Linear Interpolation

Taneaki Mori

Linear Interpolation code: https://github.com/taneaki/MyInterpolations.jl/blob/master/src/MyInterpolations.jl

1.補間関数



In [3]:

    
using MyInterpolations



In [4]:

    
grid =[1, 2, 3, 4, 5, 6, 7, 8]
vals = [2, 0, 4, -1, 3, 7, 3, 10]
f = lin_int(grid,vals)

f.([0,1, 2.7, 7.5, 8.1])









    Out[4]:





5-element Array{Any,1}:
  "error"
 2.0     
 2.8     
 6.5     
  "error"

単体テストの実行



In [5]:

    
Pkg.test("MyInterpolations")









    



INFO: Testing MyInterpolations
INFO: MyInterpolations tests passed

2.sin関数の線形補間

[-7,7]を10分割した点での補間をまず見てみる。



In [6]:

    
using Plots
plotlyjs()









    






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

 






    



WARNING: using Plots.grid in module Main conflicts with an existing identifier.






    Out[6]:





Plots.PlotlyJSBackend()



In [7]:

    
x = linspace(-7,7,10)    # x points, coase grid
y = sin.(x)  # corresponding y points

xf = -7:0.1:7  # fine grid
plot(xf, sin.(xf), label="sine function")
plot!(x, y, st=:scatter, label="sampled data", markersize=4)









    Out[7]:



In [8]:

    
li = lin_int(x, y)
y_linear_qe = li.(xf)       # evaluate at multiple points

plot(xf, sin.(xf), label="sine function")
plot!(xf, y_linear_qe, label="linear interpolation")
scatter!(x, y, label="sampled data", markersize=4)









    Out[8]:

次に、10,20,30分割した場合の補間とその残差を見てみる。



In [9]:

    
samples = [10,20,30]
grids = [linspace(-7,7,sample) for sample in samples]
interps = [lin_int(grid, sin.(grid)) for grid in grids]









    Out[9]:





3-element Array{MyInterpolations.#func#1{LinSpace{Float64},Array{Float64,1}},1}:
 MyInterpolations.func
 MyInterpolations.func
 MyInterpolations.func



In [10]:

    
labels1 = Array{String}(1, 3)
for (i, sample) in enumerate(samples)
    labels1[i] = "linear interpolation at $sample times"
end



In [11]:

    
plot(xf, [interps[i].(xf) for i in 1:3], label = labels1)
plot!(xf, sin.(xf), label = "sine function")









    Out[11]:



In [12]:

    
labels2 = Array{String}(1, 3)
for (i, sample) in enumerate(samples)
    labels2[i] = "residual at $sample times"
end



In [13]:

    
plot(xf, [sin.(xf) - interps[i].(xf) for i in 1:3], label = labels2)









    Out[13]: