2
0
Fork 0
CVE/notes.md

369 lines
12 KiB
Markdown

# General Notes for Souce Code analysis
## Search in multiple files.
Using the Linux `grep` program with the parameters `-rnw` and specifying a include files filter like the following example.
```bash
grep --include=*\.{c,h,R} -rnw '.' -e "sweep"
```
searches in all `C` source and header fils as well as `R` source files for the term _sweep_.
## Recursive dir. compair with colored sructure (more or less).
```bash
diff -r CVE_R/ CVE_C/ | grep -E "^([<>]|[^<>].*)"
```
## Parsing `bash` script parameters.
```bash
usage="$0 [-v|--verbose] [-n|--dry-run] [(-s|--stack-size) <size>] [-h|--help] [-- [p1, [p2, ...]]]"
verbose=false
help=false
dry_run=false
stack_size=0
while [ $# -gt 0 ]; do
case "$1" in
-v | --verbose ) verbose=true; shift ;;
-n | --dry-run ) dry_run=true; shift ;;
-s | --stack-size ) stack_size="$2"; shift; shift ;;
-h | --help ) echo $usage; exit ;; # On help print usage and exit.
-- ) shift; break ;; # Break param "parsing".
* ) echo $usage >&2; exit 1 ;; # Print usage and exit with failure.
esac
done
echo verbose=$verbose
echo dry_run=$dry_run
echo stack_size=$stack_size
```
# Development
## Build and install.
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.
```R
setwd("./CVE_R") # Set path to the package root.
library(devtools) # Load required `devtools` package.
document() # Create `.Rd` files and write `NAMESPACE`.
```
Next the package needs to be build, therefore (if pure `R` package, aka. `C/C++`, `Fortran`, ... code) just do the following.
```bash
R CMD build CVE_R
R CMD INSTALL CVE_0.1.tar.gz
```
Then we are ready for using the package.
```R
library(CVE)
help(package = "CVE")
```
## Build and install from within `R`.
An alternative approach is the following.
```R
setwd('./CVE_R')
getwd()
library(devtools)
document()
# No vignettes to build but "inst/doc/" is required!
(path <- build(vignettes = FALSE))
install.packages(path, repos = NULL, type = "source")
```
**Note: I only recommend this approach during development.**
# Analysing
## Logging (a `cve` run).
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.
```R
library(CVE)
# Setup histories.
(epochs <- 50)
(attempts <- 10)
loss.history <- matrix(NA, epochs + 1, attempts)
error.history <- matrix(NA, epochs + 1, attempts)
tau.history <- matrix(NA, epochs + 1, attempts)
true.error.history <- matrix(NA, epochs + 1, attempts)
# Create a dataset
ds <- dataset("M1")
X <- ds$X
Y <- ds$Y
B <- ds$B # the true `B`
(k <- ncol(ds$B))
# True projection matrix.
P <- B %*% solve(t(B) %*% B) %*% t(B)
# Define the logger for the `cve()` method.
logger <- function(env) {
# Note the `<<-` assignement!
loss.history[env$epoch + 1, env$attempt] <<- env$loss
error.history[env$epoch + 1, env$attempt] <<- env$error
tau.history[env$epoch + 1, env$attempt] <<- env$tau
# Compute true error by comparing to the true `B`
B.est <- null(env$V) # Function provided by CVE
P.est <- B.est %*% solve(t(B.est) %*% B.est) %*% t(B.est)
true.error <- norm(P - P.est, 'F') / sqrt(2 * k)
true.error.history[env$epoch + 1, env$attempt] <<- true.error
}
# Performa SDR
dr <- cve(Y ~ X, k = k, logger = logger, epochs = epochs, attempts = attempts)
# Plot history's
par(mfrow = c(2, 2))
matplot(loss.history, type = 'l', log = 'y', xlab = 'iter',
main = 'loss', ylab = expression(L(V[iter])))
matplot(error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'error', ylab = 'error')
matplot(tau.history, type = 'l', log = 'y', xlab = 'iter',
main = 'tau', ylab = 'tau')
matplot(true.error.history, type = 'l', log = 'y', xlab = 'iter',
main = 'true error', ylab = 'true error')
```
## Reading log files.
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.
```R
# Load log as `data.frame`
log <- read.csv('tmp/test0.log', sep = '\t')
# Create a error boxplot grouped by dataset.
boxplot(error ~ dataset, log)
# Overview
for (ds.name in paste0('M', seq(5))) {
ds <- subset(log, dataset == ds.name, select = c('method', 'dataset', 'time', 'error'))
print(summary(ds))
}
```
## Environments and variable lookup.
In the following a view simple examples of how `R` searches for variables.
In addition we manipulate funciton closures to alter the search path in variable lookup and outer scope variable manipulation.
```R
droids <- "These aren't the droids you're looking for."
search <- function() {
print(droids)
}
trooper.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
search()
}
jedi.seeks <- function() {
droids <- c("R2-D2", "C-3PO")
environment(search) <- environment()
search()
}
trooper.seeks()
# [1] "These aren't the droids you're looking for."
jedi.seeks()
# [1] "R2-D2", "C-3PO"
```
The next example ilustrates how to write (without local copies) to variables outside the functions local environment.
```R
counting <- function() {
count <<- count + 1 # Note the `<<-` assignment.
}
(function() {
environment(counting) <- environment()
count <- 0
for (i in 1:10) {
counting()
}
return(count)
})()
(function () {
closure <- new.env()
environment(counting) <- closure
assign("count", 0, envir = closure)
for (i in 1:10) {
counting()
}
return(closure$count)
})()
```
Another example for the usage of `do.call` where the evaluation of parameters is illustated (example taken (and altered) from `?do.call`).
```R
## examples of where objects will be found.
A <- "A.Global"
f <- function(x) print(paste("f.new", x))
env <- new.env()
assign("A", "A.new", envir = env)
assign("f", f, envir = env)
f <- function(x) print(paste("f.Global", x))
f(A) # f.Global A.Global
do.call("f", list(A)) # f.Global A.Global
do.call("f", list(A), envir = env) # f.new A.Global
do.call(f, list(A), envir = env) # f.Global A.Global
do.call("f", list(quote(A)), envir = env) # f.new A.new
do.call(f, list(quote(A)), envir = env) # f.Global A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
do.call("f", list(as.name("A")), envir = env) # f.new A.new
```
# Performance benchmarks
In this section alternative implementations of simple algorithms are compared for there performance.
### Computing the trace of a matrix multiplication.
```R
library(microbenchmark)
A <- matrix(runif(120), 12, 10)
# Check correctnes and benckmark performance.
stopifnot(
all.equal(
sum(diag(t(A) %*% A)), sum(diag(crossprod(A, A)))
),
all.equal(
sum(diag(t(A) %*% A)), sum(A * A)
)
)
microbenchmark(
MM = sum(diag(t(A) %*% A)),
cross = sum(diag(crossprod(A, A))),
elem = sum(A * A)
)
# Unit: nanoseconds
# expr min lq mean median uq max neval
# MM 4232 4570.0 5138.81 4737 4956.0 40308 100
# cross 2523 2774.5 2974.93 2946 3114.5 5078 100
# elem 582 762.5 973.02 834 964.0 12945 100
```
```R
n <- 200
M <- matrix(runif(n^2), n, n)
dnorm2 <- function(x) exp(-0.5 * x^2) / sqrt(2 * pi)
stopifnot(
all.equal(dnorm(M), dnorm2(M))
)
microbenchmark(
dnorm = dnorm(M),
dnorm2 = dnorm2(M),
exp = exp(-0.5 * M^2) # without scaling -> irrelevant for usage
)
# Unit: microseconds
# expr min lq mean median uq max neval
# dnorm 841.503 843.811 920.7828 855.7505 912.4720 2405.587 100
# dnorm2 543.510 580.319 629.5321 597.8540 607.3795 2603.763 100
# exp 502.083 535.943 577.2884 548.3745 561.3280 2113.220 100
```
### Using `crosspord()`
```R
p <- 12
q <- 10
V <- matrix(runif(p * q), p, q)
stopifnot(
all.equal(V %*% t(V), tcrossprod(V)),
all.equal(V %*% t(V), tcrossprod(V, V))
)
microbenchmark(
V %*% t(V),
tcrossprod(V),
tcrossprod(V, V)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# V %*% t(V) 2.293 2.6335 2.94673 2.7375 2.9060 19.592 100
# tcrossprod(V) 1.148 1.2475 1.86173 1.3440 1.4650 30.688 100
# tcrossprod(V, V) 1.003 1.1575 1.28451 1.2400 1.3685 2.742 100
```
### Recycling vs. Sweep
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
stopifnot(
all.equal((X_diff %*% V) * rep(vecS, q),
sweep(X_diff %*% V, 1, vecS, `*`)),
all.equal((X_diff %*% V) * rep(vecS, q),
(X_diff %*% V) * vecS)
)
microbenchmark(
rep = (X_diff %*% V) * rep(vecS, q),
sweep = sweep(X_diff %*% V, 1, vecS, `*`, check.margin = FALSE),
recycle = (X_diff %*% V) * vecS
)
# Unit: microseconds
# expr min lq mean median uq max neval
# rep 851.723 988.3655 1575.639 1203.6385 1440.578 18999.23 100
# sweep 1313.177 1522.4010 2355.269 1879.2605 2065.399 18783.24 100
# recycle 719.001 786.1265 1157.285 881.8825 1163.202 19091.79 100
```
### Scaled `crossprod` with matmul order.
```R
(n <- 200)
(p <- 12)
(q <- 10)
X_diff <- matrix(runif(n * (n - 1) / 2 * p), n * (n - 1) / 2, p)
V <- matrix(rnorm(p * q), p, q)
vecS <- runif(n * (n - 1) / 2)
ref <- crossprod(X_diff, X_diff * vecS) %*% V
stopifnot(
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS)),
all.equal(ref, crossprod(X_diff, (X_diff %*% V) * vecS))
)
microbenchmark(
inner = crossprod(X_diff, X_diff * vecS) %*% V,
outer = crossprod(X_diff, (X_diff %*% V) * vecS)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# inner 789.065 867.939 1683.812 987.9375 1290.055 16800.265 100
# outer 1141.479 1216.929 1404.702 1317.7315 1582.800 2531.766 100
```
### Fast dist matrix computation (aka. row sum of squares).
```R
library(microbenchmark)
library(CVE)
(n <- 200)
(N <- n * (n - 1) / 2)
(p <- 12)
M <- matrix(runif(N * p), N, p)
stopifnot(
all.equal(rowSums(M^2), rowSums.c(M^2)),
all.equal(rowSums(M^2), rowSquareSums.c(M))
)
microbenchmark(
sums = rowSums(M^2),
sums.c = rowSums.c(M^2),
sqSums.c = rowSquareSums.c(M)
)
# Unit: microseconds
# expr min lq mean median uq max neval
# sums 666.311 1051.036 1612.3100 1139.0065 1547.657 13940.97 100
# sums.c 342.647 672.453 1009.9109 740.6255 1224.715 13765.90 100
# sqSums.c 115.325 142.128 175.6242 153.4645 169.678 759.87 100
```
## Using `Rprof()` for performance.
The standart method for profiling where an algorithm is spending its time is with `Rprof()`.
```R
path <- '../tmp/R.prof' # path to profiling file
Rprof(path)
cve.res <- cve.call(X, Y, k = k)
Rprof(NULL)
(prof <- summaryRprof(path)) # Summarise results
```
**Note: considure to run `gc()` before measuring**, aka cleaning up by explicitely calling the garbage collector.