def linear_projection(pb, cval):
from sfepy.discrete import (FieldVariable, Material, Integral, Equation,
Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.base.base import IndexedStruct
mesh = Mesh.from_file(pb.conf.filename_mesh)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('scf', nm.float64, 'scalar', omega, approx_order=1)
g = FieldVariable('g', 'unknown', field)
f = FieldVariable('f', 'test', field, primary_var_name='g')
integral = Integral('i', order=2)
m = Material('m', function=set_grad)
t1 = Term.new('dw_volume_dot(f, g)', integral, omega, f=f, g=g)
t2 = Term.new('dw_volume_lvf(m.cs, f)', integral, omega, m=m, f=f)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'eps_a': 1e-15}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs)
pb.set_solver(nls)
out = nm.empty((g.n_dof, cval.shape[2]), dtype=nm.float64)
for ii in range(cval.shape[2]):
pb.data = nm.ascontiguousarray(cval[:, :, ii, :])
pb.time_update()
state = pb.solve()
out[:, ii] = state.get_parts()['g']
return out
