TABLE OF CONTENTS

splineUtils/nBsmom [ Functions ]

NAME

    nBsmom --- compute the N-th moment of a B-spline basis function

FUNCTION

Computes the N-th moment of the j-th B-spline basis function of order ord defined on the given set of knots.

SYNOPSIS

1540 nBsmom <- function(N, ord, j, knots)

INPUTS

    N       moment to compute
    ord     order of the spline
    j       which basis function to compute the moment for
    knots   set of knots to use

OUTPUTS

    double, containing the N-th B-spline moment

SOURCE

1543 {
1544     lknot <- knots[ki(knots, j - ord)]
1545     rknot <- knots[ki(knots, j)]
1546     if(lknot == rknot) return(rknot^N)
1547     # This is a magic recursive formula that can be computed easily using integration
1548     # by parts
1549     return(ord / (rknot - lknot) / (N + 1) * (-nBsmom(N + 1, ord - 1, j - 1, knots) + 
1550         nBsmom(N + 1, ord - 1, j, knots)))
1551 }