# JuliaArrays/OffsetArrays.jl

Fortran-like arrays with arbitrary, zero or negative starting indices. Fetching latest commit…
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# OffsetArrays.jl

OffsetArrays provides Julia users with arrays that have arbitrary indices, similar to those found in some other programming languages like Fortran.

```julia> using OffsetArrays

julia> y = OffsetArray{Float64}(undef, -1:1, -7:7, -128:512, -5:5, -1:1, -3:3, -2:2, -1:1);

julia> summary(y)
"OffsetArrays.OffsetArray{Float64,8,Array{Float64,8}} with indices -1:1×-7:7×-128:512×-5:5×-1:1×-3:3×-2:2×-1:1"

julia> y[-1,-7,-128,-5,-1,-3,-2,-1] = 14
14

julia> y[-1,-7,-128,-5,-1,-3,-2,-1] += 5
19.0```

## Example: Relativistic Notation

Suppose we have a position vector `r = [:x, :y, :z]` which is naturally one-based, ie. `r == :x`, `r == :y`, `r == :z` and we also want to cosntruct a relativistic position vector which includes time as the 0th component. This can be done with OffsetArrays like

```julia> using OffsetArrays

julia> r = [:x, :y, :z];

julia> x = OffsetVector([:t, r...], 0:3)
OffsetArray(::Array{Symbol,1}, 0:3) with eltype Symbol with indices 0:3:
:t
:x
:y
:z

julia> x
:t

julia> x[1:3]
3-element Array{Symbol,1}:
:x
:y
:z```

## Example: Polynomials

Suppose one wants to represent the Laurent polynomial

``````6/x + 5 - 2*x + 3*x^2 + x^3
``````

in julia. The coefficients of this polynomial are a naturally `-1` based list, since the `n`th element of the list (counting from `-1`) `6, 5, -2, 3, 1` is the coefficient corresponding to the `n`th power of `x`. This Laurent polynomial can be evaluated at say `x = 2` as follows.

```julia> using OffsetArrays

julia> coeffs = OffsetVector([6, 5, -2, 3, 1], -1:3)
OffsetArray(::Array{Int64,1}, -1:3) with eltype Int64 with indices -1:3:
6
5
-2
3
1

julia> polynomial(x, coeffs) = sum(coeffs[n]*x^n for n in eachindex(coeffs))
polynomial (generic function with 1 method)

julia> polynomial(2.0, coeffs)
24.0```

Notice our use of the `eachindex` function which does not assume that the given array starts at `1`.

## Notes on supporting OffsetArrays

Julia supports generic programming with arrays that doesn't require you to assume that indices start with 1, see the documentation.

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