Implements the Einstein notation for summation over repeated indices.

einstein(..., drop = TRUE)

## Arguments

...

arbitrary number of indexed arrays. See index.

drop

logical. Drop summation indices? If FALSE, keep dummy dimensions.

## Value

array.

## References

Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. doi:10.18637/jss.v104.i05

Other tensor algebra: contraction(), delta(), diagonal(), epsilon(), index()

## Examples

### A{i,j} B{j,k}
a <- array(letters[1:6], dim = c(i=2, j=3))
b <- array(letters[1:3], dim = c(j=3, k=1))
einstein(a,b)
#>      [,1]
#> [1,] "(a) * (a) + (c) * (b) + (e) * (c)"
#> [2,] "(b) * (a) + (d) * (b) + (f) * (c)"

### A{i,j} B{j,k,k} C{k,l} D{j,k}
a <- array(1:10, dim = c(i=2, j=5))
b <- array(1:45, dim = c(j=5, k=3, k=3))
c <- array(1:12, dim = c(k=3, l=4))
d <- array(1:15, dim = c(j=5, k=3))
einstein(a,b,c,d)
#>       [,1]   [,2]   [,3]   [,4]
#> [1,] 56370 118800 181230 243660
#> [2,] 66700 140500 214300 288100