'''
Differential equations for Brian models.
'''
import collections
import keyword
import re
import string
import numpy as np
import sympy
from pyparsing import (Group, ZeroOrMore, OneOrMore, Optional, Word, CharsNotIn,
Combine, Suppress, restOfLine, LineEnd, ParseException)
from brian2.core.namespace import (DEFAULT_FUNCTIONS,
DEFAULT_CONSTANTS,
DEFAULT_UNITS)
from brian2.core.variables import Constant
from brian2.core.functions import Function
from brian2.equations.codestrings import is_constant_over_dt
from brian2.parsing.sympytools import sympy_to_str, str_to_sympy
from brian2.units.fundamentalunits import (Unit, Quantity, have_same_dimensions,
get_unit, DIMENSIONLESS,
DimensionMismatchError)
from brian2.units.allunits import (metre, meter, second, amp, kelvin, mole,
candle, kilogram, radian, steradian, hertz,
newton, pascal, joule, watt, coulomb, volt,
farad, ohm, siemens, weber, tesla, henry,
celsius, lumen, lux, becquerel, gray,
sievert, katal, kgram, kgramme)
from brian2.utils.logger import get_logger
from brian2.utils.topsort import topsort
from .codestrings import Expression
from .unitcheck import check_unit
__all__ = ['Equations']
logger = get_logger(__name__)
# Equation types (currently simple strings but always use the constants,
# this might get refactored into objects, for example)
PARAMETER = 'parameter'
DIFFERENTIAL_EQUATION = 'differential equation'
SUBEXPRESSION = 'subexpression'
# variable types (FLOAT is the only one that is possible for variables that
# have dimensions). These types will be later translated into dtypes, either
# using the default values from the preferences, or explicitly given dtypes in
# the construction of the `NeuronGroup`, `Synapses`, etc. object
FLOAT = 'float'
INTEGER = 'integer'
BOOLEAN = 'boolean'
# Definitions of equation structure for parsing with pyparsing
# TODO: Maybe move them somewhere else to not pollute the namespace here?
# Only IDENTIFIER and EQUATIONS are ever used later
###############################################################################
# Basic Elements
###############################################################################
# identifiers like in C: can start with letter or underscore, then a
# combination of letters, numbers and underscores
# Note that the check_identifiers function later performs more checks, e.g.
# names starting with underscore should only be used internally
IDENTIFIER = Word(string.ascii_letters + '_',
string.ascii_letters + string.digits + '_').setResultsName('identifier')
# very broad definition here, expression will be analysed by sympy anyway
# allows for multi-line expressions, where each line can have comments
EXPRESSION = Combine(OneOrMore((CharsNotIn(':#\n') +
Suppress(Optional(LineEnd()))).ignore('#' + restOfLine)),
joinString=' ').setResultsName('expression')
# a unit
# very broad definition here, again. Whether this corresponds to a valid unit
# string will be checked later
UNIT = Word(string.ascii_letters + string.digits + '*/.- ').setResultsName('unit')
# a single Flag (e.g. "const" or "event-driven")
FLAG = Word(string.ascii_letters, string.ascii_letters + '_- ' + string.digits)
# Flags are comma-separated and enclosed in parantheses: "(flag1, flag2)"
FLAGS = (Suppress('(') + FLAG + ZeroOrMore(Suppress(',') + FLAG) +
Suppress(')')).setResultsName('flags')
###############################################################################
# Equations
###############################################################################
# Three types of equations
# Parameter:
# x : volt (flags)
PARAMETER_EQ = Group(IDENTIFIER + Suppress(':') + UNIT +
Optional(FLAGS)).setResultsName(PARAMETER)
# Static equation:
# x = 2 * y : volt (flags)
STATIC_EQ = Group(IDENTIFIER + Suppress('=') + EXPRESSION + Suppress(':') +
UNIT + Optional(FLAGS)).setResultsName(SUBEXPRESSION)
# Differential equation
# dx/dt = -x / tau : volt
DIFF_OP = (Suppress('d') + IDENTIFIER + Suppress('/') + Suppress('dt'))
DIFF_EQ = Group(DIFF_OP + Suppress('=') + EXPRESSION + Suppress(':') + UNIT +
Optional(FLAGS)).setResultsName(DIFFERENTIAL_EQUATION)
# ignore comments
EQUATION = (PARAMETER_EQ | STATIC_EQ | DIFF_EQ).ignore('#' + restOfLine)
EQUATIONS = ZeroOrMore(EQUATION)
[docs]class EquationError(Exception):
'''
Exception type related to errors in an equation definition.
'''
pass
[docs]def check_identifier_basic(identifier):
'''
Check an identifier (usually resulting from an equation string provided by
the user) for conformity with the rules. The rules are:
1. Only ASCII characters
2. Starts with a character, then mix of alphanumerical characters and
underscore
3. Is not a reserved keyword of Python
Parameters
----------
identifier : str
The identifier that should be checked
Raises
------
ValueError
If the identifier does not conform to the above rules.
'''
# Check whether the identifier is parsed correctly -- this is always the
# case, if the identifier results from the parsing of an equation but there
# might be situations where the identifier is specified directly
parse_result = list(IDENTIFIER.scanString(identifier))
# parse_result[0][0][0] refers to the matched string -- this should be the
# full identifier, if not it is an illegal identifier like "3foo" which only
# matched on "foo"
if len(parse_result) != 1 or parse_result[0][0][0] != identifier:
raise ValueError('"%s" is not a valid variable name.' % identifier)
if keyword.iskeyword(identifier):
raise ValueError(('"%s" is a Python keyword and cannot be used as a '
'variable.') % identifier)
if identifier.startswith('_'):
raise ValueError(('Variable "%s" starts with an underscore, '
'this is only allowed for variables used '
'internally') % identifier)
[docs]def check_identifier_reserved(identifier):
'''
Check that an identifier is not using a reserved special variable name. The
special variables are: 't', 'dt', and 'xi', as well as everything starting
with `xi_`.
Parameters
----------
identifier: str
The identifier that should be checked
Raises
------
ValueError
If the identifier is a special variable name.
'''
if identifier in ('t', 'dt', 'xi') or identifier.startswith('xi_'):
raise ValueError(('"%s" has a special meaning in equations and cannot '
' be used as a variable name.') % identifier)
[docs]def check_identifier_units(identifier):
'''
Make sure that identifier names do not clash with unit names.
'''
if identifier in DEFAULT_UNITS:
raise ValueError('"%s" is the name of a unit, cannot be used as a '
'variable name.' % identifier)
[docs]def check_identifier_functions(identifier):
'''
Make sure that identifier names do not clash with function names.
'''
if identifier in DEFAULT_FUNCTIONS:
raise ValueError('"%s" is the name of a function, cannot be used as a '
'variable name.' % identifier)
[docs]def check_identifier_constants(identifier):
'''
Make sure that identifier names do not clash with function names.
'''
if identifier in DEFAULT_CONSTANTS:
raise ValueError('"%s" is the name of a constant, cannot be used as a '
'variable name.' % identifier)
[docs]def unit_and_type_from_string(unit_string):
'''
Returns the unit that results from evaluating a string like
"siemens / metre ** 2", allowing for the special string "1" to signify
dimensionless units, the string "boolean" for a boolean and "integer" for
an integer variable.
Parameters
----------
unit_string : str
The string that should evaluate to a unit
Returns
-------
u, type : (Unit, {FLOAT, INTEGER or BOOL})
The resulting unit and the type of the variable.
Raises
------
ValueError
If the string cannot be evaluated to a unit.
'''
# We avoid using DEFAULT_NUMPY_NAMESPACE here as importing core.namespace
# would introduce a circular dependency between it and the equations
# package
base_units = [metre, meter, second, amp, kelvin, mole, candle, kilogram,
radian, steradian, hertz, newton, pascal, joule, watt,
coulomb, volt, farad, ohm, siemens, weber, tesla, henry,
celsius, lumen, lux, becquerel, gray, sievert, katal, kgram,
kgramme]
namespace = dict((repr(unit), unit) for unit in base_units)
namespace['Hz'] = hertz # Also allow Hz instead of hertz
unit_string = unit_string.strip()
# Special case: dimensionless unit
if unit_string == '1':
return Unit(1, dim=DIMENSIONLESS), FLOAT
# Another special case: boolean variable
if unit_string == 'boolean':
return Unit(1, dim=DIMENSIONLESS), BOOLEAN
if unit_string == 'bool':
raise TypeError("Use 'boolean' not 'bool' as the unit for a boolean "
"variable.")
# Yet another special case: integer variable
if unit_string == 'integer':
return Unit(1, dim=DIMENSIONLESS), INTEGER
# Check first whether the expression evaluates at all, using only base units
try:
evaluated_unit = eval(unit_string, namespace)
except Exception as ex:
raise ValueError(('"%s" does not evaluate to a unit when only using '
'base units (e.g. volt but not mV): %s') %
(unit_string, ex))
# Check whether the result is a unit
if not isinstance(evaluated_unit, Unit):
if isinstance(evaluated_unit, Quantity):
raise ValueError(('"%s" does not evaluate to a unit but to a '
'quantity -- make sure to only use units, e.g. '
'"siemens/metre**2" and not "1 * siemens/metre**2"') %
unit_string)
else:
raise ValueError(('"%s" does not evaluate to a unit, the result '
'has type %s instead.' % (unit_string,
type(evaluated_unit))))
# No error has been raised, all good
return evaluated_unit, FLOAT
[docs]def parse_string_equations(eqns):
"""
Parse a string defining equations.
Parameters
----------
eqns : str
The (possibly multi-line) string defining the equations. See the
documentation of the `Equations` class for details.
Returns
-------
equations : dict
A dictionary mapping variable names to
`~brian2.equations.equations.Equations` objects
"""
equations = {}
try:
parsed = EQUATIONS.parseString(eqns, parseAll=True)
except ParseException as p_exc:
raise EquationError('Parsing failed: \n' + str(p_exc.line) + '\n' +
' ' * (p_exc.column - 1) + '^\n' + str(p_exc))
for eq in parsed:
eq_type = eq.getName()
eq_content = dict(eq.items())
# Check for reserved keywords
identifier = eq_content['identifier']
# Convert unit string to Unit object
unit, var_type = unit_and_type_from_string(eq_content['unit'])
expression = eq_content.get('expression', None)
if not expression is None:
# Replace multiple whitespaces (arising from joining multiline
# strings) with single space
p = re.compile(r'\s{2,}')
expression = Expression(p.sub(' ', expression))
flags = list(eq_content.get('flags', []))
equation = SingleEquation(eq_type, identifier, unit, var_type=var_type,
expr=expression, flags=flags)
if identifier in equations:
raise EquationError('Duplicate definition of variable "%s"' %
identifier)
equations[identifier] = equation
return equations
[docs]class SingleEquation(object):
'''
Class for internal use, encapsulates a single equation or parameter.
.. note::
This class should never be used directly, it is only useful as part of
the `Equations` class.
Parameters
----------
type : {PARAMETER, DIFFERENTIAL_EQUATION, SUBEXPRESSION}
The type of the equation.
varname : str
The variable that is defined by this equation.
unit : Unit
The unit of the variable
var_type : {FLOAT, INTEGER, BOOLEAN}
The type of the variable (floating point value or boolean).
expr : `Expression`, optional
The expression defining the variable (or ``None`` for parameters).
flags: list of str, optional
A list of flags that give additional information about this equation.
What flags are possible depends on the type of the equation and the
context.
'''
def __init__(self, type, varname, unit, var_type=FLOAT, expr=None,
flags=None):
self.type = type
self.varname = varname
self.unit = unit
self.var_type = var_type
if not have_same_dimensions(unit, 1):
if var_type == BOOLEAN:
raise TypeError('Boolean variables are necessarily dimensionless.')
elif var_type == INTEGER:
raise TypeError('Integer variables are necessarily dimensionless.')
if type == DIFFERENTIAL_EQUATION:
if var_type != FLOAT:
raise TypeError('Differential equations can only define floating point variables')
self.expr = expr
if flags is None:
self.flags = []
else:
self.flags = flags
# will be set later in the sort_subexpressions method of Equations
self.update_order = -1
identifiers = property(lambda self: self.expr.identifiers
if not self.expr is None else set([]),
doc='All identifiers in the RHS of this equation.')
stochastic_variables = property(lambda self: set([variable for variable in self.identifiers
if variable =='xi' or variable.startswith('xi_')]),
doc='Stochastic variables in the RHS of this equation')
def _latex(self, *args):
if self.type == DIFFERENTIAL_EQUATION:
return (r'\frac{\mathrm{d}' + sympy.latex(self.varname) + r'}{\mathrm{d}t} = ' +
sympy.latex(str_to_sympy(self.expr.code)))
elif self.type == SUBEXPRESSION:
return (sympy.latex(self.varname) + ' = ' +
sympy.latex(str_to_sympy(self.expr.code)))
elif self.type == PARAMETER:
return sympy.latex(self.varname)
def __str__(self):
if self.type == DIFFERENTIAL_EQUATION:
s = 'd' + self.varname + '/dt'
else:
s = self.varname
if not self.expr is None:
s += ' = ' + str(self.expr)
s += ' : ' + str(self.unit)
if len(self.flags):
s += ' (' + ', '.join(self.flags) + ')'
return s
def __repr__(self):
s = '<' + self.type + ' ' + self.varname
if not self.expr is None:
s += ': ' + self.expr.code
s += ' (Unit: ' + str(self.unit)
if len(self.flags):
s += ', flags: ' + ', '.join(self.flags)
s += ')>'
return s
def _repr_pretty_(self, p, cycle):
'''
Pretty printing for ipython.
'''
if cycle:
# should never happen
raise AssertionError('Cyclical call of SingleEquation._repr_pretty')
if self.type == DIFFERENTIAL_EQUATION:
p.text('d' + self.varname + '/dt')
else:
p.text(self.varname)
if not self.expr is None:
p.text(' = ')
p.pretty(self.expr)
p.text(' : ')
p.pretty(self.unit)
if len(self.flags):
p.text(' (' + ', '.join(self.flags) + ')')
def _repr_latex_(self):
return '$' + sympy.latex(self) + '$'
[docs]class Equations(collections.Mapping):
"""
Container that stores equations from which models can be created.
String equations can be of any of the following forms:
1. ``dx/dt = f : unit (flags)`` (differential equation)
2. ``x = f : unit (flags)`` (equation)
3. ``x : unit (flags)`` (parameter)
String equations can span several lines and contain Python-style comments
starting with ``#``
Parameters
----------
eqs : `str` or list of `SingleEquation` objects
A multiline string of equations (see above) -- for internal purposes
also a list of `SingleEquation` objects can be given. This is done for
example when adding new equations to implement the refractory
mechanism. Note that in this case the variable names are not checked
to allow for "internal names", starting with an underscore.
kwds: keyword arguments
Keyword arguments can be used to replace variables in the equation
string. Arguments have to be of the form ``varname=replacement``, where
`varname` has to correspond to a variable name in the given equation.
The replacement can be either a string (replacing a name with a new
name, e.g. ``tau='tau_e'``) or a value (replacing the variable name
with the value, e.g. ``tau=tau_e`` or ``tau=10*ms``).
"""
def __init__(self, eqns, **kwds):
if isinstance(eqns, basestring):
self._equations = parse_string_equations(eqns)
# Do a basic check for the identifiers
self.check_identifiers()
else:
self._equations = {}
for eq in eqns:
if not isinstance(eq, SingleEquation):
raise TypeError(('The list should only contain '
'SingleEquation objects, not %s') % type(eq))
if eq.varname in self._equations:
raise EquationError('Duplicate definition of variable "%s"' %
eq.varname)
self._equations[eq.varname] = eq
# save these to change the keys of the dictionary later
model_var_replacements = []
for varname, replacement in kwds.iteritems():
for eq in self.itervalues():
# Replacing the name of a model variable (works only for strings)
if eq.varname == varname:
if not isinstance(replacement, basestring):
raise ValueError(('Cannot replace model variable "%s" '
'with a value') % varname)
if replacement in self:
raise EquationError(('Cannot replace model variable "%s" '
'with "%s", duplicate definition '
'of "%s".' % (varname, replacement,
replacement)))
# make sure that the replacement is a valid identifier
Equations.check_identifier(replacement)
eq.varname = replacement
model_var_replacements.append((varname, replacement))
if varname in eq.identifiers:
if isinstance(replacement, basestring):
# replace the name with another name
new_code = re.sub('\\b' + varname + '\\b',
replacement, eq.expr.code)
else:
# replace the name with a value
new_code = re.sub('\\b' + varname + '\\b',
'(' + repr(replacement) + ')',
eq.expr.code)
try:
eq.expr = Expression(new_code)
except ValueError as ex:
raise ValueError(('Replacing "%s" with "%r" failed: %s') %
(varname, replacement, ex))
# For change in model variable names, we have already changed the
# varname attribute of the SingleEquation object, but not the key of
# our dicitionary
for varname, replacement in model_var_replacements:
self._equations[replacement] = self._equations.pop(varname)
# Check for special symbol xi (stochastic term)
uses_xi = None
for eq in self._equations.itervalues():
if not eq.expr is None and 'xi' in eq.expr.identifiers:
if not eq.type == DIFFERENTIAL_EQUATION:
raise EquationError(('The equation defining %s contains the '
'symbol "xi" but is not a differential '
'equation.') % eq.varname)
elif not uses_xi is None:
raise EquationError(('The equation defining %s contains the '
'symbol "xi", but it is already used '
'in the equation defining %s.') %
(eq.varname, uses_xi))
else:
uses_xi = eq.varname
# rearrange subexpressions
self._sort_subexpressions()
def __iter__(self):
return iter(self._equations)
def __len__(self):
return len(self._equations)
def __getitem__(self, key):
return self._equations[key]
def __add__(self, other_eqns):
if isinstance(other_eqns, basestring):
other_eqns = parse_string_equations(other_eqns)
elif not isinstance(other_eqns, Equations):
return NotImplemented
return Equations(self.values() + other_eqns.values())
#: A set of functions that are used to check identifiers (class attribute).
#: Functions can be registered with the static method
#: `Equations.register_identifier_check` and will be automatically
#: used when checking identifiers
identifier_checks = {check_identifier_basic, check_identifier_reserved,
check_identifier_functions, check_identifier_units}
@staticmethod
[docs] def register_identifier_check(func):
'''
Register a function for checking identifiers.
Parameters
----------
func : callable
The function has to receive a single argument, the name of the
identifier to check, and raise a ValueError if the identifier
violates any rule.
'''
if not hasattr(func, '__call__'):
raise ValueError('Can only register callables.')
Equations.identifier_checks.add(func)
@staticmethod
[docs] def check_identifier(identifier):
'''
Perform all the registered checks. Checks can be registered via
`Equations.register_identifier_check`.
Parameters
----------
identifier : str
The identifier that should be checked
Raises
------
ValueError
If any of the registered checks fails.
'''
for check_func in Equations.identifier_checks:
check_func(identifier)
[docs] def check_identifiers(self):
'''
Check all identifiers for conformity with the rules.
Raises
------
ValueError
If an identifier does not conform to the rules.
See also
--------
Equations.check_identifier : The function that is called for each identifier.
'''
for name in self.names:
Equations.check_identifier(name)
[docs] def get_substituted_expressions(self, variables=None,
include_subexpressions=False):
'''
Return a list of ``(varname, expr)`` tuples, containing all
differential equations (and optionally subexpressions) with all the
subexpression variables substituted with the respective expressions.
Parameters
----------
variables : dict, optional
A mapping of variable names to `Variable`/`Function` objects.
include_subexpressions : bool
Whether also to return substituted subexpressions. Defaults to
``False``.
Returns
-------
expr_tuples : list of (str, `CodeString`)
A list of ``(varname, expr)`` tuples, where ``expr`` is a
`CodeString` object with all subexpression variables substituted
with the respective expression.
'''
subst_exprs = []
substitutions = {}
for eq in self.ordered:
# Skip parameters
if eq.expr is None:
continue
new_sympy_expr = str_to_sympy(eq.expr.code, variables).xreplace(substitutions)
new_str_expr = sympy_to_str(new_sympy_expr)
expr = Expression(new_str_expr)
if eq.type == SUBEXPRESSION:
substitutions.update({sympy.Symbol(eq.varname, real=True): str_to_sympy(expr.code, variables)})
if include_subexpressions:
subst_exprs.append((eq.varname, expr))
elif eq.type == DIFFERENTIAL_EQUATION:
# a differential equation that we have to check
subst_exprs.append((eq.varname, expr))
else:
raise AssertionError('Unknown equation type %s' % eq.type)
return subst_exprs
def _get_stochastic_type(self):
'''
Returns the type of stochastic differential equations (additivive or
multiplicative). The system is only classified as ``additive`` if *all*
equations have only additive noise (or no noise).
Returns
-------
type : str
Either ``None`` (no noise variables), ``'additive'`` (factors for
all noise variables are independent of other state variables or
time), ``'multiplicative'`` (at least one of the noise factors
depends on other state variables and/or time).
'''
# TODO: Add debug output
if not self.is_stochastic:
return None
for _, expr in self.get_substituted_expressions():
_, stochastic = expr.split_stochastic()
if stochastic is not None:
for factor in stochastic.itervalues():
if 't' in factor.identifiers:
# noise factor depends on time
return 'multiplicative'
for identifier in factor.identifiers:
if identifier in self.diff_eq_names:
# factor depends on another state variable
return 'multiplicative'
return 'additive'
############################################################################
# Properties
############################################################################
# Lists of equations or (variable, expression tuples)
ordered = property(lambda self: sorted(self._equations.itervalues(),
key=lambda key: key.update_order),
doc='A list of all equations, sorted '
'according to the order in which they should '
'be updated')
diff_eq_expressions = property(lambda self: [(varname, eq.expr) for
varname, eq in self.iteritems()
if eq.type == DIFFERENTIAL_EQUATION],
doc='A list of (variable name, expression) '
'tuples of all differential equations.')
eq_expressions = property(lambda self: [(varname, eq.expr) for
varname, eq in self.iteritems()
if eq.type in (SUBEXPRESSION,
DIFFERENTIAL_EQUATION)],
doc='A list of (variable name, expression) '
'tuples of all equations.')
# Sets of names
names = property(lambda self: set([eq.varname for eq in self.ordered]),
doc='All variable names defined in the equations.')
diff_eq_names = property(lambda self: set([eq.varname for eq in self.ordered
if eq.type == DIFFERENTIAL_EQUATION]),
doc='All differential equation names.')
subexpr_names = property(lambda self: set([eq.varname for eq in self.ordered
if eq.type == SUBEXPRESSION]),
doc='All subexpression names.')
eq_names = property(lambda self: set([eq.varname for eq in self.ordered
if eq.type in (DIFFERENTIAL_EQUATION,
SUBEXPRESSION)]),
doc='All equation names (including subexpressions).')
parameter_names = property(lambda self: set([eq.varname for eq in self.ordered
if eq.type == PARAMETER]),
doc='All parameter names.')
units = property(lambda self:dict([(var, eq.unit) for var, eq in
self._equations.iteritems()]),
doc='Dictionary of all internal variables and their corresponding units.')
identifiers = property(lambda self: set().union(*[eq.identifiers for
eq in self._equations.itervalues()]) -
self.names,
doc=('Set of all identifiers used in the equations, '
'excluding the variables defined in the equations'))
stochastic_variables = property(lambda self: set([variable for variable in self.identifiers
if variable =='xi' or variable.startswith('xi_')]))
# general properties
is_stochastic = property(lambda self: len(self.stochastic_variables) > 0,
doc='Whether the equations are stochastic.')
stochastic_type = property(fget=_get_stochastic_type)
def _sort_subexpressions(self):
'''
Sorts the subexpressions in a way that resolves their dependencies
upon each other. After this method has been run, the subexpressions
returned by the ``ordered`` property are in the order in which
they should be updated
'''
# Get a dictionary of all the dependencies on other subexpressions,
# i.e. ignore dependencies on parameters and differential equations
static_deps = {}
for eq in self._equations.itervalues():
if eq.type == SUBEXPRESSION:
static_deps[eq.varname] = [dep for dep in eq.identifiers if
dep in self._equations and
self._equations[dep].type == SUBEXPRESSION]
try:
sorted_eqs = topsort(static_deps)
except ValueError:
raise ValueError('Cannot resolve dependencies between static '
'equations, dependencies contain a cycle.')
# put the equations objects in the correct order
for order, static_variable in enumerate(sorted_eqs):
self._equations[static_variable].update_order = order
# Sort differential equations and parameters after subexpressions
for eq in self._equations.itervalues():
if eq.type == DIFFERENTIAL_EQUATION:
eq.update_order = len(sorted_eqs)
elif eq.type == PARAMETER:
eq.update_order = len(sorted_eqs) + 1
[docs] def check_units(self, group, run_namespace):
'''
Check all the units for consistency.
Parameters
----------
group : `Group`
The group providing the context
run_namespace : dict-like, optional
An additional namespace that is used for variable lookup (if not
defined, the implicit namespace of local variables is used).
level : int, optional
How much further to go up in the stack to find the calling frame
Raises
------
DimensionMismatchError
In case of any inconsistencies.
'''
all_variables = dict(group.variables)
external = frozenset().union(*[expr.identifiers
for _, expr in self.eq_expressions])
external -= set(all_variables.keys())
resolved_namespace = group.resolve_all(external, run_namespace,
user_identifiers=external) # all variables are user defined
all_variables.update(resolved_namespace)
for var, eq in self._equations.iteritems():
if eq.type == PARAMETER:
# no need to check units for parameters
continue
if eq.type == DIFFERENTIAL_EQUATION:
try:
check_unit(str(eq.expr), self.units[var] / second,
all_variables)
except DimensionMismatchError as ex:
raise DimensionMismatchError(('Inconsistent units in '
'differential equation '
'defining variable %s:'
'\n%s') % (eq.varname,
ex.desc),
*ex.dims)
elif eq.type == SUBEXPRESSION:
try:
check_unit(str(eq.expr), self.units[var],
all_variables)
except DimensionMismatchError as ex:
raise DimensionMismatchError(('Inconsistent units in '
'subexpression %s:'
'\n%s') % (eq.varname,
ex.desc),
*ex.dims)
else:
raise AssertionError('Unknown equation type: "%s"' % eq.type)
[docs] def check_flags(self, allowed_flags, incompatible_flags=None):
'''
Check the list of flags.
Parameters
----------
allowed_flags : dict
A dictionary mapping equation types (PARAMETER,
DIFFERENTIAL_EQUATION, SUBEXPRESSION) to a list of strings (the
allowed flags for that equation type)
incompatible_flags : list of tuple
A list of flag combinations that are not allowed for the same
equation.
Notes
-----
Not specifying allowed flags for an equation type is the same as
specifying an empty list for it.
Raises
------
ValueError
If any flags are used that are not allowed.
'''
if incompatible_flags is None:
incompatible_flags = []
for eq in self.itervalues():
for flag in eq.flags:
if not eq.type in allowed_flags or len(allowed_flags[eq.type]) == 0:
raise ValueError('Equations of type "%s" cannot have any flags.' % eq.type)
if not flag in allowed_flags[eq.type]:
raise ValueError(('Equations of type "%s" cannot have a '
'flag "%s", only the following flags '
'are allowed: %s') % (eq.type,
flag, allowed_flags[eq.type]))
# Check for incompatibilities
for flag_combinations in incompatible_flags:
if flag in flag_combinations:
remaining_flags = set(flag_combinations) - set([flag])
for remaining_flag in remaining_flags:
if remaining_flag in eq.flags:
raise ValueError("Flag '{}' cannot be "
"combined with flag "
"'{}'".format(flag,
remaining_flag))
############################################################################
# Representation
############################################################################
def __str__(self):
strings = [str(eq) for eq in self.ordered]
return '\n'.join(strings)
def __repr__(self):
return '<Equations object consisting of %d equations>' % len(self._equations)
def _latex(self, *args):
equations = []
t = sympy.Symbol('t')
for eq in self._equations.itervalues():
# do not use SingleEquations._latex here as we want nice alignment
varname = sympy.Symbol(eq.varname)
if eq.type == DIFFERENTIAL_EQUATION:
lhs = r'\frac{\mathrm{d}' + sympy.latex(varname) + r'}{\mathrm{d}t}'
else:
# Normal equation or parameter
lhs = varname
if not eq.type == PARAMETER:
rhs = str_to_sympy(eq.expr.code)
if len(eq.flags):
flag_str = ', flags: ' + ', '.join(eq.flags)
else:
flag_str = ''
if eq.type == PARAMETER:
eq_latex = r'%s &&& \text{(unit: $%s$%s)}' % (sympy.latex(lhs),
sympy.latex(eq.unit),
flag_str)
else:
eq_latex = r'%s &= %s && \text{(unit of $%s$: $%s$%s)}' % (sympy.latex(lhs),
sympy.latex(rhs),
sympy.latex(varname),
sympy.latex(eq.unit),
flag_str)
equations.append(eq_latex)
return r'\begin{align*}' + (r'\\' + '\n').join(equations) + r'\end{align*}'
def _repr_latex_(self):
return sympy.latex(self)
def _repr_pretty_(self, p, cycle):
''' Pretty printing for ipython '''
if cycle:
# Should never happen
raise AssertionError('Cyclical call of Equations._repr_pretty_')
for eq in self._equations.itervalues():
p.pretty(eq)
p.breakable('\n')
[docs]def is_stateful(expression, variables):
'''
Whether the given expression refers to stateful functions (and is therefore
not guaranteed to give the same result if called repetively).
Parameters
----------
expression : `sympy.Expression`
The sympy expression to check.
variables : dict
The dictionary mapping variable names to `Variable` or `Function`
objects.
Returns
-------
stateful : bool
``True``, if the given expression refers to a stateful function like
``rand()`` and ``False`` otherwise.
'''
func_name = str(expression.func)
func_variable = variables.get(func_name, None)
if func_variable is not None and not func_variable.stateless:
return True
for arg in expression.args:
if is_stateful(arg, variables):
return True
return False
[docs]def check_subexpressions(group, equations, run_namespace):
'''
Checks the subexpressions in the equations and raises an error if a
subexpression refers to stateful functions without being marked as
"constant over dt".
Parameters
----------
group : `Group`
The group providing the context.
equations : `Equations`
The equations to check.
run_namespace : dict
The run namespace for resolving variables.
Raises
------
SyntaxError
For subexpressions not marked as "constant over dt" that refer to
stateful functions.
'''
for eq in equations.ordered:
if eq.type == SUBEXPRESSION:
# Check whether the expression is stateful (most commonly by
# referring to rand() or randn()
variables = group.resolve_all(eq.identifiers,
run_namespace,
# we don't need to raise any warnings
# for the user here, warnings will
# be raised in create_runner_codeobj
user_identifiers=set())
expression = str_to_sympy(eq.expr.code, variables=variables)
# Check whether the expression refers to stateful functions
if is_stateful(expression, variables):
raise SyntaxError("The subexpression '{}' refers to a stateful "
"function (e.g. rand()). Such expressions "
"should only be evaluated once per timestep, "
"add the 'constant over dt'"
"flag.".format(eq.varname))