fnrfn (Spline Toolbox)

Insert additional points into the partition for a form

Syntax

g = fnrfn(f,addpts)

Description

The form in f is refined by the insertion of the entries of addpts into the knot sequence or break sequence of the form. This is of use when the sum of two or more functions of different forms is wanted or when the number of degrees of freedom in the form is to be increased to make fine local changes possible. The precise action depends on the form in f.

If the form in f is a B-form or BBform, then the entries of addpts are inserted into the existing knot sequence, subject only to the restriction that the multiplicity of no knot exceed the order of the spline, and the equivalent B-form with this refined knot sequence for the function given by f is returned.

If the form in f is a ppform, then the entries of addpts are inserted into the existing break sequence, subject only to the restriction that the break sequence be strictly increasing, and the equivalent ppform with this refined break sequence for the function in f is returned.

If the function in f is m-variate, then addknts must be a cell array, {addpts1,..., addptsm}, and the refinement is carried out in each of the variables. If the ith entry in this cell array is empty, then the knot or break sequence in the ith variable is unchanged.

Examples

See fncmb for the use of fnrfn to refine the knot or break sequences of two splines to a common refinement before forming their sum.

Algorithm

The standard knot insertion algorithm is used for the calculation of the B-form coefficients for the refined knot sequence, while Horner's method is used for the calculation of the local polynomial coefficients at the additional breaks in the refined break sequence.