2009/7/22 Maxime Boissonneault <[email protected]>: > Hello, > I am reading the documentation to do multidimensionnal minimization with > GSL. I think there is a mistake on that page : > http://www.gnu.org/software/gsl/manual/html_node/Multimin-Algorithms-without-Derivatives.html > > It says "They construct n vectors p_i from the starting vector x and the > vector step_size as follows..." According to the following, it should be > "They construct n+1 vectors p_i from the..." > > Can someone who understand the algorithm better confirm ? >
To form an n-dimensional simplex you need n+1 vectors. The initial vector is p_0. The algorithm constructs an "additional" n vectors. I agree that there is an ambiguity in the documentation. Also, the subscript to step_size (in the formulas) is a bit confusing. Usually when writing subscripts, the vector names are just a single letter. (we write x_i not zyx_i ) The improved construction could be Starting from the initial vector p_0, the algorithm constructs an additional n vectors p_i (i=1 through n) using the step size vector s as follows p_0 = (x_0, x_1, ..., x_n) p_1 = (x_0 + s_0, x_1, ..., x_n) p_2 = (x_0, x_1 + s_1, ..., x_n) ... = ... p_n = (x_0, x_1, ..., x_n + s_n) What do you guys think? If necessary, I can submit a patch for this. raju _______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
