# Model¶

The central object in Myokit is the Model. In most scenario’s, models are created by parsing a file in mmt syntax. Once parsed, a model can be validated to ensure its integrity. In models with unsound semantics (for example a cyclical reference between variables) the validate() method will raise an IntegrityError.

For models with a limited number of state variables, validation is fast. In these cases, the validate() method is run after parsing as an additional check. For larger models, validation is costly and avoided until a simulation is run or another analysis method is used.

Once created and validated, a model can be asked to compute the solvable order of its equations which can then be used by an exporter to generate runnable simulation or analysis code.

## myokit.Model¶

class myokit.Model(name=None)

Represents an electrophysiological cell model, structured in components.

Components can be added to the model using add_component(). Access to a model’s component is provided through the get() method and components().

Minimal dictionary support is provided: A component named “x” can be obtained from a model m using m["x"]. The number of components in m is given by len(m) and the presence of “x” in m can be tested using if "x" in m:.

Variables stored inside components can be accessed using get() or values(). Values defined through their derivative make up the model state and can be accessed using states(). States have initial values accessible through inits().

A model’s validity can be checked using is_valid(), which returns the latest validation status and validate(), which (re)validates the model. Warnings can be obtained using warnings()

The optional constructor argument name can be used to set a meta property “name”.

Meta-data properties can be accessed via the property meta, for example model.meta['key']= 'value'.

add_component(name)

Adds a component with the given name to this model.

This method resets the model’s validation status.

add_component_allow_renaming(name)

Attempts to add a component with the given name to this model, but uses a different name if this causes any conflicts.

The new component’s name will be modified by appending _1, _2, etc. until the conflict is resolved.

This method can be used when symbolically manipulating a model in situations where the exact names are unimportant.

Returns the newly created component.

add_function(name, arguments, template)

Adds a user function to this model.

binding(binding)

Returns the variable with the binding label binding. If no such variable is found, None is returned.

bindings()

Returns an iterator over all (binding label : variable) mappings in this model.

check_units(mode=1)

Checks the units used in this model. Models can specify units in two ways:

1. By setting a Variable unit. This is done using the in keyword in mmt syntax or through the method myokit.Variable.set_unit(). This specifies the unit the variable’s value should be in.
2. By adding units to the literals in variables’ right hand expressions. This is done using square brackets in mmt syntax (for example 5 [m] / 10 [s]) or by adding a unit when creating a Number object, for example Number(2, myokit.parse_unit('mV').

Per variable, the unit check proceeds in two steps:

1. The unit resulting from the variable’s RHS is evaluated. This may trigger an myokit.IncompatibleUnitExpression if any inompatibilities are found in the expression (see below).
2. The calculated unit is compared with the variable unit. An IncompatibleUnitError will be triggered if the two units don’t match.

Two unit-checking modes are available.

In strict mode (mode=myokit.UNIT_STRICT), all unspecified units in expressions are treated as “dimensionless”. For example, the expression 5 * V where V is in [mV] will be treated as dimensionless times millivolt (or [1] * [mV] in mmt syntax), resulting in the unit [mV]. The expression 5 + V will be interpreted as dimensionless plus millivolt, and will raise an error. In strict mode, functions such as sin and exp will check that their argument is dimensionless (so sin(3 [m]) is never allowed, only e.g. sin(3 [m] / 1 [m])).

In tolerant mode, unspecified units will be treated as whatever makes the expression work. So ? + [mV] wil be interpreted as [mV] + [mV]. In addition, functions that require dimensionless input in strict mode won’t perform this check in tolerant mode.

In both modes, when a reference is encountered, for example when checking the expression 5 * y, the system will look up the variable y’s unit, and will not look at y’s rhs. Consider the following buggy model:

x = 5 [mV] # RHS unit, no variable unit y = 3 [A] + x # RHS unit, no variable unit

When checking the expression y = 3 + x the variable x will be treated as unspecified, because no variable unit is set for x using the in keyword. In strict mode, this will lead to an error when checking x = 5 [mV] because x is dimensionless while 5 [mV] has units [mV]. In tolerant mode, no error will be raised. When tolerantly evaluating y = 3[A] + x it will be assumed that x is also in [A], because no variable unit is given that says otherwise, despite the RHS of x having units mV.

clone()

Returns a deep clone of this model.

code(line_numbers=False)

Returns this model in mmt syntax.

Line numbers can be added by setting line_numbers=True.

component_cycles()

Finds cyclical references between components and returns them. For example, if a.p depends on b.q while b.x depends on a.y, a cycle a > b > a will be returned.

For a faster way to check if there are any interdependent components (without returning the exact cycles found), use has_interdependent_components().

components(sort=False)

Returns an iterator over this model’s component objects.

count_components()

Returns the number of components in this model.

count_equations(const=None, inter=None, state=None, bound=None, deep=False)

Returns the number of equations matching the given criteria. See equations() for an explanation of the arguments.

count_states()

Returns the number of state variables in this model.

count_variables(const=None, inter=None, state=None, bound=None, deep=False)

Returns the number of variables matching the given criteria. See variables() for an explanation of the arguments.

create_unique_names()

Create a globally unique name for each Component and Variable.

Ideally, the global name equals the variable or component’s basic name. If a name is disputed the following strategy will be used:

1. For variables, the parent name will be added as a prefix to all variables claiming the disputed name.
2. If problems persist, a suffix _i will be added, where i is the first integer which doesn’t result in clashing names.
equations(const=None, inter=None, state=None, bound=None, deep=False)

Creates and returns a filtered iterator over the equations of this object’s variables.

The returned values can be filtered using the following arguments:

const=True|False|None

Set to True to return only constants’ equations. False to exclude all constants and any other value to ignore this check.

For a definition of “constant variable” see variables().

inter=True|False|None

Set to True to return only intermediary variables’ equations, False to exclude all intermediary variables and any other value to ignore this check.

For a definition of “intermediary variable” see variables().

state=True|False|None
Set to True to return only state variables’ equations, False to exclude all state variables and any other value to ignore this check.
bound=True|False|None
Set to True to return only bound variables’ equations, False to exclude all bound variables and any other value to ignore this check.
deep=True|False (by default it’s False)
Set to True to include the equations of nested variables meeting all other criteria.
eval_state_derivatives(state=None, inputs=None, precision=64, ignore_errors=False)

Evaluates and returns the values of all state variable derivatives. The values are returned in a list sorted in the same order as the state variables.

If given, the state values given by state will be used as starting point. Here state can be any object accepted as input by :meth:map_to_state().

To set the values of external inputs, a dictionary mapping binding labels to values can be passed in as inputs.

To assist in finding the origins of numerical errors, the equations can be evaluated using 32 bit floating point. To do this, set precision=myokit.SINGLE_PRECISION.

By default, the evaluation routine raises myokit.NumericalError exceptions for invalid operations. To return NaN instead, set ignore_errors=True.

expressions_for(variable)

Returns a tuple (eqs, args) where eqs is a list of Equation objects in solvable order containing the minimal set of equations needed to evaluate the given variable and args is a list of the state variables and bound variables these expressions require as input.

format_state(state=None, state2=None)

Converts the given list of floating point numbers to a string where each line has the format <full_qualified_name> = <float_value>. If no state is given the one returned by state() is used.

An optional second state can be added for display as state2.

format_state_derivatives(state=None, derivatives=None)

Like format_state() but displays the derivatives along with each state’s value.

format_warnings()

Formats all warnings generated during the last call to validate() and returns a string containing the result.

get(name, class_filter=None)

Searches for a component or variable with the given qname and returns it.

To return only objects of a certain class, pass it in as class_filter.

get_function(name, nargs)

Returns the user function with name name and nargs arguments.

has_component(name)

Returns True if this model has a component with the given name.

has_equations(const=None, inter=None, state=None, bound=None, deep=False)

Returns True if there are any equations that can be returned by calling :meth:equations with the same arguments.

has_interdependent_components()

Returns True if this model contains mutually dependent components. That is, if there exists any component A whose variables depend on variables from component B, while variables in component B depend on variables in component A.

To see the variables causing the interdependence, use component_cycles().

has_variable(name)

Returns True if the given name corresponds to a variable in this object. Accepts both single names x and qualified names x.y as input.

This function performs the same search as variable, so in most cases it will be more efficient to call variable() in a try-catch block rather than checking for existence explicitly.

has_variables(const=None, inter=None, state=None, bound=None, deep=False)

Returns True if there are any variables that can be returned by calling :meth:variables with the same arguments.

has_warnings()

Returns True if this model has any warnings.

inits()

Returns an iterator over the Equation objects defining this model’s current state.

is_valid()

Returns True if this model is valid, False if it is invalid and None if the validation status has not been determined with validate().

Valid models may still have one or more warnings.

item_at_text_position(line, char)

Finds the component, variable, or expression at the position (line, char), and returns a tuple (token, object) with a parser token and the found object, or None if nothing is found.

Both line and char should be given as integers. The first line is line 1, while the first character is char 0.

label(label)

Returns the variable with the given label. If no variable is labelled as label it returns None.

labels()

Returns an iterator over all (label : variable) mappings in this model.

load_state(filename)

Sets the model state using data from a file formatted in any style accepted by myokit.parse_state().

map_component_dependencies(omit_states=True, omit_constants=False)

Scans all equations and creates a map of inter-component dependencies.

The result is an ordered dictionary with the following structure:

{
comp1 : [dep1, dep2, dep3, ...],
comp2 : [dep1, dep2, dep3, ...],
...
}


where comp1, comp2, ... are Components and dep1, dep2, ... are the components they depend upon.

Only direct dependencies are listed: If A depends on B and B depends on C then the returned value for A is [B], not [B,C].

By default, dependencies on state variables’ current values are omitted. This behaviour can be changed by setting omit_states to False.

To omit all dependencies on constants, set omit_constants to True.

map_component_io(omit_states=False, omit_derivatives=False, omit_constants=False)

Scans all equations and creates a list of input and output variables for each component.

Input variables are taken to be any foreign variables the component needs to perform its calculations, plus the current values of its own state variables if it needs them.

Output variables are taken to be any values calculated by this component but used outside it. This includes the derivatives of the state variables it calculates.

The output can be customized using the following arguments:

include_states
Determines whether or not state variables (including the component’s own ones) should be present in the input lists.
include_derivatives
Determines if state variable derivatives should appear in the lists of inputs and outputs.
include_constants
Determines if constants should appear in the lists of inputs.

The result is a tuple containing two OrderedDict objects, each of the following structure:

{
comp1: [lhs1, lhs2, ...],
comp2: [lhs1, lhs2, ...],
...
}


The first dict contains the inputs to every component, the second dict contains every components output values. The values in the lists are :class:LhsExpression objects referring to either a variable or its derivative.

map_deep_dependencies(collapse=False, omit_states=True, filter_encompassed=False)

Scans the list of equations stored in this model and creates a map relating each equation’s left hand side to a list of other LhsExpressions it depends on, either directly or through an intermediate variable.

The method map_shallow_dependencies() performs a similar check, but only returns direct dependencies. This method expands the full dependency tree.

The result is an OrderedDict with the following structure:

{
lhs1 : [dep1, dep2, dep3, ...],
...
}


where lhs1 is a LhsExpression and dep1, dep2 and dep3 are the LhsExpression objects it depends upon.

If the system is not solvable: that is, if it contains cyclical references, a myokit.IntegrityError is raised.

If the optional parameter collapse is set to True nested variables will not be listed separatly. Instead, their dependencies will be added to the dependency lists of their parents.

By default, dependencies on state variables’ current values are omitted. This behaviour can be changed by setting omit_states to False.

In case of a dependency such as:

a = f(b)
b = g(c)


The set returned for a will include b and c. So while a here depends on both b and c, b’s sole dependency on c means a can be calculated if just c is known. To filter out the dependency on b, set filter_encompassed to True. Note that this will also filter out all dependencies on constants, since a constant’s dependencies (an empty set) can be said to be included in all other sets.

map_shallow_dependencies(collapse=False, omit_states=True, omit_constants=False)

Scans the list of equations stored in this model and creates a map relating each equation’s left hand side to a list of other LhsExpressions it depends on directly.

In contrast to the method map_deep_dependencies(), that performs a deep search for all nested dependencies, this method only returns direct dependencies. I.E. LhsExpressions named specifically in the equation’s right hand side.

The result is an OrderedDict with the following structure:

{
lhs1 : [dep1, dep2, dep3, ...],
...
}


where lhs1 is a LhsExpression and dep1, dep2 and dep3 are the LhsExpression objects it depends upon.

In special cases, the obtained result can differ from the mathematical concept of a dependency: if x = 0 * y the function will return a dependency of x on y. Similarly, for x = if(cond, a, b) the function will report a dependency of x on cond, a and b.

If the optional parameter collapse is set to True nested variables will not be listed separatly. Instead, their dependencies will be added to the dependency lists of their parents.

By default, dependencies on state variables’ current values are omitted. This behaviour can be changed by setting omit_states to False.

map_to_state(state)

This utility function accepts a number of different input types and returns a list of floats in the same order as the model’s state variables.

The following types of input are meaningfully handled:

• A dictionary mapping state variable names or objects to floats
• A dictionary mapping state variable names or objects to lists. The last value in every list will be used. This allows the dictionary returned by myokit.Simulation.run() to be used directly.
• A formatted string declaring each variable’s value using the syntax component.var_name = 1.234 or simply containing a comma or space delimited list of floats.
• A list of scalars. In this case, the list length will be checked and all values converted to float. No re-ordering takes place.
merge_interdependent_components()

Deprecated alias of resolve_interdependent_components().

name()

Returns the model meta property name, or None if it isn’t set.

prepare_bindings(labels)

Takes a mapping of binding labels to internal references as input and returns a mapping of variables to internal references. All variables appearing in the map will have their right hand side set to zero. All bindings not mapped to any internal reference will be deleted.

The argument mapping should take the form:

labels = {
'binding_label_1' : internal_name_1,
'binding_label_2' : internal_name_2,
...
}


The returned dictionary will have the form:

variables = {
variable_x : internal_name_1,
variable_y : internal_name_2,
...
}


Unsupported bindings (i.e. bindings not appearing in labels) will be ignored.

remove_component(component)

Removes a component from the model.

This will reset the model’s validation status.

reorder_state(order)

Changes the order of this model’s state variables. The argument order must be a list of state variables or their qnames.

This method does not affect the model’s validation status.

reserve_unique_names(*unames)

Reserves one or more names that won’t be used in unique names (unames).

This function can be used to add keywords to a model before exporting. After reserving one or more keywords, use create_unique_names() to reset the model’s unames.

Adding new names does _not_ clear the previously reserved names.

resolve_interdependent_components()

Checks if the model contains components that each depend on the other. If so, variables from these components will be moved to a new component called “remaining” until the issue is resolved.

save_state(filename)

Saves the model state to a file.

set_name(name=None)

Changes the value of the meta-property “name”.

set_state(state)

Changes this model’s state. Accepts any type of input handled by map_to_state().

set_value(qname, value)

Changes a variable’s defining expression to the given number or myokit.Expression.

For state variables, this updates the expression for their derivative. For all other variables, the expression for their value is updated.

This will reset the model’s validation status.

show_evaluation_of(var)

Returns a string representing the evaluation of a single variable.

The variable’s equation and value are displayed, along with the value and formula of any nested variables and the values of all dependencies.

show_expressions_for(var)

Returns a string containing the expressions needed to evaluate the given variable from the state variables.

show_line(var)

Deprecated alias of show_line_of().

show_line_of(var)

Returns a string containing the type of variable var is and the line it was defined on.

solvable_order()

Returns all equations in a solvable order. The resulting output has the following structure:

OrderedDict {
'comp1' : EquationList([eq1, eq2, eq3, ...]),
'comp2' : EquationList([eq1, eq2, eq3, ...]),
...,
'*remaining*' : EquationList([eq1, eq2, eq3])
}


The OrderedDict contains each component’s name as a key and maps it to a list of equations that can be solved for this component, stored in an :class:EquationList object which extends the list type with a number of special iterators.

The order of the components is such that the components with the fewest dependencies are listed first, in an effort to ensure as many equations as possible can be solved on a per-component basis.

The final entry in the OrderedDict is a list of all remaining equations that could not be solved on a per-component basis. For models that contain fully separable components (that is, if the model contains only components that depend on each other non-cyclically) this list will be empty.

solvable_subset(*args)

Returns all equations dependent on one or more LhsExpression objects in a solvable order. The resulting equations are stored in an EquationList.

The returned equations can be used to recalculate the model expressions, given new values for the variables in args.

The input arguments can be given as LhsExpression objects or string names of variables.

state()

Returns the current state of the model as a list of floating point numbers.

states()

Returns an iterator over this model’s state variable objects.

suggest_variable(name)

Returns a tuple (found, suggested, msg).

If the requested variable is found, only the found part of the tuple is set. If not, the second and third argument are set. Here suggested will take the form of a suggested variable with a similar name, while msg will be a suggested error message.

time()

Returns this model’s time variable.

The time variable is identified by it’s binding to the external source “time”. For a valid model, this method always returns a unique variable. If no time variable has been declared None is returned.

time_unit(mode=1)

Returns the units used by this model’s time variable.

If no time unit is set and mode is myokit.UNIT_TOLERANT (default), then None is returned. With mode set to myokit.UNIT_STRICT the returned value in this case is myokit.units.dimensionless.

user_functions()

Returns a dictionary mapping this model’s user function names to their Expression objects.

validate(remove_unused_variables=False)

Attempts to check model validity, raises errors if it isn’t.

Small issues (e.g. unused variables) will generate warnings, which can be retrieved using Model.warnings() or Model.format_warnings(). Any previously set warnings will be erased whenever validate() is run.

If remove_unused_variables is set to True, any unused variables will be removed from this model during validation.

value(qname)

Returns the value of a variable.

var(name)

Searches for the given variable and returns it if found. Accepts both single names x and qualified names x.y as input.

variables(const=None, inter=None, state=None, bound=None, deep=False, sort=False)

Creates and returns a filtered iterator over the contained variables.

The returned values can be filtered using the following arguments:

const=True|False|None

Constants are defined as variables that do not depend on state variables or derivatives. In other words, any variable whose value can be determined before starting an ODE solving routine.

Set to True to return only constants, False to exclude all constants and any other value to ignore this check.

inter=True|False|None

Intermediary variables are those variables that are not constant but are not part of the state. In other words, intermediary variables are the variables that need to be calculated at every step of an ODE solving routine before calculating the ODE derivatives and updating the state.

Set to True to return only intermediary variables, False to exclude all intermediary variables and any other value to ignore this check.

state=True|False|None
Set to True to return only state variables, False to exclude all state variables and any other value to ignore this check.
bound=True|False|None
Set to True to return only variables bound to an external value, False to exclude all bound variables and any other value to forgo this check.
deep=True|False (by default it’s False)
Set to True to return nested variables meeting all other criteria.
sort=True|False (by default it’s False)
Set to True to return the variables in a consistent order. (Note that this does _not_ mean alphabetical sorting of all variables, just that the order is consistent between calls!)
warnings()

Returns a list containing the warnings generated in this model.

## myokit.ModelPart¶

class myokit.ModelPart(parent, name)

Base class for model parts.

code()

Returns this object in mmt syntax.

has_ancestor(obj)

Returns True if the given object obj is an ancestor of this ModelPart.

is_ancestor(obj)

Returns True if this object is an ancestor of the given ModelPart object.

model()

Returns the model this object belongs to (if set).

name()

Returns this object’s name.

parent(kind=None)

Returns this object’s parent.

If the optional variable kind is set, the method will scan until an instance of the requested type is found.

qname(hide=None)

Returns this object’s fully qualified name. That is, an object named y with a parent named x will return the string x.y. If y has a child z its qname will be x.y.z.

If the optional argument hide is set to this object’s parent the parent qualifier will be omitted.

uname()

Returns a globally unique name for this object.

## Name validation¶

myokit.check_name(name)

Tests if the given name is a valid myokit name and raises a myokit.InvalidNameError` if it isn’t.