We are preparing an upgrade of the homals package on CRAN. The current non-packaged version of the code, with theory and examples, is at http://rpubs.com/deleeuw/87298. The new version implements principal component analysis, (multiset) canonical correlation analysis, multiple regression analysis, canonical discriminant analysis. multiple correspondence analysis, all with spline/polynomial x monotone/non-monotone x single/multiple optimal transformations of the variables. The article has a link to a small repository with html, pdf, Rmd versions and with R code, C code, and bib file. The iterative algorithm is now quite different from the original Gifi algorithm. It uses majorization to simplify the update steps and to make the problem embarrassingly parellel.