Vector and vector half operators

Description

The vec (vector) operator takes a d x d matrix and stacks the columns into a single vector of length d^2. The vech (vector half) operator takes a symmetric d x d matrix and stacks the lower triangular half into a single vector of length d(d+1)/2. The functions invvec and invvech are the inverses of vec and vech i.e. they form matrices from vectors.

Usage

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vec(x, byrow=FALSE)
vech(x)
invvec(x, ncol, nrow, byrow=FALSE)
invvech(x)

Arguments

x

vector or matrix

ncol,nrow

number of columns and rows for inverse of vech

byrow

flag for stacking row-wise or column-wise. Default is FALSE.

References

Magnus, J.R. & Neudecker H.M. (1999) Matrix Differential Calculus with Applications in Statistics and Econometrics (revised edition), Wiley & Sons. Chichester.

Examples

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x <- matrix(1:9, nrow=3, ncol=3)
vec(x)
invvec(vec(x))

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