cosmetic fixes

Author: MikaelSlevinsky

examples/nonlocaldiffusion.jl

@@ -1,4 +1,4 @@
-using FastTransforms
+using FastTransforms, LinearAlgebra
 
 function oprec!(n::Integer, v::AbstractVector, alpha::Real, delta2::Real)
     if n > 0
@@ -13,15 +13,19 @@ function oprec!(n::Integer, v::AbstractVector, alpha::Real, delta2::Real)
     return v
 end
 
-# This example calculates the spectrum of the nonlocal diffusion operator:
-#
-#  \mathcal{L}_\delta u = \int_{\mathbb{S}^2} \rho_\delta(|\mathbf{x}-\mathbf{y}|)\left[u(\mathbf{x}) - u(\mathbf{y})\right] \,\mathrm{d}\Omega(\mathbf{y}),
-#
-#  defined in Eq. (2) of
-#
-#    R. M. Slevinsky, H. Montanelli, and Q. Du, [A spectral method for nonlocal diffusion operators on the sphere](https://doi.org/10.1016/j.jcp.2018.06.024), *J. Comp. Phys.*, **372**:893--911, 2018.
-#
+"""
+This example calculates the spectrum of the nonlocal diffusion operator:
 
+```math
+ℒ_δ u = ∫_𝕊² ρ_δ(|𝐱-𝐲|)[u(𝐱) - u(𝐲)] dΩ(𝐲),
+```
+
+defined in Eq. (2) of
+
+    R. M. Slevinsky, H. Montanelli, and Q. Du, A spectral method for nonlocal diffusion operators on the sphere, J. Comp. Phys., 372:893--911, 2018.
+
+available at https://doi.org/10.1016/j.jcp.2018.06.024
+"""
 function evaluate_lambda(n::Integer, alpha::T, delta::T) where T
     delta2 = delta*delta
     scl = (1+alpha)*(2-delta2/2)
@@ -56,7 +60,7 @@ function evaluate_lambda(n::Integer, alpha::T, delta::T) where T
     return lambda
 end
 
-lambda = evaluate_lambda(1024, -0.5, 0.025)
-lambdabf = evaluate_lambda(1024, parse(BigFloat, "-0.5"), parse(BigFloat, "0.025"))
+lambda = evaluate_lambda(1024, -0.5, 1.0)
+lambdabf = evaluate_lambda(1024, parse(BigFloat, "-0.5"), parse(BigFloat, "1.0"))
 
-norm(lambda64-lambdabf, Inf)/norm(lambda64, Inf)
+norm(lambda-lambdabf, Inf)/norm(lambda, Inf)

examples/sphere.jl

@@ -5,8 +5,8 @@
 #
 # is actually a degree-3 polynomial on 𝕊², where P₄ is the degree-4
 # Legendre polynomial, and x,y,z ∈ 𝕊².
-# To verify, we sample the function on a 5×9 tensor product grid
-# at equispaced points-in-angle defined by:
+# To verify, we sample the function on a 5×9 equiangular grid
+# defined by:
 #
 #   θₙ = (n+1/2)π/N, for 0 ≤ n < N, and
 #

src/libfasttransforms.jl

@@ -1,18 +1,3 @@
-# This file shows how to call `libfasttransforms` from Julia.
-# It is normally built by downloading precompiled binaries assuming that
-# dependencies are already installed. However, it may also be built from source.
-
-# Step 1: In this repository,
-# `git clone -b v0.2.7 https://github.com/MikaelSlevinsky/FastTransforms.git deps/FastTransforms`
-
-# Step 2: Get the dependencies. On macOS, run `brew install gcc@8 fftw mpfr`.
-# On linux, run `apt-get gcc-8 libblas-dev libopenblas-base libfftw3-dev libmpfr-dev`.
-
-# Step 3: Build the library. On macOS, run `make CC=gcc-8 FT_USE_APPLEBLAS=1`.
-# On linux, run `make CC=gcc-8`.
-
-# Step 4: move `libfastfransforms.dylib` out of the folder to be found by ↓.
-
 const libfasttransforms = joinpath(dirname(@__DIR__), "deps", "libfasttransforms")
 
 if !(find_library(libfasttransforms) ≡ libfasttransforms)