reinstate tests

Project.toml

@@ -1,6 +1,6 @@
 name = "FastTransforms"
 uuid = "057dd010-8810-581a-b7be-e3fc3b93f78c"
-version = "0.16.7"
+version = "0.16.8"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

test/grammatrixtests.jl

@@ -0,0 +1,87 @@
+using FastTransforms, BandedMatrices, LazyArrays, LinearAlgebra, Test
+
+@testset "GramMatrix" begin
+    n = 128
+    for T in (Float32, Float64, BigFloat)
+        R = plan_leg2cheb(T, n; normcheb=true)*I
+        X = Tridiagonal([T(n)/(2n-1) for n in 1:n-1], zeros(T, n), [T(n)/(2n+1) for n in 1:n-1]) # Legendre X
+        W = Symmetric(R'R)
+        G = GramMatrix(W, X)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ W
+        @test F.U ≈ R
+
+        R = plan_leg2cheb(T, n; normcheb=true, normleg=true)*I
+        X = SymTridiagonal(zeros(T, n), [sqrt(T(n)^2/(4*n^2-1)) for n in 1:n-1]) # normalized Legendre X
+        W = Symmetric(R'R)
+        G = GramMatrix(W, X)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ W
+        @test F.U ≈ R
+
+        b = 4
+        X = BandedMatrix(SymTridiagonal(zeros(T, n+b), [sqrt(T(n)^2/(4*n^2-1)) for n in 1:n+b-1])) # normalized Legendre X
+        W = I+X^2+X^4
+        W = Symmetric(W[1:n, 1:n])
+        X = BandedMatrix(SymTridiagonal(zeros(T, n), [sqrt(T(n)^2/(4*n^2-1)) for n in 1:n-1])) # normalized Legendre X
+        G = GramMatrix(W, X)
+        @test bandwidths(G) == (b, b)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ W
+
+        X = BandedMatrix(SymTridiagonal(T[2n-1 for n in 1:n+b], T[-n for n in 1:n+b-1])) # Laguerre X, tests nonzero diagonal
+        W = I+X^2+X^4
+        W = Symmetric(W[1:n, 1:n])
+        X = BandedMatrix(SymTridiagonal(T[2n-1 for n in 1:n], T[-n for n in 1:n-1])) # Laguerre X
+        G = GramMatrix(W, X)
+        @test bandwidths(G) == (b, b)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ W
+    end
+    W = reshape([i for i in 1.0:n^2], n, n)
+    X = reshape([i for i in 1.0:4n^2], 2n, 2n)
+    @test_throws "different sizes" GramMatrix(W, X)
+    X = X[1:n, 1:n]
+    @test_throws "nonsymmetric" GramMatrix(W, X)
+    @test_throws "nontridiagonal" GramMatrix(Symmetric(W), X)
+end
+
+@testset "ChebyshevGramMatrix" begin
+    n = 128
+    for T in (Float32, Float64, BigFloat)
+        μ = FastTransforms.chebyshevmoments1(T, 2n-1)
+        G = ChebyshevGramMatrix(μ)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ G
+        R = plan_cheb2leg(T, n; normleg=true)*I
+        @test F.U ≈ R
+
+        α, β = (T(0.123), T(0.456))
+        μ = FastTransforms.chebyshevjacobimoments1(T, 2n-1, α, β)
+        G = ChebyshevGramMatrix(μ)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ G
+        R = plan_cheb2jac(T, n, α, β; normjac=true)*I
+        @test F.U ≈ R
+
+        μ = -FastTransforms.chebyshevlogmoments1(T, 2n-1)
+        G = ChebyshevGramMatrix(μ)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ G
+
+        μ = FastTransforms.chebyshevabsmoments1(T, 2n-1)
+        G = ChebyshevGramMatrix(μ)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ G
+
+        μ = PaddedVector(T(1) ./ [1,2,3,4,5], 2n-1)
+        G = ChebyshevGramMatrix(μ)
+        @test bandwidths(G) == (4, 4)
+        F = cholesky(G)
+        @test F.L*F.L' ≈ G
+        μd = Vector{T}(μ)
+        Gd = ChebyshevGramMatrix(μd)
+        Fd = cholesky(Gd)
+        @test F.L ≈ Fd.L
+    end
+end