Fitting by Polynomial
Polynomial curve fitting
polyfit(x, y, n) polyfix(x, y, n, xfix, yfix)
x |
x-coordinates of points |
y |
y-coordinates of points |
n |
degree of the fitting polynomial |
xfix,yfix |
x- and y-coordinates of points to be fixed |
polyfit finds the coefficients of a polynomial of degree n
fitting the points given by their x, y coordinates in a
least-squares sense. In polyfit, if x, y are matrices
of the same size, the coordinates are taken elementwise. Complex values are
not allowed.
polyfix finds a polynomial that fits the data in a least-squares
sense, but also passes exactly through all the points with coordinates
xfix and yfix. Degree n should be greater or equal
to the number of fixed points, but not too big to avoid ‘singular matrix’
or similar error messages
vector representing a polynomial.
Please not that polyfit2 is has been removed since 1.9.3; please use
polyfix instead.
# Fitting the sine function by a polynomial
x <- seq(0, pi, length.out=25)
y <- sin(x)
p <- polyfit(x, y, 6)
## Not run:
# Plot sin and fitted polynomial
plot(x, y, type="b")
yf <- polyval(p, x)
lines(x, yf, col="red")
grid()
## End(Not run)
## Not run:
n <- 3
N <- 100
x <- linspace(0, 2*pi, N); y = sin(x) + 0.1*rnorm(N)
xfix <- c(0, 2*pi); yfix = c(0, 0)
xs <- linspace(0, 2*pi); ys <- sin(xs)
plot(xs, ys, type = 'l', col = "gray",
main = "Polynom Approximation of Degree 3")
grid()
points(x, y, pch='o', cex=0.5)
points(xfix, yfix, col = "darkred")
p0 <- polyfit(x, y, n)
lines(xs, polyval(p0, xs), col = "blue")
p1 <- polyfix(x, y, n, xfix, yfix)
lines(xs, polyval(p1, xs), col = "red")
legend(4, 1, c("sin", "polyfit", "polyfix"),
col=c("gray", "blue", "red"), lty=c(1,1,1))
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.