Crate single_svdlib 

Sparse singular value decomposition.

Three solvers over sprs matrices, all returning the same SvdRec:

module	method	use when
irlba	thick-restarted Lanczos bidiagonalization	default. Accurate, memory bounded by the requested rank
randomized	randomized range finder, power iteration or block Krylov	very large inputs where an approximation is acceptable
lanczos	LAS2 from SVDLIBC	deprecated, numerically unreliable — behind the off-by-default las2 feature

Quick start

use single_svdlib::{sprs::TriMatI, SvdMat};

// A 4x3 matrix in triplet form, converted to CSR with u32 indices.
let mut tri = TriMatI::<f64, u32>::new((4, 3));
tri.add_triplet(0, 0, 1.0);
tri.add_triplet(1, 1, 2.0);
tri.add_triplet(2, 2, 3.0);
tri.add_triplet(3, 0, 4.0);
let a: SvdMat<f64> = tri.to_csr::<u64>();

// Two largest singular triplets.
let svd = single_svdlib::svd(&a, 2)?;

assert_eq!(svd.s.len(), 2);
assert_eq!(svd.u.dim(), (4, 2));   // left vectors are columns
assert_eq!(svd.vt.dim(), (2, 3));  // right vectors are rows
assert!(svd.s[0] >= svd.s[1]);

Index widths

SvdMat<T> defaults to u32 column indices with u64 row pointers, which is 12 bytes per non-zero for f64 data against the 16 that usize-everywhere costs (8 against 16 for f32). Name the parameters to widen: SvdMat<f64, u64, u64>.

Orientation

A ≈ u · diag(s) · vt, matching numpy.linalg.svd: u is m × d with left vectors as columns, s is descending, vt is d × n with right vectors as rows. 1.x was inconsistent between solvers on this point.

Re-exports

pub use error::Result;

pub use error::SvdLibError;

pub use matrix::MaskedCsMat;

pub use matrix::SparseMat;

pub use matrix::SparseMatDense;

pub use matrix::SvdMat;

pub use matrix::SvdMatView;

pub use matrix::DEFAULT_SCRATCH_BUDGET;

pub use types::Algorithm;

pub use types::Detail;

pub use types::Diagnostics;

pub use types::SvdFloat;

pub use types::SvdRec;

pub use sprs;

Modules

dense

Dense helpers: tall-skinny QR, and small factorizations on the reduced matrices the Krylov and randomized methods produce.

error

irlba

Thick-restarted Lanczos bidiagonalization.

lanczos

LAS2, from SVDLIBC. Deprecated and numerically unreliable — enable las2 only to keep a 1.x caller compiling while it moves to irlba. Single-vector Lanczos with selective reorthogonalization — a port of LAS2 from Doug Rohde’s SVDLIBC.

matrix

Sparse operands and the traits the solvers consume.

randomized

Randomized SVD: range finding by random projection.

types

Result and scalar types shared by every algorithm in the crate.

Functions

svd

The rank largest singular triplets.

svd_centered

PCA: the rank largest singular triplets of the implicitly mean-centered matrix.

svd_seed

The rank largest singular triplets, reproducibly.