Dot Product of Vectors or Matrices

Computes the dot product between two numeric or complex vectors, or the column-wise dot products of two matrices with identical dimensions.

Usage

dotProd(x, y)

Arguments

x: a numeric or complex vector, or a numeric/complex matrix.
y: a numeric or complex vector, or a numeric/complex matrix with the same dimensions as x.

Value

a scalar if x and y are vectors.
a numeric or complex vector containing the column-wise dot products if matrices are supplied.

Details

For vectors $x$ and $y$, the dot product is defined as: $$ \sum_i \overline{x_i} y_i $$ where $\overline{x_i}$ denotes the complex conjugate of $x_i$ (for real input this is simply $\sum_i x_i y_i$).

For matrices, the dot product of each column of x with the corresponding column of y is returned.

Note that crossprod() does not conjugate its first argument for complex input, so it computes $t(X) Y$ rather than the Hermitian inner product; this function does conjugate.

Examples

# Vector dot product
dotProd(c(1, 2, 3), c(4, 5, 6))
#> [1] 32

# Complex vectors (Hermitian inner product)
dotProd(c(1+1i, 2), c(3, 4-1i))
#> [1] 11-5i

# Matrix (column-wise dot products)
x <- matrix(1:6, ncol = 2)
y <- matrix(6:1, ncol = 2)
dotProd(x, y)
#> [1] 28 28