Apply Functions Over Array Margins

Returns a vector or array or list of values obtained by applying a function to margins of an array or matrix.

array, iteration
apply(X, MARGIN, FUN, …)

an array, including a matrix.


a vector giving the subscripts which the function will be applied over. E.g., for a matrix 1 indicates rows, 2 indicates columns, c(1, 2) indicates rows and columns. Where X has named dimnames, it can be a character vector selecting dimension names.


the function to be applied: see ‘Details’. In the case of functions like +, %*%, etc., the function name must be backquoted or quoted.

optional arguments to FUN.


If X is not an array but an object of a class with a non-null dim value (such as a data frame), apply attempts to coerce it to an array via as.matrix if it is two-dimensional (e.g., a data frame) or via as.array.

FUN is found by a call to and typically is either a function or a symbol (e.g., a backquoted name) or a character string specifying a function to be searched for from the environment of the call to apply.

Arguments in cannot have the same name as any of the other arguments, and care may be needed to avoid partial matching to MARGIN or FUN. In general-purpose code it is good practice to name the first three arguments if is passed through: this both avoids partial matching to MARGIN or FUN and ensures that a sensible error message is given if arguments named X, MARGIN or FUN are passed through .


If each call to FUN returns a vector of length n, then apply returns an array of dimension c(n, dim(X)[MARGIN]) if n > 1. If n equals 1, apply returns a vector if MARGIN has length 1 and an array of dimension dim(X)[MARGIN] otherwise. If n is 0, the result has length 0 but not necessarily the ‘correct’ dimension.

If the calls to FUN return vectors of different lengths, apply returns a list of length prod(dim(X)[MARGIN]) with dim set to MARGIN if this has length greater than one.

In all cases the result is coerced by as.vector to one of the basic vector types before the dimensions are set, so that (for example) factor results will be coerced to a character array.


Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

lapply and there, simplify2array; tapply, and convenience functions sweep and aggregate.

  • apply
library(base) # NOT RUN { ## Compute row and column sums for a matrix: x <- cbind(x1 = 3, x2 = c(4:1, 2:5)) dimnames(x)[[1]] <- letters[1:8] apply(x, 2, mean, trim = .2) col.sums <- apply(x, 2, sum) row.sums <- apply(x, 1, sum) rbind(cbind(x, Rtot = row.sums), Ctot = c(col.sums, sum(col.sums))) stopifnot( apply(x, 2, is.vector)) ## Sort the columns of a matrix apply(x, 2, sort) ## keeping named dimnames names(dimnames(x)) <- c("row", "col") x3 <- array(x, dim = c(dim(x),3), dimnames = c(dimnames(x), list(C = paste0("cop.",1:3)))) identical(x, apply( x, 2, identity)) identical(x3, apply(x3, 2:3, identity)) # } # NOT RUN { ##- function with extra args: cave <- function(x, c1, c2) c(mean(x[c1]), mean(x[c2])) apply(x, 1, cave, c1 = "x1", c2 = c("x1","x2")) ma <- matrix(c(1:4, 1, 6:8), nrow = 2) ma apply(ma, 1, table) #--> a list of length 2 apply(ma, 1, stats::quantile) # 5 x n matrix with rownames stopifnot(dim(ma) == dim(apply(ma, 1:2, sum))) ## Example with different lengths for each call z <- array(1:24, dim = 2:4) zseq <- apply(z, 1:2, function(x) seq_len(max(x))) zseq ## a 2 x 3 matrix typeof(zseq) ## list dim(zseq) ## 2 3 zseq[1,] apply(z, 3, function(x) seq_len(max(x))) # a list without a dim attribute # }
Documentation reproduced from package base, version 3.6.2, License: Part of R 3.6.2

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