contraction {calculus} R Documentation

## Numerical and Symbolic Tensor Contraction

### Description

Sums over repeated indices in an array.

### Usage

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.

### 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: delta(), diagonal(), einstein(), epsilon(), index()

### Examples

### matrix trace
x <- matrix(letters[1:4], nrow = 2)
contraction(x)

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

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

#### 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")

#### 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)



[Package calculus version 1.0.1 Index]