def get_f_expressions(self, substitute_vars=None):
if self.f_expr is None:
return []
self._substitute(self.f_expr, self.expressions, substitute_vars=substitute_vars)
return_expressions = []
# the derivative expression
dif_eq_code = self.f_expr.get_code(subs=True)
return_expressions.append(Expression(f'_df{self.var_name}_dt', dif_eq_code))
# needed variables
need_vars = tools.get_identifiers(dif_eq_code)
# get the total return expressions
for expr in self.expressions[::-1]:
if expr.var_name in need_vars:
if expr.substituted_code is None:
code = expr.code
else:
code = expr.substituted_code
return_expressions.append(Expression(expr.var_name, code))
need_vars |= tools.get_identifiers(code)
return return_expressions[::-1]
def contain_unknown_symbol(expr, scope):
"""Examine where the given expression ``expr`` has the unknown symbol in ``scope``.
Returns
-------
res : bool
True or False.
"""
ids = tools.get_identifiers(expr)
for id_ in ids:
if '.' in id_:
prefix = id_.split('.')[0].strip()
if prefix not in scope:
return True
if id_ not in scope:
return True
return False
def separate_variables(func_or_code):
"""Separate the expressions in a differential equation for each variable.
For example, take the HH neuron model as an example:
>>> eq_code = '''
>>> def integral(m, h, t, Iext, V):
>>> alpha = 0.1 * (V + 40) / (1 - np.exp(-(V + 40) / 10))
>>> beta = 4.0 * np.exp(-(V + 65) / 18)
>>> dmdt = alpha * (1 - m) - beta * m
>>>
>>> alpha = 0.07 * np.exp(-(V + 65) / 20.)
>>> beta = 1 / (1 + np.exp(-(V + 35) / 10))
>>> dhdt = alpha * (1 - h) - beta * h
>>> return dmdt, dhdt
>>> '''
>>> analyser = DiffEqReader()
>>> analyser.visit(ast.parse(eq_code))
>>> separate_variables(returns=analyser.returns,
>>> variables=analyser.variables,
>>> right_exprs=analyser.rights,
>>> code_lines=analyser.code_lines)
{'dhdt': ['alpha = 0.07 * np.exp(-(V + 65) / 20.0)\n',
'beta = 1 / (1 + np.exp(-(V + 35) / 10))\n',
'dhdt = alpha * (1 - h) - beta * h\n'],
'dmdt': ['alpha = 0.1 * (V + 40) / (1 - np.exp(-(V + 40) / 10))\n',
'beta = 4.0 * np.exp(-(V + 65) / 18)\n',
'dmdt = alpha * (1 - m) - beta * m\n']}
Parameters
----------
func_or_code : callable, str
The callable function or the function code.
Returns
-------
anlysis : dict
The expressions for each return variable.
"""
if callable(func_or_code):
func_or_code = tools.deindent(inspect.getsource(func_or_code))
assert isinstance(func_or_code, str)
analyser = DiffEqReader()
analyser.visit(ast.parse(func_or_code))
returns = analyser.returns
variables = analyser.variables
right_exprs = analyser.rights
code_lines = analyser.code_lines
return_requires = OrderedDict([(r, set(tools.get_identifiers(r))) for r in returns])
code_lines_for_returns = OrderedDict([(r, []) for r in returns])
variables_for_returns = OrderedDict([(r, []) for r in returns])
expressions_for_returns = OrderedDict([(r, []) for r in returns])
length = len(variables)
reverse_ids = list(reversed([i - length for i in range(length)]))
for r in code_lines_for_returns.keys():
for rid in reverse_ids:
dep = []
for v in variables[rid]:
if v in return_requires[r]:
dep.append(v)
if len(dep):
code_lines_for_returns[r].append(code_lines[rid])
variables_for_returns[r].append(variables[rid])
expr = right_exprs[rid]
expressions_for_returns[r].append(expr)
for d in dep:
return_requires[r].remove(d)
return_requires[r].update(tools.get_identifiers(expr))
for r in list(code_lines_for_returns.keys()):
code_lines_for_returns[r] = code_lines_for_returns[r][::-1]
variables_for_returns[r] = variables_for_returns[r][::-1]
expressions_for_returns[r] = expressions_for_returns[r][::-1]
analysis = tools.DictPlus(
code_lines_for_returns=code_lines_for_returns,
variables_for_returns=variables_for_returns,
expressions_for_returns=expressions_for_returns,
)
return analysis
def separate_variables(func_or_code):
"""Separate the expressions in a differential equation for each variable.
For example, take the HH neuron model as an example:
>>> eq_code = '''
>>> def derivative(V, m, h, n, t, C, gNa, ENa, gK, EK, gL, EL, Iext):
>>> alpha = 0.1 * (V + 40) / (1 - bp.math.exp(-(V + 40) / 10))
>>> beta = 4.0 * bp.math.exp(-(V + 65) / 18)
>>> dmdt = alpha * (1 - m) - beta * m
>>>
>>> alpha = 0.07 * bp.math.exp(-(V + 65) / 20.)
>>> beta = 1 / (1 + bp.math.exp(-(V + 35) / 10))
>>> dhdt = alpha * (1 - h) - beta * h
>>>
>>> alpha = 0.01 * (V + 55) / (1 - bp.math.exp(-(V + 55) / 10))
>>> beta = 0.125 * bp.math.exp(-(V + 65) / 80)
>>> dndt = alpha * (1 - n) - beta * n
>>>
>>> I_Na = (gNa * m ** 3.0 * h) * (V - ENa)
>>> I_K = (gK * n ** 4.0) * (V - EK)
>>> I_leak = gL * (V - EL)
>>> dVdt = (- I_Na - I_K - I_leak + Iext) / C
>>>
>>> return dVdt, dmdt, dhdt, dndt
>>> '''
>>> separate_variables(eq_code)
{'code_lines_for_returns': {'dVdt': ['I_Na = gNa * m ** 3.0 * h * (V - ENa)\n',
'I_K = gK * n ** 4.0 * (V - EK)\n',
'I_leak = gL * (V - EL)\n',
'dVdt = (-I_Na - I_K - I_leak + Iext) / C\n'],
'dhdt': ['alpha = 0.07 * bp.math.exp(-(V + 65) / 20.0)\n',
'beta = 1 / (1 + bp.math.exp(-(V + 35) / 10))\n',
'dhdt = alpha * (1 - h) - beta * h\n'],
'dmdt': ['alpha = 0.1 * (V + 40) / (1 - '
'bp.math.exp(-(V + 40) / 10))\n',
'beta = 4.0 * bp.math.exp(-(V + 65) / 18)\n',
'dmdt = alpha * (1 - m) - beta * m\n'],
'dndt': ['alpha = 0.01 * (V + 55) / (1 - '
'bp.math.exp(-(V + 55) / 10))\n',
'beta = 0.125 * bp.math.exp(-(V + 65) / 80)\n',
'dndt = alpha * (1 - n) - beta * n\n']},
'expressions_for_returns': {'dVdt': ['gNa * m ** 3.0 * h * (V - ENa)',
'gK * n ** 4.0 * (V - EK)',
'gL * (V - EL)',
'(-I_Na - I_K - I_leak + Iext) / C'],
'dhdt': ['0.07 * bp.math.exp(-(V + 65) / 20.0)',
'1 / (1 + bp.math.exp(-(V + 35) / 10))',
'alpha * (1 - h) - beta * h'],
'dmdt': ['0.1 * (V + 40) / (1 - '
'bp.math.exp(-(V + 40) / 10))',
'4.0 * bp.math.exp(-(V + 65) / 18)',
'alpha * (1 - m) - beta * m'],
'dndt': ['0.01 * (V + 55) / (1 - '
'bp.math.exp(-(V + 55) / 10))',
'0.125 * bp.math.exp(-(V + 65) / 80)',
'alpha * (1 - n) - beta * n']},
'variables_for_returns': {'dVdt': [['I_Na'], ['I_K'], ['I_leak'], ['dVdt']],
'dhdt': [['alpha'], ['beta'], ['dhdt']],
'dmdt': [['alpha'], ['beta'], ['dmdt']],
'dndt': [['alpha'], ['beta'], ['dndt']]}}
Parameters
----------
func_or_code : callable, str
The callable function or the function code.
Returns
-------
anlysis : dict
The expressions for each return variable.
"""
if callable(func_or_code):
if tools.is_lambda_function(func_or_code):
raise errors.AnalyzerError(
f'Cannot analyze lambda function: {func_or_code}.')
func_or_code = tools.deindent(inspect.getsource(func_or_code))
assert isinstance(func_or_code, str)
analyser = DiffEqReader()
analyser.visit(ast.parse(func_or_code))
returns = analyser.returns
variables = analyser.variables
right_exprs = analyser.rights
code_lines = analyser.code_lines
return_requires = OrderedDict([(r, set(tools.get_identifiers(r)))
for r in returns])
code_lines_for_returns = OrderedDict([(r, []) for r in returns])
variables_for_returns = OrderedDict([(r, []) for r in returns])
expressions_for_returns = OrderedDict([(r, []) for r in returns])
length = len(variables)
reverse_ids = list(reversed([i - length for i in range(length)]))
for r in code_lines_for_returns.keys():
for rid in reverse_ids:
dep = []
for v in variables[rid]:
if v in return_requires[r]:
dep.append(v)
if len(dep):
code_lines_for_returns[r].append(code_lines[rid])
variables_for_returns[r].append(variables[rid])
expr = right_exprs[rid]
expressions_for_returns[r].append(expr)
for d in dep:
return_requires[r].remove(d)
return_requires[r].update(tools.get_identifiers(expr))
for r in list(code_lines_for_returns.keys()):
code_lines_for_returns[r] = code_lines_for_returns[r][::-1]
variables_for_returns[r] = variables_for_returns[r][::-1]
expressions_for_returns[r] = expressions_for_returns[r][::-1]
analysis = tools.DictPlus(
code_lines_for_returns=code_lines_for_returns,
variables_for_returns=variables_for_returns,
expressions_for_returns=expressions_for_returns,
)
return analysis
def identifiers(self):
return tools.get_identifiers(self.code)