boundlab.linearop

Linear Operator Library for Expression Backpropagation.

This module defines linear operators used by BoundLab expressions during symbolic transformation and backward bound propagation.

Key operators:

• ComposedOp: Functional composition of linear maps (\(A \circ B\)), used to chain transformations efficiently.

• SumOp: Pointwise sum of linear maps, used when multiple affine contributions target the same expression.

• EinsumOp: General tensor-linear map based on Einstein summation; this is the most flexible primitive for dense affine transformations.

The module also exposes shape/indexing operators (reshape, permute, gather, scatter, slicing, padding) that are all represented as LinearOp instances and can therefore be composed, summed, and propagated uniformly.

Examples

Apply a shape operator to a concrete tensor:

>>> import torch
>>> from boundlab.linearop import ReshapeOp
>>> op = ReshapeOp(torch.Size([2, 3]), (3, 2))
>>> y = op.forward(torch.arange(6.0).reshape(2, 3))
>>> y.shape
torch.Size([3, 2])

Functions

narrow_indices	Create slice indices equivalent to tensor.narrow(dim, start, length).
select_indices	Create slice indices equivalent to tensor.select(dim, index).
pad_indices	Create slice indices for embedding input into a padded output.
pad_output_shape	Compute output shape after padding.

Classes

LinearOp	A base class for linear operators that can be applied to boundlab expressions.
ComposedOp	Composition of two LinearOps: (outer ∘ inner)(x) = outer(inner(x)).
SumOp	Sum of two LinearOps: (a + b)(x) = a(x) + b(x).
ScalarOp	A LinearOp that scales its input by a scalar factor.
ZeroOp	A LinearOp that always returns zero, regardless of input.
EinsumOp	A linear operator defined by an Einstein summation with a fixed tensor.
ReshapeOp	Reshape (view) the input tensor to target_shape.
FlattenOp	Flatten dimensions [start_dim .
UnflattenOp	Unflatten dimension dim into sizes.
PermuteOp	Permute dimensions of the input tensor.
TransposeOp	Swap two dimensions of the input tensor — special case of PermuteOp.
SqueezeOp	Remove size-1 dimension(s).
UnsqueezeOp	Insert a size-1 dimension at dim.
ExpandOp	Broadcast-expand dimensions (adjoint sums over expanded dims).
RepeatOp	Tile-repeat the tensor (adjoint folds and sums repeated blocks).
TileOp	Alias for repeat with dimension-padding handled like torch.tile.
FlipOp	Reverse elements along dims (self-adjoint).
RollOp	Circular-shift elements (adjoint is the inverse shift).
DiagOp	Extract or create a diagonal (1D↔2D).
GatherOp	A LinearOp that implements torch.gather along a specified dimension.
ScatterOp	A LinearOp that implements torch.scatter along a specified dimension.
GetIndicesOp	Advanced indexing with a tuple of index tensors.
SetIndicesOp	Scatter values to advanced index positions in a zero-initialized tensor.
GetSliceOp	Basic slicing via x[indices] where indices contains int/slice/None/Ellipsis.
SetSliceOp	Embed input into zeros at specified slice positions.
NarrowOp	Select a contiguous slice along dim.
SelectOp	Select a single index along dim, removing that dimension.
GetItemOp	Indexing / slicing via x[indices].
PadOp	Zero-pad an input tensor.