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plans.jl
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plans.jl
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struct TransformFactorization{T,Grid,Plan} <: Factorization{T}
grid::Grid
plan::Plan
end
TransformFactorization{T}(grid, plan) where T = TransformFactorization{T,typeof(grid),typeof(plan)}(grid, plan)
"""
TransformFactorization(grid, plan)
associates a planned transform with a grid. That is, if `F` is a `TransformFactorization`, then
`F \\ f` is equivalent to `F.plan * f[F.grid]`.
"""
TransformFactorization(grid, plan) = TransformFactorization{promote_type(eltype(eltype(grid)),eltype(plan))}(grid, plan)
grid(T::TransformFactorization) = T.grid
function size(T::TransformFactorization, k)
@assert k == 2 # TODO: make consistent
size(T.plan,1)
end
\(a::TransformFactorization, b::AbstractQuasiVector) = a.plan * convert(Array, b[a.grid])
\(a::TransformFactorization, b::AbstractQuasiMatrix) = a.plan * convert(Array, b[a.grid,:])
"""
InvPlan(factorization, dims)
Takes a factorization and supports it applied to different dimensions.
"""
struct InvPlan{T, Facts<:Tuple, Dims} <: Plan{T}
factorizations::Facts
dims::Dims
end
InvPlan(fact::Tuple, dims) = InvPlan{eltype(fact), typeof(fact), typeof(dims)}(fact, dims)
InvPlan(fact, dims) = InvPlan((fact,), dims)
size(F::InvPlan) = size.(F.factorizations, 1)
"""
MulPlan(matrix, dims)
Takes a matrix and supports it applied to different dimensions.
"""
struct MulPlan{T, Fact<:Tuple, Dims} <: Plan{T}
matrices::Fact
dims::Dims
end
MulPlan(mats::Tuple, dims) = MulPlan{eltype(mats), typeof(mats), typeof(dims)}(mats, dims)
MulPlan(mats::AbstractMatrix, dims) = MulPlan((mats,), dims)
for (Pln,op,fld) in ((:MulPlan, :*, :(:matrices)), (:InvPlan, :\, :(:factorizations)))
@eval begin
function *(P::$Pln{<:Any,<:Tuple,Int}, x::AbstractVector)
@assert P.dims == 1
$op(only(getfield(P, $fld)), x) # Only a single factorization when dims isa Int
end
function *(P::$Pln{<:Any,<:Tuple,Int}, X::AbstractMatrix)
if P.dims == 1
$op(only(getfield(P, $fld)), X) # Only a single factorization when dims isa Int
else
@assert P.dims == 2
permutedims($op(only(getfield(P, $fld)), permutedims(X)))
end
end
function *(P::$Pln{<:Any,<:Tuple,Int}, X::AbstractArray{<:Any,3})
Y = similar(X)
if P.dims == 1
for j in axes(X,3)
Y[:,:,j] = $op(only(getfield(P, $fld)), X[:,:,j])
end
elseif P.dims == 2
for k in axes(X,1)
Y[k,:,:] = $op(only(getfield(P, $fld)), X[k,:,:])
end
else
@assert P.dims == 3
for k in axes(X,1), j in axes(X,2)
Y[k,j,:] = $op(only(getfield(P, $fld)), X[k,j,:])
end
end
Y
end
function *(P::$Pln{<:Any,<:Tuple,Int}, X::AbstractArray{<:Any,4})
Y = similar(X)
if P.dims == 1
for j in axes(X,3), l in axes(X,4)
Y[:,:,j,l] = $op(only(getfield(P, $fld)), X[:,:,j,l])
end
elseif P.dims == 2
for k in axes(X,1), l in axes(X,4)
Y[k,:,:,l] = $op(only(getfield(P, $fld)), X[k,:,:,l])
end
elseif P.dims == 3
for k in axes(X,1), j in axes(X,2)
Y[k,j,:,:] = $op(only(getfield(P, $fld)), X[k,j,:,:])
end
elseif P.dims == 4
for k in axes(X,1), j in axes(X,2), l in axes(X,3)
Y[k,j,l,:] = $op(only(getfield(P, $fld)), X[k,j,l,:])
end
end
Y
end
*(P::$Pln{<:Any,<:Tuple,Int}, X::AbstractArray) = error("Overload")
function *(P::$Pln, X::AbstractArray)
for (fac,dim) in zip(getfield(P, $fld), P.dims)
X = $Pln(fac, dim) * X
end
X
end
end
end
*(A::AbstractMatrix, P::MulPlan) = MulPlan(Ref(A) .* P.matrices, P.dims)
inv(P::MulPlan) = InvPlan(map(factorize,P.matrices), P.dims)
inv(P::InvPlan) = MulPlan(convert.(Matrix,P.factorizations), P.dims)