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 alongjoint_dim
.other
are batch dimensions.Consider combining this operator with
RearrangeOp
to make sure the data is in the correct shape before applying.
- property H: LinearOperator[source]
Adjoint operator.
Obtains the adjoint of an instance of this operator as an
AdjointLinearOperator
, which itself is a anLinearOperator
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__(*args: Unpack) Tout [source]
Apply the forward operator.
For more information, see
forward
.
- adjoint(data: Tensor) tuple[Tensor] [source]
Apply the adjoint compression to the data.
- Parameters:
data (
Tensor
) – compressed data of shape(*other, joint_dim, n_components)
- Returns:
expanded data of shape
(*other, joint_dim, compression_dim)
- forward(data: Tensor) tuple[Tensor] [source]
Apply the compression to the data.
- Parameters:
data (
Tensor
) – data to be compressed of shape(*other, joint_dim, compression_dim)
- Returns:
compressed data of shape
(*other, joint_dim, n_components)
- 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 anValueError
.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 withbatch2
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 iterationsrelative_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 indim
reduced to a single value. The pointwise multiplication ofinitial_value
with the result of the operator norm will always be well-defined.
- __add__(other: LinearOperator | Tensor) 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 aLinearOperatorMatrix
with two rows, with(A&B)(x) == (A(x), B(x))
. Seemrpro.operators.LinearOperatorMatrix
for more information.
- __matmul__(other: LinearOperator) LinearOperator [source]
- __matmul__(other: Operator[Unpack, tuple[Tensor]]) Operator[Unpack, 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 aLinearOperatorMatrix
with two columns, with(A|B)(x1,x2) == A(x1)+B(x2)
. Seemrpro.operators.LinearOperatorMatrix
for more information.
- __radd__(other: Tensor) 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)