ptycho (version 1.1-4)

createOrthogonalX: Create Design Matrix With Orthogonal Columns

Description

Create a design matrix whose columns are orthogonal to each other.

Usage

createOrthogonalX(n, p)

Value

Matrix with n rows, p columns, and column names X1,

X2, and so forth.

Arguments

n

Number of rows in \(X\)

p

Number of columns in \(X\)

Author

Laurel Stell and Chiara Sabatti
Maintainer: Laurel Stell <[e-mail]>

Details

First create \(\hat{X} = (I_p\,\,\,I_p\,\,\,\cdots\,\,\,I_p)^T,\) where \(I_p\), the identity matrix of size \(p\), is repeated ceiling(n/p) times. If p does not divide n, remove rows at the bottom so that \(\hat{X}\) has n rows. Divide by the root mean square of the columns of \(\hat{X}\).

See Also

createData

Examples

n <- 50; p <- 5
X <- createOrthogonalX(n, p)
XtX <- t(X) %*% X
D <- diag(n-1, nrow=p)
# XtX and D are not quite equal due to roundoff error
range(XtX - D)