mrpro.operators.PCACompressionOp

class mrpro.operators.PCACompressionOp[source]

Bases: LinearOperator

PCA based compression operator.

__init__(data: Tensor, n_components: int) → None[source]

Construct a PCA based compression operator.

The operator carries out an SVD followed by a threshold of the n_components largest values along the last dimension of a data with shape (*other, joint_dim, compression_dim). A single SVD is carried out for everything along joint_dim. other are batch dimensions.

Consider combining this operator with RearrangeOp to make sure the data is in the correct shape before applying.

Parameters:

• data (Tensor) – Data of shape (*other, joint_dim, compression_dim) to be used to find the principal components.

• n_components (int) – Number of principal components to keep along the compression_dim.

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__(data: Tensor) → tuple[Tensor][source]

Apply PCA-based compression to the input data.

The data is projected onto the principal components determined during the operator’s initialization.

Parameters:

data (Tensor) – Input data to be compressed. Expected shape is (*other, joint_dim, compression_dim).

Returns:

Compressed data, with shape (*other, joint_dim, n_components).

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

Apply the adjoint of PCA-based compression (expansion).

The data, assumed to be in the compressed principal component space, is projected back to the original data space using the hermitian transpose of the compression matrix.

Parameters:

data (Tensor) – Compressed input data. Expected shape is (*other, joint_dim, n_components).

Returns:

Expanded data, with shape (*other, joint_dim, compression_dim).

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

Apply forward of PCACompressionOp.

Note

Prefer calling the instance of the PCACompressionOp 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)