def test_interpolation_two_meshes(self):
from sfepy import data_dir
from sfepy.discrete import Variables
from sfepy.discrete.fem import Mesh, FEDomain, Field
m1 = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')
m2 = Mesh.from_file(data_dir + '/meshes/3d/cube_medium_tetra.mesh')
m2.coors[:] *= 2.0
bbox = m1.get_bounding_box()
dd = bbox[1, :] - bbox[0, :]
data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])
variables1 = {
'u': ('unknown field', 'scalar_tp', 0),
'v': ('test field', 'scalar_tp', 'u'),
}
variables2 = {
'u': ('unknown field', 'scalar_si', 0),
'v': ('test field', 'scalar_si', 'u'),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
field1 = Field.from_args('scalar_tp',
nm.float64, (1, 1),
omega1,
approx_order=1)
ff1 = {field1.name: field1}
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('scalar_si',
nm.float64, (1, 1),
omega2,
approx_order=0)
ff2 = {field2.name: field2}
vv1 = Variables.from_conf(transform_variables(variables1), ff1)
u1 = vv1['u']
u1.set_from_mesh_vertices(data)
vv2 = Variables.from_conf(transform_variables(variables2), ff2)
u2 = vv2['u']
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)
fname = in_dir(self.options.out_dir)
u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))
return True
def __init__(self, equations):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
self.collect_conn_info()
def do_interpolation(m2, m1, data, field_name, force=False):
"""Interpolate data from m1 to m2. """
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
fields = {
'scalar_si': ((1, 1), 'Omega', 2),
'vector_si': ((3, 1), 'Omega', 2),
'scalar_tp': ((1, 1), 'Omega', 1),
'vector_tp': ((3, 1), 'Omega', 1),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
f = fields[field_name]
field1 = Field.from_args('f',
nm.float64,
f[0],
d1.regions[f[1]],
approx_order=f[2])
ff = {field1.name: field1}
vv = Variables.from_conf(transform_variables(variables), ff)
u1 = vv['u']
u1.set_from_mesh_vertices(data)
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('f',
nm.float64,
f[0],
d2.regions[f[1]],
approx_order=f[2])
ff2 = {field2.name: field2}
vv2 = Variables.from_conf(transform_variables(variables), ff2)
u2 = vv2['u']
if not force:
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)
else:
coors = u2.field.get_coor()
vals = u1.evaluate_at(coors, close_limit=0.5)
u2.set_data(vals)
return u1, u2
def test_interpolation_two_meshes(self):
from sfepy import data_dir
from sfepy.discrete import Variables
from sfepy.discrete.fem import Mesh, FEDomain, Field
m1 = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')
m2 = Mesh.from_file(data_dir + '/meshes/3d/cube_medium_tetra.mesh')
m2.coors[:] *= 2.0
bbox = m1.get_bounding_box()
dd = bbox[1,:] - bbox[0,:]
data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])
variables1 = {
'u' : ('unknown field', 'scalar_tp', 0),
'v' : ('test field', 'scalar_tp', 'u'),
}
variables2 = {
'u' : ('unknown field', 'scalar_si', 0),
'v' : ('test field', 'scalar_si', 'u'),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
field1 = Field.from_args('scalar_tp', nm.float64, (1,1), omega1,
approx_order=1)
ff1 = {field1.name : field1}
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('scalar_si', nm.float64, (1,1), omega2,
approx_order=0)
ff2 = {field2.name : field2}
vv1 = Variables.from_conf(transform_variables(variables1), ff1)
u1 = vv1['u']
u1.set_from_mesh_vertices(data)
vv2 = Variables.from_conf(transform_variables(variables2), ff2)
u2 = vv2['u']
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)
fname = in_dir(self.options.out_dir)
u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))
return True
def standalone_setup(self):
from sfepy.discrete import create_adof_conns, Variables
conn_info = {'aux': self.get_conn_info()}
adcs = create_adof_conns(conn_info, None)
variables = Variables(self.get_variables())
variables.set_adof_conns(adcs)
materials = self.get_materials(join=True)
for mat in materials:
mat.time_update(None, [Struct(terms=[self])])
def standalone_setup(self):
from sfepy.discrete import create_adof_conns, Variables
conn_info = {'aux' : self.get_conn_info()}
adcs = create_adof_conns(conn_info, None)
variables = Variables(self.get_variables())
variables.set_adof_conns(adcs)
materials = self.get_materials(join=True)
for mat in materials:
mat.time_update(None, [Struct(terms=[self])])
def from_conf(conf, options):
from sfepy.discrete import FieldVariable, Variables, Problem
from sfepy.discrete.fem import Mesh, FEDomain, Field
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_unit_tri.mesh')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
domain.create_region('Left', 'vertices in (x < -0.499)', 'facet')
domain.create_region(
'LeftStrip', 'vertices in (x < -0.499)'
' & (y > -0.199) & (y < 0.199)', 'facet')
domain.create_region('LeftFix', 'r.Left -v r.LeftStrip', 'facet')
domain.create_region('Right', 'vertices in (x > 0.499)', 'facet')
domain.create_region(
'RightStrip', 'vertices in (x > 0.499)'
' & (y > -0.199) & (y < 0.199)', 'facet')
domain.create_region('RightFix', 'r.Right -v r.RightStrip', 'facet')
fu = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', fu)
fp = Field.from_args('fp', nm.float64, 'scalar', omega, approx_order=2)
p = FieldVariable('p', 'unknown', fp)
pb = Problem('test', domain=domain, fields=[fu, fp], auto_conf=False)
test = Test(problem=pb,
variables=Variables([u, p]),
conf=conf,
options=options)
return test
def do_interpolation(m2, m1, data, field_name, force=False):
"""Interpolate data from m1 to m2. """
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
fields = {
'scalar_si' : ((1,1), 'Omega', 2),
'vector_si' : ((3,1), 'Omega', 2),
'scalar_tp' : ((1,1), 'Omega', 1),
'vector_tp' : ((3,1), 'Omega', 1),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
f = fields[field_name]
field1 = Field.from_args('f', nm.float64, f[0], d1.regions[f[1]],
approx_order=f[2])
ff = {field1.name : field1}
vv = Variables.from_conf(transform_variables(variables), ff)
u1 = vv['u']
u1.set_from_mesh_vertices(data)
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('f', nm.float64, f[0], d2.regions[f[1]],
approx_order=f[2])
ff2 = {field2.name : field2}
vv2 = Variables.from_conf(transform_variables(variables), ff2)
u2 = vv2['u']
if not force:
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)
else:
coors = u2.field.get_coor()
vals = u1.evaluate_at(coors, close_limit=0.5)
u2.set_data(vals)
return u1, u2
def __init__(self, equations):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
self.collect_conn_info()
def test_evaluate_at(self):
from sfepy import data_dir
from sfepy.discrete.fem import Mesh
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
meshes = {
'tp': Mesh.from_file(data_dir + '/meshes/3d/block.mesh'),
}
datas = gen_datas(meshes)
fields = {
'scalar_tp': ((1, 1), 'Omega', 1),
'vector_tp': ((3, 1), 'Omega', 1),
}
ok = True
for field_name in ['scalar_tp', 'vector_tp']:
d = FEDomain('d', meshes['tp'])
d.create_region('Omega', 'all')
f = fields[field_name]
field = Field.from_args('f',
nm.complex128,
f[0],
d.regions[f[1]],
approx_order=f[2])
ff = {field.name: field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
bbox = d.get_mesh_bounding_box()
t = nm.expand_dims(nm.linspace(0, 1, 100), 1)
coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0]
data_r = datas[field_name]
data_i = 2. / (1 + datas[field_name])
u.set_from_mesh_vertices(data_r)
vals_r = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_i)
vals_i = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_r + data_i * 1j)
vals = u.evaluate_at(coors)
_ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12)
_ok = _ok and nm.abs(vals).sum() > 1
self.report('evaluating complex field %s: %s' % (field_name, _ok))
ok = ok and _ok
return ok
def test_evaluate_at(self):
from sfepy import data_dir
from sfepy.discrete.fem import Mesh
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
meshes = {
'tp' : Mesh.from_file(data_dir + '/meshes/3d/block.mesh'),
}
datas = gen_datas(meshes)
fields = {
'scalar_tp' : ((1,1), 'Omega', 1),
'vector_tp' : ((3,1), 'Omega', 1),
}
ok = True
for field_name in ['scalar_tp', 'vector_tp']:
d = FEDomain('d', meshes['tp'])
d.create_region('Omega', 'all')
f = fields[field_name]
field = Field.from_args('f', nm.complex128, f[0],
d.regions[f[1]],
approx_order=f[2])
ff = {field.name : field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
bbox = d.get_mesh_bounding_box()
t = nm.expand_dims(nm.linspace(0, 1, 100), 1)
coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0]
data_r = datas[field_name]
data_i = 2. / (1 + datas[field_name])
u.set_from_mesh_vertices(data_r)
vals_r = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_i)
vals_i = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_r + data_i * 1j)
vals = u.evaluate_at(coors)
_ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12)
_ok = _ok and nm.abs(vals).sum() > 1
self.report('evaluating complex field %s: %s' % (field_name, _ok))
ok = ok and _ok
return ok
def test_pbc( self ):
from sfepy.discrete import Variables, Conditions
problem = self.problem
conf = self.conf
ebcs = Conditions.from_conf(conf.ebcs, problem.domain.regions)
epbcs = Conditions.from_conf(conf.epbcs, problem.domain.regions)
variables = Variables.from_conf(conf.variables, problem.fields)
variables.equation_mapping(ebcs, epbcs, None, problem.functions)
state = variables.create_state_vector()
variables.apply_ebc(state)
return variables.has_ebc(state)
def test_pbc(self):
from sfepy.discrete import Variables, Conditions
problem = self.problem
conf = self.conf
ebcs = Conditions.from_conf(conf.ebcs, problem.domain.regions)
epbcs = Conditions.from_conf(conf.epbcs, problem.domain.regions)
variables = Variables.from_conf(conf.variables, problem.fields)
variables.equation_mapping(ebcs, epbcs, None, problem.functions)
state = variables.create_state_vector()
variables.apply_ebc(state)
return variables.has_ebc(state)
def test_consistency_d_dw(self):
from sfepy.discrete import Variables
ok = True
pb = self.problem
for aux in test_terms:
term_template, (prefix, par_name, d_vars, dw_vars) = aux
print term_template, prefix, par_name, d_vars, dw_vars
term1 = term_template % ((prefix, ) + d_vars)
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in d_vars:
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)
if prefix == 'd':
val1 = pb.evaluate(term1, var_dict=variables.as_dict())
else:
val1 = pb.evaluate(term1,
call_mode='d_eval',
var_dict=variables.as_dict())
self.report('%s: %s' % (term1, val1))
term2 = term_template % (('dw', ) + dw_vars[:2])
vec, vv = pb.evaluate(term2,
mode='weak',
var_dict=variables.as_dict(),
ret_variables=True)
pvec = vv.get_state_part_view(vec, dw_vars[2])
val2 = nm.dot(variables[par_name](), pvec)
self.report('%s: %s' % (term2, val2))
err = nm.abs(val1 - val2) / nm.abs(val1)
_ok = err < 1e-12
self.report('relative difference: %e -> %s' % (err, _ok))
ok = ok and _ok
return ok
def test_invariance_qp(self):
from sfepy import data_dir
from sfepy.discrete import Variables, Integral
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.common.mappings import get_physical_qps
mesh = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')
bbox = mesh.get_bounding_box()
dd = bbox[1,:] - bbox[0,:]
data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])
variables = {
'u' : ('unknown field', 'scalar_tp', 0),
'v' : ('test field', 'scalar_tp', 'u'),
}
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('scalar_tp', nm.float64, 1, omega,
approx_order=1)
ff = {field.name : field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
u.set_from_mesh_vertices(data)
integral = Integral('i', order=2)
term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
term.setup()
val1 = term.evaluate(mode='qp')
val1 = val1.ravel()
qps = get_physical_qps(omega, integral)
coors = qps.values
val2 = u.evaluate_at(coors).ravel()
self.report('max. difference:', nm.abs(val1 - val2).max())
ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
self.report('invariance in qp: %s' % ok)
return ok
def test_consistency_d_dw(self):
from sfepy.discrete import Variables
ok = True
pb = self.problem
for aux in test_terms:
term_template, (prefix, par_name, d_vars, dw_vars) = aux
print term_template, prefix, par_name, d_vars, dw_vars
term1 = term_template % ((prefix,) + d_vars)
variables = Variables.from_conf(self.conf.variables, pb.fields)
for var_name in d_vars:
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)
if prefix == 'd':
val1 = pb.evaluate(term1, var_dict=variables.as_dict())
else:
val1 = pb.evaluate(term1, call_mode='d_eval',
var_dict=variables.as_dict())
self.report('%s: %s' % (term1, val1))
term2 = term_template % (('dw',) + dw_vars[:2])
vec, vv = pb.evaluate(term2, mode='weak',
var_dict=variables.as_dict(),
ret_variables=True)
pvec = vv.get_state_part_view(vec, dw_vars[2])
val2 = nm.dot(variables[par_name](), pvec)
self.report('%s: %s' % (term2, val2))
err = nm.abs(val1 - val2) / nm.abs(val1)
_ok = err < 1e-12
self.report('relative difference: %e -> %s' % (err, _ok))
ok = ok and _ok
return ok
def __init__(self, dim, approx_order, **kwargs):
"""
Creates Struct object with all the data necessary to test terms
:param dim: dimension
:param approx_order: approximation order
:param kwargs: velo, diffusion or penalty for prepare_materials
:return: term test scope
"""
if dim == 1:
(field, regions), mesh = prepare_dgfield_1D(approx_order)
elif dim == 2:
(field, regions), mesh = prepare_field_2D(approx_order)
self.field = field
self.regions = regions
self.mesh = mesh
self.n_cell = field.n_cell
self.n_nod = field.n_nod
self.n_el_nod = field.n_el_nod
self.u, self.v = self.prepare_variables(field)
self.u.data = [(nm.zeros(self.n_nod))]
self.variables = Variables([ self.u, self.v])
self.integral = Integral('i', order=approx_order * 2)
self.a, self.D, self.Cw = self.prepare_materials(field, **kwargs)
if dim == 1:
velo = nm.array(1.0)
elif dim == 2:
velo = nm.array([1.0, 0])
self.burg_velo = velo.T / nm.linalg.norm(velo)
self.nonlin = Material('nonlin',
values={'.fun': self.burg_fun,
'.dfun': self.burg_fun_d})
self.out = nm.zeros((self.n_cell, 1, self.n_el_nod, 1))
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 save_basis_on_mesh(mesh, options, output_dir, lin,
permutations=None, suffix=''):
if permutations is not None:
mesh = mesh.copy()
gel = GeometryElement(mesh.descs[0])
perms = gel.get_conn_permutations()[permutations]
conn = mesh.cmesh.get_cell_conn()
n_el, n_ep = conn.num, gel.n_vertex
offsets = nm.arange(n_el) * n_ep
conn.indices[:] = conn.indices.take((perms + offsets[:, None]).ravel())
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f', nm.float64, shape=1, region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
import sfepy.postprocess.plot_cmesh as pc
ax = pc.plot_wireframe(None, mesh.cmesh)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.econn,
field.poly_space.nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u', 'f', {'f' : field}, None,
Variables([var]),
mode='qp', verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def create_evaluable(expression, fields, materials, variables, integrals,
regions=None,
ebcs=None, epbcs=None, lcbcs=None, ts=None, functions=None,
auto_init=False, mode='eval', extra_args=None,
verbose=True, kwargs=None):
"""
Create evaluable object (equations and corresponding variables)
from the `expression` string.
Parameters
----------
expression : str
The expression to evaluate.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
integrals : Integrals instance
The integrals to be used.
regions : Region instance or list of Region instances
The region(s) to be used. If not given, the regions defined
within the fields domain are used.
ebcs : Conditions instance, optional
The essential (Dirichlet) boundary conditions for 'weak'
mode.
epbcs : Conditions instance, optional
The periodic boundary conditions for 'weak'
mode.
lcbcs : Conditions instance, optional
The linear combination boundary conditions for 'weak'
mode.
ts : TimeStepper instance, optional
The time stepper.
functions : Functions instance, optional
The user functions for boundary conditions, materials
etc.
auto_init : bool
Set values of all variables to all zeros.
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode - 'weak' means the finite element
assembling, 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
Returns
-------
equation : Equation instance
The equation that is ready to be evaluated.
variables : Variables instance
The variables used in the equation.
"""
if kwargs is None:
kwargs = {}
if regions is not None:
if isinstance(regions, Region):
regions = [regions]
regions = OneTypeList(Region, regions)
else:
regions = fields[fields.keys()[0]].domain.regions
# Create temporary variables.
aux_vars = Variables(variables)
if extra_args is None:
extra_args = kwargs
else:
extra_args = copy(extra_args)
extra_args.update(kwargs)
if ts is not None:
extra_args.update({'ts' : ts})
equations = Equations.from_conf({'tmp' : expression},
aux_vars, regions, materials, integrals,
user=extra_args, verbose=verbose)
equations.collect_conn_info()
# The true variables used in the expression.
variables = equations.variables
if auto_init:
for var in variables:
var.init_data(step=0)
if mode == 'weak':
equations.time_update(ts, ebcs, epbcs, lcbcs, functions,
verbose=verbose)
else:
setup_extra_data(equations.conn_info)
return equations, variables
class Equations(Container):
@staticmethod
def from_conf(conf,
variables,
regions,
materials,
integrals,
user=None,
verbose=True):
objs = OneTypeList(Equation)
conf = copy(conf)
ii = 0
for name, desc in conf.iteritems():
if verbose:
output('equation "%s":' % name)
output(desc)
eq = Equation.from_desc(name,
desc,
variables,
regions,
materials,
integrals,
user=user)
objs.append(eq)
ii += 1
obj = Equations(objs)
return obj
def __init__(self, equations):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
self.collect_conn_info()
def create_subequations(self, var_names, known_var_names=None):
"""
Create sub-equations containing only terms with the given virtual
variables.
Parameters
----------
var_names : list
The list of names of virtual variables.
known_var_names : list
The list of names of (already) known state variables.
Returns
-------
subequations : Equations instance
The sub-equations.
"""
from sfepy.discrete import FieldVariable
known_var_names = get_default(known_var_names, [])
objs = []
for iv, var_name in enumerate(var_names):
terms = [
term.copy(name=term.name) for eq in self for term in eq.terms
if term.get_virtual_name() == var_name
]
# Make parameter variables from known state variables in terms
# arguments.
for known_name in known_var_names:
for term in terms:
if known_name in term.arg_names:
ii = term.arg_names.index(known_name)
state = self.variables[known_name]
par = FieldVariable(known_name,
'parameter',
state.field,
primary_var_name='(set-to-None)')
term.args[ii] = par
term._kwargs[known_name] = par
par.set_data(state())
new_terms = Terms(terms)
objs.append(Equation('eq_%d' % iv, new_terms))
subequations = Equations(objs)
return subequations
def get_domain(self):
domain = None
for eq in self:
for term in eq.terms:
if term.has_region:
domain = term.region.domain
return domain
def collect_materials(self):
"""
Collect materials present in the terms of all equations.
"""
materials = []
for eq in self:
materials.extend(eq.collect_materials())
# Make the list items unique.
materials = list(set(materials))
return materials
def reset_materials(self):
"""
Clear material data so that next materials.time_update() is
performed even for stationary materials.
"""
self.materials.reset()
def collect_variables(self):
"""
Collect variables present in the terms of all equations.
"""
variables = []
for eq in self:
variables.extend(eq.collect_variables())
# Make the list items unique.
variables = list(set(variables))
return variables
def get_variable(self, name):
var = self.variables.get(name,
msg_if_none='unknown variable! (%s)' % name)
return var
def collect_conn_info(self):
"""
Collect connectivity information as defined by the equations.
"""
self.conn_info = {}
for eq in self:
eq.collect_conn_info(self.conn_info)
return self.conn_info
def get_variable_names(self):
"""
Return the list of names of all variables used in equations.
"""
vns = set()
for eq in self:
for term in eq.terms:
vns.update(term.get_variable_names())
return list(vns)
def get_variable_dependencies(self):
"""
For each virtual variable get names of state/parameter variables that
are present in terms with that virtual variable.
The virtual variables define the actual equations and their
dependencies define the variables needed to evaluate the equations.
Returns
-------
deps : dict
The dependencies as a dictionary with virtual variable names as
keys and sets of state/parameter variables as values.
"""
deps = {}
for eq in self:
for term in eq.terms:
dep_list = deps.setdefault(term.get_virtual_name(), set())
dep_list.update(term.get_state_names())
return deps
def invalidate_term_caches(self):
"""
Invalidate evaluate caches of variables present in equations.
"""
for var in self.variables:
var.invalidate_evaluate_cache()
def print_terms(self):
"""
Print names of equations and their terms.
"""
output('equations:')
for eq in self:
output(' %s:' % eq.name)
for term in eq.terms:
output(' %+.2e * %s.%d.%s(%s)' %
(term.sign, term.name, term.integral.order,
term.region.name, term.arg_str))
def time_update(self,
ts,
ebcs=None,
epbcs=None,
lcbcs=None,
functions=None,
problem=None,
active_only=True,
verbose=True):
"""
Update the equations for current time step.
The update involves creating the mapping of active DOFs from/to
all DOFs for all state variables, the setup of linear
combination boundary conditions operators and the setup of
active DOF connectivities.
Parameters
----------
ts : TimeStepper instance
The time stepper.
ebcs : Conditions instance, optional
The essential (Dirichlet) boundary conditions.
epbcs : Conditions instance, optional
The periodic boundary conditions.
lcbcs : Conditions instance, optional
The linear combination boundary conditions.
functions : Functions instance, optional
The user functions for boundary conditions, materials, etc.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
active_only : bool
If True, the active DOF connectivities and matrix graph have
reduced size and are created with the reduced (active DOFs only)
numbering.
verbose : bool
If False, reduce verbosity.
Returns
-------
graph_changed : bool
The flag set to True if the current time step set of active
boundary conditions differs from the set of the previous
time step.
"""
self.variables.time_update(ts, functions, verbose=verbose)
active_bcs = self.variables.equation_mapping(ebcs,
epbcs,
ts,
functions,
problem=problem,
active_only=active_only)
graph_changed = active_only and (active_bcs != self.active_bcs)
self.active_bcs = active_bcs
if graph_changed or not self.variables.adof_conns:
adcs = create_adof_conns(self.conn_info,
self.variables.adi.indx,
active_only=active_only)
self.variables.set_adof_conns(adcs)
self.variables.setup_lcbc_operators(lcbcs, ts, functions)
for eq in self:
for term in eq.terms:
term.time_update(ts)
return graph_changed
def time_update_materials(self,
ts,
mode='normal',
problem=None,
verbose=True):
"""
Update data materials for current time and possibly also state.
Parameters
----------
ts : TimeStepper instance
The time stepper.
mode : 'normal', 'update' or 'force'
The update mode, see
:func:`sfepy.discrete.materials.Material.time_update()`.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
verbose : bool
If False, reduce verbosity.
"""
self.materials.time_update(ts,
self,
mode=mode,
problem=problem,
verbose=verbose)
def setup_initial_conditions(self, ics, functions=None):
self.variables.setup_initial_conditions(ics, functions)
def get_graph_conns(self,
any_dof_conn=False,
rdcs=None,
cdcs=None,
active_only=True):
"""
Get DOF connectivities needed for creating tangent matrix graph.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
active_only : bool
If True, the active DOF connectivities have reduced size and are
created with the reduced (active DOFs only) numbering.
Returns
-------
rdcs, cdcs : arrays
The row and column DOF connectivities defining the matrix
graph blocks.
"""
if rdcs is None:
rdcs = []
cdcs = []
elif cdcs is None:
cdcs = copy(rdcs)
else:
assert_(len(rdcs) == len(cdcs))
if rdcs is cdcs: # Make sure the lists are not the same object.
rdcs = copy(rdcs)
adcs = self.variables.adof_conns
# Only volume dof connectivities are used, with the exception of trace
# surface dof connectivities.
shared = set()
for key, ii, info in iter_dict_of_lists(self.conn_info,
return_keys=True):
rvar, cvar = info.virtual, info.state
if (rvar is None) or (cvar is None):
continue
is_surface = rvar.is_surface or cvar.is_surface
dct = info.dc_type.type
if not (dct in ('volume', 'scalar', 'plate') or is_surface
or info.is_trace or any_dof_conn):
continue
rreg_name = info.get_region_name(can_trace=False)
creg_name = info.get_region_name()
rname = rvar.get_primary_name()
rkey = (rname, rreg_name, dct, False)
ckey = (cvar.name, creg_name, dct, info.is_trace)
dc_key = (rkey, ckey)
if not dc_key in shared:
rdc = adcs[rkey]
cdc = adcs[ckey]
if not active_only:
ii = nm.where(rdc < 0)
rdc = rdc.copy()
rdc[ii] = -1 - rdc[ii]
ii = nm.where(cdc < 0)
cdc = cdc.copy()
cdc[ii] = -1 - cdc[ii]
rdcs.append(rdc)
cdcs.append(cdc)
shared.add(dc_key)
return rdcs, cdcs
def create_matrix_graph(self,
any_dof_conn=False,
rdcs=None,
cdcs=None,
shape=None,
active_only=True,
verbose=True):
"""
Create tangent matrix graph, i.e. preallocate and initialize the
sparse storage needed for the tangent matrix. Order of DOF
connectivities is not important.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
shape : tuple, optional
The required shape, if it is different from the shape
determined by the equations variables. This may be needed if
additional row and column DOF connectivities are passed in.
active_only : bool
If True, the matrix graph has reduced size and is created with the
reduced (active DOFs only) numbering.
verbose : bool
If False, reduce verbosity.
Returns
-------
matrix : csr_matrix
The matrix graph in the form of a CSR matrix with
preallocated structure and zero data.
"""
if not self.variables.has_virtuals():
output('no matrix (no test variables)!')
return None
shape = get_default(shape, self.variables.get_matrix_shape())
output('matrix shape:', shape, verbose=verbose)
if nm.prod(shape) == 0:
output('no matrix (zero size)!')
return None
rdcs, cdcs = self.get_graph_conns(any_dof_conn=any_dof_conn,
rdcs=rdcs,
cdcs=cdcs,
active_only=active_only)
if not len(rdcs):
output('no matrix (empty dof connectivities)!')
return None
output('assembling matrix graph...', verbose=verbose)
tt = time.clock()
nnz, prow, icol = create_mesh_graph(shape[0], shape[1], len(rdcs),
rdcs, cdcs)
output('...done in %.2f s' % (time.clock() - tt), verbose=verbose)
output('matrix structural nonzeros: %d (%.2e%% fill)' \
% (nnz, float(nnz) / nm.prod(shape)), verbose=verbose)
data = nm.zeros((nnz, ), dtype=self.variables.dtype)
matrix = sp.csr_matrix((data, icol, prow), shape)
return matrix
def init_time(self, ts):
pass
def advance(self, ts):
for eq in self:
for term in eq.terms:
term.advance(ts)
self.variables.advance(ts)
##
# Interface to self.variables.
def create_state_vector(self):
return self.variables.create_state_vector()
def create_stripped_state_vector(self):
return self.variables.create_stripped_state_vector()
def strip_state_vector(self, vec, follow_epbc=False):
"""
Strip a full vector by removing EBC dofs.
Notes
-----
If 'follow_epbc' is True, values of EPBC master dofs are not simply
thrown away, but added to the corresponding slave dofs, just like when
assembling. For vectors with state (unknown) variables it should be set
to False, for assembled vectors it should be set to True.
"""
return self.variables.strip_state_vector(vec, follow_epbc=follow_epbc)
def make_full_vec(self, svec, force_value=None):
"""
Make a full DOF vector satisfying E(P)BCs from a reduced DOF
vector.
"""
return self.variables.make_full_vec(svec, force_value)
def set_variables_from_state(self, vec, step=0):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The state vector.
step : int
The time history step, 0 (default) = current.
"""
self.variables.set_data(vec, step=step)
def get_state_parts(self, vec=None):
"""
Return parts of a state vector corresponding to individual state
variables.
Parameters
----------
vec : array, optional
The state vector. If not given, then the data stored in the
variables are returned instead.
Returns
-------
out : dict
The dictionary of the state parts.
"""
return self.variables.get_state_parts(vec)
def set_data(self, data, step=0, ignore_unknown=False):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The dictionary of {variable_name : data vector}.
step : int, optional
The time history step, 0 (default) = current.
ignore_unknown : bool, optional
Ignore unknown variable names if `data` is a dict.
"""
self.variables.set_data(data, step=step, ignore_unknown=ignore_unknown)
def apply_ebc(self, vec, force_values=None):
"""
Apply essential (Dirichlet) boundary conditions to a state vector.
"""
self.variables.apply_ebc(vec, force_values=force_values)
def apply_ic(self, vec, force_values=None):
"""
Apply initial conditions to a state vector.
"""
self.variables.apply_ic(vec, force_values=force_values)
def state_to_output(self,
vec,
fill_value=None,
var_info=None,
extend=True):
return self.variables.state_to_output(vec,
fill_value=fill_value,
var_info=var_info,
extend=extend)
def get_lcbc_operator(self):
return self.variables.get_lcbc_operator()
def evaluate(self,
names=None,
mode='eval',
dw_mode='vector',
term_mode=None,
asm_obj=None):
"""
Evaluate the equations.
Parameters
----------
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
names : str or sequence of str, optional
Evaluate only equations of the given name(s).
Returns
-------
out : dict or result
The evaluation result. In 'weak' mode it is the
`asm_obj`. Otherwise, it is a dict of results with equation names
as keys or a single result for a single equation.
"""
if names is None:
eqs = self
single = (len(eqs) == 1)
else:
single = isinstance(names, str)
if single:
names = [names]
eqs = [self[eq] for eq in names]
if mode == 'weak':
for eq in eqs:
eq.evaluate(mode=mode,
dw_mode=dw_mode,
term_mode=term_mode,
asm_obj=asm_obj)
out = asm_obj
else:
out = {}
for eq in eqs:
eout = eq.evaluate(mode=mode,
dw_mode=dw_mode,
term_mode=term_mode)
out[eq.name] = eout
if single:
out = out.popitem()[1]
return out
def eval_residuals(self, state, by_blocks=False, names=None):
"""
Evaluate (assemble) residual vectors.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
by_blocks : bool
If True, return the individual blocks composing the whole
residual vector. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : array or dict of array
The assembled residual vector. If `by_blocks` is True, a
dictionary is returned instead, with keys given by
`block_name` part of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip() for aux in name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
residual = self.create_stripped_state_vector()
eq.evaluate(mode='weak', dw_mode='vector', asm_obj=residual)
out[key] = residual[ir]
else:
out = self.create_stripped_state_vector()
self.evaluate(mode='weak', dw_mode='vector', asm_obj=out)
return out
def eval_tangent_matrices(self,
state,
tangent_matrix,
by_blocks=False,
names=None):
"""
Evaluate (assemble) tangent matrices.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
tangent_matrix : csr_matrix
The preallocated CSR matrix with zero data.
by_blocks : bool
If True, return the individual blocks composing the whole
matrix. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : csr_matrix or dict of csr_matrix
The assembled matrix. If `by_blocks` is True, a dictionary
is returned instead, with keys given by `block_name` part
of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip() for aux in eq.name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
ic = get_indx(cname, stripped=True, allow_dual=True)
tangent_matrix.data[:] = 0.0
eq.evaluate(mode='weak',
dw_mode='matrix',
asm_obj=tangent_matrix)
out[key] = tangent_matrix[ir, ic]
else:
tangent_matrix.data[:] = 0.0
self.evaluate(mode='weak',
dw_mode='matrix',
asm_obj=tangent_matrix)
out = tangent_matrix
return out
def make_term_args(arg_shapes,
arg_kinds,
arg_types,
ats_mode,
domain,
material_value=None,
poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh), )
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii,
nm.float64,
shape,
omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v',
'test',
field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii,
'parameter',
field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii): val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii: material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Equations(Container):
@staticmethod
def from_conf(conf, variables, regions, materials, integrals,
user=None, verbose=True):
objs = OneTypeList(Equation)
conf = copy(conf)
ii = 0
for name, desc in conf.iteritems():
if verbose:
output('equation "%s":' % name)
output(desc)
eq = Equation.from_desc(name, desc, variables, regions,
materials, integrals, user=user)
objs.append(eq)
ii += 1
obj = Equations(objs)
return obj
def __init__(self, equations):
Container.__init__(self, equations)
self.variables = Variables(self.collect_variables())
self.materials = Materials(self.collect_materials())
self.domain = self.get_domain()
self.active_bcs = set()
self.collect_conn_info()
def create_subequations(self, var_names, known_var_names=None):
"""
Create sub-equations containing only terms with the given virtual
variables.
Parameters
----------
var_names : list
The list of names of virtual variables.
known_var_names : list
The list of names of (already) known state variables.
Returns
-------
subequations : Equations instance
The sub-equations.
"""
from sfepy.discrete import FieldVariable
known_var_names = get_default(known_var_names, [])
objs = []
for iv, var_name in enumerate(var_names):
terms = [term.copy(name=term.name)
for eq in self for term in eq.terms
if term.get_virtual_name() == var_name]
# Make parameter variables from known state variables in terms
# arguments.
for known_name in known_var_names:
for term in terms:
if known_name in term.arg_names:
ii = term.arg_names.index(known_name)
state = self.variables[known_name]
par = FieldVariable(known_name, 'parameter',
state.field,
primary_var_name='(set-to-None)')
term.args[ii] = par
term._kwargs[known_name] = par
par.set_data(state())
new_terms = Terms(terms)
objs.append(Equation('eq_%d' % iv, new_terms))
subequations = Equations(objs)
return subequations
def get_domain(self):
domain = None
for eq in self:
for term in eq.terms:
if term.has_region:
domain = term.region.domain
return domain
def collect_materials(self):
"""
Collect materials present in the terms of all equations.
"""
materials = []
for eq in self:
materials.extend(eq.collect_materials())
# Make the list items unique.
materials = list(set(materials))
return materials
def reset_materials(self):
"""
Clear material data so that next materials.time_update() is
performed even for stationary materials.
"""
self.materials.reset()
def collect_variables(self):
"""
Collect variables present in the terms of all equations.
"""
variables = []
for eq in self:
variables.extend(eq.collect_variables())
# Make the list items unique.
variables = list(set(variables))
return variables
def get_variable(self, name):
var = self.variables.get(name,
msg_if_none='unknown variable! (%s)' % name)
return var
def collect_conn_info(self):
"""
Collect connectivity information as defined by the equations.
"""
self.conn_info = {}
for eq in self:
eq.collect_conn_info(self.conn_info)
return self.conn_info
def get_variable_names(self):
"""
Return the list of names of all variables used in equations.
"""
vns = set()
for eq in self:
for term in eq.terms:
vns.update(term.get_variable_names())
return list(vns)
def get_variable_dependencies(self):
"""
For each virtual variable get names of state/parameter variables that
are present in terms with that virtual variable.
The virtual variables define the actual equations and their
dependencies define the variables needed to evaluate the equations.
Returns
-------
deps : dict
The dependencies as a dictionary with virtual variable names as
keys and sets of state/parameter variables as values.
"""
deps = {}
for eq in self:
for term in eq.terms:
dep_list = deps.setdefault(term.get_virtual_name(), set())
dep_list.update(term.get_state_names())
return deps
def invalidate_term_caches(self):
"""
Invalidate evaluate caches of variables present in equations.
"""
for var in self.variables:
var.invalidate_evaluate_cache()
def print_terms(self):
"""
Print names of equations and their terms.
"""
output('equations:')
for eq in self:
output(' %s:' % eq.name)
for term in eq.terms:
output(' %+.2e * %s.%d.%s(%s)'
% (term.sign, term.name, term.integral.order,
term.region.name, term.arg_str))
def time_update(self, ts, ebcs=None, epbcs=None, lcbcs=None,
functions=None, problem=None, active_only=True,
verbose=True):
"""
Update the equations for current time step.
The update involves creating the mapping of active DOFs from/to
all DOFs for all state variables, the setup of linear
combination boundary conditions operators and the setup of
active DOF connectivities.
Parameters
----------
ts : TimeStepper instance
The time stepper.
ebcs : Conditions instance, optional
The essential (Dirichlet) boundary conditions.
epbcs : Conditions instance, optional
The periodic boundary conditions.
lcbcs : Conditions instance, optional
The linear combination boundary conditions.
functions : Functions instance, optional
The user functions for boundary conditions, materials, etc.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
active_only : bool
If True, the active DOF connectivities and matrix graph have
reduced size and are created with the reduced (active DOFs only)
numbering.
verbose : bool
If False, reduce verbosity.
Returns
-------
graph_changed : bool
The flag set to True if the current time step set of active
boundary conditions differs from the set of the previous
time step.
"""
self.variables.time_update(ts, functions, verbose=verbose)
active_bcs = self.variables.equation_mapping(ebcs, epbcs, ts, functions,
problem=problem,
active_only=active_only)
graph_changed = active_only and (active_bcs != self.active_bcs)
self.active_bcs = active_bcs
if graph_changed or not self.variables.adof_conns:
adcs = create_adof_conns(self.conn_info, self.variables.adi.indx,
active_only=active_only)
self.variables.set_adof_conns(adcs)
self.variables.setup_lcbc_operators(lcbcs, ts, functions)
for eq in self:
for term in eq.terms:
term.time_update(ts)
return graph_changed
def time_update_materials(self, ts, mode='normal', problem=None,
verbose=True):
"""
Update data materials for current time and possibly also state.
Parameters
----------
ts : TimeStepper instance
The time stepper.
mode : 'normal', 'update' or 'force'
The update mode, see
:func:`sfepy.discrete.materials.Material.time_update()`.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
verbose : bool
If False, reduce verbosity.
"""
self.materials.time_update(ts, self, mode=mode, problem=problem,
verbose=verbose)
def setup_initial_conditions(self, ics, functions=None):
self.variables.setup_initial_conditions(ics, functions)
def get_graph_conns(self, any_dof_conn=False, rdcs=None, cdcs=None,
active_only=True):
"""
Get DOF connectivities needed for creating tangent matrix graph.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
active_only : bool
If True, the active DOF connectivities have reduced size and are
created with the reduced (active DOFs only) numbering.
Returns
-------
rdcs, cdcs : arrays
The row and column DOF connectivities defining the matrix
graph blocks.
"""
if rdcs is None:
rdcs = []
cdcs = []
elif cdcs is None:
cdcs = copy(rdcs)
else:
assert_(len(rdcs) == len(cdcs))
if rdcs is cdcs: # Make sure the lists are not the same object.
rdcs = copy(rdcs)
adcs = self.variables.adof_conns
# Only volume dof connectivities are used, with the exception of trace
# surface dof connectivities.
shared = set()
for key, ii, info in iter_dict_of_lists(self.conn_info,
return_keys=True):
rvar, cvar = info.virtual, info.state
if (rvar is None) or (cvar is None):
continue
is_surface = rvar.is_surface or cvar.is_surface
dct = info.dc_type.type
if not (dct in ('volume', 'scalar', 'custom') or is_surface
or info.is_trace or any_dof_conn):
continue
rreg_name = info.get_region_name(can_trace=False)
creg_name = info.get_region_name()
rname = rvar.get_primary_name()
rkey = (rname, rreg_name, dct, False)
ckey = (cvar.name, creg_name, dct, info.is_trace)
dc_key = (rkey, ckey)
if not dc_key in shared:
rdc = adcs[rkey]
cdc = adcs[ckey]
if not active_only:
ii = nm.where(rdc < 0)
rdc = rdc.copy()
rdc[ii] = -1 - rdc[ii]
ii = nm.where(cdc < 0)
cdc = cdc.copy()
cdc[ii] = -1 - cdc[ii]
rdcs.append(rdc)
cdcs.append(cdc)
shared.add(dc_key)
return rdcs, cdcs
def create_matrix_graph(self, any_dof_conn=False, rdcs=None, cdcs=None,
shape=None, active_only=True, verbose=True):
"""
Create tangent matrix graph, i.e. preallocate and initialize the
sparse storage needed for the tangent matrix. Order of DOF
connectivities is not important.
Parameters
----------
any_dof_conn : bool
By default, only volume DOF connectivities are used, with
the exception of trace surface DOF connectivities. If True,
any kind of DOF connectivities is allowed.
rdcs, cdcs : arrays, optional
Additional row and column DOF connectivities, corresponding
to the variables used in the equations.
shape : tuple, optional
The required shape, if it is different from the shape
determined by the equations variables. This may be needed if
additional row and column DOF connectivities are passed in.
active_only : bool
If True, the matrix graph has reduced size and is created with the
reduced (active DOFs only) numbering.
verbose : bool
If False, reduce verbosity.
Returns
-------
matrix : csr_matrix
The matrix graph in the form of a CSR matrix with
preallocated structure and zero data.
"""
if not self.variables.has_virtuals():
output('no matrix (no test variables)!')
return None
shape = get_default(shape, self.variables.get_matrix_shape())
output('matrix shape:', shape, verbose=verbose)
if nm.prod(shape) == 0:
output('no matrix (zero size)!')
return None
rdcs, cdcs = self.get_graph_conns(any_dof_conn=any_dof_conn,
rdcs=rdcs, cdcs=cdcs,
active_only=active_only)
if not len(rdcs):
output('no matrix (empty dof connectivities)!')
return None
output('assembling matrix graph...', verbose=verbose)
tt = time.clock()
nnz, prow, icol = create_mesh_graph(shape[0], shape[1],
len(rdcs), rdcs, cdcs)
output('...done in %.2f s' % (time.clock() - tt), verbose=verbose)
output('matrix structural nonzeros: %d (%.2e%% fill)' \
% (nnz, float(nnz) / nm.prod(shape)), verbose=verbose)
data = nm.zeros((nnz,), dtype=self.variables.dtype)
matrix = sp.csr_matrix((data, icol, prow), shape)
return matrix
def init_time(self, ts):
pass
def advance(self, ts):
for eq in self:
for term in eq.terms:
term.advance(ts)
self.variables.advance(ts)
##
# Interface to self.variables.
def create_state_vector(self):
return self.variables.create_state_vector()
def create_stripped_state_vector(self):
return self.variables.create_stripped_state_vector()
def strip_state_vector(self, vec, follow_epbc=False):
"""
Strip a full vector by removing EBC dofs.
Notes
-----
If 'follow_epbc' is True, values of EPBC master dofs are not simply
thrown away, but added to the corresponding slave dofs, just like when
assembling. For vectors with state (unknown) variables it should be set
to False, for assembled vectors it should be set to True.
"""
return self.variables.strip_state_vector(vec, follow_epbc=follow_epbc)
def make_full_vec(self, svec, force_value=None):
"""
Make a full DOF vector satisfying E(P)BCs from a reduced DOF
vector.
"""
return self.variables.make_full_vec(svec, force_value)
def set_variables_from_state(self, vec, step=0):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The state vector.
step : int
The time history step, 0 (default) = current.
"""
self.variables.set_data(vec, step=step)
def get_state_parts(self, vec=None):
"""
Return parts of a state vector corresponding to individual state
variables.
Parameters
----------
vec : array, optional
The state vector. If not given, then the data stored in the
variables are returned instead.
Returns
-------
out : dict
The dictionary of the state parts.
"""
return self.variables.get_state_parts(vec)
def set_data(self, data, step=0, ignore_unknown=False):
"""
Set data (vectors of DOF values) of variables.
Parameters
----------
data : array
The dictionary of {variable_name : data vector}.
step : int, optional
The time history step, 0 (default) = current.
ignore_unknown : bool, optional
Ignore unknown variable names if `data` is a dict.
"""
self.variables.set_data(data, step=step,
ignore_unknown=ignore_unknown)
def apply_ebc(self, vec, force_values=None):
"""
Apply essential (Dirichlet) boundary conditions to a state vector.
"""
self.variables.apply_ebc(vec, force_values=force_values)
def apply_ic(self, vec, force_values=None):
"""
Apply initial conditions to a state vector.
"""
self.variables.apply_ic(vec, force_values=force_values)
def state_to_output(self, vec, fill_value=None, var_info=None,
extend=True):
return self.variables.state_to_output(vec,
fill_value=fill_value,
var_info=var_info,
extend=extend)
def get_lcbc_operator(self):
return self.variables.get_lcbc_operator()
def evaluate(self, names=None, mode='eval', dw_mode='vector',
term_mode=None, asm_obj=None):
"""
Evaluate the equations.
Parameters
----------
mode : one of 'eval', 'el_avg', 'qp', 'weak'
The evaluation mode.
names : str or sequence of str, optional
Evaluate only equations of the given name(s).
Returns
-------
out : dict or result
The evaluation result. In 'weak' mode it is the
`asm_obj`. Otherwise, it is a dict of results with equation names
as keys or a single result for a single equation.
"""
if names is None:
eqs = self
single = (len(eqs) == 1)
else:
single = isinstance(names, str)
if single:
names = [names]
eqs = [self[eq] for eq in names]
if mode == 'weak':
for eq in eqs:
eq.evaluate(mode=mode, dw_mode=dw_mode,
term_mode=term_mode, asm_obj=asm_obj)
out = asm_obj
else:
out = {}
for eq in eqs:
eout = eq.evaluate(mode=mode, dw_mode=dw_mode,
term_mode=term_mode)
out[eq.name] = eout
if single:
out = out.popitem()[1]
return out
def eval_residuals(self, state, by_blocks=False, names=None):
"""
Evaluate (assemble) residual vectors.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
by_blocks : bool
If True, return the individual blocks composing the whole
residual vector. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : array or dict of array
The assembled residual vector. If `by_blocks` is True, a
dictionary is returned instead, with keys given by
`block_name` part of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip()
for aux in name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
residual = self.create_stripped_state_vector()
eq.evaluate(mode='weak', dw_mode='vector', asm_obj=residual)
out[key] = residual[ir]
else:
out = self.create_stripped_state_vector()
self.evaluate(mode='weak', dw_mode='vector', asm_obj=out)
return out
def eval_tangent_matrices(self, state, tangent_matrix,
by_blocks=False, names=None):
"""
Evaluate (assemble) tangent matrices.
Parameters
----------
state : array
The vector of DOF values. Note that it is needed only in
nonlinear terms.
tangent_matrix : csr_matrix
The preallocated CSR matrix with zero data.
by_blocks : bool
If True, return the individual blocks composing the whole
matrix. Each equation should then correspond to one
required block and should be named as `'block_name,
test_variable_name, unknown_variable_name'`.
names : list of str, optional
Optionally, select only blocks with the given `names`, if
`by_blocks` is True.
Returns
-------
out : csr_matrix or dict of csr_matrix
The assembled matrix. If `by_blocks` is True, a dictionary
is returned instead, with keys given by `block_name` part
of the individual equation names.
"""
self.set_variables_from_state(state)
if by_blocks:
names = get_default(names, self.names)
out = {}
get_indx = self.variables.get_indx
for name in names:
eq = self[name]
key, rname, cname = [aux.strip()
for aux in eq.name.split(',')]
ir = get_indx(rname, stripped=True, allow_dual=True)
ic = get_indx(cname, stripped=True, allow_dual=True)
tangent_matrix.data[:] = 0.0
eq.evaluate(mode='weak', dw_mode='matrix',
asm_obj=tangent_matrix)
out[key] = tangent_matrix[ir, ic]
else:
tangent_matrix.data[:] = 0.0
self.evaluate(mode='weak', dw_mode='matrix', asm_obj=tangent_matrix)
out = tangent_matrix
return out
