"""
Symbolic processor class for ANDES models.
"""
import inspect
import logging
import os
import pprint
from collections import OrderedDict, defaultdict
import numpy as np
import sympy as sp
from andes.shared import dilled_vars
from andes.thirdparty.npfunc import safe_div
from andes.thirdparty.sympymod import FixPiecewise
from andes.utils.paths import get_pycode_path
logger = logging.getLogger(__name__)
select_args_add = ["__zeros", "__ones", "__falses", "__trues"]
# the line below caches Piecewise instances
sp.OldPiecewise = sp.Piecewise
sp.Piecewise = FixPiecewise
[docs]class SymProcessor:
"""
A helper class for symbolic processing and code generation.
Parameters
----------
parent : Model
The `Model` instance to process
Attributes
----------
xy : sympy.Matrix
variables pretty print in the order of State, ExtState, Algeb, ExtAlgeb
f : sympy.Matrix
differential equations pretty print
g : sympy.Matrix
algebraic equations pretty print
df : sympy.SparseMatrix
df /d (xy) pretty print
dg : sympy.SparseMatrix
dg /d (xy) pretty print
inputs_dict : OrderedDict
All possible symbols in equations, including variables, parameters, discrete flags, and
config flags. It has the same variables as what ``get_inputs()`` returns.
vars_dict : OrderedDict
variable-only symbols, which are useful when getting the Jacobian matrices.
"""
def __init__(self, parent):
self.parent = parent
# symbols that are input to lambda functions
# including parameters, variables, services, configs, and scalars (dae_t, sys_f, sys_mva)
self.inputs_dict = OrderedDict()
self.lambdify_func = [dict(), 'numpy']
self.vars_dict = OrderedDict()
self.vars_int_dict = OrderedDict() # internal variables only
self.vars_list = list() # list of variable symbols, corresponding to `self.xy`
self.substitution_map = {} # mapping of ``SubsService`` to its expression
self.f_list, self.g_list = list(), list() # symbolic equations in lists
self.f_matrix, self.g_matrix, self.s_matrix = list(), list(), list() # equations in matrices
self.s_syms = list() # service symbols
self.j_args = dict() # Jacobian name -> argument list
self.j_calls = dict() # Jacobian name -> symbolic expressions
# pretty print of variables
self.xy = list() # variables in the order of states, algebs
self.f, self.g, self.s = list(), list(), list()
self.df, self.dg = None, None
# get references to the parent attributes
self.calls = parent.calls
self.cache = parent.cache
self.config = parent.config
self.class_name = parent.class_name
self.tex_names = OrderedDict()
[docs] def generate_symbols(self):
"""
Generate symbols for symbolic equation generations.
This function should run before other generate equations.
Attributes
----------
inputs_dict : OrderedDict
name-symbol pair of all parameters, variables and configs
vars_dict : OrderedDict
name-symbol pair of all variables, in the order of (states_and_ext + algebs_and_ext)
"""
logger.debug('- Generating symbols for %s', self.class_name)
# clear symbols storage
self.f_list, self.g_list = list(), list()
self.f_matrix, self.g_matrix = sp.Matrix([]), sp.Matrix([])
# process tex_names defined in model
# -----------------------------------------------------------
for key in self.parent.tex_names.keys():
self.tex_names[key] = sp.Symbol(self.parent.tex_names[key])
for instance in self.parent.discrete.values():
for name, tex_name in zip(instance.get_names(), instance.get_tex_names()):
self.tex_names[name] = sp.Symbol(tex_name)
# -----------------------------------------------------------
# `all_params_names` include parameters, services, exports from blocks, etc.
for var in self.cache.all_params_names:
is_real = True
if var in self.parent.services:
if self.parent.services[var].vtype == complex:
is_real = False
self.inputs_dict[var] = sp.Symbol(var, real=is_real)
for var in self.cache.all_vars_names:
tmp = sp.Symbol(var, real=True) # all DAE variables are real
self.vars_dict[var] = tmp
self.inputs_dict[var] = tmp
if var in self.cache.vars_int:
self.vars_int_dict[var] = tmp
# store tex names defined in `self.config`
for key in self.config.as_dict():
tmp = sp.Symbol(key, real=True) # not expecting complex numbers in config
self.inputs_dict[key] = tmp
if key in self.config.tex_names:
self.tex_names[tmp] = sp.Symbol(self.config.tex_names[key])
# store tex names for pretty printing replacement later
for var in self.inputs_dict:
if var in self.parent.__dict__ and self.parent.__dict__[var].tex_name is not None:
self.tex_names[sp.Symbol(var)] = sp.Symbol(self.parent.__dict__[var].tex_name)
# additional variables by conventions
self.inputs_dict['dae_t'] = sp.Symbol('dae_t')
self.inputs_dict['sys_f'] = sp.Symbol('sys_f')
self.inputs_dict['sys_mva'] = sp.Symbol('sys_mva')
# custom functions
self.lambdify_func[0]['Indicator'] = lambda x: x
self.lambdify_func[0]['imag'] = np.imag
self.lambdify_func[0]['real'] = np.real
self.lambdify_func[0]['safe_div'] = safe_div
self.vars_list = list(self.vars_dict.values()) # useful for ``.jacobian()``
def _check_expr_symbols(self, expr):
"""
Check if expression contains unknown symbols.
"""
fs = expr.free_symbols
for item in fs:
if item not in self.inputs_dict.values():
raise ValueError(f'{self.class_name} expression "{expr}" contains unknown symbol "{item}"')
fs = sorted(fs, key=lambda s: s.name)
return fs
def generate_subs_expr(self):
"""
Generate expressions for substituting ``SubsService``.
"""
for name, instance in self.parent.services_subs.items():
if instance.v_str is not None:
expr = sp.sympify(instance.v_str, locals=self.inputs_dict)
self.substitution_map[self.inputs_dict[name]] = expr
def _do_substitute(self, input_expr):
"""
Helper function to substitute ``SubsService`` with its expression.
"""
return input_expr.subs(self.substitution_map)
[docs] def generate_equations(self):
"""
Generate equations.
The pretty-print equations in matrices can be accessed in
``self.f_matrix`` and ``self.g_matrix``.
"""
logger.debug('- Generating equations for %s', self.class_name)
self.f_list, self.g_list = list(), list()
self.calls.f = None
self.calls.g = None
self.calls.f_args = list()
self.calls.g_args = list()
vars_list = [self.cache.states_and_ext, self.cache.algebs_and_ext]
expr_list = [self.f_list, self.g_list]
eqn_names = ['f', 'g']
eqn_args = [self.calls.f_args, self.calls.g_args]
for vlist, elist, ename, eargs in zip(vars_list, expr_list, eqn_names, eqn_args):
sym_args = list()
for name, instance in vlist.items():
if instance.e_str is None:
elist.append(0)
else:
try:
expr = sp.sympify(instance.e_str, locals=self.inputs_dict)
expr = self._do_substitute(expr)
except (sp.SympifyError, TypeError) as e:
logger.error('Error parsing equation "%s "for %s.%s',
instance.e_str, instance.owner.class_name, name)
raise e
free_syms = self._check_expr_symbols(expr)
for s in free_syms:
if s not in sym_args:
sym_args.append(s)
eargs.append(str(s))
elist.append(expr)
sym_args = sorted(sym_args, key=lambda s: s.name)
eargs.sort()
if len(elist) == 0 or not any(elist): # `any`, not `all`
self.calls.__dict__[ename] = None
else:
self.calls.__dict__[ename] = sp.lambdify(sym_args, tuple(elist),
modules=self.lambdify_func)
# manually append additional arguments for select.
if 'select' in inspect.getsource(self.calls.__dict__[ename]):
eargs.extend(select_args_add)
# convert to SymPy matrices
self.f_matrix = sp.Matrix(self.f_list)
self.g_matrix = sp.Matrix(self.g_list)
def generate_services(self):
"""
Generate calls for services, including ``ConstService`` and
``VarService`` among others. Sequence is preserved due to possible
dependency.
All ``VarService`` with ``sequential = False`` are generated into one
function, ``calls.sns``.
Starting from SymPy 1.9, ``Matrix`` no longer supports non-Expr objects.
Due to the use of logical conditions in services, service expressions
will not be converted to SymPy Matrix. The dictionary to look up service
name and expression is in ``self.s_syms``.
"""
s_syms = OrderedDict()
s_args = OrderedDict()
s_calls = OrderedDict()
sns_args = list() # ``sns`` means services that are non-sequential
sns_calls = None
s_calls_nonseq = list()
s_calls_nonseq_args = list()
for name, instance in self.parent.services.items():
v_str = '0' if instance.v_str is None else instance.v_str
try:
expr = sp.sympify(v_str, locals=self.inputs_dict)
expr = self._do_substitute(expr)
except (sp.SympifyError, TypeError) as e:
logger.error(f'Error parsing equation for {instance.owner.class_name}.{name}')
raise e
fs = self._check_expr_symbols(expr)
s_syms[name] = expr
args_expr = [str(i) for i in fs]
if instance.sequential is True:
s_args[name] = args_expr
s_calls[name] = sp.lambdify(s_args[name], s_syms[name], modules=self.lambdify_func)
if 'select' in inspect.getsource(s_calls[name]):
s_args[name].extend(select_args_add)
else:
s_calls_nonseq.append(expr)
s_calls_nonseq_args.extend(args_expr)
if len(s_calls_nonseq) > 0:
sns_args = sorted(list(set(s_calls_nonseq_args)))
sns_calls = sp.lambdify(sns_args, tuple(s_calls_nonseq), modules=self.lambdify_func)
if 'select' in inspect.getsource(sns_calls):
sns_args.extend(select_args_add)
self.s_syms = s_syms
self.calls.s = s_calls
self.calls.s_args = s_args
self.calls.sns = sns_calls
self.calls.sns_args = sns_args
[docs] def generate_jacobians(self, diag_eps=1e-8):
"""
Generate Jacobians and store to corresponding triplets.
The internal indices of equations and variables are stored, alongside the lambda functions.
For example, dg/dy is a sparse matrix whose elements are ``(row, col, val)``, where ``row`` and ``col``
are the internal indices, and ``val`` is the numerical lambda function. They will be stored to
row -> self.calls._igy
col -> self.calls._jgy
val -> self.calls._vgy
"""
logger.debug('- Generating Jacobians for %s', self.class_name)
from sympy import Tuple
# clear storage
self.df_syms, self.dg_syms = sp.Matrix([]), sp.Matrix([])
self.calls.clear_ijv()
# NOTE: SymPy does not allow getting the derivative of an empty array
if len(self.g_matrix) > 0:
self.dg_syms = self.g_matrix.jacobian(self.vars_list)
if len(self.f_matrix) > 0:
self.df_syms = self.f_matrix.jacobian(self.vars_list)
self.df_sparse = sp.SparseMatrix(self.df_syms)
self.dg_sparse = sp.SparseMatrix(self.dg_syms)
vars_syms_list = list(self.vars_dict)
algebs_and_ext_list = list(self.cache.algebs_and_ext)
states_and_ext_list = list(self.cache.states_and_ext)
fg_sparse = [self.df_sparse, self.dg_sparse]
j_args = defaultdict(list) # argument list for each jacobian call
j_calls = defaultdict(list) # jacobian functions (one for each type)
for idx, eq_sparse in enumerate(fg_sparse):
for item in eq_sparse.row_list():
e_idx, v_idx, e_symbolic = item
if idx == 0: # differential equation
eq_name = states_and_ext_list[e_idx]
else: # algebraic equation
eq_name = algebs_and_ext_list[e_idx]
var_name = vars_syms_list[v_idx]
eqn = self.cache.all_vars[eq_name] # `BaseVar` that corr. to the equation
var = self.cache.all_vars[var_name] # `BaseVar` that corr. to the variable
jname = f'{eqn.e_code}{var.v_code}'
# jac calls with all arguments and stored individually
# the `0` value will be used for building the Jacobian sparsity pattern
self.calls.append_ijv(jname, e_idx, v_idx, 0)
# collect unique arguments for jac calls
free_syms = self._check_expr_symbols(e_symbolic)
for fs in free_syms:
if fs not in j_args[jname]:
j_args[jname].append(fs)
j_calls[jname].append(e_symbolic)
self.j_args = j_args
self.j_calls = j_calls
for jname in j_calls:
# sort for stable argument list
j_args[jname].sort(key=lambda s: s.name)
self.calls.j_args[jname] = [str(i) for i in j_args[jname]]
# workaround for SymPy 1.10 to generate tuples with one element. See
# https://github.com/sympy/sympy/issues/23224
self.calls.j[jname] = sp.lambdify(j_args[jname], Tuple(*j_calls[jname]), modules=self.lambdify_func)
# manually append additional arguments for select
if 'select' in inspect.getsource(self.calls.j[jname]):
self.calls.j_args[jname].extend(select_args_add)
self.calls.j_names = list(j_calls.keys())
# The for-loop below is intended to add an epsilon small value to the diagonal of `gy`.
# The user should take care of the algebraic equations by using `diag_eps` in `Algeb` definition
for var in self.parent.cache.all_vars.values():
if var.diag_eps == 0.0:
continue
elif var.diag_eps is True:
if self.get_system_config('diag_eps') is not None:
eps = self.parent.system.config.diag_eps
elif diag_eps is not None:
eps = diag_eps # from function argument
else:
eps = 1e-8
else:
eps = var.diag_eps
if var.e_code == 'g':
eq_list = algebs_and_ext_list
else:
eq_list = states_and_ext_list
e_idx = eq_list.index(var.name)
v_idx = vars_syms_list.index(var.name)
self.calls.append_ijv(f'{var.e_code}{var.v_code}c', e_idx, v_idx, eps)
self.calls.need_diag_eps.append(var.name)
self.calls.need_diag_eps = sorted(list(set(self.calls.need_diag_eps)))
def generate_pretty_print(self):
"""
Generate pretty print variables and equations.
"""
logger.debug("- Generating pretty prints for %s", self.class_name)
# equation symbols for pretty printing
self.f, self.g = sp.Matrix([]), sp.Matrix([])
try:
self.xy = sp.Matrix(list(self.vars_dict.values())).subs(self.tex_names)
except TypeError as e:
logger.error("Error while substituting tex_name for variables.")
logger.error("Variable names might have conflicts with SymPy functions.")
raise e
# get pretty printing equations by substituting symbols
self.f = self.f_matrix.subs(self.tex_names)
self.g = self.g_matrix.subs(self.tex_names)
self.s = [item.subs(self.tex_names) for item in self.s_syms.values()]
# store latex strings
nx = len(self.f)
ny = len(self.g)
self.calls.x_latex = [sp.latex(item) for item in self.xy[:nx]]
self.calls.y_latex = [sp.latex(item) for item in self.xy[nx:nx + ny]]
self.calls.f_latex = [sp.latex(item) for item in self.f]
self.calls.g_latex = [sp.latex(item) for item in self.g]
self.calls.s_latex = [sp.latex(item) for item in self.s]
self.df = self.df_sparse.subs(self.tex_names)
self.dg = self.dg_sparse.subs(self.tex_names)
# store init latex strings
init_latex = OrderedDict()
for name, instance in self.cache.all_vars.items():
if instance.v_str is None and instance.v_iter is None:
init_latex[name] = ''
else:
if instance.v_str is not None:
init_latex[name] = sp.latex(self.v_str_syms[name].subs(self.tex_names))
if instance.v_iter is not None:
init_latex[name] = sp.latex(self.v_iter_syms[name].subs(self.tex_names))
self.calls.init_latex = init_latex
def generate_pycode(self, pycode_path, yapf_pycode):
"""
Create output source code file for generated code.
Generated code are stored at ``~/.andes/pycode``.
Notes
-----
In the current implementation, each model saves a ``.py`` file.
In systems with slow disk access (such as networked file systems),
this function can be the bottleneck.
"""
out = list()
yf = yapf_pycode
header = \
"""from collections import OrderedDict # NOQA
from numpy import ones_like, zeros_like, full, array # NOQA
from numpy import nan, pi, sin, cos, tan, sqrt, exp, select # NOQA
from numpy import greater_equal, less_equal, greater, less, equal # NOQA
from numpy import logical_and, logical_or, logical_not # NOQA
from numpy import real, imag, conj, angle, radians, abs # NOQA
from numpy import arcsin, arccos, arctan, arctan2 # NOQA
from numpy import log # NOQA
from andes.thirdparty.npfunc import * # NOQA
"""
# header goes first
out.append(header)
# checksum
out.append(f'md5 = "{self.calls.md5}"\n')
# equations
out.append(self._rename_func(self.calls.f, 'f_update', yf))
out.append(self._rename_func(self.calls.g, 'g_update', yf))
# jacobians
for name in self.calls.j:
out.append(self._rename_func(self.calls.j[name], f'{name}_update', yf))
# initialization: assignments
for name in self.calls.ia:
out.append(self._rename_func(self.calls.ia[name], f'{name}_ia', yf))
for name in self.calls.ii:
out.append(self._rename_func(self.calls.ii[name], f'{name}_ii', yf))
for name in self.calls.ij:
out.append(self._rename_func(self.calls.ij[name], f'{name}_ij', yf))
# services
for name in self.calls.s:
out.append(self._rename_func(self.calls.s[name], f'{name}_svc', yf))
# non-sequential services
out.append(self._rename_func(self.calls.sns, 'sns_update', yf))
# variables
for name in dilled_vars:
out.append(f'{name} = ' + pprint.pformat(self.calls.__dict__[name]) + "\n")
out_str = '\n'.join(out)
pycode_path = get_pycode_path(pycode_path, mkdir=True)
file_path = os.path.join(pycode_path, f'{self.class_name}.py')
# do not overwrite file if already up to date
if os.path.isfile(file_path):
with open(file_path, 'r') as f:
fread = f.readlines()
fread = ''.join(fread)
if fread == out_str:
logger.debug("<%s>: generated code is up-to-date and not overwritten.",
self.parent.class_name)
return
with open(file_path, 'w') as f:
f.write(out_str)
def _rename_func(self, func, func_name, yapf_pycode=False):
"""
Rename the function name and return source code.
This function performs these tasks:
1. rename ``_lambdifygenerated`` to the given ``func_name``.
2. append four arguments if ``select`` is used to pass numba
compilation.
3. remove ``Indicator`` for wrappers of logic expressions.
This function does not check for name conflicts. Install `yapf` for
optional code reformatting (takes extra processing time).
It also patches function argument list for select.
"""
if func is None:
return f"# empty {func_name}\n"
src = inspect.getsource(func)
src = src.replace("def _lambdifygenerated(", f"def {func_name}(")
# remove `Indicator`
src = src.replace("Indicator", "")
# append additional arguments for select
if 'select' in src:
right_parenthesis = ", " + ', '.join(select_args_add) + "):"
src = src.replace("):", right_parenthesis)
if yapf_pycode:
try:
from yapf.yapflib.yapf_api import FormatCode
src = FormatCode(src, style_config='pep8')[0] # drop the encoding `None`
except ImportError:
logger.warning("`yapf` not installed. Skipped code reformatting.")
src += '\n'
return src
def generate_dependency(self):
"""
Generate dependency list and initialization order.
"""
self.v_str_syms = OrderedDict()
self.v_iter_syms = OrderedDict()
deps = OrderedDict()
# convert to symbols
for name, instance in self.cache.all_vars.items():
if instance.v_str is not None:
sympified = sp.sympify(instance.v_str, locals=self.inputs_dict)
sympified = self._do_substitute(sympified)
self._check_expr_symbols(sympified)
self.v_str_syms[name] = sympified
else:
# default initial values to zero
sympified = sp.sympify('0.0', locals=self.inputs_dict)
self.v_str_syms[name] = sympified
if instance.v_iter is not None:
sympified = sp.sympify(instance.v_iter, locals=self.inputs_dict)
sympified = self._do_substitute(sympified)
self._check_expr_symbols(sympified)
self.v_iter_syms[name] = sympified
# store deps for explicit and iterative initializers
for name, expr in self.v_str_syms.items():
_store_deps(name, expr, self.vars_dict, deps)
for name, expr in self.v_iter_syms.items():
_store_deps(name, expr, self.vars_dict, deps)
# store deps for manually added dependent variables
for name, instance in self.cache.vars_int.items():
if instance.deps is not None:
deps[name].extend(instance.deps)
# resolve dependency
self.init_seq = resolve_deps(deps)
self.calls.init_seq = self.init_seq
def check_v_iter(self):
"""
Helper function to check if `v_iter` is defined for variables
with circular dependencies.
"""
for item in self.init_seq:
if not isinstance(item, list):
continue
for vi in item:
if self.cache.all_vars[vi].v_iter is None:
logger.error("%s: v_iter not defined for %s" % (self.class_name, vi))
[docs] def generate_init(self):
"""
Generate initialization equations.
"""
self.generate_dependency()
self.check_v_iter()
self.generate_init_eqn()
self.lambdify_init()
def generate_init_eqn(self):
"""
Generate initialization equations.
The RHS of assignment equations ``v = v_str(x, y)`` or RHS of iterative
initialization equations in the form of ``0 = v_iter(x, y)`` will be
stored to ``self.init_list``.
A list of flags will be stored to ``self.init_flag`` with 0 for
assignments and 1 for iterative.
For iteratively initialized variables that require assigned initial
values (to improve convergence), the initial value can be provided
through `self.v_str`.
"""
self.init_asn = OrderedDict() # assignment-type initialization
self.init_itn = OrderedDict() # iterative initialization
self.init_itn_vars = OrderedDict() # variables corr. to iterative vars
self.init_jac = OrderedDict()
for item in self.init_seq:
if isinstance(item, str):
instance = self.parent.__dict__[item]
if instance.v_str is not None:
self.init_asn[item] = self.v_str_syms[item]
if instance.v_iter is not None:
self.init_itn[item] = sp.Matrix([self.v_iter_syms[item]])
self.init_itn_vars[item] = [item]
elif isinstance(item, list):
name_concat = '_'.join(item)
eqn_set = sp.Matrix([self.v_iter_syms[name] for name in item])
self.init_itn[name_concat] = eqn_set
self.init_itn_vars[name_concat] = item
for vv in item:
instance = self.parent.__dict__[vv]
if instance.v_str is not None:
self.init_asn[vv] = self.v_str_syms[vv]
for name, expr in self.init_itn.items():
vars_iter = OrderedDict()
for item in self.init_itn_vars[name]:
vars_iter[item] = self.vars_dict[item]
self.init_jac[name] = expr.jacobian(list(vars_iter.values()))
def lambdify_init(self):
"""
Convert equations and Jacobians to lambda functions.
"""
init_a = OrderedDict()
init_i = OrderedDict()
init_j = OrderedDict()
ia_args = OrderedDict() # arguments for assignment init.
ii_args = OrderedDict() # arguments for iterative init.
ij_args = OrderedDict()
for name, expr in self.init_asn.items():
fs = self._check_expr_symbols(expr)
ia_args[name] = [str(i) for i in fs]
init_a[name] = sp.lambdify(ia_args[name], expr, modules=self.lambdify_func)
if 'select' in inspect.getsource(init_a[name]):
ia_args[name].extend(select_args_add)
for name, expr in self.init_itn.items():
fs = self._check_expr_symbols(expr)
ii_args[name] = [str(i) for i in fs]
init_i[name] = sp.lambdify(ii_args[name], expr, modules=self.lambdify_func)
if 'select' in inspect.getsource(init_i[name]):
ii_args[name].extend(select_args_add)
jexpr = self.init_jac[name]
fs = self._check_expr_symbols(jexpr)
ij_args[name] = [str(i) for i in fs]
init_j[name] = sp.lambdify(ij_args[name], jexpr, modules=self.lambdify_func)
if 'select' in inspect.getsource(init_j[name]):
ij_args[name].extend(select_args_add)
self.calls.ia = init_a
self.calls.ii = init_i
self.calls.ij = init_j
self.calls.ia_args = ia_args
self.calls.ii_args = ii_args
self.calls.ij_args = ij_args
def get_system_config(self, name):
"""
Helper function for obtaining system config.
If System is None, return None.
"""
if hasattr(self.parent.system, 'config'):
return self.parent.system.config.__dict__[name]
return None
def get_var_symbol(self, xyname, *, with_ext=False):
"""
Get a list of symbols for variables.
Parameters
----------
xyname : str
'x' or 'y'
with_ext : bool
True to include external variables
"""
if xyname not in ("x", "y"):
raise ValueError("unknown variable name %s" % xyname)
if len(self.vars_dict) == 0:
logger.warning("Symbols not generated. Trying to generate")
self.parent.prepare()
out = list()
if xyname == 'x':
if with_ext is True:
look_up_from = self.parent.cache.states_and_ext
else:
look_up_from = self.parent.states
else:
if with_ext is True:
look_up_from = self.parent.cache.algebs_and_ext
else:
look_up_from = self.parent.algebs
for name, sym in self.vars_dict.items():
if name in look_up_from:
out.append(sym)
return out
def _store_deps(name, sympified, vars_int_dict, deps):
"""
Helper function to store dependencies to a dict.
Used by ``resolve``.
"""
deps[name] = []
free_symbols = sorted(sympified.free_symbols, key=lambda s: s.name)
for fs in free_symbols:
if fs not in vars_int_dict.values():
continue
if fs not in deps[name]:
deps[name].append(str(fs))
def resolve_deps(graph):
"""
Resolve dependency for a dict-based graph using recursion.
Parameters
----------
graph : dict
Each key is a variable name, and the corresponding value
is the list of variables the key depends on.
Returns
-------
list
A list of initialization sequence. Elements are either a
variable name or a list of mutually-dependent variables
that need iterative initialization.
"""
seq = list() # sequence after resolving dependency
visited = list() # book keeper of the visited nodes
cflat = list() # flattened node in circles
circles = list() # circles as lists
def sub_resolve(name, deps, path):
for item in deps:
if (item == name) or (item in visited):
continue
# undeclared leaf node
if (item not in graph):
if item not in seq:
seq.append(item)
continue
# circular dependency
if item in path:
idx1 = path.index(item)
idx2 = path.index(name)
mn = min(idx1, idx2)
mx = max(idx1, idx2)
cflat.extend(path[mn:mx+1])
circles.append(path[mn:mx+1])
continue
path.append(item)
sub_resolve(item, graph[item], path)
# when all dependent nodes are visited
if name not in visited:
# if the current node is not in any circle
if name not in cflat:
seq.append(name)
else:
for cc in circles:
if (name in cc) and (cc not in seq):
seq.append(cc)
visited.append(name)
for name, deps in graph.items():
path = list()
sub_resolve(name, deps, path)
return seq