blas-array2

Parameter-optional BLAS wrapper by ndarray::Array (Ix1 or Ix2) in rust.

And now the wind blows against my stride (leading dimension)

And I'm losing ground to enmies on all sides ('L' / 'R')

--- Dark Sun..., OP2 of PERSONA5 the Animation

Additional documents:

• Document for develop (link for github, link for docs.rs)
• List of BLAS wrapper structs (link for github, link for docs.rs)
• Efficiency demonstration (link for github, link for docs.rs)

After v0.2, this crate have implemented most planned functionalities. This crate is considered to be almost finished, and may not be actively maintained or updated. However, we also welcome issues and PRs to further increase new features or bug fixes.

Example of simple case

For simple illustration to this package, we perform $\mathbf{C} = \mathbf{A} \mathbf{B}$ (dgemm):

use blas_array2::prelude::*;
use ndarray::prelude::*;
let a = array![[1.0, 2.0, 3.0], [3.0, 4.0, 5.0]];
let b = array![[-1.0, -2.0], [-3.0, -4.0], [-5.0, -6.0]];
let c_out = DGEMM::default()
    .a(a.view())
    .b(b.view())
    .run().unwrap()
    .into_owned();
println!("{:7.3?}", c_out);

Important points are

• using ::default() to initialize struct;
• .a, .b are setter functions;
• .run().unwrap() will perform computation;
• .into_owned() will return result matrix as Array2<f64>.

Functionality

Core Functionality

• BLAS2/BLAS3 Functionality: All (legacy) BLAS2/BLAS3 functions have been implemented.
• Optional Parameters: Convention similar to BLAST Fortran 95 binding or scipy.linalg.blas. Shape of matrix, and information of leading dimension will be checked and parsed properly, so users do not need to give these values.
• Row-major Layout: Row-major support to Fortran 77 API (CBLAS functionality without CBLAS functions). You can safely use the default libopenblas.so shipped by debian with blas-sys, where CBLAS is not automatically integrated, for example.
• Generics: For example, GEMM<F> where F: GEMMNum for f32, f64, Complex<f32>, Complex<f64> types, in one generic (template) class. The same to SYRK or GEMV, etc. Original names such as DGEMM, ZSYR2K are also available.
• Avoid explicit copy if possible: All input in row-major (or col-major) should not involve unnecessary transpositions with explicit copy. Further more, for some BLAS3 functions (GEMM, SYRK, TRMM, TRSM), if transposition does not involve BLASConjTrans, then mixed row-major or col-major also does not involve explicit transposition. Also note that in many cases, sub-matrices (sliced matrix) are also considered as row-major (or col-major), if data is stored contiguously in any dimension.

Other Functionality

• Arbitary Layout: Supports any stride that ndarray allows.
• FFI: Currently, this crate uses its custom FFI binding in blas_array2::ffi::blas as BLAS binding, similar to blas-sys. Additionally, this crate plans to (or already) support some BLAS extensions and ILP64 (by cargo features).

Cargo Features

• no_std: Disable crate feature std will be compatible to #![no_std]. However, currently those no_std features will require alloc.
• ilp64: By default, FFI binding is LP64 (32-bit integer). Crate feature ilp64 will enable ILP64 (64-bit integer).
• BLAS Extension: Some crate features will enable extension of BLAS.
  • gemmt: GEMMTR (triangular output matrix multiplication). For OpenBLAS, version 0.3.27 is required (0.3.26 will fail some tests).
• warn_on_copy: If input matrix layout is not consistent, and explicit memory copy / transposition / complex conjugate is required, then a warning message will be printed on stderr.
• error_on_copy: Similar to warn_on_copy, but will directly raise BLASError.

Example of complicated case

For complicated situation, we perform $\mathbf{C} = \mathbf{A} \mathbf{B}^\mathrm{T}$ by SGEMM = GEMM<f32>:

use blas_array2::prelude::*;
use ndarray::prelude::*;

let a = array![[1.0, 2.0, 3.0], [3.0, 4.0, 5.0]];
let b = array![[-1.0, -2.0], [-3.0, -4.0], [-5.0, -6.0]];
let mut c = Array::ones((3, 3).f());

let c_out = GEMM::<f32>::default()
    .a(a.slice(s![.., ..2]))
    .b(b.view())
    .c(c.slice_mut(s![0..3;2, ..]))
    .transb('T')
    .beta(1.5)
    .run()
    .unwrap();
// one can get the result as an owned array
// but the result may not refer to the same memory location as `c`
println!("{:4.3?}", c_out.into_owned());
// this modification on `c` is actually performed in-place
// so if `c` is pre-defined, not calling `into_owned` could be more efficient
println!("{:4.3?}", c);

Important points are

• .c is (optional) output setter, which consumes ArrayViewMut2<f64>; this matrix will be modified in-place;
• .transb, .beta are optional setters; default of transb is 'N', while default of beta is zero, which are the same convention to scipy's implementation to python interface of BLAS. You may change these default values by feeding values into optional setters.
• There are three ways to utilize output:
  • c_out.into_owned() returns output (submatrix if c was sliced when passed into setter) as Array2<f64>. Note that this output does not share the same memory address to mut c.
  • c_out.view() or c_out.view_mut() returns view of c; these views share the same memory address to mut c.
  • Or you may use c directly. DGEMM operation is performed inplace if output matrix c is given.

To make clear of the code above, this code spinnet performs matrix multiplication in-place

c = alpha * a * transpose(b) + beta * c
where
alpha = 1.0 (by default)
beta = 1.5
a = [[1.0, 2.0, ___],
     [3.0, 4.0, ___]]
        (sliced by `s![.., ..2]`)
b = [[-1.0, -2.0],
     [-3.0, -4.0],
     [-5.0, -6.0]]
c = [[1.0, 1.0, 1.0],
     [___, ___, ___],
     [1.0, 1.0, 1.0]]
        (Column-major, sliced by `s![0..3;2, ..]`)

Output of c is

[[-3.500,  -9.500, -15.500],
 [ 1.000,   1.000,   1.000],
 [-9.500, -23.500, -37.500]]

Example of generic

After v0.3, this crate now supports (somehow) simple generic usage. For example of GEMM and TRMM,

use blas_array2::prelude::*;
use ndarray::prelude::*;

fn demo<F>()
where
    F: GEMMNum + TRMMNum,
{
    let a = Array2::<F>::ones((3, 3));
    let b = Array2::<F>::ones((3, 3));
    let mut c = GEMM::<F>::default().a(a.view()).b(b.view()).run().unwrap().into_owned();
    TRMM::<F>::default().a(a.view()).b(c.view_mut()).run().unwrap();
    println!("{:}", c);
}

fn main() {
    demo::<f64>();
    demo::<c64>();
}

This will give result of

[[9, 9, 9],
 [6, 6, 6],
 [3, 3, 3]]
[[9+0i, 9+0i, 9+0i],
 [6+0i, 6+0i, 6+0i],
 [3+0i, 3+0i, 3+0i]]

Installation

This crate is available on crates.io.

If there's any difficulties encountered in compilation, then please check if BLAS library is linked properly. May be resolved by declaring

RUSTFLAGS="-lopenblas"

if using OpenBLAS as backend.

Some features (such as ilp64, gemmt) requires BLAS to be compiled with 64-bit integer, or certain BLAS extensions.

Acknowledges

This project is developed as a side project from REST.