L2機能データ間の距離（平滑化曲線）

Question

私は、スムージングを使用して2つの「関数」fd4とfd6を作成しました。

fit6 <- smooth.basis(tid6, zbegfor, fdParobj2) 
fd6 <- fit6$fd 

私は区間[0,1]上で、それらの間のL2距離を測定したいが、私は、適切な方法を見つけることができませんでした。

|| F - G || _2 = SQRT（INT（|（x）は-g f（x）が|^2,0,1））

最善の策は、この一つとなっている：How to calculate functional L_2 norm using R、

「 - ：非適合配列fdmat FACでエラーが発生しました：」私はfd6の代わりf <- function(x) x^2を使用するときには、私は次のメッセージが表示されます。

私は解決策を見つけようと時間を費やしてきました。私を助けてください！

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今再現コードで：fdwith - fdwithout：

library(fda) 

# Smoothing of movement pattern without obstacle rescaled to the interval [0,1] 
without <- c(22.5050173512478, 22.5038665040295, 22.5171851824298, 22.5368096190746, 
22.5770229184757, 22.6709727229898, 22.8195669635573, 23.0285400460222, 
23.3240853426905, 23.6895323912605, 24.0905709304813, 24.5674870961964, 
25.129085512519, 25.7433521858875, 26.4096817521118, 27.1338935155912, 
27.906416101033, 28.7207273157549, 29.5431756517467, 30.3697951466496, 
31.2214907341765, 32.0625307132683, 32.8786845916855, 33.671550678219, 
34.4449992914392, 35.1852293010227, 35.8866367048324, 36.5650863548079, 
37.1776116180247, 37.7706354957587, 38.3082855431959, 38.8044130844639, 
39.2471137254193, 39.6193031585418, 39.9685683244076, 40.2345560551869, 
40.4394442661545, 40.5712407258558, 40.6905311089523, 40.712419802203, 
40.6704560575084, 40.5583379372846, 40.3965425630546, 40.1443139907057, 
39.8421899334408, 39.4671160834355, 39.018733225651, 38.5381390971577, 
38.035680135599, 37.4625783280288, 36.8649362406917, 36.2320264206665, 
35.5599736527209, 34.8983871226943, 34.2058073957721, 33.4893682831911, 
32.7568501019309, 32.0241649500974, 31.3036406455137, 30.587636320768, 
29.8962657607091, 29.2297665999702, 28.6003939337949, 28.0003531206639, 
27.433551463149, 26.9088532545635, 26.4265682839796, 25.974193299003, 
25.5553146923473, 25.1701249455904, 24.8107813804098, 24.4776168601955, 
24.167582682288, 23.8726502760669, 23.589703789663, 23.3222235336882, 
23.0616248799115, 22.8185342685607, 22.6767541125512, 22.6567795841271, 
22.6488510112824, 22.6436058079441, 22.6391304188382) 

timewithout <- (1:length(without))/length(without) # For scaling 
splineBasis = create.bspline.basis(c(0,1), nbasis=25, norder=6) # The basis for smoothing 
basis = fdPar(fdobj=splineBasis, Lfdobj=2, lambda=0.00001) 
fitwithout <- smooth.basis(timewithout, without, basis) # Smoothing 
fdwithout <- fitwithout$fd 

# Same but movement is over an obstacle 
with <- c(22.4731637093167, 22.4655561889073, 22.4853719755102, 22.4989400065304, 
22.5495656349031, 22.666945409755, 22.8368941117498, 23.0846080078369, 
23.4160560011242, 23.8285634914224, 24.78, 24.8297004047422, 
25.4884540279408, 26.2107053559, 27.0614232848574, 27.9078055119721, 
28.8449720096674, 29.8989669834473, 30.996962022701, 32.1343108758062, 
33.3286403418359, 34.6364870430171, 35.9105342483246, 37.1883582665643, 
38.467212668323, 39.7381525466373, 41.0395064969214, 42.3095531191294, 
43.5708069740233, 44.7881178787717, 45.9965529977777, 47.1643807808923, 
48.284786275036, 49.3593991064962, 50.3863035442644, 51.3535489662494, 
52.2739716491521, 53.1338828493223, 53.9521101656512, 54.7037562884229, 
55.3593092084143, 55.9567618011946, 56.4768579145271, 56.9251919073806, 
57.2971965985674, 57.5937987523734, 57.8158626068961, 57.9554856023804, 
58.009777126789, 57.9863251605612, 57.8932199088797, 57.6988126618694, 
57.4350394069443, 57.1112025796509, 56.7580579506751, 56.2680669960935, 
55.6963799946038, 55.0574070566765, 54.3592140352073, 53.6072275005723, 
52.7876353306759, 51.9172334605074, 50.9879178368431, 49.9953932631072, 
48.9460707853802, 47.8511977258834, 46.6827266395278, 45.4635999409637, 
44.2633368255294, 43.0386729762103, 41.7880095105045, 40.4834298069985, 
39.1610223705633, 37.9241872458281, 36.7158342529737, 35.5408830466013, 
34.4070964101159, 33.307156473109, 32.2514661493348, 31.2475129673168, 
30.2990631096187, 29.4096423238141, 28.590173995037, 27.8437368908309, 
27.17493959411, 26.5779670740351, 26.0377946174036, 25.5731202027558, 
25.1761397934058, 24.8319659155494, 24.5479180062239, 24.2940808334792, 
24.09388897537, 23.934861348149, 23.7999923744404, 23.6877461628934, 
23.5982309560843, 23.5207597985246, 23.4354446383638, 23.3604065265148, 
23.2819126915765, 23.1725048152396, 23.0637455648184, 22.9426779696074, 
22.8079176617495, 22.69360227086, 22.6622165457034, 22.6671302753094, 
22.66828206305, 22.6703162730529, 22.6715781657376) 
timewith <- (1:length(with))/length(with) 
fitwith <- smooth.basis(timewith, with, basis) # Smoothing 
fdwith <- fitwith$fd 

# Plots for understanding 
plot(fdwith, col=2) # Smoothed curve for movement over obstacle 
plot(fdwithout, col=2, add = TRUE) # Same but no obstacle 

# I have to find the L2-distance between these curves 

Answer 1

まず、一つはfdオブジェクトと算術演算を実行する可能性を利用することができます。第二に、特定のポイントでfdオブジェクトから値を抽出するより良い方法があるかもしれませんが、これも動作します：predict(newdata = 0.5, fdwith - fdwithout)。だから、

sqrt(integrate(function(x) predict(newdata = x, fdwith-fdwithout)^2, lower = 0, upper = 1)$val) 
# [1] 9.592434