Add logo (#95)

* add logo image file and its source

* add misc page in the document

docs/logo.jl

@@ -0,0 +1,54 @@
+using FastGaussQuadrature, LinearAlgebra, Luxor
+logocolors = Luxor.Colors.JULIA_LOGO_COLORS
+
+@svg begin
+    n = 15
+    Drawing(500,500, "docs/src/assets/logo.svg")
+    origin()
+    unitlength = 210
+    translate(0, unitlength)
+
+    Y = (n+1/2)/π
+
+    x_lgd, w_lgd = gausslegendre(n)
+    x_cbs, w_cbs = gausschebyshev(n,3)
+    x_jcb, w_jcb = gaussjacobi(n,5/2,1/2)
+
+    c_lgd = logocolors[1]  # Red
+    c_cbs = logocolors[2]  # Green
+    c_jcb = logocolors[4]  # Purple
+
+    p_jcb = [Point(unitlength*x_jcb[i], -Y*unitlength*w_jcb[i]) for i in 1:n]
+    p_cbs = [Point(unitlength*x_cbs[i], -Y*unitlength*w_cbs[i]) for i in 1:n]
+    p_lgd = [Point(unitlength*x_lgd[i], -Y*unitlength*w_lgd[i]) for i in 1:n]
+
+    l_jcb = [norm(p_jcb[i+1]-p_jcb[i]) for i in 1:n-1]
+    l_cbs = [norm(p_cbs[i+1]-p_cbs[i]) for i in 1:n-1]
+    l_lgd = [norm(p_lgd[i+1]-p_lgd[i]) for i in 1:n-1]
+
+    r_jcb = zeros(n)
+    r_cbs = zeros(n)
+    r_lgd = zeros(n)
+
+    r_jcb[end] = norm(l_jcb[end])/2 * 0.8
+    r_cbs[end] = norm(l_cbs[end])/2 * 0.7
+    r_lgd[end] = norm(l_lgd[end])/2 * 0.75
+
+    for i in reverse(1:n-1) r_jcb[i] = l_jcb[i] - r_jcb[i+1] end
+    for i in reverse(1:n-1) r_cbs[i] = l_cbs[i] - r_cbs[i+1] end
+    for i in reverse(1:n-1) r_lgd[i] = l_lgd[i] - r_lgd[i+1] end
+
+    sethue(c_cbs)
+    for i in 5:n circle(p_cbs[i], r_cbs[i], :fill) end
+    sethue(c_jcb)
+    for i in 1:n circle(p_jcb[i], r_jcb[i], :fill) end
+    sethue(c_lgd)
+    for i in 1:n circle(p_lgd[i], r_lgd[i], :fill) end
+    sethue(c_cbs)
+    for i in 1:4 circle(p_cbs[i], r_cbs[i], :fill) end
+
+    finish()
+    preview()
+end
+
+run(`convert -density 256x256 -background transparent docs/src/assets/logo.svg -define icon:auto-resize -colors 256 docs/src/assets/favicon.ico`)

docs/make.jl

@@ -12,6 +12,7 @@ makedocs(;
         "Gaussian Quadrature" => "gaussquadrature.md",
         "Benchmark" => "benchmark.md",
         "Roots of Bessel function" => "besselroots.md",
+        "Misc." => "misc.md",
         "References" => "reference.md",
     ],
     repo = "https://github.com/JuliaApproximation/FastGaussQuadrature.jl/blob/{commit}{path}#L{line}",

docs/src/misc.md

@@ -0,0 +1,21 @@
+# Misc.
+
+## About the logo
+![](assets/logo.svg)
+
+* The center points of circles are generated from nodes(x-axis) and weights(y-axis) of Gaussian quadrature.
+    * Number of points : `n = 15`
+    * ``\textcolor{#CB3C33}{\text{\textbf{Red}}}`` : `gausslegendre(n)`
+    * ``\textcolor{#389826}{\text{\textbf{Green}}}`` : `gausschebyshev(n, 3)`
+    * ``\textcolor{#9558B2}{\text{\textbf{Purple}}}`` : `gaussjacobi(n, 5/2, 1/2)`
+* These colors are from [julia-logo-graphics](https://github.com/JuliaLang/julia-logo-graphics).
+* The logo is generated with [Luxor.jl](https://github.com/JuliaGraphics/Luxor.jl), and its source code is [here](https://github.com/JuliaApproximation/FastGaussQuadrature.jl/blob/master/docs/logo.jl).
+
+
+## Other docstrings from private methods
+
+```@autodocs
+Modules = [FastGaussQuadrature]
+Private = true
+Public = false
+```

src/gaussjacobi.jl

@@ -253,7 +253,7 @@ end
 """
 Evaluate the interior asymptotic formula at x = cos(t).
 Assumption:
-* length(t) == n ÷ 2
+* `length(t) == n ÷ 2`
 """
 function feval_asy1(n::Integer, α::Float64, β::Float64, t::AbstractVector, idx)
     # Number of terms in the expansion:

src/gausslaguerre.jl

@@ -106,16 +106,11 @@ const airy_roots = [-2.338107410459767, -4.08794944413097, -5.520559828095551,
 
 
 """
-Compute the Gauss-Laguerre rule using explicit asymptotic expansions for the nodes
-and weights.
+Compute the Gauss-Laguerre rule using explicit asymptotic expansions for the nodes and weights.
 Optional parameters are:
-- `reduced`: compute a reduced quadrature rule, discarding all points and weights
-as soon as the weights underflow
-- `T`: the order of the expansion. Set `T=-1` to determine the order adaptively
-depending on the size of the terms in the expansion
-- `recompute`: if a crude measure of the error is larger than a tolerance,
-the point and weight are recomputed using the (slower) recursion+newton approach,
-yielding more reliable accurate results.
+- `reduced`: compute a reduced quadrature rule, discarding all points and weights as soon as the weights underflow
+- `T`: the order of the expansion. Set `T=-1` to determine the order adaptively depending on the size of the terms in the expansion
+- `recompute`: if a crude measure of the error is larger than a tolerance, the point and weight are recomputed using the (slower) recursion+newton approach, yielding more reliable accurate results.
 """
 function gausslaguerre_asy(n::Integer, α;
     reduced = false,