def add_watches(self, watches):
"""Add quantities that are printed after every time step."""
from pytools import Record
class WatchInfo(Record):
pass
for watch in watches:
if isinstance(watch, tuple):
display, expr = watch
else:
display = watch
expr = watch
parsed = self._parse_expr(expr)
parsed, dep_data = self._get_expr_dep_data(parsed)
from pytools import any
self.have_nonlocal_watches = self.have_nonlocal_watches or \
any(dd.nonlocal_agg for dd in dep_data)
from pymbolic import compile
compiled = compile(parsed, [dd.varname for dd in dep_data])
watch_info = WatchInfo(display=display, parsed=parsed, dep_data=dep_data,
compiled=compiled)
self.watches.append(watch_info)
def method_matrix_func(self):
try:
return self.method_matrix_func_cache
except AttributeError:
from pymbolic import var
stepper = self.method_fac(var("dt"))
mat = self.matrix
def f2f_rhs(t, yf, ys):
return fold_constants(expand(mat[0, 0] * yf()))
def s2f_rhs(t, yf, ys):
return fold_constants(expand(mat[0, 1] * ys()))
def f2s_rhs(t, yf, ys):
return fold_constants(expand(mat[1, 0] * yf()))
def s2s_rhs(t, yf, ys):
return fold_constants(expand(mat[1, 1] * ys()))
method_matrix, _ = make_method_matrix(stepper,
rhss=(f2f_rhs, s2f_rhs,
f2s_rhs, s2s_rhs),
f_size=1,
s_size=1)
from pymbolic import compile
self.method_matrix_func_cache = compile(method_matrix)
return self.method_matrix_func_cache
def test_compile():
from pymbolic import parse, compile
code = compile(parse("x ** y"), ["x", "y"])
assert code(2, 5) == 32
# Test pickling of compiled code.
import pickle
code = pickle.loads(pickle.dumps(code))
assert code(3, 3) == 27
def test_compile():
from pymbolic import parse, compile
code = compile(parse("x ** y"), ["x", "y"])
assert code(2, 5) == 32
# Test pickling of compiled code.
import pickle
code = pickle.loads(pickle.dumps(code))
assert code(3, 3) == 27
def get_expr_dataset(self, expression, description=None, unit=None):
"""Prepare a time-series dataset for a given expression.
@arg expression: A C{pymbolic} expression that may involve
the time-series variables and the constants in this :class:`LogManager`.
If there is data from multiple ranks for a quantity occuring in
this expression, an aggregator may have to be specified.
@return: C{(description, unit, table)}, where C{table}
is a list of tuples C{(tick_nbr, value)}.
Aggregators are specified as follows:
- C{qty.min}, C{qty.max}, C{qty.avg}, C{qty.sum}, C{qty.norm2}
- C{qty[rank_nbr]}
- C{qty.loc}
"""
parsed = self._parse_expr(expression)
parsed, dep_data = self._get_expr_dep_data(parsed)
# aggregate table data
for dd in dep_data:
table = self.get_table(dd.name)
table.sort(["step"])
dd.table = table.aggregated(["step"], "value", dd.agg_func).data
# evaluate unit and description, if necessary
if unit is None:
from pymbolic import substitute, parse
unit_dict = dict((dd.varname, dd.qdat.unit) for dd in dep_data)
from pytools import all
if all(v is not None for v in six.itervalues(unit_dict)):
unit_dict = dict(
(k, parse(v)) for k, v in six.iteritems(unit_dict))
unit = substitute(parsed, unit_dict)
else:
unit = None
if description is None:
description = expression
# compile and evaluate
from pymbolic import compile
compiled = compile(parsed, [dd.varname for dd in dep_data])
data = []
for key, values in _join_by_first_of_tuple(dd.table
for dd in dep_data):
try:
data.append((key, compiled(*values)))
except ZeroDivisionError:
pass
return (description, unit, data)
def get_expr_dataset(self, expression, description=None, unit=None):
"""Prepare a time-series dataset for a given expression.
@arg expression: A C{pymbolic} expression that may involve
the time-series variables and the constants in this :class:`LogManager`.
If there is data from multiple ranks for a quantity occuring in
this expression, an aggregator may have to be specified.
@return: C{(description, unit, table)}, where C{table}
is a list of tuples C{(tick_nbr, value)}.
Aggregators are specified as follows:
- C{qty.min}, C{qty.max}, C{qty.avg}, C{qty.sum}, C{qty.norm2}
- C{qty[rank_nbr]}
- C{qty.loc}
"""
parsed = self._parse_expr(expression)
parsed, dep_data = self._get_expr_dep_data(parsed)
# aggregate table data
for dd in dep_data:
table = self.get_table(dd.name)
table.sort(["step"])
dd.table = table.aggregated(["step"], "value", dd.agg_func).data
# evaluate unit and description, if necessary
if unit is None:
from pymbolic import substitute, parse
unit_dict = dict((dd.varname, dd.qdat.unit) for dd in dep_data)
from pytools import all
if all(v is not None for v in six.itervalues(unit_dict)):
unit_dict = dict((k, parse(v)) for k, v in six.iteritems(unit_dict))
unit = substitute(parsed, unit_dict)
else:
unit = None
if description is None:
description = expression
# compile and evaluate
from pymbolic import compile
compiled = compile(parsed, [dd.varname for dd in dep_data])
data = []
for key, values in _join_by_first_of_tuple(dd.table for dd in dep_data):
try:
data.append((key, compiled(*values)))
except ZeroDivisionError:
pass
return (description, unit, data)
def fast_evaluator(matrix, sparse=False):
"""
Generate a function to evaluate a step matrix quickly.
The input comes from StepMatrixFinder.
"""
# First, rename variables in the matrix to names that are acceptable Python
# identifiers. We make use of dagrt's KeyToUniqueNameMap.
from dagrt.codegen.utils import KeyToUniqueNameMap
name_map = KeyToUniqueNameMap(forced_prefix="matrix")
def make_identifier(symbol):
from pymbolic import var
assert isinstance(symbol, var)
return var(name_map.get_or_make_name_for_key(symbol.name))
def get_var_order_from_name_map():
order = sorted(name_map)
return (order,
[name_map.get_or_make_name_for_key(key) for key in order])
from pymbolic.mapper.substitutor import SubstitutionMapper
substitutor = SubstitutionMapper(make_identifier)
from pymbolic import compile
# functools.partial ensures the resulting object is picklable.
from functools import partial
if sparse:
data = [substitutor(entry) for entry in matrix.data]
var_order, renamed_vars = get_var_order_from_name_map()
compiled_entries = [compile(entry, renamed_vars) for entry in data]
compiled_matrix = matrix.copy(data=compiled_entries)
else:
matrix = substitutor(matrix)
var_order, renamed_vars = get_var_order_from_name_map()
compiled_matrix = compile(matrix, renamed_vars)
return partial(_eval_compiled_matrix, compiled_matrix, var_order)
def add_watches(self, watches):
"""Add quantities that are printed after every time step."""
from pytools import Record
for watch in watches:
parsed = self._parse_expr(watch)
parsed, dep_data = self._get_expr_dep_data(parsed)
from pymbolic import compile
compiled = compile(parsed, [dd.varname for dd in dep_data])
watch_info = Record(expr=watch, parsed=parsed, dep_data=dep_data,
compiled=compiled)
self.watches.append(watch_info)
def get_expr_dataset(self, expression, description=None, unit=None):
"""Prepare a time-series dataset for a given expression.
@arg expression: A C{pymbolic} expression that may involve
the time-series variables and the constants in this L{LogManager}.
If there is data from multiple ranks for a quantity occuring in
this expression, an aggregator may have to be specified.
@return: C{(description, unit, table)}, where C{table}
is a list of tuples C{(tick_nbr, value)}.
Aggregators are specified as follows:
- C{qty.min}, C{qty.max}, C{qty.avg}, C{qty.sum}, C{qty.norm2}
- C{qty[rank_nbr]
"""
parsed = self._parse_expr(expression)
parsed, dep_data = self._get_expr_dep_data(parsed)
# aggregate table data
for dd in dep_data:
table = self.get_table(dd.name)
table.sort(["step"])
dd.table = table.aggregated(["step"], "value", dd.agg_func).data
# evaluate unit and description, if necessary
if unit is None:
from pymbolic import substitute, parse
unit = substitute(parsed,
dict((dd.varname, parse(dd.qdat.unit)) for dd in dep_data)
)
if description is None:
description = expression
# compile and evaluate
from pymbolic import compile
compiled = compile(parsed, [dd.varname for dd in dep_data])
return (description,
unit,
[(key, compiled(*values))
for key, values in _join_by_first_of_tuple(
dd.table for dd in dep_data)
])
def test():
from hedge.timestep.multirate_ab import \
TwoRateAdamsBashforthMethodBuilder
from pymbolic import var
stepper = TwoRateAdamsBashforthMethodBuilder(
method="Fqsr",
large_dt=var("dt"),
substep_count=2,
order=1)
mat = numpy.random.randn(2, 2)
def f2f_rhs(t, yf, ys):
return fold_constants(expand(mat[0, 0] * yf()))
def s2f_rhs(t, yf, ys):
return fold_constants(expand(mat[0, 1] * ys()))
def f2s_rhs(t, yf, ys):
return fold_constants(expand(mat[1, 0] * yf()))
def s2s_rhs(t, yf, ys):
return fold_constants(expand(mat[1, 1] * ys()))
z, vars = make_method_matrix(stepper,
rhss=(f2f_rhs, s2f_rhs, f2s_rhs, s2s_rhs),
f_size=1, s_size=1)
from pymbolic import compile
num_mat_func = compile(z)
num_mat = num_mat_func(0.1)
if False:
from pymbolic import substitute
num_mat_2 = numpy.array(
fold_constants(substitute(z, dt=0.1)),
dtype=numpy.complex128)
print(la.norm(num_mat - num_mat_2))
if True:
for row, ivar in zip(num_mat, vars):
print("".join("*" if entry else "." for entry in row), ivar)
def __init__(self,
op1_subset=full_subset,
op2_subset=full_subset,
result_subset=full_subset):
"""Construct a subset-able cross product.
:param op1_subset: The subset of indices of operand 1 to be taken into account.
Given as a 3-sequence of bools.
:param op2_subset: The subset of indices of operand 2 to be taken into account.
Given as a 3-sequence of bools.
:param result_subset: The subset of indices of the result that are calculated.
Given as a 3-sequence of bools.
"""
def subset_indices(subset):
return [
i for i, use_component in enumerate(subset) if use_component
]
self.op1_subset = op1_subset
self.op2_subset = op2_subset
self.result_subset = result_subset
import pymbolic
op1 = pymbolic.var("x")
op2 = pymbolic.var("y")
self.functions = []
self.component_lcjk = []
for i, use_component in enumerate(result_subset):
if use_component:
this_expr = 0
this_component = []
for j, j_real in enumerate(subset_indices(op1_subset)):
for k, k_real in enumerate(subset_indices(op2_subset)):
lc = levi_civita((i, j_real, k_real))
if lc != 0:
this_expr += lc * op1[j] * op2[k]
this_component.append((lc, j, k))
self.functions.append(
pymbolic.compile(this_expr, variables=[op1, op2]))
self.component_lcjk.append(this_component)
def __init__(self, kernel):
# a mapping from parameter names to a list of tuples
# (arg_name, axis_nr, function), where function is a
# unary function of kernel.arg_dict[arg_name].shape[axis_nr]
# returning the desired parameter.
self.param_to_sources = param_to_sources = {}
param_names = kernel.all_params()
from loopy.kernel.data import GlobalArg
from loopy.symbolic import DependencyMapper
from pymbolic import compile
dep_map = DependencyMapper()
from pymbolic import var
for arg in kernel.args:
if isinstance(arg, GlobalArg):
for axis_nr, shape_i in enumerate(arg.shape):
deps = dep_map(shape_i)
if len(deps) == 1:
dep, = deps
if dep.name in param_names:
from pymbolic.algorithm import solve_affine_equations_for
try:
# friggin' overkill :)
param_expr = solve_affine_equations_for([dep.name], [(shape_i, var("shape_i"))])[
dep.name
]
except:
# went wrong? oh well
pass
else:
param_func = compile(param_expr, ["shape_i"])
param_to_sources.setdefault(dep.name, []).append((arg.name, axis_nr, param_func))
def __init__(self, op1_subset=full_subset, op2_subset=full_subset, result_subset=full_subset):
"""Construct a subset-able cross product.
:param op1_subset: The subset of indices of operand 1 to be taken into account.
Given as a 3-sequence of bools.
:param op2_subset: The subset of indices of operand 2 to be taken into account.
Given as a 3-sequence of bools.
:param result_subset: The subset of indices of the result that are calculated.
Given as a 3-sequence of bools.
"""
def subset_indices(subset):
return [i for i, use_component in enumerate(subset)
if use_component]
self.op1_subset = op1_subset
self.op2_subset = op2_subset
self.result_subset = result_subset
import pymbolic
op1 = pymbolic.var("x")
op2 = pymbolic.var("y")
self.functions = []
self.component_lcjk = []
for i, use_component in enumerate(result_subset):
if use_component:
this_expr = 0
this_component = []
for j, j_real in enumerate(subset_indices(op1_subset)):
for k, k_real in enumerate(subset_indices(op2_subset)):
lc = levi_civita((i, j_real, k_real))
if lc != 0:
this_expr += lc*op1.index(j)*op2.index(k)
this_component.append((lc, j, k))
self.functions.append(pymbolic.compile(this_expr,
variables=[op1, op2]))
self.component_lcjk.append(this_component)
def __init__(self, kernel):
# a mapping from parameter names to a list of tuples
# (arg_name, axis_nr, function), where function is a
# unary function of kernel.arg_dict[arg_name].shape[axis_nr]
# returning the desired parameter.
self.param_to_sources = param_to_sources = {}
param_names = kernel.all_params()
from loopy.kernel.data import GlobalArg
from loopy.symbolic import DependencyMapper
from pymbolic import compile
dep_map = DependencyMapper()
from pymbolic import var
for arg in kernel.args:
if isinstance(arg, GlobalArg):
for axis_nr, shape_i in enumerate(arg.shape):
deps = dep_map(shape_i)
if len(deps) == 1:
dep, = deps
if dep.name in param_names:
from pymbolic.algorithm import solve_affine_equations_for
try:
# friggin' overkill :)
param_expr = solve_affine_equations_for(
[dep.name],
[(shape_i, var("shape_i"))])[dep.name]
except:
# went wrong? oh well
pass
else:
param_func = compile(param_expr, ["shape_i"])
param_to_sources.setdefault(
dep.name, []).append(
(arg.name, axis_nr, param_func))
def test_elliptic():
"""Test various properties of elliptic operators."""
from hedge.tools import unit_vector
def matrix_rep(op):
h, w = op.shape
mat = numpy.zeros(op.shape)
for j in range(w):
mat[:, j] = op(unit_vector(w, j))
return mat
def check_grad_mat():
import pyublas
if not pyublas.has_sparse_wrappers():
return
grad_mat = op.grad_matrix()
# print len(discr), grad_mat.nnz, type(grad_mat)
for i in range(10):
u = numpy.random.randn(len(discr))
mat_result = grad_mat * u
op_result = numpy.hstack(op.grad(u))
err = la.norm(mat_result - op_result) * la.norm(op_result)
assert la.norm(mat_result - op_result) * la.norm(op_result) < 1e-5
def check_matrix_tgt():
big = num.zeros((20, 20), flavor=num.SparseBuildMatrix)
small = num.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print small
from hedge._internal import MatrixTarget
tgt = MatrixTarget(big, 4, 4)
tgt.begin(small.shape[0], small.shape[1])
print "YO"
tgt.add_coefficients(4, 4, small)
print "DUDE"
tgt.finalize()
print big
import pymbolic
v_x = pymbolic.var("x")
truesol = pymbolic.parse("math.sin(x[0]**2*x[1]**2)")
truesol_c = pymbolic.compile(truesol, variables=["x"])
rhs = pymbolic.simplify(pymbolic.laplace(truesol, [v_x[0], v_x[1]]))
rhs_c = pymbolic.compile(rhs, variables=["x", "el"])
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, max_area=0.1, faces=20)
mesh = mesh.reordered_by("cuthill")
from hedge.backends import CPURunContext
rcon = CPURunContext()
from hedge.tools import EOCRecorder
eocrec = EOCRecorder()
for order in [1, 2, 3, 4, 5]:
for flux in ["ldg", "ip"]:
from hedge.discretization.local import TriangleDiscretization
discr = rcon.make_discretization(
mesh, TriangleDiscretization(order), debug=discr_class.noninteractive_debug_flags()
)
from hedge.data import GivenFunction
from hedge.models.poisson import PoissonOperator
op = PoissonOperator(
discr.dimensions,
dirichlet_tag=TAG_ALL,
dirichlet_bc=GivenFunction(lambda x, el: truesol_c(x)),
neumann_tag=TAG_NONE,
)
bound_op = op.bind(discr)
if order <= 3:
mat = matrix_rep(bound_op)
sym_err = la.norm(mat - mat.T)
# print sym_err
assert sym_err < 1e-12
# check_grad_mat()
from hedge.iterative import parallel_cg
truesol_v = discr.interpolate_volume_function(lambda x, el: truesol_c(x))
sol_v = -parallel_cg(
rcon,
-bound_op,
bound_op.prepare_rhs(discr.interpolate_volume_function(rhs_c)),
tol=1e-10,
max_iterations=40000,
)
eocrec.add_data_point(order, discr.norm(sol_v - truesol_v))
# print eocrec.pretty_print()
assert eocrec.estimate_order_of_convergence()[0, 1] > 8
def newton_interpolation_function(x, y):
return pymbolic.compile(newton_interpolation_polynomial(x, y), ["x"])
def test_elliptic():
"""Test various properties of elliptic operators."""
from hedge.tools import unit_vector
def matrix_rep(op):
h, w = op.shape
mat = numpy.zeros(op.shape)
for j in range(w):
mat[:, j] = op(unit_vector(w, j))
return mat
def check_grad_mat():
import pyublas
if not pyublas.has_sparse_wrappers():
return
grad_mat = op.grad_matrix()
#print len(discr), grad_mat.nnz, type(grad_mat)
for i in range(10):
u = numpy.random.randn(len(discr))
mat_result = grad_mat * u
op_result = numpy.hstack(op.grad(u))
err = la.norm(mat_result - op_result) * la.norm(op_result)
assert err < 1e-5
def check_matrix_tgt():
big = numpy.zeros((20, 20), flavor=numpy.SparseBuildMatrix)
small = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print small
from hedge._internal import MatrixTarget
tgt = MatrixTarget(big, 4, 4)
tgt.begin(small.shape[0], small.shape[1])
print "YO"
tgt.add_coefficients(4, 4, small)
print "DUDE"
tgt.finalize()
print big
import pymbolic
v_x = pymbolic.var("x")
truesol = pymbolic.parse("math.sin(x[0]**2*x[1]**2)")
truesol_c = pymbolic.compile(truesol, variables=["x"])
def laplace(expression, variables):
return sum(
pymbolic.diff(pymbolic.diff(expression, var), var)
for var in variables)
rhs = laplace(truesol, [v_x[0], v_x[1]])
rhs_c = pymbolic.compile(rhs, variables=["x", "el"])
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, max_area=0.1, faces=20)
mesh = mesh.reordered_by("cuthill")
from hedge.backends import CPURunContext
rcon = CPURunContext()
from hedge.tools import EOCRecorder
eocrec = EOCRecorder()
for order in [1, 2, 3, 4, 5]:
for flux in ["ldg", "ip"]:
from hedge.discretization.local import TriangleDiscretization
discr = rcon.make_discretization(
mesh,
TriangleDiscretization(order),
debug=discr_class.noninteractive_debug_flags())
from hedge.data import GivenFunction
from hedge.models.poisson import PoissonOperator
op = PoissonOperator(
discr.dimensions,
dirichlet_tag=TAG_ALL,
dirichlet_bc=GivenFunction(lambda x, el: truesol_c(x)),
neumann_tag=TAG_NONE)
bound_op = op.bind(discr)
if order <= 3:
mat = matrix_rep(bound_op)
sym_err = la.norm(mat - mat.T)
#print sym_err
assert sym_err < 1e-12
#check_grad_mat()
from hedge.iterative import parallel_cg
truesol_v = discr.interpolate_volume_function(
lambda x, el: truesol_c(x))
sol_v = -parallel_cg(rcon,
-bound_op,
bound_op.prepare_rhs(
discr.interpolate_volume_function(rhs_c)),
tol=1e-10,
max_iterations=40000)
eocrec.add_data_point(order, discr.norm(sol_v - truesol_v))
#print eocrec.pretty_print()
assert eocrec.estimate_order_of_convergence()[0, 1] > 8
