CS_11_ParallelProcessing.Rmd

---
title: "Parallel Computing with R"
subtitle: Write a parallel for loop
week: 11
type: Case Study
reading:
  - CRAN [Task View: High-Performance and Parallel Computing with R](http://cran.r-project.org/web/views/HighPerformanceComputing.html)
  - Parallel [Computing with the R Language in a Supercomputing Environment](https://link.springer.com/chapter/10.1007/978-3-642-13872-0_64)
tasks:
   - Write parallel for loops to speed up computation time.
---

```{r setup, include=FALSE, purl=F}
source("functions.R")
source("knitr_header.R")
```

# Reading

```{r reading,results='asis',echo=F,purl=F}
md_bullet(rmarkdown::metadata$reading)
```


# Tasks

```{r tasks,results='asis',echo=F, purl=F}
md_bullet(rmarkdown::metadata$tasks)
```

## Background

```{r cache=F, message=F,warning=FALSE}
library(tidyverse)

## New Packages
library(foreach)
library(doParallel)
```


Write a `foreach()` loop that:

* generates 10 sets of 100 random values from a normal distribution (`rnorm()`)
* column-binds (`cbind`) them.  

```{r, purl=F}
nset=100
n=10000

x <- foreach(i=1:nset,.combine='cbind') %do% 
  rnorm(n)

mean(x)
head(x)%>%kable()
dim(x)
```


### Sampling from a dataset with `sample_n()`

```{r}
size=5
sample_n(data,size,replace=T)
```

## Your turn
* Generate some random as follows:

```{r}
n <- 10000              # number of data points
x1 <- rnorm (n)          # make up x1 covariate
b0 <- 25                # set intercept (beta0)
b1 <- -15                # set beta1
y <- rnorm (n, b0+b1*x1,10)  # simulate data with noise
data2=cbind.data.frame(y=y,x1=x1)
```

Write a parallel `foreach()` loop that:

* selects a sample (as above) with `sample_n()`
* fits a 'normal' linear model with `lm()`
* Compiles the coefficient of determination (R^2) from each model

Hint: use `summary(M1)$r.squared` to extract the R^2 from model `M1` (see `?summary.lm` for more details).

<button data-toggle="collapse" class="btn btn-primary btn-sm round" data-target="#demo2">Show Solution</button>
<div id="demo2" class="collapse">

```{r, purl=F}
trials = 100
tsize = 100

  result <- foreach(i=1:trials,.combine = rbind.data.frame) %dopar% 
    {
      tdata=sample_n(data2,tsize,replace=TRUE)
      M1=lm(y ~ x1, data=tdata)
      cbind.data.frame(trial=i,
        t(coefficients(M1)),
        r2=summary(M1)$r.squared,
        aic=AIC(M1))
  }
```

Plot it:
```{r, purl=F}
ggplot(data2,aes(y=y,x=x1))+
  geom_point(col="grey")+
  geom_abline(data=dplyr::select(result,everything(),
                                 Intercept=contains("Intercept")),
              aes(intercept=Intercept,slope=x1),alpha=.5)
```

</div>
</div>