Free-knot spline approximation (BSFK) problem

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@BrunoLuong
My data acquisition system produce periodically 1-D measured noised data with the fixed time window length W. I want to produce smoothed data for each window W separately, with specific constraints on continuous (k=2) or smooth (k = 3 or 4) processed signal connections between consecutive time measurement windows. So, for each window W I get finally separate "pp" structure. How to set proper BSFK options setting to fulfil these constraints?
The second question is: Is there any method how to merge separate "pp" structures to one "pp" structure for several processing windows at one?
Add note: May by some processing windows overlap could be required. Do you have any experiance with using BSFK in streaming regime?
  13 Comments
Michal
Michal on 23 Sep 2022
Yes, something like this I would like to try, but I don't know how exactly implement this type of fix by "shape" and "pntcon" options. This is the main reason why I need your help.

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Accepted Answer

Bruno Luong
Bruno Luong on 23 Sep 2022
Edited: Bruno Luong on 23 Sep 2022
Here is the recursive pointwise constraint. You'll see it does the job (zoom in) the transition is not nice
data=load('result_4_8.mat')
data=data.result;
[m,n] = size(data);
x = cellfun(@(data) data.x, data, 'unif', 0);
y = cellfun(@(data) data.y, data, 'unif', 0);
j = 1; % n
close all
figure
hold on
for i = 1:m
% Normalize data so that dy/dx is comparable to y
xij = x{i,j}/10000;
yij = y{i,j}/10000;
options = struct('lambda', 1e-8);
if i >= 2
xleft = pp.breaks(end);
yleft = ppval(pp,xleft);
ydleft = ppval(ppder(pp),xleft);
xij = [xleft; xij];
yij = [yleft; yij];
pntcon = struct('p', {0 1}, 'x', {xleft,xleft}, 'v', {yleft ydleft});
options.pntcon = pntcon;
end
pp =BSFK(xij, yij, 4, [], [], options);
xi = linspace(min(xij),max(xij),1000);
yi = ppval(pp, xi);
plot(xij, yij,'c.');
plot(xi, yi, 'r', 'Linewidth', 2);
drawnow
end
function ppd = ppder(pp)
ppd = pp;
coefs = ppd.coefs;
n = size(coefs,2);
ppd.coefs = coefs(:,1:n-1).*(n-1:-1:1);
ppd.order = ppd.order-1;
end
  5 Comments
Michal
Michal on 29 Sep 2022
Of course, this is my mistake ... you are right! CPU time dependency to number of knots is ~ quadratic!!!

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