Rust ndarray arrayの任意の要素を用いて行列計算を行いたい

Question

前提・実現したいこと

rust_ndarrayを用いて、Array2の任意の場所の要素で全体のArrayを引き算したいと考えております。
pythonでは、

a = np.array([[1.,1.,], [3.,4.,], [4.,4.,]])
new_a = a - a[0]
// new_a => np.array([[0.,0.,], [2.,3.,],[3.,3.,]])

のような計算を行いたいと考えております。

発生している問題・エラーメッセージ

error[E0277]: the trait bound `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>: ScalarOperand` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `ScalarOperand` is not implemented for `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>`
   |
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0277]: the trait bound `ViewRepr<&f64>: DataOwned` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `DataOwned` is not implemented for `ViewRepr<&f64>`
   |
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0277]: the trait bound `ViewRepr<&f64>: DataMut` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `DataMut` is not implemented for `ViewRepr<&f64>`
   |
   = help: the following implementations were found:
             <ViewRepr<&'a mut A> as DataMut>
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error: aborting due to 4 previous errors; 1 warning emitted

error[E0271]: type mismatch resolving `<f64 as Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>>::Output == f64`
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ expected struct `ArrayBase`, found `f64`
   |
   = note: expected struct `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>`
                found type `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0271]: type mismatch resolving `<f64 as Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>>::Output == f64`
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ expected struct `ArrayBase`, found `f64`
   |
   = note: expected struct `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>`
                found type `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0277]: the trait bound `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>: ScalarOperand` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `ScalarOperand` is not implemented for `ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>`
   |
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0277]: the trait bound `ViewRepr<&f64>: DataOwned` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `DataOwned` is not implemented for `ViewRepr<&f64>`
   |
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error[E0277]: the trait bound `ViewRepr<&f64>: DataMut` is not satisfied
  --> src/features.rs:17:15
   |
17 |     let c = c - c.slice(s![idx, ..]);
   |               ^ the trait `DataMut` is not implemented for `ViewRepr<&f64>`
   |
   = help: the following implementations were found:
             <ViewRepr<&'a mut A> as DataMut>
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `f64`
   = note: required because of the requirements on the impl of `Sub<ArrayBase<ViewRepr<&f64>, Dim<[usize; 1]>>>` for `&ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>`

error: aborting due to 4 previous errors; 1 warning emitted

Some errors have detailed explanations: E0271, E0277.
For more information about an error, try `rustc --explain E0271`.

該当のソースコード

// c: &Array2<f64>

let c = c - c.slice(s![idx,..]);

できれば、cなどをclone()せずに行いたいと思います。

Answer 1

以下のような感じでいかがですか。ひょっとしたら内部で clone しているかもしれません（未確認）。

extern crate ndarray; // 0.14.0
use ndarray::prelude::*;

fn main() {
    let c: Array2<f64> = arr2(&[[1f64, 1f64], [3f64, 4f64], [4f64, 4f64]]);
    let axis: usize = 0usize;
    let idx: usize = 1usize;
    let c_new: Array2<f64> = &c - &c.index_axis(Axis(axis), idx).insert_axis(Axis(axis));
    println!("{:?}", c_new);
}

以下、ちょっとした説明です。

• index_axis(&self, axis: Axis, index: usize) -> ArrayView は axis に沿って index 番目の要素のビューを返します（Numpy での a[:, index] のような動作）。
• insert_axis(axis: Axis) -> ArrayBase は axis に相当する軸を追加します（Numpy での a[:, None] のような動作）。

参考：

• https://docs.rs/ndarray/0.14.0/ndarray/doc/ndarray_for_numpy_users/index.html