poly.calc {PolynomF} | R Documentation |
poly.calc
(alias poly.from.values
) computes the Lagrange
interpolating polynomial. poly.from.zeros
(alias
poly.from.roots
) computes the monic polynomial with specified
zeros. poly.orth
calculates polynomials orthogonal over a
discrete set of $x-$values, as done numerically by the standard R
function poly
.
poly.calc(x, y, tol = sqrt(.Machine$double.eps), lab = dimnames(y)[[2]]) poly.from.values(x, y, tol = sqrt(.Machine$double.eps), lab = dimnames(y)[[2]]) poly.from.zeros(...) poly.from.roots(...) poly.orth(x, degree = length(unique(x)) - 1, norm = TRUE)
x |
A numeric vector of values for the polynomial variable. |
y |
A numeric vector or matrix specifying values for the polynomial. |
tol |
A numeric tolerance |
lab |
A character vector providing names for the polylist
of polynomials. |
degree |
The maximum degree for the orthogonal polynomials required. |
norm |
Logical value. Should the polynomials be normalised to be of length 1?) |
... |
Not presently used. |
Given a vector of distinct values x
and a vector y
of
the same length, poly.calc
computes the Lagranging
intrepolating polynomial they define. If y
is a matrix, its
row size must match the length of x
and interpolating
polynomials are computed for all columns. In this case the value is a
polylist
object.
poly.from.values
is a complete alias for poly.calc
.
The function poly.from.zeros
computes the monic polynomial with
zeros as given by the arguments. The zeros may be specified either as
separate artuments or as a single numeric vector.
poly.from.roots
is a complete alias for poly.from.zeros
.
poly.orth
calculates polynomials orthogonal with respect to the
uniform measure over a discrete set of $x-$values given by the
artument x
. These are the polynomials for which the standard
function poly
can be used to compute numerical values.
A polynom
object, or, in the case of poly.calc
and
poly.orth
, possibly a polylist
object
Bill Venables
None
poly
x <- polynom() H <- polylist(1, x) for(j in 2:10) H[[j+1]] <- x*H[[j]] - (j-1)*H[[j-1]] Hf <- as.function(H) x0 <- -5:5 y0 <- Hf(x0) J <- poly.from.values(x0, y0) all.equal(H[[11]], J[[11]]) p1 <- poly.from.zeros(-3:2) p2 <- poly.from.zeros(0:4) p3 <- GCD(p1, p2) p4 <- LCM(p1, p2) solve(polylist(p1, p2, p3, p4)) po <- poly.orth(-4:4, degree = 4) plot(po) round(crossprod(as.function(po)(-4:4)), 10)