/usr/share/pyshared/ffc/quadrature/quadratureutils.py is in python-ffc 1.0.0-1.
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# Copyright (C) 2007-2010 Kristian B. Oelgaard
#
# This file is part of FFC.
#
# FFC 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.
#
# FFC 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 FFC. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2007-03-16
# Last changed: 2010-05-18
# Python modules.
import numpy
# FFC modules.
from ffc.log import debug, error, ffc_assert
from ffc.cpp import format
def create_psi_tables(tables, parameters):
"Create names and maps for tables and non-zero entries if appropriate."
debug("\nQG-utils, psi_tables:\n" + str(tables))
# Create element map {points:{element:number,},}
# and a plain dictionary {name:values,}.
element_map, flat_tables = flatten_psi_tables(tables)
debug("\nQG-utils, psi_tables, flat_tables:\n" + str(flat_tables))
# Reduce tables such that we only have those tables left with unique values
# Create a name map for those tables that are redundant.
name_map, unique_tables = unique_psi_tables(flat_tables, parameters)
debug("\nQG-utils, psi_tables, unique_tables:\n" + str(unique_tables))
debug("\nQG-utils, psi_tables, name_map:\n" + str(name_map))
return (element_map, name_map, unique_tables)
def flatten_psi_tables(tables):
"""Create a 'flat' dictionary of tables with unique names and a name
map that maps number of quadrature points and element name to a unique
element number. returns:
name_map - {num_quad_points:{ufl_element:element_number,},}.
flat_tables - {unique_table_name:values (ip,basis),}."""
generate_psi_name = format["psi name"]
# Initialise return values and element counter.
flat_tables = {}
element_map = {}
counter = 0
# Loop quadrature points and get element dictionary {elem: {tables}}.
for point in sorted(tables.keys()):
elem_dict = tables[point]
element_map[point] = {}
# Loop all elements and get all their tables.
for elem in sorted(elem_dict.keys(), lambda x, y: cmp(str(x), str(y))):
facet_tables = elem_dict[elem]
element_map[point][elem] = counter
for facet in sorted(facet_tables.keys()):
elem_table = facet_tables[facet]
# If the element value rank != 0, we must loop the components.
# before the derivatives (that's the way the values are tabulated).
if len(elem.value_shape()) != 0:
for derivs in sorted(elem_table.keys()):
comp_table = elem_table[derivs]
transposed_table = numpy.transpose(comp_table, (1,0,2))
for num_comp, psi_table in enumerate(transposed_table):
# Verify shape of basis (can be omitted for speed
# if needed I think).
ffc_assert(len(numpy.shape(psi_table)) == 2 and numpy.shape(psi_table)[1] == point, \
"Something is wrong with this table: " + str(psi_table))
# Generate the table name.
name = generate_psi_name(counter, facet, num_comp, derivs)
ffc_assert(name not in flat_tables, \
"Table name is not unique, something is wrong: " + name + str(flat_tables))
# Take transpose such that we get (ip_number, basis_number)
# instead of (basis_number, ip_number).
flat_tables[name] = numpy.transpose(psi_table)
# If we don't have any components.
else:
for derivs in sorted(elem_table.keys()):
psi_table = elem_table[derivs]
# Verify shape of basis (can be omitted for speed
# if needed I think).
ffc_assert(len(numpy.shape(psi_table)) == 2 and numpy.shape(psi_table)[1] == point, \
"Something is wrong with this table: " + str(psi_table))
# Generate the table name.
name = generate_psi_name(counter, facet, (), derivs)
ffc_assert(name not in flat_tables, \
"Table name is not unique, something is wrong: " + name + str(flat_tables))
flat_tables[name] = numpy.transpose(psi_table)
# Increase unique element counter.
counter += 1
return (element_map, flat_tables)
def unique_psi_tables(tables, parameters):
"""Returns a name map and a dictionary of unique tables. The function checks
if values in the tables are equal, if this is the case it creates a name
mapping. It also create additional information (depending on which parameters
are set) such as if the table contains all ones, or only zeros, and a list
on non-zero columns.
unique_tables - {name:values,}.
name_map - {original_name:[new_name, non-zero-columns (list), is zero (bool), is ones (bool)],}."""
# Get unique tables (from old table utility).
name_map, inverse_name_map = unique_tables(tables)
debug("\ntables: " + str(tables))
debug("\nname_map: " + str(name_map))
debug("\ninv_name_map: " + str(inverse_name_map))
# Set values to zero if they are lower than threshold.
format_epsilon = format["epsilon"]
for name in tables:
# Get values.
vals = tables[name]
for r in range(numpy.shape(vals)[0]):
for c in range(numpy.shape(vals)[1]):
if abs(vals[r][c]) < format_epsilon:
vals[r][c] = 0
tables[name] = vals
# Extract the column numbers that are non-zero.
# If optimisation option is set
# counter for non-zero column arrays.
i = 0
non_zero_columns = {}
if parameters["eliminate zeros"]:
for name in sorted(tables.keys()):
# Get values.
vals = tables[name]
# Use the first row as reference.
non_zeros = list(vals[0].nonzero()[0])
# If all columns in the first row are non zero, there's no point
# in continuing.
if len(non_zeros) == numpy.shape(vals)[1]:
continue
# If we only have one row (IP) we just need the nonzero columns.
if numpy.shape(vals)[0] == 1:
if list(non_zeros):
non_zeros.sort()
non_zero_columns[name] = (i, non_zeros)
# Compress values.
tables[name] = vals[:, non_zeros]
i += 1
# Check if the remaining rows are nonzero in the same positions, else expand.
else:
for j in range(1, numpy.shape(vals)[0]):
# All rows must have the same non-zero columns
# for the optimization to work (at this stage).
new_non_zeros = list(vals[j].nonzero()[0])
if non_zeros != new_non_zeros:
non_zeros = non_zeros + [c for c in new_non_zeros if not c in non_zeros]
# If this results in all columns being non-zero, continue.
if len(non_zeros) == numpy.shape(vals)[1]:
continue
# Only add nonzeros if it results in a reduction of columns.
if len(non_zeros) != numpy.shape(vals)[1]:
if list(non_zeros):
non_zeros.sort()
non_zero_columns[name] = (i, non_zeros)
# Compress values.
tables[name] = vals[:, non_zeros]
i += 1
# Check if we have some zeros in the tables.
names_zeros = contains_zeros(tables)
# Get names of tables with all ones.
names_ones = get_ones(tables)
# Add non-zero column, zero and ones info to inverse_name_map
# (so we only need to pass around one name_map to code generating functions).
for name in inverse_name_map:
if inverse_name_map[name] in non_zero_columns:
nzc = non_zero_columns[inverse_name_map[name]]
zero = inverse_name_map[name] in names_zeros
ones = inverse_name_map[name] in names_ones
inverse_name_map[name] = [inverse_name_map[name], nzc, zero, ones]
else:
zero = inverse_name_map[name] in names_zeros
ones = inverse_name_map[name] in names_ones
inverse_name_map[name] = [inverse_name_map[name], (), zero, ones]
# If we found non zero columns we might be able to reduce number of tables further.
if non_zero_columns:
# Try reducing the tables. This is possible if some tables have become
# identical as a consequence of compressing the tables.
# This happens with e.g., gradients of linear basis
# FE0 = {-1,0,1}, nzc0 = [0,2]
# FE1 = {-1,1,0}, nzc1 = [0,1] -> FE0 = {-1,1}, nzc0 = [0,2], nzc1 = [0,1].
# Call old utility function again.
nm, inv_nm = unique_tables(tables)
# Update name maps.
for name in inverse_name_map:
if inverse_name_map[name][0] in inv_nm:
inverse_name_map[name][0] = inv_nm[inverse_name_map[name][0]]
for name in nm:
maps = nm[name]
for m in maps:
if not name in name_map:
name_map[name] = []
if m in name_map:
name_map[name] += name_map[m] + [m]
del name_map[m]
else:
name_map[name].append(m)
# Get new names of tables with all ones (for vector constants).
names = get_ones(tables)
# Because these tables now contain ones as a consequence of compression
# we still need to consider the non-zero columns when looking up values
# in coefficient arrays. The psi entries can however we neglected and we
# don't need to tabulate the values (if option is set).
for name in names:
if name in name_map:
maps = name_map[name]
for m in maps:
inverse_name_map[m][3] = True
if name in inverse_name_map:
inverse_name_map[name][3] = True
# Write protect info and return values
for name in inverse_name_map:
inverse_name_map[name] = tuple(inverse_name_map[name])
return (inverse_name_map, tables)
def unique_tables(tables):
"""Removes tables with redundant values and returns a name_map and a
inverse_name_map. E.g.,
tables = {a:[0,1,2], b:[0,2,3], c:[0,1,2], d:[0,1,2]}
results in:
tables = {a:[0,1,2], b:[0,2,3]}
name_map = {a:[c,d]}
inverse_name_map = {a:a, b:b, c:a, d:a}."""
format_epsilon = format["epsilon"]
name_map = {}
inverse_name_map = {}
names = sorted(tables.keys())
mapped = []
# Loop all tables to see if some are redundant.
for i in range(len(names)):
name0 = names[i]
if name0 in mapped:
continue
val0 = numpy.array(tables[name0])
for j in range(i+1, len(names)):
name1 = names[j]
if name1 in mapped:
continue
val1 = numpy.array(tables[name1])
# Check if dimensions match.
if numpy.shape(val0) == numpy.shape(val1):
# Check if values are the same.
if abs(val0 - val1).max() < format_epsilon:
mapped.append(name1)
del tables[name1]
if name0 in name_map:
name_map[name0].append(name1)
else:
name_map[name0] = [name1]
# Create inverse name map.
inverse_name_map[name1] = name0
# Add self.
for name in tables:
if not name in inverse_name_map:
inverse_name_map[name] = name
return (name_map, inverse_name_map)
def get_ones(tables):
"Return names of tables for which all values are 1.0."
f_epsilon = format["epsilon"]
names = []
for name in tables:
vals = tables[name]
if abs(vals - numpy.ones(numpy.shape(vals))).max() < f_epsilon:
names.append(name)
return names
def contains_zeros(tables):
"Checks if any tables contains only zeros."
f_epsilon = format["epsilon"]
names = []
for name in tables:
vals = tables[name]
if abs(vals).max() < f_epsilon:
names.append(name)
return names
def create_permutations(expr):
# This is probably not used.
if len(expr) == 0:
return expr
# Format keys and values to lists and tuples.
if len(expr) == 1:
new = {}
for key, val in expr[0].items():
if key == ():
pass
elif not isinstance(key[0], tuple):
key = (key,)
if not isinstance(val, list):
val = [val]
new[key] = val
return new
# Create permutations of two lists.
# TODO: there could be a cleverer way of changing types of keys and vals.
if len(expr) == 2:
new = {}
for key0, val0 in expr[0].items():
if isinstance(key0[0], tuple):
key0 = list(key0)
if not isinstance(key0, list):
key0 = [key0]
if not isinstance(val0, list):
val0 = [val0]
for key1, val1 in expr[1].items():
if key1 == ():
key1 = []
elif isinstance(key1[0], tuple):
key1 = list(key1)
if not isinstance(key1, list):
key1 = [key1]
if not isinstance(val1, list):
val1 = [val1]
ffc_assert(tuple(key0 + key1) not in new, "This is not supposed to happen.")
new[tuple(key0 + key1)] = val0 + val1
return new
# Create permutations by calling this function recursively.
# This is only used for rank > 2 tensors I think.
if len(expr) > 2:
new = permutations(expr[0:2])
return permutations(new + expr[2:])
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