Cache the submodel formulas and model matrices per predictor-term set

NEWS.md

@@ -7,6 +7,12 @@ If you read this from a place other than <https://mc-stan.org/projpred/news/inde
 
 ## Major changes
 
+* Faster projections onto submodels without group-level or additive terms: the projected draws (or clusters) share one model matrix, and for the Gaussian family with the identity link, one linear solve gives the submodel fits for all draws. For example, `varsel()` with forward search for a Gaussian model with 50 observations and 200 predictor terms is about 7 times faster. (GitHub: #574)
+
+* Faster projections onto binomial and Poisson GLM submodels (and Gaussian GLM submodels with a non-identity link): the IRLS fits compute their pseudo-observations in C++, and one C++ call fits all projected draws (or clusters). For example, `cv_varsel()` with `validate_search = TRUE` for binomial and Poisson models is about 4 to 6 times faster. (GitHub: #581)
+
+* `varsel()`, `cv_varsel()` and `project()` cache the submodel formulas and model matrices per set of predictor terms, so the folds of `cv_varsel()` with `validate_search = TRUE` do not build them again. For example, `cv_varsel()` with `validate_search = TRUE` for binomial and Poisson models is about 1.3 to 1.7 times faster. (GitHub: #582)
+
 ## Minor changes
 
 ## Bug fixes and maintenance

R/RcppExports.R

@@ -9,3 +9,11 @@ glm_ridge_c <- function(x, pseudo_obs, lambda, intercept, penalty, beta_init, w_
     .Call('_projpred_glm_ridge_c', PACKAGE = 'projpred', x, pseudo_obs, lambda, intercept, penalty, beta_init, w_init, thresh, qa_updates_max, ls_iter_max, debug)
 }
 
+glm_ridge_native_c <- function(x, y, weights, offset, family_code, link_code, lambda, intercept, penalty, beta_init, w_init, thresh, qa_updates_max, ls_iter_max = 100L, debug = FALSE) {
+    .Call('_projpred_glm_ridge_native_c', PACKAGE = 'projpred', x, y, weights, offset, family_code, link_code, lambda, intercept, penalty, beta_init, w_init, thresh, qa_updates_max, ls_iter_max, debug)
+}
+
+glm_ridge_native_multi_c <- function(x, y, weights, offset, family_code, link_code, lambda, intercept, penalty, beta_init, w_init, thresh, qa_updates_max, ls_iter_max = 100L, debug = FALSE) {
+    .Call('_projpred_glm_ridge_native_multi_c', PACKAGE = 'projpred', x, y, weights, offset, family_code, link_code, lambda, intercept, penalty, beta_init, w_init, thresh, qa_updates_max, ls_iter_max, debug)
+}
+

R/cv_varsel.R

@@ -336,6 +336,10 @@ cv_varsel.refmodel <- function(
     }
     set.seed(seed)
   }
+  # Activate the cache of the projection inputs (see proj_cache_store()). This
+  # follows the `on.exit()` call above, which has no `add = TRUE`:
+  proj_cache_enter()
+  on.exit(proj_cache_exit(), add = TRUE)
 
   refmodel <- object
   nterms_all <- count_terms_in_formula(refmodel$formula) - 1L