fda (version 6.1.4)

int2Lfd: Convert Integer to Linear Differential Operator

Description

This function turns an integer specifying an order of a derivative into the equivalent linear differential operator object. It is also useful for checking that an object is of the "Lfd" class.

Usage

int2Lfd(m=0)

Value

a linear differential operator object of the "Lfd" class that is equivalent to the integer argument.

Arguments

m

either a nonnegative integer or a linear differential operator object.

Details

Smoothing is achieved by penalizing the integral of the square of the derivative of order m over rangeval:

m = 0 penalizes the squared difference from 0 of the function

1 = penalize the square of the slope or velocity

2 = penalize the squared acceleration

3 = penalize the squared rate of change of acceleration

4 = penalize the squared curvature of acceleration?

Examples

# Lfd to penalize the squared acceleration
# typical for smoothing a cubic spline (order 4)
int2Lfd(2)

# Lfd to penalize the curvature of acceleration
# used with splines of order 6
# when it is desired to study velocity and acceleration
int2Lfd(4)