StillingerWeber hessian gradient test failure

[jameskermode]

@lifelemons and I have been debugging our Newton optimiser, and tracked down a problem in the new StillingerWeber Hessian code, which appears to fail the gradient test for the ~400 atom Si configuration below.

@cortner Would you be able to take a look when you have time? We confirmed that the 2-atom bulk cell passes the test, but even adding rattle!(at, 0.01) to that test leads to fdtest errors of order 1e-5.

Expected output:

    h    | error
---------|-----------
 1.0e-02 | 1.89e-01
 1.0e-03 | 8.31e-02
 1.0e-04 | 8.31e-02
 1.0e-05 | 8.31e-02
 1.0e-06 | 8.31e-02
 1.0e-07 | 8.31e-02
 1.0e-08 | 8.31e-02
 1.0e-09 | 8.31e-02
 1.0e-10 | 8.31e-02
 1.0e-11 | 8.31e-02
---------|-----------

Code and input file (inline):

using JuLIP
using JuLIP.Potentials
using JuLIP.Testing

s = """402
Lattice="159.638145517 0.0 0.0 0.0 112.881215231 0.0 0.0 0.0 3.84029692862" Properties=species:S:1:pos:R:3:mask:I:3:Z:I:1 pbc="T T T"
Si      18.09299127      16.55715546       0.00000000        0        0        0       14 
Si      19.29109492      13.46317630       1.92014846        0        0        0       14 
Si      15.75194874      20.39757387       0.00000000        0        0        0       14 
Si      15.68099322      22.74634784       0.00000000        0        0        0       14 
Si      14.54526470      23.49431259       1.92014846        0        0        0       14 
Si      14.47284033      25.84441730       1.92014846        0        0        0       14 
Si      16.95621167      17.30276531       1.92014846        0        0        0       14 
Si      16.88875484      19.65096447       1.92014846        0        0        0       14 
Si      17.88034454      23.60223090       0.00000000        0        0        0       14 
Si      17.80301819      25.95199699       0.00000000        0        0        0       14 
Si      19.09326880      20.50877327       1.92014846        0        0        0       14 
Si      19.01828409      22.85707275       1.92014846        0        0        0       14 
Si      15.58285459      32.91284966       0.00000000        0        0        0       14 
Si      15.65681159      35.26285205       0.00000000        0        0        0       14 
Si      16.66734338      26.69887237       1.92014846        0        0        0       14 
Si      16.66739854      32.09342671       1.92014846        0        0        0       14 
Si      17.90564948      35.97306310       0.00000000        0        0        0       14 
Si      17.97923649      38.32152863       0.00000000        0        0        0       14 
Si      18.91335767      32.80266047       1.92014846        0        0        0       14 
Si      18.99253809      35.15228648       1.92014846        0        0        0       14 
Si      16.88880477      39.14133264       1.92014846        0        0        0       14 
Si      16.95625877      41.48953180       1.92014846        0        0        0       14 
Si      19.20852310      42.19705641       1.92014846        0        0        0       14 
Si      19.27127233      44.54593631       1.92014846        0        0        0       14 
Si      22.69595336      11.23013468       0.00000000        0        0        0       14 
Si      22.63993904      13.58227115       0.00000000        0        0        0       14 
Si      21.50359233      14.32505301       1.92014846        0        0        0       14 
Si      21.44037895      16.67445418       1.92014846        0        0        0       14 
Si      23.82960893      10.48618089       1.92014846        0        0        0       14 
Si      24.85369518      14.45089851       0.00000000        0        0        0       14 
Si      24.78891117      16.80472565      -0.00002067        1        1        1       14 
Si      26.04457753      11.35525340       1.92014846        0        0        0       14 
Si      25.99012513      13.71055606       1.92014846        0        0        0       14 
Si      20.30210871      17.41713083       0.00000000        0        0        0       14 
Si      20.23215034      19.76518189       0.00000000        0        0        0       14 
Si      22.43058968      20.63034104      -0.00002611        1        1        1       14 
Si      22.35347337      22.98070934      -0.00003026        1        1        1       14 
Si      21.21247822      23.71985417       1.92012559        1        1        1       14 
Si      21.13119323      26.06952904       1.92013715        1        1        1       14 
Si      23.64349864      17.54103735       1.92012935        1        1        1       14 
Si      23.57438771      19.89309126       1.92011764        1        1        1       14 
Si      24.54640902      23.85175501      -0.00006916        1        1        1       14 
Si      24.45667475      26.20158274      -0.00007096        1        1        1       14 
Si      25.77270698      20.76654096       1.92008421        1        1        1       14 
Si      25.69158529      23.11734351       1.92007153        1        1        1       14 
Si      19.99620114      26.81179139       0.00000000        0        0        0       14 
Si      19.99626068      31.98050756       0.00000000        0        0        0       14 
Si      22.23983379      32.68051066      -0.00001446        1        1        1       14 
Si      22.32499150      35.02997932      -0.00001199        1        1        1       14 
Si      21.24098289      35.85403212       1.92014022        1        1        1       14 
Si      21.32256931      38.20431403       1.92014846        0        0        0       14 
Si      23.31694697      26.93908230       1.92008856        1        1        1       14 
Si      23.31680128      31.85362683       1.92013031        1        1        1       14 
Si      24.57595241      35.72330824      -0.00002744        1        1        1       14 
Si      24.66019594      38.07354910      -0.00002034        1        1        1       14 
Si      25.56454247      32.54545882       1.92011394        1        1        1       14 
Si      25.65855070      34.89508792       1.92011620        1        1        1       14 
Si      20.23220251      39.02711497       0.00000000        0        0        0       14 
Si      20.30215717      41.37516633       0.00000000        0        0        0       14 
Si      22.55685644      42.07657605       0.00000000        0        0        0       14 
Si      22.62015117      44.42638671       0.00000000        0        0        0       14 
Si      21.52351128      45.25069667       1.92014846        0        0        0       14 
Si      21.57981130      47.60212551       1.92014846        0        0        0       14 
Si      23.57338035      38.90018586       1.92013365        1        1        1       14 
Si      23.64713665      41.25157005       1.92014379        1        1        1       14 
Si      24.87335163      45.12558272       0.00000000        0        0        0       14 
Si      24.92844396      47.47962959       0.00000000        0        0        0       14 
Si      25.90001172      41.94388842       1.92012843        1        1        1       14 
Si      25.96592980      44.29817680       1.92014339        1        1        1       14 
Si      23.82964599      48.30612086       1.92014846        0        0        0       14 
Si      26.12475013      51.36749026       1.92014846        0        0        0       14 
Si      28.35393820       7.50679855       1.92014846        0        0        0       14 
Si      31.73441323       5.26220822       0.00000000        0        0        0       14 
Si      31.69487590       7.63234189       0.00000000        0        0        0       14 
Si      32.85882440       4.51108256       1.92014846        0        0        0       14 
Si      27.22460582       8.25264284       0.00000000        0        0        0       14 
Si      27.17736011      10.61253885       0.00000000        0        0        0       14 
Si      29.39204388      11.48794204       0.00000000        0        0        0       14 
Si      29.33761379      13.84896212      -0.00002510        1        1        1       14 
Si      28.19404441      14.58722703       1.92012341        1        1        1       14 
Si      28.13557514      16.94515972       1.92009866        1        1        1       14 
Si      30.56762368       8.37933028       1.92014846        0        0        0       14 
Si      30.52300513      10.74536092       1.92014846        0        0        0       14 
Si      31.53848436      14.73573388      -0.00004990        1        1        1       14 
Si      31.48348709      17.09847634      -0.00008069        1        1        1       14 
Si      32.72557194      11.62658284       1.92012751        1        1        1       14 
Si      32.67913825      13.99399643       1.92009987        1        1        1       14 
Si      26.98996107      17.68039790      -0.00004828        1        1        1       14 
Si      26.92005149      20.03376053      -0.00006854        1        1        1       14 
Si      29.11864274      20.91691783      -0.00010853        1        1        1       14 
Si      29.03482923      23.26880167      -0.00013329        1        1        1       14 
Si      27.88426311      23.99731029       1.92002289        1        1        1       14 
Si      27.78591699      26.34701423       1.92001133        1        1        1       14 
Si      30.33672150      17.83153155       1.92006767        1        1        1       14 
Si      30.26953861      20.18857068       1.92003682        1        1        1       14 
Si      31.22798002      24.16101571      -0.00019401        1        1        1       14 
Si      31.12006211      26.51051223      -0.00022274        1        1        1       14 
Si      32.46863554      21.08621343       1.91999359        1        1        1       14 
Si      32.38595811      23.44103009       1.91994800        1        1        1       14 
Si      26.64121773      27.07877499      -0.00012481        1        1        1       14 
Si      26.63997404      31.71519169      -0.00003845        1        1        1       14 
Si      28.89232968      32.39685088      -0.00005557        1        1        1       14 
Si      28.99597669      34.74627640      -0.00005849        1        1        1       14 
Si      27.91387373      35.57924564       1.92009575        1        1        1       14 
Si      28.00202497      37.93018859       1.92010223        1        1        1       14 
Si      29.96883535      27.23435436       1.91994174        1        1        1       14 
Si      29.96556741      31.56177800       1.92009002        1        1        1       14 
Si      31.25741984      35.41791241      -0.00008829        1        1        1       14 
Si      31.34844287      37.77053386      -0.00008190        1        1        1       14 
Si      32.22425473      32.22880855       1.92007840        1        1        1       14 
Si      32.33960335      34.57769348       1.92005229        1        1        1       14 
Si      26.91486018      38.76134588      -0.00003938        1        1        1       14 
Si      26.99013241      41.11415144      -0.00002666        1        1        1       14 
Si      29.24542233      41.79997139      -0.00004520        1        1        1       14 
Si      29.30975827      44.15753107      -0.00002452        1        1        1       14 
Si      28.21818307      44.99087590       1.92013075        1        1        1       14 
Si      28.27651523      47.34936651       1.92014846        0        0        0       14 
Si      30.26089095      38.60855811       1.92007630        1        1        1       14 
Si      30.33562901      40.96429570       1.92009470        1        1        1       14 
Si      31.56183098      44.84782953      -0.00003617        1        1        1       14 
Si      31.61521255      47.21175753      -0.00000742        1        1        1       14 
Si      32.59257764      41.64380796       1.92007275        1        1        1       14 
Si      32.65270434      44.00772177       1.92010345        1        1        1       14 
Si      27.17739565      48.17976588       0.00000000        0        0        0       14 
Si      27.22463837      50.53966338       0.00000000        0        0        0       14 
Si      29.46806425      51.24390689       0.00000000        0        0        0       14 
Si      29.50900022      53.60984347       0.00000000        0        0        0       14 
Si      30.52303866      48.04694832       1.92014846        0        0        0       14 
Si      30.56765446      50.41298024       1.92014846        0        0        0       14 
Si      31.74705339      54.32033270       0.00000000        0        0        0       14 
Si      32.80752871      51.11789465       1.92014846        0        0        0       14 
Si      32.84642202      53.49030645       1.92014846        0        0        0       14 
Si      36.19102414       4.62641140       0.00000000        0        0        0       14 
Si      35.06871260       5.38080635       1.92014846        0        0        0       14 
Si      35.03089536       7.75799686       1.92014846        0        0        0       14 
Si      38.39788288       5.49475075       0.00000000        0        0        0       14 
Si      38.36097132       7.87907316       0.00000000        0        0        0       14 
Si      39.51835127       4.73583139       1.92014846        0        0        0       14 
Si      33.90618276       8.50786922       0.00000000        0        0        0       14 
Si      33.86220989      10.87766673      -0.00001956        1        1        1       14 
Si      36.06115351      11.76591763      -0.00003216        1        1        1       14 
Si      36.01568833      14.14087602      -0.00006529        1        1        1       14 
Si      34.87820953      14.88902978       1.92007926        1        1        1       14 
Si      34.82789062      17.26081047       1.92004131        1        1        1       14 
Si      37.23876745       8.63375066       1.92014846        0        0        0       14 
Si      37.19454084      11.00983050       1.92012060        1        1        1       14 
Si      38.21125995      15.04202172      -0.00007819        1        1        1       14 
Si      38.16281870      17.42485726      -0.00012311        1        1        1       14 
Si      39.39044982      11.89959516       1.92011293        1        1        1       14 
Si      39.34438231      14.28261442       1.92007701        1        1        1       14 
Si      33.68349397      17.99778253      -0.00011006        1        1        1       14 
Si      33.62285302      20.36309460      -0.00015408        1        1        1       14 
Si      35.82087359      21.28413500      -0.00019276        1        1        1       14 
Si      35.75056626      23.65418232      -0.00026633        1        1        1       14 
Si      34.58028445      24.35439960       1.91987840        1        1        1       14 
Si      34.46254897      26.70047795       1.91979714        1        1        1       14 
Si      37.02402257      18.17364158       1.92001792        1        1        1       14 
Si      36.96999808      20.55348670       1.91996231        1        1        1       14 
Si      37.94474442      24.62134115      -0.00031810        1        1        1       14 
Si      37.84925059      27.00915607      -0.00052909        1        1        1       14 
Si      39.16017854      21.49493329       1.91993805        1        1        1       14 
Si      39.09756957      23.89311050       1.91984166        1        1        1       14 
Si      33.30118009      27.41209738      -0.00032739        1        1        1       14 
Si      33.29501140      31.38729220      -0.00006633        1        1        1       14 
Si      35.56386816      32.03145540      -0.00004324        1        1        1       14 
Si      35.69129329      34.37401256      -0.00017886        1        1        1       14 
Si      34.61003867      35.22891401       1.91998906        1        1        1       14 
Si      34.69891044      37.58619775       1.92001052        1        1        1       14 
Si      36.64122129      27.62934121       1.91961253        1        1        1       14 
Si      36.62529115      31.17789039       1.92015072        1        1        1       14 
Si      37.97695308      34.96759680      -0.00039156        1        1        1       14 
Si      38.05026532      37.35992603      -0.00022452        1        1        1       14 
Si      38.94960617      31.63322066       1.91997464        1        1        1       14 
Si      39.05641606      34.05883557       1.91977948        1        1        1       14 
Si      33.61176107      38.43637657      -0.00012148        1        1        1       14 
Si      33.68207982      40.79879519      -0.00008725        1        1        1       14 
Si      35.93832686      41.47444303      -0.00010762        1        1        1       14 
Si      35.99205478      43.85005978      -0.00006480        1        1        1       14 
Si      34.90296357      44.69919951       1.92009268        1        1        1       14 
Si      34.95205383      47.07174710       1.92012322        1        1        1       14 
Si      36.96525777      38.23480223       1.91995304        1        1        1       14 
Si      37.02578345      40.61570608       1.92002675        1        1        1       14 
Si      38.23705959      44.55314867      -0.00006458        1        1        1       14 
Si      38.28341981      46.93448995      -0.00003177        1        1        1       14 
Si      39.27349261      41.31137231       1.92003417        1        1        1       14 
Si      39.32365924      43.69890974       1.92007685        1        1        1       14 
Si      33.86138877      47.91407050      -0.00001860        1        1        1       14 
Si      33.90621188      50.28444673       0.00000000        0        0        0       14 
Si      36.14162633      50.99319235       0.00000000        0        0        0       14 
Si      36.17903653      53.37280976       0.00000000        0        0        0       14 
Si      35.08086472      54.20388296       1.92014846        0        0        0       14 
Si      37.19491628      47.78144509       1.92012261        1        1        1       14 
Si      37.23879548      50.15857127       1.92014846        0        0        0       14 
Si      38.40978500      54.09207166       0.00000000        0        0        0       14 
Si      39.46971047      50.87484151       1.92014846        0        0        0       14 
Si      39.50652577      53.26134311       1.92014846        0        0        0       14 
Si      42.84153296       4.83570353       0.00000000        0        0        0       14 
Si      41.72230859       5.59995483       1.92014846        0        0        0       14 
Si      41.68542059       7.99024721       1.92014846        0        0        0       14 
Si      45.04344242       5.69306176       0.00000000        0        0        0       14 
Si      45.00610165       8.08713542       0.00000000        0        0        0       14 
Si      46.16216305       4.92334948       1.92014846        0        0        0       14 
Si      40.56507831       8.75122600       0.00000000        0        0        0       14 
Si      40.52007108      11.13343913      -0.00002982        1        1        1       14 
Si      42.71448874      12.01848498      -0.00003310        1        1        1       14 
Si      42.66651787      14.40777333      -0.00006685        1        1        1       14 
Si      41.53728938      15.18127764       1.92007359        1        1        1       14 
Si      41.48690283      17.57392829       1.92003039        1        1        1       14 
Si      43.88659546       8.85491099       1.92014846        0        0        0       14 
Si      43.84109736      11.24162072       1.92012176        1        1        1       14 
Si      44.86060608      15.29245376      -0.00006156        1        1        1       14 
Si      44.80855843      17.68882213      -0.00009626        1        1        1       14 
Si      46.03681538      12.11575879       1.92012435        1        1        1       14 
Si      45.98783677      14.50730156       1.92009549        1        1        1       14 
Si      40.35394535      18.34192622      -0.00012977        1        1        1       14 
Si      40.29939970      20.73823212      -0.00019312        1        1        1       14 
Si      42.48553437      21.66709509      -0.00016794        1        1        1       14 
Si      42.41889637      24.08457256      -0.00021709        1        1        1       14 
Si      41.27334618      24.87680837       1.91991249        1        1        1       14 
Si      41.19077695      27.32140706       1.91987382        1        1        1       14 
Si      43.67827250      18.47491749       1.92004168        1        1        1       14 
Si      43.62091549      20.87903187       1.91999691        1        1        1       14 
Si      44.62738529      24.96099550      -0.00016614        1        1        1       14 
Si      44.57500125      27.37269308      -0.00018327        1        1        1       14 
Si      45.82286414      21.75338656       1.92002629        1        1        1       14 
Si      45.76732498      24.15791092       1.91999665        1        1        1       14 
Si      40.02126906      28.12691861      -0.00029599        1        1        1       14 
Si      40.01560740      30.65829190      -0.00019492        1        1        1       14 
Si      42.29569119      31.44289254      -0.00018996        1        1        1       14 
Si      42.38892888      33.87658833      -0.00021212        1        1        1       14 
Si      41.30987049      34.76008483       1.91991892        1        1        1       14 
Si      41.38086110      37.17385166       1.91996776        1        1        1       14 
Si      43.42627833      28.18560391       1.91995188        1        1        1       14 
Si      43.42577826      30.60452939       1.91996337        1        1        1       14 
Si      44.64164429      34.65237437      -0.00015218        1        1        1       14 
Si      44.71137009      37.06217044      -0.00013122        1        1        1       14 
Si      45.68899152      31.41102481       1.92000297        1        1        1       14 
Si      45.74686467      33.81597413       1.92000421        1        1        1       14 
Si      40.30064432      38.05003642      -0.00017905        1        1        1       14 
Si      40.35755631      40.44752141      -0.00012193        1        1        1       14 
Si      42.59752067      41.17590394      -0.00009832        1        1        1       14 
Si      42.64861748      43.57045799      -0.00006503        1        1        1       14 
Si      41.56268495      44.42274091       1.92008755        1        1        1       14 
Si      41.60894133      46.81068036       1.92011734        1        1        1       14 
Si      43.62324717      37.91691460       1.92001445        1        1        1       14 
Si      43.68277664      40.31966271       1.92004812        1        1        1       14 
Si      44.88390191      44.31635052      -0.00004926        1        1        1       14 
Si      44.93133321      46.70716517      -0.00002543        1        1        1       14 
Si      45.92004482      41.07686228       1.92007356        1        1        1       14 
Si      45.97219390      43.47178109       1.92009769        1        1        1       14 
Si      40.52172687      47.65813900      -0.00002648        1        1        1       14 
Si      40.56510606      50.04110134       0.00000000        0        0        0       14 
Si      42.79263332      50.76804064       0.00000000        0        0        0       14 
Si      42.82964864      53.15986769       0.00000000        0        0        0       14 
Si      41.73420694      53.98865850       1.92014846        0        0        0       14 
Si      43.84347302      47.55085204       1.92012604        1        1        1       14 
Si      43.88662351      49.93742004       1.92014846        0        0        0       14 
Si      45.05547501      53.89673187       0.00000000        0        0        0       14 
Si      46.11265225      50.67651244       1.92014846        0        0        0       14 
Si      46.15013627      53.07128013       1.92014846        0        0        0       14 
Si      49.48220393       4.99763847       0.00000000        0        0        0       14 
Si      48.36336096       5.77230143       1.92014846        0        0        0       14 
Si      48.32573094       8.16765296       1.92014846        0        0        0       14 
Si      51.68406881       5.83768973       0.00000000        0        0        0       14 
Si      51.64679245       8.23222836       0.00000000        0        0        0       14 
Si      47.20612773       8.94162839       0.00000000        0        0        0       14 
Si      47.16211400      11.33086703      -0.00001784        1        1        1       14 
Si      49.36105203      12.19449398      -0.00000694        1        1        1       14 
Si      49.31339646      14.58208454      -0.00003395        1        1        1       14 
Si      48.18707131      15.37213742       1.92010659        1        1        1       14 
Si      48.13771284      17.76475301       1.92007819        1        1        1       14 
Si      50.52657729       9.01113945       1.92014846        0        0        0       14 
Si      50.48645876      11.40880119       1.92014846        0        0        0       14 
Si      51.51952732      15.42573639      -0.00002380        1        1        1       14 
Si      51.47463694      17.81427900      -0.00004483        1        1        1       14 
Si      52.68921592      12.24352034       1.92014846        0        0        0       14 
Si      52.64550732      14.63132140       1.92013114        1        1        1       14 
Si      47.00862637      18.55807379      -0.00008013        1        1        1       14 
Si      46.95613515      20.95606764      -0.00011036        1        1        1       14 
Si      49.16931228      21.79931153      -0.00008433        1        1        1       14 
Si      49.12684386      24.19301111      -0.00010377        1        1        1       14 
Si      47.99039975      24.99473814       1.92003427        1        1        1       14 
Si      47.95832808      27.39060600       1.92002205        1        1        1       14 
Si      50.34607686      18.60992061       1.92009555        1        1        1       14 
Si      50.30124544      21.00094639       1.92007365        1        1        1       14 
Si      51.35548131      25.01307025      -0.00007421        1        1        1       14 
Si      51.33491772      27.40015610      -0.00008354        1        1        1       14 
Si      52.52068049      21.82777141       1.92009647        1        1        1       14 
Si      52.48873451      24.21390189       1.92008236        1        1        1       14 
Si      46.81821471      28.19680429      -0.00013635        1        1        1       14 
Si      46.82105387      30.59512783      -0.00013767        1        1        1       14 
Si      49.07439249      31.39783072      -0.00010142        1        1        1       14 
Si      49.11253899      33.78998629      -0.00009837        1        1        1       14 
Si      47.99754464      34.60816670       1.92004448        1        1        1       14 
Si      48.05417066      37.00528606       1.92005665        1        1        1       14 
Si      50.20023037      28.20204345       1.92005701        1        1        1       14 
Si      50.20399904      30.59053916       1.92005390        1        1        1       14 
Si      51.36014340      34.58441153      -0.00006813        1        1        1       14 
Si      51.40472188      36.97282365      -0.00006042        1        1        1       14 
Si      52.45115446      31.39023971       1.92008370        1        1        1       14 
Si      52.47863265      33.77508445       1.92008507        1        1        1       14 
Si      46.95390994      37.83728910      -0.00009504        1        1        1       14 
Si      47.01176649      40.23560023      -0.00007458        1        1        1       14 
Si      49.24942084      41.01024082      -0.00005106        1        1        1       14 
Si      49.30042605      43.40167850      -0.00003347        1        1        1       14 
Si      48.20632917      44.23440440       1.92011520        1        1        1       14 
Si      48.25355893      46.62317577       1.92013326        1        1        1       14 
Si      50.29691960      37.79141971       1.92008501        1        1        1       14 
Si      50.34801790      40.18244421       1.92009870        1        1        1       14 
Si      51.53530973      44.17712457      -0.00001607        1        1        1       14 
Si      51.58067457      46.56544758       0.00000000        0        0        0       14 
Si      52.58589811      40.96476315       1.92011902        1        1        1       14 
Si      52.63305303      43.35091974       1.92013271        1        1        1       14 
Si      47.16393819      47.46211053      -0.00001448        1        1        1       14 
Si      47.20615609      49.85070409       0.00000000        0        0        0       14 
Si      49.43252134      50.60146282       0.00000000        0        0        0       14 
Si      49.47011722      52.99673945       0.00000000        0        0        0       14 
Si      48.37549771      53.81796733       1.92014846        0        0        0       14 
Si      50.48648839      47.38353220       1.92014846        0        0        0       14 
Si      50.52660541      49.78119250       1.92014846        0        0        0       14 
Si      52.75445696      50.54178215       1.92014846        0        0        0       14 
Si      54.97083562       8.28296685       1.92014846        0        0        0       14 
Si      53.84991955       9.06542670       0.00000000        0        0        0       14 
Si      53.81144588      11.46011760       0.00000000        0        0        0       14 
Si      56.01817593      12.28438981       0.00000000        0        0        0       14 
Si      55.98059033      14.67682147       0.00000000        0        0        0       14 
Si      54.85494205      15.46845769       1.92014337        1        1        1       14 
Si      54.81561949      17.85149503       1.92012727        1        1        1       14 
Si      57.14095434      11.49847784       1.92014846        0        0        0       14 
Si      58.19347494      15.49132760       0.00000000        0        0        0       14 
Si      58.15994049      17.87943078       0.00000000        0        0        0       14 
Si      59.35157281      12.31479254       1.92014846        0        0        0       14 
Si      59.31784833      14.70280850       1.92014846        0        0        0       14 
Si      53.68796612      18.64602839      -0.00002809        1        1        1       14 
Si      53.65097402      21.03079888      -0.00004426        1        1        1       14 
Si      55.87418642      21.84715419      -0.00002412        1        1        1       14 
Si      55.85001627      24.22775684      -0.00003540        1        1        1       14 
Si      54.71950407      25.02481431       1.92010650        1        1        1       14 
Si      54.70580734      27.40617841       1.92009929        1        1        1       14 
Si      57.03323099      18.67258336       1.92014331        1        1        1       14 
Si      57.00278869      21.05174700       1.92013091        1        1        1       14 
Si      58.08164596      25.03216206      -0.00001590        1        1        1       14 
Si      58.07240242      27.40970490      -0.00002033        1        1        1       14 
Si      59.22849922      21.85910988       1.92014846        0        0        0       14 
Si      59.20981832      24.23617497       1.92013751        1        1        1       14 
Si      53.57474924      28.20516831      -0.00005566        1        1        1       14 
Si      53.57845628      30.58763427      -0.00005885        1        1        1       14 
Si      55.82138367      31.38500066      -0.00003389        1        1        1       14 
Si      55.84291335      33.76494226      -0.00003476        1        1        1       14 
Si      54.72320713      34.56909755       1.92010949        1        1        1       14 
Si      54.75876347      36.95159572       1.92011372        1        1        1       14 
Si      56.94389225      28.20696544       1.92012271        1        1        1       14 
Si      56.94672512      30.58544901       1.92011999        1        1        1       14 
Si      58.08504734      34.55786978      -0.00001532        1        1        1       14 
Si      58.11413736      36.93579689      -0.00001388        1        1        1       14 
Si      59.18613474      31.38173491       1.92014306        1        1        1       14 
Si      59.20521895      33.75738784       1.92013691        1        1        1       14 
Si      53.64687895      37.76230111      -0.00003758        1        1        1       14 
Si      53.69058124      40.14739633      -0.00002811        1        1        1       14 
Si      55.92855105      40.93461549      -0.00001177        1        1        1       14 
Si      55.96810393      43.31811992       0.00000000        0        0        0       14 
Si      54.86918575      44.12619911       1.92014846        0        0        0       14 
Si      54.90802150      46.52021659       1.92014846        0        0        0       14 
Si      56.99968814      37.74163256       1.92013195        1        1        1       14 
Si      57.03663903      40.12226786       1.92013769        1        1        1       14 
Si      58.20501189      44.09729947       0.00000000        0        0        0       14 
Si      58.24002365      46.48671900       0.00000000        0        0        0       14 
Si      59.27492872      40.90712723       1.92014846        0        0        0       14 
Si      59.30684640      43.29370960       1.92014846        0        0        0       14 
Si      53.81147403      47.33221326       0.00000000        0        0        0       14 
Si      53.84994674      49.72690347       0.00000000        0        0        0       14 
Si      57.14098042      47.29385012       1.92014846        0        0        0       14 
Si      61.53455600      15.51118334       1.92014846        0        0        0       14 
Si      61.50564061      17.89507736       1.92014846        0        0        0       14 
Si      60.38060048      18.68511289       0.00000000        0        0        0       14 
Si      60.35431080      21.06814605       0.00000000        0        0        0       14 
Si      62.58255567      21.86723603       0.00000000        0        0        0       14 
Si      62.56539548      24.24593958       0.00000000        0        0        0       14 
Si      61.44138710      25.03726883       1.92014846        0        0        0       14 
Si      61.43153764      27.41512583       1.92014846        0        0        0       14 
Si      63.72901017      18.69680589       1.92014846        0        0        0       14 
Si      63.70697015      21.07655542       1.92014846        0        0        0       14 
Si      64.79946005      25.04080190       0.00000000        0        0        0       14 
Si      64.79149903      27.41664779       0.00000000        0        0        0       14 
Si      60.30917996      28.20721730       0.00000000        0        0        0       14 
Si      60.30918292      30.58510119       0.00000000        0        0        0       14 
Si      62.55179334      31.37664578       0.00000000        0        0        0       14 
Si      62.56094274      33.75377625       0.00000000        0        0        0       14 
Si      61.44619145      34.54792314       1.92014846        0        0        0       14 
Si      61.46455952      36.92753841       1.92014846        0        0        0       14 
Si      63.67032582      28.20819269       1.92014846        0        0        0       14 
Si      63.67032816      30.58412438       1.92014846        0        0        0       14 
Si      64.80336939      34.54364539       0.00000000        0        0        0       14 
Si      64.81847002      36.92076882       0.00000000        0        0        0       14 
Si      65.91099346      31.37522989       1.92014846        0        0        0       14 
Si      65.91845805      33.75050525       1.92014846        0        0        0       14 
Si      60.35432821      37.72417544       0.00000000        0        0        0       14 
Si      60.38062073      40.10720988       0.00000000        0        0        0       14 
Si      62.62133306      40.89297988       0.00000000        0        0        0       14 
Si      61.54467818      44.07605901       1.92014846        0        0        0       14 
Si      63.70698457      37.71576384       1.92014846        0        0        0       14 
Si      63.72902734      40.09551442       1.92014846        0        0        0       14"""

open("tmp.xyz", "w") do f
    write(f, s)
end

atoms = read("tmp.xyz")
set_calculator!(atoms, StillingerWeber())

mask = get_array(atoms, "mask")'
set_constraint!(atoms, FixedCell(atoms, mask=mask))
fdtest_hessian(x->gradient(atoms, x), x->hessian(atoms, x), dofs(atoms))

[cortner]

ouch, that's a bit embarrassing. I'll look at it as soon as I can.

[cortner]

no idea, what I did, so I reverted to a slightly older code, and replaced the hessian with an AD hessian. This should now be ok. Would you be willing to pull the latest master and rerun your tests?

[cortner]

@lifelemons - did you ever manage to check whether the hessian now works ok?

[lifelemons]

So the above script now passes the test.
And I have tested it on a decently sized crack configuration of ~2500 atoms. And it passes with the output below

---------|----------- 
    h    | error 
---------|----------- 
 1.0e-02 | 2.27e-01  
 1.0e-03 | 2.27e-02  
 1.0e-04 | 2.27e-03  
 1.0e-05 | 2.27e-04  
 1.0e-06 | 2.27e-05  
 1.0e-07 | 2.99e-06  
 1.0e-08 | 1.90e-05  
 1.0e-09 | 2.46e-04  
 1.0e-10 | 2.88e-03  
 1.0e-11 | 1.10e-02  
---------|----------- 
passed

(Our newton linesearch method still gets stuck so its probably another issue now.)

Thanks for looking into this!

[jameskermode]

Can you put together and post a minimal failing example for the Newton linesearch code?

[cortner]

So I'll close this, but if there is a line search problem please open another issue