TABLE OF CONTENTS

initRoutine/makePenalty.2deriv [ Functions ]

NAME

    makePenalty.2deriv --- compute a penalty matrix on second derivatives of B-splines

FUNCTION

This function computes a matrix P such that 

       exp(x) %*% P %*% exp(x)

is the integral of the squared second derivative of a B-spline with a given set of knots and component weights exp(x)

SYNOPSIS

1764 makePenalty.2deriv <- function(ord, knots)

INPUTS

    ord    order of the B-spline
    knots  set of basis knots

OUTPUTS

    P      a K x K matrix that penalizes the integrated squared second derivative

SOURCE

1767 {
1768     #   compute the number of spline components K
1769     nspline <- sum(knots > attr(knots, "b")[1])
1770     out <- matrix(0, nspline, nspline)
1771     for(j1 in 1:nspline){
1772         for(j2 in j1:nspline){
1773             # compute convolutions of second derivatives for each pair of basis functions
1774             out[j1, j2] <- splinederivint(2, ord, j1, 2, ord, j2, knots)
1775         }
1776     }
1777     # the matrix is symmetric
1778     for(j1 in 2:nspline){
1779         for(j2 in 1:(j1 - 1)) out[j1, j2] <- out[j2, j1]
1780     }
1781     return(out)
1782 }