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 |
i |
subset of repeated indices to sum up. If |
drop |
|
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
See Also
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]