# blas-array2

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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](docs-markdown/dev.md), link for [docs.rs](`document_dev`))
- List of BLAS wrapper structs (link for [github](docs-markdown/func.md), link for [docs.rs](`document_func`))
- Efficiency demonstration (link for [github](docs-markdown/demo_efficiency.md), link for [docs.rs](`demo_efficiency`))

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`):
```rust
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](https://netlib.org/blas/blast-forum/chapter2.pdf) 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](https://github.com/blas-lapack-rs/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>`:
```rust
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
```output
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,

```rust
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](https://github.com/igor-1982/rest).