Use SVector instead of Vec (#846)

* Use SVector instead of Vec

* Lower compat bound for BandedMatrices

Project.toml

@@ -1,13 +1,14 @@
 name = "ApproxFun"
 uuid = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
-version = "0.13.11"
+version = "0.13.12"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
 ApproxFunFourier = "59844689-9c9d-51bf-9583-5b794ec66d30"
 ApproxFunOrthogonalPolynomials = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
 ApproxFunSingularities = "f8fcb915-6b99-5be2-b79a-d6dbef8e6e7e"
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
 DomainSets = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
 DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
@@ -17,15 +18,17 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
 AbstractFFTs = "1.0"
-ApproxFunBase = "0.7.30"
+ApproxFunBase = "0.7.34"
 ApproxFunBaseTest = "0.1"
 ApproxFunFourier = "0.3"
 ApproxFunOrthogonalPolynomials = "0.5"
 ApproxFunSingularities = "0.3"
 Aqua = "0.5"
+BandedMatrices = "0.16, 0.17"
 Calculus = "0.5"
 DomainSets = "0.3, 0.4, 0.5"
 DualNumbers = "0.6.2"
@@ -34,14 +37,16 @@ FastTransforms = "0.13, 0.14"
 RecipesBase = "1.0"
 Reexport = "1.0"
 SpecialFunctions = "1.1, 2"
+StaticArrays = "1"
 julia = "1.6"
 
 [extras]
 ApproxFunBaseTest = "a931bfaf-0cfd-4a5c-b69c-bf2eed002b43"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ApproxFunBaseTest", "Aqua", "Documenter", "Random", "Test"]
+test = ["ApproxFunBaseTest", "Aqua", "BlockBandedMatrices", "Documenter", "Random", "Test"]

examples/Eigenvalue_symmetric.jl

@@ -10,6 +10,7 @@
 
 using ApproxFun
 using LinearAlgebra
+using BandedMatrices
 
 # Define parameters
 ω = 25.0
@@ -32,7 +33,7 @@ R = D1*Q;
 # This inversion is computed approximately, such that
 # ``\mathrm{C}^{-1} \mathrm{C} ≈ \mathrm{I}`` up to a certain bandwidth
 C = Conversion(domainspace(L), rangespace(L))
-P = cache(PartialInverseOperator(C, (0, ApproxFun.bandwidth(L, 1) + ApproxFun.bandwidth(R, 1) + ApproxFun.bandwidth(C, 2))));
+P = cache(PartialInverseOperator(C, (0, bandwidth(L, 1) + bandwidth(R, 1) + bandwidth(C, 2))));
 
 A = R'D1*P*L*D2*R
 B = R'R;

examples/PDE_Helmholtz.jl

@@ -18,7 +18,7 @@ L = [Dirichlet(d); Laplacian()+100I];
 
 # We compute the QR decomposition of the operator to speed up the solution
 Q = qr(L);
-ApproxFun.resizedata!(Q,:,4000);
+ApproxFunBase.resizedata!(Q,:,4000);
 
 # The boundary condition is a function that is equal to one on each edge
 boundary_cond = ones(∂(d));

src/ApproxFun.jl

@@ -10,84 +10,53 @@ import Calculus
 @reexport using ApproxFunOrthogonalPolynomials
 @reexport using ApproxFunSingularities
 
-import ApproxFunBase: normalize!, flipsign, FiniteRange, Fun, MatrixFun, UnsetSpace, VFun, RowVector,
-                    UnivariateSpace, AmbiguousSpace, SumSpace, SubSpace, WeightSpace, NoSpace, Space,
-                    HeavisideSpace, PointSpace,
-                    IntervalOrSegment, RaggedMatrix, AlmostBandedMatrix,
-                    AnyDomain, ZeroSpace, ArraySpace, TrivialInterlacer, BlockInterlacer,
-                    AbstractTransformPlan, TransformPlan, ITransformPlan,
-                    ConcreteConversion, ConcreteMultiplication, ConcreteDerivative, ConcreteIntegral, CalculusOperator,
-                    ConcreteVolterra, Volterra, VolterraWrapper,
-                    MultiplicationWrapper, ConversionWrapper, DerivativeWrapper, Evaluation, EvaluationWrapper,
-                    Conversion, defaultConversion, defaultcoefficients, default_Fun, Multiplication, Derivative, Integral, bandwidths,
-                    ConcreteEvaluation, ConcreteDefiniteLineIntegral, ConcreteDefiniteIntegral, ConcreteIntegral,
-                    DefiniteLineIntegral, DefiniteIntegral, ConcreteDefiniteIntegral, ConcreteDefiniteLineIntegral, IntegralWrapper,
-                    ReverseOrientation, ReverseOrientationWrapper, ReverseWrapper, Reverse, NegateEven,
-                    Dirichlet, ConcreteDirichlet, DirichletWrapper,
-                    TridiagonalOperator, SubOperator, Space, @containsconstants, spacescompatible,
-                    hasfasttransform, canonicalspace, domain, setdomain, prectype, domainscompatible,
-                    plan_transform, plan_itransform, plan_transform!, plan_itransform!, transform, itransform, hasfasttransform,
-                    CanonicalTransformPlan, ICanonicalTransformPlan,
-                    Integral,
-                    domainspace, rangespace, boundary,
-                    union_rule, conversion_rule, maxspace_rule, conversion_type, maxspace, hasconversion, points,
-                    rdirichlet, ldirichlet, lneumann, rneumann, ivp, bvp,
-                    linesum, differentiate, integrate, linebilinearform, bilinearform,
-                    UnsetNumber, coefficienttimes, subspace_coefficients, sumspacecoefficients, specialfunctionnormalizationpoint,
-                    Segment, IntervalOrSegmentDomain, PiecewiseSegment, isambiguous, Vec, eps, isperiodic,
-                    arclength, complexlength,
-                    invfromcanonicalD, fromcanonical, tocanonical, fromcanonicalD, tocanonicalD, canonicaldomain, setcanonicaldomain, mappoint,
-                    reverseorientation, checkpoints, evaluate, mul_coefficients, coefficients, coefficientmatrix, isconvertible,
-                    clenshaw, ClenshawPlan, sineshaw,
-                    toeplitz_getindex, toeplitz_axpy!, sym_toeplitz_axpy!, hankel_axpy!, ToeplitzOperator, SymToeplitzOperator, hankel_getindex,
-                    SpaceOperator, ZeroOperator, InterlaceOperator,
-                    interlace!, reverseeven!, negateeven!, cfstype, pad!, alternatesign!, mobius,
-                    extremal_args, hesseneigvals, chebyshev_clenshaw, recA, recB, recC, roots,splitatroots,
-                    chebmult_getindex, intpow, alternatingsum,
-                    domaintype, diagindshift, rangetype, weight, isapproxinteger, default_Dirichlet, scal!, dotu,
-                    components, promoterangespace, promotedomainspace, choosedomainspace,
-                    block, blockstart, blockstop, blocklengths, isblockbanded, pointscompatible,
+import ApproxFunBase: Fun, UnsetSpace, VFun, UnivariateSpace, SumSpace, Space,
+                    HeavisideSpace, PointSpace, IntervalOrSegment, ArraySpace,
+                    TransformPlan, ITransformPlan, Evaluation,
+                    Conversion, default_Fun, Derivative, Integral,
+                    Dirichlet, domain, plan_transform,
+                    plan_itransform, transform, domainspace,
+                    rangespace, boundary, points, differentiate, integrate,
+                    Segment, arclength, fromcanonical, checkpoints, evaluate,
+                    coefficients, coefficientmatrix, clenshaw, ClenshawPlan,
+                    SpaceOperator, InterlaceOperator, cfstype, pad!,
+                    isapproxinteger, components, promotedomainspace, choosedomainspace,
                     AbstractProductSpace, MultivariateFun, BivariateSpace,
-                    @wrapperstructure, @wrapperspaces, @wrapper, @calculus_operator, resizedata!, slnorm,
-                    sample, chop!, isbanded, colrange, bandwidth,
-                    ∇, 𝒟, Δ, ∫, ⨜, Σ, ∮, ⨍, ⨎
+                    @calculus_operator, slnorm, sample, chop!, 𝒟, ∫, ⨜, ⨍
 
 export ∫, ⨜, ⨍, 𝒟
 
 import ApproxFunOrthogonalPolynomials: order
 
+import BandedMatrices: bandwidths
 
 import AbstractFFTs: Plan, fft, ifft
-import FFTW: plan_r2r!, fftwNumber, REDFT10, REDFT01, REDFT00, RODFT00, R2HC, HC2R,
-                r2r!, r2r,  plan_fft, plan_ifft, plan_ifft!, plan_fft!
+import FFTW: plan_fft, plan_ifft, plan_ifft!
 
-import Base: values, convert, getindex, setindex!, *, +, -, ==, <, <=, >, |, !, !=, eltype, iterate,
-                >=, /, ^, \, ∪, transpose, size, tail, broadcast, broadcast!, copyto!, copy, to_index, (:),
-                similar, map, vcat, hcat, hvcat, show, summary, stride, sum, cumsum, sign, conj, inv,
-                complex, reverse, exp, sqrt, abs, abs2, sign, issubset, values, in, first, last, rand, intersect, setdiff,
-                isless, union, angle, join, isnan, isapprox, isempty, sort, merge, promote_rule,
-                minimum, maximum, extrema, argmax, argmin, findmax, findmin, isfinite,
-                zeros, zero, one, promote_rule, repeat, length, resize!, isinf,
-                getproperty, findfirst, unsafe_getindex, fld, cld, div, real, imag,
-                @_inline_meta, eachindex, firstindex, lastindex, keys, isreal, OneTo,
-                Array, Vector, Matrix, view, ones, @propagate_inbounds, print_array,
-                split
+import Base: convert, getindex, *, +, -, /, ^, \, sum, cumsum,
+                first, last, isempty, zeros, promote_rule, real,
+                # the following functions names are listed in Calculus.symbolic_derivatives_1arg(),
+                # and methods are added to them here
+                sqrt, cbrt, abs2, inv, log, log10, log2, log1p,
+                exp, exp2, expm1, sin, cos, tan, sec, csc, cot,
+                sind, cosd, tand, secd, cscd, cotd, asin, acos, atan, asec, acsc, acot,
+                asind, acosd, atand, asecd, acscd, acotd, sinh, cosh, tanh, sech, csch,
+                coth, asinh, acosh, atanh, asech, acsch, acoth, deg2rad, rad2deg
 
-import Base.Broadcast: BroadcastStyle, Broadcasted, AbstractArrayStyle, broadcastable,
-                        DefaultArrayStyle, broadcasted
+import LinearAlgebra: eigvals, dot, adjoint
 
-
-
-import LinearAlgebra: BlasInt, BlasFloat, norm, ldiv!, mul!, det, eigvals, dot, cross,
-                        qr, qr!, rank, isdiag, istril, istriu, issymmetric, ishermitian,
-                        Tridiagonal, diagm, diagm_container, factorize, nullspace,
-                        Hermitian, Symmetric, adjoint, transpose, char_uplo
+import SpecialFunctions: erf, erfinv, erfc, erfcinv, erfi, gamma, lgamma, digamma, invdigamma,
+                trigamma, airyai, airybi, airyaiprime, airybiprime, besselj0, besselj1,
+                bessely0, bessely1, erfcx, dawson
 
 # import Arpack: eigs
 
 
-import FastTransforms: ChebyshevTransformPlan, IChebyshevTransformPlan, plan_chebyshevtransform,
-                        plan_chebyshevtransform!, plan_ichebyshevtransform, plan_ichebyshevtransform!
+import FastTransforms: ChebyshevTransformPlan, plan_chebyshevtransform,
+                        plan_chebyshevtransform!, plan_ichebyshevtransform,
+                        plan_ichebyshevtransform!
+
+using StaticArrays: SVector
 
 """
 `Curve` Represents a domain defined by the image of a Fun.  Example
@@ -106,11 +75,6 @@ Curve(f::Fun{<:Space{<:ChebyshevInterval}}) = IntervalCurve(f)
 
 export Curve
 
-
-
-import Base: view
-
-
 ##Testing
 export bisectioninv
 

src/Extras/dualnumbers.jl

@@ -71,18 +71,15 @@ function dualFun(f,S,n)
 end
 
 function dualcfsFun(f,S)
-    T = float(eltype(domain(S)))
-    if T <: Complex
-        T = T.parameters[1] #get underlying real representation
-    end
+    T = real(float(eltype(domain(S))))
     r=checkpoints(S)
     f0=f(first(r))
 
     if isa(f0,AbstractArray) && size(S) ≠ size(f0)
         return dualcfsFun(f,Space(fill(S,size(f0))))
     end
 
-    tol =T==Any ? 100eps() : 100eps(T)
+    tol = 100eps(T)
 
 
     fr=typeof(f0)[f(x) for x=r]

src/Plot/Plot.jl

@@ -110,7 +110,7 @@ end
     # end
 end
 
-@recipe function f(dd::Segment{<:Vec{2}})
+@recipe function f(dd::Segment{<:SVector{2}})
     a,b = endpoints(dd)
     [a[1],b[1]], [a[2],b[2]]
 end

test/runtests.jl

@@ -1,5 +1,6 @@
 using ApproxFun, Random, Test
 using ApproxFunBase: testbandedblockbandedoperator, blocklengths, ∞
+using BlockBandedMatrices: blockbandwidths, subblockbandwidths
 
 using Aqua
 @testset "Project quality" begin
@@ -99,8 +100,8 @@ end
 
     sp = Space(dom)
     Dr = Derivative(sp, [1,0])
-    @test ApproxFunBase.blockbandwidths(Dr) == (-1,1)
-    @test ApproxFunBase.subblockbandwidths(Dr)  == (1,3)
+    @test blockbandwidths(Dr) == (-1,1)
+    @test subblockbandwidths(Dr)  == (1,3)
 
     Dθ = Derivative(sp, [0,1])
     Mr = Multiplication(Fun( (r, θ) -> r, sp ), sp)