#
# Locations of production wells (measurements)
#
n_production = (4, 3) # resolution
x_production = np.linspace(0.5, 1.5, n_production[0])
y_production = np.linspace(0.2, 0.8, n_production[1])
X, Y = np.meshgrid(x_production, y_production)
xy = np.array([X.ravel(), Y.ravel()]).T
cells_production = mesh.bin_points(xy)
# Mark vertices
for cell, dummy in cells_production:
cell.get_vertex(2).mark('production')
# Extract degrees of freedom
production_dofs = dh_Q1.get_region_dofs(entity_type='vertex',
entity_flag='production')
v_production = dh_Q1.get_dof_vertices(dofs=production_dofs)
# Target pressure at production wells
z_fn = Explicit(f=lambda x: 3 - 4 * (x[:, 0] - 1)**2 - 8 * (x[:, 1] - 0.5)**2,
dim=2,
mesh=mesh)
y_target = z_fn.eval(v_production)
#
# Locations of injection wells
#
n_injection = (5, 4) # resolution
x_injection = np.linspace(0.5, 1.5, n_injection[0])
y_injection = np.linspace(0.25, 0.75, n_injection[1])
def test_get_region_dofs(self):
"""
Test the function for returning the dofs associated with a region.
"""
#
# 2D
#
mesh = QuadMesh()
for etype in ['Q1','Q2','Q3']:
element = QuadFE(2, etype)
dofhandler = DofHandler(mesh, element)
dofhandler.distribute_dofs()
#
# Mark half-edges
#
bnd_right = lambda x,dummy: np.abs(x-1)<1e-9
mesh.mark_region('right', bnd_right, \
entity_type='half_edge', \
on_boundary=True)
# Check that mesh.mark_region is doing the right thing.
cell = mesh.cells.get_child(0)
marked_edge = False
for he in cell.get_half_edges():
if he.is_marked('right'):
#
# All vertices should be on the boundary
#
marked_edge = True
for v in he.get_vertices():
x,y = v.coordinates()
self.assertTrue(bnd_right(x,y))
else:
#
# Not all vertices on should be on the boundary
#
on_right = True
for v in he.get_vertices():
x,y = v.coordinates()
if not bnd_right(x,y):
on_right = False
self.assertFalse(on_right)
#
# Some half-edge should be marked
#
self.assertTrue(marked_edge)
#
# Check that we get the right number of dofs
#
n_dofs = {True: {'Q1': 0, 'Q2': 1, 'Q3': 2},
False: {'Q1': 2, 'Q2': 3, 'Q3': 4}}
for interior in [True, False]:
dofs = dofhandler.get_region_dofs(entity_type='half_edge', \
entity_flag='right', \
interior=interior, \
on_boundary=True)
#
# Check that we get the right number of dofs
#
self.assertEqual(len(dofs), n_dofs[interior][etype])
# ============================================================================= M = assembler.af[1]['bilinear'].get_matrix() y_train = y_data[:, i_train] y_test = y_data[:, i_test] U, S, Vt = la.svd(y_train) x = dofhandler.get_dof_vertices() m = 8 d = 7 Um = U[:, :m] plt.plot(x, Um, 'k') # Test functions i_left = dofhandler.get_region_dofs(entity_flag='left', entity_type='vertex') B = Um[i_left, :].T plt.plot(np.tile(x[i_left], B.shape), B, 'r.') plt.show() Q, R = la.qr(B, mode='full') psi = Um.dot(Q[:, 1:]) plt.plot(x, psi) plt.show() rom_tol = 1e-10 rom_error = 1 - np.cumsum(S) / np.sum(S) n_rom = np.sum(rom_error >= rom_tol) print(n_rom) Ur = U[:, :n_rom]
