Equations class

(Shortest import: from brian2 import Equations)

class brian2.equations.equations.Equations(eqns, **kwds)[source]

Bases: Hashable, Mapping

Container that stores equations from which models can be created.

String equations can be of any of the following forms:

dx/dt = f : unit (flags) (differential equation)
x = f : unit (flags) (equation)
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).

Attributes

`_substituted_expressions`	Cache for equations with the subexpressions substituted
`dependencies`	Calculate the dependencies of all differential equations and subexpressions.
`diff_eq_expressions`	A list of (variable name, expression) tuples of all differential equations.
`diff_eq_names`	All differential equation names.
`dimensions`	Dictionary of all internal variables and their corresponding physical dimensions.
`eq_expressions`	A list of (variable name, expression) tuples of all equations.
`eq_names`	All equation names (including subexpressions).
`identifier_checks`	A set of functions that are used to check identifiers (class attribute).
`identifiers`	Set of all identifiers used in the equations, excluding the variables defined in the equations
`is_stochastic`	Whether the equations are stochastic.
`names`	All variable names defined in the equations.
`ordered`	A list of all equations, sorted according to the order in which they should be updated
`parameter_names`	All parameter names.
`stochastic_type`	Returns the type of stochastic differential equations (additivive or multiplicative).
`stochastic_variables`
`subexpr_names`	All subexpression names.

Methods

`check_flags`(allowed_flags[, incompatible_flags])	Check the list of flags.
`check_identifier`(identifier)	Perform all the registered checks.
`check_identifiers`()	Check all identifiers for conformity with the rules.
`check_units`(group, run_namespace)	Check all the units for consistency.
`get_substituted_expressions`([variables, ...])	Return a list of `(varname, expr)` tuples, containing all differential equations (and optionally subexpressions) with all the subexpression variables substituted with the respective expressions.
`register_identifier_check`(func)	Register a function for checking identifiers.
`substitute`(**kwds)

Details

_substituted_expressions: Cache for equations with the subexpressions substituted

dependencies: Calculate the dependencies of all differential equations and subexpressions.

diff_eq_expressions: A list of (variable name, expression) tuples of all differential equations.

diff_eq_names: All differential equation names.

dimensions: Dictionary of all internal variables and their corresponding physical dimensions.

eq_expressions: A list of (variable name, expression) tuples of all equations.

eq_names: All equation names (including subexpressions).

identifier_checks: 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

identifiers: Set of all identifiers used in the equations, excluding the variables defined in the equations

is_stochastic: Whether the equations are stochastic.

names: All variable names defined in the equations.

ordered: A list of all equations, sorted according to the order in which they should be updated

parameter_names: All parameter names.

stochastic_type

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).

stochastic_variables

subexpr_names: All subexpression names.

check_flags(allowed_flags, incompatible_flags=None)[source]

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.

static check_identifier(identifier)[source]

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.

check_identifiers()[source]

Check all identifiers for conformity with the rules.

Raises

ValueError: If an identifier does not conform to the rules.

Tutorials and examples using this

Example COBAHH
Example IF_curve_Hodgkin_Huxley
Example advanced/COBAHH_approximated
Example advanced/float_32_64_benchmark
Example frompapers/Clopath_et_al_2010_homeostasis
Example frompapers/Clopath_et_al_2010_no_homeostasis
Example frompapers/Destexhe_et_al_1998
Example frompapers/Diehl_Cook_2015
Example frompapers/Diesmann_et_al_1999
Example frompapers/Hindmarsh_Rose_1984
Example frompapers/Jansen_Rit_1995_single_column
Example frompapers/Rossant_et_al_2011bis