Integration gauss points

GaussPointsAndWeights.m

function [xIntPoints, wIntPoints] = GaussPointsAndWeights (numGaussPoints )
%Integration Gauss Points based on https://keisan.casio.com/exec/system/1329114617
  if numGaussPoints == 1
      
      xIntPoints = 0;
     
      wIntPoints = 2;
  
  elseif numGaussPoints == 2
      
      xIntPoints = [ -sqrt(1/3) sqrt(1/3) ];

      wIntPoints = [     1          1     ];        
  
  elseif numGaussPoints == 3
      
      xIntPoints = [ -sqrt(3/5)     0  sqrt(3/5) ];

      wIntPoints = [     5/9	    8/9     5/9    ];

  elseif numGaussPoints == 4
      
      xIntPoints = [ -sqrt( 3 - 2 * sqrt(6 / 5) ) / sqrt(7),  sqrt( 3 - 2 * sqrt(6 / 5) ) / sqrt(7) ...
                     -sqrt( 3 + 2 * sqrt(6 / 5) ) / sqrt(7),  sqrt( 3 + 2 * sqrt(6 / 5) ) / sqrt(7)   ];
      
      wIntPoints = [ ( 18 + sqrt(30) ) / 36                   ( 18 + sqrt(30) ) / 36      ... 
                     ( 18 - sqrt(30) ) / 36                   ( 18 - sqrt(30) ) / 36                  ];
  
  elseif numGaussPoints == 5
      
      xIntPoints = [ -0.9061798459386639927976, -0.5384693101056830910363, 0                       , ...
                      0.5384693101056830910363,  0.9061798459386639927976                                 ] ;
      
      wIntPoints = [  0.2369268850561890875143,  0.4786286704993664680413, 0.5688888888888888888889, ...
                      0.4786286704993664680413,  0.2369268850561890875143                                 ] ;
  
  elseif numGaussPoints == 6
      
      xIntPoints = [ -0.9324695142031520278123, -0.661209386466264513661, -0.2386191860831969086305, ...
                      0.238619186083196908631 ,  0.661209386466264513661, 0.9324695142031520278123        ] ;
      
      wIntPoints = [  0.1713244923791703450403, 0.3607615730481386075698, 0.4679139345726910473899,  ...
                      0.46791393457269104739,   0.3607615730481386075698, 0.1713244923791703450403        ] ;
  
  elseif numGaussPoints == 7
  
      xIntPoints = [ -0.9491079123427585245262, -0.7415311855993944398639, -0.4058451513773971669066, ...
                      0                       ,  0.4058451513773971669066,  0.7415311855993944398639, ...
                      0.9491079123427585245262                                                            ] ;
  
      wIntPoints = [ 0.1294849661688696932706 ,  0.2797053914892766679015, 0.38183005050511894495  , ...
                     0.417959183673469387755  ,  0.38183005050511894495  ,  0.279705391489276667901, ...
                     0.129484966168869693271                                                             ] ;
  
  elseif numGaussPoints == 8

      xIntPoints = [ -0.9602898564975362316836, -0.7966664774136267395916, -0.5255324099163289858177, ...
                     -0.1834346424956498049395, 0.1834346424956498049395, 0.5255324099163289858177, ...
                      0.7966664774136267395916, 0.9602898564975362316836                                  ] ;

      wIntPoints = [  0.1012285362903762591525, 0.2223810344533744705444, 0.313706645877887287338, ...
                      0.3626837833783619829652, 0.3626837833783619829652, 0.313706645877887287338, ...
                      0.222381034453374470544, 0.1012285362903762591525                                   ] ;
  
  elseif numGaussPoints == 9
      
      xIntPoints = [ -0.9681602395076260898356, -0.8360311073266357942994, -0.6133714327005903973087, ...
                     -0.3242534234038089290385,  0                       ,  0.3242534234038089290385, ...
                      0.6133714327005903973087,  0.8360311073266357942994,  0.9681602395076260898356      ] ;
      
      wIntPoints = [  0.0812743883615744119719,  0.1806481606948574040585,  0.2606106964029354623187, ...
                      0.312347077040002840069,   0.330239355001259763165 ,  0.312347077040002840069 , ...
                      0.260610696402935462319,   0.1806481606948574040585,  0.081274388361574411972       ] ;
  
  elseif numGaussPoints == 10
      
      xIntPoints = [ -0.973906528517171720078,  -0.8650633666889845107321, -0.6794095682990244062343, ...
                     -0.4333953941292471907993, -0.1488743389816312108848,  0.1488743389816312108848, ...
                      0.4333953941292471907993,  0.6794095682990244062343,  0.8650633666889845107321, ...
                      0.973906528517171720078                                                             ] ;
      
      wIntPoints = [ 0.0666713443086881375936,   0.149451349150580593146,   0.219086362515982043996, ...
                     0.2692667193099963550912,   0.2955242247147528701739,  0.295524224714752870174, ...
                     0.269266719309996355091,    0.2190863625159820439955,  0.1494513491505805931458, ...
                     0.0666713443086881375936                                                             ] ;  
  else
      error('The number of gauss cuadrature points introduced are not implemented, only between 1 and 10')
  end
end