Error root

[jmarcellopereira]

An error occurs when using Roots.jl to solve an equation, the result should be -2.0, not -1.58. The error only occurs when I use uncertainties.

using Measurements, Roots

a = measurement(1.0 , 0.1)
b = measurement(-3.0 , 0.1)
c = measurement(-10.0, 0.1)

f(x) = ax^2 + bx + c

find_zero(f, measurement(0.0, 0.1))

−1.58±0.12

[jverzani]

Thanks for the report. I'll investigate soon.

[jverzani]

Did 2.2.3 fix this?

[jmarcellopereira]

Hi jverzani

using Measurements, Roots

a = measurement(1.0 , 0.1)
b = measurement(-3.0 , 0.1)
c = measurement(-10.0, 0.1)

f(x) = a*x^2 + b*x + c

Pkg.status("Roots"), find_zero(f, measurement(0.0, 0.1)), find_zero(f, measurement(0.5, 0.1)), find_zero(f, measurement(-1.0, 0.1))

Status `~/.julia/environments/v1.11/Project.toml`
⌃ [f2b01f46] Roots v2.2.1
Info Packages marked with ⌃ have new versions available and may be upgradable.

(nothing, -1.58 ± 0.12, -2.0 ± 0.065, -1.968 ± 0.063)

The error still persists, but when I approximate the initial value of the root the result is consistent. Thanks for answering.

[jverzani]

Thanks for following up.

In this example, the issue becomes clearer. Internally, we have some checks to terminate early if an exact zero is found using iszero, but as was pointed out, strictly speaking a value like measurement(0.0, .01) is not a zero (as Roots is expecting). This comes up in the Alefeld Potra Shi algorithms, but not Bisection. You might have more luck using this call instead of the default

find_zero(f, x, Secant(), Bisection())

With this, the following returns what you want over a range of values

a = measurement(1.0 , 0.1)
b = measurement(-3.0 , 0.1)
c = measurement(-10.0, 0.1)

f(x) = a*x^2 + b*x + c

for x in range(-3, 6, 100)
	@show x, find_zero(f, measurement(x, 0.1), Secant(), Bisection())
end