Splines: How to find vector/array from smoothing line (function - csaps), or another function (still using a smoothing parameter)?

Question

Sean Combrink 2020-8-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/584018-splines-how-to-find-vector-array-from-smoothing-line-function-csaps-or-another-function-still

评论： Sean Combrink 2020-8-28

Question: Consider the coding:

      sample = 100;         % Data points
      x = linspace(-5,5);   % Data bounds
      y= 1.6 * x.^2 +6;     % Function
      r = randn(10,sample); % Add noise
      p = 0.1;              % Specify "smoothness"
      pp = csaps(x,y,p);    % Specify Spline/Smoothing line
    
      hold on               
      plot(x,r(1,:)+y,"b")  % Blue  :Plot random data
      plot(x,y,"k")         % Black :True "y data"
      fnplt(pp,"r")         % Red   :Plot Spline/Smoothing line

Just like I have the precise data of vectors "y" and "r", I would like to have the corresponding data from the smoothing-line (Which is not exactly the same as vectors "y" and "r" -> as "p" represents an offset from the true "y" line).

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Question: Consider the graph:

I have the vectors of the black and blue lines, but I need the vector of the red line. (Notice that they are three different lines)

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If it is impossible to gather this corresponding data-points from the spline function "csaps", is there another way of obtaining this data(another spline function - While still being able to specify a smoothing parameter "p")? Maybe obtaining a "spline formula", and then by inserting the "x" vector obtain the corresponding spline data?

Thank you!