Re: fixed points piecewise-linear fitting

[Martin Helm]

I want to add my poor man's solution for least squares fit of the
piecewise polynomials
returns the node values as first argument (makes only sense for the
piecewise linear case) and the function values at all nodes as second
argument.
Simplistic but fast.

function [y, yy] = ppfit2(x, xf, yf, method)
  a = zeros (length (xf), length (x));
  for ii = 1:length (x)
    p = zeros (length (x), 1);
    p(ii) = 1;
    a(:, ii) = interp1 (x(:), p, xf(:), method);
  endfor
  y = a\yf(:);
  if (nargout==2)
    yy = interp1 (x(:), y, xf(:), method);
  endif
endfunction

%!demo
%! clf
%! x = [0 1 2 3];
%! xf = linspace(0, 3, 1000);
%! yf = xf.^3 + rand(size(xf))*2.5;
%! plot (xf, yf, "y-")
%! hold on
%! [y, yy] = ppfit2(x,xf,yf, "linear");
%! plot (xf, yy, "r-")
%! [y, yy] = ppfit2(x,xf,yf, "cubic");
%! plot (xf, yy, "g-")
%! [y, yy] = ppfit2(x,xf,yf, "spline");
%! plot (xf, yy, "b-")