def test_constants_sympy():
'''
Make sure that symbolic constants are understood correctly by sympy
'''
assert sympy_to_str(str_to_sympy('1.0/inf')) == '0'
assert sympy_to_str(str_to_sympy('sin(pi)')) == '0'
assert sympy_to_str(str_to_sympy('log(e)')) == '1'
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.
'''
if self._substituted_expressions is None:
self._substituted_expressions = []
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:
if eq.var_type == INTEGER:
sympy_var = sympy.Symbol(eq.varname, integer=True)
else:
sympy_var = sympy.Symbol(eq.varname, real=True)
substitutions.update(
{sympy_var: str_to_sympy(expr.code, variables)})
self._substituted_expressions.append((eq.varname, expr))
elif eq.type == DIFFERENTIAL_EQUATION:
# a differential equation that we have to check
self._substituted_expressions.append((eq.varname, expr))
else:
raise AssertionError('Unknown equation type %s' % eq.type)
if include_subexpressions:
return self._substituted_expressions
else:
return [(name, expr)
for name, expr in self._substituted_expressions
if self[name].type == DIFFERENTIAL_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 __init__(self, code=None, sympy_expression=None):
if code is None and sympy_expression is None:
raise TypeError('Have to provide either a string or a sympy expression')
if code is not None and sympy_expression is not None:
raise TypeError('Provide a string expression or a sympy expression, not both')
if code is None:
code = sympy_to_str(sympy_expression)
else:
# Just try to convert it to a sympy expression to get syntax errors
# for incorrect expressions
str_to_sympy(code)
super(Expression, self).__init__(code=code)
def _latex(self, *args):
equations = []
t = sympy.Symbol('t')
for eq in self._equations.values():
# 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(get_unit(eq.dim)), 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(get_unit(eq.dim)), flag_str)
equations.append(eq_latex)
return r'\begin{align*}' + (r'\\' +
'\n').join(equations) + r'\end{align*}'
def _repr_pretty_(self, p, cycle):
'''
Pretty printing for ipython.
'''
if cycle:
raise AssertionError('Cyclical call of CodeString._repr_pretty')
# Make use of sympy's pretty printing
p.pretty(str_to_sympy(self.code))
def get_conditionally_linear_system(eqs, variables=None):
'''
Convert equations into a linear system using sympy.
Parameters
----------
eqs : `Equations`
The model equations.
Returns
-------
coefficients : dict of (sympy expression, sympy expression) tuples
For every variable x, a tuple (M, B) containing the coefficients M and
B (as sympy expressions) for M * x + B
Raises
------
ValueError
If one of the equations cannot be converted into a M * x + B form.
Examples
--------
>>> from angela2 import Equations
>>> eqs = Equations("""
... dv/dt = (-v + w**2.0) / tau : 1
... dw/dt = -w / tau : 1
... """)
>>> system = get_conditionally_linear_system(eqs)
>>> print(system['v'])
(-1/tau, w**2.0/tau)
>>> print(system['w'])
(-1/tau, 0)
'''
diff_eqs = eqs.get_substituted_expressions(variables)
coefficients = {}
for name, expr in diff_eqs:
var = sp.Symbol(name, real=True)
s_expr = str_to_sympy(expr.code, variables).expand()
if s_expr.has(var):
# Factor out the variable
s_expr = sp.collect(s_expr,
var, evaluate=False)
if len(s_expr) > 2 or var not in s_expr:
raise ValueError(('The expression "%s", defining the variable %s, '
'could not be separated into linear components') %
(expr, name))
coefficients[name] = (s_expr[var], s_expr.get(1, 0))
else:
coefficients[name] = (0, s_expr)
return coefficients
def replace_func(self, x, t, expr, temp_vars, eq_symbols,
stochastic_variable=None):
'''
Used to replace a single occurance of ``f(x, t)`` or ``g(x, t)``:
`expr` is the non-stochastic (in the case of ``f``) or stochastic
part (``g``) of the expression defining the right-hand-side of the
differential equation describing `var`. It replaces the variable
`var` with the value given as `x` and `t` by the value given for
`t`. Intermediate variables will be replaced with the appropriate
replacements as well.
For example, in the `rk2` integrator, the second step involves the
calculation of ``f(k/2 + x, dt/2 + t)``. If `var` is ``v`` and
`expr` is ``-v / tau``, this will result in ``-(_k_v/2 + v)/tau``.
Note that this deals with only one state variable `var`, given as
an argument to the surrounding `_generate_RHS` function.
'''
try:
s_expr = str_to_sympy(str(expr))
except SympifyError as ex:
raise ValueError('Error parsing the expression "%s": %s' %
(expr, str(ex)))
for var in eq_symbols:
# Generate specific temporary variables for the state variable,
# e.g. '_k_v' for the state variable 'v' and the temporary
# variable 'k'.
if stochastic_variable is None:
temp_var_replacements = dict(((self.symbols[temp_var],
_symbol(temp_var+'_'+var))
for temp_var in temp_vars))
else:
temp_var_replacements = dict(((self.symbols[temp_var],
_symbol(temp_var+'_'+var+'_'+stochastic_variable))
for temp_var in temp_vars))
# In the expression given as 'x', replace 'x' by the variable
# 'var' and all the temporary variables by their
# variable-specific counterparts.
x_replacement = x.subs(self.symbols['__x'], eq_symbols[var])
x_replacement = x_replacement.subs(temp_var_replacements)
# Replace the variable `var` in the expression by the new `x`
# expression
s_expr = s_expr.subs(eq_symbols[var], x_replacement)
# If the expression given for t in the state updater description
# is not just "t" (or rather "__t"), then replace t in the
# equations by it, and replace "__t" by "t" afterwards.
if t != self.symbols['__t']:
s_expr = s_expr.subs(SYMBOLS['t'], t)
s_expr = s_expr.replace(self.symbols['__t'], SYMBOLS['t'])
return s_expr
def get_linear_system(eqs, variables):
'''
Convert equations into a linear system using sympy.
Parameters
----------
eqs : `Equations`
The model equations.
Returns
-------
(diff_eq_names, coefficients, constants) : (list of str, `sympy.Matrix`, `sympy.Matrix`)
A tuple containing the variable names (`diff_eq_names`) corresponding
to the rows of the matrix `coefficients` and the vector `constants`,
representing the system of equations in the form M * X + B
Raises
------
ValueError
If the equations cannot be converted into an M * X + B form.
'''
diff_eqs = eqs.get_substituted_expressions(variables)
diff_eq_names = [name for name, _ in diff_eqs]
symbols = [Symbol(name, real=True) for name in diff_eq_names]
coefficients = sp.zeros(len(diff_eq_names))
constants = sp.zeros(len(diff_eq_names), 1)
for row_idx, (name, expr) in enumerate(diff_eqs):
s_expr = str_to_sympy(expr.code, variables).expand()
current_s_expr = s_expr
for col_idx, symbol in enumerate(symbols):
current_s_expr = current_s_expr.collect(symbol)
constant_wildcard = Wild('c', exclude=[symbol])
factor_wildcard = Wild('c_'+name, exclude=symbols)
one_pattern = factor_wildcard*symbol + constant_wildcard
matches = current_s_expr.match(one_pattern)
if matches is None:
raise UnsupportedEquationsException(('The expression "%s", '
'defining the variable '
'%s, could not be '
'separated into linear '
'components.') %
(expr, name))
coefficients[row_idx, col_idx] = matches[factor_wildcard]
current_s_expr = matches[constant_wildcard]
# The remaining constant should be a true constant
constants[row_idx] = current_s_expr
return (diff_eq_names, coefficients, constants)
def __init__(self, description, stochastic=None, custom_check=None):
self._description = description
self.stochastic = stochastic
self.custom_check = custom_check
try:
parsed = ExplicitStateUpdater.DESCRIPTION.parseString(description,
parseAll=True)
except ParseException as p_exc:
ex = SyntaxError('Parsing failed: ' + str(p_exc.msg))
ex.text = str(p_exc.line)
ex.offset = p_exc.column
ex.lineno = p_exc.lineno
raise ex
self.statements = []
self.symbols = SYMBOLS.copy()
for element in parsed:
expression = str_to_sympy(element.expression)
# Replace all symbols used in state updater expressions by unique
# names that cannot clash with user-defined variables or functions
expression = expression.subs(sympy.Function('f'),
self.symbols['__f'])
expression = expression.subs(sympy.Function('g'),
self.symbols['__g'])
symbols = list(expression.atoms(sympy.Symbol))
unique_symbols = []
for symbol in symbols:
if symbol.name == 'dt':
unique_symbols.append(symbol)
else:
unique_symbols.append(_symbol('__' + symbol.name))
for symbol, unique_symbol in zip(symbols, unique_symbols):
expression = expression.subs(symbol, unique_symbol)
self.symbols.update(dict(((symbol.name, symbol)
for symbol in unique_symbols)))
if element.getName() == 'statement':
self.statements.append(('__'+element.identifier, expression))
elif element.getName() == 'output':
self.output = expression
else:
raise AssertionError('Unknown element name: %s' %
element.getName())
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))
def __call__(self, equations, variables=None, method_options=None):
logger.warn("The 'independent' state updater is deprecated and might be "
"removed in future versions of angela.",
'deprecated_independent', once=True)
method_options = extract_method_options(method_options, {})
if equations.is_stochastic:
raise UnsupportedEquationsException('Cannot solve stochastic '
'equations with this state '
'updater')
if variables is None:
variables = {}
diff_eqs = equations.get_substituted_expressions(variables)
t = Symbol('t', real=True, positive=True)
dt = Symbol('dt', real=True, positive=True)
t0 = Symbol('t0', real=True, positive=True)
code = []
for name, expression in diff_eqs:
rhs = str_to_sympy(expression.code, variables)
# We have to be careful and use the real=True assumption as well,
# otherwise sympy doesn't consider the symbol a match to the content
# of the equation
var = Symbol(name, real=True)
f = sp.Function(name)
rhs = rhs.subs(var, f(t))
derivative = sp.Derivative(f(t), t)
diff_eq = sp.Eq(derivative, rhs)
# TODO: simplify=True sometimes fails with 0.7.4, see:
# https://github.com/sympy/sympy/issues/2666
try:
general_solution = sp.dsolve(diff_eq, f(t), simplify=True)
except RuntimeError:
general_solution = sp.dsolve(diff_eq, f(t), simplify=False)
# Check whether this is an explicit solution
if not getattr(general_solution, 'lhs', None) == f(t):
raise UnsupportedEquationsException('Cannot explicitly solve: '
+ str(diff_eq))
# Solve for C1 (assuming "var" as the initial value and "t0" as time)
if general_solution.has(Symbol('C1')):
if general_solution.has(Symbol('C2')):
raise UnsupportedEquationsException('Too many constants in solution: %s' % str(general_solution))
constant_solution = sp.solve(general_solution, Symbol('C1'))
if len(constant_solution) != 1:
raise UnsupportedEquationsException(("Couldn't solve for the constant "
"C1 in : %s ") % str(general_solution))
constant = constant_solution[0].subs(t, t0).subs(f(t0), var)
solution = general_solution.rhs.subs('C1', constant)
else:
solution = general_solution.rhs.subs(t, t0).subs(f(t0), var)
# Evaluate the expression for one timestep
solution = solution.subs(t, t + dt).subs(t0, t)
# only try symplifying it -- it sometimes raises an error
try:
solution = solution.simplify()
except ValueError:
pass
code.append(name + ' = ' + sympy_to_str(solution))
return '\n'.join(code)
def __call__(self, eqs, variables=None, method_options=None):
'''
Apply a state updater description to model equations.
Parameters
----------
eqs : `Equations`
The equations describing the model
variables: dict-like, optional
The `Variable` objects for the model. Ignored by the explicit
state updater.
method_options : dict, optional
Additional options to the state updater (not used at the moment
for the explicit state updaters).
Examples
--------
>>> from angela2 import *
>>> eqs = Equations('dv/dt = -v / tau : volt')
>>> print(euler(eqs))
_v = -dt*v/tau + v
v = _v
>>> print(rk4(eqs))
__k_1_v = -dt*v/tau
__k_2_v = -dt*(__k_1_v/2 + v)/tau
__k_3_v = -dt*(__k_2_v/2 + v)/tau
__k_4_v = -dt*(__k_3_v + v)/tau
_v = __k_1_v/6 + __k_2_v/3 + __k_3_v/3 + __k_4_v/6 + v
v = _v
'''
method_options = extract_method_options(method_options, {})
# Non-stochastic numerical integrators should work for all equations,
# except for stochastic equations
if eqs.is_stochastic and self.stochastic is None:
raise UnsupportedEquationsException('Cannot integrate '
'stochastic equations with '
'this state updater.')
if self.custom_check:
self.custom_check(eqs, variables)
# The final list of statements
statements = []
stochastic_variables = eqs.stochastic_variables
# The variables for the intermediate results in the state updater
# description, e.g. the variable k in rk2
intermediate_vars = [var for var, expr in self.statements]
# A dictionary mapping all the variables in the equations to their
# sympy representations
eq_variables = dict(((var, _symbol(var)) for var in eqs.eq_names))
# Generate the random numbers for the stochastic variables
for stochastic_variable in stochastic_variables:
statements.append(stochastic_variable + ' = ' + 'dt**.5 * randn()')
substituted_expressions = eqs.get_substituted_expressions(variables)
# Process the intermediate statements in the stateupdater description
for intermediate_var, intermediate_expr in self.statements:
# Split the expression into a non-stochastic and a stochastic part
non_stochastic_expr, stochastic_expr = split_expression(intermediate_expr)
# Execute the statement by appropriately replacing the functions f
# and g and the variable x for every equation in the model.
# We use the model equations where the subexpressions have
# already been substituted into the model equations.
for var, expr in substituted_expressions:
for xi in stochastic_variables:
RHS = self._generate_RHS(eqs, var, eq_variables, intermediate_vars,
expr, non_stochastic_expr,
stochastic_expr, xi)
statements.append(intermediate_var+'_'+var+'_'+xi+' = '+RHS)
if not stochastic_variables: # no stochastic variables
RHS = self._generate_RHS(eqs, var, eq_variables, intermediate_vars,
expr, non_stochastic_expr,
stochastic_expr)
statements.append(intermediate_var+'_'+var+' = '+RHS)
# Process the "return" line of the stateupdater description
non_stochastic_expr, stochastic_expr = split_expression(self.output)
if eqs.is_stochastic and (self.stochastic != 'multiplicative' and
eqs.stochastic_type == 'multiplicative'):
# The equations are marked as having multiplicative noise and the
# current state updater does not support such equations. However,
# it is possible that the equations do not use multiplicative noise
# at all. They could depend on time via a function that is constant
# over a single time step (most likely, a TimedArray). In that case
# we can integrate the equations
dt_value = variables['dt'].get_value()[0] if 'dt' in variables else None
for _, expr in substituted_expressions:
_, stoch = expr.split_stochastic()
if stoch is None:
continue
# There could be more than one stochastic variable (e.g. xi_1, xi_2)
for _, stoch_expr in stoch.items():
sympy_expr = str_to_sympy(stoch_expr.code)
# The equation really has multiplicative noise, if it depends
# on time (and not only via a function that is constant
# over dt), or if it depends on another variable defined
# via differential equations.
if (not is_constant_over_dt(sympy_expr, variables, dt_value)
or len(stoch_expr.identifiers & eqs.diff_eq_names)):
raise UnsupportedEquationsException('Cannot integrate '
'equations with '
'multiplicative noise with '
'this state updater.')
# Assign a value to all the model variables described by differential
# equations
for var, expr in substituted_expressions:
RHS = self._generate_RHS(eqs, var, eq_variables, intermediate_vars,
expr, non_stochastic_expr, stochastic_expr,
stochastic_variables)
statements.append('_' + var + ' = ' + RHS)
# Assign everything to the final variables
for var, expr in substituted_expressions:
statements.append(var + ' = ' + '_' + var)
return '\n'.join(statements)
def make_statements(code, variables, dtype, optimise=True, blockname=''):
'''
make_statements(code, variables, dtype, optimise=True, blockname='')
Turn a series of abstract code statements into Statement objects, inferring
whether each line is a set/declare operation, whether the variables are
constant or not, and handling the cacheing of subexpressions.
Parameters
----------
code : str
A (multi-line) string of statements.
variables : dict-like
A dictionary of with `Variable` and `Function` objects for every
identifier used in the `code`.
dtype : `dtype`
The data type to use for temporary variables
optimise : bool, optional
Whether to optimise expressions, including
pulling out loop invariant expressions and putting them in new
scalar constants. Defaults to ``False``, since this function is also
used just to in contexts where we are not interested by this kind of
optimisation. For the main code generation stage, its value is set by
the `codegen.loop_invariant_optimisations` preference.
blockname : str, optional
A name for the block (used to name intermediate variables to avoid
name clashes when multiple blocks are used together)
Returns
-------
scalar_statements, vector_statements : (list of `Statement`, list of `Statement`)
Lists with statements that are to be executed once and statements that
are to be executed once for every neuron/synapse/... (or in a vectorised
way)
Notes
-----
If ``optimise`` is ``True``, then the
``scalar_statements`` may include newly introduced scalar constants that
have been identified as loop-invariant and have therefore been pulled out
of the vector statements. The resulting statements will also use augmented
assignments where possible, i.e. a statement such as ``w = w + 1`` will be
replaced by ``w += 1``. Also, statements involving booleans will have
additional information added to them (see `Statement` for details)
describing how the statement can be reformulated as a sequence of if/then
statements. Calls `~angela2.codegen.optimisation.optimise_statements`.
'''
code = strip_empty_lines(deindent(code))
lines = re.split(r'[;\n]', code)
lines = [LineInfo(code=line) for line in lines if len(line)]
# Do a copy so we can add stuff without altering the original dict
variables = dict(variables)
# we will do inference to work out which lines are := and which are =
defined = set(k for k, v in variables.items()
if not isinstance(v, AuxiliaryVariable))
for line in lines:
statement = None
# parse statement into "var op expr"
var, op, expr, comment = parse_statement(line.code)
if var in variables and isinstance(variables[var], Subexpression):
raise SyntaxError("Illegal line '{line}' in abstract code. "
"Cannot write to subexpression "
"'{var}'.".format(line=line.code, var=var))
if op == '=':
if var not in defined:
op = ':='
defined.add(var)
if var not in variables:
annotated_ast = angela_ast(expr, variables)
is_scalar = annotated_ast.scalar
if annotated_ast.dtype == 'boolean':
use_dtype = bool
elif annotated_ast.dtype == 'integer':
use_dtype = int
else:
use_dtype = dtype
new_var = AuxiliaryVariable(var,
dtype=use_dtype,
scalar=is_scalar)
variables[var] = new_var
elif not variables[var].is_boolean:
sympy_expr = str_to_sympy(expr, variables)
if variables[var].is_integer:
sympy_var = sympy.Symbol(var, integer=True)
else:
sympy_var = sympy.Symbol(var, real=True)
try:
collected = sympy.collect(sympy_expr,
sympy_var,
exact=True,
evaluate=False)
except AttributeError:
# If something goes wrong during collection, e.g. collect
# does not work for logical expressions
collected = {1: sympy_expr}
if (len(collected) == 2
and set(collected.keys()) == {1, sympy_var}
and collected[sympy_var] == 1):
# We can replace this statement by a += assignment
statement = Statement(var,
'+=',
sympy_to_str(collected[1]),
comment,
dtype=variables[var].dtype,
scalar=variables[var].scalar)
elif len(collected) == 1 and sympy_var in collected:
# We can replace this statement by a *= assignment
statement = Statement(var,
'*=',
sympy_to_str(collected[sympy_var]),
comment,
dtype=variables[var].dtype,
scalar=variables[var].scalar)
if statement is None:
statement = Statement(var,
op,
expr,
comment,
dtype=variables[var].dtype,
scalar=variables[var].scalar)
line.statement = statement
# for each line will give the variable being written to
line.write = var
# each line will give a set of variables which are read
line.read = get_identifiers_recursively([expr], variables)
# All writes to scalar variables must happen before writes to vector
# variables
scalar_write_done = False
for line in lines:
stmt = line.statement
if stmt.op != ':=' and variables[
stmt.var].scalar and scalar_write_done:
raise SyntaxError(
('All writes to scalar variables in a code block '
'have to be made before writes to vector '
'variables. Illegal write to %s.') % line.write)
elif not variables[stmt.var].scalar:
scalar_write_done = True
# all variables which are written to at some point in the code block
# used to determine whether they should be const or not
all_write = set(line.write for line in lines)
# backwards compute whether or not variables will be read again
# note that will_read for a line gives the set of variables it will read
# on the current line or subsequent ones. will_write gives the set of
# variables that will be written after the current line
will_read = set()
will_write = set()
for line in lines[::-1]:
will_read = will_read.union(line.read)
line.will_read = will_read.copy()
line.will_write = will_write.copy()
will_write.add(line.write)
subexpressions = dict((name, val) for name, val in variables.items()
if isinstance(val, Subexpression))
# Check that no scalar subexpression refers to a vectorised function
# (e.g. rand()) -- otherwise it would be differently interpreted depending
# on whether it is used in a scalar or a vector context (i.e., even though
# the subexpression is supposed to be scalar, it would be vectorised when
# used as part of non-scalar expressions)
for name, subexpr in subexpressions.items():
if subexpr.scalar:
identifiers = get_identifiers(subexpr.expr)
for identifier in identifiers:
if (identifier in variables and getattr(
variables[identifier], 'auto_vectorise', False)):
raise SyntaxError(('The scalar subexpression {} refers to '
'the implicitly vectorised function {} '
'-- this is not allowed since it leads '
'to different interpretations of this '
'subexpression depending on whether it '
'is used in a scalar or vector '
'context.').format(name, identifier))
# sort subexpressions into an order so that subexpressions that don't depend
# on other subexpressions are first
subexpr_deps = dict(
(name, [dep for dep in subexpr.identifiers if dep in subexpressions])
for name, subexpr in subexpressions.items())
sorted_subexpr_vars = topsort(subexpr_deps)
statements = []
# none are yet defined (or declared)
subdefined = dict((name, None) for name in subexpressions)
for line in lines:
stmt = line.statement
read = line.read
write = line.write
will_read = line.will_read
will_write = line.will_write
# update/define all subexpressions needed by this statement
for var in sorted_subexpr_vars:
if var not in read:
continue
subexpression = subexpressions[var]
# if already defined/declared
if subdefined[var] == 'constant':
continue
elif subdefined[var] == 'variable':
op = '='
constant = False
else:
op = ':='
# check if the referred variables ever change
ids = subexpression.identifiers
constant = all(v not in will_write for v in ids)
subdefined[var] = 'constant' if constant else 'variable'
statement = Statement(var,
op,
subexpression.expr,
comment='',
dtype=variables[var].dtype,
constant=constant,
subexpression=True,
scalar=variables[var].scalar)
statements.append(statement)
var, op, expr, comment = stmt.var, stmt.op, stmt.expr, stmt.comment
# constant only if we are declaring a new variable and we will not
# write to it again
constant = op == ':=' and var not in will_write
statement = Statement(var,
op,
expr,
comment,
dtype=variables[var].dtype,
constant=constant,
scalar=variables[var].scalar)
statements.append(statement)
scalar_statements = [s for s in statements if s.scalar]
vector_statements = [s for s in statements if not s.scalar]
if optimise and prefs.codegen.loop_invariant_optimisations:
scalar_statements, vector_statements = optimise_statements(
scalar_statements,
vector_statements,
variables,
blockname=blockname)
return scalar_statements, vector_statements
def test_automatic_augmented_assignments():
# We test that statements that could be rewritten as augmented assignments
# are correctly rewritten (using sympy to test for symbolic equality)
variables = {
'x': ArrayVariable('x', owner=None, size=10, device=device),
'y': ArrayVariable('y', owner=None, size=10, device=device),
'z': ArrayVariable('y', owner=None, size=10, device=device),
'b': ArrayVariable('b',
owner=None,
size=10,
dtype=np.bool,
device=device),
'clip': DEFAULT_FUNCTIONS['clip'],
'inf': DEFAULT_CONSTANTS['inf']
}
statements = [
# examples that should be rewritten
# Note that using our approach, we will never get -= or /= but always
# the equivalent += or *= statements
('x = x + 1.0', 'x += 1.0'),
('x = 2.0 * x', 'x *= 2.0'),
('x = x - 3.0', 'x += -3.0'),
('x = x/2.0', 'x *= 0.5'),
('x = y + (x + 1.0)', 'x += y + 1.0'),
('x = x + x', 'x *= 2.0'),
('x = x + y + z', 'x += y + z'),
('x = x + y + z', 'x += y + z'),
# examples that should not be rewritten
('x = 1.0/x', 'x = 1.0/x'),
('x = 1.0', 'x = 1.0'),
('x = 2.0*(x + 1.0)', 'x = 2.0*(x + 1.0)'),
('x = clip(x + y, 0.0, inf)', 'x = clip(x + y, 0.0, inf)'),
('b = b or False', 'b = b or False')
]
for orig, rewritten in statements:
scalar, vector = make_statements(orig, variables, np.float32)
try: # we augment the assertion error with the original statement
assert len(
scalar
) == 0, 'Did not expect any scalar statements but got ' + str(
scalar)
assert len(
vector
) == 1, 'Did expect a single statement but got ' + str(vector)
statement = vector[0]
expected_var, expected_op, expected_expr, _ = parse_statement(
rewritten)
assert expected_var == statement.var, 'expected write to variable %s, not to %s' % (
expected_var, statement.var)
assert expected_op == statement.op, 'expected operation %s, not %s' % (
expected_op, statement.op)
# Compare the two expressions using sympy to allow for different order etc.
sympy_expected = str_to_sympy(expected_expr)
sympy_actual = str_to_sympy(statement.expr)
assert sympy_expected == sympy_actual, (
'RHS expressions "%s" and "%s" are not identical' %
(sympy_to_str(sympy_expected), sympy_to_str(sympy_actual)))
except AssertionError as ex:
raise AssertionError(
'Transformation for statement "%s" gave an unexpected result: %s'
% (orig, str(ex)))
def __init__(self, morphology=None, model=None, threshold=None,
refractory=False, reset=None, events=None,
threshold_location=None,
dt=None, clock=None, order=0, Cm=0.9 * uF / cm ** 2, Ri=150 * ohm * cm,
name='spatialneuron*', dtype=None, namespace=None,
method=('exact', 'exponential_euler', 'rk2', 'heun'),
method_options=None):
# #### Prepare and validate equations
if isinstance(model, str):
model = Equations(model)
if not isinstance(model, Equations):
raise TypeError(('model has to be a string or an Equations '
'object, is "%s" instead.') % type(model))
# Insert the threshold mechanism at the specified location
if threshold_location is not None:
if hasattr(threshold_location,
'_indices'): # assuming this is a method
threshold_location = threshold_location._indices()
# for now, only a single compartment allowed
if len(threshold_location) == 1:
threshold_location = threshold_location[0]
else:
raise AttributeError(('Threshold can only be applied on a '
'single location'))
threshold = '(' + threshold + ') and (i == ' + str(threshold_location) + ')'
# Check flags (we have point currents)
model.check_flags({DIFFERENTIAL_EQUATION: ('point current',),
PARAMETER: ('constant', 'shared', 'linked', 'point current'),
SUBEXPRESSION: ('shared', 'point current',
'constant over dt')})
#: The original equations as specified by the user (i.e. before
#: inserting point-currents into the membrane equation, before adding
#: all the internally used variables and constants, etc.).
self.user_equations = model
# Separate subexpressions depending whether they are considered to be
# constant over a time step or not (this would also be done by the
# NeuronGroup initializer later, but this would give incorrect results
# for the linearity check)
model, constant_over_dt = extract_constant_subexpressions(model)
# Extract membrane equation
if 'Im' in model:
if len(model['Im'].flags):
raise TypeError('Cannot specify any flags for the transmembrane '
'current Im.')
membrane_expr = model['Im'].expr # the membrane equation
else:
raise TypeError('The transmembrane current Im must be defined')
model_equations = []
# Insert point currents in the membrane equation
for eq in model.values():
if eq.varname == 'Im':
continue # ignore -- handled separately
if 'point current' in eq.flags:
fail_for_dimension_mismatch(eq.dim, amp,
"Point current " + eq.varname + " should be in amp")
membrane_expr = Expression(
str(membrane_expr.code) + '+' + eq.varname + '/area')
eq = SingleEquation(eq.type, eq.varname, eq.dim, expr=eq.expr,
flags=list(set(eq.flags)-{'point current'}))
model_equations.append(eq)
model_equations.append(SingleEquation(SUBEXPRESSION, 'Im',
dimensions=(amp/meter**2).dim,
expr=membrane_expr))
model_equations.append(SingleEquation(PARAMETER, 'v', volt.dim))
model = Equations(model_equations)
###### Process model equations (Im) to extract total conductance and the remaining current
# Expand expressions in the membrane equation
for var, expr in model.get_substituted_expressions(include_subexpressions=True):
if var == 'Im':
Im_expr = expr
break
else:
raise AssertionError('Model equations did not contain Im!')
# Differentiate Im with respect to v
Im_sympy_exp = str_to_sympy(Im_expr.code)
v_sympy = sp.Symbol('v', real=True)
diffed = sp.diff(Im_sympy_exp, v_sympy)
unevaled_derivatives = diffed.atoms(sp.Derivative)
if len(unevaled_derivatives):
raise TypeError('Cannot take the derivative of "{Im}" with respect '
'to v.'.format(Im=Im_expr.code))
gtot_str = sympy_to_str(sp.simplify(-diffed))
I0_str = sympy_to_str(sp.simplify(Im_sympy_exp - diffed*v_sympy))
if gtot_str == '0':
gtot_str += '*siemens/meter**2'
if I0_str == '0':
I0_str += '*amp/meter**2'
gtot_str = "gtot__private=" + gtot_str + ": siemens/meter**2"
I0_str = "I0__private=" + I0_str + ": amp/meter**2"
model += Equations(gtot_str + "\n" + I0_str)
# Insert morphology (store a copy)
self.morphology = copy.deepcopy(morphology)
# Flatten the morphology
self.flat_morphology = FlatMorphology(morphology)
# Equations for morphology
# TODO: check whether Cm and Ri are already in the equations
# no: should be shared instead of constant
# yes: should be constant (check)
eqs_constants = Equations("""
length : meter (constant)
distance : meter (constant)
area : meter**2 (constant)
volume : meter**3
Ic : amp/meter**2
diameter : meter (constant)
Cm : farad/meter**2 (constant)
Ri : ohm*meter (constant, shared)
r_length_1 : meter (constant)
r_length_2 : meter (constant)
time_constant = Cm/gtot__private : second
space_constant = (2/pi)**(1.0/3.0) * (area/(1/r_length_1 + 1/r_length_2))**(1.0/6.0) /
(2*(Ri*gtot__private)**(1.0/2.0)) : meter
""")
if self.flat_morphology.has_coordinates:
eqs_constants += Equations('''
x : meter (constant)
y : meter (constant)
z : meter (constant)
''')
NeuronGroup.__init__(self, morphology.total_compartments,
model=model + eqs_constants,
method_options=method_options,
threshold=threshold, refractory=refractory,
reset=reset, events=events,
method=method, dt=dt, clock=clock, order=order,
namespace=namespace, dtype=dtype, name=name)
# Parameters and intermediate variables for solving the cable equations
# Note that some of these variables could have meaningful physical
# units (e.g. _v_star is in volt, _I0_all is in amp/meter**2 etc.) but
# since these variables should never be used in user code, we don't
# assign them any units
self.variables.add_arrays(['_ab_star0', '_ab_star1', '_ab_star2',
'_b_plus', '_b_minus',
'_v_star', '_u_plus', '_u_minus',
'_v_previous', '_c',
# The following two are only necessary for
# C code where we cannot deal with scalars
# and arrays interchangeably:
'_I0_all', '_gtot_all'],
size=self.N, read_only=True)
self.Cm = Cm
self.Ri = Ri
# These explict assignments will load the morphology values from disk
# in standalone mode
self.distance_ = self.flat_morphology.distance
self.length_ = self.flat_morphology.length
self.area_ = self.flat_morphology.area
self.diameter_ = self.flat_morphology.diameter
self.r_length_1_ = self.flat_morphology.r_length_1
self.r_length_2_ = self.flat_morphology.r_length_2
if self.flat_morphology.has_coordinates:
self.x_ = self.flat_morphology.x
self.y_ = self.flat_morphology.y
self.z_ = self.flat_morphology.z
# Performs numerical integration step
self.add_attribute('diffusion_state_updater')
self.diffusion_state_updater = SpatialStateUpdater(self, method,
clock=self.clock,
order=order)
# Update v after the gating variables to obtain consistent Ic and Im
self.diffusion_state_updater.order = 1
# Creation of contained_objects that do the work
self.contained_objects.extend([self.diffusion_state_updater])
if len(constant_over_dt):
self.subexpression_updater = SubexpressionUpdater(self,
constant_over_dt)
self.contained_objects.append(self.subexpression_updater)
def split_stochastic(self):
'''
Split the expression into a stochastic and non-stochastic part.
Splits the expression into a tuple of one `Expression` objects f (the
non-stochastic part) and a dictionary mapping stochastic variables
to `Expression` objects. For example, an expression of the form
``f + g * xi_1 + h * xi_2`` would be returned as:
``(f, {'xi_1': g, 'xi_2': h})``
Note that the `Expression` objects for the stochastic parts do not
include the stochastic variable itself.
Returns
-------
(f, d) : (`Expression`, dict)
A tuple of an `Expression` object and a dictionary, the first
expression being the non-stochastic part of the equation and
the dictionary mapping stochastic variables (``xi`` or starting
with ``xi_``) to `Expression` objects. If no stochastic variable
is present in the code string, a tuple ``(self, None)`` will be
returned with the unchanged `Expression` object.
'''
stochastic_variables = []
for identifier in self.identifiers:
if identifier == 'xi' or identifier.startswith('xi_'):
stochastic_variables.append(identifier)
# No stochastic variable
if not len(stochastic_variables):
return (self, None)
stochastic_symbols = [sympy.Symbol(variable, real=True)
for variable in stochastic_variables]
# Note that collect only works properly if the expression is expanded
collected = str_to_sympy(self.code).expand().collect(stochastic_symbols,
evaluate=False)
f_expr = None
stochastic_expressions = {}
for var, s_expr in collected.items():
expr = Expression(sympy_expression=s_expr)
if var == 1:
if any(s_expr.has(s) for s in stochastic_symbols):
raise AssertionError(('Error when separating expression '
'"%s" into stochastic and non-'
'stochastic term: non-stochastic '
'part was determined to be "%s" but '
'contains a stochastic symbol)' % (self.code,
s_expr)))
f_expr = expr
elif var in stochastic_symbols:
stochastic_expressions[str(var)] = expr
else:
raise ValueError(('Expression "%s" cannot be separated into '
'stochastic and non-stochastic '
'term') % self.code)
if f_expr is None:
f_expr = Expression('0.0')
return f_expr, stochastic_expressions