Correction. Yes, it's the projection of S onto the subspace orthogonal to B which is:
X <- S - (B%o%B) %*% S/ sum(B*B) and is also implied by Duncan's solution since that is what the residuals of linear regression are. On Tue, Oct 20, 2015 at 1:11 PM, Gabor Grothendieck <ggrothendi...@gmail.com > wrote: > Yes, it's the projection of S onto the subspace orthogonal to B which is: > > X <- S - B%*%B / sum(B*B) > > and is also implied by Duncan's solution since that is what the residuals > of linear regression are. > > On Tue, Oct 20, 2015 at 1:00 PM, Paul Smith <phh...@gmail.com> wrote: > >> On Tue, Oct 20, 2015 at 11:58 AM, Andy Yuan <yuan...@gmail.com> wrote: >> > >> > Please could you help me to select the most appropriate/fastest >> function to use for the following constraint optimisation issue? >> > >> > Objective function: >> > >> > Min: Sum( (X[i] - S[i] )^2) >> > >> > Subject to constraint : >> > >> > Sum (B[i] x X[i]) =0 >> > >> > where i=1…n and S[i] and B[i] are real numbers >> > >> > Need to solve for X >> > >> > Example: >> > >> > Assume n=3 >> > >> > S <- c(-0.5, 7.8, 2.3) >> > B <- c(0.42, 1.12, 0.78) >> > >> > Many thanks >> >> I believe you can solve *analytically* your optimization problem, with >> the Lagrange multipliers method, Andy. By doing so, you can derive >> clean and closed-form expression for the optimal solution. >> >> Paul >> >> ______________________________________________ >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. >> > > > > -- > Statistics & Software Consulting > GKX Group, GKX Associates Inc. > tel: 1-877-GKX-GROUP > email: ggrothendieck at gmail.com > -- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.