fixing examples

Author: dlfivefifty

Extras/.ipynb_checkpoints/Fractional Integral Equations-checkpoint.ipynb

@@ -6,7 +6,7 @@ version = "0.3.2"
 
 [[ApproxFun]]
 deps = ["AbstractFFTs", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Random", "RecipesBase", "SparseArrays", "SpecialFunctions", "StaticArrays", "Statistics", "Test", "ToeplitzMatrices"]
-path = "/Users/sheehanolver/Projects/ApproxFun.jl"
+path = "/Users/solver/Projects/ApproxFun.jl"
 uuid = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
 version = "0.9.0+"
 
@@ -49,6 +49,18 @@ git-tree-sha1 = "f60954495a7afcee4136f78d1d60350abd37a409"
 uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
 version = "0.4.1"
 
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random", "Test"]
+git-tree-sha1 = "f73b0e10f2a5756de7019818a41654686da06b09"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.7.5"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Printf", "Reexport", "Test"]
+git-tree-sha1 = "9f0a0210450acb91c730b730a994f8eef1d3d543"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.9.5"
+
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
 git-tree-sha1 = "2d9e14d19bad3f9ad5cc5e4cffabc3cfa59de825"
@@ -61,6 +73,12 @@ git-tree-sha1 = "fb86fe40cb5b35990e368709bfdc1b46dbb99dac"
 uuid = "8f4d0f93-b110-5947-807f-2305c1781a2d"
 version = "1.1.1"
 
+[[Contour]]
+deps = ["LinearAlgebra", "StaticArrays", "Test"]
+git-tree-sha1 = "b974e164358fea753ef853ce7bad97afec15bb80"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.1"
+
 [[DSP]]
 deps = ["AbstractFFTs", "Compat", "FFTW", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions"]
 git-tree-sha1 = "c90967ff4c5e99f652b278624634dcef73b58848"
@@ -121,6 +139,18 @@ git-tree-sha1 = "d87b7fc5c086cf157deabec625d53ba55eca6436"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
 version = "0.3.0"
 
+[[FixedPointNumbers]]
+deps = ["Test"]
+git-tree-sha1 = "b8045033701c3b10bf2324d7203404be7aef88ba"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.5.3"
+
+[[GR]]
+deps = ["Base64", "DelimitedFiles", "Pkg", "Random", "Serialization", "Sockets", "Test"]
+git-tree-sha1 = "18e3aa0f988f6e94c90394deaa76cb095bf87469"
+uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
+version = "0.35.0"
+
 [[HierarchicalMatrices]]
 deps = ["Compat"]
 git-tree-sha1 = "acfcaf1aa47d038f593f301ed3bdebc0129035bc"
@@ -178,6 +208,12 @@ version = "0.2.0"
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[Measures]]
+deps = ["Test"]
+git-tree-sha1 = "ddfd6d13e330beacdde2c80de27c1c671945e7d9"
+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
+version = "0.3.0"
+
 [[Missings]]
 deps = ["Dates", "InteractiveUtils", "SparseArrays", "Test"]
 git-tree-sha1 = "adc26d2ee85a49c413464110d922cf21efc9d233"
@@ -209,6 +245,24 @@ version = "1.0.2"
 deps = ["Dates", "LibGit2", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
+[[PlotThemes]]
+deps = ["PlotUtils", "Requires", "Test"]
+git-tree-sha1 = "f3afd2d58e1f6ac9be2cea46e4a9083ccc1d990b"
+uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
+version = "0.3.0"
+
+[[PlotUtils]]
+deps = ["Colors", "Dates", "Printf", "Random", "Reexport", "Test"]
+git-tree-sha1 = "fd28f30a294a38ec847de95d8ac7ac916ccd7c06"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "0.5.5"
+
+[[Plots]]
+deps = ["Base64", "Contour", "Dates", "FixedPointNumbers", "GR", "JSON", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "Random", "RecipesBase", "Reexport", "Requires", "Showoff", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "Test", "UUIDs"]
+git-tree-sha1 = "a36cbf119f1605268d0457e04e717901ae88b68c"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+version = "0.21.0"
+
 [[Polynomials]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
 git-tree-sha1 = "1a1eae52956658a6acae6fa1b6d6c3d488192895"
@@ -249,6 +303,12 @@ git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "0.2.0"
 
+[[Requires]]
+deps = ["Test"]
+git-tree-sha1 = "f6fbf4ba64d295e146e49e021207993b6b48c7d1"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "0.5.2"
+
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
@@ -259,6 +319,12 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[Showoff]]
+deps = ["Compat"]
+git-tree-sha1 = "276b24f3ace98bec911be7ff2928d497dc759085"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "0.2.1"
+
 [[Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 

Extras/Fractional Integral Equations.ipynb

@@ -1,4 +1,4 @@
-using ApproxFun,DualNumbers,Plots
+using ApproxFun, DualNumbers, LinearAlgebra, Plots
     import ApproxFun: DualFun, jacobian
 
 x=Fun(-π..π)
@@ -9,6 +9,7 @@ T0=Tk=0.
 
     (T,u)=(T0,u0)
     for k=1:4
+        global T,u
         J1=jacobian.(N(DualFun(Fun(T)),u))
         J2=jacobian.(N(T,DualFun(u)))
         J=Operator[J1 J2]

Manifest.toml

@@ -12,13 +12,14 @@ f =(x,y) -> [ y[2], -sin(y[1]) ]
 
 
 y0 = [3., 0.]
-d = Interval(0.,20.)
+d = 0..20.0
 x = Fun(identity, d)
 y0=Fun(x->y0,d)
 yn = y0
 plot(yn[1])
 
 while true
+    global yn
 	err = sum([maximum(fun^2) for fun in vec(yn'-f(x,yn))])
 	println("Length: $(length(yn)) \tMaximum point-wise squared error: $err")
 	if err < 1e-10
@@ -30,7 +31,5 @@ while true
     yn = chop(cumsum(integrand) + y0,100eps())
 end
 
-
-xts = d.a:0.01:d.b
-plot(xts,yn[1])
-plot!(xts,yn[2])
+plot(yn[1])
+plot!(yn[2])

ODEs/Multivariate newton iteration.jl

@@ -1,11 +1,11 @@
-using ApproxFun, Plots
+using ApproxFun, LinearAlgebra, Plots
 
 x = Fun(-20 .. 20)
 V = abs(x)
 D = Derivative()
-S = space(V)
+S = ApproxFun.canonicalspace(space(V))
 B = [Dirichlet(S); continuity(S,0:1)]
-λ, v = eigs(B, -D^2 + V, 500,tolerance=1E-10)
+λ, v = ApproxFun.eigs(B, -D^2 + V, 500,tolerance=1E-10)
 
 p = plot(V; legend=false)
     for k=1:20

ODEs/Picard Iteration.jl

@@ -5,11 +5,11 @@ D = Derivative()
 
 
 L=D^10 + cosh(x)*D^8 + x^3*D^6 + x^4*D^4 + cos(x)*D^2 + x^2
-d = Interval()
+d = ChebyshevInterval()
 B = [Dirichlet(d) ;
      Neumann(d)   ;
-     [Evaluation(Interval(),first,k) for k=2:4]... ;
-     [Evaluation(Interval(),last,k) for k=2:4]...]
+     [Evaluation(d,leftendpoint,k) for k=2:4]... ;
+     [Evaluation(d,rightendpoint,k) for k=2:4]...]
 
 u = [B; L] \ [ [0.,0.], [1.,1.], zeros(6)..., exp(x)]