more efficient support function

src/dwt/wvlt.jl

@@ -45,16 +45,16 @@ _vanishingmoments(::Prl, W, is_orthogonal::Type{True}) = vanishingmoments(Prl(),
 ###############################################################################
 # support/support_length
 ###############################################################################
-support{WT<:DiscreteWavelet}(side::Side, kind::Scl, ::Type{WT}, j::Int=0, k::Int=0) = (j == 0 && k == 0) ?
-    Sequences.support(filter(side, Scl(), WT)) :
-    Sequences.support(filter(side, Scl(), WT), j, k)
-
-function support{WT<:DiscreteWavelet}(side::Side, kind::Wvl, ::Type{WT}, j::Int=0, k::Int=0)
-  supp1 = support(side, Scl(), WT)
-  supp2 = support(inv(side), Scl(), WT)
-  S1 = Int(1/2*(supp1[1]-supp2[2]+1))
-  S2 = Int(1/2*(supp1[2]-supp2[1]+1))
-  (j == 0 && k == 0) ? (S1,S2) : (1/(1<<j)*(S1[1]+k), 1/(1<<j)*(S2+k))
+support{WT<:DiscreteWavelet}(side::Side, kind::Scl, ::Type{WT}) =
+    Sequences.support(filter(side, Scl(), WT))
+function support{WT<:DiscreteWavelet}(side::Side, kind::Wvl, ::Type{WT})
+    l1, r1 = support(side, Scl(), WT)
+    l2, r2 = support(inv(side), Scl(), WT)
+    ((l1-r2+1)>>1, (r1-l2+1)>>1)
+end
+function support{WT<:DiscreteWavelet}(side::Side, kind::Kind, ::Type{WT}, j::Int, k::Int)
+    l, r = support(side, kind, WT)
+    (1/(1<<j)*(l+k), 1/(1<<j)*(r+k))
 end
 
 support_length{WT<:DiscreteWavelet}(side::Side, kind::Kind,  ::Type{WT}) = support(side, kind, WT)[2] - support(side, kind, WT)[1]

src/dwt/wvlt_cdf.jl

@@ -79,7 +79,7 @@ cdf66_htilde = (16384, [-63, 378, -476, -1554, 4404, 1114, -13860, 4158, 28182,
 
 # Determine the offset of the filter such that the filter is even symmetric w.r.t
 # 0 (for filters of odd length) or 1/2 (for filters of even length).
-symmetric_offset(n) = iseven(n) ? -n>>1+1 : -(n-1)>>1
+symmetric_offset(n) = -((n-1)>>1)
 
 # The coefficients of the primal scaling function are simply a binomial sequence for all n.
 cdf_coef(n) = 1//(1<<(n-1))*[binomial(n,k) for k in 0:n]
@@ -95,11 +95,14 @@ for (p,q,htilde) in ( (1, 1, :cdf11_htilde), (1, 3, :cdf13_htilde), (1, 5, :cdf1
                       (6, 2, :cdf62_htilde), (6, 4, :cdf64_htilde), (6, 6, :cdf66_htilde)  )
     @eval filter{T}(side::Dul, kind::Cof, ::Type{CDFWavelet{$p,$q,T}}) = CompactSequence(2//$htilde[1]*$htilde[2], symmetric_offset(length($htilde[2])))
     @eval filter{T}(side::Dul, kind::Scl, ::Type{CDFWavelet{$p,$q,T}}) = CompactSequence(sqrt(T(2))/$htilde[1]*convert(Array{T,1}, $htilde[2]), symmetric_offset(length($htilde[2])))
+    @eval support{T}(side::Dul, kind::Scl, ::Type{CDFWavelet{$p,$q,T}}) = (symmetric_offset(length($htilde[2])),symmetric_offset(length($htilde[2]))+length($htilde[2])-1)
+    @eval support_length{T}(side::Dul, kind::Scl, ::Type{CDFWavelet{$p,$q,T}}) = length($htilde[2])-1
 end
 
 vanishingmoments{N1,N2,T}(::Prl, ::Type{CDFWavelet{N1,N2,T}}) = N1
 vanishingmoments{N1,N2,T}(::Dul, ::Type{CDFWavelet{N1,N2,T}}) = N2
 support{N1,N2,T}(::Prl, ::Scl, ::Type{CDFWavelet{N1,N2,T}}) = (symmetric_offset(N1+1), symmetric_offset(N1+1) + N1)
+support_length(::Prl, ::Scl, ::Type{CDFWavelet{N1,N2,T}}) where {N1,N2,T} = N1
 
 evaluate{N1,N2,T,S<:Real}(side::Prl, kind::Scl, w::CDFWavelet{N1,N2,T}, j::Int, k::Int, x::S; options...) =
       T(2)^(j/2)*evaluate_Bspline(N1-1, T(2)^j*x-T(k)-T(DWT.symmetric_offset(N1+1)), promote_type(T, eltype(x)))

src/dwt/wvlt_daubechies.jl

@@ -39,7 +39,11 @@ name{N,T}(::Type{DaubechiesWavelet{N,T}}) = string("db",N,"_",T)
 name{N}(::Type{DaubechiesWavelet{N,Float64}}) = string("db",N)
 
 support{N,T}(::Prl, ::Scl, ::Type{DaubechiesWavelet{N,T}}) = (0,2N-1)
+support_length(::Prl, ::Scl, ::Type{DaubechiesWavelet{N,T}}) where {N,T} = 2N-1
+support{N,T}(::Dul, ::Scl, ::Type{DaubechiesWavelet{N,T}}) = (0,2N-1)
+support_length(::Dul, ::Scl, ::Type{DaubechiesWavelet{N,T}}) where {N,T} = 2N-1
 vanishingmoments{N,T}(::Prl, ::Type{DaubechiesWavelet{N,T}}) = N
+vanishingmoments{N,T}(::Dul, ::Type{DaubechiesWavelet{N,T}}) = N
 
 # Commented for testing purposes
 # evaluate{T,S<:Real}(::Prl, ::Scl, w::DWT.HaarWavelet{T}, j, k, x::Number; options...) =