Lab 9.qmd

---
title: "Lab 9"
author: "Dana Gonzalez"
format: html
editor: visual
embed-resources: true
theme: cosmo
---

# Load Libraries

```{r, message=FALSE, results='hide'}
library(microbenchmark)
library(dplyr)
library(tidyverse)
library(parallel)
```

# Problem 1

```{r, message=FALSE, warning = FALSE}
# Check Number of Cores
parallel::detectCores()

# "Slow" Version
fun1 <- function(n = 100, k = 4, lambda = 4) {
  x <- NULL
  for (i in 1:n){
  x <- rbind(x, rpois(k, lambda))}
  return(x)}

# "Fast" Version
fun1alt <- function(n = 100, k = 4, lambda = 4) {
x <- matrix(rpois(n * k, lambda), nrow = n, ncol = k)
return(x)}

# Check Dimensions of "fun1" and "fun1alt"
dim(fun1())
dim(fun1alt())

# Check Distribution of Values of "fun1" and "fun1alt"
summary(fun1())
summary(fun1alt())

# Checking Speeds of "fun1" and "fun1alt"
microbenchmark::microbenchmark(
  fun1(),
  fun1alt())
```

# Problem 2

```{r, message=FALSE, warning = FALSE}
# Data Generating Process (10 x 10,000 matrix)
set.seed(1234)
x <- matrix(rnorm(1e4), nrow=10)

# Find Each Column's Max Value
fun2 <- function(x) {
  apply(x, 2, max)}

fun2alt <- function(x) {
  apply(x, 2, max)}

max.col(fun2(x))
max.col(fun2alt(x))

# Check Outputs of "fun2" and "fun2alt"
results_fun2 <- fun2(x)
results_fun2alt <- fun2alt(x)
identical(results_fun2, results_fun2alt)

# Checking Speeds of "fun2" and "fun2alt"
microbenchmark::microbenchmark(
  fun1(),
  fun1alt())
```

# Problem 3

```{r, message=FALSE, warning = FALSE}
my_boot <- function(dat, stat, R, ncpus = 1L) {

# Getting the Random Indices
n <- nrow(dat)
idx <- matrix(sample.int(n, n * R, TRUE), nrow = n, ncol = R)
  
# Parallelization
ans <- mclapply(seq_len(R), function(i) {
  result <- stat(dat[idx[, i], , drop = FALSE])
  return(result)
}, mc.cores = ncpus)

# Converting the List Into a Matrix
ans <- do.call(rbind, ans)
return(ans)
}

# Check Results by Comparing to a Parametric Model
my_stat <- function(d) {
  coef(lm(y ~ x, data = d))
}

set.seed(1)
n <- 500; R <- 1e4
x <- cbind(rnorm(n))
y <- x*5 + rnorm(n)

ans0 <- confint(lm(y~x))
ans1 <- my_boot(dat = data.frame(x, y), stat = my_stat, R = R, ncpus = 2L)

t(apply(ans1, 2, quantile, c(.025,.975)))
t(apply(ans0, 2, quantile, c(.025,.975)))

# Checking Speed
system.time(my_boot(dat = data.frame(x, y), stat = my_stat, R = R, ncpus = 1L))
system.time(my_boot(dat = data.frame(x, y), stat = my_stat, R = R, ncpus = 2L))
```