Sums over repeated indices in an array.

contraction(x, i = NULL, drop = TRUE)

## Arguments

x

indexed array. See index.

i

subset of repeated indices to sum up. If NULL, the summation takes place on all the repeated indices.

drop

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

## Value

array.

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

## Examples

### matrix trace
x <- matrix(letters[1:4], nrow = 2)
contraction(x)
#>  "a + d"

### tensor trace
x <- array(1:27, dim = c(3,3,3))
contraction(x)
#>  42

#### tensor contraction over repeated indices
x <- array(1:27, dim = c(3,3,3))
index(x) <- c("i","i","j")
contraction(x)
#>  15 42 69

#### tensor contraction over specific repeated indices only
x <- array(1:16, dim = c(2,2,2,2))
index(x) <- c("i","i","k","k")
contraction(x, i = "k")
#>      [,1] [,2]
#> [1,]   14   18
#> [2,]   16   20

#### tensor contraction keeping dummy dimensions
x <- array(letters[1:16], dim = c(2,2,2,2))
index(x) <- c("i","i","k","k")
contraction(x, drop = FALSE)
#>      [,1] [,2]
#> [1,] "a"  "m"
#> [2,] "d"  "p"