%dot% {calculus}

Numerical and Symbolic Dot Product

Description

The dot product between arrays with different dimensions is computed by taking the inner product on the last dimensions of the two arrays.

Usage

x %dot% y

Arguments

x

numeric or character array.

y

numeric or character array.

Details

The dot product between two arrays A and B is computed as:

C_{i_1\dots i_m} = \sum_{j_1\dots j_n} A_{i_1\dots i_mj_1\dots j_n}B_{j_1\dots j_n}

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 basic arithmetic: %diff%(), %div%(), %inner%(), %kronecker%(), %outer%(), %prod%(), %sum%()

Examples

### inner product 
x <- array(1:12, dim = c(3,4))
x %dot% x

### dot product 
x <- array(1:24, dim = c(3,2,4))
y <- array(letters[1:8], dim = c(2,4))
x %dot% y