pracma (version 1.8.8)

findzeros: Find All Roots

Description

Finding all roots of a unvariate function in an interval by splitting the interval in many small subintervals.

Usage

findzeros(f, a, b, n = 100, tol = .Machine$double.eps^(2/3), ...)

Arguments

f

functions whose roots shall be found.

a, b

endpoints of the interval.

n

number of subintervals to generate and search.

tol

tolerance for identifying zeros.

...

Additional parameters to be passed to the function.

Value

• Numeric vector with the x-positions of all roots found in the interval.

Details

Roots, i.e. zeros in a subinterval will be found by applying uniroot to any subinterval where the sign of the function changes. The endpoints of the interval will be tested separately.

If the function points are both positive or negative and the slope in this interval is high enough, the minimum or maximum will be determined with optimize and checked for a possible zero.

The function need not be vectorized.

See Also

findmins

Examples

f1 <- function(x) sin(pi/x)
findzeros(f1, 1/10, 1)
#  0.1000000  0.1111028  0.1250183  0.1428641  0.1666655
#  0.2000004  0.2499867  0.3333441  0.4999794  1.0000000

f2 <- function(x) 0.5*(1 + sin(10*pi*x))
findzeros(f2, 0, 1)
#  0.15  0.35  0.55  0.75  0.95

f3 <- function(x) sin(pi/x) + 1
findzeros(f3, 0.1, 0.5)
# 0.1052632 0.1333333 0.1818182 0.2857143

f4 <- function(x) sin(pi/x) - 1
findzeros(f4, 0.1, 0.5)
# 0.1176471 0.1538462 0.2222222 0.4000000

# Dini function
Dini <- function(x) x * besselJ(x, 1) + 3 * besselJ(x, 0)
findzeros(Dini, 0, 100, n = 128)
ezplot(Dini, 0, 100, n = 512)