, expression):
        """Create new quantity from other quantities using arbitrary expression

        Combine existing quantities in domain using expression and return
        result as a new quantity.

        Note, the new quantity could e.g. be used in set_quantity

        Valid expressions are limited to operators defined in class Quantity

        Examples creating derived quantities:

            Depth = domain.create_quantity_from_expression('stage-elevation')

            exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5'        
            Absolute_momentum = domain.create_quantity_from_expression(exp)

        """

        from anuga.abstract_2d_finite_volumes.util import\
             apply_expression_to_dictionary
        
        return apply_expression_to_dictionary(expression, self.quantities)



    def set_boundary(self, boundary_map):
        """Associate boundary objects with tagged boundary segments.

        Input boundary_map is a dictionary of boundary objects keyed
        by symbolic tags to matched against tags in the internal dictionary
        self.boundary.

        As result one pointer to a boundary object is stored for each vertex
        in the list self.boundary_objects.
        More entries may point to the same boundary object

        Schematically the mapping is from two dictionaries to one list
        where the index is used as pointer to the boundary_values arrays
        within each quantity.

        self.boundary:          (vol_id, edge_id): tag
        boundary_map (input):   tag: boundary_object
        ----------------------------------------------
        self.boundary_objects:  ((vol_id, edge_id), boundary_object)


        Pre-condition:
          self.boundary has been built.

        Post-condition:
          self.boundary_objects is built

        If a tag from the domain doesn't appear in the input dictionary an
        exception is raised.
        However, if a tag is not used to the domain, no error is thrown.
        FIXME: This would lead to implementation of a
        default boundary condition

        Note: If a segment is listed in the boundary dictionary and if it is
        not None, it *will* become a boundary -
        even if there is a neighbouring triangle.
        This would be the case for internal boundaries

        Boundary objects that are None will be skipped.

        If a boundary_map has already been set
        (i.e. set_boundary has been called before), the old boundary map
        will be updated with new values. The new map need not define all
        boundary tags, and can thus change only those that are needed.

        FIXME: If set_boundary is called multiple times and if Boundary
        object is changed into None, the neighbour structure will not be
        restored!!!


        """

        if self.boundary_map is None:
            # This the first call to set_boundary. Store
            # map for later updates and for use with boundary_stats.
            self.boundary_map = boundary_map 
        else:    
            # This is a modification of an already existing map
            # Update map an proceed normally

            for key in boundary_map.keys():
                self.boundary_map[key] = boundary_map[key]
                
        
        # FIXME (Ole): Try to remove the sorting and fix test_mesh.py
        x = self.boundary.keys()
        x.sort()

        # Loop through edges that lie on the boundary and associate them with
        # callable boundary objects depending on their tags
        self.boundary_objects = []        
        for k, (vol_id, edge_id) in enumerate(x):
            tag = self.boundary[ (vol_id, edge_id) ]

            if self.boundary_map.has_key(tag):
                B = self.boundary_map[tag]  # Get callable boundary object

                if B is not None:
                    self.boundary_objects.append( ((vol_id, edge_id), B) )
                    self.neighbours[vol_id, edge_id] = \
                                            -len(self.boundary_objects)
                else:
                    pass
                    #FIXME: Check and perhaps fix neighbour structure


            else:
                msg = 'ERROR (domain.py): Tag "%s" has not been ' %tag
                msg += 'bound to a boundary object.\n'
                msg += 'All boundary tags defined in domain must appear '
                msg += 'in set_boundary.\n'
                msg += 'The tags are: %s' %self.get_boundary_tags()
                raise msg


    def set_region(self, *args, **kwargs):
        """
        This method is used to set quantities based on a regional tag.
        
        It is most often called with the following parameters;
        (self, tag, quantity, X, location='vertices')
        tag: the name of the regional tag used to specify the region 
        quantity: Name of quantity to change
        X: const or function - how the quantity is changed
        location: Where values are to be stored.
            Permissible options are: vertices, centroid and unique vertices

        A callable region class or a list of callable region classes
        can also be passed into this function.
        """

        if len(args) == 1:
            self._set_region(*args, **kwargs)
        else:
            # Assume it is arguments for the region.set_region function
            func = region_set_region(*args, **kwargs)
            self._set_region(func)
            
        
    def _set_region(self, functions):
        # The order of functions in the list is used.
        if type(functions) not in [types.ListType,types.TupleType]:
            functions = [functions]
        for function in functions:
            for tag in self.tagged_elements.keys():
                function(tag, self.tagged_elements[tag], self)




    def set_quantities_to_be_monitored(self, q,
                                       polygon=None,
                                       time_interval=None):
        """Specify which quantities will be monitored for extrema.

        q must be either:
          - the name of a quantity or a derived quantity such as 'stage-elevation'
          - a list of quantity names
          - None

        In the two first cases, the named quantities will be monitored at
        each internal timestep
        
        If q is None, monitoring will be switched off altogether.

        polygon (if specified) will restrict monitoring to triangles inside polygon.
        If omitted all triangles will be included.

        time_interval (if specified) will restrict monitoring to time steps in
        that interval. If omitted all timesteps will be included.
        """

        from anuga.abstract_2d_finite_volumes.util import\
             apply_expression_to_dictionary        

        if q is None:
            self.quantities_to_be_monitored = None
            self.monitor_polygon = None
            self.monitor_time_interval = None
            self.monitor_indices = None            
            return

        if isinstance(q, basestring):
            q = [q] # Turn argument into a list

        # Check correcness and initialise
        self.quantities_to_be_monitored = {}
        for quantity_name in q:
            msg = 'Quantity %s is not a valid conserved quantity'\
                  %quantity_name
            

            if not quantity_name in self.quantities:
                # See if this expression is valid
                apply_expression_to_dictionary(quantity_name, self.quantities)

            # Initialise extrema information
            info_block = {'min': None,          # Min value
                          'max': None,          # Max value
                          'min_location': None, # Argmin (x, y)
                          'max_location': None, # Argmax (x, y)
                          'min_time': None,     # Argmin (t) 
                          'max_time': None}     # Argmax (t)
            
            self.quantities_to_be_monitored[quantity_name] = info_block

            

        if polygon is not None:
            # Check input
            if isinstance(polygon, basestring):

                # Check if multiple quantities were accidentally
                # given as separate argument rather than a list.
                msg = 'Multiple quantities must be specified in a list. '
                msg += 'Not as multiple arguments. '
                msg += 'I got "%s" as a second argument' %polygon
                
                if polygon in self.quantities:
                    raise Exception, msg
                
                try:
                    apply_expression_to_dictionary(polygon, self.quantities)
                except:
                    # At least polygon wasn't an expression involving quantitites
                    pass
                else:
                    raise Exception, msg

                # In any case, we don't allow polygon to be a string
                msg = 'argument "polygon" must not be a string: '
                msg += 'I got polygon=\'%s\' ' %polygon
                raise Exception, msg


            # Get indices for centroids that are inside polygon
            points = self.get_centroid_coordinates(absolute=True)
            self.monitor_indices = inside_polygon(points, polygon)
            

        if time_interval is not None:
            assert len(time_interval) == 2

        
        self.monitor_polygon = polygon
        self.monitor_time_interval = time_interval        
        

    #--------------------------    
    # Miscellaneous diagnostics
    #--------------------------        
    def check_integrity(self):
        Mesh.check_integrity(self)

        for quantity in self.conserved_quantities:
            msg = 'Conserved quantities must be a subset of all quantities'
            assert quantity in self.quantities, msg

        ##assert hasattr(self, 'boundary_objects')
            

    def write_time(self, track_speeds=False):
        print self.timestepping_statistics(track_speeds)


    def timestepping_statistics(self,
                                track_speeds=False,
                                triangle_id=None):
        """Return string with time stepping statistics for printing or logging

        Optional boolean keyword track_speeds decides whether to report
        location of smallest timestep as well as a histogram and percentile
        report.

        Optional keyword triangle_id can be used to specify a particular
        triangle rather than the one with the largest speed. 
        """

        from anuga.utilities.numerical_tools import histogram, create_bins
        

        # qwidth determines the text field used for quantities
        qwidth = self.qwidth = 12


        msg = ''
        if self.min_timestep == self.max_timestep:
            msg += 'Time = %.4f, delta t = %.8f, steps=%d (%d)'\
                   %(self.time, self.min_timestep, self.number_of_steps,
                     self.number_of_first_order_steps)
        elif self.min_timestep > self.max_timestep:
            msg += 'Time = %.4f, steps=%d (%d)'\
                   %(self.time, self.number_of_steps,
                     self.number_of_first_order_steps)
        else:
            msg += 'Time = %.4f, delta t in [%.8f, %.8f], steps=%d (%d)'\
                   %(self.time, self.min_timestep,
                     self.max_timestep, self.number_of_steps,
                     self.number_of_first_order_steps)

        if track_speeds is True:
            msg += '\n'


            # Setup 10 bins for speed histogram
            bins = create_bins(self.max_speed, 10)
            hist = histogram(self.max_speed, bins)

            msg += '------------------------------------------------\n'
            msg += '  Speeds in [%f, %f]\n' %(min(self.max_speed),
                                              max(self.max_speed))
            msg += '  Histogram:\n'

            hi = bins[0]
            for i, count in enumerate(hist):
                lo = hi
                if i+1 < len(bins):
                    # Open upper interval                
                    hi = bins[i+1]
                    msg += '    [%f, %f[: %d\n' %(lo, hi, count)                
                else:
                    # Closed upper interval
                    hi = max(self.max_speed)
                    msg += '    [%f, %f]: %d\n' %(lo, hi, count)


            N = len(self.max_speed)
            if N > 10:
                msg += '  Percentiles (10%):\n'
                speed = self.max_speed.tolist()
                speed.sort()

                k = 0
                lower = min(speed)
                for i, a in enumerate(speed):        
                    if i % (N/10) == 0 and i != 0:
                        # For every 10% of the sorted speeds
                        msg += '    %d speeds in [%f, %f]\n' %(i-k, lower, a)
                        lower = a
                        k = i
                        
                msg += '    %d speeds in [%f, %f]\n'\
                       %(N-k, lower, max(speed))                    
                
                      

                
            
            # Find index of largest computed flux speed
            if triangle_id is None:
                k = self.k = argmax(self.max_speed)
            else:
                errmsg = 'Triangle_id %d does not exist in mesh: %s' %(triangle_id,
                                                                    str(self))
                assert 0 <= triangle_id < len(self), errmsg
                k = self.k = triangle_id
            

            x, y = self.get_centroid_coordinates()[k]
            radius = self.get_radii()[k]
            area = self.get_areas()[k]      
            max_speed = self.max_speed[k]           

            msg += '  Triangle #%d with centroid (%.4f, %.4f), ' %(k, x, y)
            msg += 'area = %.4f and radius = %.4f ' %(area, radius)
            if triangle_id is None:
                msg += 'had the largest computed speed: %.6f m/s ' %(max_speed)
            else:
                msg += 'had computed speed: %.6f m/s ' %(max_speed)
                
            if max_speed > 0.0:
                msg += '(timestep=%.6f)\n' %(radius/max_speed)
            else:
                msg += '(timestep=%.6f)\n' %(0)     
            
            # Report all quantity values at vertices, edges and centroid
            msg += '    Quantity'
            msg += '------------\n'
            for name in self.quantities:
                q = self.quantities[name]

                V = q.get_values(location='vertices', indices=[k])[0]
                E = q.get_values(location='edges', indices=[k])[0]
                C = q.get_values(location='centroids', indices=[k])                 
                
                s  = '    %s: vertex_values =  %.4f,\t %.4f,\t %.4f\n'\
                     %(name.ljust(qwidth), V[0], V[1], V[2])

                s += '    %s: edge_values =    %.4f,\t %.4f,\t %.4f\n'\
                     %(name.ljust(qwidth), E[0], E[1], E[2])

                s += '    %s: centroid_value = %.4f\n'\
                     %(name.ljust(qwidth), C[0])                                

                msg += s

        return msg


    def write_boundary_statistics(self, quantities = None, tags = None):
        print self.boundary_statistics(quantities, tags)

    def boundary_statistics(self, quantities = None, tags = None):
        """Output statistics about boundary forcing at each timestep


        Input:
          quantities: either None, a string or a list of strings naming the
                      quantities to be reported
          tags:       either None, a string or a list of strings naming the
                      tags to be reported


        Example output:
        Tag 'wall':
            stage in [2, 5.5]
            xmomentum in []
            ymomentum in []
        Tag 'ocean'


        If quantities are specified only report on those. Otherwise take all
        conserved quantities.
        If tags are specified only report on those, otherwise take all tags.

        """

        # Input checks
        import types, string

        if quantities is None:
            quantities = self.conserved_quantities
        elif type(quantities) == types.StringType:
            quantities = [quantities] #Turn it into a list

        msg = 'Keyword argument quantities must be either None, '
        msg += 'string or list. I got %s' %str(quantities)
        assert type(quantities) == types.ListType, msg


        if tags is None:
            tags = self.get_boundary_tags()
        elif type(tags) == types.StringType:
            tags = [tags] #Turn it into a list

        msg = 'Keyword argument tags must be either None, '
        msg += 'string or list. I got %s' %str(tags)
        assert type(tags) == types.ListType, msg

        # Determine width of longest quantity name (for cosmetic purposes)
        maxwidth = 0
        for name in quantities:
            w = len(name)
            if w > maxwidth:
                maxwidth = w

        # Output statistics
        msg = 'Boundary values at time %.4f:\n' %self.time
        for tag in tags:
            msg += '    %s:\n' %tag

            for name in quantities:
                q = self.quantities[name]

                # Find range of boundary values for tag and q
                maxval = minval = None
                for i, ((vol_id, edge_id), B) in\
                        enumerate(self.boundary_objects):
                    if self.boundary[(vol_id, edge_id)] == tag:
                        v = q.boundary_values[i]
                        if minval is None or v < minval: minval = v
                        if maxval is None or v > maxval: maxval = v

                if minval is None or maxval is None:
                    msg += '        Sorry no information available about' +\
                           ' tag %s and quantity %s\n' %(tag, name)
                else:
                    msg += '        %s in [%12.8f, %12.8f]\n'\
                           %(string.ljust(name, maxwidth), minval, maxval)


        return msg


    def update_extrema(self):
        """Update extrema if requested by set_quantities_to_be_monitored.
        This data is used for reporting e.g. by running
        print domain.quantity_statistics()
        and may also stored in output files (see data_manager in shallow_water)
        """

        # Define a tolerance for extremum computations
        epsilon = 1.0e-6 # Import 'single_precision' from config
        
        if self.quantities_to_be_monitored is None:
            return

        # Observe time interval restriction if any
        if self.monitor_time_interval is not None and\
               (self.time < self.monitor_time_interval[0] or\
               self.time > self.monitor_time_interval[1]):
            return

        # Update extrema for each specified quantity subject to
        # polygon restriction (via monitor_indices).
        for quantity_name in self.quantities_to_be_monitored:

            if quantity_name in self.quantities:
                Q = self.get_quantity(quantity_name)
            else:
                Q = self.create_quantity_from_expression(quantity_name)

            info_block = self.quantities_to_be_monitored[quantity_name]

            # Update maximum
            # (n > None is always True, but we check explicitly because
            # of the epsilon)
            maxval = Q.get_maximum_value(self.monitor_indices)
            if info_block['max'] is None or\
                   maxval > info_block['max'] + epsilon:
                info_block['max'] = maxval
                maxloc = Q.get_maximum_location()
                info_block['max_location'] = maxloc
                info_block['max_time'] = self.time


            # Update minimum
            minval = Q.get_minimum_value(self.monitor_indices)
            if info_block['min'] is None or\
                   minval < info_block['min'] - epsilon:
                info_block['min'] = minval                
                minloc = Q.get_minimum_location()
                info_block['min_location'] = minloc
                info_block['min_time'] = self.time                
        


    def quantity_statistics(self, precision = '%.4f'):
        """Return string with statistics about quantities for
        printing or logging

        Quantities reported are specified through method

           set_quantities_to_be_monitored
           
        """

        maxlen = 128 # Max length of polygon string representation

        # Output statistics
        msg = 'Monitored quantities at time %.4f:\n' %self.time
        if self.monitor_polygon is not None:
            p_str = str(self.monitor_polygon)
            msg += '- Restricted by polygon: %s' %p_str[:maxlen]
            if len(p_str) >= maxlen:
                msg += '...\n'
            else:
                msg += '\n'


        if self.monitor_time_interval is not None:
            msg += '- Restricted by time interval: %s\n'\
                   %str(self.monitor_time_interval)
            time_interval_start = self.monitor_time_interval[0]
        else:
            time_interval_start = 0.0

            
        for quantity_name, info in self.quantities_to_be_monitored.items():
            msg += '    %s:\n' %quantity_name

            msg += '      values since time = %.2f in [%s, %s]\n'\
                   %(time_interval_start,
                     get_textual_float(info['min'], precision),
                     get_textual_float(info['max'], precision))       
                     
            msg += '      minimum attained at time = %s, location = %s\n'\
                   %(get_textual_float(info['min_time'], precision),
                     get_textual_float(info['min_location'], precision))
            

            msg += '      maximum attained at time = %s, location = %s\n'\
                   %(get_textual_float(info['max_time'], precision),
                     get_textual_float(info['max_location'], precision))


        return msg

    def get_timestepping_method(self):
        return self.timestepping_method

    def set_timestepping_method(self,timestepping_method):
        
        if timestepping_method in ['euler', 'rk2', 'rk3']:
            self.timestepping_method = timestepping_method
            return

        msg = '%s is an incorrect timestepping type'% timestepping_method
        raise Exception, msg

    def get_name(self):
        return self.simulation_name

    def set_name(self, name):
        """Assign a name to this simulation.
        This will be used to identify the output sww file.

        """
        if name.endswith('.sww'):
            name = name[:-4]
            
        self.simulation_name = name

    def get_datadir(self):
        return self.datadir

    def set_datadir(self, name):
        self.datadir = name

    def get_starttime(self):
        return self.starttime

    def set_starttime(self, time):
        self.starttime = float(time)        



    #--------------------------
    # Main components of evolve
    #--------------------------    

    def evolve(self,
               yieldstep = None,
               finaltime = None,
               duration = None,
               skip_initial_step = False):
        """Evolve model through time starting from self.starttime.


        yieldstep: Interval between yields where results are stored,
                   statistics written and domain inspected or
                   possibly modified. If omitted the internal predefined
                   max timestep is used.
                   Internally, smaller timesteps may be taken.

        duration: Duration of simulation

        finaltime: Time where simulation should end. This is currently
        relative time.  So it's the same as duration.

        If both duration and finaltime are given an exception is thrown.


        skip_initial_step: Boolean flag that decides whether the first
        yield step is skipped or not. This is useful for example to avoid
        duplicate steps when multiple evolve processes are dove tailed.


        Evolve is implemented as a generator and is to be called as such, e.g.

        for t in domain.evolve(yieldstep, finaltime):
            <Do something with domain and t>


        All times are given in seconds

        """

        from anuga.config import min_timestep, max_timestep, epsilon

        # FIXME: Maybe lump into a larger check prior to evolving
        msg = 'Boundary tags must be bound to boundary objects before '
        msg += 'evolving system, '
        msg += 'e.g. using the method set_boundary.\n'
        msg += 'This system has the boundary tags %s '\
               %self.get_boundary_tags()
        assert hasattr(self, 'boundary_objects'), msg


        if yieldstep is None:
            yieldstep = max_timestep
        else:
            yieldstep = float(yieldstep)

        self._order_ = self.default_order


        if finaltime is not None and duration is not None:
            # print 'F', finaltime, duration
            msg = 'Only one of finaltime and duration may be specified'
            raise msg
        else:
            if finaltime is not None:
                self.finaltime = float(finaltime)
            if duration is not None:
                self.finaltime = self.starttime + float(duration)



        N = len(self) # Number of triangles
        self.yieldtime = 0.0 # Track time between 'yields'

        # Initialise interval of timestep sizes (for reporting only)
        self.min_timestep = max_timestep
        self.max_timestep = min_timestep
        self.number_of_steps = 0
        self.number_of_first_order_steps = 0


        # Update ghosts
        self.update_ghosts()

        # Initial update of vertex and edge values
        self.distribute_to_vertices_and_edges()

        # Update extrema if necessary (for reporting)
        self.update_extrema()
        
        # Initial update boundary values
        self.update_boundary()

        # Or maybe restore from latest checkpoint
        if self.checkpoint is True:
            self.goto_latest_checkpoint()

        if skip_initial_step is False:
            yield(self.time)  # Yield initial values

        while True:

            # Evolve One Step, using appropriate timestepping method
            if self.get_timestepping_method() == 'euler':
                self.evolve_one_euler_step(yieldstep,finaltime)
                
            elif self.get_timestepping_method() == 'rk2':
                self.evolve_one_rk2_step(yieldstep,finaltime)

            elif self.get_timestepping_method() == 'rk3':
                self.evolve_one_rk3_step(yieldstep,finaltime)               
            
            # Update extrema if necessary (for reporting)
            self.update_extrema()            


            self.yieldtime += self.timestep
            self.number_of_steps += 1
            if self._order_ == 1:
                self.number_of_first_order_steps += 1

            # Yield results
            if finaltime is not None and self.time >= finaltime-epsilon:

                if self.time > finaltime:
                    # FIXME (Ole, 30 April 2006): Do we need this check?
                    # Probably not (Ole, 18 September 2008). Now changed to
                    # Exception
                    msg = 'WARNING (domain.py): time overshot finaltime. '
                    msg += 'Contact Ole.Nielsen@ga.gov.au'
                    raise Exception, msg
                    

                # Yield final time and stop
                self.time = finaltime
                yield(self.time)
                break


            if self.yieldtime >= yieldstep:
                # Yield (intermediate) time and allow inspection of domain

                if self.checkpoint is True:
                    self.store_checkpoint()
                    self.delete_old_checkpoints()

                # Pass control on to outer loop for more specific actions
                yield(self.time)

                # Reinitialise
                self.yieldtime = 0.0
                self.min_timestep = max_timestep
                self.max_timestep = min_timestep
                self.number_of_steps = 0
                self.number_of_first_order_steps = 0
                self.max_speed = zeros(N, Float)

    def evolve_one_euler_step(self, yieldstep, finaltime):
        """
        One Euler Time Step
        Q^{n+1} = E(h) Q^n
        """

        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update timestep to fit yieldstep and finaltime
        self.update_timestep(yieldstep, finaltime)

        #Update conserved quantities
        self.update_conserved_quantities()

        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()

        #Update time
        self.time += self.timestep

        


    def evolve_one_rk2_step(self, yieldstep, finaltime):
        """
        One 2nd order RK timestep
        Q^{n+1} = 0.5 Q^n + 0.5 E(h)^2 Q^n
        """

        #Save initial initial conserved quantities values
        self.backup_conserved_quantities()            

        #--------------------------------------
        #First euler step
        #--------------------------------------

        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update timestep to fit yieldstep and finaltime
        self.update_timestep(yieldstep, finaltime)

        #Update conserved quantities
        self.update_conserved_quantities()

        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()

        #Update time
        self.time += self.timestep

        #------------------------------------
        #Second Euler step
        #------------------------------------
            
        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update conserved quantities
        self.update_conserved_quantities()

        #------------------------------------
        #Combine initial and final values
        #of conserved quantities and cleanup
        #------------------------------------
        #combine steps
        self.saxpy_conserved_quantities(0.5, 0.5)
 
        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()



    def evolve_one_rk3_step(self, yieldstep, finaltime):
        """
        One 3rd order RK timestep
        Q^(1) = 3/4 Q^n + 1/4 E(h)^2 Q^n  (at time t^n + h/2)
        Q^{n+1} = 1/3 Q^n + 2/3 E(h) Q^(1) (at time t^{n+1})
        """

        #Save initial initial conserved quantities values
        self.backup_conserved_quantities()            

        initial_time = self.time
        
        #--------------------------------------
        #First euler step
        #--------------------------------------

        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update timestep to fit yieldstep and finaltime
        self.update_timestep(yieldstep, finaltime)

        #Update conserved quantities
        self.update_conserved_quantities()

        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()

        #Update time
        self.time += self.timestep

        #------------------------------------
        #Second Euler step
        #------------------------------------
            
        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update conserved quantities
        self.update_conserved_quantities()

        #------------------------------------
        #Combine steps to obtain intermediate
        #solution at time t^n + 0.5 h
        #------------------------------------

        #combine steps
        self.saxpy_conserved_quantities(0.25, 0.75)
 
        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()

        #set substep time
        self.time = initial_time + self.timestep*0.5

        #------------------------------------
        #Third Euler step
        #------------------------------------
            
        #Compute fluxes across each element edge
        self.compute_fluxes()

        #Update conserved quantities
        self.update_conserved_quantities()

        #------------------------------------
        #Combine final and initial values
        #and cleanup
        #------------------------------------
        #combine steps
        self.saxpy_conserved_quantities(2.0/3.0, 1.0/3.0)
 
        #update ghosts
        self.update_ghosts()

        #Update vertex and edge values
        self.distribute_to_vertices_and_edges()

        #Update boundary values
        self.update_boundary()

        #set new time
        self.time = initial_time + self.timestep       
        

    def evolve_to_end(self, finaltime = 1.0):
        """Iterate evolve all the way to the end
        """

        for _ in self.evolve(yieldstep=None, finaltime=finaltime):
            pass


    def backup_conserved_quantities(self):
        N = len(self) # Number_of_triangles

        # Backup conserved_quantities centroid values
        for name in self.conserved_quantities:
            Q = self.quantities[name]
            Q.backup_centroid_values()        

    def saxpy_conserved_quantities(self,a,b):
        N = len(self) #number_of_triangles

        # Backup conserved_quantities centroid values
        for name in self.conserved_quantities:
            Q = self.quantities[name]
            Q.saxpy_centroid_values(a,b)        
    

    def update_boundary(self):
        """Go through list of boundary objects and update boundary values
        for all conserved quantities on boundary.
        It is assumed that the ordering of conserved quantities is 
        consistent between the domain and the boundary object, i.e. 
        the jth element of vector q must correspond to the jth conserved
        quantity in domain.
        """

        # FIXME: Update only those that change (if that can be worked out)
        # FIXME: Boundary objects should not include ghost nodes.
        for i, ((vol_id, edge_id), B) in enumerate(self.boundary_objects):
            if B is None:
                print 'WARNING: Ignored boundary segment %d (None)'
            else:
                q = B.evaluate(vol_id, edge_id)

                for j, name in enumerate(self.conserved_quantities):
                    Q = self.quantities[name]
                    Q.boundary_values[i] = q[j]


    def compute_fluxes(self):
        msg = 'Method compute_fluxes must be overridden by Domain subclass'
        raise msg


    def update_timestep(self, yieldstep, finaltime):

        from anuga.config import min_timestep, max_timestep

        
        
        # Protect against degenerate timesteps arising from isolated
        # triangles
        # FIXME (Steve): This should be in shallow_water as it assumes x and y
        # momentum
        if self.protect_against_isolated_degenerate_timesteps is True and\
               self.max_speed > 10.0: # FIXME (Ole): Make this configurable

            # Setup 10 bins for speed histogram
            from anuga.utilities.numerical_tools import histogram, create_bins
        
            bins = create_bins(self.max_speed, 10)
            hist = histogram(self.max_speed, bins)

            # Look for characteristic signature
            if len(hist) > 1 and\
                hist[-1] > 0 and\
                hist[4] == hist[5] == hist[6] == hist[7] == hist[8] == 0:
                    # Danger of isolated degenerate triangles
                    # print self.timestepping_statistics(track_speeds=True)  
                    
                    # Find triangles in last bin
                    # FIXME - speed up using Numeric
                    d = 0
                    for i in range(self.number_of_full_triangles):
                        if self.max_speed[i] > bins[-1]:
                            msg = 'Time=%f: Ignoring isolated high ' %self.time
                            msg += 'speed triangle ' 
                            msg += '#%d of %d with max speed=%f'\
                                  %(i, self.number_of_full_triangles,
                                    self.max_speed[i])
                    
                            # print 'Found offending triangle', i,
                            # self.max_speed[i] 
                            self.get_quantity('xmomentum').set_values(0.0, indices=[i])
                            self.get_quantity('ymomentum').set_values(0.0, indices=[i])
                            self.max_speed[i]=0.0
                            d += 1
                    
                    #print 'Adjusted %d triangles' %d        
                    #print self.timestepping_statistics(track_speeds=True)      
                

                        
        # self.timestep is calculated from speed of characteristics
        # Apply CFL condition here
        timestep = min(self.CFL*self.flux_timestep, max_timestep)

        # Record maximal and minimal values of timestep for reporting
        self.max_timestep = max(timestep, self.max_timestep)
        self.min_timestep = min(timestep, self.min_timestep)

           
 
        # Protect against degenerate time steps
        if timestep < min_timestep:

            # Number of consecutive small steps taken b4 taking action
            self.smallsteps += 1

            if self.smallsteps > self.max_smallsteps:
                self.smallsteps = 0 # Reset

                if self._order_ == 1:
                    msg = 'WARNING: Too small timestep %.16f reached '\
                          %timestep
                    msg += 'even after %d steps of 1 order scheme'\
                           %self.max_smallsteps
                    print msg
                    timestep = min_timestep  # Try enforcing min_step

                    print self.timestepping_statistics(track_speeds=True)

                    raise Exception, msg
                else:
                    # Try to overcome situation by switching to 1 order
                    self._order_ = 1

        else:
            self.smallsteps = 0
            if self._order_ == 1 and self.default_order == 2:
                self._order_ = 2


        # Ensure that final time is not exceeded
        if finaltime is not None and self.time + timestep > finaltime :
            timestep = finaltime-self.time

        # Ensure that model time is aligned with yieldsteps
        if self.yieldtime + timestep > yieldstep:
            timestep = yieldstep-self.yieldtime

        self.timestep = timestep



    def compute_forcing_terms(self):
        """If there are any forcing functions driving the system
        they should be defined in Domain subclass and appended to
        the list self.forcing_terms
        """

        for f in self.forcing_terms:
            f(self)



    def update_conserved_quantities(self):
        """Update vectors of conserved quantities using previously
        computed fluxes specified forcing functions.
        """

        from Numeric import ones, sum, equal, Float

        N = len(self) # Number_of_triangles
        d = len(self.conserved_quantities)

        timestep = self.timestep

        # Compute forcing terms
        self.compute_forcing_terms()

        # Update conserved_quantities
        for name in self.conserved_quantities:
            Q = self.quantities[name]
            Q.update(timestep)

            # Note that Q.explicit_update is reset by compute_fluxes
            # Where is Q.semi_implicit_update reset?
            

    def update_ghosts(self):
        pass

    def distribute_to_vertices_and_edges(self):
        """Extrapolate conserved quantities from centroid to
        vertices and edge-midpoints for each volume

        Default implementation is straight first order,
        i.e. constant values throughout each element and
        no reference to non-conserved quantities.
        """

        for name in self.conserved_quantities:
            Q = self.quantities[name]
            if self._order_ == 1:
                Q.extrapolate_first_order()
            elif self._order_ == 2:
                Q.extrapolate_second_order()
                #Q.limit()
            else:
                raise 'Unknown order'
            #Q.interpolate_from_vertices_to_edges()


    def centroid_norm(self, quantity, normfunc):
        """Calculate the norm of the centroid values
        of a specific quantity, using normfunc.

        normfunc should take a list to a float.

        common normfuncs are provided in the module utilities.norms
        """
        return normfunc(self.quantities[quantity].centroid_values)



#------------------
# Initialise module
#------------------

# Optimisation with psyco
from anuga.config import use_psyco
if use_psyco:
    try:
        import psyco
    except:
        import os
        if os.name == 'posix' and os.uname()[4] == 'x86_64':
            pass
            # Psyco isn't supported on 64 bit systems, but it doesn't matter
        else:
            msg = 'WARNING: psyco (speedup) could not import'+\
                  ', you may want to consider installing it'
            print msg
    else:
        psyco.bind(Domain.update_boundary)
        #psyco.bind(Domain.update_timestep) # Not worth it
        psyco.bind(Domain.update_conserved_quantities)
        psyco.bind(Domain.distribute_to_vertices_and_edges)


if __name__ == "__main__":
    pass