Computes shifted Legendre polynomials.
1 |
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)
.
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.
The estimation algorithm of iqr
is optimized for objects of class “slp”,
which means that using formula.p = ~ slp(p, k)
instead of
formula.p = ~ p + I(p^2) + ... + I(p^k)
will result in a quicker
computation, even with k = 1, with equivalent results.
The default for iqr
is formula.p = ~ slp(p, k = 3)
.
Paolo Frumento paolo.frumento@ki.se
Refaat El Attar (2009), Legendre Polynomials and Functions, CreateSpace, ISBN 978-1-4414-9012-4.
plf
, for piecewise linear functions in the unit interval.
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