An object of class “slp”, i.e.,
a matrix with the same number of rows as p, and with k columns
named slp1, slp2, ... containing the SLP of the corresponding orders.
The value of k is reported as attribute.
Arguments
p
the variable for which to compute the polynomials. Must be 0 <= p <= 1.
k
the degree of the polynomial.
intercept
logical. If TRUE, the polynomials include the constant term.
Shifted Legendre polynomials (SLP) are orthogonal polynomial functions in (0,1) that can be used
to build a spline basis, typically within a call to iqr.
The constant term is omitted unless intercept = TRUE: for example,
the first two SLP are (2*p - 1, 6*p^2 - 6*p + 1),
but slp(p, k = 2) will only return (2*p, 6*p^2 - 6*p).
References
Refaat El Attar (2009), Legendre Polynomials and Functions, CreateSpace, ISBN 978-1-4414-9012-4.
See Also
plf, for piecewise linear functions in the unit interval.
p <- seq(0,1,0.1)
slp(p, k = 1) # = 2*p slp(p, k = 1, intercept = TRUE) # = 2*p - 1 (this is the true SLP of order 1) slp(p, k = 3) # a linear combination of (p, p^2, p^3), with slp(0,k) = 0