version 2021.1

DESCRIPTION

@@ -1,6 +1,6 @@
 Package: SQUAREM
-Version: 2020.5
-Date: 2020-10-21
+Version: 2021.1
+Date: 2021-01-12
 Title: Squared Extrapolation Methods for Accelerating EM-Like Monotone
         Algorithms
 Description: Algorithms for accelerating the convergence of slow,
@@ -19,5 +19,5 @@ Maintainer: Ravi Varadhan <[email protected]>
 URL: https://coah.jhu.edu/people/Faculty_personal_Pages/Varadhan.html
 Repository: CRAN
 NeedsCompilation: no
-Packaged: 2020-10-21 20:02:12 UTC; rvaradhan
-Date/Publication: 2020-10-21 21:00:02 UTC
+Packaged: 2021-01-12 23:59:02 UTC; rvaradhan
+Date/Publication: 2021-01-13 06:40:10 UTC

MD5

@@ -1,7 +1,7 @@
-8bb2006ce2485548e5d1b9c39d88678d *DESCRIPTION
+f650729f3c5ac0de565ad6d1874de336 *DESCRIPTION
 a62319b6c4374fd15963266db928a1fc *NAMESPACE
-fbff7916cf82707eab9bd5350b9503c2 *NEWS
-4ead5ae1cb6525899c0cb75b1e0e7339 *R/squarem.R
+481ab651d51595187da4c07ffac78abe *NEWS
+1d24cb6e023eb43df0368d8cbc49354f *R/squarem.R
 2ce900a9bc6751f7beb84b79942bbac3 *build/vignette.rds
 4eb525977b2cd840efcd384cada97dff *demo/00Index
 99297f5664d508013f345afcecf8d90c *demo/factoranalysis.R
@@ -13,8 +13,10 @@ ac216a9a91116475a6b28b933f34e2b4 *inst/CITATION
 4df21965b20b54fd14215afe50bff3e4 *inst/doc/SQUAREM.R
 8baa991f5faaaabb04be226d2aac8db0 *inst/doc/SQUAREM.Rnw
 87ec2678b267ecd99d38567c6937cd25 *inst/doc/SQUAREM.pdf
-028e8abac54c45e3d66ff7d5a54e5ca7 *man/fpiter.Rd
+5e1af6c79774307501a7e4e864ad1f5c *man/fpiter.Rd
 dc86f820449b08ca2a684572e599dd55 *man/internal.Rd
-1734baa4947c57dc975c3456d325435c *man/squarem.Rd
+f894e4e0dc269079cfacf0fe1703b423 *man/squarem.Rd
 1f6e68e9322bd524f4db846a970670f0 *tests/Hasselblad1969.R
 8baa991f5faaaabb04be226d2aac8db0 *vignettes/SQUAREM.Rnw
+50fb1d088187a510f7156630ee9d0a3e *vignettes/SQUAREM.pdf
+29124e75e51c284de8359c8c9cec6bbd *vignettes/SQUAREM.tex

NEWS

@@ -29,9 +29,15 @@ Log of changes to SQUAREM
 	- Modified the code to output updated parameters from EM algorithm immediately before breaking for convergence
 
   o   	August 19, 2020
-	- Fixed a couple of lines in squarem2() to output updated parameters from EM algorithm immediately before breaking for convergence - thanks to Dan Schaid (Mayo) for pointing this out
+	- Fixed a couple of lines in squarem2() to output updated parameters from EM algorithm 
+	immediately before breaking for convergence - thanks to Dan Schaid (Mayo) for pointing this out
 
 	o   October 21, 2020
 	- Added the option to either "minimize"" or "maximize" the objective function
 	- Control parameter `minimize' can be set to TRUE (for minimization) or FALSE (for maximization)
 
+	o   January 12, 2021
+	- Added the option to output the residuals when objective funcion is NOT given
+	- also added this option to `fpiter'
+	- In order to use this option, the user has to set `intermed=TRUE'
+	- this option is not available for higher-order squarem algorithms 

R/squarem.R

@@ -175,7 +175,7 @@ while (feval < maxiter) {
 
 rownames(p.inter) <- NULL
 if (!intermed) return(list(par=p, value.objfn=lold, iter= iter, fpevals=feval, objfevals = leval, convergence=conv))
-   else return(list(par=p, value.objfn=lold, iter= iter, fpevals=feval, objfevals = leval, convergence=conv, p.inter=p.inter))
+   else return(list(par=p, value.objfn=lold, iter= iter, fpevals=feval, objfevals = leval, convergence=conv, p.intermed=p.inter))
 }
 ###################################################################
 squarem2 <- function(par, fixptfn, ... , control=list() ) {
@@ -214,11 +214,13 @@ ctrl <- modifyList(control.default, control)
     mstep <- ctrl$mstep
     trace <- ctrl$trace
 if (trace) cat("Squarem-2 \n")
-
+    intermed <- ctrl$intermed
+
 iter <- 1
 feval <- 0
 kount <- 0
 conv <- TRUE
+p.inter <- rep(NA, length(par)+1)
 
 while (feval < maxiter) {
 	extrap <- TRUE
@@ -227,6 +229,7 @@ while (feval < maxiter) {
 	if (inherits(p1, "try-error") | any(is.nan(unlist(p1)))) break
 	q1 <- p1 - par
 	sr2 <- crossprod(q1)
+	p.inter <- rbind(p.inter, c(par, sqrt(sr2)))
 	if (sqrt(sr2) < tol) {par <- p1; break}
 
 	p2 <- try(fixptfn(p1, ...),silent=TRUE)
@@ -273,9 +276,12 @@ while (feval < maxiter) {
 	par <- p.new
 	iter <- iter+1
 }
-	if (feval >= maxiter) conv <- FALSE
+p.inter <- p.inter[-1, ]
+if (feval >= maxiter) conv <- FALSE
 
-return(list(par=par, value.objfn=NA, iter = iter, fpevals=feval, objfevals = 0, convergence=conv))
+if (intermed) return(list(par=par, value.objfn=NA, iter = iter, fpevals=feval, objfevals = 0, 
+                          convergence=conv, p.intermed=p.inter))
+else return(list(par=par, value.objfn=NA, iter = iter, fpevals=feval, objfevals = 0, convergence=conv))
 
 }
 #######################################################################
@@ -564,7 +570,7 @@ return(list(par=par, value.objfn=NA, iter = iter, fpevals=feval, objfevals = 0,
 #
 fpiter <- function(par, fixptfn, objfn=NULL, control=list( ), ...){
 
-control.default <- list(tol=1.e-07, maxiter=5000, trace=FALSE)
+control.default <- list(tol=1.e-07, maxiter=5000, trace=FALSE, intermed=FALSE)
 namc <- names(control)
 if (!all(namc %in% names(control.default))) 
     stop("unknown names in control: ", namc[!(namc %in% names(control.default))])
@@ -578,18 +584,22 @@ ctrl <- modifyList(control.default, control)
     tol <- ctrl$tol
     maxiter <- ctrl$maxiter
     trace <- ctrl$trace
-
+    intermed <- ctrl$intermed
+
 if (trace) cat("fpiter \n")
 
 iter <- 1
 resid <- rep(NA,1)
 objeval <- 0
 conv <- FALSE
 
+if(intermed) p.inter <- rep(NA, 1+length(par))
+
 while (iter < maxiter) {
 
 p.new <- fixptfn(par, ...)
 res <- sqrt(crossprod(p.new - par))
+if(intermed) p.inter <- rbind(p.inter, c(par, res))
 
 if ( res < tol) {conv <- TRUE; break}
 
@@ -600,10 +610,13 @@ if (trace) {
   par <- p.new
 iter <- iter+1
 }
-
+if(intermed) p.inter <- p.inter[-1,]
 loglik.best <-  if (!is.null(objfn)) objfn(par, ...) else NA
 
-return(list(par=par, value.objfn=loglik.best, fpevals=iter, objfevals = objeval, convergence=conv))
+if(!intermed) return(list(par=par, value.objfn=loglik.best, fpevals=iter, objfevals = objeval, 
+            convergence=conv))
+else return(list(par=par, value.objfn=loglik.best, fpevals=iter, objfevals = objeval, 
+                         p.intermed=p.inter, convergence=conv))
 }
 
 ###################################################################

man/fpiter.Rd

@@ -50,21 +50,25 @@
 \code{control} is list of control parameters for the algorithm.  
 
 \describe{
-\code{control = list(tol = 1.e-07, maxiter = 1500, trace = FALSE)}
+\code{control = list(tol = 1.e-07, maxiter = 1500, trace = FALSE, intermed=FALSE)}
 
-    \code{tol}{  A small, positive scalar that determines when iterations 
+    \code{tol}{ - a small, positive scalar that determines when iterations 
        should be terminated.  Iteration is terminated when 
        \eqn{||x_k - F(x_k)|| \leq tol}{abs(x[k] - F(x[k]) <= tol}.  
        Default is \code{1.e-07}.}
 
-    \code{maxiter}{  An integer denoting the maximum limit on the number of 
+    \code{maxiter}{ - an integer denoting the maximum limit on the number of 
        evaluations of  \code{fixptfn}, \eqn{F}{F}.  Default is \code{1500}.}
 
-    \code{trace}{  A logical variable denoting whether some of the intermediate 
+    \code{trace}{ - a logical variable denoting whether some of the intermediate 
        results of iterations should be displayed to the user.  
        Default is \code{FALSE}.} 
+
+    \code{intermed}}{ - a logical variable denoting whether the intermediate 
+      results of iterations should be returned. If set to \code{TRUE}, the function 
+      will return a matrix where each row corresponds to parameters at each iteration, 
+      along with the corresponding fixed-point residual value. Default is \code{FALSE}.}
   }
-}
 
 \seealso{
   \code{\link{squarem}}
@@ -101,7 +105,7 @@ poissmix.dat <- data.frame(death=0:9, freq=c(162,267,271,185,111,61,27,8,3,1))
 y <- poissmix.dat$freq
 tol <- 1.e-08
 
-# Use a preset seed so the example is reproducable. 
+# Use a preset seed so the example is reproducible. 
 require("setRNG")
 old.seed <- setRNG(list(kind="Mersenne-Twister", normal.kind="Inversion",
     seed=54321))

man/squarem.Rd

@@ -47,7 +47,7 @@ Fixed-Point Iterations}
   indicates successful convergence, whereas \code{1} denotes failure to 
   converge.}
 
-\item{p.inter}{A matrix where each row corresponds to parameters at each iteration, 
+\item{p.intermed}{A matrix where each row corresponds to parameters at each iteration, 
       along with the corresponding log-likelihood value. This object is returned only when 
       the control parameter \code{intermed} is set to \code{TRUE}.  It is not returned when 
       \code{objfn} is not specified.}
@@ -129,10 +129,9 @@ Default values of \code{control} are:
       results of iterations should be displayed to the user.  
       Default is \code{FALSE}.}
 \item{\code{intermed}}{A logical variable denoting whether the intermediate 
-      results of iterations should be returned. If set to \code{TRUE}, the function 
+      results of iterat ions should be returned. If set to \code{TRUE}, the function 
       will return a matrix where each row corresponds to parameters at each iteration, 
-      along with the corresponding log-likelihood value.  This option is inactive when 
-      \code{objfn} is not specified. 
+      along with the corresponding log-likelihood value.  When the code{objfn} is not specified it will return the fixed-point residual instead of the objective function values. 
       Default is \code{FALSE}.}
 }
 }

vignettes/SQUAREM.tex

@@ -0,0 +1,55 @@
+\documentclass[12pt]{article}
+
+\usepackage[margin=1in]{geometry}
+\usepackage{amsmath, amssymb, amsfonts}
+%\usepackage{natbib}
+\usepackage{graphicx}
+\usepackage{color} %% red, green, and blue (for screen display) and cyan, magenta, and yellow
+\definecolor{Navy}{rgb}{0,0,0.8}
+\usepackage{hyperref}
+\hypersetup{colorlinks=true, urlcolor={Navy}, linkcolor={Navy}, citecolor={Navy}}
+
+\parskip 7.2pt
+
+\newcommand{\compresslist}{%
+%\setlength{\itemsep}{1pt}%
+\setlength{\itemsep}{0pt}%
+\setlength{\parskip}{0pt}%
+\setlength{\parsep}{0pt}%
+}
+
+\newcommand{\pb}{\mathbb{P}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\V}{\mathbb{V}}
+\newcommand{\C}{\mathbb{C}}
+\newcommand{\bea}{\begin{align*}}
+\newcommand{\eea}{\end{align*}}
+\newcommand{\beq}{\begin{equation}}
+\newcommand{\eeq}{\end{equation}}
+\newcommand{\be}{\begin{enumerate}}
+\newcommand{\ee}{\end{enumerate}}
+\newcommand{\bi}{\begin{itemize}}
+\newcommand{\ei}{\end{itemize}}
+\renewcommand{\baselinestretch}{1}
+
+\title{\texttt{SQUAREM}: Accelerating the Convergence of EM, MM and Other Fixed-Point Algorithms}
+\author{Ravi Varadhan}
+\date{}
+\usepackage{Sweave}
+\begin{document}
+
+%\VignetteIndexEntry{SQUAREM Tutorial}
+%\VignetteDepends{setRNG}
+%\VignetteKeywords{EM algorithm, fixed-point iteration, acceleration, extrapolation}
+%\VignettePackage{SQUAREM}
+
+\maketitle
+
+\section{Overview of SQUAREM}
+''SQUAREM'' is a package intended for accelerating slowly-convergent contraction mappings.  It can be used for accelerating the convergence of slow, linearly convergent contraction mappings such as the EM (expectation-maximization) algorithm, MM (majorize and minimize) algorithm, and other nonlinear fixed-point iterations such as the power method for finding the dominant eigenvector.  It uses a novel approach callled squared extrapolation method (SQUAREM) that was proposed in Varadhan and Roland (Scandinavian Journal of Statistics, 35: 335-353), and also in Roland, Vardhan, and Frangakis (Numerical Algorithms, 44: 159-172).
+
+The functions in this package are made available with:
+
+\begin{Schunk}
+\begin{Sinput}
+> library("SQUAREM")