accumarray {pracma}

Accumulate Vector Elements

Description

accumarray groups elements from a data set and applies a function to each group.

Usage

accumarray(subs, val, sz = NULL, func = sum, fillval = 0)

uniq(a, first = FALSE)

Arguments

subs

vector or matrix of positive integers, used as indices for the result vector.

val

numerical vector.

sz

size of the resulting array.

func

function to be applied to a vector of numbers.

fillval

value used to fill the array when there are no indices pointing to that component.

a

numerical vector.

first

logical, shall the first or last element encountered be used.

Details

A <- accumarray(subs, val) creates an array A by accumulating elements of the vector val using the lines of subs as indices and applying func to that accumulated vector. The size of the array can be predetermined by the size vector sz.

A = uniq(a) returns a vector b identical to unique(a) and two other vectors of indices m and n such that b == a[m] and a == b[n].

Value

accumarray returns an array of size the maximum in each column of subs, or by sz.

uniq returns a list with components

b

vector of unique elements of a.

m

vector of indices such that b = a[m]

n

vector of indices such that a = b[n]

Note

The Matlab function accumarray can also handle sparse matrices.

See Also

unique

Examples

##  Examples for accumarray
val = 101:105
subs = as.matrix(c(1, 2, 4, 2, 4))
accumarray(subs, val)
# [101; 206; 0; 208]

val = 101:105
subs <- matrix(c(1,2,2,2,2, 1,1,3,1,3, 1,2,2,2,2), ncol = 3)
accumarray(subs, val)
# , , 1
# [,1] [,2] [,3]
# [1,]  101    0    0
# [2,]    0    0    0
# , , 2
# [,1] [,2] [,3]
# [1,]    0    0    0
# [2,]  206    0  208

val = 101:106
subs <- matrix(c(1, 2, 1, 2, 3, 1, 4, 1, 4, 4, 4, 1), ncol = 2, byrow = TRUE)
accumarray(subs, val, func = function(x) sum(diff(x)))
# [,1] [,2] [,3] [,4]
# [1,]    0    1    0    0
# [2,]    0    0    0    0
# [3,]    0    0    0    0
# [4,]    2    0    0    0

val = 101:105
subs = matrix(c(1, 1, 2, 1, 2, 3, 2, 1, 2, 3), ncol = 2, byrow = TRUE)
accumarray(subs, val, sz = c(3, 3), func = max, fillval = NA)
# [,1] [,2] [,3]
# [1,]  101   NA   NA
# [2,]  104   NA  105
# [3,]   NA   NA   NA

##  Examples for uniq
a <- c(1, 1, 5, 6, 2, 3, 3, 9, 8, 6, 2, 4)
A <- uniq(a); A
# A$b  1  5  6  2  3  9  8  4
# A$m  2  3 10 11  7  8  9 12
# A$n  1  1  2  3  4  5  5  6  7  3  4  8
A <- uniq(a, first = TRUE); A
# A$m  1  3  4  5  6  8  9 12

##  Example: Subset sum problem
# Distribution of unique sums among all combinations of a vectors.
allsums <- function(a) {
    S <- c(); C <- c()
    for (k in 1:length(a)) {
        U <- uniq(c(S, a[k], S + a[k]))
        S <- U$b
        C <- accumarray(U$n, c(C, 1, C))
    }
    o <- order(S); S <- S[o]; C <- C[o]
    return(list(S = S, C = C))
}
A <- allsums(seq(1, 9, by=2)); A
# A$S  1  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25
# A$C  1  1  1  1  1  1  2  2  2  1  2  2  1  2  2  2  1  1  1  1  1  1  1