Some Utility Functions

δ([T,] sz, pos=FourierTools.fft_center.(sz))

Return an array which has 1 at pos in the array of size sz.

Examples

julia> δ((3, 3))
3×3 Matrix{Int64}:
 0  0  0
 0  1  0
 0  0  0

julia> δ(Float32, (4, 3))
4×3 Matrix{Float32}:
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  0.0

julia> δ(Float32, (3, 3), (1,1))
3×3 Matrix{Float32}:
 1.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

center_set!(arr_large, arr_small)

Puts the arr_small central into arr_large. The convention, where the center is, is the same as the definition as for FFT based centered. Function works both for even and uneven arrays.

Examples

julia> FourierTools.center_set!([1, 1, 1, 1, 1, 1], [5, 5, 5])
6-element Array{Int64,1}:
 1
 1
 5
 5
 5
 1

get_indices_around_center(i_in, i_out)

A function which provides two output indices i1 and i2 where i2 - i1 = i_out The indices are chosen in a way that the set i1:i2 cuts the interval 1:i_in in a way that the center frequency stays at the center position. Works for both odd and even indices

center_extract(arr, new_size_array)

Extracts a center of an array. new_size_array must be list of sizes indicating the output size of each dimension. Centered means that a center frequency stays at the center position. Works for even and uneven. If length(new_size_array) < length(ndims(arr)) the remaining dimensions are untouched and copied.

Examples

julia> FourierTools.center_extract([1 2; 3 4], [1])
1×2 view(::Matrix{Int64}, 2:2, 1:2) with eltype Int64:
 3  4

julia> FourierTools.center_extract([1 2; 3 4], [1, 1])
1×1 view(::Matrix{Int64}, 2:2, 2:2) with eltype Int64:
 4

julia> FourierTools.center_extract([1 2 3; 3 4 5; 6 7 8], [2 2])
2×2 view(::Matrix{Int64}, 1:2, 1:2) with eltype Int64:
 1  2
 3  4

selectsizes(x, dism; keep_dims=true)

Select the sizes of x for all dims If keep_dims=true the non-selected dimensions are returned as 1.

Examples

julia> FourierTools.selectsizes(randn((4,3,2)), (2,3))
(1, 3, 2)

julia> FourierTools.selectsizes(randn((4,3,2)), (2,3), keep_dims=false)
(3, 2)

expanddims(x, ::Val{N})
expanddims(x, N::Number)

expands the dimensions of an array to a given number of dimensions.

Try to prefer the Val version because this is type-stable. Val(N) encapsulates the number in a type from which the compiler can then infer the return type.

Examples

The result is a 5D array with singleton dimensions at the end

julia> expanddims(ones((1,2,3)), Val(5))
1×2×3×1×1 Array{Float64, 5}:
[:, :, 1, 1, 1] =
 1.0  1.0

[:, :, 2, 1, 1] =
 1.0  1.0

[:, :, 3, 1, 1] =
 1.0  1.0

julia> expanddims(ones((1,2,3)), 5)
1×2×3×1×1 Array{Float64, 5}:
[:, :, 1, 1, 1] =
 1.0  1.0

[:, :, 2, 1, 1] =
 1.0  1.0

[:, :, 3, 1, 1] =
 1.0  1.0

slice(arr, dim, index)

Return a N dimensional slice (where one dimensions has size 1) of the N-dimensional arr at the index position index in the dim dimension of the array. It holds size(out)[dim] == 1.

Examples

julia> x = [1 2 3; 4 5 6; 7 8 9]
3×3 Matrix{Int64}:
 1  2  3
 4  5  6
 7  8  9

julia> FourierTools.slice(x, 1, 1)
1×3 view(::Matrix{Int64}, 1:1, 1:3) with eltype Int64:
 1  2  3

slice_indices(a, dim, index)

a should be the axes obtained by axes(arr) of an array. dim is the dimension to be selected and index the index of it.

Examples

julia> FourierTools.slice_indices((1:10, 1:20, 1:12, 1:33), 1, 3)
(3:3, 1:20, 1:12, 1:33)