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fnbrk

Name and part(s) of form

Syntax

着干活,…outn] = fnbrk (f, part1…,partm)
fnbrk (f,interval)
fnbrk(pp,j)
fnbrk (f)

Description

着干活,…outn] = fnbrk (f, part1…,partm)returns the part(s) of the form infspecified bypart1,...,partn(assuming thatn<=m). These are the parts used when the form was put together, inspmakor页makorrpmakorrsmakorstmak, but also other parts derived from these.

You only need to specify the beginning character(s) of the relevant option.

Regardless of what particular formfis in,partican be one of the following, specified as a character vector or string scalar.

'form'

The particular form used

'variables'

The dimension of the function's domain

'dimension'

The dimension of the function's target

'coefficients'

The coefficients in that particular form

'interval'

The basic interval of that form

Depending on the form inf, additional parts may be asked for.

Iffis in B-form (or BBform or rBform), then additional choices forpartiare

'knots'

The knot sequence

'coefficients'

The B-spline coefficients

'number'

The number of coefficients

'order'

The polynomial order of the spline

Iffis in ppform (or rpform), then additional choices forpartiare

'breaks'

The break sequence

'coefficients'

The local polynomial coefficients

'pieces'

The number of polynomial pieces

'order'

The polynomial order of the spline

'guide'

The local polynomial coefficients, but in the form needed forPPVALUin PGS

If the function infis multivariate, then the corresponding multivariate parts are returned. This means, e.g., that knots, breaks, and the basic interval, are cell arrays, the coefficient array is, in general, higher than two-dimensional, and order, number and pieces are vectors.

Iffis in stform, then additional choices forpartiare

'centers'

The centers

'coefficients'

The coefficients

'number'

系数或条款

'type'

The particular type

fnbrk (f,interval)withintervala 1-by-2 matrix[a b]withadoes not return a particular part. Rather, it returns a description of the univariate function described byfand in the same form but with the basic interval changed, to the interval given. If, instead,intervalis[ ],fis returned unchanged. This is of particular help when the function infism-variate, in which caseintervalmust be a cell array withmentries, with theith entry specifying the desired interval in theith dimension. If thatith entry is[ ], the basic interval in theith dimension is unchanged.

fnbrk(pp,j), with页the ppform of a univariate function andja positive integer, does not return a particular part, but returns the ppform of thejth polynomial piece of the function in页. If页is the ppform of anm-variate function, thenjmust be a cell array of lengthm. In that case, each entry ofjmust be a positive integer or else an interval, to single out a particular polynomial piece or else to specify the basic interval in that dimension.

fnbrk (f)returns nothing, but a description of the various parts of the form is printed at the command line instead.

Examples

Ifp1andp2contain the B-form of two splines of the same order, with the same knot sequence, and the same target dimension, then

p1plusp2 = spmak(fnbrk(p1,'k'),fnbrk(p1,'c')+fnbrk(p2,'c'));

provides the (pointwise) sum of those two functions.

If页contains the ppform of a bivariate spline with at least four polynomial pieces in the first variable, then页p=fnbrk(pp,{4,[-1 1]})gives the spline that agrees with the spline in页on the rectangle [b4..b5] x [-1 .. 1] , whereb4,b5are the fourth and fifth entry in the break sequence for the first variable.

See Also

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