340 lines
11 KiB
Markdown
340 lines
11 KiB
Markdown
# General Notes for Souce Code analysis
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## Search in multiple files.
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Using the Linux `grep` program with the parameters `-rnw` and specifying a include files filter like the following example.
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```bash
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grep --include=*\.{c,h,R} -rnw '.' -e "sweep"
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```
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searches in all `C` source and header fils as well as `R` source files for the term _sweep_.
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# Development
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## Build and install.
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To build the package the `devtools` package is used. This also provides `roxygen2` which is used for documentation and authomatic creaton of the `NAMESPACE` file.
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```R
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setwd("./CVE_R") # Set path to the package root.
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library(devtools) # Load required `devtools` package.
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document() # Create `.Rd` files and write `NAMESPACE`.
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```
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Next the package needs to be build, therefore (if pure `R` package, aka. `C/C++`, `Fortran`, ... code) just do the following.
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```bash
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R CMD build CVE_R
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R CMD INSTALL CVE_0.1.tar.gz
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```
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Then we are ready for using the package.
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```R
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library(CVE)
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help(package = "CVE")
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```
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## Build and install from within `R`.
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An alternative approach is the following.
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```R
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setwd('./CVE_R')
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getwd()
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library(devtools)
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document()
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# No vignettes to build but "inst/doc/" is required!
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(path <- build(vignettes = FALSE))
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install.packages(path, repos = NULL, type = "source")
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```
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**Note: I only recommend this approach during development.**
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# Analysing
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## Logging (a `cve` run).
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To log `loss`, `error` (estimated) the true error (error of current estimated `B` against the true `B`) or even the stepsize one can use the `logger` parameter. A `logger` is a function that gets the current `environment` of the CVE optimization methods (__do not alter this environment, only read from it__). This can be used to create logs like in the following example.
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```R
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library(CVE)
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# Setup histories.
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(epochs <- 50)
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(attempts <- 10)
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loss.history <- matrix(NA, epochs + 1, attempts)
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error.history <- matrix(NA, epochs + 1, attempts)
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tau.history <- matrix(NA, epochs + 1, attempts)
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true.error.history <- matrix(NA, epochs + 1, attempts)
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# Create a dataset
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ds <- dataset("M1")
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X <- ds$X
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Y <- ds$Y
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B <- ds$B # the true `B`
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(k <- ncol(ds$B))
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# True projection matrix.
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P <- B %*% solve(t(B) %*% B) %*% t(B)
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# Define the logger for the `cve()` method.
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logger <- function(env) {
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# Note the `<<-` assignement!
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loss.history[env$epoch + 1, env$attempt] <<- env$loss
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error.history[env$epoch + 1, env$attempt] <<- env$error
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tau.history[env$epoch + 1, env$attempt] <<- env$tau
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# Compute true error by comparing to the true `B`
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B.est <- null(env$V) # Function provided by CVE
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P.est <- B.est %*% solve(t(B.est) %*% B.est) %*% t(B.est)
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true.error <- norm(P - P.est, 'F') / sqrt(2 * k)
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true.error.history[env$epoch + 1, env$attempt] <<- true.error
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}
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# Performa SDR
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dr <- cve(Y ~ X, k = k, logger = logger, epochs = epochs, attempts = attempts)
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# Plot history's
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par(mfrow = c(2, 2))
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matplot(loss.history, type = 'l', log = 'y', xlab = 'iter',
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main = 'loss', ylab = expression(L(V[iter])))
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matplot(error.history, type = 'l', log = 'y', xlab = 'iter',
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main = 'error', ylab = 'error')
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matplot(tau.history, type = 'l', log = 'y', xlab = 'iter',
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main = 'tau', ylab = 'tau')
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matplot(true.error.history, type = 'l', log = 'y', xlab = 'iter',
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main = 'true error', ylab = 'true error')
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```
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## Reading log files.
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The runtime tests (upcomming further tests) are creating log files saved in `tmp/`. These log files are `CSV` files (actualy `TSV`) with a header storing the test results. Depending on the test the files may contain differnt data. As an example we use the runtime test logs which store in each line the `dataset`, the used `method` as well as the `error` (actual error of estimated `B` against real `B`) and the `time`. For reading and analysing the data see the following example.
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```R
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# Load log as `data.frame`
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log <- read.csv('tmp/test0.log', sep = '\t')
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# Create a error boxplot grouped by dataset.
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boxplot(error ~ dataset, log)
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# Overview
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for (ds.name in paste0('M', seq(5))) {
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ds <- subset(log, dataset == ds.name, select = c('method', 'dataset', 'time', 'error'))
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print(summary(ds))
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}
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```
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## Environments and variable lookup.
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In the following a view simple examples of how `R` searches for variables.
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In addition we manipulate funciton closures to alter the search path in variable lookup and outer scope variable manipulation.
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```R
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droids <- "These aren't the droids you're looking for."
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search <- function() {
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print(droids)
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}
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trooper.seeks <- function() {
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droids <- c("R2-D2", "C-3PO")
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search()
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}
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jedi.seeks <- function() {
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droids <- c("R2-D2", "C-3PO")
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environment(search) <- environment()
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search()
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}
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trooper.seeks()
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# [1] "These aren't the droids you're looking for."
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jedi.seeks()
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# [1] "R2-D2", "C-3PO"
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```
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The next example ilustrates how to write (without local copies) to variables outside the functions local environment.
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```R
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counting <- function() {
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count <<- count + 1 # Note the `<<-` assignment.
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}
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(function() {
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environment(counting) <- environment()
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count <- 0
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for (i in 1:10) {
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counting()
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}
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return(count)
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})()
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(function () {
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closure <- new.env()
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environment(counting) <- closure
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assign("count", 0, envir = closure)
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for (i in 1:10) {
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counting()
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}
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return(closure$count)
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})()
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```
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Another example for the usage of `do.call` where the evaluation of parameters is illustated (example taken (and altered) from `?do.call`).
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```R
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## examples of where objects will be found.
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A <- "A.Global"
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f <- function(x) print(paste("f.new", x))
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env <- new.env()
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assign("A", "A.new", envir = env)
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assign("f", f, envir = env)
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f <- function(x) print(paste("f.Global", x))
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f(A) # f.Global A.Global
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do.call("f", list(A)) # f.Global A.Global
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do.call("f", list(A), envir = env) # f.new A.Global
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do.call(f, list(A), envir = env) # f.Global A.Global
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do.call("f", list(quote(A)), envir = env) # f.new A.new
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do.call(f, list(quote(A)), envir = env) # f.Global A.new
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do.call("f", list(as.name("A")), envir = env) # f.new A.new
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do.call("f", list(as.name("A")), envir = env) # f.new A.new
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```
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# Performance benchmarks
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In this section alternative implementations of simple algorithms are compared for there performance.
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### Computing the trace of a matrix multiplication.
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```R
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library(microbenchmark)
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A <- matrix(runif(120), 12, 10)
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# Check correctnes and benckmark performance.
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stopifnot(
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all.equal(
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sum(diag(t(A) %*% A)), sum(diag(crossprod(A, A)))
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),
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all.equal(
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sum(diag(t(A) %*% A)), sum(A * A)
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)
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)
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microbenchmark(
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MM = sum(diag(t(A) %*% A)),
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cross = sum(diag(crossprod(A, A))),
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elem = sum(A * A)
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)
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# Unit: nanoseconds
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# expr min lq mean median uq max neval
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# MM 4232 4570.0 5138.81 4737 4956.0 40308 100
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# cross 2523 2774.5 2974.93 2946 3114.5 5078 100
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# elem 582 762.5 973.02 834 964.0 12945 100
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```
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```R
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n <- 200
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M <- matrix(runif(n^2), n, n)
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dnorm2 <- function(x) exp(-0.5 * x^2) / sqrt(2 * pi)
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stopifnot(
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all.equal(dnorm(M), dnorm2(M))
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)
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microbenchmark(
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dnorm = dnorm(M),
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dnorm2 = dnorm2(M),
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exp = exp(-0.5 * M^2) # without scaling -> irrelevant for usage
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)
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# Unit: microseconds
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# expr min lq mean median uq max neval
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# dnorm 841.503 843.811 920.7828 855.7505 912.4720 2405.587 100
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# dnorm2 543.510 580.319 629.5321 597.8540 607.3795 2603.763 100
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# exp 502.083 535.943 577.2884 548.3745 561.3280 2113.220 100
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```
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### Using `crosspord()`
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```R
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p <- 12
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q <- 10
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V <- matrix(runif(p * q), p, q)
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stopifnot(
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all.equal(V %*% t(V), tcrossprod(V)),
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all.equal(V %*% t(V), tcrossprod(V, V))
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)
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microbenchmark(
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V %*% t(V),
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tcrossprod(V),
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tcrossprod(V, V)
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)
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# Unit: microseconds
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# expr min lq mean median uq max neval
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# V %*% t(V) 2.293 2.6335 2.94673 2.7375 2.9060 19.592 100
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# tcrossprod(V) 1.148 1.2475 1.86173 1.3440 1.4650 30.688 100
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# tcrossprod(V, V) 1.003 1.1575 1.28451 1.2400 1.3685 2.742 100
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```
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### Recycling vs. Sweep
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```R
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(n <- 200)
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(p <- 12)
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(q <- 10)
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X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
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V <- matrix(rnorm(p * q), p, q)
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vecS <- runif(n * (n - 1) / 2)
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stopifnot(
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all.equal((X_diff %*% V) * rep(vecS, q),
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sweep(X_diff %*% V, 1, vecS, `*`)),
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all.equal((X_diff %*% V) * rep(vecS, q),
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(X_diff %*% V) * vecS)
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)
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microbenchmark(
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rep = (X_diff %*% V) * rep(vecS, q),
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sweep = sweep(X_diff %*% V, 1, vecS, `*`, check.margin = FALSE),
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recycle = (X_diff %*% V) * vecS
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)
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# Unit: microseconds
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# expr min lq mean median uq max neval
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# rep 851.723 988.3655 1575.639 1203.6385 1440.578 18999.23 100
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# sweep 1313.177 1522.4010 2355.269 1879.2605 2065.399 18783.24 100
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# recycle 719.001 786.1265 1157.285 881.8825 1163.202 19091.79 100
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```
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### Scaled `crossprod` with matmul order.
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```R
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(n <- 200)
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(p <- 12)
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(q <- 10)
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X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
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V <- matrix(rnorm(p * q), p, q)
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vecS <- runif(n * (n - 1) / 2)
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ref <- crossprod(X_diff, X_diff * vecS) %*% V
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stopifnot(
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all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS)),
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all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS))
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)
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microbenchmark(
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inner = crossprod(X_diff, X_diff * vecS) %*% V,
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outer = crossprod(X_diff, (X_diff %*% V) * vecS)
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)
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# Unit: microseconds
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# expr min lq mean median uq max neval
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# inner 789.065 867.939 1683.812 987.9375 1290.055 16800.265 100
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# outer 1141.479 1216.929 1404.702 1317.7315 1582.800 2531.766 100
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```
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### Fast dist matrix computation (aka. row sum of squares).
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```R
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library(microbenchmark)
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library(CVE)
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(n <- 200)
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(N <- n * (n - 1) / 2)
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(p <- 12)
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M <- matrix(runif(N * p), N, p)
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stopifnot(
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all.equal(rowSums(M^2), rowSums.c(M^2)),
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all.equal(rowSums(M^2), rowSquareSums.c(M))
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)
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microbenchmark(
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sums = rowSums(M^2),
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sums.c = rowSums.c(M^2),
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sqSums.c = rowSquareSums.c(M)
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)
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# Unit: microseconds
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# expr min lq mean median uq max neval
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# sums 666.311 1051.036 1612.3100 1139.0065 1547.657 13940.97 100
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# sums.c 342.647 672.453 1009.9109 740.6255 1224.715 13765.90 100
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# sqSums.c 115.325 142.128 175.6242 153.4645 169.678 759.87 100
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```
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## Using `Rprof()` for performance.
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The standart method for profiling where an algorithm is spending its time is with `Rprof()`.
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```R
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path <- '../tmp/R.prof' # path to profiling file
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Rprof(path)
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cve.res <- cve.call(X, Y, k = k)
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Rprof(NULL)
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(prof <- summaryRprof(path)) # Summarise results
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```
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**Note: considure to run `gc()` before measuring**, aka cleaning up by explicitely calling the garbage collector.
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