HW - Guillard & Ghio

Project.toml

@@ -3,6 +3,14 @@ uuid = "ce1ef771-b552-5ca6-80e4-7358b8c578e2"
 authors = ["Florian Oswald <florian.oswald@gmail.com>"]
 version = "0.1.0"
 
+[deps]
+ApproXD = "f0e97480-066f-5960-9ba5-e027352bc8af"
+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"
 

src/HWfuncapp.jl

@@ -9,110 +9,61 @@ import ApproXD: getBasis, BSpline
 using Distributions
 using ApproxFun
 using Plots
+export TT, ChebyT, q1
+
 
 ChebyT(x,deg) = cos(acos(x)*deg)
 unitmap(x,lb,ub) = 2 .* (x .- lb) ./ (ub .- lb) .- 1	#[a,b] -> [-1,1]
 
-function q1(n)
-	f(x) = x .+ 2x.^2 - exp.(-x)
-
-	# without using PyPlot, just erase the `PyPlot.` part
-	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png"))
-	return Dict(:error=>maximum(abs,err))
-end
-
-function q2(b::Number)
-	@assert b > 0
-	# use ApproxFun.jl to do the same:
-
-	Plots.savefig(p,joinpath(dirname(@__FILE__),"..","q2.png"))
-end
-
-function q3(b::Number)
-
-	# p is your plot
-	return (p,integral)
-end
-
-# optinal
-function q4()
-
-	return fig
-end
-
-
-# I found having those useful for q5
-mutable struct ChebyType
-	f::Function # fuction to approximate 
-	nodes::Union{Vector,LinRange} # evaluation points
-	basis::Matrix # basis evaluated at nodes
-	coefs::Vector # estimated coefficients
-
-	deg::Int 	# degree of chebypolynomial
-	lb::Float64 # bounds
-	ub::Float64
-
-	# constructor
-	function ChebyType(_nodes::Union{Vector,LinRange},_deg,_lb,_ub,_f::Function)
-		n = length(_nodes)
-		y = _f(_nodes)
-		_basis = Float64[ChebyT(unitmap(_nodes[i],_lb,_ub),j) for i=1:n,j=0:_deg]
-		_coefs = _basis \ y  # type `?\` to find out more about the backslash operator. depending the args given, it performs a different operation
-		# create a ChebyComparer with those values
-		new(_f,_nodes,_basis,_coefs,_deg,_lb,_ub)
-	end
-end
-
-# function to predict points using info stored in ChebyType
-function predict(Ch::ChebyType,x_new)
+n=15
+map(x,lb,ub) = 0.5 .* (lb .+ ub) .+ 0.5 .* (ub .- lb) .* x
 
-	true_new = Ch.f(x_new)
-	basis_new = Float64[ChebyT(unitmap(x_new[i],Ch.lb,Ch.ub),j) for i=1:length(x_new),j=0:Ch.deg]
-	basis_nodes = Float64[ChebyT(unitmap(Ch.nodes[i],Ch.lb,Ch.ub),j) for i=1:length(Ch.nodes),j=0:Ch.deg]
-	preds = basis_new * Ch.coefs
-	preds_nodes = basis_nodes * Ch.coefs
-
-	return Dict("x"=> x_new,"truth"=>true_new, "preds"=>preds, "preds_nodes" => preds_nodes)
+function Cheby(x,deg)
+len=length(x)
+psi = ones(len,deg)
+for i in 1:len
+for j in 1:deg
+psi[i,j] = ChebyT(x[i],j-1) 
 end
-
-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
-
-
-
-function q6()
-
-	# compare 2 knot vectors with runge's function
-
-	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q6.png"))
-
+return psi
 end
 
-function q7()
 
 
-	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q7.png"))
+function q1(n=15)
+lb, ub, inter, Nod = -3, 3, 100, gausschebyshev(n)[1]#Values for evaluation
+x = range(lb,stop = ub,length = n)#
+psi = map(Nod, lb, ub) #Evaluation
+
+f(x) = x .+ 2x.^2 - exp.(-x)#Function to evaluate
+PSI=inv(Cheby(Nod,n))
+ev=f(psi)
+ResEv=PSI*ev
+
+testX=range(lb, stop=ub, length=inter)
+testY=f(testX)
+
+testMap=map(testX, lb, ub)
+testPsi=Cheby(unitmap(testMap), n)
+
+ResEv=testPsi*PSI
+
+testError=ev-ResEv
+
+#PyPlot.plot()   
+p = Plots.plot(layout = 2, dpi = 400)
+Plots.plot!(p[1],testX,testY,label = "Test Y",lw = 1,linecolor = "black")
+Plots.plot!(p[1],testX,ResEv, label = "Result Evaluation", lw = 2,linestyle = :dot, linecolor = "pink")
+Plots.plot!(p[2],testX,testError, label = "Test Error", lw = 1, linecolor = "blue")
+
+# without using PyPlot, just erase the `PyPlot.` part
+PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png"))
+return Dict(:error=>maximum(abs,err))
 end
 
 
-	# function to run all questions
-function runall()
-	@info("running all questions of HW-funcapprox:")
-	q1(15)
-	q2(3)
-	q3(10)
-	q4()
-	q5()
-	q6()
-	q7()
-end
+end # module
 
 
 
-end # module