def power(self, o):
#print("\n\nVisiting Power: " + repr(o))
# Get base and exponent.
base, expo = o.ufl_operands
# Visit base to get base code.
base_code = self.visit(base)
# TODO: Are these safety checks needed?
ffc_assert(() in base_code and len(base_code) == 1,
"Only support function type base: " + repr(base_code))
# Get the base code and create power.
val = base_code[()]
# Handle different exponents
if isinstance(expo, IntValue):
return {(): create_product([val] * expo.value())}
elif isinstance(expo, FloatValue):
if self.parameters["format"] == "pyop2":
exp = create_float(expo.value())
else:
exp = format["floating point"](expo.value())
var = format["std power"][self.parameters["format"]](str(val), exp)
if self.parameters["format"] == "pyop2":
sym = create_funcall(var, [val, exp])
else:
sym = create_symbol(var, val.t, val, 1, iden=var)
return {(): sym}
elif isinstance(expo, (Coefficient, Operator)):
exp = self.visit(expo)[()]
# print "pow exp: ", exp
# print "pow val: ", val
var = format["std power"][self.parameters["format"]](str(val), exp)
if self.parameters["format"] == "pyop2":
sym = create_funcall(var, [val, exp])
else:
sym = create_symbol(var, val.t, val, 1, iden=var)
return {(): sym}
else:
error("power does not support this exponent: " + repr(expo))
def _format_scalar_value(self, value):
# print("format_scalar_value: %d" % value)
if value is None:
return {(): create_float(0.0)}
return {(): create_float(value)}
def create_function(self, ufl_function, derivatives, component, local_comp,
local_offset, ffc_element, is_quad_element,
transformation, multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
ffc_assert(
ufl_function in self._function_replace_values,
"Expecting ufl_function to have been mapped prior to this call.")
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = []
# Handle affine mappings.
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create function name.
function_name = self._create_function_name(
component, deriv, avg, is_quad_element, ufl_function,
ffc_element)
if function_name:
# Add transformation if needed.
code.append(
self.__apply_transform(function_name, derivatives,
multi, tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(
avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in [
"covariant piola", "contravariant piola"
]:
for c in range(tdim):
function_name = self._create_function_name(
c + local_offset, deriv, avg, is_quad_element,
ufl_function, ffc_element)
if function_name:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(
f_transform("JINV", c, local_comp, tdim,
gdim, self.restriction), GEO)
function_name = create_product(
[dxdX, function_name])
elif transformation == "contravariant piola":
detJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction),
GEO))
dXdx = create_symbol(
f_transform("J", local_comp, c, gdim, tdim,
self.restriction), GEO)
function_name = create_product(
[detJ, dXdx, function_name])
# Add transformation if needed.
code.append(
self.__apply_transform(function_name,
derivatives, multi,
tdim, gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(
k * tdim + l + local_offset, deriv, avg,
is_quad_element, ufl_function, ffc_element)
J1 = create_symbol(
f_transform("JINV", k, i, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("JINV", l, j, tdim, gdim,
self.restriction), GEO)
function_name = create_product(
[J1, function_name, J2])
# Add transformation if needed.
code.append(
self.__apply_transform(function_name,
derivatives, multi,
tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(
k * tdim + l + local_offset, deriv, avg,
is_quad_element, ufl_function, ffc_element)
J1 = create_symbol(
f_transform("J", i, k, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("J", j, l, tdim, gdim,
self.restriction), GEO)
invdetJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction), GEO))
function_name = create_product(
[invdetJ, invdetJ, J1, function_name, J2])
# Add transformation if needed.
code.append(
self.__apply_transform(function_name,
derivatives, multi,
tdim, gdim))
else:
error("Transformation is not supported: ",
repr(transformation))
if not code:
return create_float(0.0)
elif len(code) > 1:
code = create_sum(code)
else:
code = code[0]
return code
def create_argument(self, ufl_argument, derivatives, component, local_comp,
local_offset, ffc_element, transformation,
multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = {}
# Affine mapping
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
component, deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(basis, derivatives, multi, tdim,
gdim))
# Handle non-affine mappings.
else:
ffc_assert(
avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in [
"covariant piola", "contravariant piola"
]:
for c in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
c + local_offset, deriv, avg, ufl_argument,
ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(
f_transform("JINV", c, local_comp, tdim,
gdim, self.restriction), GEO)
basis = create_product([dxdX, basis])
elif transformation == "contravariant piola":
detJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction),
GEO))
dXdx = create_symbol(
f_transform("J", local_comp, c, gdim, tdim,
self.restriction), GEO)
basis = create_product([detJ, dXdx, basis])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(basis, derivatives, multi,
tdim, gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset, deriv, avg,
ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = create_symbol(
f_transform("JINV", k, i, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("JINV", l, j, tdim, gdim,
self.restriction), GEO)
basis = create_product([J1, basis, J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi, tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset, deriv, avg,
ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = create_symbol(
f_transform("J", i, k, gdim, tdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("J", j, l, gdim, tdim,
self.restriction), GEO)
invdetJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction),
GEO))
basis = create_product(
[invdetJ, invdetJ, J1, basis, J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi, tdim, gdim))
else:
error("Transformation is not supported: " +
repr(transformation))
# Add sums and group if necessary.
for key, val in list(code.items()):
if len(val) > 1:
code[key] = create_sum(val)
else:
code[key] = val[0]
return code
def create_function(self, ufl_function, derivatives, component, local_comp,
local_offset, ffc_element, is_quad_element,
transformation, multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
ffc_assert(
ufl_function in self._function_replace_values,
"Expecting ufl_function to have been mapped prior to this call.")
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = []
# Handle affine mappings.
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create function name.
function_name = self._create_function_name(
component, deriv, avg, is_quad_element, ufl_function,
ffc_element)
if function_name:
# Add transformation if needed.
code.append(
self.__apply_transform(function_name, derivatives,
multi, tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(
avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
for c in range(tdim):
function_name = self._create_function_name(
c + local_offset, deriv, avg, is_quad_element,
ufl_function, ffc_element)
if function_name:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(
f_transform("JINV", c, local_comp, tdim, gdim,
self.restriction),
GEO,
loop_index=[c * gdim + local_comp],
iden="K%s" % _choose_map(self.restriction))
function_name = create_product(
[dxdX, function_name])
elif transformation == "contravariant piola":
detJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction),
GEO,
iden=f_detJ(self.restriction)))
dXdx = create_symbol(f_transform("J", local_comp, c, gdim, tdim, self.restriction), GEO, \
loop_index=[local_comp*tdim + c], iden="J%s" % _choose_map(self.restriction))
function_name = create_product(
[detJ, dXdx, function_name])
else:
error("Transformation is not supported: ",
repr(transformation))
# Add transformation if needed.
code.append(
self.__apply_transform(function_name, derivatives,
multi, tdim, gdim))
if not code:
return create_float(0.0)
elif len(code) > 1:
code = create_sum(code)
else:
code = code[0]
return code
def create_argument(self, ufl_argument, derivatives, component, local_comp,
local_offset, ffc_element, transformation,
multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = {}
# Affine mapping
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
component, deriv, avg, ufl_argument, ffc_element)
if isinstance(mapping, list):
for ma, ba in zip(mapping, basis):
if not ma in code:
code[ma] = []
if basis is not None:
# Add transformation if needed.
code[ma].append(
self.__apply_transform(ba, derivatives, multi,
tdim, gdim))
else:
if not mapping in code:
code[mapping] = []
if basis is not None:
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(basis, derivatives, multi,
tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(
avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
for c in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
c + local_offset, deriv, avg, ufl_argument,
ffc_element)
if not mapping in code:
code[mapping] = []
if basis is not None:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(
f_transform("JINV", c, local_comp, tdim, gdim,
self.restriction),
GEO,
loop_index=[c * gdim + local_comp],
iden="K%s" % _choose_map(self.restriction))
basis = create_product([dxdX, basis])
elif transformation == "contravariant piola":
detJ = create_fraction(create_float(1), \
create_symbol(f_detJ(self.restriction), GEO, iden=f_detJ(self.restriction)))
dXdx = create_symbol(f_transform("J", local_comp, c, gdim, tdim, self.restriction), GEO, \
loop_index=[local_comp*tdim + c], iden="J%s" % _choose_map(self.restriction))
basis = create_product([detJ, dXdx, basis])
else:
error("Transformation is not supported: " +
repr(transformation))
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(basis, derivatives, multi,
tdim, gdim))
# Add sums and group if necessary.
for key, val in list(code.items()):
if len(val) > 1:
code[key] = create_sum(val)
else:
code[key] = val[0]
return code
def _compute_basisvalues(data, dof_data):
"""From FIAT_NEW.expansions."""
UNROLL = True
# Prefetch formats to speed up code generation.
f_comment = format["comment"]
f_add = format["add"]
f_mul = format["mul"]
f_imul = format["imul"]
f_sub = format["sub"]
f_group = format["grouping"]
f_assign = format["assign"]
f_sqrt = format["sqrt"]["ufc"]
f_x = format["x coordinate"]
f_y = format["y coordinate"]
f_z = format["z coordinate"]
f_double = format["float declaration"]
f_basisvalue = format["basisvalues"]
f_component = format["component"]
f_float = format["floating point"]
f_uint = format["uint declaration"]
f_tensor = format["tabulate tensor"]
f_loop = format["generate loop"]
f_decl = format["declaration"]
f_tmp = format["tmp value"]
f_int = format["int"]
f_r = format["free indices"][0]
# Create temporary values.
f1, f2, f3, f4, f5 = [create_symbol(f_tmp(i), CONST) for i in range(0,5)]
# Get embedded degree.
embedded_degree = dof_data["embedded_degree"]
# Create helper symbols.
symbol_p = create_symbol(f_r, CONST)
symbol_x = create_symbol(f_x, CONST)
symbol_y = create_symbol(f_y, CONST)
symbol_z = create_symbol(f_z, CONST)
int_n1 = f_int(embedded_degree + 1)
float_1 = create_float(1)
float_2 = create_float(2)
float_0_5 = create_float(0.5)
float_0_25 = create_float(0.25)
# Initialise return code.
code = [""]
# Create zero array for basisvalues.
# Get number of members of the expansion set.
num_mem = dof_data["num_expansion_members"]
code += [f_comment("Array of basisvalues")]
code += [f_decl(f_double, f_component(f_basisvalue, num_mem), f_tensor([0.0]*num_mem))]
# Declare helper variables, will be removed if not used.
code += ["", f_comment("Declare helper variables")] # Keeping this here to avoid changing references
# Get the element cell name
element_cellname = data["cellname"]
def _jrc(a, b, n):
an = float( ( 2*n+1+a+b)*(2*n+2+a+b))/ float( 2*(n+1)*(n+1+a+b))
bn = float( (a*a-b*b) * (2*n+1+a+b))/ float( 2*(n+1)*(2*n+a+b)*(n+1+a+b) )
cn = float( (n+a)*(n+b)*(2*n+2+a+b))/ float( (n+1)*(n+1+a+b)*(2*n+a+b) )
return (an,bn,cn)
# 1D
if (element_cellname == "interval"):
# FIAT_NEW.expansions.LineExpansionSet.
# FIAT_NEW code
# psitilde_as = jacobi.eval_jacobi_batch(0,0,n,ref_pts)
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs)
# The initial value basisvalue 0 is always 1.0
# FIAT_NEW code
# for ii in range(result.shape[1]):
# result[0,ii] = 1.0 + xs[ii,0] - xs[ii,0]
code += ["", f_comment("Compute basisvalues")]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs).
# result[1,:] = 0.5 * ( a - b + ( a + b + 2.0 ) * xsnew )
# The initial value basisvalue 1 is always x
code += [f_assign(f_component(f_basisvalue, 1), f_x)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs).
# apb = a + b (equal to 0 because of function arguments)
# for k in range(2,n+1):
# a1 = 2.0 * k * ( k + apb ) * ( 2.0 * k + apb - 2.0 )
# a2 = ( 2.0 * k + apb - 1.0 ) * ( a * a - b * b )
# a3 = ( 2.0 * k + apb - 2.0 ) \
# * ( 2.0 * k + apb - 1.0 ) \
# * ( 2.0 * k + apb )
# a4 = 2.0 * ( k + a - 1.0 ) * ( k + b - 1.0 ) \
# * ( 2.0 * k + apb )
# a2 = a2 / a1
# a3 = a3 / a1
# a4 = a4 / a1
# result[k,:] = ( a2 + a3 * xsnew ) * result[k-1,:] \
# - a4 * result[k-2,:]
# The below implements the above (with a = b = apb = 0)
for r in range(2, embedded_degree+1):
# Define helper variables
a1 = 2.0*r*r*(2.0*r - 2.0)
a3 = ((2.0*r - 2.0)*(2.0*r - 1.0 )*(2.0*r))/a1
a4 = (2.0*(r - 1.0)*(r - 1.0)*(2.0*r))/a1
assign_to = f_component(f_basisvalue, r)
assign_from = f_sub([f_mul([f_x, f_component(f_basisvalue, r-1), f_float(a3)]),
f_mul([f_component(f_basisvalue, r-2), f_float(a4)])])
code += [f_assign(assign_to, assign_from)]
# Scale values.
# FIAT_NEW.expansions.LineExpansionSet.
# FIAT_NEW code
# results = numpy.zeros( ( n+1 , len(pts) ) , type( pts[0][0] ) )
# for k in range( n + 1 ):
# results[k,:] = psitilde_as[k,:] * math.sqrt( k + 0.5 )
lines = []
loop_vars = [(str(symbol_p), 0, int_n1)]
# Create names.
basis_k = create_symbol(f_component(f_basisvalue, str(symbol_p)), CONST)
# Compute value.
fac1 = create_symbol( f_sqrt(str(symbol_p + float_0_5)), CONST )
lines += [format["imul"](str(basis_k), str(fac1))]
# Create loop (block of lines).
code += f_loop(lines, loop_vars)
# 2D
elif (element_cellname == "triangle"):
# FIAT_NEW.expansions.TriangleExpansionSet.
# Compute helper factors
# FIAT_NEW code
# f1 = (1.0+2*x+y)/2.0
# f2 = (1.0 - y) / 2.0
# f3 = f2**2
fac1 = create_fraction(float_1 + float_2*symbol_x + symbol_y, float_2)
fac2 = create_fraction(float_1 - symbol_y, float_2)
code += [f_decl(f_double, str(f1), fac1)]
code += [f_decl(f_double, str(f2), fac2)]
code += [f_decl(f_double, str(f3), f2*f2)]
code += ["", f_comment("Compute basisvalues")]
# The initial value basisvalue 0 is always 1.0.
# FIAT_NEW code
# for ii in range( results.shape[1] ):
# results[0,ii] = 1.0 + apts[ii,0]-apts[ii,0]+apts[ii,1]-apts[ii,1]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
def _idx2d(p, q):
return (p + q)*(p + q + 1)//2 + q
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# The initial value of basisfunction 1 is equal to f1.
# FIAT_NEW code
# results[idx(1,0),:] = f1
code += [f_assign(f_component(f_basisvalue, 1), str(f1))]
# NOTE: KBO: The order of the loops is VERY IMPORTANT!!
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 1 in FIAT)
# for p in range(1,n):
# a = (2.0*p+1)/(1.0+p)
# b = p / (p+1.0)
# results[idx(p+1,0)] = a * f1 * results[idx(p,0),:] \
# - p/(1.0+p) * f3 *results[idx(p-1,0),:]
# FIXME: KBO: Is there an error in FIAT? why is b not used?
for r in range(1, embedded_degree):
rr = _idx2d((r + 1), 0)
assign_to = f_component(f_basisvalue, rr)
ss = _idx2d(r, 0)
tt = _idx2d((r - 1), 0)
A = (2*r + 1.0)/(r + 1)
B = r/(1.0 + r)
v1 = f_mul([f_component(f_basisvalue, ss), f_float(A),
str(f1)])
v2 = f_mul([f_component(f_basisvalue, tt), f_float(B),
str(f3)])
assign_from = f_sub([v1, v2])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 2 in FIAT).
# for p in range(n):
# results[idx(p,1),:] = 0.5 * (1+2.0*p+(3.0+2.0*p)*y) \
# * results[idx(p,0)]
for r in range(0, embedded_degree):
# (p+q)*(p+q+1)//2 + q
rr = _idx2d(r, 1)
assign_to = f_component(f_basisvalue, rr)
ss = _idx2d(r, 0)
A = 0.5*(1 + 2*r)
B = 0.5*(3 + 2*r)
C = f_add([f_float(A), f_mul([f_float(B), str(symbol_y)])])
assign_from = f_mul([f_component(f_basisvalue, ss),
f_group(C)])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 3 in FIAT).
# for p in range(n-1):
# for q in range(1,n-p):
# (a1,a2,a3) = jrc(2*p+1,0,q)
# results[idx(p,q+1),:] \
# = ( a1 * y + a2 ) * results[idx(p,q)] \
# - a3 * results[idx(p,q-1)]
for r in range(0, embedded_degree - 1):
for s in range(1, embedded_degree - r):
rr = _idx2d(r, (s + 1))
ss = _idx2d(r, s)
tt = _idx2d(r, s - 1)
A, B, C = _jrc(2*r + 1, 0, s)
assign_to = f_component(f_basisvalue, rr)
assign_from = f_sub([f_mul([f_component(f_basisvalue, ss), f_group(f_add([f_float(B), f_mul([str(symbol_y), f_float(A)])]))]),
f_mul([f_component(f_basisvalue, tt), f_float(C)])])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 4 in FIAT).
# for p in range(n+1):
# for q in range(n-p+1):
# results[idx(p,q),:] *= math.sqrt((p+0.5)*(p+q+1.0))
n1 = embedded_degree + 1
for r in range(0, n1):
for s in range(0, n1 - r):
rr = _idx2d(r, s)
A = (r + 0.5)*(r + s + 1)
assign_to = f_component(f_basisvalue, rr)
code += [f_imul(assign_to, f_sqrt(A))]
# 3D
elif (element_cellname == "tetrahedron"):
# FIAT_NEW code (compute index function) TetrahedronExpansionSet.
# def idx(p,q,r):
# return (p+q+r)*(p+q+r+1)*(p+q+r+2)//6 + (q+r)*(q+r+1)//2 + r
def _idx3d(p, q, r):
return (p+q+r)*(p+q+r+1)*(p+q+r+2)//6 + (q+r)*(q+r+1)//2 + r
# FIAT_NEW.expansions.TetrahedronExpansionSet.
# Compute helper factors.
# FIAT_NEW code
# factor1 = 0.5 * ( 2.0 + 2.0*x + y + z )
# factor2 = (0.5*(y+z))**2
# factor3 = 0.5 * ( 1 + 2.0 * y + z )
# factor4 = 0.5 * ( 1 - z )
# factor5 = factor4 ** 2
fac1 = create_product([float_0_5, float_2 + float_2*symbol_x + symbol_y + symbol_z])
fac2 = create_product([float_0_25, symbol_y + symbol_z, symbol_y + symbol_z])
fac3 = create_product([float_0_5, float_1 + float_2*symbol_y + symbol_z])
fac4 = create_product([float_0_5, float_1 - symbol_z])
code += [f_decl(f_double, str(f1), fac1)]
code += [f_decl(f_double, str(f2), fac2)]
code += [f_decl(f_double, str(f3), fac3)]
code += [f_decl(f_double, str(f4), fac4)]
code += [f_decl(f_double, str(f5), f4*f4)]
code += ["", f_comment("Compute basisvalues")]
# The initial value basisvalue 0 is always 1.0.
# FIAT_NEW code
# for ii in range( results.shape[1] ):
# results[0,ii] = 1.0 + apts[ii,0]-apts[ii,0]+apts[ii,1]-apts[ii,1]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# The initial value of basisfunction 1 is equal to f1.
# FIAT_NEW code
# results[idx(1,0),:] = f1
code += [f_assign(f_component(f_basisvalue, 1), str(f1))]
# NOTE: KBO: The order of the loops is VERY IMPORTANT!!
# Only active is embedded_degree > 1
if embedded_degree > 1:
# FIAT_NEW code (loop 1 in FIAT).
# for p in range(1,n):
# a1 = ( 2.0 * p + 1.0 ) / ( p + 1.0 )
# a2 = p / (p + 1.0)
# results[idx(p+1,0,0)] = a1 * factor1 * results[idx(p,0,0)] \
# -a2 * factor2 * results[ idx(p-1,0,0) ]
for r in range(1, embedded_degree):
rr = _idx3d((r + 1), 0, 0)
ss = _idx3d(r, 0, 0)
tt = _idx3d((r - 1), 0, 0)
A = (2*r + 1.0)/(r + 1)
B = r/(r + 1.0)
assign_to = f_component(f_basisvalue, rr)
assign_from = f_sub([f_mul([f_float(A), str(f1), f_component(f_basisvalue, ss)]), f_mul([f_float(B), str(f2), f_component(f_basisvalue, tt)])])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 2 in FIAT).
# q = 1
# for p in range(0,n):
# results[idx(p,1,0)] = results[idx(p,0,0)] \
# * ( p * (1.0 + y) + ( 2.0 + 3.0 * y + z ) / 2 )
for r in range(0, embedded_degree):
rr = _idx3d(r, 1, 0)
ss = _idx3d(r, 0, 0)
assign_to = f_component(f_basisvalue, rr)
term0 = f_mul([f_float(0.5), f_group(f_add([f_float(2), f_mul([f_float(3), str(symbol_y)]), str(symbol_z)]))])
if r == 0:
assign_from = f_mul([term0, f_component(f_basisvalue, ss)])
else:
term1 = f_mul([f_float(r), f_group(f_add([f_float(1), str(symbol_y)]))])
assign_from = f_mul([f_group(f_add([term0, term1])), f_component(f_basisvalue, ss)])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 3 in FIAT).
# for p in range(0,n-1):
# for q in range(1,n-p):
# (aq,bq,cq) = jrc(2*p+1,0,q)
# qmcoeff = aq * factor3 + bq * factor4
# qm1coeff = cq * factor5
# results[idx(p,q+1,0)] = qmcoeff * results[idx(p,q,0)] \
# - qm1coeff * results[idx(p,q-1,0)]
for r in range(0, embedded_degree - 1):
for s in range(1, embedded_degree - r):
rr = _idx3d(r, (s + 1), 0)
ss = _idx3d(r, s, 0)
tt = _idx3d(r, s - 1, 0)
(A, B, C) = _jrc(2*r + 1, 0, s)
assign_to = f_component(f_basisvalue, rr)
term0 = f_mul([f_group(f_add([f_mul([f_float(A), str(f3)]), f_mul([f_float(B), str(f4)])])), f_component(f_basisvalue, ss)])
term1 = f_mul([f_float(C), str(f5), f_component(f_basisvalue, tt)])
assign_from = f_sub([term0, term1])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 4 in FIAT).
# now handle r=1
# for p in range(n):
# for q in range(n-p):
# results[idx(p,q,1)] = results[idx(p,q,0)] \
# * ( 1.0 + p + q + ( 2.0 + q + p ) * z )
for r in range(0, embedded_degree):
for s in range(0, embedded_degree - r):
rr = _idx3d(r, s, 1)
ss = _idx3d(r, s, 0)
assign_to = f_component(f_basisvalue, rr)
A = f_add([f_mul([f_float(2 + r + s), str(symbol_z)]), f_float(1 + r + s)])
assign_from = f_mul([f_group(A), f_component(f_basisvalue, ss)])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 5 in FIAT).
# general r by recurrence
# for p in range(n-1):
# for q in range(0,n-p-1):
# for r in range(1,n-p-q):
# ar,br,cr = jrc(2*p+2*q+2,0,r)
# results[idx(p,q,r+1)] = \
# (ar * z + br) * results[idx(p,q,r) ] \
# - cr * results[idx(p,q,r-1) ]
for r in range(embedded_degree - 1):
for s in range(0, embedded_degree - r - 1):
for t in range(1, embedded_degree - r - s):
rr = _idx3d(r, s, ( t + 1))
ss = _idx3d(r, s, t)
tt = _idx3d(r, s, t - 1)
(A, B, C) = _jrc(2*r + 2*s + 2, 0, t)
assign_to = f_component(f_basisvalue, rr)
az_b = f_group(f_add([f_float(B), f_mul([f_float(A), str(symbol_z)])]))
assign_from = f_sub([f_mul([f_component(f_basisvalue, ss), az_b]), f_mul([f_float(C), f_component(f_basisvalue, tt)])])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 6 in FIAT).
# for p in range(n+1):
# for q in range(n-p+1):
# for r in range(n-p-q+1):
# results[idx(p,q,r)] *= math.sqrt((p+0.5)*(p+q+1.0)*(p+q+r+1.5))
for r in range(embedded_degree + 1):
for s in range(embedded_degree - r + 1):
for t in range(embedded_degree - r - s + 1):
rr = _idx3d(r, s, t)
A = (r + 0.5)*(r + s + 1)*(r + s + t + 1.5)
assign_to = f_component(f_basisvalue, rr)
multiply_by = f_sqrt(A)
myline = f_imul(assign_to, multiply_by)
code += [myline]
else:
error("Cannot compute basis values for shape: %d" % elemet_cell_domain)
return code + [""]
def _format_scalar_value(self, value):
# print("format_scalar_value: %d" % value)
if value is None:
return {(): create_float(0.0)}
return {(): create_float(value)}
def create_function(self, ufl_function, derivatives, component, local_comp,
local_offset, ffc_element, is_quad_element,
transformation, multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
ffc_assert(ufl_function in self._function_replace_values,
"Expecting ufl_function to have been mapped prior to this call.")
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = []
# Handle affine mappings.
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create function name.
function_name = self._create_function_name(component, deriv,
avg, is_quad_element,
ufl_function,
ffc_element)
if function_name:
# Add transformation if needed.
code.append(self.__apply_transform(function_name,
derivatives, multi, tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in ["covariant piola",
"contravariant piola"]:
for c in range(tdim):
function_name = self._create_function_name(c + local_offset, deriv, avg, is_quad_element, ufl_function, ffc_element)
if function_name:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(f_transform("JINV", c,
local_comp, tdim,
gdim,
self.restriction),
GEO)
function_name = create_product([dxdX, function_name])
elif transformation == "contravariant piola":
detJ = create_fraction(create_float(1),
create_symbol(f_detJ(self.restriction),
GEO))
dXdx = create_symbol(f_transform("J", local_comp,
c, gdim, tdim,
self.restriction),
GEO)
function_name = create_product([detJ, dXdx,
function_name])
# Add transformation if needed.
code.append(self.__apply_transform(function_name,
derivatives, multi,
tdim, gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(
k * tdim + l + local_offset, deriv, avg,
is_quad_element, ufl_function, ffc_element)
J1 = create_symbol(
f_transform("JINV", k, i, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("JINV", l, j, tdim, gdim,
self.restriction), GEO)
function_name = create_product([J1, function_name,
J2])
# Add transformation if needed.
code.append(self.__apply_transform(
function_name, derivatives, multi, tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(
k * tdim + l + local_offset,
deriv, avg, is_quad_element,
ufl_function, ffc_element)
J1 = create_symbol(
f_transform("J", i, k, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("J", j, l, tdim, gdim,
self.restriction), GEO)
invdetJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction), GEO))
function_name = create_product([invdetJ, invdetJ,
J1, function_name,
J2])
# Add transformation if needed.
code.append(self.__apply_transform(function_name,
derivatives,
multi, tdim,
gdim))
else:
error("Transformation is not supported: ",
repr(transformation))
if not code:
return create_float(0.0)
elif len(code) > 1:
code = create_sum(code)
else:
code = code[0]
return code
def create_argument(self, ufl_argument, derivatives, component, local_comp,
local_offset, ffc_element, transformation,
multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = {}
# Affine mapping
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(component, deriv,
avg, ufl_argument,
ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Add transformation if needed.
code[mapping].append(self.__apply_transform(basis,
derivatives,
multi, tdim,
gdim))
# Handle non-affine mappings.
else:
ffc_assert(avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in ["covariant piola",
"contravariant piola"]:
for c in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(c + local_offset, deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(f_transform("JINV", c,
local_comp, tdim,
gdim,
self.restriction),
GEO)
basis = create_product([dxdX, basis])
elif transformation == "contravariant piola":
detJ = create_fraction(create_float(1),
create_symbol(f_detJ(self.restriction), GEO))
dXdx = create_symbol(f_transform("J", local_comp,
c, gdim, tdim,
self.restriction),
GEO)
basis = create_product([detJ, dXdx, basis])
# Add transformation if needed.
code[mapping].append(self.__apply_transform(basis,
derivatives,
multi, tdim,
gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset,
deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = create_symbol(
f_transform("JINV", k, i, tdim, gdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("JINV", l, j, tdim, gdim,
self.restriction), GEO)
basis = create_product([J1, basis, J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi,
tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset,
deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = create_symbol(
f_transform("J", i, k, gdim, tdim,
self.restriction), GEO)
J2 = create_symbol(
f_transform("J", j, l, gdim, tdim,
self.restriction), GEO)
invdetJ = create_fraction(
create_float(1),
create_symbol(f_detJ(self.restriction),
GEO))
basis = create_product([invdetJ, invdetJ, J1,
basis, J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi,
tdim, gdim))
else:
error("Transformation is not supported: " + repr(transformation))
# Add sums and group if necessary.
for key, val in list(code.items()):
if len(val) > 1:
code[key] = create_sum(val)
else:
code[key] = val[0]
return code
def create_argument(self, ufl_argument, derivatives, component, local_comp,
local_offset, ffc_element, transformation, multiindices,
tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
ffc_assert(ufl_argument in self._function_replace_values, "Expecting ufl_argument to have been mapped prior to this call.")
# Prefetch formats to speed up code generation.
f_transform = format["transform"]
f_detJ = format["det(J)"]
# Reset code
code = {}
# Affine mapping
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(self.tdim)]
if not any(deriv):
deriv = []
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(component, deriv, avg, ufl_argument, ffc_element)
if not mapping in code:
code[mapping] = []
if basis is not None:
# Add transformation if needed.
code[mapping].append(self.__apply_transform(basis, derivatives, multi, tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(avg is None, "Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(self.tdim)]
if not any(deriv):
deriv = []
for c in range(self.tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(c + local_offset, deriv, avg, ufl_argument, ffc_element)
if not mapping in code:
code[mapping] = []
if basis is not None:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = create_symbol(f_transform("JINV", c, local_comp, tdim, gdim, self.restriction), GEO)
basis = create_product([dxdX, basis])
elif transformation == "contravariant piola":
detJ = create_fraction(create_float(1), create_symbol(f_detJ(self.restriction), GEO))
dXdx = create_symbol(f_transform("J", local_comp, c, gdim, tdim, self.restriction), GEO)
basis = create_product([detJ, dXdx, basis])
else:
error("Transformation is not supported: " + repr(transformation))
# Add transformation if needed.
code[mapping].append(self.__apply_transform(basis, derivatives, multi, tdim, gdim))
# Add sums and group if necessary.
for key, val in code.items():
if len(val) > 1:
code[key] = create_sum(val)
else:
code[key] = val[0]
return code
def _compute_basisvalues(data, dof_data):
"""From FIAT_NEW.expansions."""
UNROLL = True
# Prefetch formats to speed up code generation.
f_comment = format["comment"]
f_add = format["add"]
f_mul = format["mul"]
f_imul = format["imul"]
f_sub = format["sub"]
f_group = format["grouping"]
f_assign = format["assign"]
f_sqrt = format["sqrt"]["ufc"]
f_x = format["x coordinate"]
f_y = format["y coordinate"]
f_z = format["z coordinate"]
f_double = format["float declaration"]
f_basisvalue = format["basisvalues"]
f_component = format["component"]
f_float = format["floating point"]
f_uint = format["uint declaration"]
f_tensor = format["tabulate tensor"]
f_loop = format["generate loop"]
f_decl = format["declaration"]
f_tmp = format["tmp value"]
f_int = format["int"]
f_r = format["free indices"][0]
# Create temporary values.
f1, f2, f3, f4, f5 = [create_symbol(f_tmp(i), CONST) for i in range(0, 5)]
# Get embedded degree.
embedded_degree = dof_data["embedded_degree"]
# Create helper symbols.
symbol_p = create_symbol(f_r, CONST)
symbol_x = create_symbol(f_x, CONST)
symbol_y = create_symbol(f_y, CONST)
symbol_z = create_symbol(f_z, CONST)
int_n1 = f_int(embedded_degree + 1)
float_1 = create_float(1)
float_2 = create_float(2)
float_0_5 = create_float(0.5)
float_0_25 = create_float(0.25)
# Initialise return code.
code = [""]
# Create zero array for basisvalues.
# Get number of members of the expansion set.
num_mem = dof_data["num_expansion_members"]
code += [f_comment("Array of basisvalues")]
code += [
f_decl(f_double, f_component(f_basisvalue, num_mem),
f_tensor([0.0] * num_mem))
]
# Declare helper variables, will be removed if not used.
code += ["", f_comment("Declare helper variables")
] # Keeping this here to avoid changing references
# Get the element cell name
element_cellname = data["cellname"]
def _jrc(a, b, n):
an = float((2 * n + 1 + a + b) *
(2 * n + 2 + a + b)) / float(2 * (n + 1) * (n + 1 + a + b))
bn = float((a * a - b * b) *
(2 * n + 1 + a + b)) / float(2 * (n + 1) * (2 * n + a + b) *
(n + 1 + a + b))
cn = float((n + a) * (n + b) * (2 * n + 2 + a + b)) / float(
(n + 1) * (n + 1 + a + b) * (2 * n + a + b))
return (an, bn, cn)
# 1D
if (element_cellname == "interval"):
# FIAT_NEW.expansions.LineExpansionSet.
# FIAT_NEW code
# psitilde_as = jacobi.eval_jacobi_batch(0,0,n,ref_pts)
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs)
# The initial value basisvalue 0 is always 1.0
# FIAT_NEW code
# for ii in range(result.shape[1]):
# result[0,ii] = 1.0 + xs[ii,0] - xs[ii,0]
code += ["", f_comment("Compute basisvalues")]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs).
# result[1,:] = 0.5 * ( a - b + ( a + b + 2.0 ) * xsnew )
# The initial value basisvalue 1 is always x
code += [f_assign(f_component(f_basisvalue, 1), f_x)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW.jacobi.eval_jacobi_batch(a,b,n,xs).
# apb = a + b (equal to 0 because of function arguments)
# for k in range(2,n+1):
# a1 = 2.0 * k * ( k + apb ) * ( 2.0 * k + apb - 2.0 )
# a2 = ( 2.0 * k + apb - 1.0 ) * ( a * a - b * b )
# a3 = ( 2.0 * k + apb - 2.0 ) \
# * ( 2.0 * k + apb - 1.0 ) \
# * ( 2.0 * k + apb )
# a4 = 2.0 * ( k + a - 1.0 ) * ( k + b - 1.0 ) \
# * ( 2.0 * k + apb )
# a2 = a2 / a1
# a3 = a3 / a1
# a4 = a4 / a1
# result[k,:] = ( a2 + a3 * xsnew ) * result[k-1,:] \
# - a4 * result[k-2,:]
# The below implements the above (with a = b = apb = 0)
for r in range(2, embedded_degree + 1):
# Define helper variables
a1 = 2.0 * r * r * (2.0 * r - 2.0)
a3 = ((2.0 * r - 2.0) * (2.0 * r - 1.0) * (2.0 * r)) / a1
a4 = (2.0 * (r - 1.0) * (r - 1.0) * (2.0 * r)) / a1
assign_to = f_component(f_basisvalue, r)
assign_from = f_sub([
f_mul([
f_x,
f_component(f_basisvalue, r - 1),
f_float(a3)
]),
f_mul([f_component(f_basisvalue, r - 2),
f_float(a4)])
])
code += [f_assign(assign_to, assign_from)]
# Scale values.
# FIAT_NEW.expansions.LineExpansionSet.
# FIAT_NEW code
# results = numpy.zeros( ( n+1 , len(pts) ) , type( pts[0][0] ) )
# for k in range( n + 1 ):
# results[k,:] = psitilde_as[k,:] * math.sqrt( k + 0.5 )
lines = []
loop_vars = [(str(symbol_p), 0, int_n1)]
# Create names.
basis_k = create_symbol(f_component(f_basisvalue, str(symbol_p)),
CONST)
# Compute value.
fac1 = create_symbol(f_sqrt(str(symbol_p + float_0_5)), CONST)
lines += [format["imul"](str(basis_k), str(fac1))]
# Create loop (block of lines).
code += f_loop(lines, loop_vars)
# 2D
elif (element_cellname == "triangle"):
# FIAT_NEW.expansions.TriangleExpansionSet.
# Compute helper factors
# FIAT_NEW code
# f1 = (1.0+2*x+y)/2.0
# f2 = (1.0 - y) / 2.0
# f3 = f2**2
fac1 = create_fraction(float_1 + float_2 * symbol_x + symbol_y,
float_2)
fac2 = create_fraction(float_1 - symbol_y, float_2)
code += [f_decl(f_double, str(f1), fac1)]
code += [f_decl(f_double, str(f2), fac2)]
code += [f_decl(f_double, str(f3), f2 * f2)]
code += ["", f_comment("Compute basisvalues")]
# The initial value basisvalue 0 is always 1.0.
# FIAT_NEW code
# for ii in range( results.shape[1] ):
# results[0,ii] = 1.0 + apts[ii,0]-apts[ii,0]+apts[ii,1]-apts[ii,1]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
def _idx2d(p, q):
return (p + q) * (p + q + 1) // 2 + q
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# The initial value of basisfunction 1 is equal to f1.
# FIAT_NEW code
# results[idx(1,0),:] = f1
code += [f_assign(f_component(f_basisvalue, 1), str(f1))]
# NOTE: KBO: The order of the loops is VERY IMPORTANT!!
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 1 in FIAT)
# for p in range(1,n):
# a = (2.0*p+1)/(1.0+p)
# b = p / (p+1.0)
# results[idx(p+1,0)] = a * f1 * results[idx(p,0),:] \
# - p/(1.0+p) * f3 *results[idx(p-1,0),:]
# FIXME: KBO: Is there an error in FIAT? why is b not used?
for r in range(1, embedded_degree):
rr = _idx2d((r + 1), 0)
assign_to = f_component(f_basisvalue, rr)
ss = _idx2d(r, 0)
tt = _idx2d((r - 1), 0)
A = (2 * r + 1.0) / (r + 1)
B = r / (1.0 + r)
v1 = f_mul(
[f_component(f_basisvalue, ss),
f_float(A),
str(f1)])
v2 = f_mul(
[f_component(f_basisvalue, tt),
f_float(B),
str(f3)])
assign_from = f_sub([v1, v2])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 2 in FIAT).
# for p in range(n):
# results[idx(p,1),:] = 0.5 * (1+2.0*p+(3.0+2.0*p)*y) \
# * results[idx(p,0)]
for r in range(0, embedded_degree):
# (p+q)*(p+q+1)//2 + q
rr = _idx2d(r, 1)
assign_to = f_component(f_basisvalue, rr)
ss = _idx2d(r, 0)
A = 0.5 * (1 + 2 * r)
B = 0.5 * (3 + 2 * r)
C = f_add([f_float(A), f_mul([f_float(B), str(symbol_y)])])
assign_from = f_mul(
[f_component(f_basisvalue, ss),
f_group(C)])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 3 in FIAT).
# for p in range(n-1):
# for q in range(1,n-p):
# (a1,a2,a3) = jrc(2*p+1,0,q)
# results[idx(p,q+1),:] \
# = ( a1 * y + a2 ) * results[idx(p,q)] \
# - a3 * results[idx(p,q-1)]
for r in range(0, embedded_degree - 1):
for s in range(1, embedded_degree - r):
rr = _idx2d(r, (s + 1))
ss = _idx2d(r, s)
tt = _idx2d(r, s - 1)
A, B, C = _jrc(2 * r + 1, 0, s)
assign_to = f_component(f_basisvalue, rr)
assign_from = f_sub([
f_mul([
f_component(f_basisvalue, ss),
f_group(
f_add([
f_float(B),
f_mul([str(symbol_y),
f_float(A)])
]))
]),
f_mul([f_component(f_basisvalue, tt),
f_float(C)])
])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 4 in FIAT).
# for p in range(n+1):
# for q in range(n-p+1):
# results[idx(p,q),:] *= math.sqrt((p+0.5)*(p+q+1.0))
n1 = embedded_degree + 1
for r in range(0, n1):
for s in range(0, n1 - r):
rr = _idx2d(r, s)
A = (r + 0.5) * (r + s + 1)
assign_to = f_component(f_basisvalue, rr)
code += [f_imul(assign_to, f_sqrt(A))]
# 3D
elif (element_cellname == "tetrahedron"):
# FIAT_NEW code (compute index function) TetrahedronExpansionSet.
# def idx(p,q,r):
# return (p+q+r)*(p+q+r+1)*(p+q+r+2)//6 + (q+r)*(q+r+1)//2 + r
def _idx3d(p, q, r):
return (p + q + r) * (p + q + r + 1) * (p + q + r + 2) // 6 + (
q + r) * (q + r + 1) // 2 + r
# FIAT_NEW.expansions.TetrahedronExpansionSet.
# Compute helper factors.
# FIAT_NEW code
# factor1 = 0.5 * ( 2.0 + 2.0*x + y + z )
# factor2 = (0.5*(y+z))**2
# factor3 = 0.5 * ( 1 + 2.0 * y + z )
# factor4 = 0.5 * ( 1 - z )
# factor5 = factor4 ** 2
fac1 = create_product(
[float_0_5, float_2 + float_2 * symbol_x + symbol_y + symbol_z])
fac2 = create_product(
[float_0_25, symbol_y + symbol_z, symbol_y + symbol_z])
fac3 = create_product(
[float_0_5, float_1 + float_2 * symbol_y + symbol_z])
fac4 = create_product([float_0_5, float_1 - symbol_z])
code += [f_decl(f_double, str(f1), fac1)]
code += [f_decl(f_double, str(f2), fac2)]
code += [f_decl(f_double, str(f3), fac3)]
code += [f_decl(f_double, str(f4), fac4)]
code += [f_decl(f_double, str(f5), f4 * f4)]
code += ["", f_comment("Compute basisvalues")]
# The initial value basisvalue 0 is always 1.0.
# FIAT_NEW code
# for ii in range( results.shape[1] ):
# results[0,ii] = 1.0 + apts[ii,0]-apts[ii,0]+apts[ii,1]-apts[ii,1]
code += [f_assign(f_component(f_basisvalue, 0), f_float(1.0))]
# Only continue if the embedded degree is larger than zero.
if embedded_degree > 0:
# The initial value of basisfunction 1 is equal to f1.
# FIAT_NEW code
# results[idx(1,0),:] = f1
code += [f_assign(f_component(f_basisvalue, 1), str(f1))]
# NOTE: KBO: The order of the loops is VERY IMPORTANT!!
# Only active is embedded_degree > 1
if embedded_degree > 1:
# FIAT_NEW code (loop 1 in FIAT).
# for p in range(1,n):
# a1 = ( 2.0 * p + 1.0 ) / ( p + 1.0 )
# a2 = p / (p + 1.0)
# results[idx(p+1,0,0)] = a1 * factor1 * results[idx(p,0,0)] \
# -a2 * factor2 * results[ idx(p-1,0,0) ]
for r in range(1, embedded_degree):
rr = _idx3d((r + 1), 0, 0)
ss = _idx3d(r, 0, 0)
tt = _idx3d((r - 1), 0, 0)
A = (2 * r + 1.0) / (r + 1)
B = r / (r + 1.0)
assign_to = f_component(f_basisvalue, rr)
assign_from = f_sub([
f_mul([
f_float(A),
str(f1),
f_component(f_basisvalue, ss)
]),
f_mul([
f_float(B),
str(f2),
f_component(f_basisvalue, tt)
])
])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 2 in FIAT).
# q = 1
# for p in range(0,n):
# results[idx(p,1,0)] = results[idx(p,0,0)] \
# * ( p * (1.0 + y) + ( 2.0 + 3.0 * y + z ) / 2 )
for r in range(0, embedded_degree):
rr = _idx3d(r, 1, 0)
ss = _idx3d(r, 0, 0)
assign_to = f_component(f_basisvalue, rr)
term0 = f_mul([
f_float(0.5),
f_group(
f_add([
f_float(2),
f_mul([f_float(3), str(symbol_y)]),
str(symbol_z)
]))
])
if r == 0:
assign_from = f_mul([term0, f_component(f_basisvalue, ss)])
else:
term1 = f_mul([
f_float(r),
f_group(f_add([f_float(1), str(symbol_y)]))
])
assign_from = f_mul([
f_group(f_add([term0, term1])),
f_component(f_basisvalue, ss)
])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 3 in FIAT).
# for p in range(0,n-1):
# for q in range(1,n-p):
# (aq,bq,cq) = jrc(2*p+1,0,q)
# qmcoeff = aq * factor3 + bq * factor4
# qm1coeff = cq * factor5
# results[idx(p,q+1,0)] = qmcoeff * results[idx(p,q,0)] \
# - qm1coeff * results[idx(p,q-1,0)]
for r in range(0, embedded_degree - 1):
for s in range(1, embedded_degree - r):
rr = _idx3d(r, (s + 1), 0)
ss = _idx3d(r, s, 0)
tt = _idx3d(r, s - 1, 0)
(A, B, C) = _jrc(2 * r + 1, 0, s)
assign_to = f_component(f_basisvalue, rr)
term0 = f_mul([
f_group(
f_add([
f_mul([f_float(A), str(f3)]),
f_mul([f_float(B), str(f4)])
])),
f_component(f_basisvalue, ss)
])
term1 = f_mul([
f_float(C),
str(f5),
f_component(f_basisvalue, tt)
])
assign_from = f_sub([term0, term1])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 4 in FIAT).
# now handle r=1
# for p in range(n):
# for q in range(n-p):
# results[idx(p,q,1)] = results[idx(p,q,0)] \
# * ( 1.0 + p + q + ( 2.0 + q + p ) * z )
for r in range(0, embedded_degree):
for s in range(0, embedded_degree - r):
rr = _idx3d(r, s, 1)
ss = _idx3d(r, s, 0)
assign_to = f_component(f_basisvalue, rr)
A = f_add([
f_mul([f_float(2 + r + s),
str(symbol_z)]),
f_float(1 + r + s)
])
assign_from = f_mul(
[f_group(A), f_component(f_basisvalue, ss)])
code += [f_assign(assign_to, assign_from)]
# Only active is embedded_degree > 1.
if embedded_degree > 1:
# FIAT_NEW code (loop 5 in FIAT).
# general r by recurrence
# for p in range(n-1):
# for q in range(0,n-p-1):
# for r in range(1,n-p-q):
# ar,br,cr = jrc(2*p+2*q+2,0,r)
# results[idx(p,q,r+1)] = \
# (ar * z + br) * results[idx(p,q,r) ] \
# - cr * results[idx(p,q,r-1) ]
for r in range(embedded_degree - 1):
for s in range(0, embedded_degree - r - 1):
for t in range(1, embedded_degree - r - s):
rr = _idx3d(r, s, (t + 1))
ss = _idx3d(r, s, t)
tt = _idx3d(r, s, t - 1)
(A, B, C) = _jrc(2 * r + 2 * s + 2, 0, t)
assign_to = f_component(f_basisvalue, rr)
az_b = f_group(
f_add([
f_float(B),
f_mul([f_float(A),
str(symbol_z)])
]))
assign_from = f_sub([
f_mul([f_component(f_basisvalue, ss), az_b]),
f_mul([
f_float(C),
f_component(f_basisvalue, tt)
])
])
code += [f_assign(assign_to, assign_from)]
# FIAT_NEW code (loop 6 in FIAT).
# for p in range(n+1):
# for q in range(n-p+1):
# for r in range(n-p-q+1):
# results[idx(p,q,r)] *= math.sqrt((p+0.5)*(p+q+1.0)*(p+q+r+1.5))
for r in range(embedded_degree + 1):
for s in range(embedded_degree - r + 1):
for t in range(embedded_degree - r - s + 1):
rr = _idx3d(r, s, t)
A = (r + 0.5) * (r + s + 1) * (r + s + t + 1.5)
assign_to = f_component(f_basisvalue, rr)
multiply_by = f_sqrt(A)
myline = f_imul(assign_to, multiply_by)
code += [myline]
else:
error("Cannot compute basis values for shape: %d" % elemet_cell_domain)
return code + [""]