Author mcabbott
6 Stars
Updated Last
1 Year Ago
Started In
August 2019


Github CI Tag Version Docstrings

This package exists to experiment with the arrays provided by NamedDims.jl. While that package is fairly minimal (and focused on providing a type with great performance), this one defines lots of useful functions. Some of them are only defined when other packages they need are loaded. Here's what works in v0.0.1:

Some convenient ways add names (exports named, @named, nameless):

@pirate Base
m = rand(Int8; i=3, j=4)                 # names from keywords, needs rand(Type, i=...)
m .+ ones(_=1, j=4, k=2)                 # ones(), zeros(), and fill() all work.

m .- named(parent(m), :i, :j)            # adds names, or refines existing ones, 
a_z = named(rand(4,1,1,2), :a, .., :z)   # use .. (from EllipsisNotation) to skip some.

@named g = [n^i for n in 1:20, i in 1:3] # read names (:n,:i) from generator's variables

rename(m, :i => :z')                     # renames just :i, to :z' == :z′
nameless(m, (:j, :i)) === transpose(m)   # also @named mt = m{j,i} 

Some functions controlled by them:

t = split(g, :n => (j=4, k=5))           # just reshape, new size (4,5,3),
join(t, (:i, :k) => )                  # copy if non-adjacent, size (4,15).

dropdims(a_z)                            # defaults to :_, and kills all of them
transpose(a_z, :a, :z)                   # permutes (4,2,3,1)

A hack to make lots of code propagate names (NamedInt):

d,k = size(m); @show d                   # NamedInt, which exists for:
z = zeros(d,d')                          # ones, fill, rand, etc
z .= [sqrt(i) for i in 1:d, i′ in 1:d']  # comprehensions propagate names from (1:d)
reshape(g, k,:,d) .+ g[end, d]           # reshape propagate via sizes

using Einsum, TensorCast                 # These packages dont't know about names at all,
@einsum mz[i,k] := m[i,j] * z[i,k]       # works because of Array{}(undef, NamedInt...)
@cast tm[i⊗j,k] := t[j,k,i] + m[i,j]     # works because of reshape(A, NamedInt)

Some automatic re-ordering of dimensions (align, align_sum!, align_prod!):

align(m, (:j, :k, :i))                   # lazy generalised permutedims, (:j, :_, :i)
@named q{i,j,k} = m .+ t                 # used for auto-permuted broadcasting
align(m, t) .+ t                         # or to manually fix things up

align_sum!(Int.(m), t)                   # reduce (:j, :k, :i) into (:i, :j)

Including for matrix multiplication (mul, *ᵃ, contract, batchmul):

m *ᵃ z == mul(m, z, :i) == m' * z        # matrix multiplication on shared index,
g *ᵃ m == (m *ᵃ g)'                      # typed *\^a tab.

using TensorOperations
contract(m, t)                           # shared indices i & j, leaving only k
m ⊙ᵃ t == t ⊙ᵃ m                         # infix version, \odot\^a tab
@named @tensor p[j,i′] := m[i,j] * z[i,i′] # named inputs re-arranged via Strided

using OMEinsum
contract(m, t, z)                        # sum over shared :i, leaving (:j, :k, :i′)
const *= batchmul(:k)                  # batch index :k,
t *rename(t, :i => :i')                # sum over shared :j, leaving (:i, :i′, :k)

using Zygote                             
gradient(m -> sum(contract(m,t)[1]), m)[1] # contract defines a gradient
gradient(t -> sum(t *ᵇ q), t)[1]         # OMEinsum defines this gradient

Some other bits have moved to AxisKeys.jl. If both packages are loaded:

using NamedPlus, AxisKeys, Plots
@named [n^i for n in 1:2:40, i in 2:4]   # has custom ranges
scatter(ans, yaxis=:log10)               # labels axes & series

While the functions in NamedDims.jl try very hard to be zero-cost (by working hard to exploit constant propagation), this is not true here. In particluar split, join, align, rename will cost around 1μs. (Perhaps if useful they can be made faster.) But mul and *ᵃ, and aligned broadcasting via @named, should be nearly free, perhaps 5ns.

Compared to Pytorch's new named tensors:

  • refine_namesnamed, except with .. instead of ....
  • unflattensplit exactly, and flattenjoin, except that for them "All of dims must be consecutive in order" while mine permutes if required.
  • .align_to and .align_asalign, mine allows the target to be either a subset or a superset (or neither) of the input. Theirs allows ... again.
  • No support for einsum, but torch.matmul handles batched matrix multiplication.

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