xref: /phasta/phSolver/common/GaussLegendre1D.c (revision 595995161822a203c8467e0e4a253d7bd7d6df32)

/*$Id$*/
#include <stdlib.h>

#ifdef __cplusplus
extern "C" {
#endif

/* 1 point rule points */
static double _GL_pt1[1]={
 0.000000000000000e+00};

/* 1 point rule weights */
static double _GL_wt1[1]={
 2.000000000000000e+00};

/* 2 point rule points */
static double _GL_pt2[2]={
-5.773502691896257e-01, 5.773502691896257e-01};

/* 2 point rule weights */
static double _GL_wt2[2]={
 1.000000000000000e+00, 1.000000000000000e+00};

/* 3 point rule points */
static double _GL_pt3[3]={
-7.745966692414834e-01, 0.000000000000000e+00, 7.745966692414834e-01};

/* 3 point rule weights */
static double _GL_wt3[3]={
 5.555555555555552e-01, 8.888888888888888e-01, 5.555555555555552e-01};

/* 4 point rule points */
static double _GL_pt4[4]={
-8.611363115940526e-01,-3.399810435848563e-01, 3.399810435848563e-01, 8.611363115940526e-01};

/* 4 point rule weights */
static double _GL_wt4[4]={
 3.478548451374537e-01, 6.521451548625464e-01, 6.521451548625464e-01, 3.478548451374537e-01};

/* 5 point rule points */
static double _GL_pt5[5]={
-9.061798459386640e-01,-5.384693101056831e-01, 0.000000000000000e+00, 5.384693101056831e-01, 9.061798459386640e-01};

/* 5 point rule weights */
static double _GL_wt5[5]={
 2.369268850561890e-01, 4.786286704993665e-01, 5.688888888888889e-01, 4.786286704993665e-01, 2.369268850561890e-01};

/* 6 point rule points */
static double _GL_pt6[6]={
-9.324695142031521e-01,-6.612093864662646e-01,-2.386191860831969e-01, 2.386191860831969e-01, 6.612093864662646e-01, 9.324695142031521e-01};

/* 6 point rule weights */
static double _GL_wt6[6]={
 1.713244923791705e-01, 3.607615730481386e-01, 4.679139345726913e-01, 4.679139345726913e-01, 3.607615730481386e-01, 1.713244923791705e-01};

/* 7 point rule points */
static double _GL_pt7[7]={
-9.491079123427585e-01,-7.415311855993945e-01,-4.058451513773972e-01, 0.000000000000000e+00, 4.058451513773972e-01, 7.415311855993945e-01, 9.491079123427585e-01};

/* 7 point rule weights */
static double _GL_wt7[7]={
 1.294849661688697e-01, 2.797053914892767e-01, 3.818300505051190e-01, 4.179591836734694e-01, 3.818300505051190e-01, 2.797053914892767e-01, 1.294849661688697e-01};

/* 8 point rule points */
static double _GL_pt8[8]={
-9.602898564975363e-01,-7.966664774136268e-01,-5.255324099163290e-01,-1.834346424956498e-01, 1.834346424956498e-01, 5.255324099163290e-01, 7.966664774136268e-01, 9.602898564975363e-01};

/* 8 point rule weights */
static double _GL_wt8[8]={
 1.012285362903768e-01, 2.223810344533745e-01, 3.137066458778874e-01, 3.626837833783620e-01, 3.626837833783620e-01, 3.137066458778874e-01, 2.223810344533745e-01, 1.012285362903768e-01};

/* 9 point rule points */
static double _GL_pt9[9]={
-9.681602395076261e-01,-8.360311073266359e-01,-6.133714327005905e-01,-3.242534234038089e-01, 0.000000000000000e+00, 3.242534234038089e-01, 6.133714327005905e-01, 8.360311073266359e-01, 9.681602395076261e-01};

/* 9 point rule weights */
static double _GL_wt9[9]={
 8.127438836157463e-02, 1.806481606948576e-01, 2.606106964029355e-01, 3.123470770400029e-01, 3.302393550012598e-01, 3.123470770400029e-01, 2.606106964029355e-01, 1.806481606948576e-01, 8.127438836157463e-02};

/* 10 point rule points */
static double _GL_pt10[10]={
-9.739065285171716e-01,-8.650633666889845e-01,-6.794095682990244e-01,-4.333953941292472e-01,-1.488743389816312e-01, 1.488743389816312e-01, 4.333953941292472e-01, 6.794095682990244e-01, 8.650633666889845e-01, 9.739065285171716e-01};

/* 10 point rule weights */
static double _GL_wt10[10]={
 6.667134430868774e-02, 1.494513491505805e-01, 2.190863625159822e-01, 2.692667193099962e-01, 2.955242247147529e-01, 2.955242247147529e-01, 2.692667193099962e-01, 2.190863625159822e-01, 1.494513491505805e-01, 6.667134430868774e-02};

/* 11 point rule points */
static double _GL_pt11[11]={
-9.782286581460570e-01,-8.870625997680953e-01,-7.301520055740494e-01,-5.190961292068118e-01,-2.695431559523450e-01, 0.000000000000000e+00, 2.695431559523450e-01, 5.190961292068118e-01, 7.301520055740494e-01, 8.870625997680953e-01, 9.782286581460570e-01};

/* 11 point rule weights */
static double _GL_wt11[11]={
 5.566856711617354e-02, 1.255803694649047e-01, 1.862902109277343e-01, 2.331937645919903e-01, 2.628045445102466e-01, 2.729250867779006e-01, 2.628045445102466e-01, 2.331937645919903e-01, 1.862902109277343e-01, 1.255803694649047e-01, 5.566856711617354e-02};

/* 12 point rule points */
static double _GL_pt12[12]={
-9.815606342467192e-01,-9.041172563704748e-01,-7.699026741943047e-01,-5.873179542866175e-01,-3.678314989981802e-01,-1.252334085114689e-01, 1.252334085114689e-01, 3.678314989981802e-01, 5.873179542866175e-01, 7.699026741943047e-01, 9.041172563704748e-01, 9.815606342467192e-01};

/* 12 point rule weights */
static double _GL_wt12[12]={
 4.717533638651183e-02, 1.069393259953182e-01, 1.600783285433463e-01, 2.031674267230658e-01, 2.334925365383548e-01, 2.491470458134029e-01, 2.491470458134029e-01, 2.334925365383548e-01, 2.031674267230658e-01, 1.600783285433463e-01, 1.069393259953182e-01, 4.717533638651183e-02};

/* 13 point rule points */
static double _GL_pt13[13]={
-9.841830547185881e-01,-9.175983992229780e-01,-8.015780907333099e-01,-6.423493394403402e-01,-4.484927510364468e-01,-2.304583159551348e-01, 1.232595164407831e-32, 2.304583159551348e-01, 4.484927510364468e-01, 6.423493394403402e-01, 8.015780907333099e-01, 9.175983992229780e-01, 9.841830547185881e-01};

/* 13 point rule weights */
static double _GL_wt13[13]={
 4.048400476531581e-02, 9.212149983772838e-02, 1.388735102197872e-01, 1.781459807619457e-01, 2.078160475368884e-01, 2.262831802628971e-01, 2.325515532308739e-01, 2.262831802628971e-01, 2.078160475368884e-01, 1.781459807619457e-01, 1.388735102197872e-01, 9.212149983772838e-02, 4.048400476531581e-02};

/* 14 point rule points */
static double _GL_pt14[14]={
-9.862838086968123e-01,-9.284348836635736e-01,-8.272013150697650e-01,-6.872929048116855e-01,-5.152486363581541e-01,-3.191123689278897e-01,-1.080549487073437e-01, 1.080549487073437e-01, 3.191123689278897e-01, 5.152486363581541e-01, 6.872929048116855e-01, 8.272013150697650e-01, 9.284348836635736e-01, 9.862838086968123e-01};

/* 14 point rule weights */
static double _GL_wt14[14]={
 3.511946033175199e-02, 8.015808715976037e-02, 1.215185706879031e-01, 1.572031671581936e-01, 1.855383974779378e-01, 2.051984637212955e-01, 2.152638534631578e-01, 2.152638534631578e-01, 2.051984637212955e-01, 1.855383974779378e-01, 1.572031671581936e-01, 1.215185706879031e-01, 8.015808715976037e-02, 3.511946033175199e-02};

/* 15 point rule points */
static double _GL_pt15[15]={
-9.879925180204854e-01,-9.372733924007060e-01,-8.482065834104272e-01,-7.244177313601701e-01,-5.709721726085388e-01,-3.941513470775634e-01,-2.011940939974345e-01, 1.232595164407831e-32, 2.011940939974345e-01, 3.941513470775634e-01, 5.709721726085388e-01, 7.244177313601701e-01, 8.482065834104272e-01, 9.372733924007060e-01, 9.879925180204854e-01};

/* 15 point rule weights */
static double _GL_wt15[15]={
 3.075324199611663e-02, 7.036604748810814e-02, 1.071592204671720e-01, 1.395706779261543e-01, 1.662692058169940e-01, 1.861610000155622e-01, 1.984314853271116e-01, 2.025782419255613e-01, 1.984314853271116e-01, 1.861610000155622e-01, 1.662692058169940e-01, 1.395706779261543e-01, 1.071592204671720e-01, 7.036604748810814e-02, 3.075324199611663e-02};

/* 16 point rule points */
static double _GL_pt16[16]={
-9.894009349916499e-01,-9.445750230732326e-01,-8.656312023878318e-01,-7.554044083550030e-01,-6.178762444026438e-01,-4.580167776572274e-01,-2.816035507792589e-01,-9.501250983763744e-02, 9.501250983763744e-02, 2.816035507792589e-01, 4.580167776572274e-01, 6.178762444026438e-01, 7.554044083550030e-01, 8.656312023878318e-01, 9.445750230732326e-01, 9.894009349916499e-01};

/* 16 point rule weights */
static double _GL_wt16[16]={
 2.715245941175406e-02, 6.225352393864778e-02, 9.515851168249290e-02, 1.246289712555339e-01, 1.495959888165768e-01, 1.691565193950026e-01, 1.826034150449236e-01, 1.894506104550685e-01, 1.894506104550685e-01, 1.826034150449236e-01, 1.691565193950026e-01, 1.495959888165768e-01, 1.246289712555339e-01, 9.515851168249290e-02, 6.225352393864778e-02, 2.715245941175406e-02};

/* 17 point rule points */
static double _GL_pt17[17]={
-9.905754753144174e-01,-9.506755217687678e-01,-8.802391537269859e-01,-7.815140038968014e-01,-6.576711592166907e-01,-5.126905370864769e-01,-3.512317634538763e-01,-1.784841814958479e-01, 1.232595164407831e-32, 1.784841814958479e-01, 3.512317634538763e-01, 5.126905370864769e-01, 6.576711592166907e-01, 7.815140038968014e-01, 8.802391537269859e-01, 9.506755217687678e-01, 9.905754753144174e-01};

/* 17 point rule weights */
static double _GL_wt17[17]={
 2.414830286854792e-02, 5.545952937398713e-02, 8.503614831717915e-02, 1.118838471934039e-01, 1.351363684685256e-01, 1.540457610768104e-01, 1.680041021564499e-01, 1.765627053669926e-01, 1.794464703562065e-01, 1.765627053669926e-01, 1.680041021564499e-01, 1.540457610768104e-01, 1.351363684685256e-01, 1.118838471934039e-01, 8.503614831717915e-02, 5.545952937398713e-02, 2.414830286854792e-02};

/* 18 point rule points */
static double _GL_pt18[18]={
-9.915651684209310e-01,-9.558239495713977e-01,-8.926024664975557e-01,-8.037049589725231e-01,-6.916870430603532e-01,-5.597708310739475e-01,-4.117511614628426e-01,-2.518862256915055e-01,-8.477501304173531e-02, 8.477501304173531e-02, 2.518862256915055e-01, 4.117511614628426e-01, 5.597708310739475e-01, 6.916870430603532e-01, 8.037049589725231e-01, 8.926024664975557e-01, 9.558239495713977e-01, 9.915651684209310e-01};

/* 18 point rule weights */
static double _GL_wt18[18]={
 2.161601352648315e-02, 4.971454889496984e-02, 7.642573025488918e-02, 1.009420441062872e-01, 1.225552067114784e-01, 1.406429146706506e-01, 1.546846751262652e-01, 1.642764837458327e-01, 1.691423829631435e-01, 1.691423829631435e-01, 1.642764837458327e-01, 1.546846751262652e-01, 1.406429146706506e-01, 1.225552067114784e-01, 1.009420441062872e-01, 7.642573025488918e-02, 4.971454889496984e-02, 2.161601352648315e-02};

/* 19 point rule points */
static double _GL_pt19[19]={
-9.924068438435844e-01,-9.602081521348300e-01,-9.031559036148179e-01,-8.227146565371428e-01,-7.209661773352294e-01,-6.005453046616810e-01,-4.645707413759609e-01,-3.165640999636298e-01,-1.603586456402254e-01, 1.232595164407831e-32, 1.603586456402254e-01, 3.165640999636298e-01, 4.645707413759609e-01, 6.005453046616810e-01, 7.209661773352294e-01, 8.227146565371428e-01, 9.031559036148179e-01, 9.602081521348300e-01, 9.924068438435844e-01};

/* 19 point rule weights */
static double _GL_wt19[19]={
 1.946178822972643e-02, 4.481422676569959e-02, 6.904454273764125e-02, 9.149002162245014e-02, 1.115666455473341e-01, 1.287539625393363e-01, 1.426067021736066e-01, 1.527660420658597e-01, 1.589688433939544e-01, 1.610544498487837e-01, 1.589688433939544e-01, 1.527660420658597e-01, 1.426067021736066e-01, 1.287539625393363e-01, 1.115666455473341e-01, 9.149002162245014e-02, 6.904454273764125e-02, 4.481422676569959e-02, 1.946178822972643e-02};

/* 20 point rule points */
static double _GL_pt20[20]={
-9.931285991850949e-01,-9.639719272779138e-01,-9.122344282513259e-01,-8.391169718222189e-01,-7.463319064601508e-01,-6.360536807265150e-01,-5.108670019508271e-01,-3.737060887154195e-01,-2.277858511416451e-01,-7.652652113349734e-02, 7.652652113349734e-02, 2.277858511416451e-01, 3.737060887154195e-01, 5.108670019508271e-01, 6.360536807265150e-01, 7.463319064601508e-01, 8.391169718222189e-01, 9.122344282513259e-01, 9.639719272779138e-01, 9.931285991850949e-01};

/* 20 point rule weights */
static double _GL_wt20[20]={
 1.761400713915226e-02, 4.060142980038705e-02, 6.267204833410904e-02, 8.327674157670474e-02, 1.019301198172405e-01, 1.181945319615183e-01, 1.316886384491766e-01, 1.420961093183819e-01, 1.491729864726038e-01, 1.527533871307260e-01, 1.527533871307260e-01, 1.491729864726038e-01, 1.420961093183819e-01, 1.316886384491766e-01, 1.181945319615183e-01, 1.019301198172405e-01, 8.327674157670474e-02, 6.267204833410904e-02, 4.060142980038705e-02, 1.761400713915226e-02};

int GaussLegendre1D(int npt, double **pt, double **wt) {
  switch(npt) {
  case  1: {
    *pt = _GL_pt1;
    *wt = _GL_wt1;
    break;
  }
  case  2: {
    *pt = _GL_pt2;
    *wt = _GL_wt2;
    break;
  }
  case  3: {
    *pt = _GL_pt3;
    *wt = _GL_wt3;
    break;
  }
  case  4: {
    *pt = _GL_pt4;
    *wt = _GL_wt4;
    break;
  }
  case  5: {
    *pt = _GL_pt5;
    *wt = _GL_wt5;
    break;
  }
  case  6: {
    *pt = _GL_pt6;
    *wt = _GL_wt6;
    break;
  }
  case  7: {
    *pt = _GL_pt7;
    *wt = _GL_wt7;
    break;
  }
  case  8: {
    *pt = _GL_pt8;
    *wt = _GL_wt8;
    break;
  }
  case  9: {
    *pt = _GL_pt9;
    *wt = _GL_wt9;
    break;
  }
  case 10: {
    *pt = _GL_pt10;
    *wt = _GL_wt10;
    break;
  }
  case 11: {
    *pt = _GL_pt11;
    *wt = _GL_wt11;
    break;
  }
  case 12: {
    *pt = _GL_pt12;
    *wt = _GL_wt12;
    break;
  }
  case 13: {
    *pt = _GL_pt13;
    *wt = _GL_wt13;
    break;
  }
  case 14: {
    *pt = _GL_pt14;
    *wt = _GL_wt14;
    break;
  }
  case 15: {
    *pt = _GL_pt15;
    *wt = _GL_wt15;
    break;
  }
  case 16: {
    *pt = _GL_pt16;
    *wt = _GL_wt16;
    break;
  }
  case 17: {
    *pt = _GL_pt17;
    *wt = _GL_wt17;
    break;
  }
  case 18: {
    *pt = _GL_pt18;
    *wt = _GL_wt18;
    break;
  }
  case 19: {
    *pt = _GL_pt19;
    *wt = _GL_wt19;
    break;
  }
  case 20: {
    *pt = _GL_pt20;
    *wt = _GL_wt20;
    break;
  }
  default:
    return 0;
  };
  return 1;
}

#ifdef __cplusplus
}
#endif