Recursive Array Types

VectorOfArray(u::AbstractVector)

Wrap a collection of equally shaped or ragged arrays as one column-major AbstractArray without materializing a dense concatenation. The last index selects an inner array: A[j, i] accesses component j of A.u[i], while A.u[i] returns the stored array itself.

Arguments

• u: an indexable collection of inner arrays. The first inner array determines the element type and dimensionality; later arrays may be ragged in size.

Returns

A mutable VectorOfArray with size(A) == (size(A.u[1])..., length(A.u)) for rectangular input. Ragged input is represented by the maximum inner size and reads outside an inner array as zero.

Notes

VectorOfArray implements the AbstractArray interface. Use A.u[i] or A[:, i] to access an inner array; linear indexing A[i] accesses scalar elements in column-major order.

Fields

• u: the collection of stored arrays.

Examples

A = VectorOfArray([[1, 2], [3, 4]])
size(A) == (2, 2)
A[2, 1] == 2
Array(A) == [1 3; 2 4]

DiffEqArray(u::AbstractVector, t::AbstractVector; kwargs...)

Wrap saved state arrays u and matching time points t as an AbstractDiffEqArray. The result supports the VectorOfArray interface and stores metadata used for symbolic indexing, interpolation, and plotting.

Arguments

• u: an indexable collection of saved state arrays.
• t: the time values corresponding to the entries of u.

Keyword Arguments

• discretes: discrete parameter timeseries, or nothing.
• variables: variable symbols used to construct symbolic-indexing metadata.
• parameters: parameter symbols used to construct symbolic-indexing metadata.
• independent_variables: independent-variable symbols used to construct symbolic-indexing metadata.
• interp: an interpolation object called as interp(t, idxs, deriv, p, continuity).
• dense: whether dense interpolation is available.

Returns

A mutable DiffEqArray with the saved states, times, parameters, and symbolic indexing metadata. Positional overloads additionally accept p and sys when those objects have already been constructed.

Fields

• u: the saved state arrays.
• t: the time corresponding to each entry of u.
• p: parameter values associated with the solution.
• sys: symbolic indexing metadata.
• discretes: discrete parameter timeseries, or nothing.
• interp: interpolation object for dense output, or nothing.
• dense: whether dense interpolation is available.

Examples

t = [0.0, 0.5, 1.0]
u = [[sin(ti), cos(ti)] for ti in t]
A = DiffEqArray(u, t)
A[1, :] == sin.(t)

ArrayPartition(parts...)

Wrap arrays with potentially different types as one linear AbstractVector. Indexing traverses the partitions in order, while broadcasting operates partition-by-partition without losing the individual array types.

Arguments

• parts...: arrays or scalar values to store as the partitions.
• copy_x: when constructing from a tuple with Val{true}, copy each partition; the default Val{false} preserves the supplied partition objects.

Returns

An ArrayPartition whose element type is the promoted bottom element type of the partitions.

Errors

ArrayPartition{T, S}(undef, n) throws an ArgumentError unless S describes exactly one partition.

Fields

• x: the tuple of stored arrays.

Examples

A = ArrayPartition([1, 2], [3.0, 4.0])
A[3] == 3.0
A.x[1] == [1, 2]
collect(A) == [1.0, 2.0, 3.0, 4.0]

NamedArrayPartition(; kwargs...)
NamedArrayPartition(x::NamedTuple)

Similar to an ArrayPartition but the individual arrays can be accessed via the constructor-specified names. However, unlike ArrayPartition, each individual array must have the same element type.

Arguments

• kwargs...: named partitions, for example position = [1.0, 2.0].
• x: a NamedTuple containing the named partitions.

Fields

• array_partition: the underlying ArrayPartition.
• names_to_indices: a NamedTuple mapping each constructor name to its partition index.

Returns

A named linear AbstractVector whose properties access the corresponding partitions.

Errors

Construction asserts that all partitions have the same element type.

Examples

A = NamedArrayPartition(position = [1.0, 2.0], velocity = [3.0, 4.0])
A.position == [1.0, 2.0]
collect(A) == [1.0, 2.0, 3.0, 4.0]

VA

Shorthand constructor marker for VectorOfArray. Load RecursiveArrayToolsShorthandConstructors to enable VA[arrays...] syntax.

Examples

using RecursiveArrayToolsShorthandConstructors
A = VA[[1, 2], [3, 4]]
A == VectorOfArray([[1, 2], [3, 4]])

AP

Shorthand constructor marker for ArrayPartition. Load RecursiveArrayToolsShorthandConstructors to enable AP[parts...] syntax.

Examples

using RecursiveArrayToolsShorthandConstructors
A = AP[[1, 2], [3.0, 4.0]]
A == ArrayPartition([1, 2], [3.0, 4.0])

AllObserved()

Sentinel used by symbolic indexing implementations to request all observed variables from an AbstractDiffEqArray. This is a developer interface for packages extending symbolic indexing.