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

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rust
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data

Rechercherichtung

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.

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Beschreibung

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

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