def test_spbox_2d(self):
"""
Check position of a given vertex in the deformed mesh.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_tri1.mesh')
spb = SplineBox([[-1, 1], [-1, 0.6]], mesh.coors, nsg=[2, 1])
spb.move_control_point(1, [0.1, -0.2])
spb.move_control_point(2, [0.2, -0.3])
spb.move_control_point(3, [0.0, -0.1])
pt0 = mesh.coors[175, :].copy()
mesh.cmesh.coors[:] = spb.evaluate()
pt1 = mesh.coors[175, :]
expected_distance = 0.165892726387
actual_distance = nm.linalg.norm(pt0 - pt1)
ok = nm.fabs(actual_distance - expected_distance)\
/ expected_distance < tolerance
if not ok:
self.report('expected distance:')
self.report(expected_distance)
self.report('actual distance:')
self.report(actual_distance)
return ok
def test_spbox_2d(self):
"""
Check position of a given vertex in the deformed mesh.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_tri1.mesh')
spb = SplineBox([[-1, 1], [-1, 0.6]], mesh.coors, nsg=[2,1])
spb.move_control_point(1, [0.1, -0.2])
spb.move_control_point(2, [0.2, -0.3])
spb.move_control_point(3, [0.0, -0.1])
pt0 = mesh.coors[175,:].copy()
mesh.cmesh.coors[:] = spb.evaluate()
pt1 = mesh.coors[175,:]
expected_distance = 0.165892726387
actual_distance = nm.linalg.norm(pt0 - pt1)
ok = nm.fabs(actual_distance - expected_distance)\
/ expected_distance < tolerance
if not ok:
self.report('expected distance:')
self.report(expected_distance)
self.report('actual distance:')
self.report(actual_distance)
return ok
def test_spbox_3d(self):
"""
Check volume change of the mesh which is deformed using
the SplineBox functions.
"""
from sfepy.discrete.fem import Mesh
from sfepy.mesh.splinebox import SplineBox
mesh = Mesh.from_file(data_dir + '/meshes/3d/cylinder.vtk')
conn = mesh.get_conn('3_4')
vol0 = tetravolume(conn, mesh.coors)
bbox = nm.array(mesh.get_bounding_box()).T
spbox = SplineBox(bbox, mesh.coors)
cpoints0 = spbox.get_control_points(init=True)
for ii in range(4):
for jj in range(4):
spbox.move_control_point((0, ii, jj), [-0.02, 0, 0])
coors = spbox.evaluate()
vol1 = tetravolume(conn, coors)
mesh.coors[:] = coors
spbox.set_control_points(cpoints0)
coors = spbox.evaluate()
vol2 = tetravolume(conn, coors)
ok = True
actual_volumes = (vol0, vol1, vol2)
expected_volumes = (1.22460186e-4, 1.46950423e-4, 1.22460186e-4)
for ii in range(3):
relerr = abs(actual_volumes[ii] - expected_volumes[ii])\
/ expected_volumes[ii]
ok = ok and (relerr < tolerance)
if not ok:
self.report('expected volumes:')
self.report(expected_volumes)
self.report('actual volumes:')
self.report(actual_volumes)
return ok
def test_spbox_3d(self):
"""
Check volume change of the mesh which is deformed using
the SplineBox functions.
"""
from sfepy.discrete.fem import Mesh
from sfepy.mesh.splinebox import SplineBox
mesh = Mesh.from_file(data_dir + '/meshes/3d/cylinder.vtk')
conn = mesh.get_conn('3_4')
vol0 = tetravolume(conn, mesh.coors)
bbox = nm.array(mesh.get_bounding_box()).T
spbox = SplineBox(bbox, mesh.coors)
cpoints0 = spbox.get_control_points(init=True)
for ii in range(4):
for jj in range(4):
spbox.move_control_point((0, ii, jj), [-0.02, 0, 0])
coors = spbox.evaluate()
vol1 = tetravolume(conn, coors)
mesh.coors[:] = coors
spbox.set_control_points(cpoints0)
coors = spbox.evaluate()
vol2 = tetravolume(conn, coors)
ok = True
actual_volumes = (vol0, vol1, vol2)
expected_volumes = (1.22460186e-4, 1.46950423e-4, 1.22460186e-4)
for ii in range(3):
relerr = abs(actual_volumes[ii] - expected_volumes[ii])\
/ expected_volumes[ii]
ok = ok and (relerr < tolerance)
if not ok:
self.report('expected volumes:')
self.report(expected_volumes)
self.report('actual volumes:')
self.report(actual_volumes)
return ok
def test_spbox_field(self):
"""
'Field' vs. 'coors'.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh')
coors = mesh.coors.copy()
bbox = nm.vstack((nm.amin(coors, 0), nm.amax(coors, 0))).T
coors_1 = coors.copy()
alpha = coors[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv1 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, -0.2)
c1 = spbox.evaluate()
coors_1[:, 0] = c1[:, 0]
alpha = coors[:, 1]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv2 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, 0.2)
c2 = spbox.evaluate()
coors_1[:, 1] = c2[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2])
dv = spbox.evaluate_derivative(6, [1, 1])
spbox.move_control_point(6, [-0.2, 0.2])
coors_2 = spbox.evaluate()
rel_coor_dist = nm.linalg.norm(coors_2 - coors_1)\
/ nm.linalg.norm(coors_2)
ok = rel_coor_dist < tolerance
rel_dvel_dist = nm.linalg.norm(dv - nm.hstack([dv1, dv2]))\
/ nm.linalg.norm(dv)
ok = ok and rel_dvel_dist < tolerance
if not ok:
self.report('modified coordinates do not match, relative error:')
self.report(rel_coor_dist)
self.report('derivatives do not match, relative error:')
self.report(rel_dvel_dist)
return ok
def test_sensitivity(self):
from sfepy.discrete import Variables
from sfepy.mesh.splinebox import SplineBox
tolerance = 1e-4
ok = True
pb = self.problem
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in variables.names:
var = variables[var_name]
n_dof = var.field.n_nod * var.field.shape[0]
aux = nm.arange(n_dof, dtype=nm.float64)
var.set_data(aux)
mesh = pb.domain.mesh
bbox = nm.array(mesh.get_bounding_box()).T
spbox = SplineBox(bbox, mesh.coors)
dvel_modes = [
# expand inner cylinder, no volume change
[([20, 21, 22, 23], (-1, -1, 0)),
([24, 25, 26, 27], (-1, 1, 0)),
([36, 37, 38, 39], (1, -1, 0)),
([40, 41, 42, 43], (1, 1, 0))],
# volume change
[(range(16, 32), (0.2, 0, 0)),
(range(32, 48), (0.4, 0, 0)),
(range(48, 52), (0.6, 0.2, 0.2)),
(range(52, 56), (0.8, 0.2, 0.3)),
(range(56, 60), (1.0, 0.2, 0.4)),
(range(60, 64), (1.2, 0.2, 0.5))],
]
r4 = range(4)
cp_pos = {i*16 + j*4 + k: (i, j, k)
for k in r4 for j in r4 for i in r4}
# compute design velocities
dvels = []
for dv_mode in dvel_modes:
dvel = 0
for pts, dir in dv_mode:
for pt in pts:
dvel += spbox.evaluate_derivative(cp_pos[pt], dir)
dvels.append(dvel)
for tname_sa, tname, rname, mat, var1, var2 in test_terms:
args = [] if mat is None else [mat]
args += [var1] if var2 is None else [var1, var2]
term = '%s.i.%s(%s)' % (tname, rname, ', '.join(args))
term_sa = '%s.i.%s(%s)' % (tname_sa, rname, ', '.join(args + ['V']))
val = pb.evaluate(term, var_dict=variables.as_dict())
self.report('%s: %s' % (tname, val))
dt = 1e-6
for ii, dvel in enumerate(dvels):
val = pb.evaluate(term, var_dict=variables.as_dict())
variables['V'].set_data(dvel)
val_sa = pb.evaluate(term_sa, var_dict=variables.as_dict())
self.report('%s - mesh_velocity mode %d' % (tname_sa, ii))
# mesh perturbation +
new_coors = modify_mesh(dt/2., spbox, dvel_modes[ii], cp_pos)
pb.set_mesh_coors(new_coors, update_fields=True)
val1 = pb.evaluate(term, var_dict=variables.as_dict())
# mesh perturbation -
new_coors = modify_mesh(-dt/2., spbox, dvel_modes[ii], cp_pos)
pb.set_mesh_coors(new_coors, update_fields=True)
val2 = pb.evaluate(term, var_dict=variables.as_dict())
val_fd = (val1 - val2) / dt
err = nm.abs(val_sa - val_fd) / nm.linalg.norm(val_sa)
self.report('term: %s' % val)
self.report('sensitivity term: %s' % val_sa)
self.report('finite differences: %s' % val_fd)
self.report('relative error: %s' % err)
_ok = err < tolerance
ok = ok and _ok
return ok
def test_spbox_field(self):
"""
'Field' vs. 'coors'.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh')
coors = mesh.coors.copy()
bbox = nm.vstack((nm.amin(coors, 0), nm.amax(coors, 0))).T
coors_1 = coors.copy()
alpha = coors[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv1 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, -0.2)
c1 = spbox.evaluate()
coors_1[:, 0] = c1[:, 0]
alpha = coors[:, 1]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv2 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, 0.2)
c2 = spbox.evaluate()
coors_1[:, 1] = c2[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2])
dv = spbox.evaluate_derivative(6, [1, 1])
spbox.move_control_point(6, [-0.2, 0.2])
coors_2 = spbox.evaluate()
rel_coor_dist = nm.linalg.norm(coors_2 - coors_1)\
/ nm.linalg.norm(coors_2)
ok = rel_coor_dist < tolerance
rel_dvel_dist = nm.linalg.norm(dv - nm.hstack([dv1, dv2]))\
/ nm.linalg.norm(dv)
ok = ok and rel_dvel_dist < tolerance
if not ok:
self.report('modified coordinates do not match, relative error:')
self.report(rel_coor_dist)
self.report('derivatives do not match, relative error:')
self.report(rel_dvel_dist)
return ok
