split test and doc code (#817)

Author: jishnub

Project.toml

@@ -30,7 +30,6 @@ DomainSets = "0.3, 0.4, 0.5"
 DualNumbers = "0.6.2"
 FFTW = "1"
 FastTransforms = "0.13, 0.14"
-Plots = "1"
 RecipesBase = "1.0"
 Reexport = "1.0"
 SpecialFunctions = "1.1, 2"
@@ -39,9 +38,8 @@ julia = "1.6"
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "Documenter", "Plots", "Random", "Test"]
+test = ["Aqua", "Documenter", "Random", "Test"]

docs/make.jl

@@ -3,42 +3,57 @@ using Literate
 
 # Generate examples using Literate
 # See https://github.com/fredrikekre/Literate.jl/blob/master/docs/make.jl
-example_dir = joinpath(@__DIR__, "..", "examples")
-output_dir = joinpath(@__DIR__, "src/generated")
+const example_dir = joinpath(@__DIR__, "..", "examples")
+const output_dir = joinpath(@__DIR__, "src/generated")
 
-for example in ["ODE.jl", "PDE.jl", "Sampling.jl", "Periodic.jl",
-		"Eigenvalue.jl", "NonlinearBVP.jl"]
+function replace_includes(str, included)
+    for ex in included
+        content = read(joinpath(example_dir, ex), String)
+        str = replace(str, "include(\"$(ex)\")" => content)
+    end
+    return str
+end
+
+for (example, included) in [
+            ("ODE.jl", ["ODE_BVP.jl", "ODE_increaseprec.jl"]),
+            ("PDE.jl", ["PDE1.jl"]),
+            ("Sampling.jl", String[]),
+            ("Periodic.jl", ["Periodic1.jl"]),
+            ("Eigenvalue.jl", String[]),
+            ("NonlinearBVP.jl", ["NonlinearBVP1.jl"])
+            ]
     filename = joinpath(example_dir, example)
-    Literate.markdown(filename, output_dir, documenter=true)
+    Literate.markdown(filename, output_dir, documenter=true,
+        preprocess = str -> replace_includes(str, included))
 end
 
 makedocs(
-			doctest = false,
-			clean = true,
-			format = Documenter.HTML(),
-			sitename = "ApproxFun.jl",
-			authors = "Sheehan Olver",
-			pages = Any[
-					"Home" => "index.md",
-					"Usage" => Any[
-						"Domains" => "usage/domains.md",
-						"Spaces" => "usage/spaces.md",
-						"Constructors" => "usage/constructors.md",
-						"Operators" => "usage/operators.md",
-						"Linear Equations" => "usage/equations.md"
-					],
-					"Examples" => [
-			            "generated/ODE.md",
-			            "generated/PDE.md",
-			            "generated/Sampling.md",
-			            "generated/Periodic.md",
-			            "generated/Eigenvalue.md",
-			            "generated/NonlinearBVP.md",
-			        ],
-					"Frequently Asked Questions" => "faq.md",
-					"Library" => "library.md"
-				]
-			)
+            doctest = false,
+            clean = true,
+            format = Documenter.HTML(),
+            sitename = "ApproxFun.jl",
+            authors = "Sheehan Olver",
+            pages = Any[
+                    "Home" => "index.md",
+                    "Usage" => Any[
+                        "Domains" => "usage/domains.md",
+                        "Spaces" => "usage/spaces.md",
+                        "Constructors" => "usage/constructors.md",
+                        "Operators" => "usage/operators.md",
+                        "Linear Equations" => "usage/equations.md"
+                    ],
+                    "Examples" => [
+                        "generated/ODE.md",
+                        "generated/PDE.md",
+                        "generated/Sampling.md",
+                        "generated/Periodic.md",
+                        "generated/Eigenvalue.md",
+                        "generated/NonlinearBVP.md",
+                    ],
+                    "Frequently Asked Questions" => "faq.md",
+                    "Library" => "library.md"
+                ]
+            )
 
 
 deploydocs(

examples/NonlinearBVP.jl

@@ -10,32 +10,12 @@
 # ```math
     # Nu = [u(-1)-1,\,u(1)+0.5,\,Du] = [0,0,0].
 # ```
-
-using ApproxFun
-using LinearAlgebra
-
-# Define the vector that collates the differential equation and
-# the boundary conditions
-N(u, x = Fun()) = [u(-1.)-1., u(1.)+0.5, 0.001u'' + 6(1-x^2)u' + u^2 - 1];
-
-# Solve the equation using Newton iteration
-function nbvpsolver()
-    x = Fun()
-    u0 = 0 * x # starting value
-
-    newton(N, u0)
-end
-
-u = nbvpsolver();
+include("NonlinearBVP1.jl")
 
 # We plot the solution
 import Plots
 Plots.plot(u; title = "Solution", xlabel="x", ylabel="u(x)", legend=false)
 
-#src # We verify that the solution satisfies the differential equation and the boundary conditions
-using Test #src
-@test norm(N(u)) ≤ 1000eps() #src
-
 # ## System of nonlinear differential equations
 # One can also solve a system of nonlinear ODEs with potentially nonlinear boundary conditions:
 N(u1, u2) = [u1'(0) - 0.5*u1(0)*u2(0);

examples/NonlinearBVP1.jl

@@ -0,0 +1,20 @@
+using ApproxFun
+using LinearAlgebra
+
+# Define the vector that collates the differential equation and
+# the boundary conditions
+N(u, x = Fun()) = [u(-1.)-1., u(1.)+0.5, 0.001u'' + 6(1-x^2)u' + u^2 - 1];
+
+# Solve the equation using Newton iteration
+function nbvpsolver()
+    x = Fun()
+    u0 = 0 * x # starting value
+
+    newton(N, u0)
+end
+
+u = nbvpsolver();
+
+#src # We verify that the solution satisfies the differential equation and the boundary conditions
+using Test #src
+@test norm(N(u)) ≤ 1000eps() #src

examples/ODE.jl

@@ -11,47 +11,18 @@
 
 using ApproxFun
 
-# Construct the domain
-a, b = -20, 10
-d = a..b;
-
-# We construct the Airy differential operator ``L = d^2/dx^2 - x``:
-x = Fun(d);
-D = Derivative(d);
-L = D^2 - x;
-
-# We impose boundary conditions by setting the function at
-# the boundaries equal to the values of the Airy function at these points.
-# First, we construct the Dirichlet boundary condition operator,
-# that evaluates the function at the boundaries
-B = Dirichlet(d);
-
-# The right hand side for the boundary condition is obtained by evaluating the Airy function
-# We use `airyai` from `SpecialFunctions.jl` for this
-using SpecialFunctions
-B_vals = [airyai(a), airyai(b)];
-
-# The main step, where we solve the differential equation
-u = [B; L] \ [B_vals, 0];
+include("ODE_BVP.jl")
 
 # We plot the solution
 import Plots
 Plots.plot(u, xlabel="x", ylabel="u(x)", legend=false)
 
-#src # Finally, we compare the result with the expected solution (which is an Airy function)
-using Test #src
-@test ≈(u(0), airyai(0); atol=10000eps()) #src
 
 # ## Increasing Precision
 
 # Solving differential equations with high precision types is available.
 # The following calculates ``e`` to 300 digits by solving the ODE ``u^\prime = u``:
 
-u = setprecision(1000) do
-    d = BigFloat(0)..BigFloat(1)
-    D = Derivative(d)
-    [ldirichlet(); D-1] \ [1; 0]
-end
-Plots.plot(u; legend=false, xlabel="x", ylabel="u(x)")
+include("ODE_increaseprec.jl")
 
-@test u(1) ≈ exp(BigFloat(1)) #src
+Plots.plot(u; legend=false, xlabel="x", ylabel="u(x)")

examples/ODE_BVP.jl

@@ -0,0 +1,27 @@
+using ApproxFun #src
+# Construct the domain
+a, b = -20, 10
+d = a..b;
+
+# We construct the Airy differential operator ``L = d^2/dx^2 - x``:
+x = Fun(d);
+D = Derivative(d);
+L = D^2 - x;
+
+# We impose boundary conditions by setting the function at
+# the boundaries equal to the values of the Airy function at these points.
+# First, we construct the Dirichlet boundary condition operator,
+# that evaluates the function at the boundaries
+B = Dirichlet(d);
+
+# The right hand side for the boundary condition is obtained by evaluating the Airy function
+# We use `airyai` from `SpecialFunctions.jl` for this
+using SpecialFunctions
+B_vals = [airyai(a), airyai(b)];
+
+# The main step, where we solve the differential equation
+u = [B; L] \ [B_vals, 0];
+
+#src we compare the result with the expected solution (which is an Airy function)
+using Test #src
+@test ≈(u(0), airyai(0); atol=10000eps()) #src

examples/ODE_increaseprec.jl

@@ -0,0 +1,8 @@
+using ApproxFun #src
+u = setprecision(1000) do
+    d = BigFloat(0)..BigFloat(1)
+    D = Derivative(d)
+    [ldirichlet(); D-1] \ [1; 0]
+end
+using Test #src
+@test u(1) ≈ exp(BigFloat(1)) #src

examples/PDE.jl

@@ -7,34 +7,8 @@
 # on the rectangle `-1..1 × -1..1`,
 # subject to the condition that ``y=1`` on the boundary.
 
-using ApproxFun
-using LinearAlgebra
-
-# The rectangular domain may be expressed as a tensor product of `ChebyshevInterval`s
-d = ChebyshevInterval()^2;
-
-# We construct the operator that collates the differential operator and boundary conditions
-L = [Dirichlet(d); Laplacian()+100I];
-
-# We compute the QR decomposition of the operator to speed up the solution
-Q = qr(L);
-ApproxFun.resizedata!(Q,:,4000);
-
-# The boundary condition is a function that is equal to one on each edge
-boundary_cond = ones(∂(d));
-
-# Solve the differential equation.
-# This function has weak singularities at the corner,
-# so we specify a lower tolerance to avoid resolving these singularities completely
-u = \(Q, [boundary_cond; 0.]; tolerance=1E-7);
+include("PDE1.jl")
 
 # Plot the solution
 import Plots
 Plots.plot(u; st=:surface, legend=false)
-
-#src # We verify that the solution satisfies the boundary condition
-using Test #src
-@test u(0.1,1.) ≈ 1.0 #src
-
-#src # We validate the solution at an internal point
-@test ≈(u(0.1,0.2), -0.02768276827514463; atol=1E-8) #src

examples/PDE1.jl

@@ -0,0 +1,27 @@
+using ApproxFun
+using LinearAlgebra
+
+# The rectangular domain may be expressed as a tensor product of `ChebyshevInterval`s
+d = ChebyshevInterval()^2;
+
+# We construct the operator that collates the differential operator and boundary conditions
+L = [Dirichlet(d); Laplacian()+100I];
+
+# We compute the QR decomposition of the operator to speed up the solution
+Q = qr(L);
+ApproxFun.resizedata!(Q,:,4000);
+
+# The boundary condition is a function that is equal to one on each edge
+boundary_cond = ones(∂(d));
+
+# Solve the differential equation.
+# This function has weak singularities at the corner,
+# so we specify a lower tolerance to avoid resolving these singularities completely
+u = \(Q, [boundary_cond; 0.]; tolerance=1E-7);
+
+#src # We verify that the solution satisfies the boundary condition
+using Test #src
+@test u(0.1,1.) ≈ 1.0 #src
+
+#src # We validate the solution at an internal point
+@test ≈(u(0.1,0.2), -0.02768276827514463; atol=1E-8) #src

examples/Periodic.jl

@@ -1,41 +1,5 @@
 # # Periodic Domains
-using ApproxFun
-using LinearAlgebra
-
-# We may approximate a periodic function in `Fourier` space
-f = Fun(cos, Fourier(-π..π))
-norm(differentiate(f) + Fun(sin, Fourier(-π..π))) < 100eps()
-
-# ## Boundary Value Problems
-
-# Due to the periodicity, Fourier representations allow for the asymptotic
-# savings of 2/π in the number of coefficients that need
-# to be stored compared with a Chebyshev representation.
-
-# ODEs can also be solved when the solution is periodic.
-
-# In this example, we solve
-# ```math
-# \frac{dy}{dt} + (1 + \sin(\cos(2t)))y = \exp(\sin(10t))
-# ```
-# subject to periodic boundary conditions on the domain ``[-\pi,\,\pi]``.
-
-# Solve the differential equation in Chebyshev space
-s = Chebyshev(-π..π)
-a = Fun(t-> 1+sin(cos(2t)),s)
-L = Derivative() + a
-f = Fun(t->exp(sin(10t)),s)
-B = periodic(s,0)
-uChebyshev = [B;L]\[0.,f]
-ncoefficients(uChebyshev)
-
-# Solve the differential equation in Fourier space
-s = Fourier(-π..π)
-a = Fun(t-> 1+sin(cos(2t)),s)
-L = Derivative() + a
-f = Fun(t->exp(sin(10t)),s)
-uFourier = L\f
-ncoefficients(uFourier)
+include("Periodic1.jl")
 
 # We note that the number of coefficients in the Fourier space is lower than that
 # in the Chebyshev space by a factor of approximately π/2
@@ -45,5 +9,3 @@ ncoefficients(uFourier)/ncoefficients(uChebyshev),2/π
 import Plots
 Plots.plot(uFourier, xlims=(-pi, pi), legend=false)
 
-using Test #src
-@test uChebyshev(0.) ≈ uFourier(0.) #src