def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
gridIt = lambda h: [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
gridIt = lambda h: [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
class BasicCurvTests(unittest.TestCase):
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
def gridIt(h):
return [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
def test_area_3D(self):
test_area = np.array([
1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1,
1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2,
2, 2, 1, 1, 1, 2, 2, 2
])
self.assertTrue(np.all(self.Curv3.area == test_area))
def test_vol_3D(self):
test_vol = np.array([1, 1, 1, 2, 2, 2, 4, 4, 4, 8, 8, 8])
np.testing.assert_almost_equal(self.Curv3.vol, test_vol)
self.assertTrue(True) # Pass if you get past the assertion.
def test_vol_2D(self):
test_vol = np.array([1, 1, 1, 2, 2, 2])
t1 = np.all(self.Curv2.vol == test_vol)
self.assertTrue(t1)
def test_edge_3D(self):
test_edge = np.array([
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1,
1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4
])
t1 = np.all(self.Curv3.edge == test_edge)
self.assertTrue(t1)
def test_edge_2D(self):
test_edge = np.array(
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2])
t1 = np.all(self.Curv2.edge == test_edge)
self.assertTrue(t1)
def test_tangents(self):
T = self.Curv2.tangents
self.assertTrue(
np.all(
self.Curv2.r(T, 'E', 'Ex', 'V')[0] == np.ones(self.Curv2.nEx)))
self.assertTrue(
np.all(
self.Curv2.r(T, 'E', 'Ex', 'V')[1] == np.zeros(
self.Curv2.nEx)))
self.assertTrue(
np.all(
self.Curv2.r(T, 'E', 'Ey', 'V')[0] == np.zeros(
self.Curv2.nEy)))
self.assertTrue(
np.all(
self.Curv2.r(T, 'E', 'Ey', 'V')[1] == np.ones(self.Curv2.nEy)))
T = self.Curv3.tangents
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ex', 'V')[0] == np.ones(self.Curv3.nEx)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ex', 'V')[1] == np.zeros(
self.Curv3.nEx)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ex', 'V')[2] == np.zeros(
self.Curv3.nEx)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ey', 'V')[0] == np.zeros(
self.Curv3.nEy)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ey', 'V')[1] == np.ones(self.Curv3.nEy)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ey', 'V')[2] == np.zeros(
self.Curv3.nEy)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ez', 'V')[0] == np.zeros(
self.Curv3.nEz)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ez', 'V')[1] == np.zeros(
self.Curv3.nEz)))
self.assertTrue(
np.all(
self.Curv3.r(T, 'E', 'Ez', 'V')[2] == np.ones(self.Curv3.nEz)))
def test_normals(self):
N = self.Curv2.normals
self.assertTrue(
np.all(
self.Curv2.r(N, 'F', 'Fx', 'V')[0] == np.ones(self.Curv2.nFx)))
self.assertTrue(
np.all(
self.Curv2.r(N, 'F', 'Fx', 'V')[1] == np.zeros(
self.Curv2.nFx)))
self.assertTrue(
np.all(
self.Curv2.r(N, 'F', 'Fy', 'V')[0] == np.zeros(
self.Curv2.nFy)))
self.assertTrue(
np.all(
self.Curv2.r(N, 'F', 'Fy', 'V')[1] == np.ones(self.Curv2.nFy)))
N = self.Curv3.normals
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fx', 'V')[0] == np.ones(self.Curv3.nFx)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fx', 'V')[1] == np.zeros(
self.Curv3.nFx)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fx', 'V')[2] == np.zeros(
self.Curv3.nFx)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fy', 'V')[0] == np.zeros(
self.Curv3.nFy)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fy', 'V')[1] == np.ones(self.Curv3.nFy)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fy', 'V')[2] == np.zeros(
self.Curv3.nFy)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fz', 'V')[0] == np.zeros(
self.Curv3.nFz)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fz', 'V')[1] == np.zeros(
self.Curv3.nFz)))
self.assertTrue(
np.all(
self.Curv3.r(N, 'F', 'Fz', 'V')[2] == np.ones(self.Curv3.nFz)))
def test_grid(self):
self.assertTrue(np.all(self.Curv2.gridCC == self.TM2.gridCC))
self.assertTrue(np.all(self.Curv2.gridN == self.TM2.gridN))
self.assertTrue(np.all(self.Curv2.gridFx == self.TM2.gridFx))
self.assertTrue(np.all(self.Curv2.gridFy == self.TM2.gridFy))
self.assertTrue(np.all(self.Curv2.gridEx == self.TM2.gridEx))
self.assertTrue(np.all(self.Curv2.gridEy == self.TM2.gridEy))
self.assertTrue(np.all(self.Curv3.gridCC == self.TM3.gridCC))
self.assertTrue(np.all(self.Curv3.gridN == self.TM3.gridN))
self.assertTrue(np.all(self.Curv3.gridFx == self.TM3.gridFx))
self.assertTrue(np.all(self.Curv3.gridFy == self.TM3.gridFy))
self.assertTrue(np.all(self.Curv3.gridFz == self.TM3.gridFz))
self.assertTrue(np.all(self.Curv3.gridEx == self.TM3.gridEx))
self.assertTrue(np.all(self.Curv3.gridEy == self.TM3.gridEy))
self.assertTrue(np.all(self.Curv3.gridEz == self.TM3.gridEz))
class BasicCurvTests(unittest.TestCase):
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
gridIt = lambda h: [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
def test_area_3D(self):
test_area = np.array([1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2])
self.assertTrue(np.all(self.Curv3.area == test_area))
def test_vol_3D(self):
test_vol = np.array([1, 1, 1, 2, 2, 2, 4, 4, 4, 8, 8, 8])
np.testing.assert_almost_equal(self.Curv3.vol, test_vol)
self.assertTrue(True) # Pass if you get past the assertion.
def test_vol_2D(self):
test_vol = np.array([1, 1, 1, 2, 2, 2])
t1 = np.all(self.Curv2.vol == test_vol)
self.assertTrue(t1)
def test_edge_3D(self):
test_edge = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
t1 = np.all(self.Curv3.edge == test_edge)
self.assertTrue(t1)
def test_edge_2D(self):
test_edge = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2])
t1 = np.all(self.Curv2.edge == test_edge)
self.assertTrue(t1)
def test_tangents(self):
T = self.Curv2.tangents
self.assertTrue(np.all(self.Curv2.r(T, 'E', 'Ex', 'V')[0] == np.ones(self.Curv2.nEx)))
self.assertTrue(np.all(self.Curv2.r(T, 'E', 'Ex', 'V')[1] == np.zeros(self.Curv2.nEx)))
self.assertTrue(np.all(self.Curv2.r(T, 'E', 'Ey', 'V')[0] == np.zeros(self.Curv2.nEy)))
self.assertTrue(np.all(self.Curv2.r(T, 'E', 'Ey', 'V')[1] == np.ones(self.Curv2.nEy)))
T = self.Curv3.tangents
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ex', 'V')[0] == np.ones(self.Curv3.nEx)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ex', 'V')[1] == np.zeros(self.Curv3.nEx)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ex', 'V')[2] == np.zeros(self.Curv3.nEx)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ey', 'V')[0] == np.zeros(self.Curv3.nEy)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ey', 'V')[1] == np.ones(self.Curv3.nEy)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ey', 'V')[2] == np.zeros(self.Curv3.nEy)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ez', 'V')[0] == np.zeros(self.Curv3.nEz)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ez', 'V')[1] == np.zeros(self.Curv3.nEz)))
self.assertTrue(np.all(self.Curv3.r(T, 'E', 'Ez', 'V')[2] == np.ones(self.Curv3.nEz)))
def test_normals(self):
N = self.Curv2.normals
self.assertTrue(np.all(self.Curv2.r(N, 'F', 'Fx', 'V')[0] == np.ones(self.Curv2.nFx)))
self.assertTrue(np.all(self.Curv2.r(N, 'F', 'Fx', 'V')[1] == np.zeros(self.Curv2.nFx)))
self.assertTrue(np.all(self.Curv2.r(N, 'F', 'Fy', 'V')[0] == np.zeros(self.Curv2.nFy)))
self.assertTrue(np.all(self.Curv2.r(N, 'F', 'Fy', 'V')[1] == np.ones(self.Curv2.nFy)))
N = self.Curv3.normals
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fx', 'V')[0] == np.ones(self.Curv3.nFx)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fx', 'V')[1] == np.zeros(self.Curv3.nFx)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fx', 'V')[2] == np.zeros(self.Curv3.nFx)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fy', 'V')[0] == np.zeros(self.Curv3.nFy)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fy', 'V')[1] == np.ones(self.Curv3.nFy)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fy', 'V')[2] == np.zeros(self.Curv3.nFy)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fz', 'V')[0] == np.zeros(self.Curv3.nFz)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fz', 'V')[1] == np.zeros(self.Curv3.nFz)))
self.assertTrue(np.all(self.Curv3.r(N, 'F', 'Fz', 'V')[2] == np.ones(self.Curv3.nFz)))
def test_grid(self):
self.assertTrue(np.all(self.Curv2.gridCC == self.TM2.gridCC))
self.assertTrue(np.all(self.Curv2.gridN == self.TM2.gridN))
self.assertTrue(np.all(self.Curv2.gridFx == self.TM2.gridFx))
self.assertTrue(np.all(self.Curv2.gridFy == self.TM2.gridFy))
self.assertTrue(np.all(self.Curv2.gridEx == self.TM2.gridEx))
self.assertTrue(np.all(self.Curv2.gridEy == self.TM2.gridEy))
self.assertTrue(np.all(self.Curv3.gridCC == self.TM3.gridCC))
self.assertTrue(np.all(self.Curv3.gridN == self.TM3.gridN))
self.assertTrue(np.all(self.Curv3.gridFx == self.TM3.gridFx))
self.assertTrue(np.all(self.Curv3.gridFy == self.TM3.gridFy))
self.assertTrue(np.all(self.Curv3.gridFz == self.TM3.gridFz))
self.assertTrue(np.all(self.Curv3.gridEx == self.TM3.gridEx))
self.assertTrue(np.all(self.Curv3.gridEy == self.TM3.gridEy))
self.assertTrue(np.all(self.Curv3.gridEz == self.TM3.gridEz))
def setupMesh(self, nc):
"""
For a given number of cells nc, generate a TensorMesh with uniform cells with edge length h=1/nc.
"""
if 'TensorMesh' in self._meshType:
if 'uniform' in self._meshType:
h = [nc, nc, nc]
elif 'random' in self._meshType:
h1 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h2 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h3 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h = [hi / np.sum(hi) for hi in [h1, h2, h3]] # normalize
else:
raise Exception('Unexpected meshType')
self.M = TensorMesh(h[:self.meshDimension])
max_h = max([np.max(hi) for hi in self.M.h])
return max_h
elif 'CylMesh' in self._meshType:
if 'uniform' in self._meshType:
h = [nc, nc, nc]
else:
raise Exception('Unexpected meshType')
if self.meshDimension == 2:
self.M = CylMesh([h[0], 1, h[2]])
max_h = max([np.max(hi) for hi in [self.M.hx, self.M.hz]])
elif self.meshDimension == 3:
self.M = CylMesh(h)
max_h = max([np.max(hi) for hi in self.M.h])
return max_h
elif 'Curv' in self._meshType:
if 'uniform' in self._meshType:
kwrd = 'rect'
elif 'rotate' in self._meshType:
kwrd = 'rotate'
else:
raise Exception('Unexpected meshType')
if self.meshDimension == 1:
raise Exception('Lom not supported for 1D')
elif self.meshDimension == 2:
X, Y = Utils.exampleLrmGrid([nc, nc], kwrd)
self.M = CurvilinearMesh([X, Y])
elif self.meshDimension == 3:
X, Y, Z = Utils.exampleLrmGrid([nc, nc, nc], kwrd)
self.M = CurvilinearMesh([X, Y, Z])
return 1. / nc
elif 'Tree' in self._meshType:
nc *= 2
if 'uniform' in self._meshType or 'notatree' in self._meshType:
h = [nc, nc, nc]
elif 'random' in self._meshType:
h1 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h2 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h3 = np.random.rand(nc) * nc * 0.5 + nc * 0.5
h = [hi / np.sum(hi) for hi in [h1, h2, h3]] # normalize
else:
raise Exception('Unexpected meshType')
levels = int(np.log(nc) / np.log(2))
self.M = Tree(h[:self.meshDimension], levels=levels)
def function(cell):
if 'notatree' in self._meshType:
return levels - 1
r = cell.center - np.array([0.5] * len(cell.center))
dist = np.sqrt(r.dot(r))
if dist < 0.2:
return levels
return levels - 1
self.M.refine(function, balance=False)
self.M.number(balance=False)
# self.M.plotGrid(showIt=True)
max_h = max([np.max(hi) for hi in self.M.h])
return max_h
