//http://www.timestocome.com

//linda cobb

//winter 98-99

//gaussian quadratures using legendre polynomials



#include <stdio.h>

#include <math.h>



extern double function (double);





//tables of weights and points

double DATAP2[1] ={0.577350269189626};



double DATAW2[1] ={0.999999999999999};



double DATAP4[2]={ 0.861136311594052, 0.339981043584856};



double DATAW4[2]={ 0.347854845137454, 0.652145154862546};



double DATAP6[3]={ 0.932469514203152, 0.661209386466264, 

                   0.238619186083197};



double DATAW6[3]={ 0.171324492379170, 0.360761573048139, 

                   0.467913934572691};



double DATAP8[4]={ 0.960289856497536, 0.796666477413627,

                   0.525532409916329, 0.183434642495650};



double DATAW8[4]={ 0.101228536290376, 0.222381034453374,

                   0.313706645877887, 0.362683783378362};



double DATAP10[5]={ 0.973906528517172, 0.865063366688984,

                    0.679409568299024,0.433395394129247,

                    0.148874338981631};



double DATAW10[5]={ 0.066671344308688, 0.149451349150580,

                    0.219086362515982,0.269266719309996,

                    0.295524224714753};



double DATAP12[6]={ 0.981560634246719, 0.904117256370475,

                    0.769902674194305, 0.587317954286617,

                    0.367831498998180, 0.125233408511469};

                    

double DATAW12[6]={ 0.047175336386512, 0.106939325995318,

                    0.160078328543346, 0.203167426723066,

                    0.233492536538355, 0.249147045813403};



double DATAP14[7]={ 0.986283808696812, 0.928434883663573,

                    0.827201315069765, 0.687292904811685,

                    0.515248636358154, 0.319112368927890,

                    0.108054948707344};

                    

double DATAW14[7]={ 0.035119460331752, 0.080158087159760,

                    0.121518570687903, 0.157203167158193,

                    0.185538397477938, 0.205198463721296,

                    0.215263853463158};

                    

double DATAP16[8]={ 0.989400934991650, 0.944575023073232,

                    0.865631202387832, 0.755404408355003,

                    0.617876244402644, 0.458016777657227,

                    0.281603550779259, 0.095012509837637};

                    

double DATAW16[8]={ 0.027152459411754, 0.062253523938648,

                    0.095158511682493, 0.124628971255534,

                    0.149595988816577, 0.169156519395002,

                    0.182603415044923, 0.189450610455068};

                    

double DATAP20[10]={ 0.993128599185095, 0.963971927277914,

                     0.912234428251326, 0.839116971822219,

                     0.746331906460151, 0.636053680726515,

                     0.510867001950827, 0.373706088715419,

                     0.227785851141645, 0.076526521133497};

                     

double DATAW20[10]={ 0.017614007139152, 0.040601429800387,

                     0.062672048334109, 0.083276741576705,

                     0.101930119817240, 0.118194531961518,

                     0.131688638449177, 0.142096109318382,

                     0.149172986472604, 0.152753387130726};

                     

double DATAP24[12]={ 0.995187219997021,0.974728555971309,

                     0.938274552002733, 0.886415527004401,

                     0.820001985973903, 0.740124191578554,

                     0.648093651936975, 0.545421471388839,

                     0.433793507626045, 0.315042679696163,

                     0.191118867473616, 0.064056892862606};

                          

double DATAW24[12]={0.012341229799987, 0.028531388628934,

                    0.044277438817420, 0.059298584915437,

                    0.073346481411080, 0.086190161531953,

                    0.097618652104114, 0.107444270115966,

                    0.115505668053726, 0.121670472927803,

                    0.125837456346828, 0.127938195346752};

                    

double DATAP28[14]={ 0.996442497573954, 0.981303165370873,

                     0.954259280628938, 0.915633026392132,

                     0.865892522574395, 0.805641370917179,

                     0.735610878013632, 0.656651094038865,

                     0.569720471811402, 0.475874224955118,

                     0.376251516089079, 0.272061627635178,

                     0.164569282133381, 0.055079289884034};

                     

double DATAW28[14]={ 0.009124282593094, 0.021132112592771,

                     0.032901427782304, 0.044272934759004,

                     0.055107345675717, 0.065272923966999,

                     0.074646214234569, 0.083113417228901,

                     0.090571744393033, 0.096930657997930,

                     0.102112967578061, 0.106055765922846,

                     0.108711192258294, 0.110047013016475};

                     

double DATAP32[16]={ 0.997263861849481, 0.985611511545268,

                     0.964762255587506, 0.934906075937740,

                     0.896321155766052, 0.849367613732570,

                     0.794483795967942, 0.732182118740290,

                     0.663044266930215, 0.587715757240762,

                     0.506899908932229, 0.421351276130635,

                     0.331868602282128, 0.239287362252137,

                     0.144471961582796, 0.048307665687738};

                     

double  DATAW32[16]={ 0.007018610009470, 0.016274394730906,

                      0.025392065309262, 0.034273862913021,

                      0.042835898022227, 0.050998059262376,

                      0.058684093478535, 0.065822222776362,

                      0.072345794108848, 0.078193895787070,

                      0.083311924226947, 0.087652093004404,

                      0.091173878695764, 0.093844399080804,

                      0.095638720079275, 0.096540088514728};

                      

double  DATAP40[20]={ 0.998237709710559, 0.990726238699457,

                      0.977259949983774, 0.957916819213792,

                      0.932812808278676, 0.902098806968874,

                      0.865959503212259, 0.824612230833312,

                      0.778305651426519, 0.727318255189927,

                      0.671956684614179, 0.612553889667980,

                      0.549467125095128, 0.483075801686179,

                      0.413779204371605, 0.341994090825758,

                      0.268152185007254, 0.192697580701371,

                      0.116084070675255, 0.038772417506051};

                      

double  DATAW40[20]={ 0.004521277098533, 0.010498284531153,

                      0.016421058381908, 0.022245849194167,

                      0.027937006980023, 0.033460195282548,

                      0.038782167974472, 0.043870908185673,

                      0.048695807635072, 0.053227846983937,

                      0.057439769099391, 0.061306242492929,

                      0.064804013456601, 0.067912045815234,

                      0.070611647391287, 0.072886582395804,

                      0.074723169057968, 0.076110361900626,

                      0.077039818164248, 0.077505947978425};

                      



double DATAP48[24]={ 0.998771007252426, 0.993530172266351,

                      0.984124583722827, 0.970591592546247,

                      0.952987703160431, 0.931386690706554,

                      0.905879136715570, 0.876572020274248,

                      0.843588261624393, 0.807066204029443,

                      0.767159032515740, 0.724034130923815,

                      0.677872379632664, 0.628867396776514,

                      0.577224726083973, 0.523160974722233,

                      0.466902904750958, 0.408686481990717,

                      0.348755886292161, 0.287362487355455,

                      0.224763790394689, 0.161222356068892,

                      0.097004699209463, 0.032380170962869};

                      



double DATAW48[24]={ 0.003153346052306, 0.007327553901276,

                     0.011477234579234, 0.015579315722944,

                     0.019616160457355, 0.023570760839324,

                     0.027426509708357, 0.031167227832798,

                     0.034777222564770, 0.038241351065831,

                     0.041545082943465, 0.044674560856694,

                     0.047616658492490, 0.050359035553854,

                     0.052890189485194, 0.055199503699984,

                     0.057277292100403, 0.059114839698396,

                     0.060704439165894, 0.062039423159893,

                     0.063114192286254, 0.063924238584648,

                     0.064466164435950, 0.064737696812684};

                     



double  DATAP64[32]={ 0.999305041735772, 0.996340116771955,

                      0.991013371476744, 0.983336253884626,

                      0.973326827789911, 0.961008799652054,

                      0.946411374858403, 0.929569172131939,

                      0.910522137078503, 0.889315445995114,

                      0.865999398154093, 0.840629296252580,

                      0.813265315122797, 0.783972358943341,

                      0.752819907260532, 0.719881850171611,

                      0.685236313054233, 0.648965471254657,

                      0.611155355172393, 0.571895646202634,

                      0.531279464019894, 0.489403145707053,

                      0.446366017253464, 0.402270157963992,

                      0.357220158337668, 0.311322871990211,

                      0.264687162208767, 0.217423643740007,

                      0.169644420423993, 0.121462819296120,

                      0.072993121787799, 0.024350292663424};

                      



double DATAW64[32]={ 0.001783280721696, 0.004147033260562,

                     0.006504457968978, 0.008846759826364,

                     0.011168139460131, 0.013463047896719,

                     0.015726030476025, 0.017951715775697,

                     0.020134823153530, 0.022270173808383,

                     0.024352702568711, 0.026377469715055,

                     0.028339672614259, 0.030234657072402,

                     0.032057928354851, 0.033805161837142,

                     0.035472213256882, 0.037055128540240,

                     0.038550153178616, 0.039953741132720,

                     0.041262563242623, 0.042473515123653,

                     0.043583724529323, 0.044590558163756,

                     0.045491627927418, 0.046284796581314,

                     0.046968182816210, 0.047540165714830,

                     0.047999388596458, 0.048344762234803,

                     0.048575467441503, 0.048690957009140};

  

//send the lowest point, the highest point and the 

//number of points to  calculate

//assumes a function with the equation to 

//integrate is declared in main in the form

//double function (double)



void gauss (double a, double b, int points)

{

  

 

  int i;           //loop control

  double answer;   //calculated value of integral

 

  

  //change variables... function must be btwn -1 and 1



  //calculate value

  answer = 0;

  

  switch(points){

  case 2:

    for(i=0; i < points/2; i++){     

      answer += DATAW2[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP2[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP2[i]));   

    }

    break;



  case 4:

    for(i=0; i < points/2; i++){     

      answer += DATAW4[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP4[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP4[i]));   

    }

    break;

  

  case 6:

    for(i=0; i < points/2; i++){     

      answer += DATAW6[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP6[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP6[i]));   

    }

    break;



  case 8:

    for(i=0; i < points/2; i++){     

      answer += DATAW8[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP8[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP8[i]));   

    }

    break;

  

  case 10:

    for(i=0; i < points/2; i++){     

      answer += DATAW10[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP10[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP10[i]));   

    }

    break;

  

  case 14:

    for(i=0; i < points/2; i++){     

      answer += DATAW14[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP14[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP14[i]));   

    }

    break;



  case 16:

    for(i=0; i < points/2; i++){     

      answer += DATAW16[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP16[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP16[i]));   

    }

    break;



  case 20:

    for(i=0; i < points/2; i++){     

      answer += DATAW20[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP20[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP20[i]));   

    }

    break;

 

  case 24:

    for(i=0; i < points/2; i++){     

      answer += DATAW24[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP24[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP24[i]));   

    }

   break;



  case 28:

    for(i=0; i < points/2; i++){     

      answer += DATAW28[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP28[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP28[i]));   

    }

    break;

  

  case 32:

    for(i=0; i < points/2; i++){     

      answer += DATAW32[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP32[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP32[i]));   

    }

    break;

  

  case 40:

    for(i=0; i < points/2; i++){     

      answer += DATAW40[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP40[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP40[i]));   

    }

    break;



  case 48:

    for(i=0; i < points/2; i++){     

      answer += DATAW48[i]* (function((b+a)/2.0 + (b-a)/2.0*DATAP48[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP48[i]));   

    }

    break;



  case 64:

    for(i=0; i < points/2; i++){     

      answer += DATAW64[i] * (function((b+a)/2.0 + (b-a)/2.0*DATAP64[i]) +

        function((b+a)/2.0 - (b-a)/2.0*DATAP64[i]));   

    }  

    break;

    

    default:

    printf("\n not a valid choice ");

    break;    

    

  }//end switch



  answer = answer * (b-a)/2.0;

  

  

}