ndarray_einsum_beta 0.7.0

Implementation of the einsum function for the Rust ndarray crate. As popularized in numpy, einsum (Einstein summation) implements general multidimensional tensor contraction. Many linear algebra operations and generalizations of those operations can be expressed as special cases of tensor contraction.
Documentation 
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#![feature(test)]
extern crate test;
use test::Bencher;

use ndarray_einsum_beta::*;
use ndarray::prelude::*;
use ndarray_rand::RandomExt;
use rand::distributions::Uniform;

fn rand_array<Sh, D: Dimension>(shape: Sh) -> ArrayBase<ndarray::OwnedRepr<f64>, D>
where
    Sh: ShapeBuilder<Dim = D>,
{
    Array::random(shape, Uniform::new(-5., 5.))
}

#[bench]
fn bench_multiply_builtin_tiny(b: &mut Bencher) {
    let m1 = rand_array((3, 4));
    let m2 = rand_array((4, 5));

    b.iter(|| m1.dot(&m2));
}

#[bench]
fn bench_multiply_tiny(b: &mut Bencher) {
    let m1 = rand_array((3, 4));
    let m2 = rand_array((4, 5));

    b.iter(|| einsum("ij,jk->ik", &[&m1, &m2]));
}

#[bench]
fn bench_multiply_tiny_reuse_path(b: &mut Bencher) {
    let m1 = rand_array((3, 4));
    let m2 = rand_array((4, 5));
    let ep = einsum_path("ij,jk->ik", &[&m1, &m2], OptimizationMethod::Naive).unwrap();

    b.iter(|| ep.contract_operands(&[&m1, &m2]));
}

#[bench]
fn bench_multiply_builtin_medium(b: &mut Bencher) {
    let m1 = rand_array((30, 40));
    let m2 = rand_array((40, 50));

    b.iter(|| m1.dot(&m2));
}

#[bench]
fn bench_multiply_medium(b: &mut Bencher) {
    let m1 = rand_array((30, 40));
    let m2 = rand_array((40, 50));

    b.iter(|| einsum("ij,jk->ik", &[&m1, &m2]));
}

#[bench]
fn bench_multiply_builtin_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((400, 500));

    b.iter(|| m1.dot(&m2));
}

#[bench]
fn bench_multiply_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((400, 500));

    b.iter(|| einsum("ij,jk->ik", &[&m1, &m2]));
}

#[bench]
fn bench_hadamard_builtin_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((300, 400));

    b.iter(|| (&m1 * &m2));
}

#[bench]
fn bench_hadamard_transpose_builtin_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((400, 300));

    b.iter(|| (&m1 * &m2.t()));
}

#[bench]
fn bench_hadamard_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((300, 400));

    b.iter(|| einsum("ij,ij->ij", &[&m1, &m2]));
}

#[bench]
fn bench_hadamard_transpose_large(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((400, 300));

    b.iter(|| einsum("ij,ji->ij", &[&m1, &m2]));
}

#[bench]
fn bench_hadamard_transpose_large_reuse_path(b: &mut Bencher) {
    let m1 = rand_array((300, 400));
    let m2 = rand_array((400, 300));
    let ep = einsum_path("ij,ji->ij", &[&m1, &m2], OptimizationMethod::Naive).unwrap();

    b.iter(|| ep.contract_operands(&[&m1, &m2]));
}

#[bench]
fn bench_sum_builtin_huge(b: &mut Bencher) {
    let m1 = rand_array((3000, 4000));

    b.iter(|| m1.sum());
}

#[bench]
fn bench_sum_huge(b: &mut Bencher) {
    let m1 = rand_array((3000, 4000));

    b.iter(|| einsum("ij->", &[&m1]));
}

#[bench]
fn bench_outer_product_medium(b: &mut Bencher) {
    let m1 = rand_array((300,));
    let m2 = rand_array((400,));

    b.iter(|| einsum("i,j->ij", &[&m1, &m2]));
}

#[bench]
fn bench_stacked_outer_product_medium(b: &mut Bencher) {
    let m1 = rand_array((100, 30));
    let m2 = rand_array((100, 40));

    b.iter(|| einsum("ij,ik->ijk", &[&m1, &m2]));
}

#[bench]
fn bench_double_outer_product_medium(b: &mut Bencher) {
    let m1 = rand_array((30, 10));
    let m2 = rand_array((40, 10));

    b.iter(|| einsum("ij,kl->lkij", &[&m1, &m2]));
}

#[bench]
fn bench_stacked_double_outer_product_large(b: &mut Bencher) {
    let m1 = rand_array((50, 30, 10));
    let m2 = rand_array((50, 40, 10));

    b.iter(|| einsum("ijk,ilm->ijklm", &[&m1, &m2]));
}