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First attempt at handling eltypes better
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Tomas Lycken committed Jan 1, 2015
1 parent cfe3e8a commit 345b28f
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Showing 4 changed files with 53 additions and 53 deletions.
55 changes: 33 additions & 22 deletions src/Interpolations.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -51,26 +51,34 @@ abstract InterpolationType{D<:Degree,BC<:BoundaryCondition,GR<:GridRepresentatio
include("extrapolation.jl")

abstract AbstractInterpolation{T,N,IT<:InterpolationType,EB<:ExtrapolationBehavior} <: AbstractArray{T,N}
type Interpolation{T,N,IT<:InterpolationType,EB<:ExtrapolationBehavior} <: AbstractInterpolation{T,N,IT,EB}
coefs::Array{T,N}
type Interpolation{TEl,N,TCoefs<:Real,IT<:InterpolationType,EB<:ExtrapolationBehavior} <: AbstractInterpolation{TEl,N,IT,EB}
coefs::Array{TCoefs,N}
end
function Interpolation{T,N,IT<:InterpolationType,EB<:ExtrapolationBehavior}(A::Array{T,N}, it::IT, ::EB)
function Interpolation{TIn,N,TCoefs,IT<:InterpolationType,EB<:ExtrapolationBehavior}(::Type{TCoefs}, A::AbstractArray{TIn,N}, it::IT, ::EB)
isleaftype(IT) || error("The interpolation type must be a leaf type (was $IT)")

isleaftype(T) || warn("For performance reasons, consider using an array of a concrete type T (eltype(A) == $(eltype(A)))")
isleaftype(TIn) || warn("For performance reasons, consider using an array of a concrete type T (eltype(A) == $(eltype(A)))")

Interpolation{T,N,IT,EB}(prefilter(A,it))
c = one(TCoefs)
for _ in 2:N
c *= c
end
TEl = typeof(c)

Interpolation{TEl,N,TCoefs,IT,EB}(prefilter(TCoefs,A,it))
end
Interpolation{TIn,N,IT<:InterpolationType,EB<:ExtrapolationBehavior}(A::AbstractArray{TIn,N}, it::IT, eb::EB) = Interpolation(TIn, A, it, eb)

# Unless otherwise specified, use coefficients as they are, i.e. without prefiltering
# However, all prefilters copy the array, so do that here as well
prefilter{T,N,IT<:InterpolationType}(A::AbstractArray{T,N}, ::IT) = copy(A)
# We also ensure that the coefficient array is of the correct type
prefilter{T,N,TCoefs,IT<:InterpolationType}(::Type{TCoefs}, A::AbstractArray{T,N}, ::IT) = copy!(Array(TCoefs,size(A)...), A)

size{T,N,IT<:InterpolationType}(itp::Interpolation{T,N,IT}, d::Integer) =
size(itp.coefs, d) - 2*padding(IT())
size(itp::Interpolation) = tuple([size(itp,i) for i in 1:ndims(itp)]...)
size{T,N,TCoefs,IT<:InterpolationType}(itp::Interpolation{T,N,TCoefs,IT}, d::Integer) = size(itp.coefs, d) - 2*padding(TCoefs,IT())
size(itp::AbstractInterpolation) = tuple([size(itp,i) for i in 1:ndims(itp)]...)
ndims(itp::Interpolation) = ndims(itp.coefs)
eltype(itp::Interpolation) = eltype(itp.coefs)
eltype{T}(itp::Interpolation{T}) = T
coeftype(itp::Interpolation) = eltype(itp.coefs)

offsetsym(off, d) = off == -1 ? symbol(string("ixm_", d)) :
off == 0 ? symbol(string("ix_", d)) :
Expand All @@ -89,8 +97,8 @@ include("linear.jl")
include("quadratic.jl")

# If nothing else is specified, don't pad at all
padding(::InterpolationType) = 0
padding{T,N,IT<:InterpolationType}(::Interpolation{T,N,IT}) = padding(IT())
padding{T}(::Type{T}, ::InterpolationType) = zero(T)
padding{T,N,IT<:InterpolationType}(::Interpolation{T,N,IT}) = padding(T,IT())

function pad_size_and_index(sz::Tuple, pad)
sz = Int[s+2pad for s in sz]
Expand All @@ -101,10 +109,10 @@ function pad_size_and_index(sz::Tuple, pad)
end
sz, ind
end
function copy_with_padding(A, it::InterpolationType)
function copy_with_padding(TCoefs, A, it::InterpolationType)
pad = padding(it)
sz,ind = pad_size_and_index(size(A), pad)
coefs = fill(convert(eltype(A), 0), sz...)
coefs = fill!(Array(TCoefs, sz...), 0)
coefs[ind...] = A
coefs, pad
end
Expand Down Expand Up @@ -137,8 +145,8 @@ for IT in (
gr = gridrepresentation(it)
eval(ngenerate(
:N,
:(promote_type(T, x...)),
:(getindex{T,N}(itp::Interpolation{T,N,$IT,$EB}, x::NTuple{N,Real}...)),
:T,
:(getindex{T,N,TCoefs<:Real}(itp::Interpolation{T,N,TCoefs,$IT,$EB}, x::NTuple{N,TCoefs}...)),
N->quote
# Handle extrapolation, by either throwing an error,
# returning a value, or shifting x to somewhere inside
Expand All @@ -157,11 +165,14 @@ for IT in (
ret
end
))
@ngenerate N T function getindex{T,N,TCoefs<:Real}(itp::Interpolation{T,N,TCoefs,IT,EB}, xs::NTuple{N,Real}...)
getindex(itp, [convert(TCoefs, x) for x in xs]...)
end

eval(ngenerate(
:N,
:(Array{promote_type(T,typeof(x)...),1}),
:(gradient!{T,N}(g::Array{T,1}, itp::Interpolation{T,N,$IT,$EB}, x::NTuple{N,Real}...)),
:T,
:(gradient!{T,N,TCoefs}(g::Array{T,1}, itp::Interpolation{T,N,TCoefs,$IT,$EB}, x::NTuple{N,TCoefs}...)),
N->quote
$(extrap_transform_x(gr,eb,N))
$(define_indices(it,N))
Expand All @@ -180,7 +191,7 @@ for IT in (
end
end

gradient{T}(itp::Interpolation{T}, x...) = gradient!(Array(T,ndims(itp)), itp, x...)
gradient1{T}(itp::Interpolation{T,1}, x) = gradient!(Array(T,1),itp,x)[1]

# This creates prefilter specializations for all interpolation types that need them
for IT in (
Expand All @@ -193,8 +204,8 @@ for IT in (
Quadratic{Periodic,OnGrid},
Quadratic{Periodic,OnCell},
)
@ngenerate N promote_type_grid(T, x...) function prefilter{T,N}(A::Array{T,N},it::IT)
ret, pad = copy_with_padding(A,it)
@ngenerate N promote_type_grid(T, x...) function prefilter{T,N,TCoefs}(::Type{TCoefs}, A::Array{T,N},it::IT)
ret, pad = copy_with_padding(TCoefs, A,it)

szs = collect(size(ret))
strds = collect(strides(ret))
Expand All @@ -203,7 +214,7 @@ for IT in (
n = szs[dim]
szs[dim] = 1

M, b = prefiltering_system(eltype(A), n, it)
M, b = prefiltering_system(TCoefs, n, it)

@nloops N i d->1:szs[d] begin
cc = @ntuple N i
Expand Down
13 changes: 1 addition & 12 deletions src/extrapolation.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -82,18 +82,7 @@ end

immutable ExtrapPeriodic <: ExtrapolationBehavior end
function extrap_transform_x(::GridRepresentation, ::ExtrapPeriodic, N)
quote
@nexprs $N d->begin
# translate x_d to inside the domain
n = convert(typeof(x_d), size(itp,d))
while x_d < .5
x_d += n
end
while x_d >= n + .5
x_d -= n
end
end
end
:(@nexprs $N d->(x_d = mod1(x_d, size(itp,d))))
end

immutable ExtrapLinear <: ExtrapolationBehavior end
Expand Down
6 changes: 3 additions & 3 deletions src/linear.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,9 +5,9 @@ Linear{GR<:GridRepresentation}(::GR) = Linear{GR}()
function define_indices(::Linear, N)
quote
@nexprs $N d->begin
ix_d = clamp(floor(Int,x_d), 1, size(itp,d)-1)
ixp_d = ix_d + 1
fx_d = x_d - convert(typeof(x_d), ix_d)
ix_d = clamp(floor(x_d), 1, size(itp,d)-1)
ixp_d = ix_d + one(typeof(ix_d))
fx_d = x_d - ix_d
end
end
end
Expand Down
32 changes: 16 additions & 16 deletions src/quadratic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,25 +5,25 @@ Quadratic{BC<:BoundaryCondition,GR<:GridRepresentation}(::BC, ::GR) = Quadratic{

function define_indices(q::Quadratic, N)
quote
pad = padding($q)
pad = padding(TCoefs, $q)
@nexprs $N d->begin
ix_d = clamp(round(Integer, x_d), 1, size(itp,d)) + pad
ix_d = clamp(round(x_d), 1, size(itp,d)) + pad
ixp_d = ix_d + 1
ixm_d = ix_d - 1

fx_d = x_d - convert(typeof(x_d), ix_d - pad)
fx_d = x_d - (ix_d - pad)
end
end
end
function define_indices(q::Quadratic{Periodic}, N)
quote
pad = padding($q)
pad = padding(TCoefs, $q)
@nexprs $N d->begin
ix_d = clamp(round(Integer, x_d), 1, size(itp,d)) + pad
ixp_d = mod1(ix_d + 1, size(itp,d))
ixm_d = mod1(ix_d - 1, size(itp,d))
ix_d = clamp(round(x_d), 1, size(itp,d)) + pad
ixp_d = mod1(ix_d + one(typeof(ix_d)), size(itp,d))
ixm_d = mod1(ix_d - one(typeof(ix_d)), size(itp,d))

fx_d = x_d - convert(typeof(x_d), ix_d - pad)
fx_d = x_d - (ix_d - pad)
end
end
end
Expand All @@ -36,19 +36,19 @@ function coefficients(q::Quadratic, N, d)
symm, sym, symp = symbol(string("cm_",d)), symbol(string("c_",d)), symbol(string("cp_",d))
symfx = symbol(string("fx_",d))
quote
$symm = .5 * ($symfx - .5)^2
$sym = .75 - $symfx^2
$symp = .5 * ($symfx + .5)^2
$symm = convert(TCoefs, .5) * ($symfx - convert(TCoefs, .5))^2
$sym = convert(TCoefs, .75) - $symfx^2
$symp = convert(TCoefs, .5) * ($symfx + convert(TCoefs, .5))^2
end
end

function gradient_coefficients(q::Quadratic, N, d)
symm, sym, symp = symbol(string("cm_",d)), symbol(string("c_",d)), symbol(string("cp_",d))
symfx = symbol(string("fx_",d))
quote
$symm = $symfx-.5
$sym = -2*$symfx
$symp = $symfx+.5
$symm = $symfx - convert(TCoefs, .5)
$sym = -convert(TCoefs, 2) * $symfx
$symp = $symfx + convert(TCoefs, .5)
end
end

Expand All @@ -69,10 +69,10 @@ end
# Quadratic interpolation has 1 extra coefficient at each boundary
# Therefore, make the coefficient array 1 larger in each direction,
# in each dimension.
padding(::Quadratic) = 1
padding{T}(::Type{T}, ::Quadratic) = one(T)
# For periodic boundary conditions, we don't pad - instead, we wrap the
# the coefficients
padding(::Quadratic{Periodic}) = 0
padding{T}(::Type{T}, ::Quadratic{Periodic}) = zero(T)

function inner_system_diags{T}(::Type{T}, n::Int, ::Quadratic)
du = fill(convert(T,1/8), n-1)
Expand Down

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