Implicit mode can be perform in different meaning

Hi, Constantin

I found that CRAN einsum cannot use in implicit mode without explicit indicator (->). https://github.com/const-ae/einsum/blob/a5e1152fac2b15d36f691f357f9ca586a49c51be/man/einsum.Rd#L16-L18

It'll be fine, implicit mode is sometimes misleading. However, CRAN einsum can actually be performed in different meaning like below.

For example, in Numpy's einsum, implicit mode just shows the whole data.

# Numpy (Python)
import numpy as np
data = np.random.rand(3, 4)
np.einsum('ij', data)
# array([[0.50142663, 0.845945  , 0.36696267, 0.00643327],
#        [0.14395742, 0.73767592, 0.81586026, 0.40644605],
#        [0.12538026, 0.92932431, 0.2329707 , 0.10398253]])

However, in CRAN einsum, it is interpreted as the summation over the indices i and j.

# einsum (R)
library("einsum")
data <- array(runif(3*4), dim=c(3,4))
einsum('ij', data)
# [1] 2.951262

Wouldn't it be more trouble-free to ban equation_strings containing "->"? For example, how about including the following argument check?

if(length(grep("->", "equation_string")) == 0){
    stop("Please make sure that equation_string has explicit indicator (->)")
}

const-ae / einsum

Implicit mode can be perform in different meaning #4