On Sun, May 23, 2010 at 5:09 AM, Peter Ehlers <ehl...@ucalgary.ca> wrote: > On 2010-05-23 0:56, john smith wrote: >> >> Hi, >> I am trying to implement Higham's algorithm for correcting a non positive >> definite covariance matrix. >> I found this code in R: >> >> http://projects.cs.kent.ac.uk/projects/cxxr/trac/browser/trunk/src/library/Recommended/Matrix/R/nearPD.R?rev=637 >> >> I managed to understand most of it, the only line I really don't >> understand >> is this one: >> X<- tcrossprod(Q * rep(d[p], each=nrow(Q)), Q) >> >> This line is supposed to calculate the matrix product Q*D*Q^T, Q is an n >> by >> m matrix and R is a diagonal n by n matrix. What does this mean? >> I also don't understand the meaning of a cross product between matrices, I >> only know it between vectors.
In the original S language, on which R is based, the function named crossprod was used for what statisticians view as the cross-product of the columns of a matrix, such as a multivariate data matrix or a model matrix. That is crossprod(X) := X'X This is a special case of the cross-product of the columns of two matrices with the same number of rows crossprod(X, Y) := X'Y The tcrossprod function was introduced more recently to mean the crossprod of the transpose of X. That is trcossprod(X) := crossprod(t(X)) := X %*% t(X) These definitions are unrelated to the cross-product of vectors used in Physics and related disciplines. The reason for creating such functions is that these are common operations in statistical computing and it helps to know the special structure (e.g. the result of crossprod(X) or tcrossprod(X) is a symmetric, positive semidefinite matrix). > You could have a look at the help page for crossprod which > gives the definitions of crossprod and tcrossprod. > > Perhaps this will help: > > Q <- matrix(1:12, ncol=3) > v <- rep(1:3, each=nrow(Q) > Q > v > Q * v > (Q * v) %*% t(Q) > tcrossprod(Q * v, Q) > > -Peter Ehlers > >> >> Thanks, >> Barisdad. >> >> [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
