def test_simplify_quantities():
print "Testing simplification of quantities"
from quantity import Constant, SpaceField, Quantities
zero = Constant("zero", subfields=False, value=Value(0.0))
C = Constant("C",
subfields=True,
value=Value("mat1", -1.25).set("mat2", -2.5))
a = SpaceField("a", [3], subfields=True)
b = SpaceField("b", [3])
H_exch = SpaceField("H_exch", [3], subfields=True)
rho = SpaceField("rho", [])
M_sat = Constant("M_sat", [],
subfields=True,
value=Value("mat1", 1e6).set("mat2", 0.5e6))
m = SpaceField("m", [3], subfields=True)
qs = [C, a, b, H_exch, m, rho, M_sat]
context = OpSimplifyContext(quantities=Quantities(qs),
material=["mat1", "mat2"],
is_periodic=True)
# Testing the 'periodic' amendment
pbc_in = \
"C*<d/dxj H_exch(k)||d/dxj m(k)>; periodic:H_exch(k), j:1, k:3"
# Expected result if context.is_periodic = True
pbc_out_if_pbc = \
(" (-1.25)*<d/dxj H_exch_mat1(k)||d/dxj m_mat1(k)> "
"+ (-2.5)*<d/dxj H_exch_mat2(k)||d/dxj m_mat2(k)>; "
"periodic: H_exch_mat1(k); periodic: H_exch_mat2(k),"
"j:1, k:3")
# Expected result if context.is_periodic = False
pbc_out_ifnot_pbc = \
(" (-1.25)*<d/dxj H_exch_mat1(k)||d/dxj m_mat1(k)> "
"+ (-2.5)*<d/dxj H_exch_mat2(k)||d/dxj m_mat2(k)>, "
"j:1, k:3")
strings = {}
strings[True] = \
[("<a||b>", "<a_mat1||b> + <a_mat2||b>"),
("C*<d/dxj H_exch(k)||d/dxj m(k)>, j:1, k:3",
" (-1.25)*<d/dxj H_exch_mat1(k)||d/dxj m_mat1(k)> "
"+ (-2.5)*<d/dxj H_exch_mat2(k)||d/dxj m_mat2(k)>,j:1, k:3"),
("M_sat*<rho||d/dxj m(j)> + M_sat*<rho||D/Dxj m(j)>, j:3",
" 1000000.0*<rho||d/dxj m_mat1(j)> + "
"1000000.0*<rho||D/Dxj m_mat1(j)> + "
"500000.0*<rho||d/dxj m_mat2(j)> + "
"500000.0*<rho||D/Dxj m_mat2(j)>, j:3"),
(pbc_in, pbc_out_if_pbc)]
strings[False] = [(pbc_in, pbc_out_ifnot_pbc)]
for is_periodic in (False, True):
context.is_periodic = is_periodic
for string, result in strings[is_periodic]:
parse_tree = parse(string).simplify(context=context)
my_result = str(parse_tree)
assert compare_strings(my_result, result), \
("Simplified of '%s' is '%s', but '%s' is expected."
% (string, my_result, result))
print "passed"
def test_llg():
print "Testing LLG single material"
from quantity import Constant, SpaceField, Quantities
C1 = Constant("C1", subfields=False, value=Value(-0.125))
C2 = Constant("C2", subfields=False, value=Value(-0.0625))
C3 = Constant("C3", subfields=False, value=Value(0.25))
C4 = Constant("C4", subfields=False, value=Value(0.0))
C5 = Constant("C5", subfields=False, value=Value(0.0))
m = SpaceField("m", [3], subfields=True)
dmdt = SpaceField("dmdt", [3], subfields=True)
dm_dcurrent = SpaceField("dm_dcurrent", [3], subfields=False)
pin = SpaceField("pin", subfields=False)
H_total = SpaceField("H_total", [3], subfields=True)
quantities = Quantities([C1, C2, C3, C4, C5, m, dmdt, dm_dcurrent, pin,
H_total])
eq_rhs = """
%range i:3;
(dmdt(i) <-
( C1 * (eps(i,j,k) * m(j) * H_total(k))_(j:3,k:3)
+ C2 * ( eps(i,j,k) * m(j)
* eps(k,p,q) * m(p) * H_total(q))_(j:3,k:3,p:3,q:3)
+ C3 * (1.0 - (m(j)*m(j))_(j:3)) * m(i)
+ C4 * ( eps(i,j,k) * m(j)
* eps(k,p,q) * m(p) * dm_dcurrent(q))_(j:3,k:3,p:3,q:3)
+ C5 * (eps(i,j,k) * m(j) * dm_dcurrent(k))_(j:3,k:3))*pin)_(i:3);"""
#eq_rhs = """dmdt(0) <- (-m(i))_(i:3);"""
eq_ccode = """
if (have_dmdt_a) {
dmdt_a(0) = (-0.125*(m_a(1)*H_total_a(2) + -1.0*m_a(2)*H_total_a(1)) + -0.0625*(m_a(1)*m_a(0)*H_total_a(1) + -1.0*m_a(1)*m_a(1)*H_total_a(0) + m_a(2)*m_a(0)*H_total_a(2) + -1.0*m_a(2)*m_a(2)*H_total_a(0)) + 0.25*(1.0 - (m_a(0)*m_a(0) + m_a(1)*m_a(1) + m_a(2)*m_a(2)))*m_a(0))*pin;
};
if (have_dmdt_a) {
dmdt_a(1) = (-0.125*(-1.0*m_a(0)*H_total_a(2) + m_a(2)*H_total_a(0)) + -0.0625*(-1.0*m_a(0)*m_a(0)*H_total_a(1) + m_a(0)*m_a(1)*H_total_a(0) + m_a(2)*m_a(1)*H_total_a(2) + -1.0*m_a(2)*m_a(2)*H_total_a(1)) + 0.25*(1.0 - (m_a(0)*m_a(0) + m_a(1)*m_a(1) + m_a(2)*m_a(2)))*m_a(1))*pin;
};
if (have_dmdt_a) {
dmdt_a(2) = (-0.125*(m_a(0)*H_total_a(1) + -1.0*m_a(1)*H_total_a(0)) + -0.0625*(-1.0*m_a(0)*m_a(0)*H_total_a(2) + m_a(0)*m_a(2)*H_total_a(0) + -1.0*m_a(1)*m_a(1)*H_total_a(2) + m_a(1)*m_a(2)*H_total_a(1)) + 0.25*(1.0 - (m_a(0)*m_a(0) + m_a(1)*m_a(1) + m_a(2)*m_a(2)))*m_a(2))*pin;
};"""
context = EqSimplifyContext(quantities=quantities, material='a')
context.expand_indices = True
parse_tree = parse(eq_rhs).simplify(context=context)
my_result = parse_tree.get_ccode() #.replace("\n", "")
assert compare_strings(my_result, eq_ccode), \
("Simplified of '%s' is '%s', but '%s' is expected."
% (eq_rhs, my_result, eq_ccode))
print "passed"
def __init__(self, name, mesh, mesh_unit, region_materials,
min_region=-1):
"""
:Parameters:
`region_materials` : list of list of string
region_materials[region_nr] is a list of names (strings) of field
components (like "mat1", "mat2") available in the mesh region
with number 'region_nr'. For example, for a mesh with three
regions and region_materials=[["one", "two"], ["one", "three"],
["one"]], a field 'f' defined 'per-material' will have three
sub-fields 'f_one', 'f_two' and 'f_three' with: 'f_one' defined
everywhere, 'f_two' defined in region 0 and 'f_three' defined in
region 1.
"""
# Just save the relevant stuff
self.name = name
self.mesh = mesh
self.mesh_unit = mesh_unit
self.dim = mesh.dim
self.region_materials = region_materials
self.min_region = min_region
self.regions = \
MeshRegions(region_materials, min_region=min_region)
# Things that get constructed when the object is "used"
self.computations = Computations()
self.quantities = Quantities()
self.timesteppers = Timesteppers()
# Initialise some members
self.quantities.primary = None
self.quantities.derived = None
self.quantities.dependencies = None
self.targets = []
self.intensive_params = []
self.elems_by_field = {} # For each field: list of elems ordered
# per region
self.prototype_elems = [] # List of the prototype elements
self.sibling_elems = {}
self.mwes = {} # All the MWEs
self.lam = None
self._built = {}
def test_simplify_quantities():
print "Testing simplification of quantities"
from quantity import Constant, SpaceField, Quantities
zero = Constant("zero", subfields=False, value=Value(0.0))
gamma = Constant("gamma", subfields=False, value=Value(1.23))
m = SpaceField("m", [3], subfields=True)
H_ext = SpaceField("H_ext", [3])
context = \
EqSimplifyContext(quantities=Quantities([gamma, m, H_ext, zero]))
strings = [("m(0) <- -zero*(m(1)*H_ext(2) - m(2)*H_ext(1));",
"m(0) <- 0.0;")]
for string, result in strings:
parse_tree = parse(string).simplify(context=context)
my_result = str(parse_tree).replace("\n", "")
assert my_result == result, ("Simplified of '%s' is '%s', but '%s' "
"is expected." %
(string, my_result, result))
print "passed"
def test_llg_multimaterial():
print "Testing LLG multi-material"
from quantity import Constant, SpaceField, Quantities
C1 = Constant("C1", subfields=False, value=Value(-0.125))
C2 = Constant("C2", subfields=False, value=Value(-0.0625))
C3 = Constant("C3", subfields=False, value=Value(0.25))
C4 = Constant("C4", subfields=False, value=Value(0.0))
C5 = Constant("C5", subfields=False, value=Value(0.0))
m = SpaceField("m", [3], subfields=True)
dmdt = SpaceField("dmdt", [3], subfields=True)
dm_dcurrent = SpaceField("dm_dcurrent", [3], subfields=False)
pin = SpaceField("pin", subfields=False)
H_total = SpaceField("H_total", [3], subfields=True)
quantities = Quantities(
[C1, C2, C3, C4, C5, m, dmdt, dm_dcurrent, pin, H_total])
eq_rhs = """%range i:3, j:3, k:3, p:3, q:3;
dmdt(i) <- C1 * eps(i,j,k) * m(j) * H_total(k) * pin
+ C2 * eps(i,j,k) * m(j) * eps(k,p,q) * m(p) * H_total(q) * pin
+ C3 * (1.0 - m(j)*m(j)) * m(i) * pin
+ C4 * eps(i,j,k) * m(j) * eps(k,p,q) * m(p) * dm_dcurrent(q) * pin
+ C5 * eps(i,j,k) * m(j) * dm_dcurrent(k) * pin;"""
result = condensed_string("""%range i:3, j:3, k:3, p:3, q:3;
dmdt_Py(i) <-
-0.125*eps(i,j,k)*m_Py(j)*H_total_Py(k)*pin
+ -0.0625*eps(i,j,k)*m_Py(j)*eps(k,p,q)*m_Py(p)*H_total_Py(q)*pin
+ 0.25*(1.0 - m_Py(j)*m_Py(j))*m_Py(i)*pin;
dmdt_Co(i) <-
-0.125*eps(i,j,k)*m_Co(j)*H_total_Co(k)*pin
+ -0.0625*eps(i,j,k)*m_Co(j)*eps(k,p,q)*m_Co(p)*H_total_Co(q)*pin
+ 0.25*(1.0 - m_Co(j)*m_Co(j))*m_Co(i)*pin;""")
context = EqSimplifyContext(quantities=quantities, material=['Py', 'Co'])
parse_tree = parse(eq_rhs).simplify(context=context)
my_result = condensed_string(str(parse_tree))
assert compare_strings(my_result, result), \
("Simplified of '%s' is '%s', but '%s' is expected."
% (eq_rhs, my_result, result))
print "passed"
def test_multimaterial():
print "Testing multimaterial simplification"
from quantity import Constant, SpaceField, Quantities
C1 = Constant("C1", subfields=False, value=Value(-0.17688))
C2 = Constant("C2", subfields=True, value=Value(-0.08844))
m = SpaceField("m", [3], subfields=True)
dmdt = SpaceField("dmdt", [3], subfields=True)
quantities = Quantities([C1, C2, m, dmdt])
strings = [
("%range i:3; m <- 0;", "%range i:3; m_Py <- 0.0; m_Co <- 0.0;"),
]
context = EqSimplifyContext(quantities=quantities, material=['Py', 'Co'])
for string, result in strings:
my_result = \
str(parse(string).simplify(context=context)).replace("\n", "")
assert compare_strings(my_result, result), \
("Simplified of '%s' is '%s', but '%s' is expected."
% (string, my_result, result))
print "passed"
