Find All Minima

Finding all local(!) minima of a unvariate function in an interval by splitting the interval in many small subintervals.

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

Arguments

f

functions whose minima shall be found.

a, b

endpoints of the interval.

n

number of subintervals to generate and search.

tol

has no effect at this moment.

...

Additional parameters to be passed to the function.

Details

Local minima are found by looking for one minimum in each subinterval. It will be found by applying optimize to any two adjacent subinterval where the first slope is negative and the second one positive.

If the function is minimal on a whole subinterval, this will cause problems. If some minima are apparently not found, increase the number of subintervals.

Note that the endpoints of the interval will never be considered to be local minima. The function need not be vectorized.

Value

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

See also

optimize

Examples

fun <- function(x) x * cos(0.1*exp(x)) * sin(0.1*pi*exp(x))
if (FALSE) ezplot(fun, 0, 5, n = 1001) # \dontrun{}

# If n is smaller, the rightmost minimum will not be found.
findmins(fun, 0, 5, n= 1000)
#>  [1] 2.537727 3.248481 3.761840 4.023021 4.295831 4.455115 4.641481 4.756263
#>  [9] 4.897461 4.987802
#  2.537727 3.248481 3.761840 4.023021 4.295831
#  4.455115 4.641481 4.756263 4.897461 4.987802