# Microbial Informatics

## Lecture 19

Patrick D. Schloss, PhD (microbialinformatics.github.io)
Department of Microbiology & Immunology

## Announcements

• Homework is due Friday
• Note: for histogram problem, you should have the word names on the x-axis and their frequency in the y-axis (hist will not work...)
• We will not be meeting on Friday

## Review

• Loops: for, while, repeat loops
• Loops are slow in R beacuase variables are copied, destroyed, and recreated each time a vector is modified
• Conditionals: ifelse and if...else if...else

## Learning objectives

• Be able to vectorize loops in R and see the improved speed
• Understand when to use Various flavors of apply
• apply
• lapply
• sapply
• mapply
• vapply
• replicate

## Simple vectorization

z <- sum(1:10)

my.sum <- function(x){
sum <- 0
for(i in x){
sum <- sum+i
}
return(sum)
}

my.z <- my.sum(1:10)

z == my.z

## [1] TRUE


## apply

• As we've seen before if we have a matrix, we can't easily perform functions on the rows...
my.matrix <- matrix(runif(100), nrow=25, ncol=4)
mean(my.matrix)

## [1] 0.4569663

• How do we get out the mean for each column?

## apply

• For the columns...
apply(my.matrix, 2, sum)

## [1] 11.03565 12.39229 10.82431 11.44439

• For the rows...
apply(my.matrix, 1, sum)

##  [1] 2.6943111 2.0101876 2.9360609 1.2017400 2.0563487 1.8594455 1.0698792
##  [8] 2.2443721 1.7925920 1.5564715 2.3986392 0.6921058 0.9243032 2.4423091
## [15] 2.1361687 2.2463989 1.2584018 1.1983626 1.9852243 2.2287206 2.0006690
## [22] 2.3374191 1.6519987 1.3962797 1.3782208


## Something more complex...

• What if we want the sum of each column where each value is raised to some arbitrary power?
power <- function(x, pow=2){
value <- sum(x^pow)
return(value)
}

• We could just loop across the columns and apply our power function:
sum.pow <- rep(0, ncol(my.matrix))
for(c in 1:ncol(my.matrix)){
sum.pow[c] <- power(my.matrix[,c], 3)
}
sum.pow

## [1] 6.165161 5.160410 5.221504 5.517061


## Let's try the apply function...

apply(my.matrix, 2, power)

## [1] 7.636707 7.586525 7.010534 7.436073

• and a user defined power (pow=3)?
apply(my.matrix, 2, power, pow=3)

## [1] 6.165161 5.160410 5.221504 5.517061


## What's going on?

• “Returns a vector or array or list of values obtained by applying a function to margins of an array or matrix.”
• apply extracts the rows/columns, converts them to a vector
• The function is applied
• Output generated
• Again, the benefit is seen with larger datasets and more complex functions
• Remember that apply uses a matrix as input

## What if you want to use a list as your input?

my.list <- list(popA = runif(20), popB = runif(40), popC = runif(25))
my.list

## $popA ## [1] 0.789888926 0.732228612 0.593445162 0.458747080 0.294085842 ## [6] 0.107231901 0.629430934 0.178869322 0.314758766 0.782433687 ## [11] 0.310015731 0.423296753 0.230681855 0.808566388 0.126439277 ## [16] 0.006074851 0.049667654 0.576524630 0.404983133 0.595498108 ## ##$popB
##  [1] 0.65757852 0.88621404 0.65655682 0.49551514 0.26531379 0.71324740
##  [7] 0.98365988 0.26544527 0.88064996 0.05184048 0.71307293 0.15256234
## [13] 0.39815559 0.43867842 0.63324371 0.63029916 0.50362772 0.64338183
## [19] 0.92875425 0.73931652 0.19609726 0.13118313 0.82240801 0.27533289
## [25] 0.09853017 0.07492592 0.82060901 0.15400064 0.70062609 0.09482273
## [31] 0.18038604 0.10514004 0.65993975 0.07324145 0.22970452 0.88344762
## [37] 0.97923670 0.48778723 0.44308235 0.32717377
##
## $popC ## [1] 0.28673732 0.90222068 0.42826622 0.73754070 0.86552149 0.90414823 ## [7] 0.75340600 0.40306787 0.05688030 0.21527692 0.83641013 0.26666650 ## [13] 0.20038611 0.30979278 0.98551179 0.19881024 0.39904960 0.17845245 ## [19] 0.27976597 0.39437142 0.09518894 0.51354819 0.73536761 0.53127758 ## [25] 0.06071723  ## Now I want to apply my power function to the elements in the list power(my.list)  ## Error in x^pow: non-numeric argument to binary operator  • Ooops! ## lapply • lapply returns a list of the same length as X, each element of which is the result of applying FUN to the corresponding element of X.” • Give list (or vector) and lapply will perform the function over the elements within the list. lapply(my.list, power)  ##$popA
## [1] 4.811932
##
## $popB ## [1] 12.88558 ## ##$popC
## [1] 7.411836

• Note that it returns a list.

## sapply

• "sapply is a user-friendly version of lapply by default returning a vector or matrix if appropriate"
• If your output has the same length you can use the sapply option and you will get a vector as output
sapply(my.list, power)

##      popA      popB      popC
##  4.811932 12.885584  7.411836

• Remember that you can give it a vector as well

## vapply

• vapply is similar to sapply, but has a pre-specified type of return value, so it can be safer (and sometimes faster) to use.”
• The syntax is a bit different: vapply(X, FUN, FUN.VALUE, ...) where FUN.VALUE is a vector with the name of the output from the function and its initial value
vapply(my.list, power, c(value=0))

##      popA      popB      popC
##  4.811932 12.885584  7.411836


## mapply

• What if you have two vectors that you want to feed to a function?
• Say I want to raise each value to the power of it's position in the vector
• "mapply is a multivariate version of sapply. mapply applies FUN to the first elements of each (…) argument, the second elements, the third elements, and so on"
my.vector <- runif(10)
my.powers <- 1:10
mapply(power, x=my.vector, pow=my.powers)

##  [1] 4.171556e-01 7.897012e-01 4.681264e-01 6.333021e-01 8.812617e-01
##  [6] 1.022080e-04 1.656555e-04 3.573678e-07 4.372390e-03 5.555364e-04

• Note that the function goes first and then the two vectors

## replicate

• Already saw this with the X2 distribution homework problem...
chi.sq <- function(k){
rand.chisq <- sum(rnorm(k)^2)
return(rand.chisq)
}

values <- replicate(1000, chi.sq(k=3))

## [1] 4.465741 4.659456 2.113572 4.509903 4.487471 2.440302

• Note that you need an actual function call for the second replicate arguement.

## Here's a problem...

• We have a table of relative abundances...
relabund <- matrix(rep(runif(20000)), ncol=20, nrow=100)
relabund[5,] <- c(runif(10,0,0.4), runif(10, 0.3,0.7))
colnames(relabund) <- c(paste0("Lean", 1:10), paste0("Obese", 1:10))
rownames(relabund) <- paste0("Species", 1:100)
treatments <- c(rep("lean", 10), rep("obese", 10))


##               Lean1     Lean2     Lean3     Lean4      Lean5      Lean6
## Species1 0.45992030 0.1428930 0.4322384 0.3729109 0.05659417 0.06476572
## Species2 0.03645101 0.5725126 0.9252554 0.6107523 0.11545734 0.11449512
## Species3 0.77170892 0.6552959 0.8607983 0.4644144 0.33418951 0.44612894
## Species4 0.75570539 0.7634057 0.1559501 0.5506424 0.69429557 0.84163000
## Species5 0.32899703 0.3241863 0.1874539 0.2455034 0.25689773 0.36368362
## Species6 0.47711036 0.5511257 0.6855532 0.5031633 0.06045581 0.39569183
##              Lean7     Lean8     Lean9    Lean10     Obese1    Obese2
## Species1 0.6779481 0.5738132 0.8175298 0.8428322 0.65944885 0.4919339
## Species2 0.1648704 0.7982613 0.2866036 0.7992521 0.04250725 0.6212290
## Species3 0.8140707 0.3656166 0.1883101 0.7702504 0.30776358 0.1351630
## Species4 0.5965393 0.3391652 0.8025482 0.2769966 0.49466093 0.2824831
## Species5 0.1236927 0.3888515 0.3009191 0.1555885 0.39248920 0.4272460
## Species6 0.1396910 0.2977878 0.7089633 0.7007966 0.94012800 0.6098367
##              Obese3    Obese4    Obese5    Obese6     Obese7     Obese8
## Species1 0.42922560 0.7522052 0.2156365 0.7145572 0.81468404 0.17986371
## Species2 0.03288946 0.3474433 0.4942115 0.8332294 0.55526575 0.04792325
## Species3 0.39247333 0.5468630 0.2921891 0.5850028 0.68829769 0.22548501
## Species4 0.74335846 0.9107194 0.6471540 0.6923879 0.47329088 0.28037523
## Species5 0.34735529 0.6330881 0.3266993 0.5208572 0.65454003 0.57744110
## Species6 0.94926348 0.1203434 0.8804260 0.1353925 0.03820587 0.60905916
##              Obese9   Obese10
## Species1 0.58361216 0.3560410
## Species2 0.60881250 0.9367382
## Species3 0.27749078 0.5503687
## Species4 0.09470825 0.8734746
## Species5 0.60896504 0.5688232
## Species6 0.35554762 0.6061802


## Here's a problem...

• Perform a wilcoxon test on each Species differentiating between lean and obese individuals

• Write R code, without the use of for loops that produces the following output:

• Species5 was significantly different between the two groups
• In this statement, the "Species5" should be produced by r code
• Be sure to correct for multiple comparisons!