update progress meter

add arXiv reference

Author: MikaelSlevinsky

README.md

@@ -108,10 +108,10 @@ julia> norm(F-H)
 julia> F = sphrandn(Float64, 1024, 1024);
 
 julia> G = sph2fourier(F; sketch = :none);
-Pre-computing thin plan...100%|██████████████████████████████████████████████████| Time: 0:00:04
+Pre-computing...100%|███████████████████████████████████████████| Time: 0:00:04
 
 julia> H = fourier2sph(G; sketch = :none);
-Pre-computing thin plan...100%|██████████████████████████████████████████████████| Time: 0:00:04
+Pre-computing...100%|███████████████████████████████████████████| Time: 0:00:04
 
 julia> norm(F-H)
 1.1510623098225283e-12
@@ -130,6 +130,6 @@ As with other fast transforms, `plan_sph2fourier` saves effort by caching the pr
 
    [4]  R. M. Slevinsky. <a href="https://doi.org/10.1093/imanum/drw070">On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev—Jacobi transform</a>, in press at *IMA J. Numer. Anal.*, 2017.
 
-   [5]  R. M. Slevinsky. <a href="https://arxiv.org/abs/">Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series</a>, arXiv, 2017.
+   [5]  R. M. Slevinsky. <a href="https://arxiv.org/abs/1705.05448">Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series</a>, arXiv, 2017.
 
    [6]  A. Townsend, M. Webb, and S. Olver. <a href="https://doi.org/10.1090/mcom/3277">Fast polynomial transforms based on Toeplitz and Hankel matrices</a>, in press at *Math. Comp.*, 2017.

docs/src/index.md

@@ -6,7 +6,7 @@ In numerical analysis, it is customary to expand a function in a basis:
 ```math
 f(x) \sim \sum_{\ell=0}^{\infty} f_{\ell} \phi_{\ell}(x).
 ```
-It may be more convenient to transform our representation to one in a new basis, say, ``\{\psi_m(x)\}_{m\ge0}``:
+It may be necessary to transform our representation to one in a new basis, say, ``\{\psi_m(x)\}_{m\ge0}``:
 ```math
 f(x) \sim \sum_{m=0}^{\infty} g_m \psi_m(x).
 ```

src/SphericalHarmonics/fastplan.jl

@@ -22,7 +22,7 @@ function FastSphericalHarmonicPlan{T}(A::Matrix{T}, L::Int; opts...)
     Ce = eye(T, M)
     Co = eye(T, M)
     BF = Vector{Butterfly{T}}(n-2)
-    P = Progress(n-2, 0.1, "Pre-computing fast plan...", 50)
+    P = Progress(n-2, 0.1, "Pre-computing...", 43)
     for j = 1:2:n-2
         A_mul_B!(Ce, RP.layers[j])
         BF[j] = Butterfly(Ce, L; isorthogonal = true, opts...)

src/SphericalHarmonics/thinplan.jl

@@ -26,7 +26,7 @@ function ThinSphericalHarmonicPlan{T}(A::Matrix{T}, L::Int; opts...)
     Ce = eye(T, M)
     Co = eye(T, M)
     BF = Vector{Butterfly{T}}(n-2)
-    P = Progress(n-2, 0.1, "Pre-computing thin plan...", 50)
+    P = Progress(n-2, 0.1, "Pre-computing...", 43)
     for j = 1:2:n-2
         A_mul_B!(Ce, RP.layers[j])
         checklayer(j+1) && (BF[j] = Butterfly(Ce, L; isorthogonal = true, opts...))

test/sphericalharmonictests.jl

@@ -35,7 +35,6 @@ for θ in (0.123, 0.456)
     S0 = sum(cospi((ℓ-1)*θ)*B[ℓ,1] for ℓ in 1:n+1)
     SA = sum(sphevaluatepi(θ,ℓ-1,0)*A[ℓ,1] for ℓ in 1:n+1)
     @test norm(S0-SA) < 1000eps()
-    push!(nrms, norm(S0-SA))
     for m in 3:2:n+1
         S0 = sum(cospi((ℓ-1)*θ)*B[ℓ,2m-2] for ℓ in 1:n+1)
         SA = sum(sphevaluatepi(θ,ℓ+m-2,m-1)*A[ℓ,2m-2] for ℓ in 1:n+1)