[Feature request] `ArrayRef<A, Ix2>.dot()` for axis greater than `Ix2`

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Assessment

Difficulty
4/5
Estimated time
3-5 days
Newbie friendliness
45/100
Issue type
Feature
Clarity
Mostly clear
Activity status
Stale
Tech stack
rust
Domain
data

Research direction

Start from the ndarray dot() entry point and inspect how dimensions are currently constrained. Compare the requested behavior with the provided Ix3-by-Ix2 example, then verify that higher-rank left-hand arrays produce the expected NumPy-compatible shape while preserving existing Ix2 behavior.

Written by the indexing model from the issue text.

Description

enhancement question

In NumPy, the left-hand side of a matrix multiplication can have as many axes as desired, as long as it has more than 2 axes and the last axis's dimension matches that of the 0th axis of the right-hand side, e.g.:

import numpy as np
x = np.random.random((3, 2, 5, 9, 12))
y = np.random.random((12, 13))
(x @ y).shape

# (3, 2, 5, 9, 13)

In ndarray, you can't do this directly:

// Doesn't compile:
use ndarray::prelude::*;
use ndarray_rand::RandomExt;
use ndarray_rand::rand_distr::Uniform;


fn main() {
    let x: Array<f64, Ix3> = Array::random(
        (12, 4, 3),
        Uniform::new(0., 1.).unwrap()
    );
    let y: Array<f64, Ix2> = Array::random(
        (3, 2),
        Uniform::new(0., 1.).unwrap()
    );
    let x_y = x.dot(&y);
    println!("{}", x_y);
}
Compiler Output 
$ cargo run
   Compiling playground v0.1.0 (/home/connor/RustroverProjects/playground)
error[E0275]: overflow evaluating the requirement `&ArrayBase<_, _, _>: Not`
  --> src/main.rs:15:17
   |
15 |     let x_y = x.dot(&y);
   |                 ^^^
   |
   = help: consider increasing the recursion limit by adding a `#![recursion_limit = "256"]` attribute to your crate (`playground`)
   = note: required for `&ArrayBase<_, _, _>` to implement `Not`
   = note: 127 redundant requirements hidden
   = note: required for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 3]>, f64>` to implement `Not`

For more information about this error, try `rustc --explain E0275`.
error: could not compile `playground` (bin "playground") due to 1 previous error

Emulating the behavior in the previous NumPy example requires a non-trivial amount of work, e.g. for x with 3 axes:

use ndarray::prelude::*;
use ndarray_rand::RandomExt;
use ndarray_rand::rand_distr::Uniform;


fn main() {
    let x: Array<f64, Ix3> = Array::random((12, 4, 3), Uniform::new(0., 1.).unwrap());
    let y = Array::random((3, 2), Uniform::new(0., 1.).unwrap());

    let (a, b, c) = (x.len_of(Axis(0)), x.len_of(Axis(1)), x.len_of(Axis(2)));
    let d = y.len_of(Axis(1));

    let x_y: Array3<f64> = x
        .to_shape((a * b, c)).unwrap()
        .dot(&y)
        .to_shape((a, b, d)).unwrap()
        .to_owned();
    println!("{:?}", x_y);
}

Therefore, I think it would be nice to have dot() be implemented for axis numbers greater than Ix2

Dominant language
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