TABLE OF CONTENTS

CsplineUtils/csplineeval [ Functions ]

NAME

    csplineeval --- evaluate a B-spline function

FUNCTION

Evaluates a B-spline function at a given value. This is the lowest-level B-spline evaluator in this code. It uses the simple recursive formulation of a B-spline basis function.

Given a set of knots, this routine evaluates at x the basis function of order ord that has support on knots [j-ord,j]. Note that because negative array indices are not allowed, knot -ord is stored in knots[0] here.

SYNOPSIS

127 double csplineeval( double x, int j, int ord, double *knots, int splord, int nj)

INPUTS

    x     the value at which it should be evaluated
    j     which of the basis functions should be evaluated
    ord   order of the spline
    knots knots on which the spline is defined
    splord order of the spline, but remains unchanged throughout evaluation
    nj    number of basis functions defined on the knots (length(knots)-splord)

OUTPUTS

    The j-th basis function evaluated at x: B_j(x)

SOURCE

131 {
132     double knotj=knots[j+splord];
133     double knotjm1=knots[j-1+splord];
134     // base case for ord=1
135     if(ord==1) {
136         if((x >= knotjm1) & (x < knotj)) return 1.0;
137         if((x==knotj) & (j+splord==nj)) return 1.0;
138         return 0.0;
139     }
140     // recursive formula otherwise
141     double out = 0;
142     double knotjmn=knots[j-ord+splord];
143     double denom1 = (knotjm1 - knotjmn);
144     if(denom1>0){
145         double numer1 = (x-knotjmn);
146         double rec1 = csplineeval(x,j-1,ord-1,knots,splord,nj);
147         out += numer1/denom1*rec1;
148     }
149     double knotjmn1=knots[j-ord+1+splord];
150     double denom2 = (knotj - knotjmn1);
151     if(denom2>0){
152         double numer2 = (knotj-x);
153         double rec2 = csplineeval(x,j,ord-1,knots,splord,nj);
154         out += numer2/denom2*rec2;
155     }
156     return out;
157 }