# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program 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 this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or
# initial documentation
# :author: Francois Gallard
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""
Analytic MDODiscipline based on symbolic expressions
****************************************************
"""
from __future__ import division, unicode_literals
import logging
from numpy import array, float64, heaviside, zeros
from six import string_types
from sympy import Expr, lambdify, symbols
from sympy.parsing.sympy_parser import parse_expr
from gemseo.core.discipline import MDODiscipline
from gemseo.utils.py23_compat import PY2
LOGGER = logging.getLogger(__name__)
[docs]class AnalyticDiscipline(MDODiscipline):
"""Discipline based on analytic expressions list, using the symbolic calculation
SymPy engine.
Automatically differentiates the expressions to obtain
the Jacobian matrices.
See also
--------
gemseo.core.discipline.MDODiscipline : abstract class defining
the key concept of discipline
"""
def __init__(self, name=None, expressions_dict=None, fast_evaluation=True):
"""Constructor.
:param name: name of the discipline.
:type name: str
:param expressions_dict: dictionary of outputs and their expressions
for instance : { 'y_1':'2*x**2', 'y_2':'4*x**2+5+z**3'}
will create a discipline with outputs y_1, y_2
and inputs x, and z.
Expressions may be passed as strings or SymPy expressions.
:type expressions_dict: dict(str or sympy.Expr)
:param fast_evaluation: if True then sympy.lambdify is applied to the
expressions to accelerate their numerical evaluation (requires NumPy),
otherwise the expressions are evaluated with sympy.Expr.evalf.
:type fast_evaluation: bool
"""
super(AnalyticDiscipline, self).__init__(name)
if not expressions_dict:
raise ValueError("expressions_dict is a mandatory argument")
self.expressions_dict = expressions_dict
self.expr_symbols_dict = {}
self.input_names = []
self._sympy_exprs = {}
self._sympy_funcs = {}
self._sympy_jac_exprs = {}
self._sympy_jac_funcs = {}
self._fast_evaluation = fast_evaluation
self._init_expressions()
self._init_grammars()
self._init_default_inputs()
self.re_exec_policy = self.RE_EXECUTE_DONE_POLICY
def _init_grammars(self):
"""Initialize the |g| grammars from the expressions dictionary."""
zero = zeros(2)
in_dict = {k: zero for k in self.input_names}
self.input_grammar.initialize_from_base_dict(in_dict)
out_dict = {k: zero for k in self.expressions_dict}
self.output_grammar.initialize_from_base_dict(out_dict)
def _init_expressions(self):
"""Parse the expressions (get SymPy expressions from string expressions) and
their Jacobian expressions."""
input_symbols = []
for out_var, expr in self.expressions_dict.items():
if isinstance(expr, Expr):
parsed = expr
elif isinstance(expr, string_types):
parsed = parse_expr(expr)
else:
raise TypeError("Expression must be a SymPy expression or a string")
args = list(parsed.free_symbols)
self._sympy_exprs[out_var] = parsed
input_symbols += args
args_names = [arg.name for arg in args]
self.expr_symbols_dict[out_var] = args_names
self._sympy_jac_exprs[out_var] = {}
for arg in args_names:
jac_expr = parsed.diff(arg)
self._sympy_jac_exprs[out_var][arg] = jac_expr
self.input_names = sorted([symb.name for symb in set(input_symbols)])
if self._fast_evaluation:
self._lambdify_expressions()
def _lambdify_expressions(self):
"""Lambdify the SymPy expressions."""
numpy_str = "numpy"
if PY2:
numpy_str = numpy_str.encode("ascii")
modules = [numpy_str, {"Heaviside": lambda x: heaviside(x, 1)}]
for out_var, expr in self._sympy_exprs.items():
args_names = self.expr_symbols_dict[out_var]
args = symbols(args_names)
self._sympy_funcs[out_var] = lambdify(args, expr)
self._sympy_jac_funcs[out_var] = dict()
for in_var in args_names:
jac_expr = self._sympy_jac_exprs[out_var][in_var]
self._sympy_jac_funcs[out_var][in_var] = lambdify(
args, jac_expr, modules
)
def _init_default_inputs(self):
"""Initialize the default inputs of the discipline with zeros."""
zeros_array = zeros(1)
self.default_inputs = {k: zeros_array for k in self.input_names}
def _run(self):
"""Run the discipline."""
outputs = {}
# Do not pass useless tokens to the expr, this may
# fail when tokens contains dots, or slow down the process
filtered_inputs = {key: float(val.real) for key, val in self.local_data.items()}
if self._fast_evaluation:
for out_var, func in self._sympy_funcs.items():
args_names = self.expr_symbols_dict[out_var]
args = (filtered_inputs[name] for name in args_names)
out_val = func(*args)
outputs[out_var] = array([out_val], dtype=float64)
else:
for out_var, expr in self._sympy_exprs.items():
try:
out_val = expr.evalf(subs=filtered_inputs)
outputs[out_var] = array([out_val], dtype=float64)
except TypeError:
LOGGER.error("Failed to evaluate expression : %s", str(expr))
LOGGER.error("With inputs : %s", str(self.local_data))
raise
self.store_local_data(**outputs)
def _compute_jacobian(self, inputs=None, outputs=None):
"""Compute the Jacobian.
:param inputs: names of the differentiation inputs (Default value = None)
:type inputs: list(str)
:param outputs: names of the outputs to be differentiated (Default value = None)
:type outputs: list(str)
"""
# otherwise there may be missing terms
# if some formula have no dependency
self._init_jacobian(inputs, outputs, with_zeros=True)
filtered_inputs = {key: float(val.real) for key, val in self.local_data.items()}
if self._fast_evaluation:
for out_var, grad in self._sympy_jac_funcs.items():
args_names = self.expr_symbols_dict[out_var]
for in_var, func in grad.items():
args = (filtered_inputs[name] for name in args_names)
jac_val = func(*args)
self.jac[out_var][in_var] = array([[jac_val]], dtype=float64)
else:
for out_var, expr in self._sympy_exprs.items():
for arg in expr.free_symbols:
j_expr = self._sympy_jac_exprs[out_var][arg.name]
jac_val = j_expr.evalf(subs=filtered_inputs)
self.jac[out_var][arg.name] = array([[jac_val]], dtype=float64)
