Struct RandomProjectionFrameSketch 

pub struct RandomProjectionFrameSketch { /* private fields */ }

A concrete AtomFrameSketch built from raw decoder column blocks B_k.

For each atom it orthonormalizes the decoder columns (modified Gram–Schmidt) to obtain a frame U_k with orthonormal columns spanning the decoder range, then sketches via a single shared seeded Gaussian random projection R ∈ ℝ^{s×p} applied to the in-range component of a direction:

• atom_sketch(k) = normalize( R · u_k0 ), the sketch of the atom’s first (dominant) frame column — a stable representative point used to bucket the atom.
• project_direction(k, d) = R · (U_k U_kᵀ d), the sketch of the part of d that lies in the atom’s range.
• alignment(k, d) = ‖U_kᵀ d‖ / ‖d‖, the exact in-range energy fraction.

The shared R is a Johnson–Lindenstrauss style random projection, so sketch inner products approximately preserve angles between in-range directions — exactly what the LSH index needs. Everything is seeded; the same atoms + seed always produce the same sketches.

Implementations

impl RandomProjectionFrameSketch

pub fn from_decoder_blocks( decoder_blocks: &[Array2<f64>], sketch_dim: usize, seed: u64, ) -> Result<Self, String>

Build the sketch from decoder column blocks.

decoder_blocks[k] is B_k with shape (p, m_k): p rows in output space, m_k decoder columns for atom k. (SaeManifoldAtom stores the transpose (m_k, p); orient it p-rows before passing in.) All blocks must share the same p. sketch_dim is the target sketch length s; seed makes the projection deterministic.

Trait Implementations

impl AtomFrameSketch for RandomProjectionFrameSketch

fn query_sketch(&self, direction: ArrayView1<'_, f64>) -> Array1<f64>

Exact O(p·s) probe (#994): every atom shares the one projection R, and the table representatives are normalize(R · u_k0), so the correct cosine-LSH probe for a direction is simply normalize(R · d) — no atom is touched, and no masked-average approximation is involved.

fn sketch_dim(&self) -> usize

Dimension of the sketch vectors this implementor produces. Must be the same positive value for every atom in one dictionary so the index can build a single hyperplane bank.

fn output_dim(&self) -> usize

Dimension of the ambient output space the query directions live in.

fn num_atoms(&self) -> usize

Number of atoms this source can sketch.

fn atom_sketch(&self, atom_id: usize) -> Array1<f64>

Sketch of atom atom_id’s frame itself (a representative point of the atom’s column-space on the sphere of sketch space), used to place the atom into the LSH tables at build time. Returns a vector of length AtomFrameSketch::sketch_dim.

fn project_direction( &self, atom_id: usize, direction: ArrayView1<'_, f64>, ) -> Array1<f64>

Sketch of a query direction d (length AtomFrameSketch::output_dim) as seen through atom atom_id’s frame: the direction’s component inside the atom’s column-space, mapped into sketch coordinates. Used at query time to score how strongly a row residual aligns with the atom.

fn alignment(&self, atom_id: usize, direction: ArrayView1<'_, f64>) -> f64

Alignment score in [0, 1]: the fraction of the query direction’s energy that lies inside atom atom_id’s column-space. 1.0 means the direction lies fully in the atom’s range, 0.0 means it is orthogonal. Used to rank the (small) candidate set the index returns.