Thanks again for your help
At 14:55 07/07/2004, Spencer Graves wrote:
How about generating matrices (X1|X2), dim(X1) = c(n, k1), dim(X2) = c(n, k2), with mean 0 and covariance matrix as follows:
(S11 | S12)
(S21 | S22),
with S12 = W, S22 = Z and S11 = whatever you want? With X = t(X1), and Q = X2, we have E(XQ) = W and E(Q'Q) = Z.
This can be done using rmvnorm in package mvtnorm.
hope this helps. spencer graves
Stephane DRAY wrote:
thanks,
I want to create matrices for simulation purpose (in order to evaluate the efficiency of different methods on this simulated data set). So, I want to create a data matrix Q (m individuals and r variables). I want to specify the variance-covariance structure for this matrix (t(Q)%*%Q=Z ) but I want also to create another constraint due to another matrix of data. I want that the covariance of Q and X are equal to those given in W (XQ=W).
The example I gave is just to illustrate my problem and perhaps it has no solution (I cannot see it because I have no idea how to construct Q such as Q=Q1=Q2)
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.
St�phane DRAY
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D�partement des Sciences Biologiques Universit� de Montr�al, C.P. 6128, succursale centre-ville Montr�al, Qu�bec H3C 3J7, Canada
Tel : 514 343 6111 poste 1233
E-mail : [EMAIL PROTECTED]
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St�phane DRAY
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D�partement des Sciences Biologiques Universit� de Montr�al, C.P. 6128, succursale centre-ville Montr�al, Qu�bec H3C 3J7, Canada
Tel : 514 343 6111 poste 1233
E-mail : [EMAIL PROTECTED]
--------------------------------------------------------------------------------------------------
Web
http://www.steph280.freesurf.fr/
--------------------------------------------------------------------------------------------------
St�phane DRAY
--------------------------------------------------------------------------------------------------
D�partement des Sciences Biologiques Universit� de Montr�al, C.P. 6128, succursale centre-ville Montr�al, Qu�bec H3C 3J7, Canada
Tel : 514 343 6111 poste 1233
E-mail : [EMAIL PROTECTED]
--------------------------------------------------------------------------------------------------
Web http://www.steph280.freesurf.fr/
______________________________________________ [EMAIL PROTECTED] 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
