Piecewise linear least square fit

Fit experimental data with linear piecewise continuos function with given x-axis break points.

Generates 1-D look-up table (LUT) optimal (least-square sense with continuity constraint) y-axis points from experimental (x,y) data given a vector of x-axis break points.

Note that x-axis break points should be chosen such that every bin has enough data points for correct estimation.

Please see lsq_lut_piecewise_test.m for an example with (synthetic) experimental data points.

No toolbox required.

% LSQ_LUT_PIECEWISE Piecewise linear interpolation for 1-D interpolation (table lookup)
% YI = lsq_lut_piecewise( x, y, XI ) obtain optimal (least-square sense)
% vector to be used with linear interpolation routine.
% The target is finding Y given X the minimization of function
% f = |y-interp1(XI,YI,x)|^2
%
% INPUT
% x measured data vector
% y measured data vector
% XI break points of 1-D table
%
% OUTPUT
% YI interpolation points of 1-D table
% y = interp1(XI,YI,x)
%