1. Ch.6 Efficient calculations

2. 6.1 Vectorized computations  Replacing numbers with ‘for’ expression tmp <- Sys.time() x <- rnorm(15000) for (i in 1:length(x)){ if(x[i] > 1){ x[i] <- 1 } Sys.time - tmp Time difference of 0.2110000 secs

3. 6.1 Vectorized computations  Replacing numbers with a ‘vectorized’ function tmp <- Sys.time() x <- rnorm(15000) x[x>1] <- 1 Sys.time() - tmp Time difference of 0.0400002 secs

4. 6.1 Vectorized computations  The if-else expression tmp <- Sys.time() x <- rnorm(15000) for (i in 1:length(x)){ if(x[i] > 1){ x[i] <- 1 } else { x[i] <- -1 } } Sys.time() - tmp Time difference of 0.3009999 secs

5. 6.1 Vectorized computations  a vectorized function ‘ifelse’ tmp <- Sys.time() x <- rnorm(15000) x 1,1,-1) tmp - Sys.time() Time difference of 0.02999997 secs

6. 6.1 Vectorized computations  The cumsum function x <- 1:10 y <- cumsum(x) y [1] 1 3 6 10 15 21 28 36 45 55

7. 6.1 Vectorized computations  Matrix multiplication C <- A%*%B  If we choose the elements of the matrices A and B ‘cleverly' explicit for-loops could be avoided. For example: A <- matrix(rnorm(1000),ncol=10) n <- dim(A)[1] mat.means <- t(A)%*%rep(1/n,n)

8. 6.2 The apply and outer functions  To calculate the means of all columns in a matrix, use the following syntax: M <- matrix(rnorm(10000),ncol=100) apply(M,1,mean) colMeans(M) rowMeans(M) 6.2.1 the apply function

9. 6.2 The apply and outer functions  The function apply can also be used with a function that you have written yourself.  Extra arguments to your function must now be passed trough the apply function.  The following construction calculates the number of entries that is larger than a threshold d for each column in a matrix. 6.2.1 the apply function

10. 6.2 The apply and outer functions tresh d) } M <- matrix(rnorm(10000),ncol=100) apply(M,1,tresh,d=0.6) [1] 32 26 26 31 34 23 34 31 36 27 21 25 26 22 31 28 [17] 28 24 26 34 25 30 30 30 30 30 36 30 29 22 34 29 [33] 26 16 25 25 33 33 21 31 33 30 30 26 29 25 28 26 [49] 21 22 32 17 28 30 27 36 22 35 33 26 21 20 23 30 [65] 24 30 31 19 22 33 27 30 31 23 23 24 29 29 36 32 [81] 30 30 29 28 25 17 26 18 24 31 21 31 28 20 23 29 [97] 32 23 32 34 ?lapply ?sapply 6.2.1 the apply function

11. 6.2 The apply and outer functions  This function is used to run another function on the cells of a so called ragged array. A ragged array is a pair of two vectors of the same size. One of them contains data and the other contains grouping information. The following data vector x en grouping vector y form an example of a ragged array. x <- rnorm(50) y <- as.factor(sample(c("A","B","C","D"), size=50, replace=T)) tapply(x, y, mean, trim = 0.3) A B C D -0.4492093 -0.1506878 0.4427229 -0.1265299 6.2.3 The tapply function

12. 6.2 The apply and outer functions  For every combination of the vector elements of x and y this function is evaluated. Some examples are given by the code below. x <- 1:3 y <- 1:3 z <- outer(x,y,FUN="-") z [,1] [,2] [,3] [1,] 0 -1 -2 [2,] 1 0 -1 [3,] 2 1 0 6.2.5 The outer function

13. 6.2 The apply and outer functions x <- c("A", "B", "C", "D") y <- 1:9 z <- outer(x, y, paste, sep = "") z # function with grid combination x <- seq(-4,4,l=50) y <- x myf <- function(x,y){ sin(x)+cos(y)} z <- outer(x,y, FUN = myf) persp(x,y,z, theta=45, phi=45, shade = 0.45) 6.2.5 The outer function

14. 6.2 The apply and outer functions 6.2.5 The outer function

15. 6.2 Other vectorized functions colSums (x, na.rm = FALSE, dims = 1) rowSums (x, na.rm = FALSE, dims = 1) colMeans(x, na.rm = FALSE, dims = 1) rowMeans(x, na.rm = FALSE, dims = 1) rowsum(x, group, reorder = TRUE,...) aggregate(x, by, FUN,..., simplify = TRUE) sweep(x, MARGIN, STATS, FUN="-",...) scale(x, center = TRUE, scale = TRUE) …

16. “The quiet statisticians have changed our world -not by discovering new facts or technical developments but by changing the ways that we reason, experiment and form our opinions... “ - by Ian Hacking Thank you !