Update docs, bump REQUIRE

README.md

@@ -53,7 +53,7 @@ base functions are overridden for the purposes of calculus. Because the exponent
 derivative, the `norm` is small:
 
 ```julia
-f = Fun(x->exp(x),-1..1)
+f = Fun(x->exp(x), -1..1)
 norm(f-f')
 ```
 
@@ -81,12 +81,12 @@ h = airyai(10asin(f)+2g)
 Solve the Airy ODE `u'' - x u = 0` as a BVP on `[-1000,200]`:
 
 ```julia
-x = Fun(identity,-1000..200)
+x = Fun(identity, -1000..200)
 d = domain(x)
 D = Derivative(d)
 B = Dirichlet(d)
 L = D^2 - x
-u = [B;L] \ [[airyai(d.a),airyai(d.b)],0]
+u = [B;L] \ [[airyai(d.a), airyai(d.b)], 0]
 plot(u)
 ```
 
@@ -98,11 +98,11 @@ plot(u)
 Solve a nonlinear boundary value problem satisfying the ODE `0.001u'' + 6*(1-x^2)*u' + u^2 = 1` with boundary conditions `u(-1)==1`, `u(1)==-0.5` on `[-1,1]`:
 
 ```julia
-x=Fun()
-u0=0.0x
+x  = Fun()
+u₀ = 0.0x
 
-N=u->[u(-1)-1,u(1)+0.5,0.001u''+6*(1-x^2)*u'+u^2-1]
-u=newton(N,u0)
+N = u -> [u(-1)-1, u(1)+0.5, 0.001u'' + 6*(1-x^2)*u' + u^2 - 1]
+u = newton(N,u0)
 plot(u)
 ```
 
@@ -117,8 +117,8 @@ There is also support for Fourier representations of functions on periodic inter
 Specify the space `Fourier` to ensure that the representation is periodic:
 
 ```julia
-f = Fun(cos,Fourier(-π..π))
-norm(f' + Fun(sin,Fourier(-π..π))
+f = Fun(cos, Fourier(-π..π))
+norm(f' + Fun(sin, Fourier(-π..π))
 ```
 
 Due to the periodicity, Fourier representations allow for the asymptotic savings of `2/π`
@@ -127,16 +127,16 @@ ODEs can also be solved when the solution is periodic:
 
 ```julia
 s = Chebyshev(-π..π)
-a = Fun(t-> 1+sin(cos(2t)),s)
+a = Fun(t-> 1+sin(cos(2t)), s)
 L = Derivative() + a
-f = Fun(t->exp(sin(10t)),s)
+f = Fun(t->exp(sin(10t)), s)
 B = periodic(s,0)
-uChebyshev = [B;L]\[0.;f]
+uChebyshev = [B;L] \ [0.;f]
 
 s = Fourier(-π..π)
-a = Fun(t-> 1+sin(cos(2t)),s)
+a = Fun(t-> 1+sin(cos(2t)), s)
 L = Derivative() + a
-f = Fun(t->exp(sin(10t)),s)
+f = Fun(t->exp(sin(10t)), s)
 uFourier = L\f
 
 ncoefficients(uFourier)/ncoefficients(uChebyshev),2/π
@@ -154,7 +154,7 @@ Other operations including random number sampling using [Olver & Townsend 2013].
 following code samples 10,000 from a PDF given as the absolute value of the sine function on `[-5,5]`:
 
 ```julia
-f = abs(Fun(sin,-5..5))
+f = abs(Fun(sin, -5..5))
 x = ApproxFun.sample(f,10000)
 histogram(x;normed=true)
 plot!(f/sum(f))
@@ -175,7 +175,7 @@ completely.
 d = Interval()^2                            # Defines a rectangle
 Δ = Laplacian(d)                            # Represent the Laplacian
 f = ones(∂(d))                              # one at the boundary
-u = \([Dirichlet(d);Δ+100I],[f;0.];         # Solve the PDE
+u = \([Dirichlet(d); Δ+100I], [f;0.];       # Solve the PDE
                 tolerance=1E-5)             
 surface(u)                                  # Surface plot
 ```
@@ -203,9 +203,9 @@ Solving differential equations with high precision types is available.  The foll
 
 ```julia
 setprecision(1000) do
-    d=BigFloat(0)..BigFloat(1)
-    D=Derivative(d)
-    u=[ldirichlet();D-I]\[1;0]
+    d = BigFloat(0)..BigFloat(1)
+    D = Derivative(d)
+    u = [ldirichlet(); D-I] \ [1; 0]
     @test u(1) ≈ exp(BigFloat(1))
 end
 ```

REQUIRE

@@ -1,16 +1,16 @@
 julia 0.7
-FastGaussQuadrature 0.2.1
+FastGaussQuadrature 0.3.2
 FastTransforms 0.4.1
-RecipesBase 0.1
-DualNumbers 0.2.2
-BandedMatrices 0.4
-ToeplitzMatrices 0.2
+RecipesBase 0.5
+DualNumbers 0.4
+BandedMatrices 0.5.1
+ToeplitzMatrices 0.4
 Calculus 0.1.15
-IntervalSets 0.0.2
-StaticArrays 0.3
-BlockArrays 0.3.1
+IntervalSets 0.2
+StaticArrays 0.8.3
+BlockArrays 0.4.1
 BlockBandedMatrices 0.1
 AbstractFFTs 0.3.1
-FFTW 0.0.4
-SpecialFunctions 0.6
-LowRankApprox 0.1.3
+FFTW 0.2.4
+SpecialFunctions 0.7
+LowRankApprox 0.1.4

docs/make.jl

@@ -24,7 +24,7 @@ makedocs(modules=[ApproxFun],
 deploydocs(
     repo   = "github.com/JuliaApproximation/ApproxFun.jl.git",
     latest = "development",
-    julia  = "0.6",
+    julia  = "0.7",
     osname = "linux",
     target = "build",
     deps   = nothing,

docs/src/internals/multivariate.md

@@ -32,7 +32,7 @@ A `Fun` is only one possible way to represent a bivariate function.  This mirror
 Another format for representing bivariate functions in ApproxFun is a `ProductFun`:  for example, the previous function could also be represented by
 
 ```julia
-f=ProductFun((x,y)->exp(-x^2-y^2),Interval()^2)
+f = ProductFun((x,y)->exp(-x^2-y^2),Interval()^2)
 ```
 
 A `ProductFun` also has two fields: `f.coefficients` and `f.space`, where `f.space` must be an `AbstractProductSpace`.   Here, `f.coefficients` is a `Vector{Fun{S,T}}` that represents a list of functions in `x`, where
@@ -41,10 +41,6 @@ A `ProductFun` also has two fields: `f.coefficients` and `f.space`, where `f.spa
 space(f.coefficients[k]) == columnspace(f.space,k)
 ```
 
-
-
-
-
 ## LowRankFun
 
 `LowRankFun`

docs/src/usage/constructors.md

@@ -46,19 +46,19 @@ Chebyshev(【-1.0,-0.9000000000000002】)⨄Chebyshev(【-0.9000000000000002,-0.
 The default space is `Chebyshev`, which can represent non-periodic functions on intervals.  Each `Space` type has a default domain: for `Chebyshev` this is `-1..1`, for Fourier and Laurent this is `-π..π`.  Thus the following
 are synonyms:
 ```julia
-Fun(exp,Chebyshev(Interval(-1,1)))
-Fun(exp,Chebyshev(Interval()))
-Fun(exp,Chebyshev(-1..1))
-Fun(exp,Chebyshev())
-Fun(exp,-1..1)
-Fun(exp,Interval())
-Fun(exp,Interval(-1,1))
+Fun(exp, Chebyshev(Interval(-1,1)))
+Fun(exp, Chebyshev(Interval()))
+Fun(exp, Chebyshev(-1..1))
+Fun(exp, Chebyshev())
+Fun(exp, -1..1)
+Fun(exp, Interval())
+Fun(exp, Interval(-1,1))
 Fun(exp)
 ```
 If a function is not specified, then it is taken to be `identity`.  Thus we have the
 following synonyms:
 ```julia
-x = Fun(identity,-1..1)
+x = Fun(identity, -1..1)
 x = Fun(-1..1)
 x = Fun(identity)
 x = Fun()
@@ -70,12 +70,12 @@ x = Fun()
 It is sometimes necessary to specify coefficients explicitly.  This is possible
 via specifying the space followed by a vector of coefficients:
 ```jldoctest
-julia> f = Fun(Taylor(),[1,2,3]);  # represents 1 + 2z + 3z^2
+julia> f = Fun(Taylor(), [1,2,3]);  # represents 1 + 2z + 3z^2
 
 julia> f(0.1)
 1.23
 
-julia> 1+2*0.1+3*0.1^2
+julia> 1 + 2*0.1 + 3*0.1^2
 1.23
 ```
 

docs/src/usage/equations.md

@@ -33,9 +33,9 @@ $$u + {\rm e}^x \int_{-1}^1 \cos x \, u(x) {\rm d}x = \cos {\rm e}^x$$
 
 We can solve this equation as follows:
 ```jldoctest
-julia> Σ = DefiniteIntegral(Chebyshev()); x=Fun();
+julia> Σ = DefiniteIntegral(Chebyshev()); x = Fun();
 
-julia> u = (I+exp(x)*Σ[cos(x)])\cos(exp(x));
+julia> u = (I+exp(x)*Σ[cos(x)]) \ cos(exp(x));
 
 julia> u(0.1)
 0.21864294855628802
@@ -193,7 +193,7 @@ g = exp.(-10(x+0.2)^2-20(y-0.1)^2)
 Many PDEs have weak singularities at the corners, in which case it is beneficial to
 specify a tolerance to reduce the time:
 ```julia
-\(A,[zeros(∂(d));f]; tolerance=1E-6)
+\(A, [zeros(∂(d));f]; tolerance=1E-6)
 ```
 
 
@@ -210,6 +210,6 @@ $$\begin{align*}
 This can be solved using
 ```julia
 x = Fun()
-N = u->[u(-1.)-c;u(1.);ε*u''+6*(1-x^2)*u'+u^2-1.]
+N = u -> [u(-1.)-c; u(1.); ε*u'' + 6*(1-x^2)*u' + u^2 - 1.0]
 u = newton(N,u0)
 ```