Function Approximation



In [1]:

    
using BasisMatrices
using Plots



In [2]:

    
plotlyjs()









    Out[2]:





Plots.PlotlyJSBackend()

Chebychev polynomials



In [3]:

    
n = 10
a, b = 0, 1
basis1 = Basis(ChebParams(n, a, b))









    Out[3]:





1 dimensional Basis on the hypercube formed by [0.0] × [1.0].
Basis families are BasisMatrices.Cheb



In [4]:

    
xgrid = collect(linspace(a, b, 101))
ys = []
m = 9
for i in 1:m
    c = zeros(n)
    c[i] = 1
    y = funeval(c, basis1, xgrid)
    push!(ys, y)
end
ylims = (-1.1, 1.1)
plot(xgrid, ys, layout=m, ylims=ylims, leg=false)









    






 
 Plotly javascript loaded.
 To load again call 
init_notebook(true)

 






    



[Plots.jl] Initializing backend: plotlyjs






    Out[4]:

Linear Spline



In [5]:

    
n = 10
a, b = 0, 1
basis2 = Basis(LinParams(n, a, b))









    Out[5]:





1 dimensional Basis on the hypercube formed by [0.0] × [1.0].
Basis families are BasisMatrices.Lin



In [6]:

    
xgrid = collect(linspace(a, b, 101))
ys = []
m = 9
for i in 1:m
    c = zeros(n)
    c[i] = 1
    y = funeval(c, basis2, xgrid)
    push!(ys, y)
end
ylims = (-1.1, 1.1)
plot(xgrid, ys, layout=m, ylims=ylims, leg=false)









    Out[6]:

Cubic Spline



In [7]:

    
breaks = [a, b]
evennum = 7
k = 3
basis3 = Basis(SplineParams(breaks, evennum, k))









    Out[7]:





1 dimensional Basis on the hypercube formed by [0.0] × [1.0].
Basis families are BasisMatrices.Spline



In [12]:

    
xgrid = collect(linspace(a, b, 101))
ys = []
m = 9
for i in 1:m
    c = zeros(basis3.n[1], basis3.n[1])
    c[i, i] = 1
    y = funeval(c, basis3, xgrid)
    push!(ys, y[:, i])
end
ylims = (-1.1, 1.1)
plot(xgrid, ys, layout=m, ylims=ylims, leg=false)









    Out[12]:



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