sommer (version 3.6)

hadamard.prod: Hadamard product of two matrices

Description

This function returns the Hadamard or Shur product of two matrices, x and y, that have the same row and column dimensions.

Usage

hadamard.prod(x, y)

Arguments

x

a numeric matrix or vector object

y

a numeric matrix or vector object

Value

A matrix.

Details

The Hadamard product is an element-by-element product of the two matrices. Let $\mathbf{x}$ and $\mathbf{x}$ be two $m\times n$ numeric matrices. The Hadamard product is $\mathbf{x}\circ \mathbf{y}=\left[\begin{array}{cccc}{x}_{1,1}{y}_{1,1}& x_{1,2}{y}_{1,2}& \cdots & x_{1,n}{y}_{1,n}\\ x_{2,1}{y}_{121}& x_{2,2}{y}_{2,2}& \cdots & x_{2,n}{y}_{2,n}\\ \cdots & \cdots & \cdots & \cdots \\ x_{m,1}{y}_{m,1}& x_{m,2}{y}_{m,2}& \cdots & x_{m,n}{y}_{m,n}\end{array}\right]$. It uses the * operation in R.

References

Hadamard, J (1983). Resolution d'une question relative aux determinants, Bulletin des Sciences Mathematiques, 17, 240-246.

Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis, Linear Algebra and Its Applications, Elsevier, 6, 217-240.

Examples

# NOT RUN {
x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
z <- hadamard.prod( x, y )
print( z )
# }