Then, what is the best way to test if a number is equal to 0.0?
2015-09-06 22:47 GMT-03:00 Tim Holy <[email protected]>:
> 0 is a special case because there is no "scale" by which to measure
> "closeness":
>
> julia> eps(1.0)
> 2.220446049250313e-16
>
> julia> eps(1e-10)
> 1.2924697071141057e-26
>
> julia> eps(1e-100)
> 1.2689709186578246e-116
>
> --Tim
>
> On Sunday, September 06, 2015 06:39:06 PM Diego Javier Zea wrote:
> > Thanks Tim! But I don't fully understand it, because I believed that*
> > isapprox()* should be *true*, but gives me *false* in this case. My
> > particular function with the problem use the *std()* output in the next
> > way. Is this correct? I'm using *isapprox* and
> > * !isapprox*
> > function calculatezscore{T,N}(value::AbstractArray{T,N}, average::
> > AbstractArray{T,N}, sd::AbstractArray{T,N})
> > zscore = similar(value)
> > if size(value) == size(average) == size(sd)
> > for i in eachindex(zscore)
> > val = value[i]
> > ave = average[i]
> > sta = sd[i]
> > if val ≈ ave
> > zscore[i] = 0.0
> > elseif sta ≉ 0.0
> > zscore[i] = (val - ave)/sta
> > else
> > zscore[i] = NaN
> > end
> > end
> > else
> > throw(ErrorException("The elements should have the same size"))
> > end
> > zscore
> > end
> >
> > Are there other ways to manage the reality of the float arithmetic?
> >
> > El domingo, 6 de septiembre de 2015, 22:27:23 (UTC-3), Tim Holy escribió:
> > > 1e-17 is indistinguishable from mathematical zero if it's based on
> > > differences
> > > among numbers that are O(1).
> > >
> > > julia> a = fill(total, 100);
> > >
> > > julia> sum(a)/100 == total
> > > false
> > >
> > > julia> sum(a)/100 - total
> > > -1.3877787807814457e-17
> > >
> > > But this is off by only one ulp:
> > >
> > > julia> nextfloat(sum(a)/100) == total
> > > true
> > >
> > > So my advice is that you should write your algorithms in a manner that
> > > takes
> > > the realities of floating-point arithmetic into account.
> > >
> > > --Tim
> > >
> > > On Sunday, September 06, 2015 05:19:36 PM Diego Javier Zea wrote:
> > > > The returned value from std should be zero if all the values are
> equal
> > > > (since the distance between the mean and the values should be zero).
> > > > However, the returned value isn't zero:
> > > >
> > > > julia> total
> > > > 0.11008615848501174
> > > >
> > > > julia> mean(Float64[total for i in 1:100])
> > > > 0.11008615848501173
> > > >
> > > > julia> std(Float64[total for i in 1:100])
> > > > 1.3947701538996772e-17
> > > >
> > > > julia> std(Float64[total for i in 1:100]) ≈ zero(Float64)
> > > > false
> > > >
> > > > julia> mean(Float64[total for i in 1:100]) ≈ total
> > > > true
> > > >
> > > >
> > > > How can I get a more precise result from *std()*?
> > > >
> > > > Best,
>
>
--
Diego Javier Zea
Departamento de Ciencia y Tecnología
Universidad Nacional de Quilmes
Roque Saenz Pena 182
1876 Bernal
Argentina
Phone:+541143657100 ext 4135
