added ClenshawCurtis; fixes #1

ranocha · Feb 15, 2018 · ce9d1ff · ce9d1ff
1 parent eee0d15
commit ce9d1ff
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Showing 7 changed files with 60 additions and 9 deletions.
diff --git a/REQUIRE b/REQUIRE
@@ -3,4 +3,5 @@ julia 0.6
 ArgCheck
 Requires
 Parameters
+FastTransforms
 FastGaussQuadrature
diff --git a/src/PolynomialBases.jl b/src/PolynomialBases.jl
@@ -6,6 +6,7 @@ using ArgCheck
 using Requires
 using Parameters
 using FastGaussQuadrature
+using FastTransforms: clenshawcurtis
 
 
 # types
@@ -31,7 +32,8 @@ include("hahn.jl")
 
 # export
 ## types
-export NodalBasis, LobattoLegendre, GaussLegendre, GaussJacobi, ClosedNewtonCotes
+export NodalBasis, LobattoLegendre, GaussLegendre, GaussJacobi, ClosedNewtonCotes,
+        ClenshawCurtis
 
 ## mappings
 export map_to_canonical, map_to_canonical!, map_from_canonical, map_from_canonical!
@@ -61,7 +63,7 @@ export legendre, legendre_vandermonde, legendre_D, legendre_M,
 export hahn
 
 ## other utilities
-export utility_matrices, includes_boundaries
+export utility_matrices, includes_boundaries, satisfies_sbp
 
 
 end # module
diff --git a/src/nodal_bases.jl b/src/nodal_bases.jl
@@ -253,6 +253,8 @@ end
 
 @inline includes_boundaries(basis::LobattoLegendre) = Val{true}()
 
+@inline satisfies_sbp(basis::LobattoLegendre) = Val{true}()
+
 
 """
     GaussLegendre{T}
@@ -376,6 +378,8 @@ end
 
 @inline includes_boundaries(basis::GaussLegendre) = Val{false}()
 
+@inline satisfies_sbp(basis::GaussLegendre) = Val{true}()
+
 
 """
     GaussJacobi{T<:Real}
@@ -423,6 +427,8 @@ end
 
 @inline includes_boundaries(basis::GaussJacobi) = Val{false}()
 
+@inline satisfies_sbp(basis::GaussJacobi) = Val{false}()
+
 
 """
     ClosedNewtonCotes{T}
@@ -477,3 +483,45 @@ function ClosedNewtonCotes(p::Int, T=Float64)
 end
 
 @inline includes_boundaries(basis::ClosedNewtonCotes) = Val{true}()
+
+@inline satisfies_sbp(basis::ClosedNewtonCotes) = Val{false}()
+
+
+"""
+    ClenshawCurtis{T}
+
+The nodal basis corresponding to the Clenshaw Curtis quadrature in [-1,1] with
+scalar type `T`.
+"""
+struct ClenshawCurtis{T} <: NodalBasis{Line}
+    nodes::Vector{T}
+    weights::Vector{T}
+    baryweights::Vector{T}
+    D::Matrix{T}
+
+    function ClenshawCurtis(nodes::Vector{T}, weights::Vector{T}, baryweights::Vector{T}, D::Matrix{T}) where {T}
+        @argcheck length(nodes) == length(weights) == length(baryweights) == size(D,1) == size(D,2)
+        new{T}(nodes, weights, baryweights, D)
+    end
+end
+
+"""
+    ClenshawCurtis(p::Int, T=Float64)
+
+Generate the `ClenshawCurtis` basis of degree `p` with scalar type `T`.
+"""
+function ClenshawCurtis(p::Int, T=Float64)
+    if p == 0
+        nodes = T[0]
+        weights = T[2]
+    else
+        nodes, weights = clenshawcurtis(p+1, zero(T), zero(T))
+    end
+    baryweights = barycentric_weights(nodes)
+    D = derivative_matrix(nodes, baryweights)
+    ClenshawCurtis(nodes, weights, baryweights, D)
+end
+
+@inline includes_boundaries(basis::ClenshawCurtis) = Val{true}()
+
+@inline satisfies_sbp(basis::ClenshawCurtis) = Val{false}()
diff --git a/test/derivative_test.jl b/test/derivative_test.jl
@@ -77,6 +77,6 @@ for basis_type in subtypes(PolynomialBases.NodalBasis{PolynomialBases.Line})
         xplot = linspace(-1, 1, 100)
         u1 = derivative_at(xplot, u, basis)
         u2 = interpolate(xplot, basis.D*u, basis)
-        @test norm(u1 - u2, Inf) < 5.f-4
+        @test norm(u1 - u2, Inf) < 5.f-3
     end
 end
diff --git a/test/integration_test.jl b/test/integration_test.jl
@@ -6,7 +6,7 @@ function tolerance(p, T=Float64)
     if p <= 2
         1.
     elseif p <= 4
-        0.65
+        0.78
     elseif p <= 6
         0.02
     elseif p <= 8
@@ -39,7 +39,7 @@ function tolerance(p, T=Float64)
 end
 
 for basis_type in subtypes(PolynomialBases.NodalBasis{PolynomialBases.Line})
-    basis_type <: ClosedNewtonCotes && continue
+    basis_type <: Union{ClosedNewtonCotes,ClenshawCurtis} && continue
     for p in 3:15, T in (Float32, Float64)
         basis = basis_type(p, T)
         u = ufunc.(basis.nodes)

diff --git a/test/interpolation_test.jl b/test/interpolation_test.jl
@@ -15,7 +15,7 @@ function tolerance(p, ufunc::typeof(ufunc₁))
     elseif p <= 8
         2.e-3
     elseif p <= 10
-        5.e-5
+        9.5e-4
     else
         2.e-7
     end

diff --git a/test/utilities_test.jl b/test/utilities_test.jl
@@ -22,9 +22,9 @@ for basis_type in subtypes(PolynomialBases.NodalBasis{PolynomialBases.Line})
             @test !(Ru[end] ≈ u[end])
         end
 
-        basis_type <: ClosedNewtonCotes && continue
-
         # SBP property
-        @test norm(M*D + D'*M - R'*B*R) < 1.e-14
+        if satisfies_sbp(basis) == Val{true}()
+            @test norm(M*D + D'*M - R'*B*R) < 1.e-14
+        end
     end
 end