File an issue :)
On Tuesday, May 31, 2016 at 6:59:24 PM UTC+2, Boylan, Ross wrote:
>
> I believe Calculus.hessian does finite differences. I had not expected it
> to computer both h[i, j] and h[j, i], since they should be the same. That
> is, AFAIK they are the same mathematically; numerically some differences
> dependent on the order of operations seem inevitable.
>
> The double calculation has the potential advantage of alerting you if the
> numerical issues are significant, but returning a matrix that lacks the
> expected symmetry seems a pretty high price.
> Ross
> ------------------------------
> *From:* julia...@googlegroups.com <javascript:> [julia...@googlegroups.com
> <javascript:>] on behalf of Kristoffer Carlsson [kcarl...@gmail.com
> <javascript:>]
> *Sent:* Tuesday, May 31, 2016 1:26 AM
> *To:* julia-users
> *Subject:* [julia-users] Re: Calculus.hessian result oddities
>
> Doesn't Calculu's Hessian just do finite difference? There will naturally
> be floating point errors.
>
> isposdef returns false if the matrix is not hermitian, under the hood,
> potrf from Lapack is used which work with hermitian matrices.
>
> On Tuesday, May 31, 2016 at 7:04:04 AM UTC+2, Boylan, Ross wrote:
>>
>> The hessian produced by Calculus.hessian has some properties that seem
>> odd to me. First, the resulting matrix is not symmetric (though it's
>> really close). Second, it is not positive definite even though the
>> eigenvalues are all positive. This might partly be the result of the first
>> problem.
>>
>> Comments?
>>
>> julia> @time h6 = Calculus.hessian(RB.mylike, sol6[2])
>> 206.988247 seconds (2.43 G allocations: 83.830 GB, 15.48% gc time)
>> 10x10 Array{Float64,2}:
>> ....
>> julia> issym(h6)
>> false
>> julia> isposdef(h6)
>> false
>> julia> eigvals(h6)
>> 10-element Array{Float64,1}:
>> 3.27548e5
>> 41407.1
>> 1873.44
>> 809.515
>> 385.469
>> 336.118
>> 269.82
>> 64.4228
>> 117.009
>> 122.845
>> julia> [det(h6[1:i, 1:i]) for i in 1:10] # all submatrix determinants
>> are positive
>> 10-element Array{Any,1}:
>> 583.356
>> 2.93666e5
>> 3.76334e7
>> 4.26776e9
>> 3.17529e12
>> 6.53405e14
>> 1.12477e17
>> 8.54011e21
>> 3.75658e26
>> 6.65866e29
>>
>> julia> showall(h6)
>> [583.356378500377 -215.9519377704782 42.707753088841706
>> -12.046905619427504 100.26418659571075 30.907721733245413
>> 5.1999446295105445 -3522.0797654066855 4410.401341876791 29.123944464570087
>> -215.95193777047822 583.3512842422355 -12.0619061856546
>> 42.69860798380086 -82.01778794681003 -20.00373356894301 -8.643894790795585
>> 1484.6195212852567 -3316.905502014349 -2.7622075180025965
>> 42.7077530888417 -12.061906185654598 131.30467049554812
>> -44.14799847519552 16.748039679197223 -10.98960509547607 43.02830286169418
>> 234.68906012694512 -1258.6622801992237 9.86994636336174
>> -12.046905619427504 42.69860798380086 -44.147998475195514
>> 131.35743705036847 -17.498616283805696 4.724998443749094
>> -31.481387268916205 -95.390157895702 209.5245372890838 12.903636963625035
>> 100.26418659571075 -82.01778794681003 16.748039679197223
>> -17.498616283805696 766.6651018177663 -20.766430168130857
>> -2.164074090378522 610.206909770971 -6927.858446549729 -200.4409796490271
>> 30.907721733245413 -20.00373356894301 -10.98960509547607
>> 4.724998443749093 -20.766430168130857 209.8283757716871 -60.222027409043555
>> 280.3888402431943 -1638.62573982097 -158.60599205247166
>> 5.199944629510544 -8.643894790795585 43.02830286169418
>> -31.4813872689162 -2.164074090378524 -60.222027409043555 204.34068072875016
>> -3.631354965653126 314.50383342119943 30.12788292183477
>> -3522.079765406686 1484.6195212852565 234.6890601269451
>> -95.39015789570199 610.2069097709712 280.3888402431943 -3.631354965653125
>> 102596.98982032725 -117630.58331133435 267.23733374838395
>> 4410.401341876791 -3316.9055020143487 -1258.6622801992235
>> 209.5245372890838 -6927.858446549729 -1638.62573982097 314.5038334211995
>> -117630.58331133435 265600.50878023007 5508.687364627178
>> 29.123944464570084 -2.762207518002596 9.86994636336174
>> 12.903636963625033 -200.4409796490271 -158.6059920524717 30.12788292183477
>> 267.23733374838395 5508.687364627178 2125.8954716959997]
>>
>> The largest absolute difference between symmetrical entries is < 5e-13.
>>
>> Ross Boylan
>>
>>
