插值函数绘图时，有几个原始数据点没有画出来，为什么呀？

Question

现有原始数据集uvlst，用ListPlot画图，记为guvlst；然后，用插值函数得到uvlst的插值函数iuvfun1，用Plot画图，记为giuvfun1。用Show[giuvfun1, guvlst]一起显示两图，发现giuvfun1显示的并不完整，有几个uvlst存在的数据点没有一起画出来，为什么呢？

源代码如下：

---

 

ClearAll["Global`*"]

uvlst = {{0.447958, 0.35463}, {0.357897, 0.360331}, {0.286791, 
    0.356864}, {0.23895, 0.342519}, {0.210788, 0.322504}, {0.195889, 
    0.303568}, {0.188468, 0.289283}, {0.184765, 0.279803}, {0.182826, 
    0.273849}};
{umin, umax} = (Sort[uvlst[[;; , 1]]])[[{1, -1}]];
guvlst = ListPlot[uvlst, PlotStyle -> Red, PlotRange -> All]

l = {-0.0866839, -0.024446, 0.156504, 0.497302, 0.998973, 1.62946, 
   2.29314, 2.86806, 3.29327};
data = Transpose@{uvlst, l} /. {{m1_, m2_}, m3_} -> {{m1}, m2, m3};

iuvfun1 = Interpolation[data, InterpolationOrder -> 3];
giuvfun1 = 
 Plot[iuvfun1[u], {u, umin, umax}, 
  Epilog -> {Green, PointSize[Large], Point[{0.182826, 0.273849}]}]

Show[giuvfun1, guvlst, PlotRange -> All]


ClearAll["Global`*"]

 

---

运行结果如下：

Answer 1

当绘图不完整时，首先要想到设置 PlotRange -> All，也可以指定绘图区域，详见帮助。

其它还有两小点建议修改一下，详见下面代码中的注释。

uvlst = {{0.447958, 0.35463}, {0.357897, 0.360331}, {0.286791, 
    0.356864}, {0.23895, 0.342519}, {0.210788, 0.322504}, {0.195889, 
    0.303568}, {0.188468, 0.289283}, {0.184765, 0.279803}, {0.182826, 
    0.273849}};
{umin, umax} = MinMax[uvlst[[;; , 1]]];(* Mma 10 以后可以用 MinMax 函数 *)
guvlst = ListPlot[uvlst, PlotStyle -> Red, PlotRange -> All]

l = {-0.0866839, -0.024446, 0.156504, 0.497302, 0.998973, 1.62946, 
   2.29314, 2.86806, 3.29327};
data = Transpose@{uvlst, l} /. {{m1_, m2_}, m3_} :> {{m1}, m2, 
    m3};(* 此处应该使用 :> 代替 -> *)

iuvfun1 = Interpolation[data, InterpolationOrder -> 6];
giuvfun1 = 
 Plot[iuvfun1[u], {u, umin, umax}, PlotRange -> All, 
  Epilog -> {Green, PointSize[Large], 
    Point[{0.182826, 0.273849}]}](* 有时 Plot 中需要设置 PlotRange -> All*)

Show[giuvfun1, guvlst, PlotRange -> All]

 

Comments

嗯，问题已解决，谢谢。剩下 -> 以及  :> 这两个的区别了，我抽空研究一下区别。-> 目前看也能用的