Structured arrays for Julia

StructuredArrays is a small Julia package which provides multi-dimensional arrays behaving like regular arrays but whose elements have the same given value or are computed by applying a given function to their indices. The main advantage of such arrays is that they are very light in terms of memory: their storage requirement is O(1) whatever their size instead of O(n) for a usual array of n elements.

Note that StructuredArrays has a different purpose than StructArrays which is designed for arrays whose elements are struct.

Uniform arrays

All elements of a uniform array have the same value. To build such an array, call:

A = UniformArray(val, dims)

which yields an array A behaving as a read-only array of size dims whose values are all val. The array dimensions may be specified as multiple arguments.

Uniform arrays implement conventional linear indexing: A[i] yields val for all linear indices i in the range 1:length(A).

Statements like A[i] = val are however not implemented because uniform arrays are considered as read-only. You may call MutableUniformArray(val,dims) to create a uniform array, say B, whose element value can be changed:

B = MutableUniformArray(val, dims)

A statement like B[i] = val is allowed to change the value of all the elements of B provided index i represents all possible indices in B. Typically B[:] = val or B[1:end] = val are accepted but not B[1] = val unless B has a single element.

Apart from all values being the same, uniform arrays should behaves like ordinary Julia arrays.

Fast uniform arrays

A fast uniform array is like an immutable uniform array but with the elements value being part of the signature so that this value is known at compile time. To build such an array, call:

A = FastUniformArray(val, dims)

Structured arrays

The values of the elements of a structured array are computed on the fly as a function of their indices. To build such an array, call:

A = StructuredArray(func, dims)

which yields an array A behaving as a read-only array of size dims whose entries are computed as a given function, here func, of its indices: A[i] yields func(i). The array dimensions may be specified as multiple arguments.

An optional leading argument S may be used to specify another index style than the default IndexCartesian:

A = StructuredArray(S, func, dims)

where S may be a sub-type of IndexStyle or an instance of such a sub-type. If S is IndexCartesian (the default), the function func will be called with N integer arguments, N being the number of dimensions. If S is IndexLinear, the function func will be called with a single integer argument.

A structured array can be used to specify the location of structural non-zeros in a sparse matrix. For instance, the structure of a lower triangular matrix of size m×n would be given by:

StructuredArray((i,j) -> (i ≥ j), m, n)

but with a constant small storage requirement whatever the size of the matrix.

Although the callable object func may not be a pure function, its return type shall be stable and structured arrays are considered as immutable in the sense that a statement like A[i] = val is not implemented. The type of the elements of structured array is guessed by applying func to the unit index. The element type, say T, may also be explicitely specified:

StructuredArray{T}([S = IndexCartesian,] func, dims)