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

# include "pyramid_jaskowiec_rule.h"

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

void comp_next ( int n, int k, int a[], int *more, int *h, int *t )

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

    comp_next() computes the compositions of the integer N into K parts.

  Discussion:

    A composition of the integer N into K parts is an ordered sequence
    of K nonnegative integers which sum to N.  The compositions (1,2,1)
    and (1,1,2) are considered to be distinct.

    The routine computes one composition on each call until there are no more.
    For instance, one composition of 6 into 3 parts is
    3+2+1, another would be 6+0+0.

    On the first call to this routine, set MORE = FALSE.  The routine
    will compute the first element in the sequence of compositions, and
    return it, as well as setting MORE = TRUE.  If more compositions
    are desired, call again, and again.  Each time, the routine will
    return with a new composition.

    However, when the LAST composition in the sequence is computed 
    and returned, the routine will reset MORE to FALSE, signaling that
    the end of the sequence has been reached.

    This routine originally used a STATIC statement to maintain the
    variables H and T.  I have decided (based on an wasting an
    entire morning trying to track down a problem) that it is safer
    to pass these variables as arguments, even though the user should
    never alter them.  This allows this routine to safely shuffle
    between several ongoing calculations.


    There are 28 compositions of 6 into three parts.  This routine will
    produce those compositions in the following order:

     I         A
     -     ---------
     1     6   0   0
     2     5   1   0
     3     4   2   0
     4     3   3   0
     5     2   4   0
     6     1   5   0
     7     0   6   0
     8     5   0   1
     9     4   1   1
    10     3   2   1
    11     2   3   1
    12     1   4   1
    13     0   5   1
    14     4   0   2
    15     3   1   2
    16     2   2   2
    17     1   3   2
    18     0   4   2
    19     3   0   3
    20     2   1   3
    21     1   2   3
    22     0   3   3
    23     2   0   4
    24     1   1   4
    25     0   2   4
    26     1   0   5
    27     0   1   5
    28     0   0   6

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    02 July 2008

  Author:

    Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf.
    C version by John Burkardt.

  Reference:

    Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms for Computers and Calculators,
    Second Edition,
    Academic Press, 1978,
    ISBN: 0-12-519260-6,
    LC: QA164.N54.

  Parameters:

    Input, int N, the integer whose compositions are desired.

    Input, int K, the number of parts in the composition.

    Input/output, int A[K], the parts of the composition.

    Input/output, int *MORE.
    Set MORE = FALSE on first call.  It will be reset to TRUE on return
    with a new composition.  Each new call returns another composition until
    MORE is set to FALSE when the last composition has been computed
    and returned.

    Input/output, int *H, *T, two internal parameters needed for the
    computation.  The user should allocate space for these in the calling
    program, include them in the calling sequence, but never alter them!
*/
{
  int i;

  if ( !( *more ) )
  {
    *t = n;
    *h = 0;
    a[0] = n;
    for ( i = 1; i < k; i++ )
    {
       a[i] = 0;
    }
  }
  else
  {
    if ( 1 < *t )
    {
      *h = 0;
    }
    *h = *h + 1;
    *t = a[*h-1];
    a[*h-1] = 0;
    a[0] = *t - 1;
    a[*h] = a[*h] + 1;
  }

  *more = ( a[k-1] != n );

  return;
}
/******************************************************************************/

double *monomial_value ( int m, int n, int e[], double x[] )

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

    monomial_value() evaluates a monomial.

  Discussion:

    This routine evaluates a monomial of the form

      product ( 1 <= i <= m ) x(i)^e(i)

    The combination 0.0^0 is encountered is treated as 1.0.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 August 2014

  Author:

    John Burkardt

  Input:

    int M, the spatial dimension.

    int N, the number of evaluation points.

    int E[M], the exponents.

    double X[M*N], the point coordinates.

  Output:

    double MONOMIAL_VALUE[N], the monomial values.
*/
{
  int i;
  int j;
  double *v;

  v = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    v[j] = 1.0;
  }

  for ( i = 0; i < m; i++ )
  {
    if ( 0 != e[i] )
    {
      for ( j = 0; j < n; j++ )
      {
        v[j] = v[j] * pow ( x[i+j*m], e[i] );
      }
    }
  }

  return v;
}
/******************************************************************************/

void pyramid_jaskowiec_rule ( int p, int n, double x[], double y[], 
  double z[], double w[] )

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

    pyramid_jaskowiec_rule() returns a pyramid quadrature rule of given precision.

  Discussion:

    The unit pyramid with square base is the region

      -1 <= X <= 1
      -1 <= Y <= 1
       0 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    16 May 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int p: the precision, 0 <= p <= 20.

    int n: the order of the rule.

  Output:

    double x(n), y(n), z(n): the coordinates of quadrature points.

    double w(n): the quadrature weights.
*/
{
  if ( p < 0 ) 
  {
    printf ( "\n" );
    printf ( "pyramid_jaskowiec_rule(): Fatal error!\n" );
    printf ( "  Input p < 0.\n" );
    exit ( 1 );
  }

  if ( 20 < p )
  {
    printf ( "\n" );
    printf ( "pyramid_jaskowiec_rule(): Fatal error!\n" );
    printf ( "  Input 20 < p.\n" );
    exit ( 1 );
  }

  if ( p == 0 )
  {
    rule00 ( n, x, y, z, w );
  }
  else if ( p == 1 )
  {
    rule01 ( n, x, y, z, w );
  }
  else if ( p == 2 )
  {
    rule02 ( n, x, y, z, w );
  }
  else if ( p == 3 )
  {
    rule03 ( n, x, y, z, w );
  }
  else if ( p == 4 )
  {
    rule04 ( n, x, y, z, w );
  }
  else if ( p == 5 )
  {
    rule05 ( n, x, y, z, w );
  }
  else if ( p == 6 )
  {
    rule06 ( n, x, y, z, w );
  }
  else if ( p == 7 )
  {
    rule07 ( n, x, y, z, w );
  }
  else if ( p == 8 )
  {
    rule08 ( n, x, y, z, w );
  }
  else if ( p == 9 )
  {
    rule09 ( n, x, y, z, w );
  }
  else if ( p == 10 )
  {
    rule10 ( n, x, y, z, w );
  }
  else if ( p == 11 )
  {
    rule11 ( n, x, y, z, w );
  }
  else if ( p == 12 )
  {
    rule12 ( n, x, y, z, w );
  }
  else if ( p == 13 )
  {
    rule13 ( n, x, y, z, w );
  }
  else if ( p == 14 )
  {
    rule14 ( n, x, y, z, w );
  }
  else if ( p == 15 )
  {
    rule15 ( n, x, y, z, w );
  }
  else if ( p == 16 )
  {
    rule16 ( n, x, y, z, w );
  }
  else if ( p == 17 )
  {
    rule17 ( n, x, y, z, w );
  }
  else if ( p == 18 )
  {
    rule18 ( n, x, y, z, w );
  }
  else if ( p == 19 )
  {
    rule19 ( n, x, y, z, w );
  }
  else if ( p == 20 )
  {
    rule20 ( n, x, y, z, w );
  }

  return;
}
/******************************************************************************/

double pyramid_volume ( double h, double s )

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

    pyramid_volume() computes the volume of a pyramid with square base.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Input:

    double h, s: the height of the pyramid, and the length of one
    side of the square base.

  Output:

    double pyramid_volume: the volume of the pyramid.
*/
{
  double value;

  value = s * s * h / 3.0;

  return value;
}
/******************************************************************************/

double pyramid_unit_monomial_integral ( int expon[3] )

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

    pyramid_unit_monomial_integral(): monomial integral in a unit pyramid.

  Discussion:

    This function returns the value of the integral of X^ALPHA Y^BETA Z^GAMMA
    over the unit pyramid.

    The integration region is:

    - ( 1 - Z ) <= X <= 1 - Z
    - ( 1 - Z ) <= Y <= 1 - Z
              0 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 March 2008

  Author:

    John Burkardt

  Reference:

    Arthur Stroud,
    Approximate Calculation of Multiple Integrals,
    Prentice Hall, 1971,
    ISBN: 0130438936,
    LC: QA311.S85.

  Input:

    int EXPON[3], the exponents.

  Output:

    double pyramid_unit_monomial_integral, the integral of the monomial
    over the pyramid.
*/
{
  int i;
  int i_hi;
  double mop;
  double value;

  value = 0.0;

  if ( ( expon[0] % 2 ) == 0 && ( expon[1] % 2 ) == 0 )
  {
    i_hi = 2 + expon[0] + expon[1];

    mop = 1.0;
    for ( i = 0; i <= i_hi; i++ )
    {
      value = value + mop * r8_choose ( i_hi, i )
      / ( double ) ( i + expon[2] + 1 );
      mop = - mop;
    }

    value = value
          * 2.0 / ( double ) ( expon[0] + 1 )
          * 2.0 / ( double ) ( expon[1] + 1 );
  }

  return value;
}
/******************************************************************************/

double pyramid_unit_volume ( )

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

    pyramid_unit_volume(): volume of a unit pyramid with square base.

  Discussion:

    The volume of this unit pyramid is 4/3.

    The integration region is:

      - ( 1 - Z ) <= X <= 1 - Z
      - ( 1 - Z ) <= Y <= 1 - Z
                0 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Output:

    double pyramid_unit_volume: the volume of the unit pyramid.
*/
{
  double volume;

  volume = 4.0 / 3.0;

  return volume;
}
/******************************************************************************/

double r8_choose ( int n, int k )

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

    r8_choose() computes the combinatorial coefficient C(N,K).

  Discussion:

    Real arithmetic is used, and C(N,K) is computed directly, via
    Gamma functions, rather than recursively.

    C(N,K) is the number of distinct combinations of K objects
    chosen from a set of N distinct objects.  A combination is
    like a set, in that order does not matter.

    C(N,K) = N! / ( (N-K)! * K! )

  Example:

    The number of combinations of 2 things chosen from 5 is 10.

    C(5,2) = ( 5 * 4 * 3 * 2 * 1 ) / ( ( 3 * 2 * 1 ) * ( 2 * 1 ) ) = 10.

    The actual combinations may be represented as:

      (1,2), (1,3), (1,4), (1,5), (2,3),
      (2,4), (2,5), (3,4), (3,5), (4,5).

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    25 July 2011

  Author:

    John Burkardt

  Input:

    int N, the value of N.

    int K, the value of K.

  Output:

    double R8_CHOOSE, the value of C(N,K)
*/
{
  double arg;
  double fack;
  double facn;
  double facnmk;
  double value;

  if ( n < 0 )
  {
    value = 0.0;
  }
  else if ( k == 0 )
  {
    value = 1.0;
  }
  else if ( k == 1 )
  {
    value = ( double ) ( n );
  }
  else if ( 1 < k && k < n - 1 )
  {
    arg = ( double ) ( n + 1 );
    facn = lgamma ( arg );

    arg = ( double ) ( k + 1 );
    fack = lgamma ( arg );

    arg = ( double ) ( n - k + 1 );
    facnmk = lgamma ( arg );

    value = round ( exp ( facn - fack - facnmk ) );
  }
  else if ( k == n - 1 )
  {
    value = ( double ) ( n );
  }
  else if ( k == n )
  {
    value = 1.0;
  }
  else
  {
    value = 0.0;
  }

  return value;
}
/******************************************************************************/

void r8vec_copy ( int n, double a1[], double a2[] )

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

    r8vec_copy() copies an R8VEC.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    03 July 2005

  Author:

    John Burkardt

  Input:

    int N, the number of entries in the vectors.

    double A1[N], the vector to be copied.

  Output:

    double A2[N], the copy of A1.
*/
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a2[i] = a1[i];
  }
  return;
}
/******************************************************************************/

int rule_order ( int p )

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

    rule_order() returns the order of a quadrature rule of given precision.

  Discussion:

    The "order" of a quadrature rule is the number of points involved.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int p: the precision, 0 <= p <= 20.

  Output:

    int rule_order: the order of the rule.
*/
{
  int order;
  static int order_save[] = {
      1, 
      1,   5,   6,  10,  15, 
     23,  31,  47,  62,  80, 
    103, 127, 152, 184, 234, 
    285, 319, 357, 418, 489 };

  if ( p < 0 ) 
  {
    printf ( "\n" );
    printf ( "rule_order(): Fatal error!\n" );
    printf ( "  Input p < 0.\n" );
    exit ( 1 );
  }

  if ( 20 < p )
  {
    printf ( "\n" );
    printf ( "rule_order(): Fatal error!\n" );
    printf ( "  Input 20 < p.\n" );
    exit ( 1 );
  }

  order = order_save[p];

  return order;
}
void rule00 ( int n, double x[], double y[], double z[], double w[] )

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

   rule00() returns the pyramid quadrature rule of precision 0.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000 };

  static double y_save[] = {
      0.00000000000000000000 };

  static double z_save[] = {
      0.25000000000000000000 };

  double w_save[] = {
      1.00000000000000000000 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule01 ( int n, double x[], double y[], double z[], double w[] )

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

   rule01() returns the pyramid quadrature rule of precision 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000 };

  static double y_save[] = {
      0.00000000000000000000 };

  static double z_save[] = {
      0.25000000000000000000 };

  double w_save[] = {
      1.00000000000000000000 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule02 ( int n, double x[], double y[], double z[], double w[] )

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

   rule02() returns the pyramid quadrature rule of precision 2.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.52699748736717488828,
     -0.52699748736717488828,
      0.52699748736717488828,
     -0.52699748736717488828 };

  static double y_save[] = {
      0.00000000000000000000,
      0.52699748736717488828,
      0.52699748736717488828,
     -0.52699748736717488828,
     -0.52699748736717488828 };

  static double z_save[] = {
      0.56063221253561712487,
      0.12927845700902559911,
      0.12927845700902559911,
      0.12927845700902559911,
      0.12927845700902559911 };

  double w_save[] = {
      0.27986667890163369199,
      0.18003333027459159088,
      0.18003333027459159088,
      0.18003333027459159088,
      0.18003333027459159088 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule03 ( int n, double x[], double y[], double z[], double w[] )

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

   rule03() returns the pyramid quadrature rule of precision 3.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.58459636639471157515,
     -0.58459636639471157515,
      0.58459636639471157515,
     -0.58459636639471157515 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.58459636639471157515,
      0.58459636639471157515,
     -0.58459636639471157515,
     -0.58459636639471157515 };

  static double z_save[] = {
      0.03032132711145601317,
      0.56560718797897435728,
      0.16666666666666665741,
      0.16666666666666665741,
      0.16666666666666665741,
      0.16666666666666665741 };

  double w_save[] = {
      0.15345064748545933497,
      0.26133122207480513621,
      0.14630453260993386833,
      0.14630453260993386833,
      0.14630453260993386833,
      0.14630453260993386833 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule04 ( int n, double x[], double y[], double z[], double w[] )

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

   rule04() returns the pyramid quadrature rule of precision 4.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.65058155639823256333,
      0.00000000000000000000,
     -0.65058155639823256333,
      0.00000000000000000000,
      0.65796699712169004481,
     -0.65796699712169004481,
      0.65796699712169004481,
     -0.65796699712169004481 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.65058155639823256333,
      0.00000000000000000000,
     -0.65058155639823256333,
      0.65796699712169004481,
      0.65796699712169004481,
     -0.65796699712169004481,
     -0.65796699712169004481 };

  static double z_save[] = {
      0.12513695310874645150,
      0.67723278888613736015,
      0.32238414957821365237,
      0.32238414957821365237,
      0.32238414957821365237,
      0.32238414957821365237,
      0.03924828389881535040,
      0.03924828389881535040,
      0.03924828389881535040,
      0.03924828389881535040 };

  double w_save[] = {
      0.20688340258955226214,
      0.11374188317064193310,
      0.10632458788932550031,
      0.10632458788932550031,
      0.10632458788932550031,
      0.10632458788932550031,
      0.06351909067062594394,
      0.06351909067062594394,
      0.06351909067062594394,
      0.06351909067062594394 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule05 ( int n, double x[], double y[], double z[], double w[] )

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

   rule05() returns the pyramid quadrature rule of precision 5.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.75344061307932941318,
      0.00000000000000000000,
     -0.75344061307932941318,
      0.00000000000000000000,
      0.41715200242575134482,
     -0.41715200242575134482,
      0.41715200242575134482,
     -0.41715200242575134482,
      0.67402251647787037037,
     -0.67402251647787037037,
      0.67402251647787037037,
     -0.67402251647787037037 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.75344061307932941318,
      0.00000000000000000000,
     -0.75344061307932941318,
      0.41715200242575134482,
      0.41715200242575134482,
     -0.41715200242575134482,
     -0.41715200242575134482,
      0.67402251647787037037,
      0.67402251647787037037,
     -0.67402251647787037037,
     -0.67402251647787037037 };

  static double z_save[] = {
      0.73070946955479043616,
      0.00619723285819058847,
      0.26844580953431373960,
      0.12500000000000000000,
      0.12500000000000000000,
      0.12500000000000000000,
      0.12500000000000000000,
      0.42182171100285947851,
      0.42182171100285947851,
      0.42182171100285947851,
      0.42182171100285947851,
      0.06579572180745926757,
      0.06579572180745926757,
      0.06579572180745926757,
      0.06579572180745926757 };

  double w_save[] = {
      0.06773442693037112772,
      0.06470893518150579171,
      0.17727154901514516339,
      0.05910777216655192096,
      0.05910777216655192096,
      0.05910777216655192096,
      0.05910777216655192096,
      0.06537546219121122271,
      0.06537546219121122271,
      0.06537546219121122271,
      0.06537546219121122271,
      0.04808803786048133910,
      0.04808803786048133910,
      0.04808803786048133910,
      0.04808803786048133910 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule06 ( int n, double x[], double y[], double z[], double w[] )

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

   rule06() returns the pyramid quadrature rule of precision 6.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.42104595182782333929,
      0.00000000000000000000,
     -0.42104595182782333929,
      0.00000000000000000000,
      0.83584092506524387822,
      0.00000000000000000000,
     -0.83584092506524387822,
      0.00000000000000000000,
      0.51341781341302172859,
     -0.51341781341302172859,
      0.51341781341302172859,
     -0.51341781341302172859,
      0.87197953364266822529,
     -0.87197953364266822529,
      0.87197953364266822529,
     -0.87197953364266822529,
      0.47733155776773072976,
     -0.47733155776773072976,
      0.47733155776773072976,
     -0.47733155776773072976 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.42104595182782333929,
      0.00000000000000000000,
     -0.42104595182782333929,
      0.00000000000000000000,
      0.83584092506524387822,
      0.00000000000000000000,
     -0.83584092506524387822,
      0.51341781341302172859,
      0.51341781341302172859,
     -0.51341781341302172859,
     -0.51341781341302172859,
      0.87197953364266822529,
      0.87197953364266822529,
     -0.87197953364266822529,
     -0.87197953364266822529,
      0.47733155776773072976,
      0.47733155776773072976,
     -0.47733155776773072976,
     -0.47733155776773072976 };

  static double z_save[] = {
      0.13353121706321477435,
      0.80839181878746035892,
      0.37840352066355309457,
      0.55635774022808082151,
      0.55635774022808082151,
      0.55635774022808082151,
      0.55635774022808082151,
      0.09682668434012106640,
      0.09682668434012106640,
      0.09682668434012106640,
      0.09682668434012106640,
      0.25547807503740499468,
      0.25547807503740499468,
      0.25547807503740499468,
      0.25547807503740499468,
      0.03348911098405843445,
      0.03348911098405843445,
      0.03348911098405843445,
      0.03348911098405843445,
      0.02776222122928558023,
      0.02776222122928558023,
      0.02776222122928558023,
      0.02776222122928558023 };

  double w_save[] = {
      0.10236994192337051102,
      0.02544552509057920395,
      0.10744358342269332007,
      0.03715744178992643615,
      0.03715744178992643615,
      0.03715744178992643615,
      0.03715744178992643615,
      0.03663269740345383857,
      0.03663269740345383857,
      0.03663269740345383857,
      0.03663269740345383857,
      0.07134885171305939411,
      0.07134885171305939411,
      0.07134885171305939411,
      0.07134885171305939411,
      0.00865946139444006419,
      0.00865946139444006419,
      0.00865946139444006419,
      0.00865946139444006419,
      0.03738678508995950389,
      0.03738678508995950389,
      0.03738678508995950389,
      0.03738678508995950389 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule07 ( int n, double x[], double y[], double z[], double w[] )

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

   rule07() returns the pyramid quadrature rule of precision 7.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.61721339984836764980,
      0.00000000000000000000,
     -0.61721339984836764980,
      0.00000000000000000000,
      0.86409875978771466531,
      0.00000000000000000000,
     -0.86409875978771466531,
      0.00000000000000000000,
      0.52488756030374572603,
     -0.52488756030374572603,
      0.52488756030374572603,
     -0.52488756030374572603,
      0.25419682219463812789,
     -0.25419682219463812789,
      0.25419682219463812789,
     -0.25419682219463812789,
      0.35405111881016937403,
     -0.35405111881016937403,
      0.35405111881016937403,
     -0.35405111881016937403,
      0.61427194545119712110,
     -0.61427194545119712110,
      0.61427194545119712110,
     -0.61427194545119712110,
      0.80282248626994900942,
     -0.80282248626994900942,
      0.80282248626994900942,
     -0.80282248626994900942 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.61721339984836764980,
      0.00000000000000000000,
     -0.61721339984836764980,
      0.00000000000000000000,
      0.86409875978771466531,
      0.00000000000000000000,
     -0.86409875978771466531,
      0.52488756030374572603,
      0.52488756030374572603,
     -0.52488756030374572603,
     -0.52488756030374572603,
      0.25419682219463812789,
      0.25419682219463812789,
     -0.25419682219463812789,
     -0.25419682219463812789,
      0.35405111881016937403,
      0.35405111881016937403,
     -0.35405111881016937403,
     -0.35405111881016937403,
      0.61427194545119712110,
      0.61427194545119712110,
     -0.61427194545119712110,
     -0.61427194545119712110,
      0.80282248626994900942,
      0.80282248626994900942,
     -0.80282248626994900942,
     -0.80282248626994900942 };

  static double z_save[] = {
      0.39365048525928414413,
      0.83863414272299030561,
      0.00001985131073852604,
      0.33333333333333331483,
      0.33333333333333331483,
      0.33333333333333331483,
      0.33333333333333331483,
      0.06666666666666666574,
      0.06666666666666666574,
      0.06666666666666666574,
      0.06666666666666666574,
      0.29045491084254104752,
      0.29045491084254104752,
      0.29045491084254104752,
      0.29045491084254104752,
      0.60547835568141594731,
      0.60547835568141594731,
      0.60547835568141594731,
      0.60547835568141594731,
      0.12931884631055998169,
      0.12931884631055998169,
      0.12931884631055998169,
      0.12931884631055998169,
      0.00010086339268113571,
      0.00010086339268113571,
      0.00010086339268113571,
      0.00010086339268113571,
      0.08012951317750569014,
      0.08012951317750569014,
      0.08012951317750569014,
      0.08012951317750569014 };

  double w_save[] = {
      0.10051398177493840735,
      0.01571901760701541889,
      0.02499658963028165634,
      0.02871093749999999861,
      0.02871093749999999861,
      0.02871093749999999861,
      0.02871093749999999861,
      0.02669175929300291600,
      0.02669175929300291600,
      0.02669175929300291600,
      0.02669175929300291600,
      0.03572750182264943647,
      0.03572750182264943647,
      0.03572750182264943647,
      0.03572750182264943647,
      0.02951904528668866309,
      0.02951904528668866309,
      0.02951904528668866309,
      0.02951904528668866309,
      0.06594160872648228977,
      0.06594160872648228977,
      0.06594160872648228977,
      0.06594160872648228977,
      0.01333274388639105884,
      0.01333274388639105884,
      0.01333274388639105884,
      0.01333274388639105884,
      0.01476900623172677438,
      0.01476900623172677438,
      0.01476900623172677438,
      0.01476900623172677438 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule08 ( int n, double x[], double y[], double z[], double w[] )

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

   rule08() returns the pyramid quadrature rule of precision 8.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.25367856157821822016,
      0.00000000000000000000,
     -0.25367856157821822016,
      0.00000000000000000000,
      0.71027375776907275551,
      0.00000000000000000000,
     -0.71027375776907275551,
      0.00000000000000000000,
      0.63643362359838895337,
      0.00000000000000000000,
     -0.63643362359838895337,
      0.00000000000000000000,
      0.62337928196226433109,
      0.00000000000000000000,
     -0.62337928196226433109,
      0.00000000000000000000,
      0.51225968171005897833,
     -0.51225968171005897833,
      0.51225968171005897833,
     -0.51225968171005897833,
      0.37965901379429650708,
     -0.37965901379429650708,
      0.37965901379429650708,
     -0.37965901379429650708,
      0.69140086940529510429,
     -0.69140086940529510429,
      0.69140086940529510429,
     -0.69140086940529510429,
      0.86742190798549856368,
     -0.86742190798549856368,
      0.86742190798549856368,
     -0.86742190798549856368,
      0.31712322629106232119,
     -0.31712322629106232119,
      0.31712322629106232119,
     -0.31712322629106232119,
      0.89374797161835639603,
      0.40528326346564669258,
     -0.89374797161835639603,
      0.40528326346564669258,
      0.89374797161835639603,
     -0.40528326346564669258,
     -0.89374797161835639603,
     -0.40528326346564669258 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.25367856157821822016,
      0.00000000000000000000,
     -0.25367856157821822016,
      0.00000000000000000000,
      0.71027375776907275551,
      0.00000000000000000000,
     -0.71027375776907275551,
      0.00000000000000000000,
      0.63643362359838895337,
      0.00000000000000000000,
     -0.63643362359838895337,
      0.00000000000000000000,
      0.62337928196226433109,
      0.00000000000000000000,
     -0.62337928196226433109,
      0.51225968171005897833,
      0.51225968171005897833,
     -0.51225968171005897833,
     -0.51225968171005897833,
      0.37965901379429650708,
      0.37965901379429650708,
     -0.37965901379429650708,
     -0.37965901379429650708,
      0.69140086940529510429,
      0.69140086940529510429,
     -0.69140086940529510429,
     -0.69140086940529510429,
      0.86742190798549856368,
      0.86742190798549856368,
     -0.86742190798549856368,
     -0.86742190798549856368,
      0.31712322629106232119,
      0.31712322629106232119,
     -0.31712322629106232119,
     -0.31712322629106232119,
      0.40528326346564669258,
      0.89374797161835639603,
      0.40528326346564669258,
     -0.89374797161835639603,
     -0.40528326346564669258,
      0.89374797161835639603,
     -0.40528326346564669258,
     -0.89374797161835639603 };

  static double z_save[] = {
      0.07395194949759914538,
      0.48064180778578036168,
      0.89787700126494018882,
      0.70399494392200201442,
      0.70399494392200201442,
      0.70399494392200201442,
      0.70399494392200201442,
      0.15999762291015326432,
      0.15999762291015326432,
      0.15999762291015326432,
      0.15999762291015326432,
      0.34740846408160180880,
      0.34740846408160180880,
      0.34740846408160180880,
      0.34740846408160180880,
      0.01127682420195143774,
      0.01127682420195143774,
      0.01127682420195143774,
      0.01127682420195143774,
      0.06351022006373874262,
      0.06351022006373874262,
      0.06351022006373874262,
      0.06351022006373874262,
      0.46284226887006968409,
      0.46284226887006968409,
      0.46284226887006968409,
      0.46284226887006968409,
      0.19177130509938980496,
      0.19177130509938980496,
      0.19177130509938980496,
      0.19177130509938980496,
      0.01630913438364359896,
      0.01630913438364359896,
      0.01630913438364359896,
      0.01630913438364359896,
      0.23681987030130632887,
      0.23681987030130632887,
      0.23681987030130632887,
      0.23681987030130632887,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785,
      0.05005997974535449785 };

  double w_save[] = {
      0.05595524252285600381,
      0.06694668391641565852,
      0.00475252306983395441,
      0.01488586682102476834,
      0.01488586682102476834,
      0.01488586682102476834,
      0.01488586682102476834,
      0.02455698624881830563,
      0.02455698624881830563,
      0.02455698624881830563,
      0.02455698624881830563,
      0.01608138988371909592,
      0.01608138988371909592,
      0.01608138988371909592,
      0.01608138988371909592,
      0.01442915622061930955,
      0.01442915622061930955,
      0.01442915622061930955,
      0.01442915622061930955,
      0.02488836268558412140,
      0.02488836268558412140,
      0.02488836268558412140,
      0.02488836268558412140,
      0.03016542061786949003,
      0.03016542061786949003,
      0.03016542061786949003,
      0.03016542061786949003,
      0.01825943823062004326,
      0.01825943823062004326,
      0.01825943823062004326,
      0.01825943823062004326,
      0.00405270511408486935,
      0.00405270511408486935,
      0.00405270511408486935,
      0.00405270511408486935,
      0.05109969513593878160,
      0.05109969513593878160,
      0.05109969513593878160,
      0.05109969513593878160,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688,
      0.00983368333222240688 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule09 ( int n, double x[], double y[], double z[], double w[] )

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

   rule09() returns the pyramid quadrature rule of precision 9.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.21993584526338003093,
      0.00000000000000000000,
     -0.21993584526338003093,
      0.00000000000000000000,
      0.25580155737930071469,
      0.00000000000000000000,
     -0.25580155737930071469,
      0.00000000000000000000,
      0.87392422284165005575,
      0.00000000000000000000,
     -0.87392422284165005575,
      0.00000000000000000000,
      0.62069706482035569284,
      0.00000000000000000000,
     -0.62069706482035569284,
      0.00000000000000000000,
      0.48088720239801563405,
      0.00000000000000000000,
     -0.48088720239801563405,
      0.00000000000000000000,
      0.54766337559892563913,
      0.00000000000000000000,
     -0.54766337559892563913,
      0.00000000000000000000,
      0.31716782120661740629,
     -0.31716782120661740629,
      0.31716782120661740629,
     -0.31716782120661740629,
      0.58114214633277661015,
     -0.58114214633277661015,
      0.58114214633277661015,
     -0.58114214633277661015,
      0.52308134436113074006,
     -0.52308134436113074006,
      0.52308134436113074006,
     -0.52308134436113074006,
      0.87278863855859856180,
     -0.87278863855859856180,
      0.87278863855859856180,
     -0.87278863855859856180,
      0.27447830261314615230,
     -0.27447830261314615230,
      0.27447830261314615230,
     -0.27447830261314615230,
      0.45787401929460586070,
      0.76874559686548982196,
     -0.45787401929460586070,
      0.76874559686548982196,
      0.45787401929460586070,
     -0.76874559686548982196,
     -0.45787401929460586070,
     -0.76874559686548982196,
      0.52945920866195028687,
      0.86516329503292388470,
     -0.52945920866195028687,
      0.86516329503292388470,
      0.52945920866195028687,
     -0.86516329503292388470,
     -0.52945920866195028687,
     -0.86516329503292388470 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.21993584526338003093,
      0.00000000000000000000,
     -0.21993584526338003093,
      0.00000000000000000000,
      0.25580155737930071469,
      0.00000000000000000000,
     -0.25580155737930071469,
      0.00000000000000000000,
      0.87392422284165005575,
      0.00000000000000000000,
     -0.87392422284165005575,
      0.00000000000000000000,
      0.62069706482035569284,
      0.00000000000000000000,
     -0.62069706482035569284,
      0.00000000000000000000,
      0.48088720239801563405,
      0.00000000000000000000,
     -0.48088720239801563405,
      0.00000000000000000000,
      0.54766337559892563913,
      0.00000000000000000000,
     -0.54766337559892563913,
      0.31716782120661740629,
      0.31716782120661740629,
     -0.31716782120661740629,
     -0.31716782120661740629,
      0.58114214633277661015,
      0.58114214633277661015,
     -0.58114214633277661015,
     -0.58114214633277661015,
      0.52308134436113074006,
      0.52308134436113074006,
     -0.52308134436113074006,
     -0.52308134436113074006,
      0.87278863855859856180,
      0.87278863855859856180,
     -0.87278863855859856180,
     -0.87278863855859856180,
      0.27447830261314615230,
      0.27447830261314615230,
     -0.27447830261314615230,
     -0.27447830261314615230,
      0.76874559686548982196,
      0.45787401929460586070,
      0.76874559686548982196,
     -0.45787401929460586070,
     -0.76874559686548982196,
      0.45787401929460586070,
     -0.76874559686548982196,
     -0.45787401929460586070,
      0.86516329503292388470,
      0.52945920866195028687,
      0.86516329503292388470,
     -0.52945920866195028687,
     -0.86516329503292388470,
      0.52945920866195028687,
     -0.86516329503292388470,
     -0.52945920866195028687 };

  static double z_save[] = {
      0.90338060334285785746,
      0.56496444359597119966,
      0.74856124635194676298,
      0.74856124635194676298,
      0.74856124635194676298,
      0.74856124635194676298,
      0.13469976629555441283,
      0.13469976629555441283,
      0.13469976629555441283,
      0.13469976629555441283,
      0.05467616134251215843,
      0.05467616134251215843,
      0.05467616134251215843,
      0.05467616134251215843,
      0.18946269484050054510,
      0.18946269484050054510,
      0.18946269484050054510,
      0.18946269484050054510,
      0.02248423582708249449,
      0.02248423582708249449,
      0.02248423582708249449,
      0.02248423582708249449,
      0.41340822589276282617,
      0.41340822589276282617,
      0.41340822589276282617,
      0.41340822589276282617,
      0.55077233639120526387,
      0.55077233639120526387,
      0.55077233639120526387,
      0.55077233639120526387,
      0.31914147555912980581,
      0.31914147555912980581,
      0.31914147555912980581,
      0.31914147555912980581,
      0.08935238781868591607,
      0.08935238781868591607,
      0.08935238781868591607,
      0.08935238781868591607,
      0.06151583405729108001,
      0.06151583405729108001,
      0.06151583405729108001,
      0.06151583405729108001,
      0.32642198515966086569,
      0.32642198515966086569,
      0.32642198515966086569,
      0.32642198515966086569,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.17557242043675652665,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947,
      0.01570840570495662947 };

  double w_save[] = {
      0.00351798245822128233,
      0.04216520928063208912,
      0.00852104325745563912,
      0.00852104325745563912,
      0.00852104325745563912,
      0.00852104325745563912,
      0.02087072229798967934,
      0.02087072229798967934,
      0.02087072229798967934,
      0.02087072229798967934,
      0.01073969585101612438,
      0.01073969585101612438,
      0.01073969585101612438,
      0.01073969585101612438,
      0.02521321637389669496,
      0.02521321637389669496,
      0.02521321637389669496,
      0.02521321637389669496,
      0.01961258547003659133,
      0.01961258547003659133,
      0.01961258547003659133,
      0.01961258547003659133,
      0.01643323197880764905,
      0.01643323197880764905,
      0.01643323197880764905,
      0.01643323197880764905,
      0.01830589291063876300,
      0.01830589291063876300,
      0.01830589291063876300,
      0.01830589291063876300,
      0.01130841811263377274,
      0.01130841811263377274,
      0.01130841811263377274,
      0.01130841811263377274,
      0.02507245299443831496,
      0.02507245299443831496,
      0.02507245299443831496,
      0.02507245299443831496,
      0.00441940990434765493,
      0.00441940990434765493,
      0.00441940990434765493,
      0.00441940990434765493,
      0.04065272607298718588,
      0.04065272607298718588,
      0.04065272607298718588,
      0.04065272607298718588,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.01219793270502279002,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839,
      0.00651697071549649839 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule10 ( int n, double x[], double y[], double z[], double w[] )

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

   rule10() returns the pyramid quadrature rule of precision 10.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.65420170176119341043,
      0.00000000000000000000,
     -0.65420170176119341043,
      0.00000000000000000000,
      0.76633927991746164654,
      0.00000000000000000000,
     -0.76633927991746164654,
      0.00000000000000000000,
      0.80421056101815546757,
      0.00000000000000000000,
     -0.80421056101815546757,
      0.00000000000000000000,
      0.21719757883626783501,
      0.00000000000000000000,
     -0.21719757883626783501,
      0.00000000000000000000,
      0.20937347351036650345,
      0.00000000000000000000,
     -0.20937347351036650345,
      0.00000000000000000000,
      0.52830709053289259813,
      0.00000000000000000000,
     -0.52830709053289259813,
      0.00000000000000000000,
      0.34681490190497532566,
     -0.34681490190497532566,
      0.34681490190497532566,
     -0.34681490190497532566,
      0.54234774233239257946,
     -0.54234774233239257946,
      0.54234774233239257946,
     -0.54234774233239257946,
      0.42965769544556714488,
     -0.42965769544556714488,
      0.42965769544556714488,
     -0.42965769544556714488,
      0.71871414601724947779,
     -0.71871414601724947779,
      0.71871414601724947779,
     -0.71871414601724947779,
      0.76244008578748778682,
     -0.76244008578748778682,
      0.76244008578748778682,
     -0.76244008578748778682,
      0.96427350086319296718,
     -0.96427350086319296718,
      0.96427350086319296718,
     -0.96427350086319296718,
      0.27897388698743774693,
     -0.27897388698743774693,
      0.27897388698743774693,
     -0.27897388698743774693,
      0.73124529835235163588,
      0.37115067890003261564,
     -0.73124529835235163588,
      0.37115067890003261564,
      0.73124529835235163588,
     -0.37115067890003261564,
     -0.73124529835235163588,
     -0.37115067890003261564,
      0.92194807057971739361,
      0.41966522833393532510,
     -0.92194807057971739361,
      0.41966522833393532510,
      0.92194807057971739361,
     -0.41966522833393532510,
     -0.92194807057971739361,
     -0.41966522833393532510,
      0.19954261519157223681,
      0.44340097447242488027,
     -0.19954261519157223681,
      0.44340097447242488027,
      0.19954261519157223681,
     -0.44340097447242488027,
     -0.19954261519157223681,
     -0.44340097447242488027 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.65420170176119341043,
      0.00000000000000000000,
     -0.65420170176119341043,
      0.00000000000000000000,
      0.76633927991746164654,
      0.00000000000000000000,
     -0.76633927991746164654,
      0.00000000000000000000,
      0.80421056101815546757,
      0.00000000000000000000,
     -0.80421056101815546757,
      0.00000000000000000000,
      0.21719757883626783501,
      0.00000000000000000000,
     -0.21719757883626783501,
      0.00000000000000000000,
      0.20937347351036650345,
      0.00000000000000000000,
     -0.20937347351036650345,
      0.00000000000000000000,
      0.52830709053289259813,
      0.00000000000000000000,
     -0.52830709053289259813,
      0.34681490190497532566,
      0.34681490190497532566,
     -0.34681490190497532566,
     -0.34681490190497532566,
      0.54234774233239257946,
      0.54234774233239257946,
     -0.54234774233239257946,
     -0.54234774233239257946,
      0.42965769544556714488,
      0.42965769544556714488,
     -0.42965769544556714488,
     -0.42965769544556714488,
      0.71871414601724947779,
      0.71871414601724947779,
     -0.71871414601724947779,
     -0.71871414601724947779,
      0.76244008578748778682,
      0.76244008578748778682,
     -0.76244008578748778682,
     -0.76244008578748778682,
      0.96427350086319296718,
      0.96427350086319296718,
     -0.96427350086319296718,
     -0.96427350086319296718,
      0.27897388698743774693,
      0.27897388698743774693,
     -0.27897388698743774693,
     -0.27897388698743774693,
      0.37115067890003261564,
      0.73124529835235163588,
      0.37115067890003261564,
     -0.73124529835235163588,
     -0.37115067890003261564,
      0.73124529835235163588,
     -0.37115067890003261564,
     -0.73124529835235163588,
      0.41966522833393532510,
      0.92194807057971739361,
      0.41966522833393532510,
     -0.92194807057971739361,
     -0.41966522833393532510,
      0.92194807057971739361,
     -0.41966522833393532510,
     -0.92194807057971739361,
      0.44340097447242488027,
      0.19954261519157223681,
      0.44340097447242488027,
     -0.19954261519157223681,
     -0.44340097447242488027,
      0.19954261519157223681,
     -0.44340097447242488027,
     -0.19954261519157223681 };

  static double z_save[] = {
      0.91766654896784238815,
      0.70900937404687269794,
      0.22713967401042231553,
      0.06874011069480644165,
      0.12392544997399050632,
      0.12392544997399050632,
      0.12392544997399050632,
      0.12392544997399050632,
      0.02096299791450871586,
      0.02096299791450871586,
      0.02096299791450871586,
      0.02096299791450871586,
      0.16577313546766450636,
      0.16577313546766450636,
      0.16577313546766450636,
      0.16577313546766450636,
      0.49340520933953563310,
      0.49340520933953563310,
      0.49340520933953563310,
      0.49340520933953563310,
      0.78969767134839341516,
      0.78969767134839341516,
      0.78969767134839341516,
      0.78969767134839341516,
      0.47169288904858786005,
      0.47169288904858786005,
      0.47169288904858786005,
      0.47169288904858786005,
      0.02011394567580290782,
      0.02011394567580290782,
      0.02011394567580290782,
      0.02011394567580290782,
      0.36822101998927786459,
      0.36822101998927786459,
      0.36822101998927786459,
      0.36822101998927786459,
      0.12661594867701117528,
      0.12661594867701117528,
      0.12661594867701117528,
      0.12661594867701117528,
      0.02433819982878694319,
      0.02433819982878694319,
      0.02433819982878694319,
      0.02433819982878694319,
      0.12701442502569038062,
      0.12701442502569038062,
      0.12701442502569038062,
      0.12701442502569038062,
      0.01067692573406054529,
      0.01067692573406054529,
      0.01067692573406054529,
      0.01067692573406054529,
      0.59704297313030385563,
      0.59704297313030385563,
      0.59704297313030385563,
      0.59704297313030385563,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.21756166315495037433,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.04137857207280886546,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173,
      0.32615365723990619173 };

  double w_save[] = {
      0.00222688724675269151,
      0.01676862119517166794,
      0.05218524659101939772,
      0.02912684113372536118,
      0.02061250827144200243,
      0.02061250827144200243,
      0.02061250827144200243,
      0.02061250827144200243,
      0.01001318317045431922,
      0.01001318317045431922,
      0.01001318317045431922,
      0.01001318317045431922,
      0.00380589471978953851,
      0.00380589471978953851,
      0.00380589471978953851,
      0.00380589471978953851,
      0.01603356460939567643,
      0.01603356460939567643,
      0.01603356460939567643,
      0.01603356460939567643,
      0.00421057398582402181,
      0.00421057398582402181,
      0.00421057398582402181,
      0.00421057398582402181,
      0.00812973230941097316,
      0.00812973230941097316,
      0.00812973230941097316,
      0.00812973230941097316,
      0.01345646795638386767,
      0.01345646795638386767,
      0.01345646795638386767,
      0.01345646795638386767,
      0.01016376299548378027,
      0.01016376299548378027,
      0.01016376299548378027,
      0.01016376299548378027,
      0.02981645762492043245,
      0.02981645762492043245,
      0.02981645762492043245,
      0.02981645762492043245,
      0.00865712783423741410,
      0.00865712783423741410,
      0.00865712783423741410,
      0.00865712783423741410,
      0.00953199916493123987,
      0.00953199916493123987,
      0.00953199916493123987,
      0.00953199916493123987,
      0.00071395826747580517,
      0.00071395826747580517,
      0.00071395826747580517,
      0.00071395826747580517,
      0.01519293397619959039,
      0.01519293397619959039,
      0.01519293397619959039,
      0.01519293397619959039,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.01008533639437561233,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.00585933822996072967,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530,
      0.02134779341185568530 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule11 ( int n, double x[], double y[], double z[], double w[] )

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

   rule11() returns the pyramid quadrature rule of precision 11.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.30959144111215058937,
      0.00000000000000000000,
     -0.30959144111215058937,
      0.00000000000000000000,
      0.76993922081029786408,
      0.00000000000000000000,
     -0.76993922081029786408,
      0.00000000000000000000,
      0.70027038117446127607,
      0.00000000000000000000,
     -0.70027038117446127607,
      0.00000000000000000000,
      0.46095035429072822586,
      0.00000000000000000000,
     -0.46095035429072822586,
      0.00000000000000000000,
      0.29928938216959510843,
      0.00000000000000000000,
     -0.29928938216959510843,
      0.00000000000000000000,
      0.59114943757155702375,
      0.00000000000000000000,
     -0.59114943757155702375,
      0.00000000000000000000,
      0.01861308147704909821,
      0.00000000000000000000,
     -0.01861308147704909821,
      0.00000000000000000000,
      0.16034290975464657314,
      0.00000000000000000000,
     -0.16034290975464657314,
      0.00000000000000000000,
      0.14450753554447465232,
     -0.14450753554447465232,
      0.14450753554447465232,
     -0.14450753554447465232,
      0.59369450979675508773,
     -0.59369450979675508773,
      0.59369450979675508773,
     -0.59369450979675508773,
      0.27490141802950085470,
     -0.27490141802950085470,
      0.27490141802950085470,
     -0.27490141802950085470,
      0.29680077247241393179,
     -0.29680077247241393179,
      0.29680077247241393179,
     -0.29680077247241393179,
      0.59849263706569033605,
     -0.59849263706569033605,
      0.59849263706569033605,
     -0.59849263706569033605,
      0.61031415307328662490,
     -0.61031415307328662490,
      0.61031415307328662490,
     -0.61031415307328662490,
      0.37345023081856359992,
     -0.37345023081856359992,
      0.37345023081856359992,
     -0.37345023081856359992,
      0.26245991463277401623,
     -0.26245991463277401623,
      0.26245991463277401623,
     -0.26245991463277401623,
      0.36860635719790568743,
     -0.36860635719790568743,
      0.36860635719790568743,
     -0.36860635719790568743,
      0.87026293442361135622,
     -0.87026293442361135622,
      0.87026293442361135622,
     -0.87026293442361135622,
      0.81025745002423155139,
     -0.81025745002423155139,
      0.81025745002423155139,
     -0.81025745002423155139,
      0.78967657467472973654,
      0.35527213835047594115,
     -0.78967657467472973654,
      0.35527213835047594115,
      0.78967657467472973654,
     -0.35527213835047594115,
     -0.78967657467472973654,
     -0.35527213835047594115,
      0.92805034944130604391,
      0.41484210234755791724,
     -0.92805034944130604391,
      0.41484210234755791724,
      0.92805034944130604391,
     -0.41484210234755791724,
     -0.92805034944130604391,
     -0.41484210234755791724,
      0.23313789083599262275,
      0.55628779191329114084,
     -0.23313789083599262275,
      0.55628779191329114084,
      0.23313789083599262275,
     -0.55628779191329114084,
     -0.23313789083599262275,
     -0.55628779191329114084 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.30959144111215058937,
      0.00000000000000000000,
     -0.30959144111215058937,
      0.00000000000000000000,
      0.76993922081029786408,
      0.00000000000000000000,
     -0.76993922081029786408,
      0.00000000000000000000,
      0.70027038117446127607,
      0.00000000000000000000,
     -0.70027038117446127607,
      0.00000000000000000000,
      0.46095035429072822586,
      0.00000000000000000000,
     -0.46095035429072822586,
      0.00000000000000000000,
      0.29928938216959510843,
      0.00000000000000000000,
     -0.29928938216959510843,
      0.00000000000000000000,
      0.59114943757155702375,
      0.00000000000000000000,
     -0.59114943757155702375,
      0.00000000000000000000,
      0.01861308147704909821,
      0.00000000000000000000,
     -0.01861308147704909821,
      0.00000000000000000000,
      0.16034290975464657314,
      0.00000000000000000000,
     -0.16034290975464657314,
      0.14450753554447465232,
      0.14450753554447465232,
     -0.14450753554447465232,
     -0.14450753554447465232,
      0.59369450979675508773,
      0.59369450979675508773,
     -0.59369450979675508773,
     -0.59369450979675508773,
      0.27490141802950085470,
      0.27490141802950085470,
     -0.27490141802950085470,
     -0.27490141802950085470,
      0.29680077247241393179,
      0.29680077247241393179,
     -0.29680077247241393179,
     -0.29680077247241393179,
      0.59849263706569033605,
      0.59849263706569033605,
     -0.59849263706569033605,
     -0.59849263706569033605,
      0.61031415307328662490,
      0.61031415307328662490,
     -0.61031415307328662490,
     -0.61031415307328662490,
      0.37345023081856359992,
      0.37345023081856359992,
     -0.37345023081856359992,
     -0.37345023081856359992,
      0.26245991463277401623,
      0.26245991463277401623,
     -0.26245991463277401623,
     -0.26245991463277401623,
      0.36860635719790568743,
      0.36860635719790568743,
     -0.36860635719790568743,
     -0.36860635719790568743,
      0.87026293442361135622,
      0.87026293442361135622,
     -0.87026293442361135622,
     -0.87026293442361135622,
      0.81025745002423155139,
      0.81025745002423155139,
     -0.81025745002423155139,
     -0.81025745002423155139,
      0.35527213835047594115,
      0.78967657467472973654,
      0.35527213835047594115,
     -0.78967657467472973654,
     -0.35527213835047594115,
      0.78967657467472973654,
     -0.35527213835047594115,
     -0.78967657467472973654,
      0.41484210234755791724,
      0.92805034944130604391,
      0.41484210234755791724,
     -0.92805034944130604391,
     -0.41484210234755791724,
      0.92805034944130604391,
     -0.41484210234755791724,
     -0.92805034944130604391,
      0.55628779191329114084,
      0.23313789083599262275,
      0.55628779191329114084,
     -0.23313789083599262275,
     -0.55628779191329114084,
      0.23313789083599262275,
     -0.55628779191329114084,
     -0.23313789083599262275 };

  static double z_save[] = {
      0.69295639647508833203,
      0.91101523446275922691,
      0.25032929072548470995,
      0.05040798390564713710,
      0.05040798390564713710,
      0.05040798390564713710,
      0.05040798390564713710,
      0.01178348626907169128,
      0.01178348626907169128,
      0.01178348626907169128,
      0.01178348626907169128,
      0.10103940902556154957,
      0.10103940902556154957,
      0.10103940902556154957,
      0.10103940902556154957,
      0.34272757605804599068,
      0.34272757605804599068,
      0.34272757605804599068,
      0.34272757605804599068,
      0.62869898216776509692,
      0.62869898216776509692,
      0.62869898216776509692,
      0.62869898216776509692,
      0.25822848523085090156,
      0.25822848523085090156,
      0.25822848523085090156,
      0.25822848523085090156,
      0.43583449548328001555,
      0.43583449548328001555,
      0.43583449548328001555,
      0.43583449548328001555,
      0.21928319414297889334,
      0.21928319414297889334,
      0.21928319414297889334,
      0.21928319414297889334,
      0.78797433053468768360,
      0.78797433053468768360,
      0.78797433053468768360,
      0.78797433053468768360,
      0.30892958869107134401,
      0.30892958869107134401,
      0.30892958869107134401,
      0.30892958869107134401,
      0.01781185684646453826,
      0.01781185684646453826,
      0.01781185684646453826,
      0.01781185684646453826,
      0.11127033608982600521,
      0.11127033608982600521,
      0.11127033608982600521,
      0.11127033608982600521,
      0.02444716310077480956,
      0.02444716310077480956,
      0.02444716310077480956,
      0.02444716310077480956,
      0.12041875519309763742,
      0.12041875519309763742,
      0.12041875519309763742,
      0.12041875519309763742,
      0.57752532555241498091,
      0.57752532555241498091,
      0.57752532555241498091,
      0.57752532555241498091,
      0.49169801908816329616,
      0.49169801908816329616,
      0.49169801908816329616,
      0.49169801908816329616,
      0.26311325712772259955,
      0.26311325712772259955,
      0.26311325712772259955,
      0.26311325712772259955,
      0.01908681361607608359,
      0.01908681361607608359,
      0.01908681361607608359,
      0.01908681361607608359,
      0.11692619926762114202,
      0.11692619926762114202,
      0.11692619926762114202,
      0.11692619926762114202,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.17968095390177224457,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.03535559961728908934,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898,
      0.41464402024224555898 };

  double w_save[] = {
      0.01286363653695535118,
      0.00259572122542773513,
      0.00817638570047552610,
      0.00511941439804289126,
      0.00511941439804289126,
      0.00511941439804289126,
      0.00511941439804289126,
      0.00684699666646234988,
      0.00684699666646234988,
      0.00684699666646234988,
      0.00684699666646234988,
      0.02021405278036775971,
      0.02021405278036775971,
      0.02021405278036775971,
      0.02021405278036775971,
      0.01240017518258633086,
      0.01240017518258633086,
      0.01240017518258633086,
      0.01240017518258633086,
      0.01050060859922616330,
      0.01050060859922616330,
      0.01050060859922616330,
      0.01050060859922616330,
      0.01207523991498536502,
      0.01207523991498536502,
      0.01207523991498536502,
      0.01207523991498536502,
      0.00794549439937168242,
      0.00794549439937168242,
      0.00794549439937168242,
      0.00794549439937168242,
      0.00897930801963979161,
      0.00897930801963979161,
      0.00897930801963979161,
      0.00897930801963979161,
      0.00432861007717266853,
      0.00432861007717266853,
      0.00432861007717266853,
      0.00432861007717266853,
      0.00959150593850333251,
      0.00959150593850333251,
      0.00959150593850333251,
      0.00959150593850333251,
      0.00845889607542490291,
      0.00845889607542490291,
      0.00845889607542490291,
      0.00845889607542490291,
      0.02093917618186586990,
      0.02093917618186586990,
      0.02093917618186586990,
      0.02093917618186586990,
      0.01007335618421271312,
      0.01007335618421271312,
      0.01007335618421271312,
      0.01007335618421271312,
      0.01474935950898293054,
      0.01474935950898293054,
      0.01474935950898293054,
      0.01474935950898293054,
      0.00405432020025909591,
      0.00405432020025909591,
      0.00405432020025909591,
      0.00405432020025909591,
      0.01768012056788626288,
      0.01768012056788626288,
      0.01768012056788626288,
      0.01768012056788626288,
      0.02349367280688881635,
      0.02349367280688881635,
      0.02349367280688881635,
      0.02349367280688881635,
      0.00300355345952720053,
      0.00300355345952720053,
      0.00300355345952720053,
      0.00300355345952720053,
      0.00433057971890565482,
      0.00433057971890565482,
      0.00433057971890565482,
      0.00433057971890565482,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00788297764391489818,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00509491185532656536,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943,
      0.00667542222774531943 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule12 ( int n, double x[], double y[], double z[], double w[] )

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

   rule12() returns the pyramid quadrature rule of precision 12.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.61752408228797095457,
      0.00000000000000000000,
     -0.61752408228797095457,
      0.00000000000000000000,
      0.95383417813475923630,
      0.00000000000000000000,
     -0.95383417813475923630,
      0.00000000000000000000,
      0.59503005801385822071,
      0.00000000000000000000,
     -0.59503005801385822071,
      0.00000000000000000000,
      0.43539359820232903520,
      0.00000000000000000000,
     -0.43539359820232903520,
      0.00000000000000000000,
      0.13291355561208040292,
      0.00000000000000000000,
     -0.13291355561208040292,
      0.00000000000000000000,
      0.79714363482446959353,
      0.00000000000000000000,
     -0.79714363482446959353,
      0.00000000000000000000,
      0.31078295049399401462,
      0.00000000000000000000,
     -0.31078295049399401462,
      0.00000000000000000000,
      0.46896896703369211901,
      0.00000000000000000000,
     -0.46896896703369211901,
      0.00000000000000000000,
      0.06329314929065793516,
      0.00000000000000000000,
     -0.06329314929065793516,
      0.00000000000000000000,
      0.11694124473665239161,
     -0.11694124473665239161,
      0.11694124473665239161,
     -0.11694124473665239161,
      0.47710850655214198657,
     -0.47710850655214198657,
      0.47710850655214198657,
     -0.47710850655214198657,
      0.34796735400888462175,
     -0.34796735400888462175,
      0.34796735400888462175,
     -0.34796735400888462175,
      0.21748093989891267852,
     -0.21748093989891267852,
      0.21748093989891267852,
     -0.21748093989891267852,
      0.67426207541025851011,
     -0.67426207541025851011,
      0.67426207541025851011,
     -0.67426207541025851011,
      0.65415312577816908668,
     -0.65415312577816908668,
      0.65415312577816908668,
     -0.65415312577816908668,
      0.26043868995957136780,
     -0.26043868995957136780,
      0.26043868995957136780,
     -0.26043868995957136780,
      0.27442107868377230151,
     -0.27442107868377230151,
      0.27442107868377230151,
     -0.27442107868377230151,
      0.51259022737109982693,
     -0.51259022737109982693,
      0.51259022737109982693,
     -0.51259022737109982693,
      0.86878873539049084052,
     -0.86878873539049084052,
      0.86878873539049084052,
     -0.86878873539049084052,
      0.71181681800308360675,
     -0.71181681800308360675,
      0.71181681800308360675,
     -0.71181681800308360675,
      0.36754569532388259301,
     -0.36754569532388259301,
      0.36754569532388259301,
     -0.36754569532388259301,
      0.84896937482456835689,
      0.51203646317203110883,
     -0.84896937482456835689,
      0.51203646317203110883,
      0.84896937482456835689,
     -0.51203646317203110883,
     -0.84896937482456835689,
     -0.51203646317203110883,
      0.97385403135997028468,
      0.74670340940557777820,
     -0.97385403135997028468,
      0.74670340940557777820,
      0.97385403135997028468,
     -0.74670340940557777820,
     -0.97385403135997028468,
     -0.74670340940557777820,
      0.32302405518012644592,
      0.62555613253804132068,
     -0.32302405518012644592,
      0.62555613253804132068,
      0.32302405518012644592,
     -0.62555613253804132068,
     -0.32302405518012644592,
     -0.62555613253804132068,
      0.19450076345283720536,
      0.69805959364273262313,
     -0.19450076345283720536,
      0.69805959364273262313,
      0.19450076345283720536,
     -0.69805959364273262313,
     -0.19450076345283720536,
     -0.69805959364273262313,
      0.32894885387189143344,
      0.85383152896625225114,
     -0.32894885387189143344,
      0.85383152896625225114,
      0.32894885387189143344,
     -0.85383152896625225114,
     -0.32894885387189143344,
     -0.85383152896625225114 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.61752408228797095457,
      0.00000000000000000000,
     -0.61752408228797095457,
      0.00000000000000000000,
      0.95383417813475923630,
      0.00000000000000000000,
     -0.95383417813475923630,
      0.00000000000000000000,
      0.59503005801385822071,
      0.00000000000000000000,
     -0.59503005801385822071,
      0.00000000000000000000,
      0.43539359820232903520,
      0.00000000000000000000,
     -0.43539359820232903520,
      0.00000000000000000000,
      0.13291355561208040292,
      0.00000000000000000000,
     -0.13291355561208040292,
      0.00000000000000000000,
      0.79714363482446959353,
      0.00000000000000000000,
     -0.79714363482446959353,
      0.00000000000000000000,
      0.31078295049399401462,
      0.00000000000000000000,
     -0.31078295049399401462,
      0.00000000000000000000,
      0.46896896703369211901,
      0.00000000000000000000,
     -0.46896896703369211901,
      0.00000000000000000000,
      0.06329314929065793516,
      0.00000000000000000000,
     -0.06329314929065793516,
      0.11694124473665239161,
      0.11694124473665239161,
     -0.11694124473665239161,
     -0.11694124473665239161,
      0.47710850655214198657,
      0.47710850655214198657,
     -0.47710850655214198657,
     -0.47710850655214198657,
      0.34796735400888462175,
      0.34796735400888462175,
     -0.34796735400888462175,
     -0.34796735400888462175,
      0.21748093989891267852,
      0.21748093989891267852,
     -0.21748093989891267852,
     -0.21748093989891267852,
      0.67426207541025851011,
      0.67426207541025851011,
     -0.67426207541025851011,
     -0.67426207541025851011,
      0.65415312577816908668,
      0.65415312577816908668,
     -0.65415312577816908668,
     -0.65415312577816908668,
      0.26043868995957136780,
      0.26043868995957136780,
     -0.26043868995957136780,
     -0.26043868995957136780,
      0.27442107868377230151,
      0.27442107868377230151,
     -0.27442107868377230151,
     -0.27442107868377230151,
      0.51259022737109982693,
      0.51259022737109982693,
     -0.51259022737109982693,
     -0.51259022737109982693,
      0.86878873539049084052,
      0.86878873539049084052,
     -0.86878873539049084052,
     -0.86878873539049084052,
      0.71181681800308360675,
      0.71181681800308360675,
     -0.71181681800308360675,
     -0.71181681800308360675,
      0.36754569532388259301,
      0.36754569532388259301,
     -0.36754569532388259301,
     -0.36754569532388259301,
      0.51203646317203110883,
      0.84896937482456835689,
      0.51203646317203110883,
     -0.84896937482456835689,
     -0.51203646317203110883,
      0.84896937482456835689,
     -0.51203646317203110883,
     -0.84896937482456835689,
      0.74670340940557777820,
      0.97385403135997028468,
      0.74670340940557777820,
     -0.97385403135997028468,
     -0.74670340940557777820,
      0.97385403135997028468,
     -0.74670340940557777820,
     -0.97385403135997028468,
      0.62555613253804132068,
      0.32302405518012644592,
      0.62555613253804132068,
     -0.32302405518012644592,
     -0.62555613253804132068,
      0.32302405518012644592,
     -0.62555613253804132068,
     -0.32302405518012644592,
      0.69805959364273262313,
      0.19450076345283720536,
      0.69805959364273262313,
     -0.19450076345283720536,
     -0.69805959364273262313,
      0.19450076345283720536,
     -0.69805959364273262313,
     -0.19450076345283720536,
      0.85383152896625225114,
      0.32894885387189143344,
      0.85383152896625225114,
     -0.32894885387189143344,
     -0.85383152896625225114,
      0.32894885387189143344,
     -0.85383152896625225114,
     -0.32894885387189143344 };

  static double z_save[] = {
      0.45700700424071905026,
      0.96248480104808953328,
      0.02656531684537740551,
      0.00537472082577391923,
      0.00537472082577391923,
      0.00537472082577391923,
      0.00537472082577391923,
      0.03942123626649530338,
      0.03942123626649530338,
      0.03942123626649530338,
      0.03942123626649530338,
      0.07619184421748394220,
      0.07619184421748394220,
      0.07619184421748394220,
      0.07619184421748394220,
      0.52461875533620183631,
      0.52461875533620183631,
      0.52461875533620183631,
      0.52461875533620183631,
      0.83871994031142604875,
      0.83871994031142604875,
      0.83871994031142604875,
      0.83871994031142604875,
      0.20075189777897944898,
      0.20075189777897944898,
      0.20075189777897944898,
      0.20075189777897944898,
      0.68265469105314702247,
      0.68265469105314702247,
      0.68265469105314702247,
      0.68265469105314702247,
      0.31713382467521444852,
      0.31713382467521444852,
      0.31713382467521444852,
      0.31713382467521444852,
      0.12709629034671870995,
      0.12709629034671870995,
      0.12709629034671870995,
      0.12709629034671870995,
      0.67124174294922867023,
      0.67124174294922867023,
      0.67124174294922867023,
      0.67124174294922867023,
      0.45862802718642248223,
      0.45862802718642248223,
      0.45862802718642248223,
      0.45862802718642248223,
      0.11938890613701966248,
      0.11938890613701966248,
      0.11938890613701966248,
      0.11938890613701966248,
      0.25741784866521960629,
      0.25741784866521960629,
      0.25741784866521960629,
      0.25741784866521960629,
      0.02260502558938975656,
      0.02260502558938975656,
      0.02260502558938975656,
      0.02260502558938975656,
      0.08746307755558260788,
      0.08746307755558260788,
      0.08746307755558260788,
      0.08746307755558260788,
      0.67140164127972612462,
      0.67140164127972612462,
      0.67140164127972612462,
      0.67140164127972612462,
      0.47604255048878973966,
      0.47604255048878973966,
      0.47604255048878973966,
      0.47604255048878973966,
      0.22777955815540271156,
      0.22777955815540271156,
      0.22777955815540271156,
      0.22777955815540271156,
      0.05850272176027389998,
      0.05850272176027389998,
      0.05850272176027389998,
      0.05850272176027389998,
      0.22053995731942055425,
      0.22053995731942055425,
      0.22053995731942055425,
      0.22053995731942055425,
      0.02548724290196442005,
      0.02548724290196442005,
      0.02548724290196442005,
      0.02548724290196442005,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.11145836537804799937,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.00339220824679912656,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.32725151644051669875,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.14805166861898322317,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195,
      0.02487563023274973195 };

  double w_save[] = {
      0.02715854620871203245,
      0.00043531424244899530,
      0.01391222140872406220,
      0.00387288146649252939,
      0.00387288146649252939,
      0.00387288146649252939,
      0.00387288146649252939,
      0.00217967971593618394,
      0.00217967971593618394,
      0.00217967971593618394,
      0.00217967971593618394,
      0.01267133485574918096,
      0.01267133485574918096,
      0.01267133485574918096,
      0.01267133485574918096,
      0.00873464163035380693,
      0.00873464163035380693,
      0.00873464163035380693,
      0.00873464163035380693,
      0.00289146731615850605,
      0.00289146731615850605,
      0.00289146731615850605,
      0.00289146731615850605,
      0.00336686848511522736,
      0.00336686848511522736,
      0.00336686848511522736,
      0.00336686848511522736,
      0.00147603803134411875,
      0.00147603803134411875,
      0.00147603803134411875,
      0.00147603803134411875,
      0.01998444773599242219,
      0.01998444773599242219,
      0.01998444773599242219,
      0.01998444773599242219,
      0.00618927170644437228,
      0.00618927170644437228,
      0.00618927170644437228,
      0.00618927170644437228,
      0.00820078705478863301,
      0.00820078705478863301,
      0.00820078705478863301,
      0.00820078705478863301,
      0.00509651546458162342,
      0.00509651546458162342,
      0.00509651546458162342,
      0.00509651546458162342,
      0.01739298850473944280,
      0.01739298850473944280,
      0.01739298850473944280,
      0.01739298850473944280,
      0.01948797782027694020,
      0.01948797782027694020,
      0.01948797782027694020,
      0.01948797782027694020,
      0.00538896243467025700,
      0.00538896243467025700,
      0.00538896243467025700,
      0.00538896243467025700,
      0.00676911731451347500,
      0.00676911731451347500,
      0.00676911731451347500,
      0.00676911731451347500,
      0.00467587609366508332,
      0.00467587609366508332,
      0.00467587609366508332,
      0.00467587609366508332,
      0.01838172037009152757,
      0.01838172037009152757,
      0.01838172037009152757,
      0.01838172037009152757,
      0.01407964506457294943,
      0.01407964506457294943,
      0.01407964506457294943,
      0.01407964506457294943,
      0.00283370063460703292,
      0.00283370063460703292,
      0.00283370063460703292,
      0.00283370063460703292,
      0.00479137222817773486,
      0.00479137222817773486,
      0.00479137222817773486,
      0.00479137222817773486,
      0.00990680633819146332,
      0.00990680633819146332,
      0.00990680633819146332,
      0.00990680633819146332,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00535574363023301383,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00081681851071822213,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.00854175372189276694,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.01018769584471248754,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812,
      0.00572367792672661812 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule13 ( int n, double x[], double y[], double z[], double w[] )

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

   rule13() returns the pyramid quadrature rule of precision 13.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.41223892088328983885,
      0.00000000000000000000,
     -0.41223892088328983885,
      0.00000000000000000000,
      0.94482408797958883362,
      0.00000000000000000000,
     -0.94482408797958883362,
      0.00000000000000000000,
      0.15012306550295120844,
      0.00000000000000000000,
     -0.15012306550295120844,
      0.00000000000000000000,
      0.36338283577562219273,
      0.00000000000000000000,
     -0.36338283577562219273,
      0.00000000000000000000,
      0.32897122373450704558,
      0.00000000000000000000,
     -0.32897122373450704558,
      0.00000000000000000000,
      0.55704935891608620135,
      0.00000000000000000000,
     -0.55704935891608620135,
      0.00000000000000000000,
      0.71060354437421247020,
      0.00000000000000000000,
     -0.71060354437421247020,
      0.00000000000000000000,
      0.88531748708681257121,
      0.00000000000000000000,
     -0.88531748708681257121,
      0.00000000000000000000,
      0.48884754503841615358,
     -0.48884754503841615358,
      0.48884754503841615358,
     -0.48884754503841615358,
      0.45031772456672747307,
     -0.45031772456672747307,
      0.45031772456672747307,
     -0.45031772456672747307,
      0.65872956915547864476,
     -0.65872956915547864476,
      0.65872956915547864476,
     -0.65872956915547864476,
      0.62588271911798842861,
     -0.62588271911798842861,
      0.62588271911798842861,
     -0.62588271911798842861,
      0.25178960033193620305,
     -0.25178960033193620305,
      0.25178960033193620305,
     -0.25178960033193620305,
      0.91338191280449132492,
     -0.91338191280449132492,
      0.91338191280449132492,
     -0.91338191280449132492,
      0.11117861641720541699,
     -0.11117861641720541699,
      0.11117861641720541699,
     -0.11117861641720541699,
      0.37814924987375336807,
     -0.37814924987375336807,
      0.37814924987375336807,
     -0.37814924987375336807,
      0.23146195691577758913,
     -0.23146195691577758913,
      0.23146195691577758913,
     -0.23146195691577758913,
      0.18598667282576661353,
     -0.18598667282576661353,
      0.18598667282576661353,
     -0.18598667282576661353,
      0.72941490542892961635,
     -0.72941490542892961635,
      0.72941490542892961635,
     -0.72941490542892961635,
      0.80419241777926819825,
     -0.80419241777926819825,
      0.80419241777926819825,
     -0.80419241777926819825,
      0.47036082838417470064,
     -0.47036082838417470064,
      0.47036082838417470064,
     -0.47036082838417470064,
      0.27535657520011547206,
     -0.27535657520011547206,
      0.27535657520011547206,
     -0.27535657520011547206,
      0.25840443662578793660,
     -0.25840443662578793660,
      0.25840443662578793660,
     -0.25840443662578793660,
      0.77456301686419115615,
      0.43978938971942055369,
     -0.77456301686419115615,
      0.43978938971942055369,
      0.77456301686419115615,
     -0.43978938971942055369,
     -0.77456301686419115615,
     -0.43978938971942055369,
      0.72014146551340840752,
      0.22174790443082656455,
     -0.72014146551340840752,
      0.22174790443082656455,
      0.72014146551340840752,
     -0.22174790443082656455,
     -0.72014146551340840752,
     -0.22174790443082656455,
      0.17509849556381359981,
      0.58560797514860796209,
     -0.17509849556381359981,
      0.58560797514860796209,
      0.17509849556381359981,
     -0.58560797514860796209,
     -0.17509849556381359981,
     -0.58560797514860796209,
      0.93762547318055500245,
      0.73982675325131319610,
     -0.93762547318055500245,
      0.73982675325131319610,
      0.93762547318055500245,
     -0.73982675325131319610,
     -0.93762547318055500245,
     -0.73982675325131319610,
      0.92588822421370353677,
      0.50002093145521131490,
     -0.92588822421370353677,
      0.50002093145521131490,
      0.92588822421370353677,
     -0.50002093145521131490,
     -0.92588822421370353677,
     -0.50002093145521131490,
      0.26820739210416322251,
      0.56185198689199644662,
     -0.26820739210416322251,
      0.56185198689199644662,
      0.26820739210416322251,
     -0.56185198689199644662,
     -0.26820739210416322251,
     -0.56185198689199644662,
      0.36207959439737902319,
      0.79245628070986395830,
     -0.36207959439737902319,
      0.79245628070986395830,
      0.36207959439737902319,
     -0.79245628070986395830,
     -0.36207959439737902319,
     -0.79245628070986395830 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.41223892088328983885,
      0.00000000000000000000,
     -0.41223892088328983885,
      0.00000000000000000000,
      0.94482408797958883362,
      0.00000000000000000000,
     -0.94482408797958883362,
      0.00000000000000000000,
      0.15012306550295120844,
      0.00000000000000000000,
     -0.15012306550295120844,
      0.00000000000000000000,
      0.36338283577562219273,
      0.00000000000000000000,
     -0.36338283577562219273,
      0.00000000000000000000,
      0.32897122373450704558,
      0.00000000000000000000,
     -0.32897122373450704558,
      0.00000000000000000000,
      0.55704935891608620135,
      0.00000000000000000000,
     -0.55704935891608620135,
      0.00000000000000000000,
      0.71060354437421247020,
      0.00000000000000000000,
     -0.71060354437421247020,
      0.00000000000000000000,
      0.88531748708681257121,
      0.00000000000000000000,
     -0.88531748708681257121,
      0.48884754503841615358,
      0.48884754503841615358,
     -0.48884754503841615358,
     -0.48884754503841615358,
      0.45031772456672747307,
      0.45031772456672747307,
     -0.45031772456672747307,
     -0.45031772456672747307,
      0.65872956915547864476,
      0.65872956915547864476,
     -0.65872956915547864476,
     -0.65872956915547864476,
      0.62588271911798842861,
      0.62588271911798842861,
     -0.62588271911798842861,
     -0.62588271911798842861,
      0.25178960033193620305,
      0.25178960033193620305,
     -0.25178960033193620305,
     -0.25178960033193620305,
      0.91338191280449132492,
      0.91338191280449132492,
     -0.91338191280449132492,
     -0.91338191280449132492,
      0.11117861641720541699,
      0.11117861641720541699,
     -0.11117861641720541699,
     -0.11117861641720541699,
      0.37814924987375336807,
      0.37814924987375336807,
     -0.37814924987375336807,
     -0.37814924987375336807,
      0.23146195691577758913,
      0.23146195691577758913,
     -0.23146195691577758913,
     -0.23146195691577758913,
      0.18598667282576661353,
      0.18598667282576661353,
     -0.18598667282576661353,
     -0.18598667282576661353,
      0.72941490542892961635,
      0.72941490542892961635,
     -0.72941490542892961635,
     -0.72941490542892961635,
      0.80419241777926819825,
      0.80419241777926819825,
     -0.80419241777926819825,
     -0.80419241777926819825,
      0.47036082838417470064,
      0.47036082838417470064,
     -0.47036082838417470064,
     -0.47036082838417470064,
      0.27535657520011547206,
      0.27535657520011547206,
     -0.27535657520011547206,
     -0.27535657520011547206,
      0.25840443662578793660,
      0.25840443662578793660,
     -0.25840443662578793660,
     -0.25840443662578793660,
      0.43978938971942055369,
      0.77456301686419115615,
      0.43978938971942055369,
     -0.77456301686419115615,
     -0.43978938971942055369,
      0.77456301686419115615,
     -0.43978938971942055369,
     -0.77456301686419115615,
      0.22174790443082656455,
      0.72014146551340840752,
      0.22174790443082656455,
     -0.72014146551340840752,
     -0.22174790443082656455,
      0.72014146551340840752,
     -0.22174790443082656455,
     -0.72014146551340840752,
      0.58560797514860796209,
      0.17509849556381359981,
      0.58560797514860796209,
     -0.17509849556381359981,
     -0.58560797514860796209,
      0.17509849556381359981,
     -0.58560797514860796209,
     -0.17509849556381359981,
      0.73982675325131319610,
      0.93762547318055500245,
      0.73982675325131319610,
     -0.93762547318055500245,
     -0.73982675325131319610,
      0.93762547318055500245,
     -0.73982675325131319610,
     -0.93762547318055500245,
      0.50002093145521131490,
      0.92588822421370353677,
      0.50002093145521131490,
     -0.92588822421370353677,
     -0.50002093145521131490,
      0.92588822421370353677,
     -0.50002093145521131490,
     -0.92588822421370353677,
      0.56185198689199644662,
      0.26820739210416322251,
      0.56185198689199644662,
     -0.26820739210416322251,
     -0.56185198689199644662,
      0.26820739210416322251,
     -0.56185198689199644662,
     -0.26820739210416322251,
      0.79245628070986395830,
      0.36207959439737902319,
      0.79245628070986395830,
     -0.36207959439737902319,
     -0.79245628070986395830,
      0.36207959439737902319,
     -0.79245628070986395830,
     -0.36207959439737902319 };

  static double z_save[] = {
      0.92974005864256004106,
      0.58387036044479012631,
      0.10942458150673148309,
      0.30043598129646631456,
      0.40351765144169587929,
      0.40351765144169587929,
      0.40351765144169587929,
      0.40351765144169587929,
      0.00554139647030791119,
      0.00554139647030791119,
      0.00554139647030791119,
      0.00554139647030791119,
      0.84979294403286831372,
      0.84979294403286831372,
      0.84979294403286831372,
      0.84979294403286831372,
      0.60719504362173426504,
      0.60719504362173426504,
      0.60719504362173426504,
      0.60719504362173426504,
      0.02033792783786766978,
      0.02033792783786766978,
      0.02033792783786766978,
      0.02033792783786766978,
      0.10601199873730246526,
      0.10601199873730246526,
      0.10601199873730246526,
      0.10601199873730246526,
      0.24910419915320258788,
      0.24910419915320258788,
      0.24910419915320258788,
      0.24910419915320258788,
      0.08107956240970674855,
      0.08107956240970674855,
      0.08107956240970674855,
      0.08107956240970674855,
      0.00950815168106079051,
      0.00950815168106079051,
      0.00950815168106079051,
      0.00950815168106079051,
      0.48819360509214093646,
      0.48819360509214093646,
      0.48819360509214093646,
      0.48819360509214093646,
      0.27690831156608641805,
      0.27690831156608641805,
      0.27690831156608641805,
      0.27690831156608641805,
      0.12248093820428122835,
      0.12248093820428122835,
      0.12248093820428122835,
      0.12248093820428122835,
      0.22323057279864513824,
      0.22323057279864513824,
      0.22323057279864513824,
      0.22323057279864513824,
      0.01207165002118426068,
      0.01207165002118426068,
      0.01207165002118426068,
      0.01207165002118426068,
      0.75518724716690510679,
      0.75518724716690510679,
      0.75518724716690510679,
      0.75518724716690510679,
      0.08424825204838617965,
      0.08424825204838617965,
      0.08424825204838617965,
      0.08424825204838617965,
      0.63188577231776799081,
      0.63188577231776799081,
      0.63188577231776799081,
      0.63188577231776799081,
      0.39892977659234107879,
      0.39892977659234107879,
      0.39892977659234107879,
      0.39892977659234107879,
      0.02502635713295603415,
      0.02502635713295603415,
      0.02502635713295603415,
      0.02502635713295603415,
      0.12038000765135539738,
      0.12038000765135539738,
      0.12038000765135539738,
      0.12038000765135539738,
      0.29270359357039776871,
      0.29270359357039776871,
      0.29270359357039776871,
      0.29270359357039776871,
      0.70742748921558806785,
      0.70742748921558806785,
      0.70742748921558806785,
      0.70742748921558806785,
      0.52832746509410000169,
      0.52832746509410000169,
      0.52832746509410000169,
      0.52832746509410000169,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.19538409012904675577,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.02260035188498128386,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.21608520533637087802,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.06232437306564607427,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.01929314718254383776,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.40102466550487736452,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482,
      0.09200529105614789482 };

  double w_save[] = {
      0.00120366956557754735,
      0.01890734566258640142,
      0.02412883548353303431,
      0.01430958560741040810,
      0.01462233467606358257,
      0.01462233467606358257,
      0.01462233467606358257,
      0.01462233467606358257,
      0.00131047133506746131,
      0.00131047133506746131,
      0.00131047133506746131,
      0.00131047133506746131,
      0.00131534859459711507,
      0.00131534859459711507,
      0.00131534859459711507,
      0.00131534859459711507,
      0.00604172938779333306,
      0.00604172938779333306,
      0.00604172938779333306,
      0.00604172938779333306,
      0.00828934369195859742,
      0.00828934369195859742,
      0.00828934369195859742,
      0.00828934369195859742,
      0.01293341373858935758,
      0.01293341373858935758,
      0.01293341373858935758,
      0.01293341373858935758,
      0.00563885419154383245,
      0.00563885419154383245,
      0.00563885419154383245,
      0.00563885419154383245,
      0.00450499139881360439,
      0.00450499139881360439,
      0.00450499139881360439,
      0.00450499139881360439,
      0.00363618420610894565,
      0.00363618420610894565,
      0.00363618420610894565,
      0.00363618420610894565,
      0.00388842116802182820,
      0.00388842116802182820,
      0.00388842116802182820,
      0.00388842116802182820,
      0.00402365320826360111,
      0.00402365320826360111,
      0.00402365320826360111,
      0.00402365320826360111,
      0.00955901949244871221,
      0.00955901949244871221,
      0.00955901949244871221,
      0.00955901949244871221,
      0.01938656716858040696,
      0.01938656716858040696,
      0.01938656716858040696,
      0.01938656716858040696,
      0.00096875488373819618,
      0.00096875488373819618,
      0.00096875488373819618,
      0.00096875488373819618,
      0.00502214350286199571,
      0.00502214350286199571,
      0.00502214350286199571,
      0.00502214350286199571,
      0.01448769412031481602,
      0.01448769412031481602,
      0.01448769412031481602,
      0.01448769412031481602,
      0.00459976431383042356,
      0.00459976431383042356,
      0.00459976431383042356,
      0.00459976431383042356,
      0.01107636061349879207,
      0.01107636061349879207,
      0.01107636061349879207,
      0.01107636061349879207,
      0.00469260200432727610,
      0.00469260200432727610,
      0.00469260200432727610,
      0.00469260200432727610,
      0.00285194982449880072,
      0.00285194982449880072,
      0.00285194982449880072,
      0.00285194982449880072,
      0.01323033835935080553,
      0.01323033835935080553,
      0.01323033835935080553,
      0.01323033835935080553,
      0.00111972343972882474,
      0.00111972343972882474,
      0.00111972343972882474,
      0.00111972343972882474,
      0.00918246462138119605,
      0.00918246462138119605,
      0.00918246462138119605,
      0.00918246462138119605,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00456490653701050169,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00547503483442879964,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00992261207645742799,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00110382912156457261,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00236228293958670472,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00630666584934871672,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885,
      0.00675492513102409885 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule14 ( int n, double x[], double y[], double z[], double w[] )

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

   rule14() returns the pyramid quadrature rule of precision 14.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.42182613673485974681,
      0.00000000000000000000,
     -0.42182613673485974681,
      0.00000000000000000000,
      0.08465613435886885918,
      0.00000000000000000000,
     -0.08465613435886885918,
      0.00000000000000000000,
      0.95167131965923157377,
      0.00000000000000000000,
     -0.95167131965923157377,
      0.00000000000000000000,
      0.12212881781145627780,
      0.00000000000000000000,
     -0.12212881781145627780,
      0.00000000000000000000,
      0.34597557868730360875,
      0.00000000000000000000,
     -0.34597557868730360875,
      0.00000000000000000000,
      0.32500209212470398956,
      0.00000000000000000000,
     -0.32500209212470398956,
      0.00000000000000000000,
      0.85274656175184737616,
      0.00000000000000000000,
     -0.85274656175184737616,
      0.00000000000000000000,
      0.63827756477152641779,
      0.00000000000000000000,
     -0.63827756477152641779,
      0.00000000000000000000,
      0.67231147414585012978,
      0.00000000000000000000,
     -0.67231147414585012978,
      0.00000000000000000000,
      0.85374960595109017358,
      0.00000000000000000000,
     -0.85374960595109017358,
      0.00000000000000000000,
      0.32351828528149095821,
      0.00000000000000000000,
     -0.32351828528149095821,
      0.00000000000000000000,
      0.49697514832376565863,
      0.00000000000000000000,
     -0.49697514832376565863,
      0.00000000000000000000,
      0.50417062955844949013,
     -0.50417062955844949013,
      0.50417062955844949013,
     -0.50417062955844949013,
      0.63853202881303905425,
     -0.63853202881303905425,
      0.63853202881303905425,
     -0.63853202881303905425,
      0.76432244824860651189,
     -0.76432244824860651189,
      0.76432244824860651189,
     -0.76432244824860651189,
      0.56133306193833287789,
     -0.56133306193833287789,
      0.56133306193833287789,
     -0.56133306193833287789,
      0.28786805395155073972,
     -0.28786805395155073972,
      0.28786805395155073972,
     -0.28786805395155073972,
      0.90163083827576329110,
     -0.90163083827576329110,
      0.90163083827576329110,
     -0.90163083827576329110,
      0.09459747575878657555,
     -0.09459747575878657555,
      0.09459747575878657555,
     -0.09459747575878657555,
      0.26275744057316757774,
     -0.26275744057316757774,
      0.26275744057316757774,
     -0.26275744057316757774,
      0.38640915363814193340,
     -0.38640915363814193340,
      0.38640915363814193340,
     -0.38640915363814193340,
      0.22823005779855418118,
     -0.22823005779855418118,
      0.22823005779855418118,
     -0.22823005779855418118,
      0.70578722692835427210,
     -0.70578722692835427210,
      0.70578722692835427210,
     -0.70578722692835427210,
      0.91478755244276455105,
     -0.91478755244276455105,
      0.91478755244276455105,
     -0.91478755244276455105,
      0.50883064513682729757,
     -0.50883064513682729757,
      0.50883064513682729757,
     -0.50883064513682729757,
      0.21833905510549736495,
     -0.21833905510549736495,
      0.21833905510549736495,
     -0.21833905510549736495,
      0.20524210043072979581,
     -0.20524210043072979581,
      0.20524210043072979581,
     -0.20524210043072979581,
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     -0.61926152278826551711,
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     -0.61926152278826551711 };

  static double y_save[] = {
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     -0.61926152278826551711,
     -0.29079659566096877077 };

  static double z_save[] = {
      0.94550960783801574205,
      0.61382435648399280570,
      0.24540497180596210214,
      0.41832825390859845749,
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      0.00783483739567485994 };

  double w_save[] = {
      0.00060098284109148011,
      0.01255487583666288487,
      0.02319377258130698310,
      0.01905556551345680832,
      0.01191795956205729361,
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      0.00386718441233280599,
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      0.00192376309517474221,
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      0.00789729756886463005,
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      0.00789729756886463005,
      0.00789729756886463005,
      0.00789729756886463005,
      0.00789729756886463005,
      0.00789729756886463005,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495,
      0.00269662856611711495 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule15 ( int n, double x[], double y[], double z[], double w[] )

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

   rule15() returns the pyramid quadrature rule of precision 15.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.70014035742397184858,
      0.00000000000000000000,
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     -0.69286495782397328203,
     -0.47557663390649029811,
     -0.69286495782397328203 };

  static double y_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.70014035742397184858,
      0.00000000000000000000,
     -0.70014035742397184858,
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  static double z_save[] = {
      0.95167840606392661851,
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      0.10372522326204723642,
      0.10372522326204723642,
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      0.18913057164406818500,
      0.18913057164406818500,
      0.18913057164406818500,
      0.15549793195551472880,
      0.15549793195551472880,
      0.15549793195551472880,
      0.15549793195551472880,
      0.00490511032939973824,
      0.00490511032939973824,
      0.00490511032939973824,
      0.00490511032939973824,
      0.06238803484862592841,
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      0.53284146417918532013,
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      0.68148251405524751245,
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      0.23097535663334242684,
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      0.32949702529445068500,
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      0.02375108271645150898,
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      0.09182493970820698737,
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      0.09182493970820698737,
      0.01061641469954416848,
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      0.18699248305545079774,
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      0.07551964039133612916,
      0.07551964039133612916,
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      0.07551964039133612916,
      0.07551964039133612916,
      0.07551964039133612916,
      0.07551964039133612916,
      0.07551964039133612916,
      0.28631001132523614672,
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      0.28631001132523614672,
      0.28631001132523614672,
      0.28631001132523614672,
      0.28631001132523614672,
      0.28631001132523614672 };

  double w_save[] = {
      0.00042533015548600539,
      0.01525748792328103336,
      0.00528017662585705642,
      0.00528017662585705642,
      0.00528017662585705642,
      0.00528017662585705642,
      0.00244639458990403638,
      0.00244639458990403638,
      0.00244639458990403638,
      0.00244639458990403638,
      0.00097370603129723528,
      0.00097370603129723528,
      0.00097370603129723528,
      0.00097370603129723528,
      0.00777612495382315819,
      0.00777612495382315819,
      0.00777612495382315819,
      0.00777612495382315819,
      0.00267697092767919202,
      0.00267697092767919202,
      0.00267697092767919202,
      0.00267697092767919202,
      0.00619081284266621932,
      0.00619081284266621932,
      0.00619081284266621932,
      0.00619081284266621932,
      0.00065618656167288063,
      0.00065618656167288063,
      0.00065618656167288063,
      0.00065618656167288063,
      0.00656994056618269082,
      0.00656994056618269082,
      0.00656994056618269082,
      0.00656994056618269082,
      0.00267308743214515841,
      0.00267308743214515841,
      0.00267308743214515841,
      0.00267308743214515841,
      0.00175949530216048481,
      0.00175949530216048481,
      0.00175949530216048481,
      0.00175949530216048481,
      0.00331285760856183092,
      0.00331285760856183092,
      0.00331285760856183092,
      0.00331285760856183092,
      0.00751034506572093984,
      0.00751034506572093984,
      0.00751034506572093984,
      0.00751034506572093984,
      0.00893166529089345351,
      0.00893166529089345351,
      0.00893166529089345351,
      0.00893166529089345351,
      0.00556841825996671948,
      0.00556841825996671948,
      0.00556841825996671948,
      0.00556841825996671948,
      0.00264945739278132876,
      0.00264945739278132876,
      0.00264945739278132876,
      0.00264945739278132876,
      0.00197028999055473379,
      0.00197028999055473379,
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      0.00513483903966016272,
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      0.00742192548155929527,
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      0.00164485721629859362,
      0.00164485721629859362,
      0.00164485721629859362,
      0.00164485721629859362,
      0.00553453693910099451,
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      0.00553453693910099451,
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      0.00325628156420546379,
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      0.00325628156420546379,
      0.00325628156420546379,
      0.00151506082426114191,
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      0.00151506082426114191,
      0.00591126556727756668,
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      0.00591126556727756668,
      0.00591126556727756668,
      0.00083923797814166039,
      0.00083923797814166039,
      0.00083923797814166039,
      0.00083923797814166039,
      0.00402240401025226024,
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      0.00402240401025226024,
      0.00402240401025226024,
      0.00223169575519892738,
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      0.00615688200816193708,
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      0.00864232058920194786,
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      0.00864232058920194786,
      0.00745270338750553870,
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      0.00502880383507017109,
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      0.00879638512225545434,
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      0.00174781246088704756,
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      0.00918989383822925963,
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      0.00620807391936788796,
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      0.00568398055245949909,
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      0.00183658571623211762,
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      0.00122995761226799547,
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      0.00195493878423380618,
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      0.00346763933769407258,
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      0.00346763933769407258,
      0.00346763933769407258,
      0.00346763933769407258,
      0.00346763933769407258,
      0.00346763933769407258,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00677026604334400768,
      0.00167829416355688515,
      0.00167829416355688515,
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      0.00167829416355688515,
      0.00167829416355688515,
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      0.00713079759016688013,
      0.00713079759016688013,
      0.00713079759016688013,
      0.00713079759016688013,
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      0.00713079759016688013,
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      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00467547289885053390,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854,
      0.00253420752420773854 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule16 ( int n, double x[], double y[], double z[], double w[] )

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

   rule16() returns the pyramid quadrature rule of precision 16.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.51870388022974789344,
      0.00000000000000000000,
     -0.51870388022974789344,
      0.00000000000000000000,
      0.91531292456766799592,
      0.00000000000000000000,
     -0.91531292456766799592,
      0.00000000000000000000,
      0.01655472656731888509,
      0.00000000000000000000,
     -0.01655472656731888509,
      0.00000000000000000000,
      0.36912135575078097727,
      0.00000000000000000000,
     -0.36912135575078097727,
      0.00000000000000000000,
      0.02060330211667108294,
      0.00000000000000000000,
     -0.02060330211667108294,
      0.00000000000000000000,
      0.87194193710104261896,
      0.00000000000000000000,
     -0.87194193710104261896,
      0.00000000000000000000,
      0.31538420787936460865,
      0.00000000000000000000,
     -0.31538420787936460865,
      0.00000000000000000000,
      0.61399555563153074278,
      0.00000000000000000000,
     -0.61399555563153074278,
      0.00000000000000000000,
      0.09765007634893953237,
      0.00000000000000000000,
     -0.09765007634893953237,
      0.00000000000000000000,
      0.73176464480784220168,
      0.00000000000000000000,
     -0.73176464480784220168,
      0.00000000000000000000,
      0.84054220943522905962,
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      0.00000000000000000000,
      0.26438021717351822826,
      0.00000000000000000000,
     -0.26438021717351822826,
      0.00000000000000000000,
      0.13755031468645742554,
     -0.13755031468645742554,
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      0.55599929975376194413,
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      0.55599929975376194413,
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      0.68037602529077279012,
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      0.10668464068510881415,
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     -0.08721470315267314255,
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      0.36285963939710730308,
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      0.83163011923015617288,
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      0.11180046767985268863,
      0.11180046767985268863,
      0.45799604201643168144,
      0.45799604201643168144,
      0.45799604201643168144,
      0.45799604201643168144,
      0.81600939659279747573,
      0.81600939659279747573,
      0.81600939659279747573,
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      0.05597294995869231404,
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      0.05597294995869231404,
      0.05597294995869231404,
      0.12573106601315930941,
      0.12573106601315930941,
      0.12573106601315930941,
      0.12573106601315930941,
      0.10680199134354546875,
      0.10680199134354546875,
      0.10680199134354546875,
      0.10680199134354546875,
      0.64658620070888050968,
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      0.25409417136336337473,
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      0.78917660780490361816,
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      0.18689788541072827055,
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      0.18689788541072827055,
      0.18689788541072827055,
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      0.18689788541072827055,
      0.01494308906905271982,
      0.01494308906905271982,
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      0.39770246065633879651,
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      0.35631158631326498298,
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      0.35631158631326498298,
      0.35631158631326498298,
      0.35631158631326498298,
      0.35631158631326498298,
      0.35631158631326498298,
      0.00597525511512164969,
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      0.00597525511512164969,
      0.00597525511512164969,
      0.00597525511512164969,
      0.00597525511512164969,
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      0.01006650964023972882,
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      0.01006650964023972882,
      0.01006650964023972882,
      0.01006650964023972882,
      0.01006650964023972882,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.47619683731341805322,
      0.05836635447459245785,
      0.05836635447459245785,
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      0.05836635447459245785,
      0.05836635447459245785,
      0.05836635447459245785,
      0.05836635447459245785,
      0.05836635447459245785,
      0.16495562918454476087,
      0.16495562918454476087,
      0.16495562918454476087,
      0.16495562918454476087,
      0.16495562918454476087,
      0.16495562918454476087,
      0.16495562918454476087,
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      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.15963984721353552398,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938,
      0.01331460692424766938 };

  double w_save[] = {
      0.00027672120207682897,
      0.00734944257707945050,
      0.00734944257707945050,
      0.00734944257707945050,
      0.00734944257707945050,
      0.00148740437072881278,
      0.00148740437072881278,
      0.00148740437072881278,
      0.00148740437072881278,
      0.00387693638421187639,
      0.00387693638421187639,
      0.00387693638421187639,
      0.00387693638421187639,
      0.01030614824039441553,
      0.01030614824039441553,
      0.01030614824039441553,
      0.01030614824039441553,
      0.00272673198843895789,
      0.00272673198843895789,
      0.00272673198843895789,
      0.00272673198843895789,
      0.00244629213408558690,
      0.00244629213408558690,
      0.00244629213408558690,
      0.00244629213408558690,
      0.00554924399761744409,
      0.00554924399761744409,
      0.00554924399761744409,
      0.00554924399761744409,
      0.00502262417466419701,
      0.00502262417466419701,
      0.00502262417466419701,
      0.00502262417466419701,
      0.00067111170084793834,
      0.00067111170084793834,
      0.00067111170084793834,
      0.00067111170084793834,
      0.00316873518673754882,
      0.00316873518673754882,
      0.00316873518673754882,
      0.00316873518673754882,
      0.00230707268685653678,
      0.00230707268685653678,
      0.00230707268685653678,
      0.00230707268685653678,
      0.00223355434035575010,
      0.00223355434035575010,
      0.00223355434035575010,
      0.00223355434035575010,
      0.00228685693132126217,
      0.00228685693132126217,
      0.00228685693132126217,
      0.00228685693132126217,
      0.00583888699964928409,
      0.00583888699964928409,
      0.00583888699964928409,
      0.00583888699964928409,
      0.00412038756118528714,
      0.00412038756118528714,
      0.00412038756118528714,
      0.00412038756118528714,
      0.00173037948168740284,
      0.00173037948168740284,
      0.00173037948168740284,
      0.00173037948168740284,
      0.00410680906602167630,
      0.00410680906602167630,
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      0.00410680906602167630,
      0.00635438948067259222,
      0.00635438948067259222,
      0.00635438948067259222,
      0.00635438948067259222,
      0.00043262101844333546,
      0.00043262101844333546,
      0.00043262101844333546,
      0.00043262101844333546,
      0.00345263292981801964,
      0.00345263292981801964,
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      0.00345263292981801964,
      0.00424071455736505301,
      0.00424071455736505301,
      0.00424071455736505301,
      0.00424071455736505301,
      0.00340526631678994204,
      0.00340526631678994204,
      0.00340526631678994204,
      0.00340526631678994204,
      0.00700942929302337137,
      0.00700942929302337137,
      0.00700942929302337137,
      0.00700942929302337137,
      0.00371184509938299149,
      0.00371184509938299149,
      0.00371184509938299149,
      0.00371184509938299149,
      0.00655769989421819445,
      0.00655769989421819445,
      0.00655769989421819445,
      0.00655769989421819445,
      0.00169996297833195664,
      0.00169996297833195664,
      0.00169996297833195664,
      0.00169996297833195664,
      0.00134740004835729398,
      0.00134740004835729398,
      0.00134740004835729398,
      0.00134740004835729398,
      0.00363396950461261376,
      0.00363396950461261376,
      0.00363396950461261376,
      0.00363396950461261376,
      0.00121619462900863910,
      0.00121619462900863910,
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      0.00549579708316756677,
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      0.00549579708316756677,
      0.00097330273562793888,
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      0.00097330273562793888,
      0.00725393003232855348,
      0.00725393003232855348,
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      0.00261600067059077025,
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      0.00261600067059077025,
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      0.00548333692337083910,
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      0.00150187064516151079,
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      0.00224211276351870626,
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      0.00224211276351870626,
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      0.00112651998000158019,
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      0.00423443304160556894,
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      0.00402977998773114843,
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      0.00366973681687540396,
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      0.00248888728757531682,
      0.00248888728757531682,
      0.00248888728757531682,
      0.00248888728757531682,
      0.00248888728757531682,
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      0.00248888728757531682,
      0.00048888922605729013,
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      0.00048888922605729013,
      0.00048888922605729013,
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      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00325264515509947555,
      0.00495505909145715732,
      0.00495505909145715732,
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      0.00495505909145715732,
      0.00495505909145715732,
      0.00495505909145715732,
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      0.00457024218025166729,
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      0.00457024218025166729,
      0.00457024218025166729,
      0.00457024218025166729,
      0.00481061764241353957,
      0.00481061764241353957,
      0.00481061764241353957,
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      0.00481061764241353957,
      0.00481061764241353957,
      0.00481061764241353957,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00538791794721728626,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339,
      0.00246928056742645339 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule17 ( int n, double x[], double y[], double z[], double w[] )

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

   rule17() returns the pyramid quadrature rule of precision 17.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.00000000000000000000,
      0.95241408581244602072,
      0.00000000000000000000,
     -0.95241408581244602072,
      0.00000000000000000000,
      0.08275692125030435775,
      0.00000000000000000000,
     -0.08275692125030435775,
      0.00000000000000000000,
      0.26578545043127727032,
      0.00000000000000000000,
     -0.26578545043127727032,
      0.00000000000000000000,
      0.81155940028479511827,
      0.00000000000000000000,
     -0.81155940028479511827,
      0.00000000000000000000,
      0.35232799954016802424,
      0.00000000000000000000,
     -0.35232799954016802424,
      0.00000000000000000000,
      0.60303771218972423984,
      0.00000000000000000000,
     -0.60303771218972423984,
      0.00000000000000000000,
      0.78402604202159054125,
      0.00000000000000000000,
     -0.78402604202159054125,
      0.00000000000000000000,
      0.49346472198646390561,
      0.00000000000000000000,
     -0.49346472198646390561,
      0.00000000000000000000,
      0.35038751648906635294,
      0.00000000000000000000,
     -0.35038751648906635294,
      0.00000000000000000000,
      0.00336404312107426752,
      0.00000000000000000000,
     -0.00336404312107426752,
      0.00000000000000000000,
      0.43074512679067450405,
      0.00000000000000000000,
     -0.43074512679067450405,
      0.00000000000000000000,
      0.59254801282947688890,
      0.00000000000000000000,
     -0.59254801282947688890,
      0.00000000000000000000,
      0.22550686036585329552,
      0.00000000000000000000,
     -0.22550686036585329552,
      0.00000000000000000000,
      0.63975863740336180729,
     -0.63975863740336180729,
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     -0.63975863740336180729,
      0.16463474879631256886,
     -0.16463474879631256886,
      0.16463474879631256886,
     -0.16463474879631256886,
      0.49303563319629611916,
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     -0.49303563319629611916,
      0.74791280396309745004,
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     -0.74791280396309745004,
      0.26251317864285966808,
     -0.26251317864285966808,
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     -0.26251317864285966808,
      0.17484215589868074003,
     -0.17484215589868074003,
      0.17484215589868074003,
     -0.17484215589868074003,
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      0.43512552408987620334,
     -0.43512552408987620334,
      0.43512552408987620334,
     -0.43512552408987620334,
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      0.00034532641662137929,
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      0.00034532641662137929,
      0.00034532641662137929,
      0.00034532641662137929,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241,
      0.00242508950332979241 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule18 ( int n, double x[], double y[], double z[], double w[] )

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

   rule18() returns the pyramid quadrature rule of precision 18.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.73869275831950009792,
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      0.76806657302952874300,
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     -0.31179783227055996031,
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     -0.31179783227055996031 };

  static double y_save[] = {
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      0.15557252093495238521,
      0.15557252093495238521,
      0.15557252093495238521,
      0.15557252093495238521,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.26467312835339185106,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.01193065095103094247,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976,
      0.00729413025649284976 };

  double w_save[] = {
      0.00013400520132544013,
      0.00653282923653435328,
      0.00653282923653435328,
      0.00653282923653435328,
      0.00653282923653435328,
      0.00246267782986044981,
      0.00246267782986044981,
      0.00246267782986044981,
      0.00246267782986044981,
      0.00236266319877590381,
      0.00236266319877590381,
      0.00236266319877590381,
      0.00236266319877590381,
      0.00241284626019594179,
      0.00241284626019594179,
      0.00241284626019594179,
      0.00241284626019594179,
      0.00563939918988414120,
      0.00563939918988414120,
      0.00563939918988414120,
      0.00563939918988414120,
      0.00530879464537392220,
      0.00530879464537392220,
      0.00530879464537392220,
      0.00530879464537392220,
      0.00330320967760970065,
      0.00330320967760970065,
      0.00330320967760970065,
      0.00330320967760970065,
      0.00715709687293028703,
      0.00715709687293028703,
      0.00715709687293028703,
      0.00715709687293028703,
      0.00356020900079922868,
      0.00356020900079922868,
      0.00356020900079922868,
      0.00356020900079922868,
      0.00286908910615377545,
      0.00286908910615377545,
      0.00286908910615377545,
      0.00286908910615377545,
      0.00119238795542696220,
      0.00119238795542696220,
      0.00119238795542696220,
      0.00119238795542696220,
      0.00023570897730274608,
      0.00023570897730274608,
      0.00023570897730274608,
      0.00023570897730274608,
      0.00332415202652309181,
      0.00332415202652309181,
      0.00332415202652309181,
      0.00332415202652309181,
      0.00064424498387906620,
      0.00064424498387906620,
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      0.00064424498387906620,
      0.00093040828397316332,
      0.00093040828397316332,
      0.00093040828397316332,
      0.00093040828397316332,
      0.00061531263855177734,
      0.00061531263855177734,
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      0.00061531263855177734,
      0.00028907482286127771,
      0.00028907482286127771,
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      0.00256243378291242307,
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      0.00256243378291242307,
      0.00197009710848232650,
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      0.00178378503667077598,
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      0.00046154884778758861,
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      0.00383567352584877853,
      0.00383567352584877853,
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      0.00424323389268952030,
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      0.00297709850925886605,
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      0.00208064231905125911,
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      0.00676296550091519920,
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      0.00569473175276393340,
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      0.00329345228074993208,
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      0.00319343074693561636,
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      0.00319343074693561636,
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      0.00300785963957934336,
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      0.00621018081426024000,
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      0.00151792165402074965,
      0.00151792165402074965,
      0.00151792165402074965,
      0.00151792165402074965 };

  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule19 ( int n, double x[], double y[], double z[], double w[] )

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

   rule19() returns the pyramid quadrature rule of precision 19.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
  static double x_save[] = {
      0.00000000000000000000,
      0.00000000000000000000,
      0.37365721634528792361,
      0.00000000000000000000,
     -0.37365721634528792361,
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  static double z_save[] = {
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      0.53408664015576723383 };

  double w_save[] = {
      0.00012870022397472401,
      0.00539076125430030910,
      0.00666687105780559754,
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  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}
void rule20 ( int n, double x[], double y[], double z[], double w[] )

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

   rule20() returns the pyramid quadrature rule of precision 20.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2023

  Author:

    John Burkardt

  Reference:

    Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

  Input:

    int n: the number of quadrature points for this rule.

  Output:

    double x[n], y[n], z[n]: the coordinates of quadrature points.

    double w[n]: the quadrature weights.
*/
{
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  r8vec_copy ( n, x_save, x );
  r8vec_copy ( n, y_save, y );
  r8vec_copy ( n, z_save, z );
  r8vec_copy ( n, w_save, w );

  return;
}