function [ x, y, w ] = rule31 ( )

%*****************************************************************************80
%
%% RULE31 returns the rule of degree 31.
%
%  Discussion:
%
%    Order 31 (181 pts)
%    1/6 data for 31-th order quadrature with 37 nodes.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    26 June 2014
%
%  Author:
%
%    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
%    This MATLAB version by John Burkardt.
%
%  Parameters:
%
%    Output, real X(*), Y(*), the coordinates of the nodes.
%
%    Output, real W(*), the weights.
%
  x = [ ...
      0.00000000000000000000000000000000, ...
      0.00000000000000000000000000000000, ...
     -0.61514906219173326038112958639798, ...
      0.00000000000000000000000000000000, ...
     -0.60227258275696561313011448174463, ...
     -0.50981188019097632901132686993753, ...
      0.00000000000000000000000000000000, ...
     -0.93815432009933315159290706133886, ...
      0.00000000000000000000000000000000, ...
     -0.20647073303633426254589462709978, ...
     -0.14400331667261834628330435968823, ...
     -0.48161033312898040755998550507708, ...
     -0.10037070511088677024119003378018, ...
     -0.69003405314433981556933467756463, ...
     -0.45131857503676764396920554079559, ...
     -0.84660740995916577326254742794424, ...
     -0.14911203462776176458914390755779, ...
     -0.55167853197329218224541056875306, ...
     -0.88689641508961216382151190186048, ...
      0.00000000000000000000000000000000, ...
      0.00000000000000000000000000000000, ...
      0.00000000000000000000000000000000, ...
     -0.27328678036217323411592305906149, ...
     -0.33518301010596487973294137974615, ...
     -0.41995122085501584151906684983796, ...
     -0.18328764721779652677839208920087, ...
     -0.36991861294507902457366355095885, ...
     -0.19826213773515198256349732520883, ...
      0.00000000000000000000000000000000, ...
     -0.32037552704774453797884509286080, ...
      0.00000000000000000000000000000000, ...
      0.00000000000000000000000000000000, ...
     -0.78037306571931027109013054924730, ...
      0.00000000000000000000000000000000, ...
     -0.63930924222334969496336881416464, ...
      0.00000000000000000000000000000000, ...
     -0.73284741377468351220017427799278 ];
  y = [ ... ...
      0.00000000000000000000000000000000, ...
     -0.52938101092158436217989944700065, ...
     -0.39259296230588589577692024633618, ...
     -0.29879521023518401246203229051833, ...
     -0.57170178188865743017272606769990, ...
     -0.55459143708784673167882967475209, ...
      0.88032014667050929273459147232799, ...
     -0.57328995909056364047175904022464, ...
      0.10932773428047454311567544236664E+01, ...
     -0.57395302409498325748592469605497, ...
     -0.31297598217411644944584755018888, ...
     -0.38089192422910876315233159687303, ...
     -0.48291646123243918459436362644262, ...
     -0.47237945269405575937245782085877, ...
     -0.51224429424952928367019627443114, ...
     -0.56975292247630686483425195330683, ...
     -0.54743183795864664399668537119941, ...
     -0.46896195562367563745199360999814, ...
     -0.54546676966840707030987521015721, ...
      0.39801431704076458186329655275394, ...
      0.55731348796377460751706837305857, ...
      0.97770163996668454891174645987393, ...
     -0.50303973149300230512177279576695, ...
     -0.55450610597908806787792991531332, ...
     -0.57527720939459095316883310890960, ...
     -0.19780119278968994222147469745240, ...
     -0.43682917497899069302689014620258, ...
     -0.41232373405740865931876786653227, ...
     -0.56955126226549368079464495424716, ...
     -0.32293156387181891591095890622273, ...
     -0.17956217803484541051959756627326, ...
      0.12415978610574965002707225626963, ...
     -0.52966581912912838443677982459313, ...
      0.11370931699099784490463357476566E+01, ...
     -0.53253326710134984412140457620381, ...
     -0.40532624526153890211957544149763, ...
     -0.56730901867998811775513569725020 ];
  w = [ ... ...
      0.18300274150131503530218918260118E-02, ...
      0.26610940186702783315047214273191E-02, ...
      0.76415116557529348094479438274031E-02, ...
      0.58190756304798839792080800346536E-02, ...
      0.16896438572357084969785073782623E-02, ...
      0.37199019857877275953974147517983E-02, ...
      0.27793705473843310754776111206512E-02, ...
      0.66528731990096257950775283571449E-03, ...
      0.64939444386637490706930367932606E-03, ...
      0.17144436271854393525611545784889E-02, ...
      0.13414188931651306592837821888099E-01, ...
      0.10353383822703655875877567178813E-01, ...
      0.93715119938232228413834490764269E-02, ...
      0.65331420598530105269402018636481E-02, ...
      0.71547540812742549665898738315076E-02, ...
      0.15168844552172759195105122436401E-02, ...
      0.54989950731761515927595152639621E-02, ...
      0.83734196392879596672486354136481E-02, ...
      0.23857385517888400677977593831317E-02, ...
      0.73943641501760668515497495971065E-02, ...
      0.62903046982657749327353939866577E-02, ...
      0.21445996231349418275012329739199E-02, ...
      0.88044815101158239329257671015790E-02, ...
      0.47901323321320787218271749114584E-02, ...
      0.12231201498467946837374439661990E-02, ...
      0.16971546653439500088953398556642E-01, ...
      0.11154908721966859054415465858694E-01, ...
      0.12663626772734683766437904485010E-01, ...
      0.15316868409913918465476865568287E-02, ...
      0.15266022971056427587974399198100E-01, ...
      0.90410304859438967096315948145332E-02, ...
      0.81327060196892968093589471350676E-02, ...
      0.48254994785913298058391441904342E-02, ...
      0.22662885264281957658336382036483E-03, ...
      0.58503938090777195674071616162139E-02, ...
      0.68659431853565733752147231623839E-02, ...
      0.23969034602009614667762140991332E-02 ];

  return
end
