mrpro.operators.ElementaryProximableFunctional

class mrpro.operators.ElementaryProximableFunctional[source]

Bases: ElementaryFunctional, ProximableFunctional

Elementary proximable functional base class.

Here, an ‘elementary’ functional is a functional that can be written as \(f(x) = \phi ( \mathrm{weight} ( x - \mathrm{target}))\), returning a real value. It does not require another functional for initialization.

A proximable functional is a functional \(f(x)\) that has a prox implementation, i.e. a function that yields \(\mathrm{argmin}_x \sigma f(x) + 1/2 \|x - y\|^2\).

__init__(target: Tensor | None | complex = None, weight: Tensor | complex = 1.0, dim: int | Sequence[int] | None = None, divide_by_n: bool = False, keepdim: bool = False) → None[source]

Initialize a Functional.

We assume that functionals are given in the form \(f(x) = \phi ( \mathrm{weight} ( x - \mathrm{target}))\) for some functional \(\phi\).

Parameters:

• target (Tensor | None | complex, default: None) – target element - often data tensor (see above)

• weight (Tensor | complex, default: 1.0) – weight parameter (see above)

• dim (int | Sequence[int] | None, default: None) – dimension(s) over which functional is reduced. All other dimensions of weight ( x - target) will be treated as batch dimensions.

• divide_by_n (bool, default: False) – if true, the result is scaled by the number of elements of the dimensions index by dim in the tensor weight ( x - target). If true, the functional is thus calculated as the mean, else the sum.

• keepdim (bool, default: False) – if true, the dimension(s) of the input indexed by dim are maintained and collapsed to singletons, else they are removed from the result.

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

Apply the operator by calling the forward method.

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

Apply forward operator.

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

Apply proximal operator.

Yields \(\mathrm{prox}_{\sigma f}(x) = \mathrm{argmin}_{p} \sigma f(p) + 1/2 \|x-p\|_2^2\) given \(x\) and \(\sigma\).

Parameters:

• x (Tensor) – input tensor

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

Returns:

Proximal operator applied to the input tensor

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

Apply proximal operator of convex conjugate of functional.

Yields \(\mathrm{prox}_{\sigma f^*}(x) = \mathrm{argmin}_{p} \sigma f^*(p) + 1/2 \|x-p\|_2^2\), where \(f^*\) denotes the convex conjugate of \(f\), given \(x\) and \(\sigma\).

Parameters:

• x (Tensor) – input tensor

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

Returns:

Proximal operator of the convex conjugate applied to the input tensor

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

__add__(other: Tensor | complex) → 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], tuple[Tensor, ...]]) → 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[Tensor, Tensor][source]

Create a ProximableFunctionalSeparableSum object from two proximable functionals.

Parameters:

other (ProximableFunctional) – second functional to be summed

Returns:

ProximableFunctionalSeparableSum object

__radd__(other: Tensor | complex) → 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.