#!/usr/bin/env python
from optparse import OptionParser
import numpy as nm

from sfepy.base.base import IndexedStruct
from sfepy.fem import Mesh, Domain, Field, FieldVariable, Material, Integral
from sfepy.fem import Function, Equation, Equations, ProblemDefinition
from sfepy.terms import Term
from sfepy.fem.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess import Viewer

def shift_u_fun(ts, coors, bc=None, shift=0.0):
    """
    Define a displacement depending on the y coordinate.
    """
    val = shift * coors[:,1]**2

    return val

usage = """%prog [options]"""
help = {
    'show' : 'show the results figure',
}

def main():
    from sfepy import data_dir

    parser = OptionParser(usage=usage, version='%prog')
    parser.add_option('-s', '--show',
                      action="store_true", dest='show',
                      default=False, help=help['show'])
    options, args = parser.parse_args()

    mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
    domain = Domain('domain', mesh)

    min_x, max_x = domain.get_mesh_bounding_box()[:,0]
    eps = 1e-8 * (max_x - min_x)
    omega = domain.create_region('Omega', 'all')
    gamma1 = domain.create_region('Gamma1',
                                  'nodes in x < %.10f' % (min_x + eps))
    gamma2 = domain.create_region('Gamma2',
                                  'nodes in x > %.10f' % (max_x - eps))

    field = Field('fu', nm.float64, 'vector', omega,
                  space='H1', poly_space_base='lagrange', approx_order=2)

    u = FieldVariable('u', 'unknown', field, mesh.dim)
    v = FieldVariable('v', 'test', field, mesh.dim, primary_var_name='u')

    m = Material('m', lam=1.0, mu=1.0)
    f = Material('f', val=[[0.02], [0.01]])

    integral = Integral('i', order=3)

    t1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
         integral, omega, m=m, v=v, u=u)
    t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
    eq = Equation('balance', t1 + t2)
    eqs = Equations([eq])

    fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})

    bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift' : 0.01})
    shift_u = EssentialBC('shift_u', gamma2, {'u.0' : bc_fun})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({}, lin_solver=ls, status=nls_status)

    pb = ProblemDefinition('elasticity', equations=eqs, nls=nls, ls=ls)
    pb.save_regions_as_groups('regions')

    pb.time_update(ebcs=Conditions([fix_u, shift_u]))

    vec = pb.solve()
    print nls_status

    pb.save_state('linear_elasticity.vtk', vec)

    if options.show:
        view = Viewer('linear_elasticity.vtk')
        view(vector_mode='warp_norm', rel_scaling=2,
             is_scalar_bar=True, is_wireframe=True)

if __name__ == '__main__':
    main()
