Databases
StackOverflow2013
Postsdbo
POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
    primarykey
    data
    text
    <p>I am trying to implement the first derivative of the multivariate normal distribution in R building on the <code>rcpp</code> implementation of the multivariate normal distribution posted <a href="https://stackoverflow.com/questions/17617618/dmvnorm-mvn-density-rcpparmadillo-implementation-slower-than-r-package-includi">here</a> and <a href="http://gallery.rcpp.org/articles/dmvnorm_arma/" rel="nofollow noreferrer">here</a>.</p> <p>Here is a quick R implementation</p> <pre><code>mvnormDeriv = function(..., mu=rep(0,length(list(...))), sigma=diag(length(list(...)))) { if(sd(laply(list(...),length))!=0) stop("The vectors not same length.") fn = function(x) -1 * c((1/sqrt(det(2*pi*sigma))) * exp(-0.5*t(x-mu)%*%solve(sigma)%*%(x-mu))) * solve(sigma,(x-mu)) out = t(apply(cbind(...),1,fn)) colnames(out) = c('x', 'y') return(out[,1]) } </code></pre> <p>and some test data with benchmark:</p> <pre><code>set.seed(123456789) sigma = rWishart(1, 2, diag(2)) means = rnorm(2) X = rmvnorm(10000, means, sigma[,,1]) x1 = X[,1] x2 = X[,2] benchmark(mvnormDeriv(x1,x2,mu=means,sigma=sigma), order="relative", replications=5)[,1:4] </code></pre> <p>The formula can be found in the matrix cookbook (2012), formula 346.</p> <p>I failed to modify the <code>rcpp</code> implementation of the multivariate normal from <a href="http://gallery.rcpp.org/articles/dmvnorm_arma/" rel="nofollow noreferrer">here</a>. Here is some code, which I used to try</p> <pre><code>// [[Rcpp::export]] arma::vec dmvnormDeriv_arma(arma::mat x, SEXP mu_sexp, arma::mat sigma, bool log = false) { // create Rcpp vector and matrix from SEXP arguments Rcpp::NumericVector mu_rcpp(mu_sexp); // create views for arma objects(reuses memory and avoids extra copy) arma::vec mu_vec(mu_rcpp.begin(), mu_rcpp.size(), false); arma::rowvec mu(mu_rcpp.begin(), mu_rcpp.size(), false); // return(mu_vec); arma::vec distval = Mahalanobis(x, mu, sigma); double logdet = sum(arma::log(arma::eig_sym(sigma))); double log2pi = std::log(2.0 * M_PI); arma::vec val = exp(-( (x.n_cols * log2pi + logdet + distval)/2)); // x.each_row() -= mu; // arma::vec val2 = solve(sigma, x.row(1)); // arma::vec retval = -1 * val(1) * solve(sigma, x.row(1)-mu_vec); return(val); } </code></pre> <p>This is not complete, of course. Any ideas how I can implement the <code>* solve(sigma,(x-mu))</code> part in <code>rcpp</code> or with <code>Armadillo</code>? I have problems handling the different variables types and running the solve for each row of x.</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USCommunity
    1. USuser2503795
    plurals
    1. PL
      singulars
      1. LTLinked
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. This table or related slice is empty.
      1. VTApproveEditSuggestion
    2. VO
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. USStéphane Laurent
      1. VTFavorite
    1. COIsn't that `solve()` just a (possibly Matlab-)shorthand for `inv()`? In which case you can take it straight from the Armadillo docs. [ And we're about to update the Gallery post you referred to; keep an eye out for it. And then submit one with this :) ]
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. USDirk Eddelbuettel
    2. COThanks, I have added a solution below. I will submit something for the Gallery if that is of interest. Let me know if you have suggestions for improvements.
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. USuser2503795
    3. COSlightly OT but you mentioned using the Matrix Cookbook from 2012, can you provide a link in the question? It's quite hard to find. On-topic, it may have value in making the question a bit more self-contained. Thank you!
      singulars
      1. POfirst derivative of multivariate normal/gaussian with rcpp and RcppArmadillo
      1. USJotaf
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload