Mercurial > repos > public > sbplib_julia
changeset 468:a52f38e72258 feature/outer_product
Start implementing function for outer products
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 22 Oct 2020 10:18:57 +0200 |
| parents | a0e40d16ba0e |
| children | 481e86e77c22 |
| files | src/LazyTensors/lazy_tensor_operations.jl test/testLazyTensors.jl |
| diffstat | 2 files changed, 58 insertions(+), 0 deletions(-) [+] |
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--- a/src/LazyTensors/lazy_tensor_operations.jl Wed Oct 21 22:02:07 2020 +0200 +++ b/src/LazyTensors/lazy_tensor_operations.jl Thu Oct 22 10:18:57 2020 +0200 @@ -273,3 +273,55 @@ flatten_tuple(t::NTuple{N, Number} where N) = t flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify? flatten_tuple(ts::Vararg) = flatten_tuple(ts) + + +""" + LazyOuterProduct(tms...) + +Creates a `TensorComposition` for the outerproduct of `tms...`. +This is done by separating the outer product into regular products of outer products involving only identity mappings and one non-identity mapping. + +First let +```math +A = A_{I,J} +B = B_{M,N} +C = C_{P,Q} +``` + +where ``I``, ``M``, ``P`` are multi-indexes for the ranges of ``A``, ``B``, ``C``, and ``J``, ``N``, ``Q`` are multi-indexes of the domains. + +We use ``⊗`` to denote the outer product +```math +(A⊗B)_{IM,JN} = A_{I,J}B_{M,N} +``` + +We note that +```math +A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q} +``` +And that +```math +A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C) +``` +where |.| of a multi-index is a vector of sizes for each dimension. ``I_v`` denotes the identity tensor of size ``v[i]`` in each direction +To apply ``A⊗B⊗C`` we evaluate + +(A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]] +""" +function LazyOuterProduct end +export LazyOuterProduct + +function LazyOuterProduct(tm1::TensorMapping, tm2::TensorMapping) + itm1 = InflatedTensorMapping(tm1, IdentityMapping(range_size(tm2))) + itm2 = InflatedTensorMapping(IdentityMapping(domain_size(tm1)),tm2) + + return itm1∘itm2 +end + +# length(tms) is always >= 1 since the two argument method is more specific. Right?? +LazyOuterProduct(tm::TensorMapping, tms::Vararg{TensorMapping}) = tm∘LazyOuterProduct(tms...) + +⊗(a::TensorMapping,b::TensorMapping) = LazyOuterProduct(a,b) +⊗(a,b,cs::Vararg{TensorMapping}) = ⊗(a⊗b, cs...) + +# TODO: Can we implement compositions and kroneckers of LazyIdentities to just return new LazyIdentities?