source: inundation/pyvolution/test_shallow_water.py @ 1812

#!/usr/bin/env python

import unittest, os
from math import sqrt, pi

from config import g, epsilon
from Numeric import allclose, array, zeros, ones, Float, take
from shallow_water import *



#Variable windfield implemented using functions
def speed(t,x,y):
    """Large speeds halfway between center and edges
    Low speeds at center and edges
    """

    from math import sqrt, exp, cos, pi

    x = array(x)
    y = array(y)

    N = len(x)
    s = 0*x  #New array

    for k in range(N):

        r = sqrt(x[k]**2 + y[k]**2)

        factor = exp( -(r-0.15)**2 )

        s[k] = 4000 * factor * (cos(t*2*pi/150) + 2)

    return s


def scalar_func(t,x,y):
    """Function that returns a scalar.
    Used to test error message when Numeric array is expected
    """

    return 17.7


def angle(t,x,y):
    """Rotating field
    """
    from math import sqrt, atan, pi

    x = array(x)
    y = array(y)

    N = len(x)
    a = 0*x  #New array

    for k in range(N):
        r = sqrt(x[k]**2 + y[k]**2)

        angle = atan(y[k]/x[k])

        if x[k] < 0:
            angle+=pi #atan in ]-pi/2; pi/2[

        #Take normal direction
        angle -= pi/2

        #Ensure positive radians
        if angle < 0:
            angle += 2*pi

        a[k] = angle/pi*180

    return a


class Test_Shallow_Water(unittest.TestCase):
    def setUp(self):
        pass

    def tearDown(self):
        pass

    def test_rotate(self):
        normal = array([0.0,-1.0])

        q = array([1.0,2.0,3.0])

        r = rotate(q, normal, direction = 1)
        assert r[0] == 1
        assert r[1] == -3
        assert r[2] == 2

        w = rotate(r, normal, direction = -1)
        assert allclose(w, q)

        #Check error check
        try:
            rotate(r, array([1,1,1]) )
        except:
            pass
        else:
            raise 'Should have raised an exception'

    def test_flux_zero_case(self):
        ql = zeros( 3, Float )
        qr = zeros( 3, Float )
        normal = zeros( 2, Float )
        zl = zr = 0.
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [0,0,0])
        assert max_speed == 0.

    def test_flux_constants(self):
        w = 2.0

        normal = array([1.,0])
        ql = array([w, 0, 0])
        qr = array([w, 0, 0])
        zl = zr = 0.
        h = w - (zl+zr)/2

        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [0., 0.5*g*h**2, 0.])
        assert max_speed == sqrt(g*h)

    #def test_flux_slope(self):
    #    #FIXME: TODO
    #    w = 2.0
    #
    #    normal = array([1.,0])
    #    ql = array([w, 0, 0])
    #    qr = array([w, 0, 0])
    #    zl = zr = 0.
    #    h = w - (zl+zr)/2
    #
    #    flux, max_speed = flux_function(normal, ql, qr, zl, zr)
    #
    #    assert allclose(flux, [0., 0.5*g*h**2, 0.])
    #    assert max_speed == sqrt(g*h)


    def test_flux1(self):
        #Use data from previous version of pyvolution
        normal = array([1.,0])
        ql = array([-0.2, 2, 3])
        qr = array([-0.2, 2, 3])
        zl = zr = -0.5
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [2.,13.77433333, 20.])
        assert allclose(max_speed, 8.38130948661)


    def test_flux2(self):
        #Use data from previous version of pyvolution
        normal = array([0., -1.])
        ql = array([-0.075, 2, 3])
        qr = array([-0.075, 2, 3])
        zl = zr = -0.375
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [-3.,-20.0, -30.441])
        assert allclose(max_speed, 11.7146428199)

    def test_flux3(self):
        #Use data from previous version of pyvolution
        normal = array([-sqrt(2)/2, sqrt(2)/2])
        ql = array([-0.075, 2, 3])
        qr = array([-0.075, 2, 3])
        zl = zr = -0.375
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [sqrt(2)/2, 4.40221112, 7.3829019])
        assert allclose(max_speed, 4.0716654239)

    def test_flux4(self):
        #Use data from previous version of pyvolution
        normal = array([-sqrt(2)/2, sqrt(2)/2])
        ql = array([-0.34319278, 0.10254161, 0.07273855])
        qr = array([-0.30683287, 0.1071986, 0.05930515])
        zl = zr = -0.375
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux, [-0.04072676, -0.07096636, -0.01604364])
        assert allclose(max_speed, 1.31414103233)

    def test_sw_domain_simple(self):
        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe, daf, dae
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        domain.check_integrity()

        for name in ['stage', 'xmomentum', 'ymomentum',
                     'elevation', 'friction']:
            assert domain.quantities.has_key(name)


        assert domain.get_conserved_quantities(0, edge=1) == 0.


    def test_boundary_conditions(self):

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4] ]
        boundary = { (0, 0): 'Third',
                     (0, 2): 'First',
                     (2, 0): 'Second',
                     (2, 1): 'Second',
                     (3, 1): 'Second',
                     (3, 2): 'Third'}


        domain = Domain(points, vertices, boundary)
        domain.check_integrity()


        domain.set_quantity('stage', [[1,2,3], [5,5,5],
                                      [0,0,9], [-6, 3, 3]])

        domain.set_quantity('xmomentum', [[1,1,1], [2,2,2],
                                          [3,3,3], [4, 4, 4]])

        domain.set_quantity('ymomentum', [[10,10,10], [20,20,20],
                                          [30,30,30], [40, 40, 40]])


        D = Dirichlet_boundary([5,2,1])
        T = Transmissive_boundary(domain)
        R = Reflective_boundary(domain)
        domain.set_boundary( {'First': D, 'Second': T, 'Third': R})

        domain.update_boundary()

        #Stage
        assert domain.quantities['stage'].boundary_values[0] == 2.5
        assert domain.quantities['stage'].boundary_values[0] ==\
               domain.get_conserved_quantities(0, edge=0)[0] #Reflective (2.5)
        assert domain.quantities['stage'].boundary_values[1] == 5. #Dirichlet
        assert domain.quantities['stage'].boundary_values[2] ==\
               domain.get_conserved_quantities(2, edge=0)[0] #Transmissive (4.5)
        assert domain.quantities['stage'].boundary_values[3] ==\
               domain.get_conserved_quantities(2, edge=1)[0] #Transmissive (4.5)
        assert domain.quantities['stage'].boundary_values[4] ==\
               domain.get_conserved_quantities(3, edge=1)[0] #Transmissive (-1.5)
        assert domain.quantities['stage'].boundary_values[5] ==\
               domain.get_conserved_quantities(3, edge=2)[0] #Reflective (-1.5)

        #Xmomentum
        assert domain.quantities['xmomentum'].boundary_values[0] == 1.0 #Reflective
        assert domain.quantities['xmomentum'].boundary_values[1] == 2. #Dirichlet
        assert domain.quantities['xmomentum'].boundary_values[2] ==\
               domain.get_conserved_quantities(2, edge=0)[1] #Transmissive
        assert domain.quantities['xmomentum'].boundary_values[3] ==\
               domain.get_conserved_quantities(2, edge=1)[1] #Transmissive
        assert domain.quantities['xmomentum'].boundary_values[4] ==\
               domain.get_conserved_quantities(3, edge=1)[1] #Transmissive
        assert domain.quantities['xmomentum'].boundary_values[5] == -4.0  #Reflective

        #Ymomentum
        assert domain.quantities['ymomentum'].boundary_values[0] == -10.0 #Reflective
        assert domain.quantities['ymomentum'].boundary_values[1] == 1.  #Dirichlet
        assert domain.quantities['ymomentum'].boundary_values[2] == 30. #Transmissive
        assert domain.quantities['ymomentum'].boundary_values[3] == 30. #Transmissive
        assert domain.quantities['ymomentum'].boundary_values[4] == 40. #Transmissive
        assert domain.quantities['ymomentum'].boundary_values[5] == 40. #Reflective


    def test_boundary_conditionsII(self):

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4] ]
        boundary = { (0, 0): 'Third',
                     (0, 2): 'First',
                     (2, 0): 'Second',
                     (2, 1): 'Second',
                     (3, 1): 'Second',
                     (3, 2): 'Third',
                     (0, 1): 'Internal'}


        domain = Domain(points, vertices, boundary)
        domain.check_integrity()


        domain.set_quantity('stage', [[1,2,3], [5,5,5],
                                      [0,0,9], [-6, 3, 3]])

        domain.set_quantity('xmomentum', [[1,1,1], [2,2,2],
                                          [3,3,3], [4, 4, 4]])

        domain.set_quantity('ymomentum', [[10,10,10], [20,20,20],
                                          [30,30,30], [40, 40, 40]])


        D = Dirichlet_boundary([5,2,1])
        T = Transmissive_boundary(domain)
        R = Reflective_boundary(domain)
        domain.set_boundary( {'First': D, 'Second': T,
                              'Third': R, 'Internal': None})

        domain.update_boundary()
        domain.check_integrity()


    def test_compute_fluxes0(self):
        #Do a full triangle and check that fluxes cancel out for
        #the constant stage case

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        domain.set_quantity('stage', [[2,2,2], [2,2,2],
                                      [2,2,2], [2,2,2]])
        domain.check_integrity()

        assert allclose(domain.neighbours, [[-1,1,-1], [2,3,0], [-1,-1,1],[1,-1,-1]])
        assert allclose(domain.neighbour_edges, [[-1,2,-1], [2,0,1], [-1,-1,0],[1,-1,-1]])

        zl=zr=0. #Assume flat bed

        #Flux across right edge of volume 1
        normal = domain.get_normal(1,0)
        ql = domain.get_conserved_quantities(vol_id=1, edge=0)
        qr = domain.get_conserved_quantities(vol_id=2, edge=2)
        flux0, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Check that flux seen from other triangles is inverse
        tmp = qr; qr=ql; ql=tmp
        normal = domain.get_normal(2,2)
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)
        assert allclose(flux + flux0, 0.)

        #Flux across upper edge of volume 1
        normal = domain.get_normal(1,1)
        ql = domain.get_conserved_quantities(vol_id=1, edge=1)
        qr = domain.get_conserved_quantities(vol_id=3, edge=0)
        flux1, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Check that flux seen from other triangles is inverse
        tmp = qr; qr=ql; ql=tmp
        normal = domain.get_normal(3,0)
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)
        assert allclose(flux + flux1, 0.)

        #Flux across lower left hypotenuse of volume 1
        normal = domain.get_normal(1,2)
        ql = domain.get_conserved_quantities(vol_id=1, edge=2)
        qr = domain.get_conserved_quantities(vol_id=0, edge=1)
        flux2, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Check that flux seen from other triangles is inverse
        tmp = qr; qr=ql; ql=tmp
        normal = domain.get_normal(0,1)
        flux, max_speed = flux_function(normal, ql, qr, zl, zr)
        assert allclose(flux + flux2, 0.)


        #Scale by edgelengths, add up anc check that total flux is zero
        e0 = domain.edgelengths[1, 0]
        e1 = domain.edgelengths[1, 1]
        e2 = domain.edgelengths[1, 2]

        assert allclose(e0*flux0+e1*flux1+e2*flux2, 0.)

        #Now check that compute_flux yields zeros as well
        domain.compute_fluxes()

        for name in ['stage', 'xmomentum', 'ymomentum']:
            #print name, domain.quantities[name].explicit_update
            assert allclose(domain.quantities[name].explicit_update[1], 0)



    def test_compute_fluxes1(self):
        #Use values from previous version

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        domain.set_quantity('stage', [[val0, val0, val0], [val1, val1, val1],
                                      [val2, val2, val2], [val3, val3, val3]])
        domain.check_integrity()

        zl=zr=0. #Assume flat bed

        #Flux across right edge of volume 1
        normal = domain.get_normal(1,0)
        ql = domain.get_conserved_quantities(vol_id=1, edge=0)
        qr = domain.get_conserved_quantities(vol_id=2, edge=2)
        flux0, max_speed = flux_function(normal, ql, qr, zl, zr)
        assert allclose(flux0, [-15.3598804, 253.71111111, 0.])
        assert allclose(max_speed, 9.21592824046)


        #Flux across upper edge of volume 1
        normal = domain.get_normal(1,1)
        ql = domain.get_conserved_quantities(vol_id=1, edge=1)
        qr = domain.get_conserved_quantities(vol_id=3, edge=0)
        flux1, max_speed = flux_function(normal, ql, qr, zl, zr)
        assert allclose(flux1, [2.4098563, 0., 123.04444444])
        assert allclose(max_speed, 7.22956891292)

        #Flux across lower left hypotenuse of volume 1
        normal = domain.get_normal(1,2)
        ql = domain.get_conserved_quantities(vol_id=1, edge=2)
        qr = domain.get_conserved_quantities(vol_id=0, edge=1)
        flux2, max_speed = flux_function(normal, ql, qr, zl, zr)

        assert allclose(flux2, [9.63942522, -61.59685738, -61.59685738])
        assert allclose(max_speed, 7.22956891292)

        #Scale, add up and check that compute_fluxes is correct for vol 1
        e0 = domain.edgelengths[1, 0]
        e1 = domain.edgelengths[1, 1]
        e2 = domain.edgelengths[1, 2]

        total_flux = -(e0*flux0+e1*flux1+e2*flux2)/domain.areas[1]
        assert allclose(total_flux, [-0.68218178, -166.6, -35.93333333])


        domain.compute_fluxes()

        #assert allclose(total_flux, domain.explicit_update[1,:])
        for i, name in enumerate(['stage', 'xmomentum', 'ymomentum']):
            assert allclose(total_flux[i],
                            domain.quantities[name].explicit_update[1])

        #assert allclose(domain.explicit_update, [
        #    [0., -69.68888889, -69.68888889],
        #    [-0.68218178, -166.6, -35.93333333],
        #    [-111.77316251, 69.68888889, 0.],
        #    [-35.68522449, 0., 69.68888889]])

        assert allclose(domain.quantities['stage'].explicit_update,
                        [0., -0.68218178, -111.77316251, -35.68522449])
        assert allclose(domain.quantities['xmomentum'].explicit_update,
                        [-69.68888889, -166.6, 69.68888889, 0])
        assert allclose(domain.quantities['ymomentum'].explicit_update,
                        [-69.68888889, -35.93333333, 0., 69.68888889])


        #assert allclose(domain.quantities[name].explicit_update





    def test_compute_fluxes2(self):
        #Random values, incl momentum

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        zl=zr=0 #Assume flat zero bed

        domain.set_quantity('elevation', zl*ones( (4,3) ))


        domain.set_quantity('stage', [[val0, val0-1, val0-2],
                                      [val1, val1+1, val1],
                                      [val2, val2-2, val2],
                                      [val3-0.5, val3, val3]])

        domain.set_quantity('xmomentum',
                            [[1, 2, 3], [3, 4, 5],
                             [1, -1, 0], [0, -2, 2]])

        domain.set_quantity('ymomentum',
                            [[1, -1, 0], [0, -3, 2],
                             [0, 1, 0], [-1, 2, 2]])


        domain.check_integrity()



        #Flux across right edge of volume 1
        normal = domain.get_normal(1,0)
        ql = domain.get_conserved_quantities(vol_id=1, edge=0)
        qr = domain.get_conserved_quantities(vol_id=2, edge=2)
        flux0, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Flux across upper edge of volume 1
        normal = domain.get_normal(1,1)
        ql = domain.get_conserved_quantities(vol_id=1, edge=1)
        qr = domain.get_conserved_quantities(vol_id=3, edge=0)
        flux1, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Flux across lower left hypotenuse of volume 1
        normal = domain.get_normal(1,2)
        ql = domain.get_conserved_quantities(vol_id=1, edge=2)
        qr = domain.get_conserved_quantities(vol_id=0, edge=1)
        flux2, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Scale, add up and check that compute_fluxes is correct for vol 1
        e0 = domain.edgelengths[1, 0]
        e1 = domain.edgelengths[1, 1]
        e2 = domain.edgelengths[1, 2]

        total_flux = -(e0*flux0+e1*flux1+e2*flux2)/domain.areas[1]


        domain.compute_fluxes()
        for i, name in enumerate(['stage', 'xmomentum', 'ymomentum']):
            assert allclose(total_flux[i],
                            domain.quantities[name].explicit_update[1])
        #assert allclose(total_flux, domain.explicit_update[1,:])


    def test_compute_fluxes3(self):
        #Random values, incl momentum

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        zl=zr=-3.75 #Assume constant bed (must be less than stage)
        domain.set_quantity('elevation', zl*ones( (4,3) ))


        domain.set_quantity('stage', [[val0, val0-1, val0-2],
                                      [val1, val1+1, val1],
                                      [val2, val2-2, val2],
                                      [val3-0.5, val3, val3]])

        domain.set_quantity('xmomentum',
                            [[1, 2, 3], [3, 4, 5],
                             [1, -1, 0], [0, -2, 2]])

        domain.set_quantity('ymomentum',
                            [[1, -1, 0], [0, -3, 2],
                             [0, 1, 0], [-1, 2, 2]])


        domain.check_integrity()



        #Flux across right edge of volume 1
        normal = domain.get_normal(1,0)
        ql = domain.get_conserved_quantities(vol_id=1, edge=0)
        qr = domain.get_conserved_quantities(vol_id=2, edge=2)
        flux0, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Flux across upper edge of volume 1
        normal = domain.get_normal(1,1)
        ql = domain.get_conserved_quantities(vol_id=1, edge=1)
        qr = domain.get_conserved_quantities(vol_id=3, edge=0)
        flux1, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Flux across lower left hypotenuse of volume 1
        normal = domain.get_normal(1,2)
        ql = domain.get_conserved_quantities(vol_id=1, edge=2)
        qr = domain.get_conserved_quantities(vol_id=0, edge=1)
        flux2, max_speed = flux_function(normal, ql, qr, zl, zr)

        #Scale, add up and check that compute_fluxes is correct for vol 1
        e0 = domain.edgelengths[1, 0]
        e1 = domain.edgelengths[1, 1]
        e2 = domain.edgelengths[1, 2]

        total_flux = -(e0*flux0+e1*flux1+e2*flux2)/domain.areas[1]

        domain.compute_fluxes()
        for i, name in enumerate(['stage', 'xmomentum', 'ymomentum']):
            assert allclose(total_flux[i],
                            domain.quantities[name].explicit_update[1])



    def test_catching_negative_heights(self):

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        zl=zr=4  #Too large
        domain.set_quantity('elevation', zl*ones( (4,3) ))
        domain.set_quantity('stage', [[val0, val0-1, val0-2],
                                      [val1, val1+1, val1],
                                      [val2, val2-2, val2],
                                      [val3-0.5, val3, val3]])

        #Should fail
        try:
            domain.check_integrity()
        except:
            pass




    #####################################################
    def test_initial_condition(self):
        """Test that initial condition is output at time == 0
        """

        from config import g
        import copy

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Set up for a gradient of (3,0) at mid triangle
        def slope(x, y):
            return 3*x

        h = 0.1
        def stage(x,y):
            return slope(x,y)+h

        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage', stage)

        initial_stage = copy.copy(domain.quantities['stage'].vertex_values)

        domain.set_boundary({'exterior': Reflective_boundary(domain)})

        #Evolution
        for t in domain.evolve(yieldstep = 1.0, finaltime = 2.0):
            stage = domain.quantities['stage'].vertex_values

            if t == 0.0:
                assert allclose(stage, initial_stage)
            else:
                assert not allclose(stage, initial_stage)




    #####################################################
    def test_gravity(self):
        #Assuming no friction

        from config import g

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Set up for a gradient of (3,0) at mid triangle
        def slope(x, y):
            return 3*x

        h = 0.1
        def stage(x,y):
            return slope(x,y)+h

        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage', stage)

        for name in domain.conserved_quantities:
            assert allclose(domain.quantities[name].explicit_update, 0)
            assert allclose(domain.quantities[name].semi_implicit_update, 0)

        domain.compute_forcing_terms()

        assert allclose(domain.quantities['stage'].explicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].explicit_update, -g*h*3)
        assert allclose(domain.quantities['ymomentum'].explicit_update, 0)


    def test_manning_friction(self):
        from config import g

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Set up for a gradient of (3,0) at mid triangle
        def slope(x, y):
            return 3*x

        h = 0.1
        def stage(x,y):
            return slope(x,y)+h

        eta = 0.07
        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage', stage)
        domain.set_quantity('friction', eta)

        for name in domain.conserved_quantities:
            assert allclose(domain.quantities[name].explicit_update, 0)
            assert allclose(domain.quantities[name].semi_implicit_update, 0)

        domain.compute_forcing_terms()

        assert allclose(domain.quantities['stage'].explicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].explicit_update, -g*h*3)
        assert allclose(domain.quantities['ymomentum'].explicit_update, 0)

        assert allclose(domain.quantities['stage'].semi_implicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].semi_implicit_update, 0)
        assert allclose(domain.quantities['ymomentum'].semi_implicit_update, 0)

        #Create some momentum for friction to work with
        domain.set_quantity('xmomentum', 1)
        S = -g * eta**2 / h**(7.0/3)

        domain.compute_forcing_terms()
        assert allclose(domain.quantities['stage'].semi_implicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].semi_implicit_update, S)
        assert allclose(domain.quantities['ymomentum'].semi_implicit_update, 0)

        #A more complex example
        domain.quantities['stage'].semi_implicit_update[:] = 0.0
        domain.quantities['xmomentum'].semi_implicit_update[:] = 0.0
        domain.quantities['ymomentum'].semi_implicit_update[:] = 0.0

        domain.set_quantity('xmomentum', 3)
        domain.set_quantity('ymomentum', 4)

        S = -g * eta**2 * 5 / h**(7.0/3)


        domain.compute_forcing_terms()

        assert allclose(domain.quantities['stage'].semi_implicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].semi_implicit_update, 3*S)
        assert allclose(domain.quantities['ymomentum'].semi_implicit_update, 4*S)

    def test_constant_wind_stress(self):
        from config import rho_a, rho_w, eta_w
        from math import pi, cos, sin, sqrt

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]


        domain = Domain(points, vertices)

        #Flat surface with 1m of water
        domain.set_quantity('elevation', 0)
        domain.set_quantity('stage', 1.0)
        domain.set_quantity('friction', 0)

        Br = Reflective_boundary(domain)
        domain.set_boundary({'exterior': Br})

        #Setup only one forcing term, constant wind stress
        s = 100
        phi = 135
        domain.forcing_terms = []
        domain.forcing_terms.append( Wind_stress(s, phi) )

        domain.compute_forcing_terms()


        const = eta_w*rho_a/rho_w

        #Convert to radians
        phi = phi*pi/180

        #Compute velocity vector (u, v)
        u = s*cos(phi)
        v = s*sin(phi)

        #Compute wind stress
        S = const * sqrt(u**2 + v**2)

        assert allclose(domain.quantities['stage'].explicit_update, 0)
        assert allclose(domain.quantities['xmomentum'].explicit_update, S*u)
        assert allclose(domain.quantities['ymomentum'].explicit_update, S*v)


    def test_variable_wind_stress(self):
        from config import rho_a, rho_w, eta_w
        from math import pi, cos, sin, sqrt

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Flat surface with 1m of water
        domain.set_quantity('elevation', 0)
        domain.set_quantity('stage', 1.0)
        domain.set_quantity('friction', 0)

        Br = Reflective_boundary(domain)
        domain.set_boundary({'exterior': Br})


        domain.time = 5.54 #Take a random time (not zero)

        #Setup only one forcing term, constant wind stress
        s = 100
        phi = 135
        domain.forcing_terms = []
        domain.forcing_terms.append( Wind_stress(s = speed, phi = angle) )

        domain.compute_forcing_terms()

        #Compute reference solution
        const = eta_w*rho_a/rho_w

        N = domain.number_of_elements

        xc = domain.get_centroid_coordinates()
        t = domain.time

        x = xc[:,0]
        y = xc[:,1]
        s_vec = speed(t,x,y)
        phi_vec = angle(t,x,y)


        for k in range(N):
            #Convert to radians
            phi = phi_vec[k]*pi/180
            s = s_vec[k]

            #Compute velocity vector (u, v)
            u = s*cos(phi)
            v = s*sin(phi)

            #Compute wind stress
            S = const * sqrt(u**2 + v**2)

            assert allclose(domain.quantities['stage'].explicit_update[k], 0)
            assert allclose(domain.quantities['xmomentum'].explicit_update[k], S*u)
            assert allclose(domain.quantities['ymomentum'].explicit_update[k], S*v)




    def test_windfield_from_file(self):
        from config import rho_a, rho_w, eta_w
        from math import pi, cos, sin, sqrt
        from config import time_format
        from util import file_function
        import time


        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Flat surface with 1m of water
        domain.set_quantity('elevation', 0)
        domain.set_quantity('stage', 1.0)
        domain.set_quantity('friction', 0)

        Br = Reflective_boundary(domain)
        domain.set_boundary({'exterior': Br})


        domain.time = 7 #Take a time that is represented in file (not zero)

        #Write wind stress file (ensure that domain.time is covered)
        #Take x=1 and y=0
        filename = 'test_windstress_from_file'
        start = time.mktime(time.strptime('2000', '%Y'))
        fid = open(filename + '.txt', 'w')
        dt = 1  #One second interval
        t = 0.0
        while t <= 10.0:
            t_string = time.strftime(time_format, time.gmtime(t+start))

            fid.write('%s, %f %f\n' %(t_string,
                                      speed(t,[1],[0])[0],
                                      angle(t,[1],[0])[0]))
            t += dt

        fid.close()


        #Convert ASCII file to NetCDF (Which is what we really like!)
        from data_manager import timefile2swww        
        timefile2swww(filename)


        
        #Setup wind stress
        F = file_function(filename + '.sww', quantities = ['Attribute0',
                                                           'Attribute1'])

        #print 'F(5)', F(5)

        #print 'F(5,x,y)', F(5,x=zeros(3),y=zeros(3))
        
        #print dir(F)
        #print F.T
        #print F.precomputed_values
        #
        #F = file_function(filename + '.txt')        
        #
        #print dir(F)
        #print F.T        
        #print F.Q
        
        W = Wind_stress(F)

        domain.forcing_terms = []
        domain.forcing_terms.append(W)

        domain.compute_forcing_terms()

        #Compute reference solution
        const = eta_w*rho_a/rho_w

        N = domain.number_of_elements

        t = domain.time

        s = speed(t,[1],[0])[0]
        phi = angle(t,[1],[0])[0]

        #Convert to radians
        phi = phi*pi/180


        #Compute velocity vector (u, v)
        u = s*cos(phi)
        v = s*sin(phi)

        #Compute wind stress
        S = const * sqrt(u**2 + v**2)

        for k in range(N):
            assert allclose(domain.quantities['stage'].explicit_update[k], 0)
            assert allclose(domain.quantities['xmomentum'].explicit_update[k], S*u)
            assert allclose(domain.quantities['ymomentum'].explicit_update[k], S*v)

        #os.remove(filename + '.txt')

    def test_wind_stress_error_condition(self):
        """Test that windstress reacts properly when forcing functions
        are wrong - e.g. returns a scalar
        """

        from config import rho_a, rho_w, eta_w
        from math import pi, cos, sin, sqrt

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        #Flat surface with 1m of water
        domain.set_quantity('elevation', 0)
        domain.set_quantity('stage', 1.0)
        domain.set_quantity('friction', 0)

        Br = Reflective_boundary(domain)
        domain.set_boundary({'exterior': Br})


        domain.time = 5.54 #Take a random time (not zero)

        #Setup only one forcing term, bad func
        domain.forcing_terms = []

        try:
            domain.forcing_terms.append(Wind_stress(s = scalar_func,
                                                    phi = angle))
        except AssertionError:
            pass
        else:
            msg = 'Should have raised exception'
            raise msg


        try:
            domain.forcing_terms.append(Wind_stress(s = speed,
                                                    phi = scalar_func))
        except AssertionError:
            pass
        else:
            msg = 'Should have raised exception'
            raise msg

        try:
            domain.forcing_terms.append(Wind_stress(s = speed,
                                                    phi = 'xx'))
        except:
            pass
        else:
            msg = 'Should have raised exception'
            raise msg


    #####################################################
    def test_first_order_extrapolator_const_z(self):

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        zl=zr=-3.75 #Assume constant bed (must be less than stage)
        domain.set_quantity('elevation', zl*ones( (4,3) ))
        domain.set_quantity('stage', [[val0, val0-1, val0-2],
                                      [val1, val1+1, val1],
                                      [val2, val2-2, val2],
                                      [val3-0.5, val3, val3]])



        domain.order = 1
        domain.distribute_to_vertices_and_edges()

        #Check that centroid values were distributed to vertices
        C = domain.quantities['stage'].centroid_values
        for i in range(3):
            assert allclose( domain.quantities['stage'].vertex_values[:,i], C)


    def test_first_order_limiter_variable_z(self):
        #Check that first order limiter follows bed_slope
        from Numeric import alltrue, greater_equal
        from config import epsilon

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0,0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0,0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        val0 = 2.+2.0/3
        val1 = 4.+4.0/3
        val2 = 8.+2.0/3
        val3 = 2.+8.0/3

        domain.set_quantity('elevation', [[0,0,0], [6,0,0],
                                          [6,6,6], [6,6,6]])
        domain.set_quantity('stage', [[val0, val0, val0],
                                      [val1, val1, val1],
                                      [val2, val2, val2],
                                      [val3, val3, val3]])

        E = domain.quantities['elevation'].vertex_values
        L = domain.quantities['stage'].vertex_values


        #Check that some stages are not above elevation (within eps)
        #- so that the limiter has something to work with
        assert not alltrue(alltrue(greater_equal(L,E-epsilon)))

        domain.order = 1
        domain.distribute_to_vertices_and_edges()

        #Check that all stages are above elevation (within eps)
        assert alltrue(alltrue(greater_equal(L,E-epsilon)))


    #####################################################
    def test_distribute_basic(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)

        val0 = 2.
        val1 = 4.
        val2 = 8.
        val3 = 2.

        domain.set_quantity('stage', [val0, val1, val2, val3],
                            location='centroids')
        L = domain.quantities['stage'].vertex_values

        #First order
        domain.order = 1
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], val1)

        #Second order
        domain.order = 2
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], [2.2, 4.9, 4.9])



    def test_distribute_away_from_bed(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        L = domain.quantities['stage'].vertex_values

        def stage(x,y):
            return x**2

        domain.set_quantity('stage', stage, location='centroids')

        a, b = domain.quantities['stage'].compute_gradients()
        assert allclose(a[1], 3.33333334)
        assert allclose(b[1], 0.0)

        domain.order = 1
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], 1.77777778)

        domain.order = 2
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], [0.57777777, 2.37777778, 2.37777778])



    def test_distribute_away_from_bed1(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)
        L = domain.quantities['stage'].vertex_values

        def stage(x,y):
            return x**4+y**2

        domain.set_quantity('stage', stage, location='centroids')
        #print domain.quantities['stage'].centroid_values

        a, b = domain.quantities['stage'].compute_gradients()
        assert allclose(a[1], 25.18518519)
        assert allclose(b[1], 3.33333333)

        domain.order = 1
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], 4.9382716)

        domain.order = 2
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], [1.07160494, 6.46058131, 7.28262855])



    def test_distribute_near_bed(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)


        #Set up for a gradient of (3,0) at mid triangle
        def slope(x, y):
            return 10*x

        h = 0.1
        def stage(x,y):
            return slope(x,y)+h

        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage', stage, location='centroids')

        #print domain.quantities['elevation'].centroid_values
        #print domain.quantities['stage'].centroid_values

        E = domain.quantities['elevation'].vertex_values
        L = domain.quantities['stage'].vertex_values

        #print E
        domain.order = 1
        domain.distribute_to_vertices_and_edges()
        ##assert allclose(L[1], [0.19999999, 20.05, 20.05])
        assert allclose(L[1], [0.1, 20.1, 20.1])

        domain.order = 2
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], [0.1, 20.1, 20.1])

    def test_distribute_near_bed1(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]
        #bac, bce, ecf, dbe
        vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]]

        domain = Domain(points, vertices)


        #Set up for a gradient of (3,0) at mid triangle
        def slope(x, y):
            return x**4+y**2

        h = 0.1
        def stage(x,y):
            return slope(x,y)+h

        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage', stage)

        #print domain.quantities['elevation'].centroid_values
        #print domain.quantities['stage'].centroid_values

        E = domain.quantities['elevation'].vertex_values
        L = domain.quantities['stage'].vertex_values

        #print E
        domain.order = 1
        domain.distribute_to_vertices_and_edges()
        ##assert allclose(L[1], [4.19999999, 16.07142857, 20.02857143])
        assert allclose(L[1], [4.1, 16.1, 20.1])

        domain.order = 2
        domain.distribute_to_vertices_and_edges()
        assert allclose(L[1], [4.1, 16.1, 20.1])



    def test_second_order_distribute_real_data(self):
        #Using test data generated by pyvolution-2
        #Assuming no friction and flat bed (0.0)

        a = [0.0, 0.0]
        b = [0.0, 1.0/5]
        c = [0.0, 2.0/5]
        d = [1.0/5, 0.0]
        e = [1.0/5, 1.0/5]
        f = [1.0/5, 2.0/5]
        g = [2.0/5, 2.0/5]

        points = [a, b, c, d, e, f, g]
        #bae, efb, cbf, feg
        vertices = [ [1,0,4], [4,5,1], [2,1,5], [5,4,6]]

        domain = Domain(points, vertices)

        def slope(x, y):
            return -x/3

        domain.set_quantity('elevation', slope)
        domain.set_quantity('stage',
                            [0.01298164, 0.00365611,
                             0.01440365, -0.0381856437096],
                            location='centroids')
        domain.set_quantity('xmomentum',
                            [0.00670439, 0.01263789,
                             0.00647805, 0.0178180740668],
                            location='centroids')
        domain.set_quantity('ymomentum',
                            [-7.23510980e-004, -6.30413883e-005,
                             6.30413883e-005, 0.000200907255866],
                            location='centroids')

        E = domain.quantities['elevation'].vertex_values
        L = domain.quantities['stage'].vertex_values
        X = domain.quantities['xmomentum'].vertex_values
        Y = domain.quantities['ymomentum'].vertex_values

        #print E
        domain.order = 2
        domain.beta_h = 0.0 #Use first order in h-limiter
        domain.distribute_to_vertices_and_edges()

        #print L[1,:]
        #print X[1,:]
        #print Y[1,:]

        assert allclose(L[1,:], [-0.00825735775384,
                                 -0.00801881482869,
                                 0.0272445025825])
        assert allclose(X[1,:], [0.0143507718962,
                                 0.0142502147066,
                                 0.00931268339717])
        assert allclose(Y[1,:], [-0.000117062180693,
                                 7.94434448109e-005,
                                 -0.000151505429018])



    def test_balance_deep_and_shallow(self):
        """Test that balanced limiters preserve conserved quantites.
        """
        import copy

        a = [0.0, 0.0]
        b = [0.0, 2.0]
        c = [2.0, 0.0]
        d = [0.0, 4.0]
        e = [2.0, 2.0]
        f = [4.0, 0.0]

        points = [a, b, c, d, e, f]

        #bac, bce, ecf, dbe
        elements = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4] ]

        mesh = Domain(points, elements)
        mesh.check_integrity()

        #Create a deliberate overshoot
        mesh.set_quantity('stage', [[3,0,3], [2,2,6], [5,3,8], [8,3,5]])
        mesh.set_quantity('elevation', 0) #Flat bed
        stage = mesh.quantities['stage']

        ref_centroid_values = copy.copy(stage.centroid_values[:]) #Copy

        #Limit
        mesh.distribute_to_vertices_and_edges()

        #Assert that quantities are conserved
        from Numeric import sum
        for k in range(mesh.number_of_elements):
            assert allclose (ref_centroid_values[k],
                             sum(stage.vertex_values[k,:])/3)


        #Now try with a non-flat bed - closely hugging initial stage in places
        #This will create alphas in the range [0, 0.478260, 1]
        mesh.set_quantity('stage', [[3,0,3], [2,2,6], [5,3,8], [8,3,5]])
        mesh.set_quantity('elevation', [[0,0,0],
                                        [1.8,1.9,5.9],
                                        [4.6,0,0],
                                        [0,2,4]])
        stage = mesh.quantities['stage']

        ref_centroid_values = copy.copy(stage.centroid_values[:]) #Copy
        ref_vertex_values = copy.copy(stage.vertex_values[:]) #Copy

        #Limit
        mesh.distribute_to_vertices_and_edges()


        #Assert that all vertex quantities have changed
        for k in range(mesh.number_of_elements):
            #print ref_vertex_values[k,:], stage.vertex_values[k,:]
            assert not allclose (ref_vertex_values[k,:], stage.vertex_values[k,:])
        #and assert that quantities are still conserved
        from Numeric import sum
        for k in range(mesh.number_of_elements):
            assert allclose (ref_centroid_values[k],
                             sum(stage.vertex_values[k,:])/3)


        #Also check that Python and C version produce the same
        assert allclose (stage.vertex_values,
                         [[2,2,2],
                          [1.93333333, 2.03333333, 6.03333333],
                          [6.93333333, 4.53333333, 4.53333333],
                          [5.33333333, 5.33333333, 5.33333333]])




    def test_conservation_1(self):
        """Test that stage is conserved globally

        This one uses a flat bed, reflective bdries and a suitable
        initial condition
        """
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        #IC
        def x_slope(x, y):
            return x/3

        domain.set_quantity('elevation', 0)
        domain.set_quantity('friction', 0)
        domain.set_quantity('stage', x_slope)

        # Boundary conditions (reflective everywhere)
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #domain.visualise = True #If you want to take a sticky beak

        initial_volume = domain.quantities['stage'].get_integral()
        initial_xmom = domain.quantities['xmomentum'].get_integral()

        #print initial_xmom

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 5.0):
            volume =  domain.quantities['stage'].get_integral()
            assert allclose (volume, initial_volume)

            #I don't believe that the total momentum should be the same
            #It starts with zero and ends with zero though
            #xmom = domain.quantities['xmomentum'].get_integral()
            #print xmom
            #assert allclose (xmom, initial_xmom)



    def test_conservation_2(self):
        """Test that stage is conserved globally

        This one uses a slopy bed, reflective bdries and a suitable
        initial condition
        """
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        #IC
        def x_slope(x, y):
            return x/3

        domain.set_quantity('elevation', x_slope)
        domain.set_quantity('friction', 0)
        domain.set_quantity('stage', 0.4) #Steady

        # Boundary conditions (reflective everywhere)
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #domain.visualise = True #If you want to take a sticky beak

        initial_volume = domain.quantities['stage'].get_integral()
        initial_xmom = domain.quantities['xmomentum'].get_integral()

        #print initial_xmom

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 5.0):
            volume =  domain.quantities['stage'].get_integral()
            assert allclose (volume, initial_volume)

            #FIXME: What would we expect from momentum
            #xmom = domain.quantities['xmomentum'].get_integral()
            #print xmom
            #assert allclose (xmom, initial_xmom)


    def test_conservation_3(self):
        """Test that stage is conserved globally

        This one uses a larger grid, convoluted bed, reflective bdries and a suitable
        initial condition
        """
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(2, 1)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.2

        #IC
        def x_slope(x, y):
            z = 0*x
            for i in range(len(x)):
                if x[i] < 0.3:
                    z[i] = x[i]/3
                if 0.3 <= x[i] < 0.5:
                    z[i] = -0.5
                if 0.5 <= x[i] < 0.7:
                    z[i] = 0.39
                if 0.7 <= x[i]:
                    z[i] = x[i]/3
            return z



        domain.set_quantity('elevation', x_slope)
        domain.set_quantity('friction', 0)
        domain.set_quantity('stage', 0.4) #Steady

        # Boundary conditions (reflective everywhere)
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #domain.visualise = True #If you want to take a sticky beak

        initial_volume = domain.quantities['stage'].get_integral()
        initial_xmom = domain.quantities['xmomentum'].get_integral()

        import copy
        ref_centroid_values =\
                 copy.copy(domain.quantities['stage'].centroid_values)

        #print 'ORG', domain.quantities['stage'].centroid_values
        domain.distribute_to_vertices_and_edges()


        #print domain.quantities['stage'].centroid_values
        assert allclose(domain.quantities['stage'].centroid_values,
                        ref_centroid_values)


        #Check that initial limiter doesn't violate cons quan
        assert allclose (domain.quantities['stage'].get_integral(),
                         initial_volume)

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 10):
            volume =  domain.quantities['stage'].get_integral()
            #print t, volume, initial_volume
            assert allclose (volume, initial_volume)


    def test_conservation_4(self):
        """Test that stage is conserved globally

        This one uses a larger grid, convoluted bed, reflective bdries and a suitable
        initial condition
        """
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.0

        #IC
        def x_slope(x, y):
            z = 0*x
            for i in range(len(x)):
                if x[i] < 0.3:
                    z[i] = x[i]/3
                if 0.3 <= x[i] < 0.5:
                    z[i] = -0.5
                if 0.5 <= x[i] < 0.7:
                    #z[i] = 0.3 #OK with beta == 0.2
                    z[i] = 0.34 #OK with beta == 0.0
                    #z[i] = 0.35#Fails after 80 timesteps with an error
                                #of the order 1.0e-5
                if 0.7 <= x[i]:
                    z[i] = x[i]/3
            return z



        domain.set_quantity('elevation', x_slope)
        domain.set_quantity('friction', 0)
        domain.set_quantity('stage', 0.4) #Steady

        # Boundary conditions (reflective everywhere)
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #domain.visualise = True #If you want to take a sticky beak

        initial_volume = domain.quantities['stage'].get_integral()
        initial_xmom = domain.quantities['xmomentum'].get_integral()

        import copy
        ref_centroid_values =\
                 copy.copy(domain.quantities['stage'].centroid_values)

        #Test limiter by itself
        domain.distribute_to_vertices_and_edges()

        #Check that initial limiter doesn't violate cons quan
        assert allclose (domain.quantities['stage'].get_integral(),
                         initial_volume)
        #NOTE: This would fail if any initial stage was less than the
        #corresponding bed elevation - but that is reasonable.


        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 10.0):
            volume =  domain.quantities['stage'].get_integral()

            #print t, volume, initial_volume


            #if not allclose (volume, initial_volume):
            #    print 't==4.05'
            #    for k in range(domain.number_of_elements):
            #       pass
            #       print domain.quantities['stage'].centroid_values[k] -\
            #             ref_centroid_values[k]

            assert allclose (volume, initial_volume)





    def test_conservation_5(self):
        """Test that momentum is conserved globally in
        steady state scenario

        This one uses a slopy bed, dirichlet and reflective bdries
        """
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        #IC
        def x_slope(x, y):
            return x/3

        domain.set_quantity('elevation', x_slope)
        domain.set_quantity('friction', 0)
        domain.set_quantity('stage', 0.4) #Steady

        # Boundary conditions (reflective everywhere)
        Br = Reflective_boundary(domain)
        Bleft = Dirichlet_boundary([0.5,0,0])
        Bright = Dirichlet_boundary([0.1,0,0])
        domain.set_boundary({'left': Bleft, 'right': Bright,
                             'top': Br, 'bottom': Br})

        domain.check_integrity()

        #domain.visualise = True #If you want to take a sticky beak

        initial_volume = domain.quantities['stage'].get_integral()
        initial_xmom = domain.quantities['xmomentum'].get_integral()


        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 15.0):
            stage =  domain.quantities['stage'].get_integral()
            xmom = domain.quantities['xmomentum'].get_integral()
            ymom = domain.quantities['ymomentum'].get_integral()

            if allclose(t, 6):  #Steady state reached
                steady_xmom = domain.quantities['xmomentum'].get_integral()
                steady_ymom = domain.quantities['ymomentum'].get_integral()
                steady_stage = domain.quantities['stage'].get_integral()

            if t > 6:
                #print '%.2f %14.8f %14.8f' %(t, ymom, steady_ymom)
                assert allclose(xmom, steady_xmom)
                assert allclose(ymom, steady_ymom)
                assert allclose(stage, steady_stage)








    def test_conservation_real(self):
        """Test that momentum is conserved globally
        
        Stephen finally made a test that revealed the problem.
        This test failed with code prior to 25 July 2005
        """

        yieldstep = 0.01
        finaltime = 0.05
        min_depth = 1.0e-2


        import sys
        from os import sep; sys.path.append('..'+sep+'pyvolution')
        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary


        #Create shallow water domain
        points, vertices, boundary = rectangular(10, 10, len1=500, len2=500)
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.visualise = False
        domain.default_order = 1
        domain.minimum_allowed_height = min_depth

        # Set initial condition
        class Set_IC:
            """Set an initial condition with a constant value, for x0<x<x1
            """

            def __init__(self, x0=0.25, x1=0.5, h=1.0):
                self.x0 = x0
                self.x1 = x1
                self.h  = h

            def __call__(self, x, y):
                return self.h*((x>self.x0)&(x<self.x1))


        domain.set_quantity('stage', Set_IC(200.0,300.0,5.0))


        #Boundaries
        R = Reflective_boundary(domain)
        domain.set_boundary( {'left': R, 'right': R, 'top':R, 'bottom': R})

        ref = domain.quantities['stage'].get_integral()

        # Evolution
        for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime):
            pass
            #print 'Integral stage = ',\
            #      domain.quantities['stage'].get_integral(),\
            #      ' Time = ',domain.time


        now = domain.quantities['stage'].get_integral()

        msg = 'Stage not conserved: was %f, now %f' %(ref, now)
        assert allclose(ref, now), msg 



    def test_second_order_flat_bed_onestep(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        # Boundary conditions
        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([0.1, 0., 0.])
        domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.05):
            pass# domain.write_time()

        #Data from earlier version of pyvolution
        assert allclose(domain.min_timestep, 0.0396825396825)
        assert allclose(domain.max_timestep, 0.0396825396825)

        assert allclose(domain.quantities['stage'].centroid_values[:12],
                        [0.00171396, 0.02656103, 0.00241523, 0.02656103,
                        0.00241523, 0.02656103, 0.00241523, 0.02656103,
                        0.00241523, 0.02656103, 0.00241523, 0.0272623])

        domain.distribute_to_vertices_and_edges()
        assert allclose(domain.quantities['stage'].vertex_values[:12,0],
                        [0.0001714, 0.02656103, 0.00024152,
                        0.02656103, 0.00024152, 0.02656103,
                        0.00024152, 0.02656103, 0.00024152,
                        0.02656103, 0.00024152, 0.0272623])

        assert allclose(domain.quantities['stage'].vertex_values[:12,1],
                        [0.00315012, 0.02656103, 0.00024152, 0.02656103,
                         0.00024152, 0.02656103, 0.00024152, 0.02656103,
                         0.00024152, 0.02656103, 0.00040506, 0.0272623])

        assert allclose(domain.quantities['stage'].vertex_values[:12,2],
                        [0.00182037, 0.02656103, 0.00676264,
                         0.02656103, 0.00676264, 0.02656103,
                         0.00676264, 0.02656103, 0.00676264,
                         0.02656103, 0.0065991, 0.0272623])

        assert allclose(domain.quantities['xmomentum'].centroid_values[:12],
                        [0.00113961, 0.01302432, 0.00148672,
                         0.01302432, 0.00148672, 0.01302432,
                         0.00148672, 0.01302432, 0.00148672 ,
                         0.01302432, 0.00148672, 0.01337143])

        assert allclose(domain.quantities['ymomentum'].centroid_values[:12],
                        [-2.91240050e-004 , 1.22721531e-004,
                         -1.22721531e-004, 1.22721531e-004 ,
                         -1.22721531e-004, 1.22721531e-004,
                         -1.22721531e-004 , 1.22721531e-004,
                         -1.22721531e-004, 1.22721531e-004,
                         -1.22721531e-004, -4.57969873e-005])



    def test_second_order_flat_bed_moresteps(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary,\
             Dirichlet_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        # Boundary conditions
        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([0.1, 0., 0.])
        domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})

        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.1):
            pass

        #Data from earlier version of pyvolution
        #assert allclose(domain.min_timestep, 0.0396825396825)
        #assert allclose(domain.max_timestep, 0.0396825396825)
        #print domain.quantities['stage'].centroid_values


    def test_flatbed_first_order(self):
        from mesh_factory import rectangular
        from shallow_water import Domain,\
             Reflective_boundary, Dirichlet_boundary

        from Numeric import array

        #Create basic mesh
        N = 8
        points, vertices, boundary = rectangular(N, N)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.visualise = False
        domain.default_order=1

        # Boundary conditions
        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([0.2,0.,0.])

        domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})
        domain.check_integrity()


        #Evolution
        for t in domain.evolve(yieldstep = 0.02, finaltime = 0.5):
            pass
            #domain.write_time()

        #FIXME: These numbers were from version before 25/10
        #assert allclose(domain.min_timestep, 0.0140413643926)
        #assert allclose(domain.max_timestep, 0.0140947355753)

        for i in range(3):
            #assert allclose(domain.quantities['stage'].edge_values[:4,i],
            #                [0.10730244,0.12337617,0.11200126,0.12605666])

            assert allclose(domain.quantities['xmomentum'].edge_values[:4,i],
                            [0.07610894,0.06901572,0.07284461,0.06819712])

            #assert allclose(domain.quantities['ymomentum'].edge_values[:4,i],
            #                [-0.0060238, -0.00157404, -0.00309633, -0.0001637])

    def test_flatbed_second_order(self):
        from mesh_factory import rectangular
        from shallow_water import Domain,\
             Reflective_boundary, Dirichlet_boundary

        from Numeric import array

        #Create basic mesh
        N = 8
        points, vertices, boundary = rectangular(N, N)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.visualise = False
        domain.default_order=2
        #domain.minimum_allowed_height = 0.0 #Makes it like the 'oldstyle' balance

        # Boundary conditions
        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([0.2,0.,0.])

        domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})
        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.01, finaltime = 0.03):
            pass


        assert allclose(domain.min_timestep, 0.0210448446782)
        assert allclose(domain.max_timestep, 0.0210448446782)

        #print domain.quantities['stage'].vertex_values[:4,0]
        #print domain.quantities['xmomentum'].vertex_values[:4,0]
        #print domain.quantities['ymomentum'].vertex_values[:4,0]

        #FIXME: These numbers were from version before 25/10
        #assert allclose(domain.quantities['stage'].vertex_values[:4,0],
        #                [0.00101913,0.05352143,0.00104852,0.05354394])

        assert allclose(domain.quantities['xmomentum'].vertex_values[:4,0],
                        [ 0.00064835, 0.03685719, 0.00085073, 0.03687313])

        #assert allclose(domain.quantities['xmomentum'].vertex_values[:4,0],
        #                [0.00090581,0.03685719,0.00088303,0.03687313])

        assert allclose(domain.quantities['ymomentum'].vertex_values[:4,0],
                        [-0.00139463,0.0006156,-0.00060364,0.00061827])



    def test_flatbed_second_order_distribute(self):
        #Use real data from pyvolution 2
        #painfully setup and extracted.
        from mesh_factory import rectangular
        from shallow_water import Domain,\
             Reflective_boundary, Dirichlet_boundary

        from Numeric import array

        #Create basic mesh
        N = 8
        points, vertices, boundary = rectangular(N, N)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.visualise = False
        domain.default_order=domain.order=2

        # Boundary conditions
        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([0.2,0.,0.])

        domain.set_boundary({'left': Bd, 'right': Br, 'top': Br, 'bottom': Br})
        domain.check_integrity()



        for V in [False, True]:
            if V:
                #Set centroids as if system had been evolved
                L = zeros(2*N*N, Float)
                L[:32] = [7.21205592e-003, 5.35214298e-002, 1.00910824e-002,
                          5.35439433e-002, 1.00910824e-002, 5.35439433e-002,
                          1.00910824e-002, 5.35439433e-002, 1.00910824e-002,
                          5.35439433e-002, 1.00910824e-002, 5.35439433e-002,
                          1.00910824e-002, 5.35393928e-002, 1.02344264e-002,
                          5.59605058e-002, 0.00000000e+000, 3.31027800e-004,
                          0.00000000e+000, 4.37962142e-005, 0.00000000e+000,
                          4.37962142e-005, 0.00000000e+000, 4.37962142e-005,
                          0.00000000e+000, 4.37962142e-005, 0.00000000e+000,
                          4.37962142e-005, 0.00000000e+000, 4.37962142e-005,
                          0.00000000e+000, 5.57305948e-005]

                X = zeros(2*N*N, Float)
                X[:32] = [6.48351607e-003, 3.68571894e-002, 8.50733285e-003,
                          3.68731327e-002, 8.50733285e-003, 3.68731327e-002,
                          8.50733285e-003, 3.68731327e-002, 8.50733285e-003,
                          3.68731327e-002, 8.50733285e-003, 3.68731327e-002,
                          8.50733285e-003, 3.68693861e-002, 8.65220973e-003,
                          3.85055387e-002, 0.00000000e+000, 2.86060840e-004,
                          0.00000000e+000, 3.58905503e-005, 0.00000000e+000,
                          3.58905503e-005, 0.00000000e+000, 3.58905503e-005,
                          0.00000000e+000, 3.58905503e-005, 0.00000000e+000,
                          3.58905503e-005, 0.00000000e+000, 3.58905503e-005,
                          0.00000000e+000, 4.57662812e-005]

                Y = zeros(2*N*N, Float)
                Y[:32]=[-1.39463104e-003, 6.15600298e-004, -6.03637382e-004,
                        6.18272251e-004, -6.03637382e-004, 6.18272251e-004,
                        -6.03637382e-004, 6.18272251e-004, -6.03637382e-004,
                        6.18272251e-004, -6.03637382e-004, 6.18272251e-004,
                        -6.03637382e-004, 6.18599320e-004, -6.74622797e-004,
                        -1.48934756e-004, 0.00000000e+000, -5.35079969e-005,
                        0.00000000e+000, -2.57264987e-005, 0.00000000e+000,
                        -2.57264987e-005, 0.00000000e+000, -2.57264987e-005,
                        0.00000000e+000, -2.57264987e-005, 0.00000000e+000,
                        -2.57264987e-005, 0.00000000e+000, -2.57264987e-005,
                        0.00000000e+000, -2.57635178e-005]


                domain.set_quantity('stage', L, location='centroids')
                domain.set_quantity('xmomentum', X, location='centroids')
                domain.set_quantity('ymomentum', Y, location='centroids')

                domain.check_integrity()
            else:
                #Evolution
                for t in domain.evolve(yieldstep = 0.01, finaltime = 0.03):
                    pass
                assert allclose(domain.min_timestep, 0.0210448446782)
                assert allclose(domain.max_timestep, 0.0210448446782)


            #Centroids were correct but not vertices.
            #Hence the check of distribute below.
            assert allclose(domain.quantities['stage'].centroid_values[:4],
                            [0.00721206,0.05352143,0.01009108,0.05354394])

            assert allclose(domain.quantities['xmomentum'].centroid_values[:4],
                            [0.00648352,0.03685719,0.00850733,0.03687313])

            assert allclose(domain.quantities['ymomentum'].centroid_values[:4],
                            [-0.00139463,0.0006156,-0.00060364,0.00061827])

            #print 'C17=', domain.quantities['xmomentum'].centroid_values[17]
            #print 'C19=', domain.quantities['xmomentum'].centroid_values[19]

            #assert allclose(domain.quantities['xmomentum'].centroid_values[17],0.00028606084)
            ##print domain.quantities['xmomentum'].centroid_values[17], V
            ##print
            if not V:
                assert allclose(domain.quantities['xmomentum'].centroid_values[17], 0.0)
            else:
                assert allclose(domain.quantities['xmomentum'].centroid_values[17], 0.00028606084)

            import copy
            XX = copy.copy(domain.quantities['xmomentum'].centroid_values)
            assert allclose(domain.quantities['xmomentum'].centroid_values, XX)

            domain.distribute_to_vertices_and_edges()

            #assert allclose(domain.quantities['xmomentum'].centroid_values, XX)

            assert allclose(domain.quantities['xmomentum'].centroid_values[17],
                            0.0)


            #FIXME: These numbers were from version before 25/10
            #assert allclose(domain.quantities['stage'].vertex_values[:4,0],
            #                [0.00101913,0.05352143,0.00104852,0.05354394])

            assert allclose(domain.quantities['ymomentum'].vertex_values[:4,0],
                            [-0.00139463,0.0006156,-0.00060364,0.00061827])


            assert allclose(domain.quantities['xmomentum'].vertex_values[:4,0],
                            [0.00064835,0.03685719,0.00085073,0.03687313])


            #NB NO longer relvant:

            #This was the culprit. First triangles vertex 0 had an
            #x-momentum of 0.0064835 instead of 0.00090581 and
            #third triangle had 0.00850733 instead of 0.00088303
            #print domain.quantities['xmomentum'].vertex_values[:4,0]

            #print domain.quantities['xmomentum'].vertex_values[:4,0]
            #assert allclose(domain.quantities['xmomentum'].vertex_values[:4,0],
            #                [0.00090581,0.03685719,0.00088303,0.03687313])





    def test_bedslope_problem_first_order(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=1

        #Bed-slope and friction
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.05):
            pass# domain.write_time()

        assert allclose(domain.min_timestep, 0.050010003001)
        assert allclose(domain.max_timestep, 0.050010003001)


    def test_bedslope_problem_first_order_moresteps(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=1
        domain.beta_h = 0.0 #Use first order in h-limiter

        #Bed-slope and friction
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.5):
            pass# domain.write_time()

        #Data from earlier version of pyvolution
        #print domain.quantities['stage'].centroid_values

        assert allclose(domain.quantities['stage'].centroid_values,
                        [-0.02998628, -0.01520652, -0.03043492,
                        -0.0149132, -0.03004706, -0.01476251,
                        -0.0298215, -0.01467976, -0.02988158,
                        -0.01474662, -0.03036161, -0.01442995,
                        -0.07624583, -0.06297061, -0.07733792,
                        -0.06342237, -0.07695439, -0.06289595,
                        -0.07635559, -0.0626065, -0.07633628,
                        -0.06280072, -0.07739632, -0.06386738,
                        -0.12161738, -0.11028239, -0.1223796,
                        -0.11095953, -0.12189744, -0.11048616,
                        -0.12074535, -0.10987605, -0.12014311,
                        -0.10976691, -0.12096859, -0.11087692,
                        -0.16868259, -0.15868061, -0.16801135,
                        -0.1588003, -0.16674343, -0.15813323,
                        -0.16457595, -0.15693826, -0.16281096,
                        -0.15585154, -0.16283873, -0.15540068,
                        -0.17450362, -0.19919913, -0.18062882,
                        -0.19764131, -0.17783111, -0.19407213,
                        -0.1736915, -0.19053624, -0.17228678,
                        -0.19105634, -0.17920133, -0.1968828,
                        -0.14244395, -0.14604641, -0.14473537,
                        -0.1506107, -0.14510055, -0.14919522,
                        -0.14175896, -0.14560798, -0.13911658,
                        -0.14439383, -0.13924047, -0.14829043])


    def test_bedslope_problem_second_order_one_step(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        assert allclose(domain.quantities['stage'].centroid_values,
                        [0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963])


        #print domain.quantities['stage'].extrapolate_second_order()
        #domain.distribute_to_vertices_and_edges()
        #print domain.quantities['stage'].vertex_values[:,0]

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.05):
            #domain.write_time()
            pass


        #print domain.quantities['stage'].centroid_values
        assert allclose(domain.quantities['stage'].centroid_values,
                 [0.01290985, 0.02356019, 0.01619096, 0.02356019, 0.01619096,
                  0.02356019, 0.01619096, 0.02356019, 0.01619096, 0.02356019,
                  0.01619096, 0.0268413, -0.04411074, -0.0248011, -0.04186556,
                  -0.0248011, -0.04186556, -0.0248011, -0.04186556, -0.0248011,
                  -0.04186556, -0.0248011, -0.04186556, -0.02255593,
                  -0.09966629, -0.08035666, -0.09742112, -0.08035666,
                  -0.09742112, -0.08035666, -0.09742112, -0.08035666,
                  -0.09742112, -0.08035666, -0.09742112, -0.07811149,
                  -0.15522185, -0.13591222, -0.15297667, -0.13591222,
                  -0.15297667, -0.13591222, -0.15297667, -0.13591222,
                  -0.15297667, -0.13591222, -0.15297667, -0.13366704,
                  -0.2107774, -0.19146777, -0.20853223, -0.19146777,
                  -0.20853223, -0.19146777, -0.20853223, -0.19146777,
                  -0.20853223, -0.19146777, -0.20853223, -0.1892226,
                  -0.26120669, -0.24776246, -0.25865535, -0.24776246,
                  -0.25865535, -0.24776246, -0.25865535, -0.24776246,
                  -0.25865535, -0.24776246, -0.25865535, -0.24521113])



    def test_bedslope_problem_second_order_two_steps(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.0 #Use first order in h-limiter

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        assert allclose(domain.quantities['stage'].centroid_values,
                        [0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963])


        #print domain.quantities['stage'].extrapolate_second_order()
        #domain.distribute_to_vertices_and_edges()
        #print domain.quantities['stage'].vertex_values[:,0]

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.1):
            pass


        #Data from earlier version of pyvolution ft=0.1
        assert allclose(domain.min_timestep, 0.0376895634803)
        assert allclose(domain.max_timestep, 0.0415635655309)


        assert allclose(domain.quantities['stage'].centroid_values,
                        [0.00855788, 0.01575204, 0.00994606, 0.01717072,
                         0.01005985, 0.01716362, 0.01005985, 0.01716299,
                         0.01007098, 0.01736248, 0.01216452, 0.02026776,
                         -0.04462374, -0.02479045, -0.04199789, -0.0229465,
                         -0.04184033, -0.02295693, -0.04184013, -0.02295675,
                         -0.04184486, -0.0228168, -0.04028876, -0.02036486,
                         -0.10029444, -0.08170809, -0.09772846, -0.08021704,
                         -0.09760006, -0.08022143, -0.09759984, -0.08022124,
                         -0.09760261, -0.08008893, -0.09603914, -0.07758209,
                         -0.15584152, -0.13723138, -0.15327266, -0.13572906,
                         -0.15314427, -0.13573349, -0.15314405, -0.13573331,
                         -0.15314679, -0.13560104, -0.15158523, -0.13310701,
                         -0.21208605, -0.19283913, -0.20955631, -0.19134189,
                         -0.20942821, -0.19134598, -0.20942799, -0.1913458,
                         -0.20943005, -0.19120952, -0.20781177, -0.18869401,
                         -0.25384082, -0.2463294, -0.25047649, -0.24464654,
                         -0.25031159, -0.24464253, -0.25031112, -0.24464253,
                         -0.25031463, -0.24454764, -0.24885323, -0.24286438])




    def test_bedslope_problem_second_order_two_yieldsteps(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.0 #Use first order in h-limiter

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        assert allclose(domain.quantities['stage'].centroid_values,
                        [0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963])


        #print domain.quantities['stage'].extrapolate_second_order()
        #domain.distribute_to_vertices_and_edges()
        #print domain.quantities['stage'].vertex_values[:,0]

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.1):   #0.05??
            #domain.write_time()
            pass



        assert allclose(domain.quantities['stage'].centroid_values,
                 [0.00855788, 0.01575204, 0.00994606, 0.01717072, 0.01005985,
                  0.01716362, 0.01005985, 0.01716299, 0.01007098, 0.01736248,
                  0.01216452, 0.02026776, -0.04462374, -0.02479045, -0.04199789,
                  -0.0229465, -0.04184033, -0.02295693, -0.04184013,
                  -0.02295675, -0.04184486, -0.0228168, -0.04028876,
                  -0.02036486, -0.10029444, -0.08170809, -0.09772846,
                  -0.08021704, -0.09760006, -0.08022143, -0.09759984,
                  -0.08022124, -0.09760261, -0.08008893, -0.09603914,
                  -0.07758209, -0.15584152, -0.13723138, -0.15327266,
                  -0.13572906, -0.15314427, -0.13573349, -0.15314405,
                  -0.13573331, -0.15314679, -0.13560104, -0.15158523,
                  -0.13310701, -0.21208605, -0.19283913, -0.20955631,
                  -0.19134189, -0.20942821, -0.19134598, -0.20942799,
                  -0.1913458, -0.20943005, -0.19120952, -0.20781177,
                  -0.18869401, -0.25384082, -0.2463294, -0.25047649,
                  -0.24464654, -0.25031159, -0.24464253, -0.25031112,
                  -0.24464253, -0.25031463, -0.24454764, -0.24885323,
                  -0.24286438])



    def test_bedslope_problem_second_order_more_steps(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(6, 6)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.0 #Use first order in h-limiter

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        assert allclose(domain.quantities['stage'].centroid_values,
                        [0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        0.01296296, 0.03148148, 0.01296296,
                        0.03148148, 0.01296296, 0.03148148,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.04259259, -0.02407407, -0.04259259,
                        -0.02407407, -0.04259259, -0.02407407,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.09814815, -0.07962963, -0.09814815,
                        -0.07962963, -0.09814815, -0.07962963,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.1537037 , -0.13518519, -0.1537037,
                        -0.13518519, -0.1537037, -0.13518519,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.20925926, -0.19074074, -0.20925926,
                        -0.19074074, -0.20925926, -0.19074074,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963,
                        -0.26481481, -0.2462963, -0.26481481,
                        -0.2462963, -0.26481481, -0.2462963])


        #print domain.quantities['stage'].extrapolate_second_order()
        #domain.distribute_to_vertices_and_edges()
        #print domain.quantities['stage'].vertex_values[:,0]

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.5):
            pass


        assert allclose(domain.quantities['stage'].centroid_values,
     [-0.02907028, -0.01475478, -0.02973417, -0.01447186, -0.02932665, -0.01428285,
      -0.02901975, -0.0141361,  -0.02898816, -0.01418135, -0.02961409, -0.01403487,
      -0.07597998, -0.06252591, -0.07664854, -0.06312532, -0.07638287, -0.06265139,
      -0.07571145, -0.06235231, -0.0756817,  -0.06245309, -0.07652292, -0.06289946,
      -0.12367464, -0.11088981, -0.12237277, -0.11115338, -0.1218934,  -0.1107174,
      -0.12081485, -0.11000491, -0.12038451, -0.11010335, -0.12102113, -0.11012105,
      -0.16909116, -0.15831543, -0.16730214, -0.15786249, -0.1665493,  -0.15697919,
      -0.16496618, -0.15559852, -0.16338679, -0.15509088, -0.16364092, -0.15424423,
      -0.18771107, -0.19903904, -0.18903759, -0.19858437, -0.18701552, -0.19697797,
      -0.1833593,  -0.19505871, -0.1818806,  -0.19418042, -0.18586159, -0.19576946,
      -0.13986873, -0.14170053, -0.14132188, -0.14560674, -0.14095617, -0.14373292,
      -0.13785933, -0.14033364, -0.13592955, -0.13936356, -0.13596008, -0.14216296])

        assert allclose(domain.quantities['xmomentum'].centroid_values,
     [ 0.00831121,  0.00317948,  0.00731797,  0.00334939,  0.00764717,  0.00348053,
       0.00788729,  0.00356522,  0.00780649,  0.00341919,  0.00693525,  0.00310375,
       0.02166196,  0.01421475,  0.02017737,  0.01316839,  0.02037015,  0.01368659,
       0.02106,     0.01399161,  0.02074514,  0.01354935,  0.01887407,  0.0123113,
       0.03775083,  0.02855197,  0.03689337,  0.02759782,  0.03732848,  0.02812072,
       0.03872545,  0.02913348,  0.03880939,  0.02803804,  0.03546499,  0.0260039,
       0.0632131,   0.04730634,  0.0576324,   0.04592336,  0.05790921,  0.04690514,
       0.05986467,  0.04871165,  0.06170068,  0.04811572,  0.05657041,  0.04416292,
       0.08489642,  0.07188097,  0.07835261,  0.06843406,  0.07986412,  0.0698247,
       0.08201071,  0.07216756,  0.08378418,  0.07273624,  0.080399,    0.06645841,
       0.01631548,  0.04691608,  0.0206632,   0.044409,    0.02115518,  0.04560305,
       0.02160608,  0.04663725,  0.02174734,  0.04795559,  0.02281427,  0.05667111])


        assert allclose(domain.quantities['ymomentum'].centroid_values,
     [ 1.45876601e-004, -3.24627393e-004, -1.57572719e-004, -2.92790187e-004,
      -9.90988382e-005, -3.06677335e-004, -1.62493106e-004, -3.71310004e-004,
      -1.99445058e-004, -3.28493467e-004,  6.68217349e-005, -8.42042805e-006,
       5.05093371e-004, -1.42842214e-004, -6.81454718e-005, -5.02084057e-004,
      -8.50583861e-005, -4.65443981e-004, -1.96406564e-004, -5.88889562e-004,
      -2.70160173e-004, -5.35485454e-004,  2.60780997e-004,  3.12145471e-005,
       5.16189608e-004,  1.07069062e-004,  9.29989252e-005, -3.71211119e-004,
       1.16350246e-004, -3.82407830e-004, -1.62077969e-004, -6.30906636e-004,
      -4.74025708e-004, -6.94463009e-004,  6.15092843e-005,  2.22106820e-004,
      -6.29589294e-004,  2.43611937e-004, -5.88125094e-004, -6.94293192e-005,
      -4.17914641e-004,  6.64609019e-005, -7.68334577e-004, -3.40232101e-004,
      -1.67424308e-003, -7.39485066e-004, -1.59966988e-003,  5.68262838e-005,
      -1.48470633e-003, -1.84554882e-003, -2.27200099e-003, -1.67506848e-003,
      -1.95610258e-003, -1.47638801e-003, -1.73779477e-003, -1.85498791e-003,
      -2.01357843e-003, -2.17675471e-003, -1.65783870e-003, -1.15818681e-003,
      -1.18663036e-003, -2.94229849e-003, -3.59309018e-003, -5.13496584e-003,
      -6.17359400e-003, -5.98761937e-003, -6.00540116e-003, -5.01121966e-003,
      -4.50964850e-003, -3.06319963e-003,  6.08950810e-004, -4.79537921e-004])




    def test_temp_play(self):

        from mesh_factory import rectangular
        from shallow_water import Domain, Reflective_boundary, Constant_height
        from Numeric import array

        #Create basic mesh
        points, vertices, boundary = rectangular(5, 5)

        #Create shallow water domain
        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.default_order=2
        domain.beta_h = 0.0 #Use first order in h-limiter

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        def x_slope(x, y):
            return -x/3

        domain.set_quantity('elevation', x_slope)

        # Boundary conditions
        Br = Reflective_boundary(domain)
        domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br})

        #Initial condition
        domain.set_quantity('stage', Constant_height(x_slope, 0.05))
        domain.check_integrity()

        #Evolution
        for t in domain.evolve(yieldstep = 0.05, finaltime = 0.1):
            pass

        assert allclose(domain.quantities['stage'].centroid_values[:4],
                        [0.00206836, 0.01296714, 0.00363415, 0.01438924])
        assert allclose(domain.quantities['xmomentum'].centroid_values[:4],
                        [0.01360154, 0.00671133, 0.01264578, 0.00648503])
        assert allclose(domain.quantities['ymomentum'].centroid_values[:4],
                        [-1.19201077e-003, -7.23647546e-004,
                        -6.39083123e-005, 6.29815168e-005])


    def test_complex_bed(self):
        #No friction is tested here

        from shallow_water import Domain, Reflective_boundary, Dirichlet_boundary,\
             Transmissive_boundary, Time_boundary,\
             Weir_simple as Weir, Constant_height

        from mesh_factory import rectangular
        from Numeric import array

        N = 12
        points, vertices, boundary = rectangular(N, N/2, len1=1.2,len2=0.6,
                                                 origin=(-0.07, 0))


        domain = Domain(points, vertices, boundary)
        domain.smooth = False
        domain.visualise = False
        domain.default_order=2


        inflow_stage = 0.1
        Z = Weir(inflow_stage)
        domain.set_quantity('elevation', Z)

        Br = Reflective_boundary(domain)
        Bd = Dirichlet_boundary([inflow_stage, 0.0, 0.0])
        domain.set_boundary({'left': Bd, 'right': Br, 'bottom': Br, 'top': Br})

        domain.set_quantity('stage', Constant_height(Z, 0.))

        for t in domain.evolve(yieldstep = 0.02, finaltime = 0.2):
            pass


        #print domain.quantities['stage'].centroid_values

        #FIXME: These numbers were from version before 25/10
        #assert allclose(domain.quantities['stage'].centroid_values,
# [3.95822638e-002,  5.61022588e-002,  4.66437868e-002,  5.73081011e-002,
#  4.72394613e-002,  5.74684939e-002,  4.74309483e-002,  5.77458084e-002,
#  4.80628177e-002,  5.85656225e-002,  4.90498542e-002,  6.02609831e-002,
#  1.18470315e-002,  1.75136443e-002,  1.18035266e-002,  2.15565695e-002,
#  1.31620268e-002,  2.14351640e-002,  1.32351076e-002,  2.15450687e-002,
#  1.36414028e-002,  2.24274619e-002,  1.51689511e-002,  2.21789655e-002,
# -7.54337535e-003, -6.86362021e-004, -7.74146760e-003, -1.83756530e-003,
# -8.16773628e-003, -4.49916813e-004, -8.08202599e-003, -3.91118720e-004,
# -8.10292716e-003, -3.88584984e-004, -7.35226124e-003,  2.73985295e-004,
#  1.86166683e-001,  8.74070369e-002,  1.86166712e-001,  8.74035875e-002,
#  6.11666935e-002, -3.76173225e-002, -6.38333276e-002, -3.76147365e-002,
#  6.11666725e-002,  8.73846774e-002,  1.86166697e-001,  8.74171550e-002,
# -4.83333333e-002,  1.18333333e-001, -4.83333333e-002,  1.18333333e-001,
# -4.83333333e-002, -6.66666667e-003, -1.73333333e-001, -1.31666667e-001,
# -1.73333333e-001, -6.66666667e-003, -4.83333333e-002,  1.18333333e-001,
# -2.48333333e-001, -2.31666667e-001, -2.48333333e-001, -2.31666667e-001,
# -2.48333333e-001, -2.31666667e-001, -2.48333333e-001, -2.31666667e-001,
# -2.48333333e-001, -2.31666667e-001, -2.48333333e-001, -2.31666667e-001,
# -4.65000000e-001, -3.65000000e-001, -4.65000000e-001, -3.65000000e-001,
# -4.65000000e-001, -3.65000000e-001, -4.65000000e-001, -3.65000000e-001,
# -4.65000000e-001, -3.65000000e-001, -4.65000000e-001, -3.65000000e-001,
# -5.98333333e-001, -5.81666667e-001, -5.98333333e-001, -5.81666667e-001,
# -5.98333333e-001, -5.81666667e-001, -5.98333333e-001, -5.81666667e-001,
# -5.98333333e-001, -5.81666667e-001, -5.98333333e-001, -5.81666667e-001,
# -6.48333333e-001, -6.31666667e-001, -6.48333333e-001, -6.31666667e-001,
# -6.48333333e-001, -6.31666667e-001, -6.48333333e-001, -6.31666667e-001,
# -6.48333333e-001, -6.31666667e-001, -6.48333333e-001, -6.31666667e-001,
# -5.31666667e-001, -5.98333333e-001, -5.31666667e-001, -5.98333333e-001,
# -5.31666667e-001, -5.98333333e-001, -5.31666667e-001, -5.98333333e-001,
# -5.31666667e-001, -5.98333333e-001, -5.31666667e-001, -5.98333333e-001,
# -4.98333333e-001, -4.81666667e-001, -4.98333333e-001, -4.81666667e-001,
# -4.98333333e-001, -4.81666667e-001, -4.98333333e-001, -4.81666667e-001,
# -4.98333333e-001, -4.81666667e-001, -4.98333333e-001, -4.81666667e-001,
# -5.48333333e-001, -5.31666667e-001, -5.48333333e-001, -5.31666667e-001,
# -5.48333333e-001, -5.31666667e-001, -5.48333333e-001, -5.31666667e-001,
# -5.48333333e-001, -5.31666667e-001, -5.48333333e-001, -5.31666667e-001])



    def test_spatio_temporal_boundary(self):
        """Test that boundary values can be read from file and interpolated
        in both time and space.

        Verify that the same steady state solution is arrived at and that
        time interpolation works.

        The full solution history is not exactly the same as
        file boundary must read and interpolate from *smoothed* version
        as stored in sww.
        """
        import time

        #Create sww file of simple propagation from left to right
        #through rectangular domain

        from mesh_factory import rectangular

        #Create basic mesh
        points, vertices, boundary = rectangular(3, 3)

        #Create shallow water domain
        domain1 = Domain(points, vertices, boundary)

        from util import mean
        domain1.reduction = mean
        domain1.smooth = False  #Exact result

        domain1.default_order = 2
        domain1.store = True
        domain1.set_datadir('.')
        domain1.set_name('spatio_temporal_boundary_source' + str(time.time()))

        #FIXME: This is extremely important!
        #How can we test if they weren't stored?
        domain1.quantities_to_be_stored = ['stage', 'xmomentum', 'ymomentum']


        #Bed-slope and friction at vertices (and interpolated elsewhere)
        domain1.set_quantity('elevation', 0)
        domain1.set_quantity('friction', 0)

        # Boundary conditions
        Br = Reflective_boundary(domain1)
        Bd = Dirichlet_boundary([0.3,0,0])
        domain1.set_boundary({'left': Bd, 'top': Bd, 'right': Br, 'bottom': Br})
        #Initial condition
        domain1.set_quantity('stage', 0)
        domain1.check_integrity()

        finaltime = 5
        #Evolution  (full domain - large steps)
        for t in domain1.evolve(yieldstep = 0.671, finaltime = finaltime):
            pass
            #domain1.write_time()

        cv1 = domain1.quantities['stage'].centroid_values


        #Create an triangle shaped domain (reusing coordinates from domain 1),
        #formed from the lower and right hand  boundaries and
        #the sw-ne diagonal
        #from domain 1. Call it domain2

        points = [ [0,0], [1.0/3,0], [1.0/3,1.0/3],
                   [2.0/3,0], [2.0/3,1.0/3], [2.0/3,2.0/3],
                   [1,0], [1,1.0/3], [1,2.0/3], [1,1]]

        vertices = [ [1,2,0], [3,4,1], [2,1,4], [4,5,2],
                     [6,7,3], [4,3,7], [7,8,4], [5,4,8], [8,9,5]]

        boundary = { (0,1):'bottom', (1,1):'bottom', (4,1): 'bottom',
                     (4,2):'right', (6,2):'right', (8,2):'right',
                     (0,0):'diagonal', (3,0):'diagonal', (8,0):'diagonal'}

        domain2 = Domain(points, vertices, boundary)

        domain2.reduction = domain1.reduction
        domain2.smooth = False
        domain2.default_order = 2

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        domain2.set_quantity('elevation', 0)
        domain2.set_quantity('friction', 0)
        domain2.set_quantity('stage', 0)

        # Boundary conditions
        Br = Reflective_boundary(domain2)
        Bf = Spatio_temporal_boundary(domain1.filename + '.' + domain1.format,
                                      domain2)
        domain2.set_boundary({'right':Br, 'bottom':Br, 'diagonal':Bf})
        domain2.check_integrity()



        #Evolution (small steps)
        for t in domain2.evolve(yieldstep = 0.0711, finaltime = finaltime):
            pass


        #Use output from domain1 as spatio-temporal boundary for domain2
        #and verify that results at right hand side are close.

        cv2 = domain2.quantities['stage'].centroid_values

        #print take(cv1, (12,14,16))  #Right
        #print take(cv2, (4,6,8))
        #print take(cv1, (0,6,12))  #Bottom
        #print take(cv2, (0,1,4))
        #print take(cv1, (0,8,16))  #Diag
        #print take(cv2, (0,3,8))

        assert allclose( take(cv1, (0,8,16)), take(cv2, (0,3,8))) #Diag
        assert allclose( take(cv1, (0,6,12)), take(cv2, (0,1,4))) #Bottom
        assert allclose( take(cv1, (12,14,16)), take(cv2, (4,6,8))) #RHS

        #Cleanup
        os.remove(domain1.filename + '.' + domain1.format)



    def test_spatio_temporal_boundary_2(self):
        """Test that boundary values can be read from file and interpolated
        in both time and space.
        This is a more basic test, verifying that boundary object
        produces the expected results


        """
        import time

        #Create sww file of simple propagation from left to right
        #through rectangular domain

        from mesh_factory import rectangular

        #Create basic mesh
        points, vertices, boundary = rectangular(3, 3)

        #Create shallow water domain
        domain1 = Domain(points, vertices, boundary)

        from util import mean
        domain1.reduction = mean
        domain1.smooth = True #To mimic MOST output

        domain1.default_order = 2
        domain1.store = True
        domain1.set_datadir('.')
        domain1.set_name('spatio_temporal_boundary_source' + str(time.time()))

        #FIXME: This is extremely important!
        #How can we test if they weren't stored?
        domain1.quantities_to_be_stored = ['stage', 'xmomentum', 'ymomentum']


        #Bed-slope and friction at vertices (and interpolated elsewhere)
        domain1.set_quantity('elevation', 0)
        domain1.set_quantity('friction', 0)

        # Boundary conditions
        Br = Reflective_boundary(domain1)
        Bd = Dirichlet_boundary([0.3,0,0])
        domain1.set_boundary({'left': Bd, 'top': Bd, 'right': Br, 'bottom': Br})
        #Initial condition
        domain1.set_quantity('stage', 0)
        domain1.check_integrity()

        finaltime = 5
        #Evolution  (full domain - large steps)
        for t in domain1.evolve(yieldstep = 1, finaltime = finaltime):
            pass
            #domain1.write_time()


        #Create an triangle shaped domain (coinciding with some
        #coordinates from domain 1),
        #formed from the lower and right hand  boundaries and
        #the sw-ne diagonal
        #from domain 1. Call it domain2

        points = [ [0,0], [1.0/3,0], [1.0/3,1.0/3],
                   [2.0/3,0], [2.0/3,1.0/3], [2.0/3,2.0/3],
                   [1,0], [1,1.0/3], [1,2.0/3], [1,1]]

        vertices = [ [1,2,0],
                     [3,4,1], [2,1,4], [4,5,2],
                     [6,7,3], [4,3,7], [7,8,4], [5,4,8], [8,9,5]]

        boundary = { (0,1):'bottom', (1,1):'bottom', (4,1): 'bottom',
                     (4,2):'right', (6,2):'right', (8,2):'right',
                     (0,0):'diagonal', (3,0):'diagonal', (8,0):'diagonal'}

        domain2 = Domain(points, vertices, boundary)

        domain2.reduction = domain1.reduction
        domain2.smooth = False
        domain2.default_order = 2

        #Bed-slope and friction at vertices (and interpolated elsewhere)
        domain2.set_quantity('elevation', 0)
        domain2.set_quantity('friction', 0)
        domain2.set_quantity('stage', 0)


        #Read results for specific timesteps t=1 and t=2
        from Scientific.IO.NetCDF import NetCDFFile
        fid = NetCDFFile(domain1.filename + '.' + domain1.format)

        x = fid.variables['x'][:]
        y = fid.variables['y'][:]
        s1 = fid.variables['stage'][1,:]
        s2 = fid.variables['stage'][2,:]
        fid.close()

        from Numeric import take, reshape, concatenate
        shp = (len(x), 1)
        points = concatenate( (reshape(x, shp), reshape(y, shp)), axis=1)
        #The diagonal points of domain 1 are 0, 5, 10, 15

        #print points[0], points[5], points[10], points[15]
        assert allclose( take(points, [0,5,10,15]),
                         [[0,0], [1.0/3, 1.0/3], [2.0/3, 2.0/3], [1,1]])


        # Boundary conditions
        Br = Reflective_boundary(domain2)
        Bf = Spatio_temporal_boundary(domain1.filename + '.' + domain1.format,
                                      domain2)
        domain2.set_boundary({'right':Br, 'bottom':Br, 'diagonal':Bf})
        domain2.check_integrity()

        #Test that interpolation points are the mid points of the all boundary
        #segments

        boundary_midpoints = [[1.0/6, 0], [1.0/2, 0], [5.0/6,0],
                              [1.0, 1.0/6], [1.0, 1.0/2], [1.0, 5.0/6],
                              [1.0/6, 1.0/6], [0.5, 0.5], [5.0/6, 5.0/6]]

        boundary_midpoints.sort()
        R = Bf.F.interpolation_points.tolist()
        R.sort()
        assert allclose(boundary_midpoints, R)

        #Check spatially interpolated output at time == 1
        domain2.time = 1

        #First diagonal midpoint
        R0 = Bf.evaluate(0,0)
        assert allclose(R0[0], (s1[0] + s1[5])/2)

        #Second diagonal midpoint
        R0 = Bf.evaluate(3,0)
        assert allclose(R0[0], (s1[5] + s1[10])/2)

        #First diagonal midpoint
        R0 = Bf.evaluate(8,0)
        assert allclose(R0[0], (s1[10] + s1[15])/2)

        #Check spatially interpolated output at time == 2
        domain2.time = 2

        #First diagonal midpoint
        R0 = Bf.evaluate(0,0)
        assert allclose(R0[0], (s2[0] + s2[5])/2)

        #Second diagonal midpoint
        R0 = Bf.evaluate(3,0)
        assert allclose(R0[0], (s2[5] + s2[10])/2)

        #First diagonal midpoint
        R0 = Bf.evaluate(8,0)
        assert allclose(R0[0], (s2[10] + s2[15])/2)


        #Now check temporal interpolation

        domain2.time = 1 + 2.0/3

        #First diagonal midpoint
        R0 = Bf.evaluate(0,0)
        assert allclose(R0[0], ((s1[0] + s1[5])/2 + 2.0*(s2[0] + s2[5])/2)/3)

        #Second diagonal midpoint
        R0 = Bf.evaluate(3,0)
        assert allclose(R0[0], ((s1[5] + s1[10])/2 + 2.0*(s2[5] + s2[10])/2)/3)

        #First diagonal midpoint
        R0 = Bf.evaluate(8,0)
        assert allclose(R0[0], ((s1[10] + s1[15])/2 + 2.0*(s2[10] + s2[15])/2)/3)



        #Cleanup
        os.remove(domain1.filename + '.' + domain1.format)


        #-------------------------------------------------------------
if __name__ == "__main__":
    suite = unittest.makeSuite(Test_Shallow_Water,'test')
    runner = unittest.TextTestRunner()
    runner.run(suite)