mrpro.operators.AveragingOp

class mrpro.operators.AveragingOp[source]

Bases: LinearOperator

Averaging operator.

This operator averages the input tensor along a specified dimension. The averaging is performed over groups of elements defined by the idx parameter. The output tensor will have the same shape as the input tensor, except for the dim dimension, which will have a size equal to the number of groups specified in idx. For each group, the average of the elements in that group is computed.

For example, this operator can be used to simulate the effect of a sliding window average on a signal model.

__init__(dim: int, idx: Sequence[Sequence[int] | Tensor | slice] | Tensor = (slice(None),), domain_size: int | None = None) → None[source]

Initialize the averaging operator.

Parameters:

• dim (int) – The dimension along which to average.

• idx (Sequence[Sequence[int] | Tensor | slice] | Tensor, default: (slice(None),)) – The indices of the input tensor to average over. Each element of the sequence will result in a separate entry in the dim dimension of the output tensor. The entries can be either a sequence of integers or an integer tensor, a slice object, or a boolean tensor.

• domain_size (int | None, default: None) – The size of the input along dim. It is only used in the adjoint method. If not set, the size will be guessed from the input tensor during the forward pass.

property H: LinearOperator[source]

Adjoint operator.

Obtains the adjoint of an instance of this operator as an AdjointLinearOperator, which itself is a an LinearOperator that can be applied to tensors.

Note: linear_operator.H.H == linear_operator

property gram: LinearOperator[source]

Gram operator.

For a LinearOperator \(A\), the self-adjoint Gram operator is defined as \(A^H A\).

Note

This is the inherited default implementation.

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

Apply the averaging operator to the input tensor.

Parameters:

x (Tensor) – Input tensor to be averaged.

Returns:

Averaged tensor.

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

Apply the adjoint of the averaging operator.

The adjoint operation distributes the values from the input tensor x (which corresponds to the output of the forward pass) back to a tensor matching the original domain size. Each element in the output of the adjoint receives a contribution from x divided by the number of elements in its original averaging group.

Parameters:

x (Tensor) – Input tensor, corresponding to the output of the forward operation.

Returns:

Tensor with values distributed back to the original domain.

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

Apply forward of AveragingOp.

Note

Prefer calling the instance of the AveragingOp operator as operator(x) over directly calling this method. See this PyTorch discussion.

operator_norm(initial_value: Tensor, dim: Sequence[int] | None, max_iterations: int = 20, relative_tolerance: float = 1e-4, absolute_tolerance: float = 1e-5, callback: Callable[[Tensor], None] | None = None) → Tensor[source]

Power iteration for computing the operator norm of the operator.

Parameters:

• initial_value (Tensor) – initial value to start the iteration; must be element of the domain. if the initial value contains a zero-vector for one of the considered problems, the function throws an ValueError.

• dim (Sequence[int] | None) –

  The dimensions of the tensors on which the operator operates. The choice of dim determines how the operator norm is inperpreted. For example, for a matrix-vector multiplication with a batched matrix tensor of shape (batch1, batch2, row, column) and a batched input tensor of shape (batch1, batch2, row):

  • If dim=None, the operator is considered as a block diagonal matrix with batch1*batch2 blocks and the result is a tensor containing a single norm value (shape (1, 1, 1)).

  • If dim=(-1), batch1*batch2 matrices are considered, and for each a separate operator norm is computed.

  • If dim=(-2,-1), batch1 matrices with batch2 blocks are considered, and for each matrix a separate operator norm is computed.

  Thus, the choice of dim determines implicitly determines the domain of the operator.

• max_iterations (int, default: 20) – maximum number of iterations

• relative_tolerance (float, default: 1e-4) – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration.

• absolute_tolerance (float, default: 1e-5) – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration.

• callback (Callable[[Tensor], None] | None, default: None) – user-provided function to be called at each iteration

Returns:

An estimaton of the operator norm. Shape corresponds to the shape of the input tensor initial_value with the dimensions specified in dim reduced to a single value. The pointwise multiplication of initial_value with the result of the operator norm will always be well-defined.

__add__(other: LinearOperator | Tensor | complex) → LinearOperator[source]

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

Operator addition.

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

__and__(other: LinearOperator) → LinearOperatorMatrix[source]

Vertical stacking of two LinearOperators.

A&B is a LinearOperatorMatrix with two rows, with (A&B)(x) == (A(x), B(x)). See mrpro.operators.LinearOperatorMatrix for more information.

__matmul__(other: LinearOperator) → LinearOperator[source]

__matmul__(other: Operator[Unpack[Tin2], tuple[Tensor]] | Operator[Unpack[Tin2], tuple[Tensor, ...]]) → Operator[Unpack[Tin2], tuple[Tensor]]

Operator composition.

Returns lambda x: self(other(x))

__mul__(other: Tensor | complex) → LinearOperator[source]

Operator elementwise left multiplication with tensor/scalar.

Returns lambda x: self(x*other)

__or__(other: LinearOperator) → LinearOperatorMatrix[source]

Horizontal stacking of two LinearOperators.

A|B is a LinearOperatorMatrix with two columns, with (A|B)(x1,x2) == A(x1) + B(x2). See mrpro.operators.LinearOperatorMatrix for more information.

__radd__(other: Tensor | complex) → LinearOperator[source]

Operator addition.

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

__rmul__(other: Tensor | complex) → LinearOperator[source]

Operator elementwise right multiplication with tensor/scalar.

Returns lambda x: other*self(x)