[R] LME: internal workings of QR factorization --repost
Hi: I've been reading Computational Methods for Multilevel Modeling by Pinheiro and Bates, the idea of embedding the technique in my own c-level code. The basic idea is to rewrite the joint density in a form to mimic a single least squares problem conditional upon the variance parameters. The paper is fairly clear except that some important level of detail is missing. For instance, when we first meet Q_(i): /\ / \ | Z_i X_i y_i | | R_11(i) R_10(i) c_1(i) | || = Q_(i) | | | Delta 0 0| | 0 R_00(i) c_0(i) | \/ \ / the text indicates that the Q-R factorization is limited to the first q columns of the augmented matrix on the left. If one plunks the first q columns of the augmented matrix on the left into a qr factorization, one obtains an orthogonal matrix Q that is (n_i + q) x q and a nonsingular upper triangular matrix R that is q x q. While the text describes R as a nonsingular upper triangular q x q, the matrix Q_(i) is described as a square (n_i + q) x (n_i + q) orthogonal matrix. The remaining columns in the matrix to the right are defined by applying transpose(Q_(i)) to both sides. The question is how to augment my Q which is orthogonal (n_i + q) x q with the missing (n_i + q) x n_i portion producing the orthogonal square matrix mentioned in the text? I tried appending the n_i x n_i identity matrix to the block diagonal, but this doesn't work as the resulting likelihood is insensitive to the variance parameters. Grant Izmirlian NCI __ [EMAIL PROTECTED] 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] LME: internal workings of QR factorization
Hi: I've been reading Computational Methods for Multilevel Modeling by Pinheiro and Bates, the idea of embedding the technique in my own c-level code. The basic idea is to rewrite the joint density in a form to mimic a single least squares problem conditional upon the variance parameters. The paper is fairly clear except that some important level of detail is missing. For instance, when we first meet Q_(i): /\ / \ | Z_i X_i y_i | | R_11(i) R_10(i) c_1(i) | || = Q_(i) | | | Delta 0 0| | 0 R_00(i) c_0(i) | \/ \ / the text indicates that the Q-R factorization is limited to the first q columns of the augmented matrix on the left. If one plunks the first q columns of the augmented matrix on the left into a qr factorization, one obtains an orthogonal matrix Q that is (n_i + q) x q and a nonsingular upper triangular matrix R that is q x q. While the text describes R as a nonsingular upper triangular q x q, the matrix Q_(i) is described as a square (n_i + q) x (n_i + q) orthogonal matrix. The remaining columns in the matrix to the right are defined by applying transpose(Q_(i)) to both sides. The question is how to augment my Q which is orthogonal (n_i + q) x q with the missing (n_i + q) x n_i portion producing the orthogonal square matrix mentioned in the text? I tried appending the n_i x n_i identity matrix to the block diagonal, but this doesn't work as the resulting likelihood is insensitive to the variance parameters. Grant Izmirlian NCI __ [EMAIL PROTECTED] 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.
Re: [R] Adding .R to source file keeps R from reading it?
So...are you trying to modify a contributed package by adding a *.R file to the 'R' subdirectory in the package? One thing to consider besides the previous tip is that the package might be using a NAMESPACE, which lives in the package root directory (one directory up from the 'R' subdirectory). If so, then you must add the name of your function to the argument list of the call to 'export' in the NAMESPACE file e.g. export(sortgenes, pvalues, MyFunction) -Original Message- From: John Tillinghast [mailto:[EMAIL PROTECTED] Sent: Thu 9/21/2006 9:55 PM To: r-help@stat.math.ethz.ch Subject: Re: [R] Adding .R to source file keeps R from reading it? Yes, this was exactly the problem: I was using the unzipped package, not the source. Now it works! -- Forwarded message -- From: Deepayan Sarkar [EMAIL PROTECTED] Date: Sep 21, 2006 2:58 PM Subject: Re: [R] Adding .R to source file keeps R from reading it? To: John Tillinghast [EMAIL PROTECTED] Cc: r-help@stat.math.ethz.ch On 9/21/06, John Tillinghast [EMAIL PROTECTED] wrote: Hi, I'm updating the LMGene package from Bioconductor. Writing R Extensions suggests that all source files (the ones in the R directory) have a .R ending, so I added it to the (one) source file. The next time I installed and ran R, R didn't understand any of the functions. I tried various things and eventually went back to the file and dropped the .R ending, installed, ran R. It worked! For purposes of distributing the package, do I want to leave the name without the .R, or add the .R and change something else? I'm guessing that the source you are working on has been obtained by unzipping the windows binary zip file. Despite appearances, that is not the source code. For the proper source code, download the file that's marked as source. In this case, http://bioconductor.org/packages/1.8/bioc/html/LMGene.html clearly labels the following as Source (and the corresponding zip file as Windows Binary) http://bioconductor.org/packages/1.8/bioc/src/contrib/LMGene_1.0.0.tar.gz This likely answers your other question as well. -Deepayan [[alternative HTML version deleted]] __ R-help@stat.math.ethz.ch 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.
Re: [R] Geometrical Interpretation of Eigen value and Eigen vector
Ok, I had a look at it. It seems like awefully far to dig for the main point which is easily summarized in a few sentences. If we super-impose the pre-image and image spaces (plot the input and output in the same picture), then in 1 dimension, a linear function, say 'a x', takes its input, x, and stretches it by a factor |a|. If 'a' is negative, then the direction that 'x' points is reversed. Understanding several dimensions, as is usually the case, requires us to refine our understanding of the 1-dimensional case. In several dimensions, a linear function, say 'A x' (where 'A' is an m by m matrix and 'x' is an 'm' vector) will result in the stretching of the input, 'x', along the direction its pointing, by a factor 'a'. However, this is the case _only_ if 'x' lies in one of the 'characteristic directions' corresponding to 'A'. Since 'A' is an m by m matrix, there will be at most m such 'characteristic directions'. Each of the characteristic directions has its associated stretching factor. The characteristic directions are called eigenvectors and the corresponding stretching factors are called eigenvalues. Think about what this means in 1-dimension (hint: there's only one dimension so only one possible direction). The number of linearly independent characteristic directions (eigenvectors) is called the rank of the matrix, A. If you understand the concept of 'basis' then you know that any m vector can be expressed in terms of the basis of eigenvectors of 'A' (that is unless A is not of 'full rank' and has less than m linearly independent eigenvectors, in which case we decomponse 'x' into two orthogonal components, one as a linear combination of the eigenvectors of A and the other gets mapped to 0 by A.) Thus to each input 'x' is assigned an output 'y' which is the sum of coefficients in the eigenvector basis representation of 'x' times corresponding eigenvalues. This can be understood as the diagonalization of 'A'. By the way, the referenced page was in error because the singular value decomposition (I think the page actually called it the single value decomposition...free translation(s).com anyone) is not the same thing as the diagonalization. There, it took a little more than a few sentences, but at least by the close of the second paragraph one gets the basic idea. Now, in closing, Arun, please spend some time thinking about the answer to your question before you cut and paste it into your homework assignment. -Original Message- From: Dirk Enzmann [mailto:[EMAIL PROTECTED] Sent: Sat 8/12/2006 7:01 AM To: r-help@stat.math.ethz.ch Cc: [EMAIL PROTECTED] Subject: Re: [R] Geometrical Interpretation of Eigen value and Eigen vector Arun, have a look at: http://149.170.199.144/multivar/eigen.htm HTH, Dirk Arun Kumar Saha [EMAIL PROTECTED] wrote: It is not a R related problem rather than statistical/mathematical. However I am posting this query hoping that anyone can help me on this matter. My problem is to get the Geometrical Interpretation of Eigen value and Eigen vector of any square matrix. Can anyone give me a light on it? __ R-help@stat.math.ethz.ch 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.
