mrpro.operators.ScaledProximableFunctional

class mrpro.operators.ScaledProximableFunctional[source]

Bases: ProximableFunctional

Proximable Functional scaled by a scalar.

__init__(functional: ProximableFunctional, scale: Tensor | float) → None[source]

Initialize a scaled proximable functional.

A scaled functional is a functional that is scaled by a scalar factor \(\alpha\), i.e. \(f(x) = \alpha g(x)\).

Parameters:

• functional (ProximableFunctional) – proximable functional to be scaled

• scale (Tensor | float) – scaling factor, must be real and positive

__call__(*args: Unpack[Tin]) → Tout[source]

Apply the forward operator.

For more information, see forward.

Note

Prefer using operator_instance(*parameters), i.e. using __call__ over using forward.

forward(x: Tensor) → tuple[Tensor][source]

Forward method.

Parameters:

x (Tensor) – input tensor

Returns:

scaled output of the functional

prox(x: Tensor, sigma: Tensor | float = 1.0) → tuple[Tensor][source]

Proximal Mapping.

Parameters:

• x (Tensor) – input tensor

• sigma (Tensor | float, default: 1.0) – scaling factor

Returns:

Proximal mapping applied to the input tensor

prox_convex_conj(x: Tensor, sigma: Tensor | float = 1.0) → tuple[Tensor][source]

Proximal Mapping of the convex conjugate.

Parameters:

• x (Tensor) – input tensor

• sigma (Tensor | float, default: 1.0) – scaling factor

Returns:

Proximal mapping of the convex conjugate applied to the input tensor

__add__(other: Operator[Unpack[Tin], Tout]) → Operator[Unpack[Tin], Tout][source]

__add__(other: Tensor) → Operator[Unpack[Tin], tuple[Unpack[Tin]]]

Operator addition.

Returns lambda x: self(x) + other(x) if other is a operator, lambda x: self(x) + other*x if other is a tensor

__matmul__(other: Operator[Unpack[Tin2], tuple[Unpack[Tin]]]) → Operator[Unpack[Tin2], Tout][source]

Operator composition.

Returns lambda x: self(other(x))

__mul__(other: Tensor | complex) → Operator[Unpack[Tin], Tout][source]

Operator multiplication with tensor.

Returns lambda x: self(x*other)

__or__(other: ProximableFunctional) → ProximableFunctionalSeparableSum[source]

Create a ProximableFunctionalSeparableSum object from two proximable functionals.

Parameters:

other (ProximableFunctional) – second functional to be summed

Returns:

ProximableFunctionalSeparableSum object

__radd__(other: Tensor) → Operator[Unpack[Tin], tuple[Unpack[Tin]]][source]

Operator right addition.

Returns lambda x: other*x + self(x)

__rmul__(scalar: Tensor | complex) → ProximableFunctional[source]

Multiply functional with scalar.