From: Stephane DRAY <stephane.dray_at_umontreal.ca>

Date: Thu 08 Jul 2004 - 04:32:51 EST

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Jul 08 04:35:34 2004

Date: Thu 08 Jul 2004 - 04:32:51 EST

At 00:00 07/07/2004, Spencer Graves wrote:

> Is a solution even possible for the matrices in your example?

*>I've tried a few things that have suggested that a solution may not be
**>possible.
**> What can you tell us of the problem that you've translated into
**> this? I see a minimization problem subject to constraints, but I'm not
**> certain which are the constraints and what is the objective function.
**>For example, are you trying to find Q to minimize sum((Z-X'X)^2) subject
**>to XQ=W or do you want to minimize sum((XQ-W)^2) subject to Q'Q=Z or
**>something else?
**> If it were my problem, I think I would work for a while with the
**> singular value decompositions of X, W and Z, and see if that would lead
**> me to more information about Q, including conditions under which a
**> solution existed, expressions for Q when multiple solutions existed, and
**> a solution minimizing your chosen objective function when solutions do
**> not exist. (A google search produced many hits for "singular value
**> decomposition", implemented as "svd" in R.)
**> hope this helps. spencer graves
**>
**>Stephane DRAY wrote:
**>
**>>Hello,
**>>I have a question that is not directly related to R ... but I try to do
**>>it in R ;-) :
**>>
**>>I would like to generate a matrix Q satisfying (for a given Z, X and W)
**>>the two following conditions:
**>>
**>>t(Q)%*%Q=Z (1)
**>>XQ=W (2)
**>>
**>>where:
**>>Q is m rows and r columns
**>>X is p rows and m columns
**>>D is p rows and r columns
**>>C is r rows and r columns
**>>with m>p,r
**>>
**>>
**>>e.g:
**>>m=6,
**>>p=2
**>>r=3
**>>
**>>Z=matrix(c(1,.2,.5,.2,1,.45,.5,.45,1),3,3)
**>>X=matrix(c(.1,.3,.5,.6,.2,.1,.8,1,.4,.2,.2,.9),2,6)
**>>W=matrix(c(0,.8,.4,.6,.2,0),2,3)
**>>
**>>#Create a matrix satisfying (1) is easy:
**>>
**>>A=matrix(runif(18),6,3)
**>>Q1=svd(A)$u%*%chol(Z)
**>>
**>>
**>>#For the second condition (2), a solution is given by
**>>
**>>Q2=A%*%ginv(X%*%A)%*%W
**>>
**>>
**>>
**>>
**>>
**>>I do not know how to create a matrix Q that satisfies the two
**>>conditions. I have try to construct an iterative procedure without
**>>success (no convergence):
**>>
**>>eps=10
**>>i=0
**>>while(eps>.5)
**>>{
**>>Q1=svd(Q2)$u%*%chol(Z)
**>>Q2=Q1%*%ginv(X%*%Q1)%*%W
**>>eps=sum(abs(Q1-Q2))
**>>cat(i,":",eps,"\n")
**>>i=i+1
**>>}
**>>
**>>Perhaps someone could have any idea to solve the problem, or a reference
**>>on this kind of question or the email of another list where I should ask
**>>this question.
**>>
**>>Thanks in advance,
**>>
**>>Sincerely.
**>>
**>>Stéphane DRAY
**>>--------------------------------------------------------------------------------------------------
**>>
**>>Département des Sciences Biologiques
**>>Université de Montréal, C.P. 6128, succursale centre-ville
**>>Montréal, Québec H3C 3J7, Canada
**>>
**>>Tel : 514 343 6111 poste 1233
**>>E-mail : stephane.dray@umontreal.ca
**>>--------------------------------------------------------------------------------------------------
**>>
**>>Web
**>>http://www.steph280.freesurf.fr/
**>>
**>>______________________________________________
**>>R-help@stat.math.ethz.ch mailing list
**>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
**>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
**>
*

Stéphane DRAY

Département des Sciences Biologiques

Université de Montréal, C.P. 6128, succursale centre-ville
Montréal, Québec H3C 3J7, Canada

Tel : 514 343 6111 poste 1233

E-mail : stephane.dray@umontreal.ca

Web http://www.steph280.freesurf.fr/ ______________________________________________R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Jul 08 04:35:34 2004

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