search for: orthonorm

Hi: Does R have a function as gsorth is SAS, that perform a the Gram-Schmidt orthonormal factorization of the m ?n matrix A, where m is greater than or equal to n? That is, the GSORTH subroutine in SAS computes the column-orthonormal m ?n matrix P and the upper triangular n ?n matrix T such that A = P*T. or any other version of Gram-Schmidt orthonormal factorization? I search the h...

Hello List, I would like to orthonormalize vectors contained in a matrix X taking into account row weights (matrix diagonal D). ie, I want to obtain Z=XA with t(Z)%*%D%*%Z=diag(1) I can do the Gram-Schmidt orthogonalization with subsequent weighted regressions. I know that in the case of uniform weights, qr can do the trick. I wo...

...0) c <- c(2,1,0) x <- matrix(c(a,b,c),3,3) ########################## # Gram-Schmidt ########################## A <- matrix(a,3,1) q1 <- (1/sqrt(sum(A^2)))*A B <- b - (q1%*%b)%*%q1 q2 <- (1/sqrt(sum(B^2)))*B C <- c - (q1%*%c)%*%q1 - (q2%*%c)%*%q2 q3 <- (1/sqrt(sum(C^2)))*C Orthonormal.basis <- matrix(c(q1,q2,q3),3,3) > Orthonormal.basis [,1] [,2] [,3] [1,] 0.7071068 0.7071068 0 [2,] 0.0000000 0.0000000 1 [3,] 0.7071068 -0.7071068 0 ########################## # QR Factorisation X = QR ########################## x.qr <- qr(x) Q...

Hey, R-listers, I have a question about determining the orthogonal basis vectors. In the d-dimensinonal space, if I already know the first r orthogonal basis vectors, should I be able to determine the remaining d-r orthognal basis vectors automatically? Or the answer is not unique? Thanks for your attention. Fred

It is not clear to me that one can. If the singular value decomposition of A is the triple product P d Q', then the singular value decomposition of A'A=S is Q d^2 Q'. The information about the orthonormal matrix P is lost, is it not? ********************************************************** Cliff Lunneborg, Professor Emeritus, Statistics & Psychology, University of Washington, Seattle Visiting: Melbourne, Feb-May 1999, Brisbane, Jun-Aug 1999, Sydney, Sep-Nov 1999, Perth, Dec 1999-Feb 2000 cli...

...the standard deviations of the components in order by descending value; the squares are the eigenvalues of the covariance matrix - the matrix, loadings, has dimension CxC, and the columns are the eigenvectors of the covariance matrix, in the same order as the sdev vector; the columns are orthonormal: sum(dmpca$loadings[,i]*dmpca$loadings[,j]) = 1 if i == j, ~ 0 if i != j - the vector, center, of length C, contains the means of the variable columns in the original data matrix, in the same order as the original columns - the vector, scale, of length C, contains the scalings applied to eac...

Dear R community: I want to simulate a regression matrix which is generated from an orthonormal matrix X of dimension 30*10 with different between-column pairwise correlation coefficients generated from uniform distribution U(-1,1). Thanks in advance! Rui [[alternative HTML version deleted]]

...o and the ridge in a simulation of a linear regression model of 30 observations and 10 regressors Y = beta0 + beta1*x1 + ... + beta10*x10 + epsilon, where epsilon follows a normal distribution with mean mu and standard deviation sigma. Ten regression matrices {X}m, m=1,...,10, are generated from an orthonormal matrix X of dimension 30*10 with different between-column pairwise correlation coefficients {rho}m generated from uniform distribution U(-1, 1). Thanks in advance. Rui [[alternative HTML version deleted]]

...es E<-eigen(m, sym=TRUE) Q<-E$vectors V<-E$values n<-nrow(m) ##normalize the eigenvectors for(i in 1:n){ Q[,i]<-Q[,i]/sqrt(sum(Q[,i]^2)) } ##verify dot product of vectors are orthogonal sum(Q[,1]*Q[,2]) sum(Q[,1]*Q[,3]) sum(Q[,2]*Q[,3]) ##Begin creating QDQ^T matrix. Where Q are orthonormal eigenvectors, and D is a diagonal matrix with 1/eigenvalues on the diagonal. and Q^T is the transpose of Q. R<-t(Q) D<-mat.or.vec(n,n) for(i in 1:n) { D[i,i]<-1/V[i] } P<-Q*D*R ## P should be the inverse of the matrix m. Check using solve(m) ## solve(m) does not equal P? Any...

Dear R list users, the singluar value decomposition of a symmetric matrix M is UDV^(T), where U = V. La.svd(M) gives as output three elements: the diagonal of D and the two orthogonal matrices u and vt (which is already the transpose of v). I noticed that the transpose of vt is not exactly u. Why is that? thank you for your attention and your help Stefano AVVISO IMPORTANTE: Questo messaggio di

...ental data d, which has two numeric predictors, p1 and p2, and one numeric response, r. The aim is to compare polynomial models in p1 and p2 up to third order. I don't understand why lm() doesn't return coefficients for the p1^3 and p2^3 terms. Similar loss of terms happened when I tried orthonormal polynomials to third order. I'm satisfied with the second-order regression, by the way, but I'd still like to understand why the third-order regression doesn't work like I'd expect. Can anyone offer a pointer to help me understand this? Here's what I'm seeing in R 1.9.1...

Dear all, Can any one tell me how can i perform Orthogonal Polynomial Regression parameter estimation in R? -------------------------------------------- Here is an "Orthogonal Polynomial" Regression problem collected from Draper, Smith(1981), page 269. Note that only value of alpha0 (intercept term) and signs of each estimate match with the result obtained from coef(orth.fit). What

...e first l columns of V, with gives a (l X l) matrix, i know that i than have a sub-space (R^L)of the original (R^M) space. I know that this sub-space basis is optimal in the least squares sense. The question is: given one 3-dim space generated by 6 vectors (A is a 6X3 matrix), i define a 2-dim orthonormal basis by taking the 2 first columns of V, how i can then project a new 3-dim vector in this 2-dim sub-space just defined? Thanks in advance. Jos? Augusto M. de Andrade Jr. Business Adm. Student University of Sao Paulo - Brazil

Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given

Hi all, We know that Hermite polynomial is for Gaussian, Laguerre polynomial for Exponential distribution, Legendre polynomial for uniform distribution, Jacobi polynomial for Beta distribution. Does anyone know which kind of polynomial deals with the log-normal, Student抯 t, Inverse gamma and Fisher抯 F distribution? Thank you in advance! David [[alternative HTML version deleted]]

Dear all, Does anybody have an idea or suggestion how to construct (plot) 4-dimensional hypercube in R. Thanks in advance for any pointers. Regards, Andrej

Hello, I am new to R and I have a question about the difference between correspondence analysis in R and SPSS. This is the input table I am working with (4 products and 18 attributes): > mytable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 15 11 20 4 14 7 1 2 1 4 12 12 17 19 11 20 9 10 2 19 18 14 14 16 4 14 11 11 15 22 19 22 16 21 19 15 16 3 16 13 10 9 15 4 10 7 11 13 18

hi all i have a question that about the eigen analysis found in R and in eviews. i used the same data set in the two packages and found different answers. which is incorrect? the data is: aa ( a correlation matrix) 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 0.9801 0.9801 0.9801 0.9801 0.9801 1 now > svd(aa) $d [1] 4.9204

Hi, I would like to fit my data with a 4th order polynomial. Now I have only 5 data point, I should have a polynomial that exactly pass the five point Then I would like to compute the "fitted" or "predict" value with a relatively large x dataset. How can I do it? BTW, I thought the model "prodfn" should pass by (0,0), but I just wonder why the const is

Can I ask a small stat. related question here? Suppose I have two predictors for a time series processes and accuracy of predictor is measured from MSEs. My question is, if two predictors give same MSE then, necessarily they have to be identical? Can anyone provide me any counter example? Thanks. -- View this message in context: