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"""System integration tests for ufl-derivative-jit-assembly chain."""
# Copyright (C) 2011 Martin S. Alnaes
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2011-20-09
# Last changed: 2011-20-09
import unittest
import numpy
import math
from dolfin import *
def test_diff_then_integrate():
# Define 1D geometry
n = 21
mesh = UnitIntervalMesh(n)
# Shift and scale mesh
x0, x1 = 1.5, 3.14
mesh.coordinates()[:] *= (x1 - x0)
mesh.coordinates()[:] += x0
x = SpatialCoordinate(mesh)[0]
xs = 0.1+0.8*x/x1 # scaled to be within [0.1,0.9]
# Define list of expressions to test, and configure
# accuracies these expressions are known to pass with.
# The reason some functions are less accurately integrated is
# likely that the default choice of quadrature rule is not perfect
F_list = []
def reg(exprs, acc=10):
for expr in exprs:
F_list.append((expr, acc))
# FIXME: 0*dx and 1*dx fails in the ufl-ffc-jit framework somewhere
#reg([Constant(0.0, cell=cell)])
#reg([Constant(1.0, cell=cell)])
monomial_list = [x**q for q in range(2, 6)]
reg(monomial_list)
reg([2.3*p+4.5*q for p in monomial_list for q in monomial_list])
reg([x**x])
reg([x**(x**2)], 8)
reg([x**(x**3)], 6)
reg([x**(x**4)], 2)
# Special functions:
reg([atan(xs)], 8)
reg([sin(x), cos(x), exp(x)], 5)
reg([ln(xs), pow(x, 2.7), pow(2.7, x)], 3)
reg([asin(xs), acos(xs)], 1)
reg([tan(xs)], 7)
try:
import scipy
except:
scipy = None
if hasattr(math, 'erf') or scipy is not None:
reg([erf(xs)])
else:
print("Warning: skipping test of erf, old python version and no scipy.")
if 0:
print("Warning: skipping tests of bessel functions, doesn't build on all platforms.")
elif scipy is None:
print("Warning: skipping tests of bessel functions, missing scipy.")
else:
for nu in (0,1,2):
# Many of these are possibly more accurately integrated,
# but 4 covers all and is sufficient for this test
reg([bessel_J(nu, xs), bessel_Y(nu, xs), bessel_I(nu, xs), bessel_K(nu, xs)], 4)
# To handle tensor algebra, make an x dependent input tensor
# xx and square all expressions
def reg2(exprs, acc=10):
for expr in exprs:
F_list.append((inner(expr,expr), acc))
xx = as_matrix([[2*x**2, 3*x**3], [11*x**5, 7*x**4]])
x3v = as_vector([3*x**2, 5*x**3, 7*x**4])
cc = as_matrix([[2, 3], [4, 5]])
reg2([xx])
reg2([x3v])
reg2([cross(3*x3v, as_vector([-x3v[1], x3v[0], x3v[2]]))])
reg2([xx.T])
reg2([tr(xx)])
reg2([det(xx)])
reg2([dot(xx, 0.1*xx)])
reg2([outer(xx, xx.T)])
reg2([dev(xx)])
reg2([sym(xx)])
reg2([skew(xx)])
reg2([elem_mult(7*xx, cc)])
reg2([elem_div(7*xx, xx+cc)])
reg2([elem_pow(1e-3*xx, 1e-3*cc)])
reg2([elem_pow(1e-3*cc, 1e-3*xx)])
reg2([elem_op(lambda z: sin(z) + 2, 0.03*xx)], 2) # pretty inaccurate...
# FIXME: Add tests for all UFL operators:
# These cause discontinuities and may be harder to test in the
# above fashion:
#'inv', 'cofac',
#'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not',
#'conditional', 'sign',
#'jump', 'avg',
#'LiftingFunction', 'LiftingOperator',
# FIXME: Test other derivatives: (but algorithms for operator
# derivatives are the same!):
#'variable', 'diff',
#'Dx', 'grad', 'div', 'curl', 'rot', 'Dn', 'exterior_derivative',
# Run through all operators defined above and compare integrals
debug = 0
for F, acc in F_list:
# Apply UFL differentiation
f = diff(F, SpatialCoordinate(mesh))[...,0]
if debug:
print(F)
print(x)
print(f)
# Apply integration with DOLFIN
# (also passes through form compilation and jit)
M = f*dx
f_integral = assemble(M)
# Compute integral of f manually from anti-derivative F
# (passes through PyDOLFIN interface and uses UFL evaluation)
F_diff = F((x1,)) - F((x0,))
# Compare results. Using custom relative delta instead
# of decimal digits here because some numbers are >> 1.
delta = min(abs(f_integral), abs(F_diff)) * 10**-acc
assert f_integral - F_diff <= delta
def test_div_grad_then_integrate_over_cells_and_boundary():
# Define 2D geometry
n = 10
mesh = RectangleMesh(Point(0.0, 0.0), Point(2.0, 3.0), 2*n, 3*n)
x, y = SpatialCoordinate(mesh)
xs = 0.1+0.8*x/2 # scaled to be within [0.1,0.9]
ys = 0.1+0.8*y/3 # scaled to be within [0.1,0.9]
n = FacetNormal(mesh)
# Define list of expressions to test, and configure accuracies
# these expressions are known to pass with. The reason some
# functions are less accurately integrated is likely that the
# default choice of quadrature rule is not perfect
F_list = []
def reg(exprs, acc=10):
for expr in exprs:
F_list.append((expr, acc))
# FIXME: 0*dx and 1*dx fails in the ufl-ffc-jit framework somewhere
#reg([Constant(0.0, cell=cell)])
#reg([Constant(1.0, cell=cell)])
monomial_list = [x**q for q in range(2, 6)]
reg(monomial_list)
reg([2.3*p+4.5*q for p in monomial_list for q in monomial_list])
reg([xs**xs])
reg([xs**(xs**2)], 8) # Note: Accuracies here are from 1D case, not checked against 2D results.
reg([xs**(xs**3)], 6)
reg([xs**(xs**4)], 2)
# Special functions:
reg([atan(xs)], 8)
reg([sin(x), cos(x), exp(x)], 5)
reg([ln(xs), pow(x, 2.7), pow(2.7, x)], 3)
reg([asin(xs), acos(xs)], 1)
reg([tan(xs)], 7)
# To handle tensor algebra, make an x dependent input tensor
# xx and square all expressions
def reg2(exprs, acc=10):
for expr in exprs:
F_list.append((inner(expr,expr), acc))
xx = as_matrix([[2*x**2, 3*x**3], [11*x**5, 7*x**4]])
xxs = as_matrix([[2*xs**2, 3*xs**3], [11*xs**5, 7*xs**4]])
x3v = as_vector([3*x**2, 5*x**3, 7*x**4])
cc = as_matrix([[2, 3], [4, 5]])
reg2([xx]) # TODO: Make unit test for UFL from this, results in listtensor with free indices
reg2([x3v])
reg2([cross(3*x3v, as_vector([-x3v[1], x3v[0], x3v[2]]))])
reg2([xx.T])
reg2([tr(xx)])
reg2([det(xx)])
reg2([dot(xx,0.1*xx)])
reg2([outer(xx,xx.T)])
reg2([dev(xx)])
reg2([sym(xx)])
reg2([skew(xx)])
reg2([elem_mult(7*xx, cc)])
reg2([elem_div(7*xx, xx+cc)])
reg2([elem_pow(1e-3*xxs, 1e-3*cc)])
reg2([elem_pow(1e-3*cc, 1e-3*xx)])
reg2([elem_op(lambda z: sin(z)+2, 0.03*xx)], 2) # pretty inaccurate...
# FIXME: Add tests for all UFL operators:
# These cause discontinuities and may be harder to test in the
# above fashion:
#'inv', 'cofac',
#'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not',
#'conditional', 'sign',
#'jump', 'avg',
#'LiftingFunction', 'LiftingOperator',
# FIXME: Test other derivatives: (but algorithms for operator
# derivatives are the same!):
#'variable', 'diff',
#'Dx', 'grad', 'div', 'curl', 'rot', 'Dn', 'exterior_derivative',
# Run through all operators defined above and compare integrals
debug = 0
if debug:
k = 2
F_list = F_list[1:]
for F,acc in F_list:
if debug: print('\n', "F:", str(F))
# Integrate over domain and its boundary
int_dx = assemble(div(grad(F))*dx(mesh))
int_ds = assemble(dot(grad(F), n)*ds(mesh))
if debug: print(int_dx, int_ds)
# Compare results. Using custom relative delta instead of
# decimal digits here because some numbers are >> 1.
delta = min(abs(int_dx), abs(int_ds)) * 10**-acc
assert int_dx - int_ds <= delta
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