Abind {DescTools}

Combine Multidimensional Arrays

Description

Base R functions cbind and rbind bind columns and rows, but there's no built-in function for binding higher dimensional datastructures like matrices. Abind takes a sequence of vectors, matrices, or arrays and produces a single array of the same or higher dimension.

Usage

Abind(..., along = N, rev.along = NULL, new.names = NULL, force.array = TRUE,
      make.names = FALSE, use.first.dimnames = FALSE, hier.names = FALSE,
      use.dnns = FALSE)

Arguments

...

Any number of vectors, matrices, arrays, or data frames. The dimensions of all the arrays must match, except on one dimension (specified by along=). If these arguments are named, the name will be used for the name of the dimension along which the arrays are joined. Vectors are treated as having a dim attribute of length one.

Alternatively, there can be one (and only one) list argument supplied, whose components are the objects to be bound together. Names of the list components are treated in the same way as argument names.

along

The dimension along which to bind the arrays. The default is the last dimension, i.e., the maximum length of the dim attribute of the supplied arrays. along= can take any non-negative value up to the minimum length of the dim attribute of supplied arrays plus one. When along= has a fractional value, a value less than 1, or a value greater than N (N is the maximum of the lengths of the dim attribute of the objects to be bound together), a new dimension is created in the result. In these cases, the dimensions of all arguments must be identical.

rev.along

Alternate way to specify the dimension along which to bind the arrays: along = N + 1 - rev.along. This is provided mainly to allow easy specification of along = N + 1 (by supplying rev.along=0). If both along and rev.along are supplied, the supplied value of along is ignored.

new.names

If new.names is a list, it is the first choice for the dimnames attribute of the result. It should have the same structure as a dimnames attribute. If the names for a particular dimension are NULL, names for this dimension are constructed in other ways.

If new.names is a character vector, it is used for dimension names in the same way as argument names are used. Zero length ("") names are ignored.

force.array

If FALSE, rbind or cbind are called when possible, i.e., when the arguments are all vectors, and along is not 1, or when the arguments are vectors or matrices or data frames and along is 1 or 2. If rbind or cbind are used, they will preserve the data.frame classes (or any other class that r/cbind preserve). Otherwise, Abind will convert objects to class array. Thus, to guarantee that an array object is returned, supply the argument force.array=TRUE. Note that the use of rbind or cbind introduces some subtle changes in the way default dimension names are constructed: see the examples below.

make.names

If TRUE, the last resort for dimnames for the along dimension will be the deparsed versions of anonymous arguments. This can result in cumbersome names when arguments are expressions. The default is FALSE.

use.first.dimnames

When dimension names are present on more than one argument, should dimension names for the result be take from the first available (the default is to take them from the last available, which is the same behavior as rbind and cbind.)

hier.names

If TRUE, dimension names on the concatenated dimension will be composed of the argument name and the dimension names of the objects being bound. If a single list argument is supplied, then the names of the components serve as the argument names. hier.names can also have values "before" or "after"; these determine the order in which the argument name and the dimension name are put together (TRUE has the same effect as "before").

use.dnns

(default FALSE) Use names on dimensions, e.g., so that names(dimnames(x)) is non-empty. When there are multiple possible sources for names of dimnames, the value of use.first.dimnames determines the result.

Details

The dimensions of the supplied vectors or arrays do not need to be identical, e.g., arguments can be a mixture of vectors and matrices. Abind coerces arguments by the addition of one dimension in order to make them consistent with other arguments and along=. The extra dimension is added in the place specified by along=.

The default action of Abind is to concatenate on the last dimension, rather than increase the number of dimensions. For example, the result of calling Abind with vectors is a longer vector (see first example below). This differs from the action of rbind and cbind which is to return a matrix when called with vectors. Abind can be made to behave like cbind on vectors by specifying along=2, and like rbind by specifying along=0.

The dimnames of the returned object are pieced together from the dimnames of the arguments, and the names of the arguments. Names for each dimension are searched for in the following order: new.names, argument name, dimnames (or names) attribute of last argument, dimnames (or names) attribute of second last argument, etc. (Supplying the argument use.first.dimnames=TRUE changes this to cause Abind to use dimnames or names from the first argument first. The default behavior is the same as for rbind and cbind: use dimnames from later arguments.) If some names are supplied for the along dimension (either as argument names or dimnames in arguments), names are constructed for anonymous arguments unless maken.ames=FALSE.

Value

An array with a dim attribute calculated as follows.

Let rMin=min(sapply(list(...), function(x) length(dim(x)))) and
rMax=max(sapply(list(...), function(x) length(dim(x)))) (where the length of the dimensions of a vector are taken to be 1). Then rMax should be equal to or one greater than rMin.

If along refers to an existing dimension, then the length of the dim attribute of the result is rMax. If along does not refer to an existing dimension, then rMax should equal rMin and the length of the dim attribute of the result will be rMax+1.

rbind or cbind are called to compute the result if (a) force.array=FALSE; and (b) the result will be a two-dimensional object.

Note

It would be nice to make Abind() an S3 generic, but S3 generics cannot dispatch off anonymous arguments.

The ability of Abind() to accept a single list argument removes much of the need for constructs like do.call("Abind", list.of.arrays). Instead, just do Abind(list.of.arrays). The direct construct is preferred because do.call() construct can sometimes consume more memory during evaluation.

Author(s)

Tony Plate <[e-mail]> and Richard Heiberger

See Also

rbind, cbind, array

Examples

# Five different ways of binding together two matrices
x <- matrix(1:12, 3, 4)
y <- x + 100
dim(Abind(x, y, along=0))     # binds on new dimension before first
dim(Abind(x, y, along=1))     # binds on first dimension
dim(Abind(x, y, along=1.5))
dim(Abind(x, y, along=2))
dim(Abind(x, y, along=3))
dim(Abind(x, y, rev.along=1)) # binds on last dimension
dim(Abind(x, y, rev.along=0)) # binds on new dimension after last

# Unlike cbind or rbind in that the default is to bind
# along the last dimension of the inputs, which for vectors
# means the result is a vector (because a vector is
# treated as an array with length(dim(x))==1).
Abind(x=1:4, y=5:8)

# Like cbind
Abind(x=1:4, y=5:8, along=2)
Abind(x=1:4, matrix(5:20, nrow=4), along=2)
Abind(1:4, matrix(5:20, nrow=4), along=2)

# Like rbind
Abind(x=1:4, matrix(5:20, nrow=4), along=1)
Abind(1:4, matrix(5:20, nrow=4), along=1)

# Create a 3-d array out of two matrices
Abind(x=matrix(1:16, nrow=4), y=matrix(17:32, nrow=4), along=3)

# Use of hier.names
Abind(x=cbind(a=1:3, b=4:6), y=cbind(a=7:9, b=10:12), hier.names=TRUE)

# Use a list argument
Abind(list(x=x, y=x), along=3)
# Use lapply(..., get) to get the objects
an <- c('x', 'y')
names(an) <- an
Abind(lapply(an, get), along=3)