lsq2topb
Purpose
Fits a polynomial to the top/(bottom) of data.
Synopsis
[yi,resnorm,residual,options] =
lsq2topb(x,y,order,res,options)
Description
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.
INPUTS:
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].
OPTIONAL INPUTS:
k = number of components {default = rank of
X-block}, and
OUTPUTS:
yi = the fit to input (y).
resnorm = squared 2-norm of the residual.
residual
= y - yi.
Options
options =
structure array with the following fields :
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
baseline, baselinew, fastnnls
