R help - May 2010 - need help in understanding R code, and maybe some math

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.

Thanks,
Barisdad.

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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.
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]]