Merge pull request #782 from jishnub/trailingwhitespace

trim trailing whitespace

Author: jishnub

src/ApproxFun.jl

@@ -5,7 +5,7 @@ using Base, Reexport,
 
 import Calculus
 
-@reexport using ApproxFunBase    
+@reexport using ApproxFunBase
 @reexport using ApproxFunFourier
 @reexport using ApproxFunOrthogonalPolynomials
 @reexport using ApproxFunSingularities
@@ -14,40 +14,40 @@ import ApproxFunBase: normalize!, flipsign, FiniteRange, Fun, MatrixFun, UnsetSp
                     UnivariateSpace, AmbiguousSpace, SumSpace, SubSpace, WeightSpace, NoSpace, Space,
                     HeavisideSpace, PointSpace,
                     IntervalOrSegment, RaggedMatrix, AlmostBandedMatrix,
-                    AnyDomain, ZeroSpace, ArraySpace, TrivialInterlacer, BlockInterlacer, 
+                    AnyDomain, ZeroSpace, ArraySpace, TrivialInterlacer, BlockInterlacer,
                     AbstractTransformPlan, TransformPlan, ITransformPlan,
                     ConcreteConversion, ConcreteMultiplication, ConcreteDerivative, ConcreteIntegral, CalculusOperator,
                     ConcreteVolterra, Volterra, VolterraWrapper,
                     MultiplicationWrapper, ConversionWrapper, DerivativeWrapper, Evaluation, EvaluationWrapper,
-                    Conversion, defaultConversion, defaultcoefficients, default_Fun, Multiplication, Derivative, Integral, bandwidths, 
+                    Conversion, defaultConversion, defaultcoefficients, default_Fun, Multiplication, Derivative, Integral, bandwidths,
                     ConcreteEvaluation, ConcreteDefiniteLineIntegral, ConcreteDefiniteIntegral, ConcreteIntegral,
                     DefiniteLineIntegral, DefiniteIntegral, ConcreteDefiniteIntegral, ConcreteDefiniteLineIntegral, IntegralWrapper,
-                    ReverseOrientation, ReverseOrientationWrapper, ReverseWrapper, Reverse, NegateEven, 
+                    ReverseOrientation, ReverseOrientationWrapper, ReverseWrapper, Reverse, NegateEven,
                     Dirichlet, ConcreteDirichlet, DirichletWrapper,
                     TridiagonalOperator, SubOperator, Space, @containsconstants, spacescompatible,
-                    hasfasttransform, canonicalspace, domain, setdomain, prectype, domainscompatible, 
-                    plan_transform, plan_itransform, plan_transform!, plan_itransform!, transform, itransform, hasfasttransform, 
+                    hasfasttransform, canonicalspace, domain, setdomain, prectype, domainscompatible,
+                    plan_transform, plan_itransform, plan_transform!, plan_itransform!, transform, itransform, hasfasttransform,
                     CanonicalTransformPlan, ICanonicalTransformPlan,
-                    Integral, 
-                    domainspace, rangespace, boundary, 
-                    union_rule, conversion_rule, maxspace_rule, conversion_type, maxspace, hasconversion, points, 
-                    rdirichlet, ldirichlet, lneumann, rneumann, ivp, bvp, 
-                    linesum, differentiate, integrate, linebilinearform, bilinearform, 
+                    Integral,
+                    domainspace, rangespace, boundary,
+                    union_rule, conversion_rule, maxspace_rule, conversion_type, maxspace, hasconversion, points,
+                    rdirichlet, ldirichlet, lneumann, rneumann, ivp, bvp,
+                    linesum, differentiate, integrate, linebilinearform, bilinearform,
                     UnsetNumber, coefficienttimes, subspace_coefficients, sumspacecoefficients, specialfunctionnormalizationpoint,
                     Segment, IntervalOrSegmentDomain, PiecewiseSegment, isambiguous, Vec, eps, isperiodic,
                     arclength, complexlength,
                     invfromcanonicalD, fromcanonical, tocanonical, fromcanonicalD, tocanonicalD, canonicaldomain, setcanonicaldomain, mappoint,
                     reverseorientation, checkpoints, evaluate, mul_coefficients, coefficients, coefficientmatrix, isconvertible,
                     clenshaw, ClenshawPlan, sineshaw,
-                    toeplitz_getindex, toeplitz_axpy!, sym_toeplitz_axpy!, hankel_axpy!, ToeplitzOperator, SymToeplitzOperator, hankel_getindex, 
+                    toeplitz_getindex, toeplitz_axpy!, sym_toeplitz_axpy!, hankel_axpy!, ToeplitzOperator, SymToeplitzOperator, hankel_getindex,
                     SpaceOperator, ZeroOperator, InterlaceOperator,
                     interlace!, reverseeven!, negateeven!, cfstype, pad!, alternatesign!, mobius,
                     extremal_args, hesseneigvals, chebyshev_clenshaw, recA, recB, recC, roots,splitatroots,
                     chebmult_getindex, intpow, alternatingsum,
                     domaintype, diagindshift, rangetype, weight, isapproxinteger, default_Dirichlet, scal!, dotu,
                     components, promoterangespace, promotedomainspace, choosedomainspace,
                     block, blockstart, blockstop, blocklengths, isblockbanded, pointscompatible,
-                    AbstractProductSpace, MultivariateFun, BivariateSpace, 
+                    AbstractProductSpace, MultivariateFun, BivariateSpace,
                     @wrapperstructure, @wrapperspaces, @wrapper, @calculus_operator, resizedata!, slnorm,
                     sample, chop!, isbanded, colrange, bandwidth
 
@@ -99,7 +99,7 @@ const Curve{S,T} = Union{IntervalCurve{S,T},PeriodicCurve{S,T}}
 Curve(f::Fun{<:Space{<:PeriodicDomain}}) = PeriodicCurve(f)
 
 #TODO: Make type stable
-Curve(f::Fun{<:Space{<:ChebyshevInterval}}) = IntervalCurve(f) 
+Curve(f::Fun{<:Space{<:ChebyshevInterval}}) = IntervalCurve(f)
 
 export Curve
 

src/Extras/autodifferentiation.jl

@@ -120,44 +120,44 @@ end
 function newton(N, u0::Array{T,1}; maxiterations=15, tolerance=1E-15) where T <: Fun
     u = copy(u0)
     err = Inf
-    
+
     numf = length(u0)   # number of functions
 
     if numf == 0
         error("u0 must contain at least 1 function")
     end
-    
+
     Js = Array{Any,2}(undef,1,numf) # jacobians
-    
+
     for k = 1:maxiterations
         # ------ calculate Jacobian for each function - O(numf^2) ----
-        
+
         # use the first call to populate the value of the functions
         # this saves one call to N()
         F = N([ (j == 1 ? DualFun(u[j]) : u[j]) for j = 1:numf ]...)
         @inbounds Js[1] = jacobian.(F)
         F = map(d -> typeof(d) <: DualFun ? d.f : d, F)
-        
+
         for i = 2:numf
             @inbounds Js[i] = jacobian.(N([ (j == i ? DualFun(u[j]) : u[j]) for j = 1:numf ]...))
         end
-        
+
         F = N(u...)
         J = Base.typed_hcat(Operator, Js...)
-        
+
         # ------- update step ---------
         unew = u .- J\F
         err = maximum(norm.(unew-u)) # use the max norm error as the overall error
-        
+
         if err ≤ 10*tolerance
             return unew
         else
             u = map(q -> chop(q, tolerance), unew)
         end
     end
-    
+
     @warn "Maximum number of iterations $maxiterations reached, with approximate accuracy of $err."
-    
+
     return u
 end
 

test/ExtrasTest.jl

@@ -87,9 +87,9 @@ import ApproxFun: eigs
         N_dep = (u1,u2) -> [
                 u1(0)*u1(0)*u1(0) - 0.125;
                 u2(0) - 1;
-                u1' - u1*u1;  
+                u1' - u1*u1;
                 u2' + u1*u1*u2;
-            ] 
+            ]
         u1,u2 = newton(N_dep, [u1,u2])
 
         u1_exact = -1 / (x - 2)
@@ -104,12 +104,12 @@ import ApproxFun: eigs
         N_ind = (u1,u2) -> [
                 u1(0)*u1(0)*u1(0) - 0.125;
                 u2(0)*u2(0)*u2(0) + 0.125;
-                u1' - u1*u1;  
+                u1' - u1*u1;
                 u2' - u2*u2;
-            ] 
+            ]
 
         # note takes a few more iterations to converge to accuracy
-        u1,u2 = newton(N_ind, [u1,u2], maxiterations=25) 
+        u1,u2 = newton(N_ind, [u1,u2], maxiterations=25)
 
         u1_exact = -1 / (x - 2)
         u2_exact = -1 / (x + 2)

test/FractionalTest.jl

@@ -1,6 +1,6 @@
 using ApproxFun, Test
     import ApproxFunBase: testfunctional, testbandedoperator
-    
+
 @testset "Fractional" begin
     @testset "Jupyer example" begin
         S = Legendre() ⊕ JacobiWeight(0.5,0.,Ultraspherical(1))