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test_msm_symbolic.py
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test_msm_symbolic.py
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# c: 07.05.2007, r: 08.07.2008
from sfepy import data_dir
filename_mesh = data_dir + '/meshes/2d/special/circle_in_square.mesh'
dim = 2
field_1 = {
'name' : 'a_harmonic_field',
'dtype' : 'real',
'shape' : 'scalar',
'region' : 'Omega',
'approx_order' : 1,
}
variables = {
't': ('unknown field', 'a_harmonic_field', 0),
's': ('test field', 'a_harmonic_field', 't'),
}
regions = {
'Omega' : ('all', {}),
'Left' : ('nodes in (x < 0.001) & (y < 0.001)', {}),
'Right' : ('nodes in (x > 0.999)', {}),
'Gamma' : ('nodes of surface', {}),
}
ebcs = {
't_left' : ('Gamma', {'t.0' : 'ebc'}),
# 't_right' : ('Right', {'t.0' : 'ebc'}),
}
integral_1 = {
'name' : 'i1',
'kind' : 'v',
'order' : 2,
}
material_1 = {
'name' : 'coef',
'values' : {
'val' : 12.0,
'K' : [[1.0, 0.3], [0.3, 2.0]],
}
}
material_2 = {
'name' : 'rhs',
'function' : 'rhs',
}
equations = {
'Laplace' :
"""2 * dw_laplace.i1.Omega( coef.val, s, t )
""",
'Diffusion' :
"""3 * dw_diffusion.i1.Omega( coef.K, s, t )
""",
}
equations_rhs = {
'Laplace' :
"""= - dw_volume_lvf.i1.Omega( rhs.val, s )""",
'Diffusion' :
"""= - dw_volume_lvf.i1.Omega( rhs.val, s )""",
}
solutions = {
'sincos' : ('t', 'sin( 3.0 * x ) * cos( 4.0 * y )'),
'poly' : ('t', '(x**2) + (y**2)'),
'polysin' : ('t', '((x - 0.5)**3) * sin( 5.0 * y )'),
}
solver_0 = {
'name' : 'ls',
'kind' : 'ls.scipy_direct',
}
solver_1 = {
'name' : 'newton',
'kind' : 'nls.newton',
'i_max' : 1,
'eps_a' : 1e-10,
'eps_r' : 1.0,
'macheps' : 1e-16,
'lin_red' : 1e-2, # Linear system error < (eps_a * lin_red).
'ls_red' : 0.1,
'ls_red_warp' : 0.001,
'ls_on' : 1.1,
'ls_min' : 1e-5,
'check' : 0,
'delta' : 1e-6,
'is_plot' : False,
'problem' : 'nonlinear', # 'nonlinear' or 'linear' (ignore i_max)
}
import numpy as nm
try:
import sympy_operators as sops
except ImportError, exc:
sops = None
from sfepy.base.testing import TestCommon
from sfepy.base.base import debug, pause
output_name = 'test_msm_symbolic_%s.vtk'
##
# c: 07.05.2007, r: 09.05.2008
solution = ['']
def ebc(ts, coor, solution=None):
expression = solution[0]
val = TestCommon.eval_coor_expression( expression, coor )
return nm.atleast_1d( val )
def rhs(ts, coor, mode=None, expression=None, **kwargs):
if mode == 'qp':
if expression is None:
expression = '0.0 * x'
val = TestCommon.eval_coor_expression( expression, coor )
val.shape = (val.shape[0], 1, 1)
return {'val' : val}
functions = {
'ebc' : (lambda ts, coor, **kwargs:
ebc(ts, coor, solution=solution),),
'rhs' : (rhs,),
}
##
# c: 07.05.2008
class Test( TestCommon ):
##
# c: 07.05.2007, r: 25.06.2008
def from_conf( conf, options ):
from sfepy.fem import ProblemDefinition
problem = ProblemDefinition.from_conf( conf, init_equations = False )
test = Test( problem = problem,
conf = conf, options = options )
return test
from_conf = staticmethod( from_conf )
##
# c: 09.05.2007, r: 08.07.2008
def _build_rhs( self, equation, sols ):
problem = self.problem
rhss = {}
self.report( '%s:' % equation.name )
self.report( 'evaluating terms, "<=" is solution, "=>" is the rhs:' )
for term in equation.terms:
if not hasattr( term, 'symbolic' ):
self.report( 'term %s has no symbolic description!' % term.name )
raise ValueError
expr = term.symbolic['expression']
arg_map = term.symbolic['map']
self.report( '%s( %s )' %\
(term.name, ', '.join( term.ats )) )
self.report( 'multiplicator: %f' % term.sign )
self.report( ' symbolic:', expr )
self.report( ' using argument map:', arg_map )
for sol_name, sol in sols.iteritems():
rhs = self._eval_term( sol[1], term, sops )
srhs = "(%s * (%s))" % (term.sign, rhs)
rhss.setdefault( sol_name, [] ).append( srhs )
for key, val in rhss.iteritems():
rhss[key] = '+'.join( val )
return rhss
##
# c: 09.05.2007, r: 25.06.2008
def _eval_term( self, sol, term, sops ):
"""Works for scalar, single unknown terms only!"""
expr = term.symbolic['expression']
arg_map = term.symbolic['map']
env = {'x' : sops.Symbol( 'x' ),
'y' : sops.Symbol( 'y' ),
'z' : sops.Symbol( 'z' ),
'dim' : dim}
for key, val in arg_map.iteritems():
if val == 'state':
env[key] = sol
else:
term.set_current_group(0)
env[key] = term.get_args( [val] )[0]
if 'material' in val:
# Take the first value - constant in all QPs.
aux = env[key][0,0]
if nm.prod( aux.shape ) == 1:
env[key] = aux.squeeze()
else:
import sympy
env[key] = sympy.Matrix( aux )
# print env
self.report( ' <= ', sol )
sops.set_dim( dim )
val = str( eval( expr, sops.__dict__, env ) )
self.report( ' =>', val )
return val
##
# c: 07.05.2007, r: 30.06.2008
def _test_msm_symbolic( self, equations ):
import os.path as op
if sops is None:
self.report( 'cannot import sympy, skipping' )
return True
problem = self.problem
ok = True
for eq_name, equation in equations.iteritems():
problem.set_equations( {eq_name : equation} )
problem.update_materials()
rhss = self._build_rhs( problem.equations[eq_name],
self.conf.solutions )
erhs = problem.conf.equations_rhs[eq_name]
problem.set_equations( {eq_name : equation + erhs} )
variables = problem.get_variables()
materials = problem.get_materials()
rhs_mat = materials['rhs']
for sol_name, sol in problem.conf.solutions.iteritems():
self.report( 'testing', sol_name )
var_name, sol_expr = sol
rhs_expr = rhss[sol_name]
self.report( 'sol:', sol_expr )
self.report( 'rhs:', rhs_expr )
globals()['solution'][0] = sol_expr
rhs_mat.function.set_extra_args(expression=rhs_expr)
problem.time_update()
state = problem.solve()
coor = variables[var_name].field.get_coor()
ana_sol = self.eval_coor_expression( sol_expr, coor )
num_sol = state(var_name)
ana_norm = nm.linalg.norm( ana_sol, nm.inf )
ret = self.compare_vectors( ana_sol, num_sol,
allowed_error = ana_norm * 1e-2,
label1 = 'analytical %s' % var_name,
label2 = 'numerical %s' % var_name,
norm = nm.inf )
if not ret:
self.report( 'variable %s: failed' % var_name )
fname = op.join( self.options.out_dir, self.conf.output_name )
out = {}
astate = state.copy()
astate.set_full(ana_sol)
aux = astate.create_output_dict()
out['ana_t'] = aux['t']
aux = state.create_output_dict()
out['num_t'] = aux['t']
problem.domain.mesh.write( fname % '_'.join( (sol_name, eq_name) ),
io = 'auto', out = out )
ok = ok and ret
return ok
##
# c: 30.06.2008, r: 30.06.2008
def _get_equations( self, name ):
"""Choose a sub-problem from all equations."""
return {name : self.problem.conf.equations[name]}
##
# c: 30.06.2008, r: 30.06.2008
def test_msm_symbolic_laplace( self ):
return self._test_msm_symbolic( self._get_equations( 'Laplace' ) )
##
# c: 30.06.2008, r: 30.06.2008
def test_msm_symbolic_diffusion( self ):
return self._test_msm_symbolic( self._get_equations( 'Diffusion' ) )