apply, with and by summary

apply(X, MARGIN, FUN), MARGIN 1 indicates rows, 2 indicates columns
tapply(X, INDEX, FUN) Apply a function to each cell of a factored array
lapply returns a list each element of which is the result of applying FUN to the corresponding list
sapply is a “user-friendly” version of lapply by default returning a vector or matrix if appropriate.
mapply is a multivariate version of sapply applies FUN to the first elements of each ... argument

ex. apply(x, 2, sum), x is a matrix

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.

> x <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE)) >
> x
$a
[1] 1 2 3 4 5 6 7 8 9 10
$beta
[1] 0.04978707 0.13533528 0.36787944 1.00000000 2.71828183 7.38905610 20.08553692
$logic
[1] TRUE FALSE FALSE TRUE
> # compute the list mean for each list element
> lapply(x,mean)
$a
[1] 5.5
$beta
[1] 4.535125
$logic
[1] 0.5

> # median and quartiles for each list element
> lapply(x, quantile, probs = 1:3/4)
$a
25% 50% 75%
3.25 5.50 7.75
$beta
25% 50% 75%
0.2516074 1.0000000 5.0536690
$logic
25% 50% 75%
0.0 0.5 1.0

> sapply(x, quantile)
a beta logic
0% 1.00 0.04978707 0.0
25% 3.25 0.25160736 0.0
50% 5.50 1.00000000 0.5
75% 7.75 5.05366896 1.0
100% 10.00 20.08553692 1.0

sapply is a “user-friendly” version of lapply by default returning a vector or matrix if appropriate.

mapply is a multivariate version of sapply. mapply applies FUN to the first elements of each ... argument
> mapply(rep, 1:4, 4:1)
[[1]]
[1] 1 1 1 1
[[2]]
[1] 2 2 2
[[3]]
[1] 3 3
[[4]]
[1] 4

> mapply(rep, times=1:4, x=4:1)
[[1]]
[1] 4
[[2]]
[1] 3 3
[[3]]
[1] 2 2 2
[[4]]
[1] 1 1 1 1

tapply(X, INDEX, FUN) Apply a function to each cell of a factored array
> n <- 17; fac <- factor(rep(1:3, len = n), levels = 1:5) > table(fac)
fac
1 2 3 4 5
6 6 5 0
> tapply(1:n, fac, sum)
1 2 3 4 5
51 57 45 NA NA

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From http://www.statmethods.net/stats/withby.html
With

The with( ) function applys an expression to a dataset. It is similar to DATA= in SAS.

# with(data, expression)
# example applying a t-test to dataframe mydata
with(mydata, t.test(y1,y2))
By

The by( ) function applys a function to each level of a factor or factors. It is similar to BY processing in SAS.

# by(data, factorlist, function)
# example apply a t-test separately for men and women
by(mydata, gender, t.test(y1,y2))