Not getting roots using "IntervalRootFinding.jl" package in Pluto.jl notebook

General Usage
1

Hello

I am trying to find the roots of an equation using “IntervalRootFinding.jl” package in Pluto.jl notebook. But I am not able to get the roots; could you please check the code?

using IntervalArithmetic, IntervalRootFinding, ForwardDiff
begin
	f(x) = a - b * x^2 	#Function
	
	∇f = ∇(f) 	#gradient operator
	
	a = (100..200) #Interval parameters
	b = (1..2)
	
	X_int = (0..200) #Interval
	
	rts = roots(f, X_int)
	rts_deri = roots(∇f, X_int)
	
	@show rts, rts_deri
end

Thank you

2

I think there are just too many roots, the calculation ran for ~20min before I remembered it was still running and interrupted it. Try making only one of a or b an interval and reducing the range of the other until the calculation completes in a reasonable time.

This doesn’t make any sense:

∇f = ∇(f) 	#gradient operator

f is a function of a scalar value (if you had used .^ and .-, it would accept a vector) and IntervalRootFinding.gradient is only defined for functions of a vector argument. Perhaps you meant to define f as taking a vector or perhaps you meant

f′(x) = IntervalRootFinding.derivative(f, x)
3

Dear @contradict, Thank you for the helpful suggestions. I have checked with what you suggested. But I am still getting nothing. I proceeded with the following code-

begin
	f(x) = a - b * x
	a = 10
	b = (2..3)
	X_int = (0..5)
	rts = roots(f, X_int)
	@show rts
end

Thank you

4

Try an even smaller range for b. This returns instantly for me. You don’t need the show at the end, Pluto will print the result of the last evaluation in a cell.

begin
	f(x) = a - b * x
	a = 10
	b = (2.5..3)
	X_int = (0..5)
	rts = roots(f, X_int)
end