# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <time.h>

# include "alpert_rule.h"

/******************************************************************************/

void rule_power ( int rule, int j, double x[], double w[] )

/******************************************************************************/
/*
  Purpose:

    RULE_POWER returns an Alpert rule for power singular functions.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    04 December 2015

  Author:

    John Burkardt

  Reference:

    Bradley Alpert,
    Hybrid Gauss-Trapezoidal Quadrature Rules,
    SIAM Journal on Scientific Computing,
    Volume 20, Number 5, pages 1551-1584, 1999.

  Parameters:

    Input, int RULE, the index of the rule, between 1 and 12.

    Input, int J, the number of points in the rule.

    Output, double X[J], W[J], the points and weights for the rule.
*/
{
  double x01[1] = {
    1.172258571393266E-01 };
  double w01[1] = {
    5.000000000000000E-01 };
  double x02[2] = {
    9.252112715421378E-02,
    1.000000000000000E-00 };
  double w02[2] = {
    4.198079625266162E-01,
    1.080192037473384E+00 };
  double x03[2] = {
    6.023873796408450E-02,
    8.780704050676215E-01 };
  double w03[2] = {
    2.858439990420468E-01,
    1.214156000957953E+00 };
  double x04[3] = {
    7.262978413470474E-03,
    2.246325512521893E-01,
    1.000000000000000E+00 };
  double w04[3] = {
    3.907638767531813E-02,
    4.873484056646474E-01,
    9.735752066600344E-01 };
  double x05[3] = {
    1.282368909458828E-02,
    2.694286346792474E-01,
    1.018414523786358E+00 };
  double w05[3] = {
    6.363996663105925E-02,
    5.077434578043636E-01,
    9.286165755645772E-01 };
  double x06[4] = {
    1.189242434021285E-02,
    2.578220434738662E-01,
    1.007750064585281E+00,
    2.000000000000000E+00 };
  double w06[4] = {
    5.927215035616424E-02,
    4.955981740306228E-01,
    9.427131290628058E-01,
    1.002416546550407E+00 };
  double x07[6] = {
    3.317925942699451E-03,
    8.283019705296352E-02,
    4.136094925726231E-01,
    1.088744373688402E+00,
    2.006482101852379E+00,
    3.000000000000000E+00 };
  double w07[6] = {
    1.681780929883469E-02,
    1.755244404544475E-01,
    5.039350503858001E-01,
    8.266241339680867E-01,
    9.773065848981277E-01,
    9.997919809947032E-01 };
  double x08[8] = {
    1.214130606523435E-03,
    3.223952700027058E-02,
    1.790935383649920E-01,
    5.437663805244631E-01,
    1.176116628396759E+00,
    2.031848210716014E+00,
    3.001961225690812E+00,
    4.000000000000000E+00 };
  double w08[8] = {
    6.199844884297793E-03,
    7.106286791720044E-02,
    2.408930104410471E-01,
    4.975929263668960E-01,
    7.592446540441226E-01,
    9.322446399614420E-01,
    9.928171438160095E-01,
    9.999449125689846E-01 };
  double x09[10] = {
    1.745862989163252E-04,
    8.613670540457314E-03,
    6.733385088703690E-02,
    2.514488774733840E-01,
    6.341845573737690E-01,
    1.248404055083152E+00,
    2.065688031953401E+00,
    3.009199358662542E+00,
    4.000416269690208E+00,
    5.000000000000000E+00 };
  double w09[10] = {
    1.016950985948944E-03,
    2.294670686517670E-02,
    1.076657968022888E-01,
    2.734577662465576E-01,
    4.978815591924992E-01,
    7.256208919565360E-01,
    8.952638690320078E-01,
    9.778157465381624E-01,
    9.983390781399277E-01,
    9.999916342408948E-01 };
  double x10[12] = {
    5.710218427206990E-04,
    1.540424351115548E-02,
    8.834248407196555E-02,
    2.824462054509770E-01,
    6.574869892305580E-01,
    1.246541060977993E+00,
    2.039218495130811E+00,
    2.979333487049800E+00,
    3.985772595393049E+00,
    4.997240804311428E+00,
    5.999868793951190E+00,
    7.000000000000000E+00 };
  double w10[12] = {
    2.921018926912141E-03,
    3.431130611256885E-02,
    1.224669495638615E-01,
    2.761108242022520E-01,
    4.797809643010337E-01,
    6.966555677271379E-01,
    8.790077941972658E-01,
    9.868622449294327E-01,
    1.015142389688201E+00,
    1.006209712632210E+00,
    1.000528829922287E+00,
    1.000002397796838E+00 };
  double x11[14] = {
    3.419821460249725E-04,
    9.296593430187960E-03,
    5.406214771755252E-02,
    1.763945096508648E-01,
    4.218486605653738E-01,
    8.274022895884040E-01,
    1.410287585637014E+00,
    2.160997505238153E+00,
    3.043504749358223E+00,
    4.005692579069439E+00,
    4.999732707905968E+00,
    5.999875191971098E+00,
    6.999994560568667E+00,
    8.000000000000000E+00 };
  double w11[14] = {
    1.750957243202047E-03,
    2.080726584287380E-02,
    7.586830616433430E-02,
    1.766020526671851E-01,
    3.206624362072232E-01,
    4.934405290553812E-01,
    6.707497030698472E-01,
    8.244959025366557E-01,
    9.314646742162802E-01,
    9.845768443163154E-01,
    9.992852769154770E-01,
    1.000273112957723E+00,
    1.000022857402321E+00,
    1.000000081405180E+00 };
  double x12[16] = {
    2.158438988280793E-04,
    5.898432743709196E-03,
    3.462795956896131E-02,
    1.145586495070213E-01,
    2.790344218856415E-01,
    5.600113798653321E-01,
    9.814091242883119E-01,
    1.553594853974655E+00,
    2.270179114036658E+00,
    3.108234601715371E+00,
    4.032930893996553E+00,
    5.006803270228157E+00,
    6.000815466735179E+00,
    7.000045035079542E+00,
    8.000000738923901E+00,
    9.000000000000000E+00 };
  double w12[16] = {
    1.105804873501181E-03,
    1.324499944707956E-02,
    4.899842307592144E-02,
    1.165326192868815E-01,
    2.178586693194957E-01,
    3.481766016945031E-01,
    4.964027915911545E-01,
    6.469026189623831E-01,
    7.823688971783889E-01,
    8.877772445893361E-01,
    9.551665077035583E-01,
    9.876285579741800E-01,
    9.979929183863017E-01,
    9.998470620634641E-01,
    9.999962891645340E-01,
    9.999999946893169E-01 };

  if ( rule < 1 || 12 < rule )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "RULE_POWER - Fatal error!\n" );
    fprintf ( stderr, "  Input value of RULE is not between 1 and 12.\n" );
    exit ( 1 );
  }

  if ( rule == 1 )
  {
    r8vec_copy ( j, x01, x );
    r8vec_copy ( j, w01, w );
  }
  else if ( rule == 2 )
  {
    r8vec_copy ( j, x02, x );
    r8vec_copy ( j, w02, w );
  }
  else if ( rule == 3 )
  {
    r8vec_copy ( j, x03, x );
    r8vec_copy ( j, w03, w );
  }
  else if ( rule == 4 )
  {
    r8vec_copy ( j, x04, x );
    r8vec_copy ( j, w04, w );
  }
  else if ( rule == 5 )
  {
    r8vec_copy ( j, x05, x );
    r8vec_copy ( j, w05, w );
  }
  else if ( rule == 6 )
  {
    r8vec_copy ( j, x06, x );
    r8vec_copy ( j, w06, w );
  }
  else if ( rule == 7 )
  {
    r8vec_copy ( j, x07, x );
    r8vec_copy ( j, w07, w );
  }
  else if ( rule == 8 )
  {
    r8vec_copy ( j, x08, x );
    r8vec_copy ( j, w08, w );
  }
  else if ( rule == 9 )
  {
    r8vec_copy ( j, x09, x );
    r8vec_copy ( j, w09, w );
  }
  else if ( rule == 10 )
  {
    r8vec_copy ( j, x10, x );
    r8vec_copy ( j, w10, w );
  }
  else if ( rule == 11 )
  {
    r8vec_copy ( j, x11, x );
    r8vec_copy ( j, w11, w );
  }
  else if ( rule == 12 )
  {
    r8vec_copy ( j, x12, x );
    r8vec_copy ( j, w12, w );
  }

  return;
}