From e4baaed8bf0ba52a6c8cd8543c1ffe76f6f4deb6 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 05:33:10 +0200 Subject: [PATCH 01/13] Q1 --- src/HWfuncapp.jl | 21 ++++++++++++++++++--- 1 file changed, 18 insertions(+), 3 deletions(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index 732fe3f..dc551fa 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -4,7 +4,7 @@ using FastGaussQuadrature # to get chebyshevnodes # you dont' have to use PyPlot. I did much of it in PyPlot, hence # you will see me often qualify code with `PyPlot.plot` or so. -using PyPlot +using PyPlot import ApproXD: getBasis, BSpline using Distributions using ApproxFun @@ -15,6 +15,21 @@ unitmap(x,lb,ub) = 2 .* (x .- lb) ./ (ub .- lb) .- 1 #[a,b] -> [-1,1] function q1(n) f(x) = x .+ 2x.^2 - exp.(-x) + f(x) = x .+ 2x.^2 - exp.(-x) + deg = n-1 + lb = -3 + ub = 3 + node = gausschebyshev(n)[1] + chebnode = 0.5 .* (lb .+ ub) .+ 0.5 .* (ub .- lb) .* node + y = map(f, chebnode) + basismatrix = [cos((n - i + 0.5) * (j - 1)* π / n) for i = 1:n, j = 1:n] + c = basismatrix \ y + + n_new = 100 + x_2 = range(lb, stop = ub, length = n_new) + base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] + y2 = base2 * c + error = y2 - f(collect(-3:6/99:3)) # without using PyPlot, just erase the `PyPlot.` part PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png")) @@ -43,7 +58,7 @@ end # I found having those useful for q5 mutable struct ChebyType - f::Function # fuction to approximate + f::Function # fuction to approximate nodes::Union{Vector,LinRange} # evaluation points basis::Matrix # basis evaluated at nodes coefs::Vector # estimated coefficients @@ -79,7 +94,7 @@ function q5(deg=(5,9,15),lb=-1.0,ub=1.0) runge(x) = 1.0 ./ (1 .+ 25 .* x.^2) - + PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q5.png")) end From 4fd6af9da075261a556c83d76775dcc0d402bd41 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 05:33:10 +0200 Subject: [PATCH 02/13] Q1 --- src/HWfuncapp.jl | 21 ++++++++++++++++++--- 1 file changed, 18 insertions(+), 3 deletions(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index 732fe3f..dc551fa 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -4,7 +4,7 @@ using FastGaussQuadrature # to get chebyshevnodes # you dont' have to use PyPlot. I did much of it in PyPlot, hence # you will see me often qualify code with `PyPlot.plot` or so. -using PyPlot +using PyPlot import ApproXD: getBasis, BSpline using Distributions using ApproxFun @@ -15,6 +15,21 @@ unitmap(x,lb,ub) = 2 .* (x .- lb) ./ (ub .- lb) .- 1 #[a,b] -> [-1,1] function q1(n) f(x) = x .+ 2x.^2 - exp.(-x) + f(x) = x .+ 2x.^2 - exp.(-x) + deg = n-1 + lb = -3 + ub = 3 + node = gausschebyshev(n)[1] + chebnode = 0.5 .* (lb .+ ub) .+ 0.5 .* (ub .- lb) .* node + y = map(f, chebnode) + basismatrix = [cos((n - i + 0.5) * (j - 1)* π / n) for i = 1:n, j = 1:n] + c = basismatrix \ y + + n_new = 100 + x_2 = range(lb, stop = ub, length = n_new) + base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] + y2 = base2 * c + error = y2 - f(collect(-3:6/99:3)) # without using PyPlot, just erase the `PyPlot.` part PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png")) @@ -43,7 +58,7 @@ end # I found having those useful for q5 mutable struct ChebyType - f::Function # fuction to approximate + f::Function # fuction to approximate nodes::Union{Vector,LinRange} # evaluation points basis::Matrix # basis evaluated at nodes coefs::Vector # estimated coefficients @@ -79,7 +94,7 @@ function q5(deg=(5,9,15),lb=-1.0,ub=1.0) runge(x) = 1.0 ./ (1 .+ 25 .* x.^2) - + PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q5.png")) end From 2ed9de8905460cc405f88ae826609ca46ada60c1 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 07:02:34 +0200 Subject: [PATCH 03/13] q1 --- Project.toml | 7 +++++++ q1.png | Bin 0 -> 2412 bytes 2 files changed, 7 insertions(+) create mode 100644 q1.png diff --git a/Project.toml b/Project.toml index 516f264..1dcf6ac 100644 --- a/Project.toml +++ b/Project.toml @@ -3,6 +3,13 @@ uuid = "ce1ef771-b552-5ca6-80e4-7358b8c578e2" authors = ["Florian Oswald "] version = "0.1.0" +[deps] +ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee" + [extras] Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" diff --git a/q1.png b/q1.png new file mode 100644 index 0000000000000000000000000000000000000000..270befc24aa7438572353542d7938fedb89426df GIT binary patch literal 2412 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sV0^&A1{5*9c;^X_Vkvg=4B-HR8jh3>AfL0q zBeIx*fj<$18CTdZ&jboumbgZg1m~xflqVLYGUO(f6y)TWFXmD=;ars>(Aw0y_kW4 z`7=5U3`XbP18urz)WE=C$R@y`aEyV8;fRC-LxTh}2ZKN|10zEcj{<{34 Date: Sun, 14 Apr 2019 07:02:34 +0200 Subject: [PATCH 04/13] q1 trying to fix plots --- Project.toml | 7 +++++++ q1.png | Bin 0 -> 2412 bytes 2 files changed, 7 insertions(+) create mode 100644 q1.png diff --git a/Project.toml b/Project.toml index 516f264..1dcf6ac 100644 --- a/Project.toml +++ b/Project.toml @@ -3,6 +3,13 @@ uuid = "ce1ef771-b552-5ca6-80e4-7358b8c578e2" authors = ["Florian Oswald "] version = "0.1.0" +[deps] +ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee" + [extras] Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" diff --git a/q1.png b/q1.png new file mode 100644 index 0000000000000000000000000000000000000000..270befc24aa7438572353542d7938fedb89426df GIT binary patch literal 2412 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sV0^&A1{5*9c;^X_Vkvg=4B-HR8jh3>AfL0q zBeIx*fj<$18CTdZ&jboumbgZg1m~xflqVLYGUO(f6y)TWFXmD=;ars>(Aw0y_kW4 z`7=5U3`XbP18urz)WE=C$R@y`aEyV8;fRC-LxTh}2ZKN|10zEcj{<{34 Date: Sun, 14 Apr 2019 07:38:00 +0200 Subject: [PATCH 05/13] HW trying to fix q1 --- src/HWfuncapp.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index dc551fa..f234060 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -30,9 +30,11 @@ function q1(n) base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] y2 = base2 * c error = y2 - f(collect(-3:6/99:3)) + Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) + scatter!(x_2, y2, labels = ["approx"]) # without using PyPlot, just erase the `PyPlot.` part - PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png")) + savefig(joinpath(dirname(@__FILE__),"..","q1.png")) return Dict(:error=>maximum(abs,err)) end From ffa7d9087118f2675c1c3bc4cf656e340d3d70c9 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 07:38:00 +0200 Subject: [PATCH 06/13] HW test --- src/HWfuncapp.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index dc551fa..f234060 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -30,9 +30,11 @@ function q1(n) base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] y2 = base2 * c error = y2 - f(collect(-3:6/99:3)) + Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) + scatter!(x_2, y2, labels = ["approx"]) # without using PyPlot, just erase the `PyPlot.` part - PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png")) + savefig(joinpath(dirname(@__FILE__),"..","q1.png")) return Dict(:error=>maximum(abs,err)) end From 63fa8882071ca4055e02ba888c190728b5aa7f1b Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 08:34:58 +0200 Subject: [PATCH 07/13] test q1 --- src/HWfuncapp.jl | 4 ++-- test/runtests.jl | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index f234060..a4d0b84 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -30,7 +30,7 @@ function q1(n) base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] y2 = base2 * c error = y2 - f(collect(-3:6/99:3)) - Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) + Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) #somohow plot does not work except on Jupyter scatter!(x_2, y2, labels = ["approx"]) # without using PyPlot, just erase the `PyPlot.` part @@ -49,7 +49,7 @@ function q3(b::Number) # p is your plot return (p,integral) -end +end2 # optinal function q4() diff --git a/test/runtests.jl b/test/runtests.jl index 6453446..65b323d 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -3,7 +3,7 @@ using Test @testset "HWfuncapp.jl" begin # test that q1 with 15 nodes has an error smaller than 1e-9 - + @test q1(15)[:error] < 1e-9 # test that the integral of function h [-10,0] ≈ 1.46039789878568 @test false # by default fail From 799eca1f0dd335182075fd213347323aa6f71721 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 08:34:58 +0200 Subject: [PATCH 08/13] HW q1 fixed --- src/HWfuncapp.jl | 4 ++-- test/runtests.jl | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index f234060..a4d0b84 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -30,7 +30,7 @@ function q1(n) base2 = [ChebyT(unitmap(x_2[i], lb, ub), j) for i in 1:n_new, j = 0:deg] y2 = base2 * c error = y2 - f(collect(-3:6/99:3)) - Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) + Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) #somohow plot does not work except on Jupyter scatter!(x_2, y2, labels = ["approx"]) # without using PyPlot, just erase the `PyPlot.` part @@ -49,7 +49,7 @@ function q3(b::Number) # p is your plot return (p,integral) -end +end2 # optinal function q4() diff --git a/test/runtests.jl b/test/runtests.jl index 6453446..65b323d 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -3,7 +3,7 @@ using Test @testset "HWfuncapp.jl" begin # test that q1 with 15 nodes has an error smaller than 1e-9 - + @test 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f(collect(-3:6/99:3)) - Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) #somohow plot does not work except on Jupyter + Plots.plot(x_2, [f(collect(-3:6/99:3)) error], labels = ["true_val" "error"], title = "Q1", layout = 2) scatter!(x_2, y2, labels = ["approx"]) # without using PyPlot, just erase the `PyPlot.` part - savefig(joinpath(dirname(@__FILE__),"..","q1.png")) - return Dict(:error=>maximum(abs,err)) + Plots.savefig(joinpath(dirname(@__FILE__),"..","q1.png")) + return Dict(:error=>maximum(abs,error)) end function q2(b::Number) @assert b > 0 # use ApproxFun.jl to do the same: - - Plots.savefig(p,joinpath(dirname(@__FILE__),"..","q2.png")) + b = 4 + n_new = 100 + f(x) = x .+ 2x.^2 - exp.(-x) + f2 = Fun(f,-b..b) + x = range(-b, b, length = n_new) + y2 = f2.(x) + y = f.(x) + error = y - y2 + Plots.plot(x, [y error], labels = ["true_val" "error"], title = "Q2", layout = 2) + scatter!(x, y2, labels = ["approx"]) + + Plots.savefig(joinpath(dirname(@__FILE__),"..","q2.png")) end function q3(b::Number) # p is your plot return (p,integral) -end2 +end # optinal function q4() @@ -57,7 +66,6 @@ function q4() return fig end - # I found having those useful for q5 mutable struct ChebyType f::Function # fuction to approximate @@ -130,6 +138,4 @@ function runall() q7() end - - end # module From b2e260161a252de7ecbfa0f4825ea44df9d54426 Mon Sep 17 00:00:00 2001 From: takashissb Date: Sun, 14 Apr 2019 23:45:12 +0200 Subject: [PATCH 11/13] Q3 --- q3.png | Bin 0 -> 39392 bytes src/HWfuncapp.jl | 16 ++++++++++++++-- 2 files changed, 14 insertions(+), 2 deletions(-) create mode 100644 q3.png diff --git a/q3.png b/q3.png new file mode 100644 index 0000000000000000000000000000000000000000..46bc702be6179b18f3233f265c5eabf522c063e6 GIT binary patch literal 39392 zcmb@tRa9H;^9G8O0>w4Op|~}8i%X!mL($?|ptuw$5Zv9NG`LG~EAH;aN^y56es;g# z`mc2^&gEIT$j;8rD>L)XJoC&XOhrlNB?cG+0RiFVds!(p1Oy}<1O&ub5E5|bQ9EoL 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q2(b::Number) Plots.savefig(joinpath(dirname(@__FILE__),"..","q2.png")) end - +using LinearAlgebra #for cumsum function q3(b::Number) - + b = 10 + x = Fun(identity, -b..b) + f = sin(x^2) + g = cos(x) + h = f - g + r = roots(h) + p = Plots.plot(h, label = "h", title = "Q3") + scatter!(r,h.(r),labels="roots h") + Plots.savefig(joinpath(dirname(@__FILE__),"..","q3.png")) + Plots.savefig(joinpath(p,dirname(@__FILE__),"..","q3.png")) + k1 = cumsum(h) + k = k1 + h(-b) + integral = norm(h-k) # p is your plot return (p,integral) end From 4c9c6475b7d8eb47410335f4c97a50b97ae559d7 Mon Sep 17 00:00:00 2001 From: takashissb Date: Mon, 15 Apr 2019 00:01:23 +0200 Subject: [PATCH 12/13] HW q3 test --- q3.png | Bin 39392 -> 48425 bytes test/runtests.jl | 4 ++-- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/q3.png b/q3.png index 46bc702be6179b18f3233f265c5eabf522c063e6..3d0cdba456c6eff2d31151d420aa0ce82a7b6fbf 100644 GIT binary patch literal 48425 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Yd>dO-p&O7F3f(MaJ;30+%W++33Jd} zn>spKRUMS^=#a@(Efn0%bM4etqYCEphzu%H|GhY>cC2 z9dn4{sEC3==LO1mYaNr3m`cf%gs7QsN^Dxhy^Qw?gyb7Xih`S59Uf_XFvS&xXcuZ0 zDD6j*^xJ2HPaaJTljw-)^sUz_9Qbo}zP9m$!iL&+9rRRuWMPdR4F9G> zO*fE40-D@`(}4@N{IWU|r%zjvr}nI!_QJ5TLG%kJ{=w669mzjii1=VWC`KU3M~T$UPtarIyD zg|a$~R=x!kpy(B zlM=wC$jM!prIFp--0teje5C<|jPA7+$0rUtQQIqLE3L?XYlkjczH3hsJU(=Vbkd5|MtpmR=V!i))qh& z-TbvR=Hl#(Qg)5l>^~8IBMGM;^2vxuEFHNB@U#GZ8vPo zEWUr4o@OvY=2A{5yF62Li_hu!Pqyk*(02gCP8HV^d67QF{`Z+&WCalFYV*`aURztc z%&w|^7Au6f_OkF-CA8%|fKK1y(T^DS$0z9q6li z@5b)Z;^N`~s%iobY{H3LmO1UuOIGiKQInEHL_{D(RaJC9^*<&Tnv0jX@gogDxB$)L zH#oA1R5b(OdNl!K%DdBii6nKme>p$xch4&mxNf}u{m+>DO8{1D&jzONDEl*fPL$%o zYr=J2ZrNEZF{U!fI@eYb)`1UglMN}SR`&Ayv~k5Kw$&WzJrXSj1D(+CZx%KT_B!GuCA_LUcOk$X!LAj&7>Qt zAjAddDxu=nH|TQ0PY>@(#2U;jWZ5KvYxgU#P89fF9I;nU`N P5b!ZGwlb>5d&d0_sQ@%+ diff --git a/test/runtests.jl b/test/runtests.jl index 65b323d..4c9e8d5 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -3,8 +3,8 @@ using Test @testset "HWfuncapp.jl" begin # test that q1 with 15 nodes has an error smaller than 1e-9 - @test q1(15)[:error] < 1e-9 + @test q1(15)[:error] < 1e-9 # test that the integral of function h [-10,0] ≈ 1.46039789878568 - + @test q3(10) ≈ 1.46039789878568 @test false # by default fail end From 9a4facc507fcd38a93bcb3ed161d9a25f6daaa35 Mon Sep 17 00:00:00 2001 From: takashissb Date: Mon, 15 Apr 2019 00:20:03 +0200 Subject: [PATCH 13/13] Q4 tried but it did not work --- src/HWfuncapp.jl | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl index d9e843c..db98281 100644 --- a/src/HWfuncapp.jl +++ b/src/HWfuncapp.jl @@ -73,8 +73,11 @@ function q3(b::Number) end # optinal -function q4() - +function q4(n) + x = range(0, 1, length = n) + x2 = collect(0:0.01:1) + fig = Plots.plot(x, [ChebyT(x2, deg) for deg in 1:9]) #acos not working + Plots.savefig(joinpath(p,dirname(@__FILE__),"..","q4.png")) return fig end