Maple 中的正弦回归
Sine regression in Maple
您好，我正在努力在 Maple 中执行正弦回归，我曾尝试使用互联网上的代码，但没有奏效。如有任何帮助，我们将不胜感激。
我的数据集是：
xy2 := [8.00, -.506679048120256], [8.08, 0.281910754667817e-1], [8.16, .559664265569177], [8.24, 1.01070100324046], [8.32, 1.31611672505376], [8.40, 1.43196427035055], [8.48, 1.34023337273233], [8.56, 1.05272193513947], [8.64, .611568467681354], [8.72, 0.811397528142090e-1], [8.80, -.461438501129773], [8.88, -.937510436115816], [8.96, -1.27829712008967], [9.04, -1.43481210421374], [9.12, -1.38382085374637], [9.20, -1.13084364570752], [9.28, -.712970794810407], [9.36, -.191272835454596], [9.44, .358331090663093], [9.52, .856136430555551], [9.60, 1.23021604773045], [9.68, 1.42679944926732], [9.76, 1.41736947469857], [9.84, 1.20128507880053], [9.92, .810092632128225], [10.00, .301065940880780], [10.08, -.251648449233878], [10.16, -.767849176869750], [10.24, -1.17292120742612], [10.32, -1.40861259493884], [10.40, -1.44110418232058], [10.48, -1.26379776830055], [10.56, -.902269772395664], [10.64, -.409554051221942], [10.72, .142501522971709], [10.80, .673734976975030], [10.88, 1.10731447772044], [10.96, 1.38084402685540], [11.04, 1.45522841363022], [11.12, 1.31817268904005], [11.20, .988929300957682], [11.28, .515897968446476], [11.36, -0.318624454182872e-1], [11.44, -.574750512030218], [11.52, -1.03419534660239], [11.60, -1.34402349055817], [11.68, -1.45994449557100], [11.76, -1.36423262002034], [11.84, -1.06956673456288], [11.92, -.619350106423691], [12.00, -0.793958770633476e-1], [12.08, .471761289512621], [12.16, .954294022860301], [12.24, 1.29864164214636], [12.32, 1.45551063055783], [12.40, 1.40182920346040], [12.48, 1.14373164965961], [12.56, .719231990114759], [12.64, .190472087224845], [12.72, -.365570174515493], [12.80, -.868296154301247], [12.88, -1.24516814950451], [12.96, -1.44215768668732], [13.04, -1.43084370975717], [13.12, -1.21101958959963], [13.20, -.814918996519041], [13.28, -.300617712320080], [13.36, .256936910993194], [13.44, .776860662411496], [13.52, 1.18406604455853], [13.60, 1.42009393305225], [13.68, 1.45118920522256], [13.76, 1.27106808636091], [13.84, .905832007489113], [13.92, .409125471244190], [14.00, -.146591404838158], [14.08, -.680632305076273], [14.16, -1.11580154033477], [14.24, -1.38954335200116], [14.32, -1.46281456021820], [14.40, -1.32355502489098], [14.48, -.991432071017881], [14.56, -.515321026695257], [14.64, 0.352425325998812e-1], [14.72, .580250581641171], [14.80, 1.04085183402835], [14.88, 1.35075391063922], [14.96, 1.46571651564137], [15.04, 1.36819902679830], [15.12, 1.07121797171521], [15.20, .618559572280749], [15.28, 0.764165939267409e-1], [15.36, -.476354929024263], [15.44, -.959710193024244], [15.52, -1.30400243735277], [15.60, -1.45998995251031], [15.68, -1.40476029253913], [15.76, -1.14472632247135], [15.84, -.718223841180242], [15.92, -.187706295906662], [16.00, .369587917409398], [16.08, .872888602357739], [16.16, 1.24959729981774], [16.24, 1.44574029144576], [16.32, 1.43304191884974]}
优化程序不知道数据是什么样的，当提供尽可能多的数据时，它可能会将正弦回归误认为是例如白噪声和近似算法很可能会失败。然而，我们很容易看到模式并且可以帮助例程，这在这种情况下是必要的。
让我们从绘制数据开始：
with(plots):
pointplot({xy2});
人类可以很容易地看到这里发生的模式。但是一个简单的拟合会得到一个糟糕的结果：
## Split data
X := [seq(xy2[i][1], i = 1..numelems({xy2}))]:
Y := [seq(xy2[i][2], i = 1..numelems({xy2}))]:
## Fit a sine curve to data
fit := Statistics:-NonlinearFit(a*sin(b*x+c)+d,X,Y,x);
## Plot
fitplot := plot(fit,x = min(X)..max(X),view = min(Y)..max(Y),legend = evalf(fit,4)):
display(pointplot(X,Y),fitplot);
Output:
fit := 0.0099 * sin(28.6850 * x - 365.4958) + 0.0448
我们可以将优化例程限制在参数范围内（例如 a 似乎在 1 和 2 之间）。在进行优化时，良好的初始猜测也很重要。摆弄 parameterranges 和 initialvalues 可以很好地收敛。
fit := Statistics:-NonlinearFit(a*sin(b*x+c)+d,X,Y,x,
parameterranges = [a=1..2,b = 1..10],
initialvalues = [a = 1.5,b = 5]);
## Plot
fitplot :=plot(fit,x = min(X)..max(X),view = min(Y)..max(Y),legend = evalf(fit,4)):
display(pointplot(X,Y),fitplot);
Output
fit := 1.457*sin(4.790*x+11.58)-0.5483e-3
您好，我正在努力在 Maple 中执行正弦回归，我曾尝试使用互联网上的代码，但没有奏效。如有任何帮助，我们将不胜感激。
我的数据集是：
xy2 := [8.00, -.506679048120256], [8.08, 0.281910754667817e-1], [8.16, .559664265569177], [8.24, 1.01070100324046], [8.32, 1.31611672505376], [8.40, 1.43196427035055], [8.48, 1.34023337273233], [8.56, 1.05272193513947], [8.64, .611568467681354], [8.72, 0.811397528142090e-1], [8.80, -.461438501129773], [8.88, -.937510436115816], [8.96, -1.27829712008967], [9.04, -1.43481210421374], [9.12, -1.38382085374637], [9.20, -1.13084364570752], [9.28, -.712970794810407], [9.36, -.191272835454596], [9.44, .358331090663093], [9.52, .856136430555551], [9.60, 1.23021604773045], [9.68, 1.42679944926732], [9.76, 1.41736947469857], [9.84, 1.20128507880053], [9.92, .810092632128225], [10.00, .301065940880780], [10.08, -.251648449233878], [10.16, -.767849176869750], [10.24, -1.17292120742612], [10.32, -1.40861259493884], [10.40, -1.44110418232058], [10.48, -1.26379776830055], [10.56, -.902269772395664], [10.64, -.409554051221942], [10.72, .142501522971709], [10.80, .673734976975030], [10.88, 1.10731447772044], [10.96, 1.38084402685540], [11.04, 1.45522841363022], [11.12, 1.31817268904005], [11.20, .988929300957682], [11.28, .515897968446476], [11.36, -0.318624454182872e-1], [11.44, -.574750512030218], [11.52, -1.03419534660239], [11.60, -1.34402349055817], [11.68, -1.45994449557100], [11.76, -1.36423262002034], [11.84, -1.06956673456288], [11.92, -.619350106423691], [12.00, -0.793958770633476e-1], [12.08, .471761289512621], [12.16, .954294022860301], [12.24, 1.29864164214636], [12.32, 1.45551063055783], [12.40, 1.40182920346040], [12.48, 1.14373164965961], [12.56, .719231990114759], [12.64, .190472087224845], [12.72, -.365570174515493], [12.80, -.868296154301247], [12.88, -1.24516814950451], [12.96, -1.44215768668732], [13.04, -1.43084370975717], [13.12, -1.21101958959963], [13.20, -.814918996519041], [13.28, -.300617712320080], [13.36, .256936910993194], [13.44, .776860662411496], [13.52, 1.18406604455853], [13.60, 1.42009393305225], [13.68, 1.45118920522256], [13.76, 1.27106808636091], [13.84, .905832007489113], [13.92, .409125471244190], [14.00, -.146591404838158], [14.08, -.680632305076273], [14.16, -1.11580154033477], [14.24, -1.38954335200116], [14.32, -1.46281456021820], [14.40, -1.32355502489098], [14.48, -.991432071017881], [14.56, -.515321026695257], [14.64, 0.352425325998812e-1], [14.72, .580250581641171], [14.80, 1.04085183402835], [14.88, 1.35075391063922], [14.96, 1.46571651564137], [15.04, 1.36819902679830], [15.12, 1.07121797171521], [15.20, .618559572280749], [15.28, 0.764165939267409e-1], [15.36, -.476354929024263], [15.44, -.959710193024244], [15.52, -1.30400243735277], [15.60, -1.45998995251031], [15.68, -1.40476029253913], [15.76, -1.14472632247135], [15.84, -.718223841180242], [15.92, -.187706295906662], [16.00, .369587917409398], [16.08, .872888602357739], [16.16, 1.24959729981774], [16.24, 1.44574029144576], [16.32, 1.43304191884974]}
优化程序不知道数据是什么样的，当提供尽可能多的数据时，它可能会将正弦回归误认为是例如白噪声和近似算法很可能会失败。然而，我们很容易看到模式并且可以帮助例程，这在这种情况下是必要的。
让我们从绘制数据开始：
with(plots):
pointplot({xy2});
人类可以很容易地看到这里发生的模式。但是一个简单的拟合会得到一个糟糕的结果：
## Split data
X := [seq(xy2[i][1], i = 1..numelems({xy2}))]:
Y := [seq(xy2[i][2], i = 1..numelems({xy2}))]:
## Fit a sine curve to data
fit := Statistics:-NonlinearFit(a*sin(b*x+c)+d,X,Y,x);
## Plot
fitplot := plot(fit,x = min(X)..max(X),view = min(Y)..max(Y),legend = evalf(fit,4)):
display(pointplot(X,Y),fitplot);
Output:
fit := 0.0099 * sin(28.6850 * x - 365.4958) + 0.0448
我们可以将优化例程限制在参数范围内（例如 a 似乎在 1 和 2 之间）。在进行优化时，良好的初始猜测也很重要。摆弄 parameterranges 和 initialvalues 可以很好地收敛。
fit := Statistics:-NonlinearFit(a*sin(b*x+c)+d,X,Y,x,
parameterranges = [a=1..2,b = 1..10],
initialvalues = [a = 1.5,b = 5]);
## Plot
fitplot :=plot(fit,x = min(X)..max(X),view = min(Y)..max(Y),legend = evalf(fit,4)):
display(pointplot(X,Y),fitplot);
Output
fit := 1.457*sin(4.790*x+11.58)-0.5483e-3