grapes-dot-grapes: Numerical and Symbolic Dot Product

In calculus: High Dimensional Numerical and Symbolic 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. \Sexpr[results=rd]{tools:::Rd_expr_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

calculus documentation built on March 31, 2023, 11:03 p.m.