e02bbf

Purpose

Synopsis

[s,ifail] = e02bbf(lamda,c,x<,ifail>)

Description

 
 This routine evaluates the cubic spline s(x) at a prescribed 
 argument x from its augmented knot set (lambda) , for 
                                                i     
           _                                                  
 i=1,2,...,n+7, (see E02BAF) and from the coefficients c , for 
                                                        i     
 i=1,2,...,q in its B-spline representation
 
                               q      
                               --     
                         s(x)= >  c N (x)
                               --  i i
                               i=1    
 
        _          _                                           
 Here q=n+3, where n is the number of intervals of the spline, and
 N (x) denotes the normalised B-spline of degree 3 defined upon 
  i                                                            
 the knots (lambda) ,(lambda)   ,...,(lambda)   . The prescribed 
                   i         i+1             i+4                
 argument x must satisfy (lambda) <=x<=(lambda)_  .
                                 4             n+4
 
                                                          _    
 It is assumed that (lambda) >=(lambda)   , for j=2,3,...,n+7, and
                            j          j-1                     
 (lambda)   >(lambda) .
         _           4
         n+4          
 
 It is expected that a common use of E02BBF will be the evaluation
 of the cubic spline approximations produced by E02BAF. A 
 generalization of E02BBF which also forms the derivative of s(x) 
 is E02BCF. E02BCF takes about 50% longer than E02BBF.
 

Parameters

e02bbf

Required Input Arguments:

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

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

s                                     real
ifail                                 integer