blas-array2

Implementation of 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 at github, link at docs.rs)
List of BLAS wrapper structs (link at github, link at docs.rs)
Efficiency demonstration (link at github, link at docs.rs)

Simple example

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: BLASFloat 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.

Complicated example

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]]

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.

Limitation of this crate

Though I believe this crate provides many functionalities that interests audiences in scientific computation, there are also some points that this crate is lack of, or is not going to support with by design.

For the features that will not support with,

Supports to other types of matrices. Currently crates such as ndarray, nalgebra, matrix, faer-rs, rulinalg, rest_tensors represent typical matrix implementations in rust. Though some crates are extremely fast (comparable to MKL or OpenBLAS, especially faer-rs) in linalgs, it seems that ndarray could better support features in high-dimension tensors and sub-matrices, as well as advanced slicing/view. This is also related to concept of "leading dimension" in BLAS. So ndarray is choosen to represent matrix in this crate. Matrices defined in other crates should be able to easily casted to ndarray, without explicit memory copy (by rust's moving or by tensor view of slice from raw-data), and thus not providing BLAS to other types of matrices.
Other targets (GPU). This may well require a new data structure (such as numpy v.s. torch/jax). Though machine learning frameworks (such as candle, burn, etc.) seem to be promising, an API-stable tensor structure that accepts various targets, with advanced slicing/stride support has probably yet existed in rust.
Arbitary data types. Currently, this crate supports f32/f64/c32/c64, which should be supported by legacy BLAS standard. However, this crate will not implement something like int8/rug. To address this issue, a BLAS reference implementation to any types is required, and is out of scope for this crate, which is only a high-level wrapper to BLAS (or BLAS-like) functions.
Fn instead of struct. A common sense for using BLAS functions with matrices, is function with optional parameters. However, this is not possible in rust, syntactically. So we choose to use struct (with derive_build) to pass optional parameters. In this way, there is at least one additional drawback: no IDE-time/compile-time check to non-optional parameters, so errors may occur in runtime; this require programmers to use this crate with caution.
Lapack wrapper. This is surely important, but will probably be implemented in a new crate.

For the features that can be added, but currently haven't been added (probably I'm not interested in for the moment I'm writing this crate) and may be implemented in a later time, or may be implemented after someone giving feature requests in issues/PRs.

BLAS1 functions. I think that in many cases, functionality of BLAS1 can be simply covered by iterators, or features in matrix libraries such as ndarray. Efficiency of BLAS1 can be achieved by compiler optimization (especially for serial/single-thread usage), using BLAS may not significantly improve efficiency if your code is mostly computation-bounded instead of memory-bounded.
Other kinds of floats. With development of machine learning nowadays, demands of low-precision BLAS is increasing; MKL and OpenBLAS has already implemented some BF16 features.
BLAS extensions. There are some important BLAS extensions, such as omatcopy, imatcopy, gemmt, gemm3m, that has already been implemented in both OpenBLAS, MKL and BLIS. Currently, gemmt has been implemented. Others are on-going work.
Documents. I hope that this crate is clear and simple to use by itself, especially to programmers from C/C++/F77. This crate want to be scipy.linalg.blas replacement in rust. So documentation may not be of that important (https://netlib.org/lapack/explore-html/ is farely well documented), but probably it's still required to newcommers.
Tests. It works, but it is messy. Boundary conditions have not been fully checked.

Acknowledges

This project is developed as a side project from REST.

blas-array2 0.2.0