Functional Programming in R

Functional Programming in R
A Pragmatic Introduction
Soumendra Prasad Dhanee
Data Scientist
.com
18th October, 2014
8th November, 2014
(delivered at R Meetup, Mumbai)
Soumendra Prasad Dhanee Functional Programming in R Slide 1/51

1 Introduction
Getting Started
Vectorization
Vectorization in Practice
Problem 1
Higher-order Functions
First-class Functions
2 More about functions
Problem 2
Anonymous Functions
Problem 3
3 Applicative Programming
Map
mapply
Filter
Negate
4 Closure

Introduction
More about functions
Applicative Programming
Closure
Overview
We'll start by reviewing basics
We'll see the ideas at action

rst (by solving problems) and
abstractions later
We'll digress a lot

Next ...
1 Introduction
Getting Started
Vectorization
Problem 1
Problem 2
Anonymous Functions
Problem 3
Map
mapply
Filter
Negate
4 Closure

Introduction
Closure
Getting Started
Vectorization
Problem 1
Writing a function in R
func t ionname < f u n c t i o n ( arg1 , arg2 , . . . ) f 1
e x p r e s s i o n s 2
[ r e t u r n (e x p r e s s i o n ) ] 3
g 4
return() is optional
last statement of the function body is returned by default

Introduction
Closure
Getting Started
Vectorization
Problem 1
Example of a Function
s q u a r e . o f f u n c t i o n ( x ) f 1
x*x 2
g 3
Call the function
s q u a r e . o f ( 4 ) 1
y s q u a r e . o f ( x=4) 2
s q u a r e . o f ( z=4) 3

Introduction
Closure
Getting Started
Vectorization
Problem 1
More on Functions
Arguments of R functions can be either required or optional,
indicated by syntax
Required arguments have no default value
Optional arguments are de

ned to have a default value

Introduction
Closure
Getting Started
Vectorization
Problem 1
More on Functions - Example
add f u n c t i o n ( x , y = 2) f 1
x+y 2
g 3
add ( 3 ) 1
add ( 3 , 2 ) 2
add ( x=3) 3
add ( x=3, y=2) 4
add ( y=2) 5
add ( , 3) 6

Introduction
Closure
Getting Started
Vectorization
Problem 1
Example - Computing Power I
Write a function that computes the kth power of an argument x,
using one default argument, and one optional argument, i.e. an
argument that has a default value.
We'll be coming back to this function later on.

Introduction
Closure
Getting Started
Vectorization
Problem 1
Example - Computing Power II
power f u n c t i o n ( x , k=2) x^k 1

Introduction
Closure
Getting Started
Vectorization
Problem 1
The apply family of functions
lapply(X, FUN, ...)
returns a list of the same length as X, each element of which is
the result of applying FUN to the corresponding element of X
sapply(X, FUN, ...)
a user-friendly version of lapply by default returning a vector
or matrix if appropriate
Read the Documentation

Introduction
Closure
Getting Started
Vectorization
Problem 1
Vectorized Functions
... functions that operate on vectors or matrices or dataframes.
Often much faster than looping over a vector, often use
.Internal or .Primitive
Higher abstraction - less code to write, less to debug

Introduction
Closure
Getting Started
Vectorization
Problem 1
.Internal and .Primitive - I
log
## function (x, base = exp(1)) .Primitive(log)
paste
## function (..., sep = , collapse = NULL)
## .Internal(paste(list(...), sep, collapse))
## bytecode: 0x1f8a2c8
## environment: namespace:base

Introduction
Closure
Getting Started
Vectorization
Problem 1
.Internal and .Primitive - II
colMeans
## function (x, na.rm = FALSE, dims = 1L)
## {
## if (is.data.frame(x))
## x - as.matrix(x)
## if (!is.array(x) || length(dn - dim(x)) 2L)
## stop(
x
must be an array of at least two dimensions)
## if (dims 1L || dims length(dn) - 1L)
## stop(invalid
dims
)
## n - prod(dn[1L:dims])
## dn - dn[-(1L:dims)]
## z - if (is.complex(x))
## .Internal(colMeans(Re(x), n, prod(dn), na.rm)) + Soumendra Prasad Dhanee Functional Programming in R Slide 14/51
## .Internal(colMeans(Im(x), n, prod(dn), na.rm))

Introduction
Closure
Getting Started
Vectorization
Problem 1
Examples of Vectorized Functions
ifelse()
is.na()
log()
sqrt()
rnorm()
colMeans()
rowSums()
x y
x == y
!x

Introduction
Closure
Getting Started
Vectorization
Problem 1
Primality Testing I
Given a number, decide if it is a prime or not.
Hint 1 : min(x) gives the lowest element of vector x
min(c(2, 1, 3))
## [1] 1

Introduction
Closure
Getting Started
Vectorization
Problem 1
Primality Testing II
min ( x%%( 2 : ( x1) ) )0 1
The Deconstruction
2 : ( x1) 1
x%%( 2 : ( x1) ) 2
min ( x%%( 2 : ( x1) ) )0 3

Introduction
Closure
Getting Started
Vectorization
Problem 1
Lists of functions
x - 1:10
funs - list(
sum = sum,
mean = mean,
median = median
)
sapply(funs, function(f) f(x))
## sum mean median
## 55.0 5.5 5.5

Introduction
Closure
Getting Started
Vectorization
Problem 1
Let's get started
Problem 1
Input
A numeric vector (1:200000)
Output
A vector containing the even numbers in the input
vector, listed in the order they appeared in the input
vector

Introduction
Closure
Getting Started
Vectorization
Problem 1
Solution - for loop I
Solution using for loop
x 1:200000 1
ans l o g i c a l (200000) 2
f o r ( i i n x ) 3
f 4
i f ( i%%2==0) f ans [ i ] = TRUE g e l s e f 5
ans [ i ] = FALSE g 6
g 7
x [ ans ] 8
## user system elapsed
## 0.542 0.005 0.546

Introduction
Closure
Getting Started
Vectorization
Problem 1
Solution - for loop II
Solution using for loop
x 1:200000 1
ans c ( ) 2
f o r ( i i n x ) 3
f 4
i f ( i%%2==0) f ans [ i ] = TRUE g e l s e f 5
ans [ i ] = FALSE g 6
g 7
x [ ans ] 8
## 56.511 2.631 59.333

Introduction
Closure
Getting Started
Vectorization
Problem 1
Solution - vectorized functions
Solution using vectorized functions
x 1:200000 1
ans x%%2==0 2
x [ ans ] 3
## 0.013 0.000 0.013

Introduction
Closure
Getting Started
Vectorization
Problem 1
Solution - higher-order functions
Solution using higher-order functions
x 1:200000 1
ans s a p p l y ( x , f u n c t i o n ( i ) i%%2==0) 2
x [ ans ] 3
## 0.554 0.011 0.566

Introduction
Closure
Getting Started
Vectorization
Problem 1
What are higher-order functions?
A higher-order function (also functional form, functional or
functor) is a function that does at least one of the following:
takes one or more functions as an input
outputs a function
-source - Wikipedia

Introduction
Closure
Getting Started
Vectorization
Problem 1
An example
sapply
sapply(X, FUN, ...)

Introduction
Closure
Getting Started
Vectorization
Problem 1
What are

rst-class functions?
First-class functions are functions that can be treated like any
other piece of data ...
can be stored in a variable
can be stored in a list
can be stored in an object
can be passed to other functions
can be returned from other functions
... just like any other piece of data.

Next ...
1 Introduction
Getting Started
Vectorization
Problem 1
Problem 2
Anonymous Functions
Problem 3
Map
mapply
Filter
Negate
4 Closure

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Rounding o
Problem 2a
Input
A numeric vector (rnorm(100, 0, 1))
Output
A vector containing all the numbers in the input vector
rounded to the nearest integer

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Solution 2a - Rounding o
Solution using sapply
s a p p l y ( rnorm (100 , 0 , 1) , round ) 1

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Rounding o
Problem 2b
Input
A numeric vector (rnorm(100, 0, 1))
Output
A vector containing all the numbers in the input vector
rounded to two decimal places

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Solution 2b - Rounding o
Solution using sapply
s a p p l y ( rnorm (100 , 0 , 1) , f u n c t i o n ( x ) round ( x , 2) ) 1

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Anonymous Functions
Anonymous Functions
Anonymous function is a function that is not bound to an
identi

er.
source - Wikipedia

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Acting on Matrices
Problem 3
Input
A 3-by-3 matrix (matrix(1:9, ncol=3))
Output
Add 1 to row 1, 4 to row 2, 7 to row 3

Introduction
Closure
Problem 2
Anonymous Functions
Problem 3
Solution 3 - Matrix Addition
Solution using sweep
m ma t r i x ( 1 : 9 , n c o l=3) 1
sweep (m, 1 , c ( 1 , 4 , 7) , + ) 2
## [,1] [,2] [,3]
## [1,] 2 5 8
## [2,] 6 9 12
## [3,] 10 13 16

Next ...
1 Introduction
Getting Started
Vectorization
Problem 1
Problem 2
Anonymous Functions
Problem 3
Map
mapply
Filter
Negate
4 Closure

Introduction
Closure
Map
mapply
Filter
Negate
Calling by function B of function A, where function A was
originally supplied to function B as an argument.
Examples
map
reduce (fold)

lter

Introduction
Closure
Map
mapply
Filter
Negate
Map
Map(f, x, ...)
1
f u n c t i o n ( f , . . . ) 2
f 3
f match . fun ( f ) 4
mapply (FUN = f , . . . , SIMPLIFY = FALSE) 5
g 6
by t e code : 0 x402ad90 7
env i ronment : namespace : base 8

Introduction
Closure
Map
mapply
Filter
Negate
mapply
mapply is a multivariate version of sapply.
mapply ( rep , 1 : 4 , 4 : 1 ) 1
2
mapply ( rep , t ime s = 1 : 4 , x = 4 : 1 ) 3
4
mapply ( rep , x = 1 : 4 , t ime s = 4 : 1 ) 5

Introduction
Closure
Map
mapply
Filter
Negate
Filter I
Choose all the even numbers.
F i l t e r ( f u n c t i o n ( x ) x%%2 , 1:200000) 1
## 0.419 0.004 0.424

Introduction
Closure
Map
mapply
Filter
Negate
Filter II
The previous solution was wrong.
Now what is the output of the following -
F i l t e r ( c (T, F) , 1:200000) 1

Introduction
Closure
Map
mapply
Filter
Negate
Filter III
f u n c t i o n ( f , x ) 1
f 2
i n d as . l o g i c a l ( u n l i s t ( l a p p l y ( x , f ) ) ) 3
x [ ! i s . na ( i n d ) i n d ] 4
g 5
by t e code : 0 x4f87f00 6

Introduction
Closure
Map
mapply
Filter
Negate
Negate I
What is the outcome?
Negate ( c (T, F) , 1 : 1 0 ) 1

Introduction
Closure
Map
mapply
Filter
Negate
Negate II
What is the outcome?
F i l t e r ( Negate ( f u n c t i o n ( x ) x%%2) , 1 : 1 0 ) 1

Introduction
Closure
Map
mapply
Filter
Negate
Negate III
f u n c t i o n ( f ) 1
f 2
f match . fun ( f ) 3
f u n c t i o n ( . . . ) ! f ( . . . ) 4
g 5
by t e code : 0 x4e9c250 6

Next ...
1 Introduction
Getting Started
Vectorization
Problem 1
Problem 2
Anonymous Functions
Problem 3
Map
mapply
Filter
Negate
4 Closure

Introduction
Closure
Computing Power Revisited
Write a function that computes the kth power of an argument x,
using one default argument, and one optional argument, i.e. an
argument that has a default value.
power f u n c t i o n ( x , k=2) f 1
x^k 2
g 3

Functional Programming in R

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