svdlibrs

A Rust port of LAS2 from SVDLIBC

It performs singular value decomposition on a sparse input CscMatrix using the Lanczos algorithm, and returns the decomposition as ndarray components.

SVD Example

SVD using R

```text $ Rscript -e 'options(digits=12);m<-matrix(1:9,nrow=3)^2;print(m);r<-svd(m);print(r);r$u%%diag(r$d)%%t(r$v)'

• This the input matrix: M [,1] [,2] [,3] [1,] 1 16 49 [2,] 4 25 64 [3,] 9 36 81

• The diagonal matrix (singular values): S $d [1] 123.676578742544 6.084527896514 0.287038004183

• The left singular vectors: U $u [,1] [,2] [,3] [1,] -0.415206840886 -0.753443585619 -0.509829424976 [2,] -0.556377565194 -0.233080213641 0.797569820742 [3,] -0.719755016815 0.614814099788 -0.322422608499

• The right singular vectors: V $v [,1] [,2] [,3] [1,] -0.0737286909592 0.632351847728 -0.771164846712 [2,] -0.3756889918995 0.698691000150 0.608842071210 [3,] -0.9238083467338 -0.334607272761 -0.186054055373

• Recreating the original input matrix: r$u %% diag(r$d) %% t(r$v) [,1] [,2] [,3] [1,] 1 16 49 [2,] 4 25 64 [3,] 9 36 81 ```

SVD using svdlibrs

```rust extern crate ndarray; use ndarray::prelude::*; use svdlibrs::{svdLAS2, SvdRec};

let mut coo = nalgebra_sparse::coo::CooMatrix::::new(3, 3); coo.push(0, 0, 1.0); coo.push(0, 1, 16.0); coo.push(0, 2, 49.0); coo.push(1, 0, 4.0); coo.push(1, 1, 25.0); coo.push(1, 2, 64.0); coo.push(2, 0, 9.0); coo.push(2, 1, 36.0); coo.push(2, 2, 81.0);

let csc = nalgebra_sparse::csc::CscMatrix::from(&coo); let svd: SvdRec = svdLAS2( &csc, // SVDLIBC (SMat) Matrix 0, // upper limit of desired number of singular triplets (0 == all) &[-1.0e-30, 1.0e-30], // left,right end of interval containing unwanted eigenvalues 1e-6, // relative accuracy of ritz values acceptable as eigenvalues 3141, // a supplied random seed false, // verbose output ) .unwrap(); println!("svd.d = {}\n", svd.d); println!("U =\n{:#?}\n", svd.ut.t()); println!("S =\n{:#?}\n", svd.s); println!("V =\n{:#?}\n", svd.vt.t());

// Note: svd.ut & svd.vt are returned in transposed form // M = USV* let M = svd.ut.t().dot(&Array2::from_diag(&svd.s)).dot(&svd.vt);

let epsilon = 1.0e-12; assert_eq!(svd.d, 3);

assert!((M[[0, 0]] - 1.0).abs() < epsilon); assert!((M[[0, 1]] - 16.0).abs() < epsilon); assert!((M[[0, 2]] - 49.0).abs() < epsilon); assert!((M[[1, 0]] - 4.0).abs() < epsilon); assert!((M[[1, 1]] - 25.0).abs() < epsilon); assert!((M[[1, 2]] - 64.0).abs() < epsilon); assert!((M[[2, 0]] - 9.0).abs() < epsilon); assert!((M[[2, 1]] - 36.0).abs() < epsilon); assert!((M[[2, 2]] - 81.0).abs() < epsilon);

assert!((svd.s[0] - 123.676578742544).abs() < epsilon); assert!((svd.s[1] - 6.084527896514).abs() < epsilon); assert!((svd.s[2] - 0.287038004183).abs() < epsilon); ```

Output

```text svd.d = 3

U = [[-0.4152068408862081, -0.7534435856189199, -0.5098294249756481], [-0.556377565193878, -0.23308021364108839, 0.7975698207417085], [-0.719755016814907, 0.6148140997884891, -0.3224226084985998]], shape=[3, 3], strides=[1, 3], layout=Ff (0xa), const ndim=2

S = [123.67657874254405, 6.084527896513759, 0.2870380041828973], shape=[3], strides=[1], layout=CFcf (0xf), const ndim=1

V = [[-0.07372869095916511, 0.6323518477280158, -0.7711648467120451], [-0.3756889918994792, 0.6986910001499903, 0.6088420712097343], [-0.9238083467337805, -0.33460727276072516, -0.18605405537270261]], shape=[3, 3], strides=[1, 3], layout=Ff (0xa), const ndim=2 ```