amici.de_model_components

Objects for AMICI’s internal differential equation model representation

Classes

`AlgebraicEquation`(identifier, value)	An AlgebraicEquation defines an algebraic equation.
`AlgebraicState`(identifier, name, init)	An AlgebraicState defines an entity that is algebraically determined
`ConservationLaw`(identifier, name, value, ...)	A conservation law defines the absolute the total amount of a (weighted) sum of states
`Constant`(identifier, name, value)	A Constant is a fixed variable in the model with respect to which sensitivities cannot be computed, abbreviated by `k`.
`DifferentialState`(identifier, name, init, dt)	A State variable defines an entity that evolves with time according to the provided time derivative, abbreviated by `x`.
`Event`(identifier, name, value, state_update)	An Event defines either a SBML event or a root of the argument of a Heaviside function.
`EventObservable`(identifier, name, value, event)	An Event Observable links model simulations to event related experimental measurements, abbreviated by `z`.
`Expression`(identifier, name, value)	An Expression is a recurring elements in symbolic formulas.
`LogLikelihood`(identifier, name, value)	A LogLikelihood defines the distance between measurements and experiments for a particular observable.
`LogLikelihoodRZ`(identifier, name, value)	Loglikelihood for event observables regularization
`LogLikelihoodY`(identifier, name, value)	Loglikelihood for observables
`LogLikelihoodZ`(identifier, name, value)	Loglikelihood for event observables
`ModelQuantity`(identifier, name, value)	Base class for model components
`Observable`(identifier, name, value[, ...])	An Observable links model simulations to experimental measurements, abbreviated by `y`.
`Parameter`(identifier, name, value)	A Parameter is a free variable in the model with respect to which sensitivities may be computed, abbreviated by `p`.
`Sigma`(identifier, name, value)	A Standard Deviation Sigma rescales the distance between simulations and measurements when computing residuals or objective functions, abbreviated by `sigma{y,z}`.
`SigmaY`(identifier, name, value)	Standard deviation for observables
`SigmaZ`(identifier, name, value)	Standard deviation for event observables
`State`(identifier, name, value)	Base class for differential and algebraic model states

class amici.de_model_components.AlgebraicEquation(identifier, value)[source]

An AlgebraicEquation defines an algebraic equation.

__init__(identifier, value)[source]

Create a new AlgebraicEquation instance.

Parameters:: value (sympy.core.expr.Expr) – Formula of the algebraic equation, the solution is given by formula == 0

get_free_symbols()[source]

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.AlgebraicState(identifier, name, init)[source]

An AlgebraicState defines an entity that is algebraically determined

__init__(identifier, name, init)[source]

Create a new AlgebraicState instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the AlgebraicState
name (str) – individual name of the AlgebraicState (does not need to be unique)
init (sympy.core.expr.Expr) – initial value of the AlgebraicState

get_dx_rdata_dx_solver(state_id)

Returns the expression that allows computation of dx_rdata_dx_solver for this state, accounting for conservation laws.

Returns:: dx_rdata_dx_solver expression

get_free_symbols()[source]

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

get_x_rdata()[source]

Returns the expression that allows computation of x_rdata for this state, accounting for conservation laws.

Returns:: x_rdata expression

has_conservation_law()[source]

Checks whether this state has a conservation law assigned.

Returns:: True if assigned, False otherwise

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.ConservationLaw(identifier, name, value, coefficients, state_id)[source]

A conservation law defines the absolute the total amount of a (weighted) sum of states

__init__(identifier, name, value, coefficients, state_id)[source]

Create a new ConservationLaw instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the ConservationLaw
name (str) – individual name of the ConservationLaw (does not need to be unique)
value (sympy.core.expr.Expr) – formula (sum of states)
coefficients (dict[sympy.core.symbol.Symbol, sympy.core.expr.Expr]) – coefficients of the states in the sum
state_id (sympy.core.symbol.Symbol) – identifier of the state that this conservation law replaces

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_ncoeff(state_id)[source]

Computes the normalized coefficient a_i/a_j where i is the index of the provided state_id and j is the index of the state that is replaced by this conservation law. This can be used to compute both dtotal_cl/dx_rdata (=ncoeff) and dx_rdata/dx_solver (=-ncoeff).

Parameters:: state_id – identifier of the state
Return type:: sympy.core.expr.Expr | int | float
Returns:: normalized coefficent of the state

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

get_x_rdata()[source]

Returns the expression that allows computation of x_rdata for the state that this conservation law replaces.

Returns:: x_rdata expression

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.Constant(identifier, name, value)[source]

A Constant is a fixed variable in the model with respect to which sensitivities cannot be computed, abbreviated by k.

__init__(identifier, name, value)[source]

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Constant
name (str) – individual name of the Constant (does not need to be unique)
value (numbers.Number) – numeric value

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.DifferentialState(identifier, name, init, dt)[source]

A State variable defines an entity that evolves with time according to the provided time derivative, abbreviated by x.

Variables:

_conservation_law – algebraic formula that allows computation of this state according to a conservation law
_dt – algebraic formula that defines the temporal derivative of this state

__init__(identifier, name, init, dt)[source]

Create a new State instance. Extends ModelQuantity.__init__() by dt

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the state
name (str) – individual name of the state (does not need to be unique)
init (sympy.core.expr.Expr) – initial value
dt (sympy.core.expr.Expr) – time derivative

get_dt()[source]

Gets the time derivative

Return type:: sympy.core.expr.Expr
Returns:: time derivative

get_dx_rdata_dx_solver(state_id)

Returns the expression that allows computation of dx_rdata_dx_solver for this state, accounting for conservation laws.

Returns:: dx_rdata_dx_solver expression

get_free_symbols()[source]

Gets the set of free symbols in time derivative and initial conditions

Return type:: set[sympy.core.basic.Basic]
Returns:: free symbols

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

get_x_rdata()

Returns the expression that allows computation of x_rdata for this state, accounting for conservation laws.

Returns:: x_rdata expression

has_conservation_law()[source]

Checks whether this state has a conservation law assigned.

Returns:: True if assigned, False otherwise

set_conservation_law(law)[source]

Sets the conservation law of a state.

If a conservation law is set, the respective state will be replaced by an algebraic formula according to the respective conservation law.

Parameters:: law (amici.de_model_components.ConservationLaw) – linear sum of states that if added to this state remain constant over time
Return type:: None

set_dt(dt)[source]

Sets the time derivative

Parameters:: dt (sympy.core.expr.Expr) – time derivative
Return type:: None

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.Event(identifier, name, value, state_update, initial_value=True)[source]

An Event defines either a SBML event or a root of the argument of a Heaviside function. The Heaviside functions will be tracked via the vector h during simulation and are needed to inform the solver about a discontinuity in either the right-hand side or the states themselves, causing a reinitialization of the solver.

__init__(identifier, name, value, state_update, initial_value=True)[source]

Create a new Event instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Event
name (str) – individual name of the Event (does not need to be unique)
value (sympy.core.expr.Expr) – formula for the root / trigger function
state_update (sympy.core.expr.Expr | None) – formula for the bolus function (None for Heaviside functions, zero vector for events without bolus)
initial_value (bool | None) – initial boolean value of the trigger function at t0. If set to False, events may trigger at t==t0, otherwise not.

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_initial_value()[source]

Return the initial value for the root function.

Return type:: bool
Returns:: initial value formula

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_trigger_time()[source]

Get the time at which the event triggers.

Only for events that trigger at a single fixed time-point.

Return type:: sympy.core.numbers.Float

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

triggers_at_fixed_timepoint()[source]

Check whether the event triggers at a (single) fixed time-point.

Return type:: bool

class amici.de_model_components.EventObservable(identifier, name, value, event, measurement_symbol=None, transformation='lin')[source]

An Event Observable links model simulations to event related experimental measurements, abbreviated by z.

Variables:: _event – symbolic event identifier

__init__(identifier, name, value, event, measurement_symbol=None, transformation='lin')[source]

Create a new EventObservable instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – See Observable.__init__().
name (str) – See Observable.__init__().
value (sympy.core.expr.Expr) – See Observable.__init__().
transformation (amici.import_utils.ObservableTransformation | None) – See Observable.__init__().
event (sympy.core.symbol.Symbol) – Symbolic identifier of the corresponding event.

get_event()[source]

Get the symbolic identifier of the corresponding event.

Return type:: sympy.core.symbol.Symbol
Returns:: symbolic identifier

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_measurement_symbol()

Return type:: sympy.core.symbol.Symbol

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_regularization_symbol()

Return type:: sympy.core.symbol.Symbol

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.Expression(identifier, name, value)[source]

An Expression is a recurring elements in symbolic formulas. Specifying this may yield more compact expression which may lead to substantially shorter model compilation times, but may also reduce model simulation time. Abbreviated by w.

__init__(identifier, name, value)[source]

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Expression
name (str) – individual name of the Expression (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.LogLikelihoodRZ(identifier, name, value)[source]

Loglikelihood for event observables regularization

__init__(identifier, name, value)

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the LogLikelihood
name (str) – individual name of the LogLikelihood (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.LogLikelihoodY(identifier, name, value)[source]

Loglikelihood for observables

__init__(identifier, name, value)

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the LogLikelihood
name (str) – individual name of the LogLikelihood (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.LogLikelihoodZ(identifier, name, value)[source]

Loglikelihood for event observables

__init__(identifier, name, value)

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the LogLikelihood
name (str) – individual name of the LogLikelihood (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.ModelQuantity(identifier, name, value)[source]

Base class for model components

__init__(identifier, name, value)[source]

Create a new ModelQuantity instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the quantity
name (str) – individual name of the quantity (does not need to be unique)
value (typing.SupportsFloat | numbers.Number | sympy.core.expr.Expr) – either formula, numeric value or initial value

get_id()[source]

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()[source]

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()[source]

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)[source]

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.Observable(identifier, name, value, measurement_symbol=None, transformation=ObservableTransformation.LIN)[source]

An Observable links model simulations to experimental measurements, abbreviated by y.

Variables:

_measurement_symbol – sympy symbol used in the objective function to represent measurements to this observable
trafo – observable transformation, only applies when evaluating objective function or residuals

__init__(identifier, name, value, measurement_symbol=None, transformation=ObservableTransformation.LIN)[source]

Create a new Observable instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Observable
name (str) – individual name of the Observable (does not need to be unique)
value (sympy.core.expr.Expr) – formula
transformation (None | amici.import_utils.ObservableTransformation) – observable transformation, only applies when evaluating objective function or residuals

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_measurement_symbol()[source]

Return type:: sympy.core.symbol.Symbol

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_regularization_symbol()[source]

Return type:: sympy.core.symbol.Symbol

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.Parameter(identifier, name, value)[source]

A Parameter is a free variable in the model with respect to which sensitivities may be computed, abbreviated by p.

__init__(identifier, name, value)[source]

Create a new Expression instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Parameter
name (str) – individual name of the Parameter (does not need to be unique)
value (numbers.Number) – numeric value

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.SigmaY(identifier, name, value)[source]

Standard deviation for observables

__init__(identifier, name, value)

Create a new Standard Deviation instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Standard Deviation
name (str) – individual name of the Standard Deviation (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.SigmaZ(identifier, name, value)[source]

Standard deviation for event observables

__init__(identifier, name, value)

Create a new Standard Deviation instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the Standard Deviation
name (str) – individual name of the Standard Deviation (does not need to be unique)
value (sympy.core.expr.Expr) – formula

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity

class amici.de_model_components.State(identifier, name, value)[source]

Base class for differential and algebraic model states

__init__(identifier, name, value)

Create a new ModelQuantity instance.

Parameters:

identifier (sympy.core.symbol.Symbol) – unique identifier of the quantity
name (str) – individual name of the quantity (does not need to be unique)
value (typing.SupportsFloat | numbers.Number | sympy.core.expr.Expr) – either formula, numeric value or initial value

get_dx_rdata_dx_solver(state_id)[source]

Returns the expression that allows computation of dx_rdata_dx_solver for this state, accounting for conservation laws.

Returns:: dx_rdata_dx_solver expression

get_id()

ModelQuantity identifier

Return type:: sympy.core.symbol.Symbol
Returns:: identifier of the ModelQuantity

get_name()

ModelQuantity name

Return type:: str
Returns:: name of the ModelQuantity

get_val()

ModelQuantity value

Return type:: sympy.core.expr.Expr
Returns:: value of the ModelQuantity

get_x_rdata()[source]

Returns the expression that allows computation of x_rdata for this state, accounting for conservation laws.

Returns:: x_rdata expression

abstract has_conservation_law()[source]

Checks whether this state has a conservation law assigned.

Returns:: True if assigned, False otherwise

set_val(val)

Set ModelQuantity value

Returns:: value of the ModelQuantity