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fnxtr

Extrapolate spline

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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.

example

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

Examples

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Open Live Script

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

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Cubic smoothing spline, Extrapolating spline.

Open Live Script

Create and plot a bivariate B-spline.

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

Figure contains an axes object. The axes object contains an object of type surface.

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)

Figure contains an axes object. The axes object contains an object of type surface.

Input Arguments

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

Data Types: struct

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

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

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

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.

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

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 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.

Dimensionality of the target function, returned as a scalar.

Version History

Introduced in R2006a

See Also

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