Lecture 3 Working with vectors.Rmd

---
title: 'Lecture 3: Working with vectors'
author: "David McAllister"
date: "Monday 31st October, 2016"
output:
  ioslides_presentation: default
---

# Working in R is mainly about working with vectors

## Objective of section
* To be able to create and manipulate atomic vectors
* To describe what coercion means (a term used often in help menu)

## Mathematical operations
```{r}
a <- 1:10
b <- seq(100,1000,100)
a*b
a+b
a-b^a
```

## Simple functions
```{r}
max(a,b)
min(a,b)
pmax(a,b)
pmin (a,b)
```

## Logical operations
```{r, eval = 1:3, echo = -3}
a <- rpois (6, lambda = 5)
b <- rpois (6, lambda = 5)
data.frame (a = a, b = b, "'a>b'" = a>b, "'a==b'" = a==b, "'a-b > 0'" = (a-b) >0, "'a < median(b)'" = a < median(b), check.names = FALSE)
a > b
a == b
(a-b) > 0
a < median(b)
```

## Operations with characters
```{r}
fruits <- c("oranges", "apples", "bananas", "tomatoes", "grapes")
print (fruits)
sub (pattern = "o", replacement = "O", x = fruits)
toupper (fruits)
tolower(fruits)
```


## Quick look at help file
? max

**Value**:

>For min or max, a length-one vector. For pmin or pmax, a vector of length the longest of the input vectors, or length zero if >one of the inputs had zero length.
>The type of the result will be that of the highest of the inputs in the hierarchy integer < double < character.
>For min and max if there are only numeric inputs and all are empty (after possible removal of NAs), the result is double (Inf or-Inf).

## Coercion happens inside functions
Just like c() combining

* Most mathematical functions (`+`, `log`, `abs`, etc.) > double or integer
* logical operations (`==`, `&`, `|`, `any`, etc) > logical
* Most string operations > character
* explicitly coerce
    + as.character()
    + as.double()
    + as.integer()
    + as.logical()


## Vector recycling
```{r, warning = TRUE}
# create three vectors of different lengths
vect1 <- 1:10
vect2 <- 1:2
vect3 <- 1:3
# Multiply vectors
vect1 * vect2
vect1 * vect3
```

## Complex functions also work with vectors
```{r, eval = FALSE}
model1 <- lm (y ~ x, data = mydata)
## Is equivalent to
model1 <- lm (mydata$y ~ mydata$x) # subsetting, we get onto next
```
R often talks about wrappers and non-standard evaluation

* minimise typing for interactive analysis
* harder to follow what's going on

## Vectorisation
```{r, echo = -(1:2)}
(a <- c(1,2,3,4))
(b <- c(10,20,30,40))
new.value <- vector (length = 4L)
for (i in 1:4) {
  new.value[i] <- a[i] + b[i]
}
new.value
# R handles this for you
a^b + b^(a*b)
```

## Vectorisation
Think about it when

* applying non-vectorised function, eg `if`
* making own functions