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Fits a polynomial to the top/(bottom) of data.


[yi,resnorm,residual,options] = lsq2topb(x,y,order,res,options)


For order=1 and fitting to top of data cloud, LSQ2TOPB finds yi that minimizes sum( (W\*( y - yi )).\^2 ) where W is a diagonal weighting matrix given by:

>> tsq = residual/res; % (res) is an input

>> tsqst = ttestp(1-options.tsqlim,5000,2); % T-test limit from table

>> ii = find(tsq<-tsqst); % finds residuals below the line

>> w(ii) = 1./(0.5+tsq(ii)/tsqst); %de-weights pts significantly below line

i.e. w(ii) is smaller for residuals far below/(above) the fit line.


  • x = independent variable Mx1 vector.
  • y = dependent variable, Mx1 vector.
  • order = order of polynomial [scalar] for polynomial function of input (x). If (order) is empty, (options.p) must contain a MxK matrix of basis vectors to fit in lieu of polynomials of (x).
  • res = approximate fit residual [scalar].


  • k = number of components {default = rank of X-block}.


  • yi = the fit to input (y).
  • resnorm = squared 2-norm of the residual.
  • residual = y - yi.


  • p: [ ] If (options.p) is empty, input (order) must be >0. Otherwise, options.p is a MxK matrix of basis vectors.
  • smooth: [ ] if >0 this adds smoothing by adding a penalty to the magnitude of the 2nd derivative. (empty or <=0 means no smooth).
  • display: [ 'off' | {'on'} ] governs level of display to command window.
  • trbflag: [{'top'} | 'bottom' | 'middle'] flag that tells algorithm to fit (yi) to the top, bottom, or middle of the data cloud.
  • tsqlim: [0.99] limit that govers whether a data point is outside the fit residual defined by input (res).
  • stopcrit: [1e-4 1e-4 1000 360] stopping criteria, iteration is continued until one of the stopping criterion is met [(rel tol) (abs tol) (max \# iterations) (max time [seconds])].
  • initwt: [ ] empty or Mx1 vector of initial weights (0<=w<=1).

See Also

baseine, baselinew, fastnnls