e02bcf

Purpose

Synopsis

[s,ifail] = e02bcf(lamda,c,x<,left,ifail>)

Description

 
 This routine evaluates the cubic spline s(x) and its first three 
 derivatives at a prescribed argument x. It is assumed that s(x) 
 is represented in terms of its B-spline coefficients c , for 
                                                       i     
           _                                                  
 i=1,2,...,n+3 and (augmented) ordered knot set (lambda) , for 
                                                        i     
           _                  
 i=1,2,...,n+7, (see E02BAF), i.e.,
 
                               q      
                               --     
                         s(x)= >  c N (x)
                               --  i i
                               i=1    
 
        _    _                                                   
 Here q=n+3, n is the number of intervals of the spline and N (x) 
                                                             i   
 denotes the normalised B-spline of degree 3 (order 4) defined 
 upon the knots (lambda) ,(lambda)   ,...,(lambda)   . The 
                        i         i+1             i+4     
 prescribed argument x must satisfy
 
                     (lambda) <=x<=(lambda)_ 
                             4             n+4
 
 At a simple knot (lambda)  (i.e., one satisfying 
                          i                      
 (lambda)   <(lambda) <(lambda)   ), the third derivative of the 
         i-1         i         i+1                              
 spline is in general discontinuous. At a multiple knot (i.e., two
 or more knots with the same value), lower derivatives, and even 
 the spline itself, may be discontinuous. Specifically, at a point
 x=u where (exactly) r knots coincide (such a point is termed a 
 knot of multiplicity r), the values of the derivatives of order 
 4-j, for j=1,2,...,r, are in general discontinuous. (Here 
 1<=r<=4;r>4 is not meaningful.) The user must specify whether the
 value at such a point is required to be the left- or right-hand 
 derivative.
 
 E02BCF can be used to compute the values and derivatives of cubic
 spline fits and interpolants produced by E02BAF.
 
 If only values and not derivatives are required, E02BBF may be 
 used instead of E02BCF, which takes about 50% longer than E02BBF.
 

Parameters

e02bcf

Required Input Arguments:

lamda (:)                             real
c (:)                                 real
x                                     real

Optional Input Arguments:                       <Default>

left                                  integer  0
ifail                                 integer  -1

Output Arguments:

s (4)                                 real
ifail                                 integer