PLS_Toolbox Documentation: b3spline< autocor baseline >

b3spline

Purpose

Univariate spline fit and prediction.

Synopsis

 

modl = b3spline(x,y,t,options);

pred = b3spline(x,modl,options);

valid = b3spline(x,y,modl,options);

Description

Curve fitting using second order splines where

yi = f(xi) for i=1,...,M.

See (options.algorithm) for more information.

INPUTS:

                         x =   Mx1 vector of independent variable values.

                         y =   Mx1 vector of corresponding dependendent variable values.

                          t =   defines the number of knots or knot positions.

                                 = 1x1 scalar integer defining the number of uniformly distributed INTERIOR knots. There will be t+2 knots positioned at:

                                 modl.t = linspace(min(x),max(x),t+2)';

                                 = Kx1 vector defining manually placed knot positions,

                                 where modl.t = sort(t);

                                 Note that knot positions need not be uniform, and that t(1) can be <min(x) and t(K) can be >max(x).

Note that knot positions must be such that there are at least 3 unique data points between each knot:  tk,tk+1 for k=1,...,K.

OUTPUTS:

                   modl =   standard model structure containing the spline model (See MODELSTRUCT).

                   pred =   structure array with predictions.

                    valid =   structure array with predictions.

Options

             options =   a structure array with the following fields:

               display:   [ {'on'} | 'off' ] level of display to command window.

                   plots:   [ {'final'} | 'none' ] governs level of plotting. If 'final' and calibrating a model, the plot shows plot(xi,yi) and plot(xi,f(xi),'-') with knots.

           algorithm:   [ {'b3spline'} | 'b3_0' | 'b3_01' ] fitting algorithm

                                 'b3spline': fits quadradic polynomials f{k,k+1} to the data between knots tk, k=1,...,K, subject to:

                                 f{k,k+1}(tk+1)  = f{k+1,k+2}(tk+1) and

                                 f'{k,k+1}(tk+1) = f'{k+1,k+2}(tk+1) for k=1,...,K-1.

                                 'b3_0': is the same as 'b3spline' but also constrains the ends to 0: f{1,2}(t1) = 0 and f{K-1,K}(tK) = 0.

                                 'b3_01': is 'b3_0' but also constrains the derivatives at the ends to 0: f'{1,2}(t1) = 0 and f'{K-1,K}(tK) = 0.

 

 

                   order:   positive integer for polynomial order {default = 1}.

The default options can be retreived using: options = baseline('options');.

See Also


< autocor baseline >