R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("adapt-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('adapt')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "adapt"
> 
> ### * adapt
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: adapt
> ### Title: Adaptive Numerical Integration in 2-20 Dimensions
> ### Aliases: adapt print.integration
> ### Keywords: math utilities
> 
> ### ** Examples
> 
> ## Example of  p - dimensional spherical normal distribution:
> ir2pi <- 1/sqrt(2*pi)
> fred <- function(z) { ir2pi^length(z) * exp(-0.5 * sum(z * z))}
> 
> adapt(2, lo = c(-5,-5), up = c(5,5), functn = fred)
       value       relerr       minpts       lenwrk        ifail 
    1.039222 0.0007911264          231           73            0 
> adapt(2, lo = c(-5,-5), up = c(5,5), functn = fred, eps = 1e-4)
       value       relerr       minpts       lenwrk        ifail 
    1.000237 1.653498e-05          655          143            0 
> adapt(2, lo = c(-5,-5), up = c(5,5), functn = fred, eps = 1e-6)
      value      relerr      minpts      lenwrk       ifail 
   1.000039 3.22439e-07        1719         283           0 
> ## adapt "sees" function ~= constantly 0 --> wrong result
> adapt(2, lo = c(-9,-9), up = c(9,9), functn = fred)
      value      relerr      minpts      lenwrk       ifail 
    1.14355 0.004778851         427          73           0 
> ## fix by using much finer initial grid:
> adapt(2, lo = c(-9,-9), up = c(9,9), functn = fred, min = 1000)
       value       relerr       minpts       lenwrk        ifail 
    1.003012 0.0004258552         1021          283            0 
> adapt(2, lo = c(-9,-9), up = c(9,9), functn = fred, min = 1000, eps = 1e-6)
       value       relerr       minpts       lenwrk        ifail 
    1.000017 8.541229e-07         2713          563            0 
> 
> i1 <- print(integrate(dnorm, -2, 2))$value
0.9544997 with absolute error < 1.8e-11
> 
> ## True values for the following example:
> i1 ^ c(3,5)
[1] 0.8696158 0.7922807
> 
> for(p in c(3,5)) {
+   cat("\np = ", p, "\n------\n")
+   f.lo <- rep(-2., p)
+   f.up <- rep(+2., p)
+   ## not enough evaluations:
+   print(adapt(p, lo=f.lo, up=f.up, max=100*p, functn = fred))
+   ## enough evaluations:
+   print(adapt(p, lo=f.lo, up=f.up, max=10^p,  functn = fred))
+   ## no upper limit; p=3: 7465 points, ie 5 attempts (on an Athlon/gcc/g77):
+   print(adapt(p, lo=f.lo, up=f.up, functn = fred, eps = 1e-5))
+ }

p =  3 
------
Warning in adapt(p, lo = f.lo, up = f.up, max = 100 * p, functn = fred) : 
	 Ifail=1, maxpts was too small. Check the returned relerr!
                                                    value 
                                                0.8694218 
                                                   relerr 
                                               0.01110889 
                                                   minpts 
                                                      357 
                                                   lenwrk 
                                                       34 
                                                    ifail 
                                                        1 
                                                     warn 
Ifail=1, maxpts was too small. Check the returned relerr! 
       value       relerr       minpts       lenwrk        ifail 
   0.8691975 2.579554e-05          561          104            0 
       value       relerr       minpts       lenwrk        ifail 
   0.8696156 1.902827e-06         7465          804            0 

p =  5 
------
Warning in adapt(p, lo = f.lo, up = f.up, max = 100 * p, functn = fred) : 
	 Ifail=1, maxpts was too small. Check the returned relerr!
                                                    value 
                                               -0.9022304 
                                                   relerr 
                                                        1 
                                                   minpts 
                                                      251 
                                                   lenwrk 
                                                       35 
                                                    ifail 
                                                        1 
                                                     warn 
Ifail=1, maxpts was too small. Check the returned relerr! 
      value      relerr      minpts      lenwrk       ifail 
  0.7967753 0.006314478        7597        5758           0 
       value       relerr       minpts       lenwrk        ifail 
    0.792253 9.562748e-06        45017         3687            0 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  2.11 0.01 2.13 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')