cashocs.MinMaxFunctional

class cashocs.MinMaxFunctional(integrand: ufl_legacy.Form, lower_bound: float | int | None = None, upper_bound: float | int | None = None, mu: float | int = 1.0, lambd: float | int = 0.0)

Bases: Functional

Cost functional involving a maximum of 0 and a integral term squared.

Initializes self.

Methods Summary

coefficients()	Computes the ufl coefficients which are used in the functional.
derivative(argument, direction)	Computes the derivative of the functional w.r.t.
evaluate()	Evaluates the functional.
scale(scaling_factor)	Scales the functional by a scalar.
update()	Updates the functional after solving the state equation.

Methods Documentation

Parameters:

• integrand (ufl.Form)

• lower_bound (float | int | None)

• upper_bound (float | int | None)

• mu (float | int)

• lambd (float | int)

coefficients() → tuple[fenics.Function]

Computes the ufl coefficients which are used in the functional.

Returns:

The set of used coefficients.

Return type:

tuple[fenics.Function]

derivative(argument: ufl_legacy.core.expr.Expr, direction: ufl_legacy.core.expr.Expr) → ufl_legacy.Form

Computes the derivative of the functional w.r.t. argument towards direction.

Parameters:

• argument (ufl_legacy.core.expr.Expr) – The argument, w.r.t. which the functional is differentiated

• direction (ufl_legacy.core.expr.Expr) – The direction into which the derivative is computed

Returns:

A form of the resulting derivative

Return type:

ufl_legacy.Form

evaluate() → float

Evaluates the functional.

Returns:

The current value of the functional.

Return type:

float

scale(scaling_factor: float | int) → None

Scales the functional by a scalar.

Parameters:

scaling_factor (float | int) – The scaling factor used to scale the functional

Return type:

None

update() → None

Updates the functional after solving the state equation.

Return type:

None