Replicate and the Apply Family of Functions

# Replicate and the Apply Family of Functions - 1

## Introductory Computer Programming

### Deepayan Sarkar

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# Topics

* Replicating a simulation experiment

* The `*apply()` family of functions

* Functions can be arguments of other functions

-->

# Loop alternatives

* R has several general purpose functions that provide alternatives to loops

* We will discuss two of the main approaches today:

- `replicate()` for repeating a simulation experiment
	
	- Various `*apply()` functions to loop over varying function arguments

* These are not necessarily more efficient than loops (unlike true vectorized operations)

* However, they are conceptually simpler (and easier to parallelize)

---

# Replicating a simulation experiment

---

* Consider this example from our previous assignment:

```r
n <- 20
x <- sample(n, 2)
max(x) %% min(x) == 0
```

```
[1] FALSE
```

* To estimate the probability of this event, we want to run it several
  times and compute proportion

---

* We have seen how to do this using a loop

* An alternative approach is to use the `replicate()` function

```r
replicate(10, {
    x <- sample(n, 2)
    max(x) %% min(x) == 0
})
```

```
 [1]  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
```

* `replicate()` takes the _expression_ supplied as its second argument
  and evauates it multiple times

```r
s <- replicate(5000, {
    x <- sample(n, 2)
    max(x) %% min(x) == 0
})
sum(s) / length(s) # estimated probability of success
```

```
[1] 0.2398
```

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# Return value of `replicate()`

---

* The return value of `replicate()` depends on what the expression returns when evaluated

* In the above example, each evaluation results in a scalar logical

* In that case, the results are aggregated to produce a vector
--

* If the result is always a vector of same length (greater than one), the result is combined into a matrix

```r
quantile(rnorm(500), probs = c(0.25, 0.5, 0.75))
```

```
        25%         50%         75% 
-0.66396457 -0.01230398  0.57424684 
```

```r
replicate(6, quantile(rnorm(500), probs = c(0.25, 0.5, 0.75)))
```

```
           [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
25% -0.64963116 -0.70360965 -0.67474961 -0.69725569 -0.67091756 -0.61606464
50%  0.03544182 -0.06543701 -0.01299035 -0.09834945 -0.03744973  0.06074351
75%  0.67997507  0.66759673  0.69118021  0.64266682  0.60572714  0.69812549
```

---

* If the result has inconsistent length, the result is a list

```r
set.seed(20200101)
replicate(6, unique(sample(10, 5, replace = TRUE)))
```

```
[[1]]
[1] 1 4 5 8

[[2]]
[1] 4 7 8 6

[[3]]
[1] 10  9  5  2  1

[[4]]
[1] 6 4 1 2

[[5]]
[1] 6 9 2 3

[[6]]
[1] 1 9 6 2 4
```

---

* This may sometimes lead to unanticipated behaviour

```r
set.seed(20200101)
replicate(2, unique(sample(10, 5, replace = TRUE)))
```

```
     [,1] [,2]
[1,]    1    4
[2,]    4    7
[3,]    5    8
[4,]    8    6
```
--

* When output length is known to be variable, it is better to
  explicitly disable simplification

```r
set.seed(20200101)
replicate(2, unique(sample(10, 5, replace = TRUE)), simplify = FALSE) # always return list
```

```
[[1]]
[1] 1 4 5 8

[[2]]
[1] 4 7 8 6
```

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# Questions?