fnxtr

Extrapolate spline

Syntax

pp = fnxtr(f,order)

pp = fnxtr(f)

Description

pp = fnxtr(f,order) returns a spline of order order that extrapolates the spline f. pp equals f on its basic interval, but pp is a polynomial of the given order outside that interval. pp satisfies at least order smoothness conditions at the ends of the basic interval of f, that is, at the new breaks. It is most useful to use a positive value of order that is smaller than the order of f.

pp = fnxtr(f) uses an extrapolation order equal to 2. It is equivalent to fnxtr(f,2).

Examples

Extrapolate Cubic Smoothing Spline

Create a cubic smoothing spline on the unit interval.

x = rand(1,21);
spline = csaps(x,x.^3); 

Create an extrapolating spline of order 2.

order = 2;
extrSpline = fnxtr(spline,order);

Plot the original spline together with the extrapolating spline.

fnplt(spline,[-.5 1.4])
hold on
fnplt(extrSpline,[-.5 1.4])
legend('Cubic smoothing spline','Extrapolating spline')
hold off

Extrapolate Bivariate B-Spline

Create and plot a bivariate B-spline.

spline = spmak({0:3,0:4},1);
fnplt(spline)

Create an extrapolating spline. To extrapolate in the first variable only, specify a negative integer as the extrapolation order in the second variable.

order = [3,-1];
extrSpline = fnxtr(spline,order);
fnplt(extrSpline)

Input Arguments

f — Spline to extrapolate

structure

Spline to extrapolate, specified as a structure. f must be a spline in B-form, BBform, or ppform.

Data Types: struct

order — Order of extrapolating spline

integer | vector of integers

Order of extrapolating spline, specified as an integer or a vector of integers.

If order is zero, then the extrapolating spline describes the same spline as fn2fm(f,'B-'), but is in ppform and has a larger basic interval.

If order is at least as large as the order of f, then the extrapolating spline is the same spline as gn2fm(f,'pp'), but uses two more pieces and has a larger basic interval.

If f is m-variate, then order can be a vector with m elements, where order(i) is the order used to extrapolate in the i-th variable. To exclude the i-th variable from being used in the extrapolation, specify order(i) as a negative integer.

Example: 1

Output Arguments

pp — Spline in ppform

spline structure

Spline in ppform, returned as a structure with these fields.

Form — Form of spline

pp

Form of the spline, returned as pp. pp indicates that the spline is given in piecewise polynomial form.

Breaks — Knot locations of spline

vector | cell array

Knot positions of the spline, returned as a vector or as a cell array of vectors for multivariate data. Vectors contain strictly increasing elements that represent the start and end of each of the intervals over which the polynomial pieces are defined.

Coefs — Coefficients of polynomials

matrix | array

Coefficients of polynomials for each piece, returned as a matrix or as an array for multivariate data.

Pieces — Number of polynomial pieces

scalar | vector

Number of polynomial pieces describing the spline, returned as a scalar or as a vector of numbers of pieces in each variable for multivariate data.

Order — Order of polynomials

scalar | vector

Order of the polynomial function describing each polynomial piece of the spline, returned as a scalar or as a vector containing the order in each variable for multivariate data.

Dim — Dimensionality

scalar

Dimensionality of the target function, returned as a scalar.

Version History

Introduced in R2006a