Some miscellaneous topics

• Matrices and arrays: construction and operations

• Replacement functions

• do.call()

Matrix construction

• matrix(data, nrow, ncol) : data + dimension

matrix(month.abb, 3, 4)

     [,1]  [,2]  [,3]  [,4] 
[1,] "Jan" "Apr" "Jul" "Oct"
[2,] "Feb" "May" "Aug" "Nov"
[3,] "Mar" "Jun" "Sep" "Dec"

matrix(month.abb, 3, 4, byrow = TRUE)

     [,1]  [,2]  [,3]  [,4] 
[1,] "Jan" "Feb" "Mar" "Apr"
[2,] "May" "Jun" "Jul" "Aug"
[3,] "Sep" "Oct" "Nov" "Dec"

• array(data, dim) similarly allows construction of general arrays

Matrix construction

• rbind(...) : construct matrix by combining rows

• cbind(...) : construct matrix by combining columns

X <- with(mtcars, cbind(Int = 1, am = am, wt = wt)) # design matrix
X

      Int am    wt
 [1,]   1  1 2.620
 [2,]   1  1 2.875
 [3,]   1  1 2.320
 [4,]   1  0 3.215
 [5,]   1  0 3.440
 [6,]   1  0 3.460
 [7,]   1  0 3.570
 [8,]   1  0 3.190
 [9,]   1  0 3.150
[10,]   1  0 3.440
[11,]   1  0 3.440
[12,]   1  0 4.070
[13,]   1  0 3.730
[14,]   1  0 3.780
[15,]   1  0 5.250
[16,]   1  0 5.424
[17,]   1  0 5.345
[18,]   1  1 2.200
[19,]   1  1 1.615
[20,]   1  1 1.835
[21,]   1  0 2.465
[22,]   1  0 3.520
[23,]   1  0 3.435
[24,]   1  0 3.840
[25,]   1  0 3.845
[26,]   1  1 1.935
[27,]   1  1 2.140
[28,]   1  1 1.513
[29,]   1  1 3.170
[30,]   1  1 2.770
[31,]   1  1 3.570
[32,]   1  1 2.780

Matrix operations

• t(x) : transpose of matrix

• aperm(x, perm) : general array permutation

• a * b : element-wise multiplication

• a %*% b : matrix multiplication

• crossprod(x) : More efficient version of t(x) %*% x

• crossprod(x, y) : More efficient version of t(x) %*% y

• tcrossprod(x, y): Similar version of x %*% t(y)

Matrix operations

t(X) %*% X

        Int     am       wt
Int  32.000 13.000 102.9520
am   13.000 13.000  31.3430
wt  102.952 31.343 360.9011

crossprod(X)

        Int     am       wt
Int  32.000 13.000 102.9520
am   13.000 13.000  31.3430
wt  102.952 31.343 360.9011

Matrix operations

• solve(A, b) : solve system of linear equations $Ax=b$

y <- mtcars$mpg
solve(crossprod(X), crossprod(X, y))

           [,1]
Int 37.32155131
am  -0.02361522
wt  -5.35281145

• Compare with

coef(lm(mpg ~ 1 + am + wt, data = mtcars))

(Intercept)          am          wt 
37.32155131 -0.02361522 -5.35281145

Matrix operations

• lm() is more numerically efficient (it does not actually compute crossprod(X))

• It also handles factor (categorical) variables through its formula interface

• The model.matrix() function computes just the design matrix without fitting the model

Replacement functions

• We have seen several examples of the form:

x[i] <- value
attr(x, "name") <- value
colnames(x) <- value

• All these calls have a "complex" expression on the LHS of the assignment

• These are known as replacement functions

Replacement functions

• We have seen several examples of the form:

x[i] <- value
attr(x, "name") <- value
colnames(x) <- value

• All these calls have a "complex" expression on the LHS of the assignment

• These are known as replacement functions

• These are very natural once you get used to them

• However, they are somewhat unusual, and we should be aware of why they are needed

• The main reason is that R functions are not allowed to modify their arguments

Replacement functions

• Example: setting names

d <- data.frame(1, mtcars$wt, mtcars$am)
names(d)

[1] "X1"        "mtcars.wt" "mtcars.am"

• Suppose we want to change the names to "Int", "wt", "am"

• In other languages, we would have something like

setNames(d, c("Int", "wt", "am"))

Replacement functions

• Unfortunately, such a function cannot modify d

• The best it can do is to return a modified version of d:

d <- setNames(d, c("Int", "wt", "am"))

• This is similar to how transform(), dplyr::mutate(), etc., work

Replacement functions

• Replacement functions provide a more "natural" alternative

str(d)

'data.frame':    32 obs. of  3 variables:
 $ X1       : num  1 1 1 1 1 1 1 1 1 1 ...
 $ mtcars.wt: num  2.62 2.88 2.32 3.21 3.44 ...
 $ mtcars.am: num  1 1 1 0 0 0 0 0 0 0 ...

names(d) <- c("Int", "wt", "am")
str(d)

'data.frame':    32 obs. of  3 variables:
 $ Int: num  1 1 1 1 1 1 1 1 1 1 ...
 $ wt : num  2.62 2.88 2.32 3.21 3.44 ...
 $ am : num  1 1 1 0 0 0 0 0 0 0 ...

• It is easy to write your own replacement functions

• For now, those details are not important

The do.call() function to call a function

• It is easy to manipulate the language itself in R (e.g., quote())

• Such manipulation is usually only needed for advanced programming, not routine use

• But one particular tool is very useful in practice: do.call()

The do.call() function to call a function

• Example

am.summary <- with(mtcars, tapply(mpg, am, FUN = summary))
am.summary

$`0`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  10.40   14.95   17.30   17.15   19.20   24.40 
$`1`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.00   21.00   22.80   24.39   30.40   33.90

• Suppose we want to combine these into a matrix:

cbind(am.summary[[1]], am.summary[[2]])

            [,1]     [,2]
Min.    10.40000 15.00000
1st Qu. 14.95000 21.00000
Median  17.30000 22.80000
Mean    17.14737 24.39231
3rd Qu. 19.20000 30.40000
Max.    24.40000 33.90000

The do.call() function to call a function

gear.summary <- with(mtcars, tapply(mpg, gear, FUN = summary)) # different variable
gear.summary

$`3`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  10.40   14.50   15.50   16.11   18.40   21.50 
$`4`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  17.80   21.00   22.80   24.53   28.07   33.90 
$`5`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.00   15.80   19.70   21.38   26.00   30.40

cbind(gear.summary[[1]], gear.summary[[2]], gear.summary[[3]]) # three arguments instead of two

            [,1]     [,2]  [,3]
Min.    10.40000 17.80000 15.00
1st Qu. 14.50000 21.00000 15.80
Median  15.50000 22.80000 19.70
Mean    16.10667 24.53333 21.38
3rd Qu. 18.40000 28.07500 26.00
Max.    21.50000 33.90000 30.40

The do.call() function to call a function

• Alternative: do.call(what, args)

  • what is a function

  • args is a list of arguments

  • Calls the function what with arguments given in args

• The following are equivalent:

FUN(val1, val2, arg3 = val3)

• and

do.call(FUN, args = list(val1, val2, arg3 = val3))

The do.call() function to call a function

• So we can rewrite the previous cbind() calls as

do.call(cbind, am.summary)

               0        1
Min.    10.40000 15.00000
1st Qu. 14.95000 21.00000
Median  17.30000 22.80000
Mean    17.14737 24.39231
3rd Qu. 19.20000 30.40000
Max.    24.40000 33.90000

do.call(cbind, gear.summary)

               3        4     5
Min.    10.40000 17.80000 15.00
1st Qu. 14.50000 21.00000 15.80
Median  15.50000 22.80000 19.70
Mean    16.10667 24.53333 21.38
3rd Qu. 18.40000 28.07500 26.00
Max.    21.50000 33.90000 30.40