rapl
Enjoyable, composable, hackable N-dimensional arrays for Rust.
rapl combines the familiar parts of NumPy with a lot of inspiration from array
programming languages like APL and BQN. Ranks are part of the type, so rank
mistakes are compile errors.
rapl has a small core, and every operation can be built from a small set of
composable primitives.
use rapl::*;
fn main() -> Result<(), DimError> {
let x = Ndarr::from([3, 1, 4, 1, 5, 9, 2, 6]);
let w = x.slice(s![Win(3)])?; // every window of 3: a [6, 3] view, no copy
println!("{w}");
// ┌→────┐
// ↓3 1 4│
// │1 4 1│
// │4 1 5│
// │1 5 9│
// │5 9 2│
// │9 2 6│
// └~────┘
let peaks = w.reduce(1, i32::max)?; // 4 4 5 9 9 9
let hops = w.slice(s![..;2, ..])?; // a stride is just a step on the positions
// ┌→────┐
// ↓3 1 4│
// │4 1 5│
// │5 9 2│
// └~────┘
// The same in 2-D: every 2×2 patch of an image, then max pooling.
let img = Ndarr::from([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]);
let pooled = img
.slice(s![Win(2), Win(2)])? // [2, 2, 3, 2]: row, kh, col, kw
.reduce(3, i32::max)?
.reduce(1, i32::max)?;
// ┌→───────┐
// ↓ 6 7 8│
// │10 11 12│
// └~───────┘
Ok(())
}
rapl is in early development. The API is still settling, and speed is not yet
a priority (see Philosophy), so it is not yet recommended for
speed-sensitive applications.
What makes rapl different
Rank generic. Every operation works on arrays of any rank: a vector, a
matrix, a batch of images, a stack of attention heads. The rank lives in the
type (Ndarr<f32, U3>), so a rank mismatch is a compile error.
Type generic where possible. Elements are any T, not just floats:
strings, chars, tuples, your own structs. Arithmetic needs arithmetic and sin
needs a float. Everything else (slicing, permuting, mapping, folding, outer
products) works for any element type.
Enjoyable, composable, hackable. rapl is not the fastest ndarray library
in Rust and does not try to be. It tries to be pleasant to write, read and
modify: a small core, three small dependencies, and conveniences defined as short
compositions of public primitives rather than private kernels.
A taste
A 2-D convolution from windows and one fused contraction:
// image: [h, w, c_in], filters: [kh, kw, c_in, c_out]
let patches = image
.slice(s![Win(3), Win(3), ..])? // [h', 3, w', 3, c_in], a view
.permute_axes(&[0, 2, 1, 3, 4])?; // [h', w', 3, 3, c_in]
let features = patches.contract(&filters, U3::new(), |x, w| x * w, |a, b| a + b)?;
The examples include
AlexNet with hand-written backpropagation, multi-head attention, an
ultra-compact APL-style Conway's Game of Life, an Ising model, and FFT edge
detection.
A tour
Snippets assume use rapl::*; and a function that returns Result, so ?
works.
Creating arrays
let words = Ndarr::from(vec!["a", "b", "c"]); // any element type
let matrix = Ndarr::from([[1, 2], [3, 4]]); // rank from the literal
let range = Ndarr::from(1..7).reshape([2, 3])?;
let chars = Ndarr::from("Hello rapl!"); // Ndarr<char, U1>
let zeros = Ndarr::<f64, U3>::zeros([2, 3, 4]);
let filled = Ndarr::fill("a", [5]);
let line = Ndarr::linspace(0.0, 1.0, 5);
// `from_fn` passes each element's coordinates:
let identity = Ndarr::from_fn([3, 3], |ix| i32::from(ix[0] == ix[1]));
// ┌→────┐
// ↓1 0 0│
// │0 1 0│
// │0 0 1│
// └~────┘
Random arrays use the same from_fn with a generator you own; rapl does not
choose a PRNG.
Element-wise math and broadcasting
// Shapes broadcast from the right, as in NumPy, and complex numbers are native:
let a = Ndarr::from([1 + 1.i(), 2 + 1.i()]);
let b = Ndarr::from([[1, 2], [3, 4]]);
assert_eq!(a + b - 2, Ndarr::from([[1.i(), 2 + 1.i()], [2 + 1.i(), 4 + 1.i()]]));
let x = Ndarr::linspace(-1.0_f64, 1.0, 5);
let y = x.sin() * 2.0 + x.tanh();
let relu = x.map(|v| v.max(0.0)); // anything else is one `map` away
// Combine two arrays, of different element types if needed:
let grid = Ndarr::from([[1, 2, 3], [4, 5, 6]]);
let labels = grid.zip_with(&Ndarr::from(vec!["a", "b", "c"]), |n, s| format!("{s}{n}"))?;
// ┌→───────┐
// ↓a1 b2 c3│
// │a4 b5 c6│
// └~───────┘
Indexing, slicing and views
let mut a = Ndarr::from([[0, 1, 2, 3], [4, 5, 6, 7]]);
assert_eq!(a[[1, 2]], 6); // fixed or dynamic rank alike
let row = a.slice(s![1, ..])?; // an integer drops the axis
let evens = a.slice(s![.., ..;2])?; // ranges with steps
let reversed = a.slice(s![.., ..;-1])?; // negative steps, as in NumPy
let start = 1usize;
let tail = a.slice(s![0, start..])?; // any integer type, no casts
a.slice_mut(s![.., 0])?.map_in_place(|v| v * 10); // mutable views, same syntax
Views are O(1): slice, t_view, windows and broadcasts share the original
buffer. permute_axes and reshape consume their input and keep its storage,
so they never copy; to_owned_array() is the explicit copy.
Reductions, scans and cells
use std::ops::Add;
let m = Ndarr::from([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]);
let col_sums = m.reduce(0, f64::add)?; // [5, 7, 9], axis removed
let row_max = m.reduce(Keep(1), f64::max)?; // [[3], [6]], axis kept
let centered = &m - &row_max; // so it broadcasts back
let running = m.scan_axis(1, ScanDirection::Forward, |acc, x| acc + x)?;
// Cells: any function over the trailing axes, e.g. the max of each window.
let windows = m.slice(s![Win(2), Win(2)])?.permute_axes(&[0, 2, 1, 3])?;
let window_max = windows.map_cells(U2::new(), |w| {
w.iter_elems().copied().fold(f64::NEG_INFINITY, f64::max)
})?;
Products
let a = Ndarr::from(1..7).reshape([2, 3])?;
let b = Ndarr::from(1..7).reshape([3, 2])?;
let product = a.mat_mul(&b)?;
// `mat_mul` batches leading axes like NumPy's `@`:
let batch = Ndarr::from(1..13).reshape([2, 2, 3])?;
assert_eq!(batch.mat_mul(&b)?.shape(), &[2, 2, 2]);
// The general form: any number of contracted axes, any combining functions.
let tensordot = a.contract(&b, U1::new(), |x, y| x * y, |x, y| x + y)?;
// Outer products combine every pair, for any element type:
let suits = Ndarr::from(vec!["♣", "♠", "♥", "♦"]);
let ranks = Ndarr::from(vec!["2", "3", "4", "5", "6", "7", "8", "9", "10", "J", "Q", "K", "A"]);
let deck = ranks.outer_product(&suits, |rank, suit| format!("{rank}{suit}"))?;
assert_eq!(deck.len(), 52);
println!("{deck}");
// ┌→──────────────┐
// ↓2♣ 2♠ 2♥ 2♦ │
// │3♣ 3♠ 3♥ 3♦ │
// │4♣ 4♠ 4♥ 4♦ │
// │5♣ 5♠ 5♥ 5♦ │
// │6♣ 6♠ 6♥ 6♦ │
// │7♣ 7♠ 7♥ 7♦ │
// │8♣ 8♠ 8♥ 8♦ │
// │9♣ 9♠ 9♥ 9♦ │
// │10♣ 10♠ 10♥ 10♦│
// │J♣ J♠ J♥ J♦ │
// │Q♣ Q♠ Q♥ Q♦ │
// │K♣ K♠ K♥ K♦ │
// │A♣ A♠ A♥ A♦ │
// └~──────────────┘
Rank checking, static and dynamic
let m = Ndarr::from([[1, 2], [3, 4]]);
let v: Ndarr<i32, U1> = m.reduce(0, |a, b| a + b)?; // U2 -> U1, checked at compile time
let [rows, cols] = m.dim().to_array(); // destructure a fixed-rank shape
let d = m.clone().into_dyn(); // rank known only at runtime
let w: Ndarr<i32, Dyn> = d.reduce(0, |a, b| a + b)?; // same API, checked at runtime
Complex numbers and FFT
let z = 1 + 2.i();
assert_eq!(z - 3, -2 + 2.i());
let shifted = Ndarr::from([1, 2, 3]) + -1 + 2.i(); // complex arrays
assert_eq!(shifted.im(), Ndarr::from([2, 2, 2]));
// 1-D and 2-D FFT with the `fft` feature, implemented in rapl itself:
let signal = Ndarr::linspace(-10.0, 10.0, 100).sin();
let spectrum = signal.to_complex().fft();
Philosophy
- Small core, everything composes.
rapl exposes a handful of structural
and higher-order primitives: cells, windows, scans, reduce, contraction.
Conveniences are short definitions over them, so improving a primitive
improves everything built on it.
- Clarity over speed. There are no SIMD kernels, BLAS bindings or
special-cased fast paths. If a clear composition of primitives can express
something, that composition is the implementation. For heavy production
workloads, use a performance-oriented crate;
rapl is meant for exploring,
prototyping, teaching and scripting.
- Minimal dependencies. Every dependency has to earn its place. Today
there are three small, widely used crates and nothing else at runtime:
typenum and generic-array carry the compile-time rank system, and
num-traits provides the numeric traits. Features like the FFT are
implemented in rapl itself rather than pulled in.
- Hackable. No
unsafe, and a codebase meant to be read. A missing
function is usually a map, a reduce or a contract away, and we would
rather document the composition than grow the catalog.
Plotting
rapl-plot draws Ndarrs
directly, to SVG or PNG. The shape of the data decides what is drawn, and
labels, colors and widths broadcast like any other array.
use rapl::*;
use rapl_plot::*;
let x = Ndarr::linspace(0.0, 10.0, 200);
// [200, 2]: one curve per column.
let waves = Ndarr::from_fn([200, 2], |ix| (x[[ix[0]]] + ix[1] as f64).sin());
line(&x, &waves).label(["sin(x)", "sin(x + 1)"]).save("waves.svg")?;
Getting started
cargo add rapl
# or, with the FFT:
cargo add rapl --features fft
Complex numbers are enabled by default. Contributions and issues are welcome.
rapl 是一个用于 N 维数组(ndarray)的 Rust 库，它把数组的秩(rank)编码进类型里，秩不匹配就会变成编译错误。它结合了 NumPy 以及 APL、BQN 等数组语言的思想。