rationalfit | R Documentation |
Fitting a rational function to data points.
rationalfit(x, y, d1 = 5, d2 = 5)
x |
numeric vector; points on the x-axis; needs to be sorted; at least three points required. |
y |
numeric vector; values of the assumed underlying function;
|
d1 , d2 |
maximal degrees of numerator ( |
A rational fit is a rational function of two polynomials p1
and
p2
(of user specified degrees d1
and d2
) such that
p1(x)/p2(x)
approximates y
in a least squares sense.
d1
and d2
must be large enough to get a good fit and usually
d1=d2
gives good results
List with components p1
and p2
for the polynomials in
numerator and denominator of the rational function.
This implementation will later be replaced by a 'barycentric rational interpolation'.
Copyright (c) 2006 by Paul Godfrey for a Matlab version available from the MatlabCentral under BSD license. R re-implementation by Hans W Borchers.
Press, W. H., S. A. Teukolsky, W. T Vetterling, and B. P. Flannery (2007). Numerical Recipes: The Art of Numerical Computing. Third Edition, Cambridge University Press, New York.
ratinterp
## Not run:
x <- linspace(0, 15, 151); y <- sin(x)/x
rA <- rationalfit(x, y, 10, 10); p1 <- rA$p1; p2 <- rA$p2
ys <- polyval(p1,x) / polyval(p2,x)
plot(x, y, type="l", col="blue", ylim=c(-0.5, 1.0))
points(x, Re(ys), col="red") # max(abs(y-ys), na.rm=TRUE) < 1e-6
grid()
# Rational approximation of the Zeta function
x <- seq(-5, 5, by = 1/16)
y <- zeta(x)
rA <- rationalfit(x, y, 10, 10); p1 <- rA$p1; p2 <- rA$p2
ys <- polyval(p1,x) / polyval(p2,x)
plot(x, y, type="l", col="blue", ylim=c(-5, 5))
points(x, Re(ys), col="red")
grid()
# Rational approximation to the Gamma function
x <- seq(-5, 5, by = 1/32); y <- gamma(x)
rA <- rationalfit(x, y, 10, 10); p1 <- rA$p1; p2 <- rA$p2
ys <- polyval(p1,x) / polyval(p2,x)
plot(x, y, type="l", col = "blue")
points(x, Re(ys), col="red")
grid()
## End(Not run)
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