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Avoid recursive call in SemiclassicalJacobiFamily #138

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Avoid recursive call in SemiclassicalJacobiFamily #138

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7 changes: 6 additions & 1 deletion src/SemiclassicalOrthogonalPolynomials.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -174,6 +174,11 @@ function semiclassical_jacobimatrix(t, a, b, c)
end
end

function semiclassical_jacobimatrix_raise_c_by_2(Q)
X = jacobimatrix(Q)
qr_jacobimatrix(Q.t*I-X,X)[1]
end

function semiclassical_jacobimatrix(Q::SemiclassicalJacobi, a, b, c)
Δa = a-Q.a
Δb = b-Q.b
Expand Down Expand Up @@ -202,7 +207,7 @@ function semiclassical_jacobimatrix(Q::SemiclassicalJacobi, a, b, c)
elseif iszero(Δa) && isone(Δb/2) && iszero(Δc)
qr_jacobimatrix(I-X,X)[1]
elseif iszero(Δa) && iszero(Δb) && isone(Δc/2)
qr_jacobimatrix(Q.t*I-X,X)[1]
semiclassical_jacobimatrix_raise_c_by_2(Q)
elseif isone(Δa) && iszero(Δb) && iszero(Δc) # raising by 1
cholesky_jacobimatrix(X,X)[1]
elseif iszero(Δa) && isone(Δb) && iszero(Δc)
Expand Down
14 changes: 11 additions & 3 deletions src/family.jl
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Expand Up @@ -53,13 +53,21 @@ Base.broadcasted(::Type{SemiclassicalJacobi{T}}, t::Number, a::Union{AbstractUni
_broadcast_getindex(a,k) = a[k]
_broadcast_getindex(a::Number,k) = a

function LazyArrays.cache_filldata!(P::SemiclassicalJacobiFamily, inds::AbstractUnitRange)
function LazyArrays.cache_filldata!(P::SemiclassicalJacobiFamily{T,<:Number,<:Number,<:AbstractUnitRange}, inds::AbstractUnitRange) where T
t,a,b,c = P.t,P.a,P.b,P.c
for k in inds
Pprev = P.data[k-2]
P.data[k] = SemiclassicalJacobi{T}(Pprev.t, Pprev.a, Pprev.b, Pprev.c+2, semiclassical_jacobimatrix_raise_c_by_2(Pprev))
end
P
end

function LazyArrays.cache_filldata!(P::SemiclassicalJacobiFamily{<:Number,<:Number,<:AbstractUnitRange}, inds::AbstractUnitRange)
t,a,b,c = P.t,P.a,P.b,P.c
isrange = P.b isa AbstractUnitRange
for k in inds
# If P.data[k-2] is not normalised (aka b = -1), cholesky fails. With the current design, this is only a problem if P.b
# is a range since we can translate between polynomials that both have b = -1.
Pprev = (isrange && P.b[k-2] == -1) ? P.data[k-1] : P.data[k-2] # isrange && P.b[k-2] == -1 could also be !isnormalized(P.data[k-2])
Pprev = P.b[k-2] == -1 ? P.data[k-1] : P.data[k-2] # isrange && P.b[k-2] == -1 could also be !isnormalized(P.data[k-2])
P.data[k] = SemiclassicalJacobi(t, _broadcast_getindex(a,k), _broadcast_getindex(b,k), _broadcast_getindex(c,k), Pprev)
end
P
Expand Down
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