Gaussian Sketching¶

template<Number T, DataLocation L = Host> class GaussianSketch¶

Gaussian Embedding is a random matrix \( \Gamma \in \mathbb{R}^{n \times s}\) where each entry is i.i.d. random variable from the Gaussian distribution \( \mathcal{N}(0, s^{-1})\). This sketching operator has the strongest theoretical support among all sketching methods, but it requires O(ns) space in memory to be stored and can be applied to a vector in O(ns) operations. It can be applied in both sides of the matrix and can be used on accelerators.

Template Parameters:

T – Data type of the sketching matrix.
L – Location of the data.

Public Functions

GaussianSketch() = default¶: Creates a new sketching operator.

inline GaussianSketch(const GaussianSketchOptions &options)¶

Creates a new sketching operator according to options.

Parameters:: options – [in] sketching parameters

virtual ~GaussianSketch() = default¶: Destructor.

inline void set_params(const GaussianSketchOptions &options)¶

Sets the parameter of the sketching.

Parameters:: options – [in] sketching parameters

inline DCTResultVec operator()(VectorMap<T, L> v)¶

Calculates the random sketch of a vector v.

Parameters:: v – [in] input vector
Returns:: An abstract object representing the sketch

inline DCTResultMat operator()(MatrixMap<T, L> A)¶

Calculates the random sketch of a matrix A. The sketching is applied to each column of the matrix.

Parameters:: A – [in] input matrix
Returns:: An abstract object representing the sketch

struct GaussianSketchOptions¶

Options for the GaussianSketch.

Public Members

index_t input_size¶: The number of rows of the input.

index_t sketch_size¶: Sketch size.

uint128_t seed = random::DefaultGenerator::default_seed¶: Random seed for the random number generator.

uint128_t stream = random::DefaultGenerator::default_stream¶: Random stream for the random number generator.

OpSide side = kLeft ¶: Specify which side to apply the sketching operator.