Undefined near, solve, tr for dolfinx-v0.6.0

General
1 
from contextlib import ExitStack

import numpy as np


#from dolfinx import *
from dolfinx import la

from dolfinx.cpp.function import near
from dolfinx.fem import (Expression, Function, FunctionSpace,
                         VectorFunctionSpace, dirichletbc, form,
                         locate_dofs_topological, Constant)
from dolfinx.fem.petsc import (apply_lifting, assemble_matrix, assemble_vector,
                               set_bc)
from dolfinx.io import XDMFFile
from dolfinx.mesh import (CellType, GhostMode, create_box, create_rectangle,
                          locate_entities_boundary)
import ufl 
from ufl import dx, grad, inner, sym, Identity, TrialFunction, TestFunction

from mpi4py import MPI
from petsc4py import PETSc
comm = MPI.COMM_SELF
L = 25.
H = 1.
Nx = 250
Ny = 10

mesh = create_rectangle(comm=comm, points=((0.0, 0.0), (L, H)), n=(Nx, Ny),
                            cell_type=CellType.triangle)

def eps(v):
    return sym(grad(v))

E = Constant(1e5)
nu = Constant(0.3)
model = "plane_stress"

mu = E/2/(1+nu)
lmbda = E*nu/(1+nu)/(1-2*nu)
if model == "plane_stress":
    lmbda = 2*mu*lmbda/(lmbda+2*mu)

#def sigma(v):
#    return lmbda*tr(eps(v))*Identity(2) + 2.0*mu*eps(v)

def sigma(v):
    return lmbda*eps(v)*Identity(2) + 2.0*mu*eps(v)

rho_g = 1e-3
f = Constant((0, -rho_g))

V = VectorFunctionSpace(mesh, 'Lagrange', degree=2)
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du), eps(u_))*dx
l = inner(f, u_)*dx

def left(x, on_boundary):
    return near(x[0], 0.)

bc = dirichletbc(V, Constant((0.,0.)), left)

u = Function(V, name="Displacement")
#solve(a == l, u, bc)

problem = PETSc.LinearProblem(a, L, bcs=[bc], petsc_options={"ksp_type": "preonly", "pc_type": "lu"})
uh = problem.solve()

#plot(1e3*u, mode="displacement")


print('done...')

I moved this code into dolfinx-0.6.0 from:
https://comet-fenics.readthedocs.io/en/latest/demo/elasticity/2D_elasticity.py.html

So far there seems to be a difficulty with import dolfinx.cpp.funtion.near. I see there is a way to implement a linear solver from fenicsx tutorials if that is the same type of solver as was meant by the author of 2D_elasticity.html tutorial. So far the function tr() is undefined. Could it be stated what that tr() was originally meant to compute it?

2

Please look at the dolfinx demos or the dolfinx tutorial for syntax on how to describe Dirichlet boundary conditions. The input to the dorichletbc constructor should not be a function to locate dofs/entities, but a list of dofs.

In DOLFINx you use locate_dofs_topological or locate_dofs_geometrical where near is replaced by np.isclose

tr is the trace operator, and it can be imported from ufl.

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