search for: nonsingular

.../ 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 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 side...

>I'm rusty, but not *that* rusty here, I hope. > >If W (=Z*Z' in your case) is singular, it can not have >inverse, which by >definition also mean that nothing multiply by it will >produce the identity >matrix (for otherwise it would have an inverse and >thus nonsingular). > >The definition of a generalized inverse is something >like: If A is a >non-null matrix, and G satisfy AGA = A, then G is >called a generalized >inverse of A. This is not unique, but a unique one >that satisfy some >additional properties is the Moore-Penrose inverse....

Hi; I am having problems inverting matrices using the function solve() For example R can not invert the following matrix [,1] [,2] [,3] [,4] [,5] [1,] 25 500 11250 275000 7.106250e+06 [2,] 500 11250 275000 7106250 1.906250e+08

...ator<Inverse<T> > scc_end(Inverse<T> G) { + return scc_iterator<Inverse<T> >::end(G); +} + +/*Discover whether a graph node is part of any cycle, including a self-cycle.*/ +template<class T> +bool bb_reachable(T* bb) +{ + /*Return true iff we are in a nonsingular SCC.*/ + scc_iterator<T*> cur = scc_begin(bb); + while(cur!=scc_end(bb)) + { + for(typename std::vector<typename GraphTraits<T*>::NodeType*>::iterator i = (*cur).begin(); i!=(*cur).end(); i++) + if(*i==bb) +...

...: > (C <- matrix(c(NaN, NaN, 0, 0), 2L, 2L)) [,1] [,2] [1,] NaN 0 [2,] NaN 0 > det(C) [1] NaN > (D <- t(C)) [,1] [,2] [1,] NaN NaN [2,] 0 0 > det(D) [1] 0 Furthermore, the proposed change should _not_ decrease the performance of determinant(A) for nonsingular 'A' ... For those looking, the relevant C-level function is det_ge_real(), defined in R-devel/src/modules/lapack/Lapack.c (at line 1260 in r83320). Mikael [1] https://github.com/Reference-LAPACK/lapack/blob/master/SRC/dgetrf.f

Dear r-users! I have another question regarding the dlm package and I would be very happy if someone could give me a hint! I am using the dlm package to get estimates for an endogenous rate of capacity utilization over time. The general form of a state space model is (1) b_t = G * b_t-1 + w_t w_t ~ N(0,W) (2) y_t= A' * x_t + H' * b_t + v_t v_t ~ N(0,V) (Hamilton 1984: 372) The

I was looking for an R-package that would reduce matrices to row-echelon form, but Google was not my friend; any leads? If not, I wonder if the problem could be expressed in terms of constraint satisfaction...

...erse<T> > scc_end(const Inverse<T>& G) { + return scc_iterator<Inverse<T> >::end(G); +} + +/*Discover whether a graph node is part of any cycle, including a self-cycle.*/ +template<class T> +bool is_in_cycle(T* bb) +{ + /*Return true iff we are in a nonsingular SCC.*/ + scc_iterator<T*> cur = scc_begin(bb); + while(cur!=scc_end(bb)) + { + for(typename std::vector<typename GraphTraits<T*>::NodeType*>::iterator i = (*cur).begin(); i!=(*cur).end(); i++) + if(*i==bb) +...

...tor<Inverse<T> > scc_end(Inverse<T> G) { + return scc_iterator<Inverse<T> >::end(G); +} + +/*Discover whether a graph node is part of any cycle, including a self-cycle.*/ +template<class T> +bool bb_reachable(T* bb) +{ + /*Return true iff we are in a nonsingular SCC.*/ + scc_iterator<T*> cur = scc_begin(bb); + while(cur!=scc_end(bb)) + { + for(typename vector<typename GraphTraits<T*>::NodeType*>::iterator i = (*cur).begin(); i!=(*cur).end(); i++) + if(*i==bb) +...

...re-crash are stored. But I want to study cases where 90% of all the cases fail fatally; it would never get off the ground. I accept that if you know what will cause the fatal fail you can program in a test for it --- sometimes. What about this one: likely fatal error due to solve(mat,x) having nonsingular matrix. Yes, yes, check there aren't any zeros on the diagonal of the SVD ... but mine are 512x512 matrices. It isn't efficient programming to completely re-write solve (or indeed to re-write any built-in) with it's built-in fatal return changed to an error return, and it isn't...

Hi, I am trying to figure how to use dlm with constant terms (possibly time-dependent) added to both equations y_t = c_t + F_t\theta_t + v_t \theta_t = d_t + G_t\theta_{t-1} + w_t, in the way that S-PLUS Finmetrics does? Is there any straightforward way to transform the above to the default setup? Thanks, Tsvetan -------------------------------------------------------- NOTICE: If received in

...<T> G) { > + return scc_iterator<Inverse<T> >::end(G); > +} > + > +/*Discover whether a graph node is part of any cycle, including a > self-cycle.*/ > +template<class T> > +bool bb_reachable(T* bb) > +{ > + /*Return true iff we are in a nonsingular SCC.*/ > + scc_iterator<T*> cur = scc_begin(bb); > + while(cur!=scc_end(bb)) > + { > + for(typename std::vector<typename > GraphTraits<T*>::NodeType*>::iterator i = (*cur).begin(); > i!=(*cur).end(); i++) > +...

I'm rusty, but not *that* rusty here, I hope. If W (=Z*Z' in your case) is singular, it can not have inverse, which by definition also mean that nothing multiply by it will produce the identity matrix (for otherwise it would have an inverse and thus nonsingular). The definition of a generalized inverse is something like: If A is a non-null matrix, and G satisfy AGA = A, then G is called a generalized inverse of A. This is not unique, but a unique one that satisfy some additional properties is the Moore-Penrose inverse. I don't know if this is what...

Dear R-users, I couldn't find a function or some help in R-project web about the Generalized Singular Value Decomposition. In MatLab there is a simple function for this algebric issue (gsvd). Is there anything like that in R? And, if not, could you help me to apply this method in R? Thanks in advance, Giancarlo +++++ This mail has been sent through the MPI for Demographic Rese...{{dropped}}

Hi all, If presented with a singular design matrix, lm drops columns to make the design matrix non-singular. What algorithm is used to select which (and how many) column(s) to drop? Particularly, given a factor, how does lm choose levels of the factor to discard? Thanks for the help. Best, Anirban [[alternative HTML version deleted]]

Dear All Maybe the following is a stupid question. Assume I have 3 coordinate points (not limited to be in 2D or 3D space) a, b, c. It is known that these 3 points will define a plane. The problem is how to get the normal direction that is orthogonal to this plane. Is there an easy way to calculate it using the values of a, b, and c? Thanks for any point or help on this. Fred

Hello. Consider the following matrix: mp <- matrix(c(0,1/4,1/4,3/4,0,1/4,1/4,3/4,1/2),3,3,byrow=T) > mp [,1] [,2] [,3] [1,] 0.00 0.25 0.25 [2,] 0.75 0.00 0.25 [3,] 0.25 0.75 0.50 The eigenvectors of the previous matrix are 1, 0.25 and 0.25 and it is not a diagonalizable matrix. When you try to find the eigenvalues and eigenvectors with R, R responses: > eigen(mp) $values [1]

...ings") # Analysis with log data tsdata <- log(hotann) buildfun <- function (x) { dlmModPoly(order = 2, dV = exp(x[1]), dW = c(0,exp(x[2]))) } fit <- dlmMLE(y=tsdata, parm=c(0,0), build=buildfun) # Warning: a numerically singular 'V' has been slightly perturbed to make it nonsingular fit$conv dlmTsdata <- buildfun(fit$par) tsdataFilter <- dlmFilter(tsdata, mod=dlmTsdata) tsdataSmooth <- dlmSmooth(tsdata, mod=dlmTsdata) plot(tsdata, lwd=2) for (i in 1:10) lines(lty=6, col="blue", dropFirst(dlmBSample(tsdataFilter))[,1]) # looks ok! tsdataForecast <- d...

On Aug 6, 2009, at 4:19 PM, Patrick Alexander Simmons wrote: > Chris Lattner wrote: >> On Aug 4, 2009, at 3:48 PM, Patrick Alexander Simmons wrote: >> >> >>> Hi, >>> >>> I've been using scc_iterator, and I added the templates necessary to >>> make it work with inverse graphs. I also added a "bb_reachable" >>>