# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <cmath>
# include <ctime>

using namespace std;

# include "square_exactness.hpp"

int main ( );
void test01 ( );
void test02 ( );
void legendre_2d_set ( double a[], double b[], int nx, int ny, double x[], 
  double y[], double w[] );
void legendre_set ( int n, double x[], double w[] );
void padua_point_set ( int l, double x[], double y[] );
void padua_weight_set ( int l, double w[] );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for SQUARE_EXACTNESS_PRB.
//
//  Discussion:
//
//    SQUARE_EXACTNESS_PRB tests the SQUARE_EXACTNESS library.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    31 May 2014
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );

  cout << "\n";
  cout << "SQUARE_EXACTNESS_PRB\n";
  cout << "  C++ version\n";
  cout << "  Test the SQUARE_EXACTNESS library.\n";

  test01 ( );
  test02 ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "SQUARE_EXACTNESS_PRB\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void test01 ( )

//****************************************************************************80
//
//  Purpose:
//
//    TEST01 tests product Gauss-Legendre rules for the Legendre 2D integral.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    31 May 2014
//
//  Author:
//
//    John Burkardt
//
{
  double a[2];
  double b[2];
  int l;
  int n;
  int n_1d;
  int p_max;
  int t;
  double *w;
  double *x;
  double *y;

  a[0] = -1.0;
  a[1] = -1.0;
  b[0] = +1.0;
  b[1] = +1.0;

  cout << "\n";
  cout << "TEST01\n";
  cout << "  Product Gauss-Legendre rules for the 2D Legendre integral.\n";
  cout << "  Density function rho(x) = 1.\n";
  cout << "  Region: -1 <= x <= +1.\n";
  cout << "  Region: -1 <= y <= +1.\n";
  cout << "  Level: L\n";
  cout << "  Exactness: 2*L+1\n";
  cout << "  Order: N = (L+1)*(L+1)\n";

  for ( l = 0; l <= 5; l++ )
  {
    n_1d = l + 1;
    n = n_1d * n_1d;
    t = 2 * l + 1;

    w = new double[n];
    x = new double[n];
    y = new double[n];

    legendre_2d_set ( a, b, n_1d, n_1d, x, y, w );

    p_max = t + 1;
    legendre_2d_exactness ( a, b, n, x, y, w, p_max );

    delete [] x;
    delete [] y;
    delete [] w;
  }

  return;
}
//****************************************************************************80

void test02 ( )

//****************************************************************************80
//
//  Purpose:
//
//    TEST02 tests Padua rules for the Legendre 2D integral.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    31 May 2014
//
//  Author:
//
//    John Burkardt
//
{
  double a[2];
  double b[2];
  int l;
  int n;
  int p_max;
  int t;
  double *w;
  double *x;
  double *y;

  a[0] = -1.0;
  a[1] = -1.0;
  b[0] = +1.0;
  b[1] = +1.0;

  cout << "\n";
  cout << "TEST02\n";
  cout << "  Padua rule for the 2D Legendre integral.\n";
  cout << "  Density function rho(x) = 1.\n";
  cout << "  Region: -1 <= x <= +1.\n";
  cout << "  Region: -1 <= y <= +1.\n";
  cout << "  Level: L\n";
  cout << "  Exactness: L+1 when L is 0,\n";
  cout << "             L   otherwise.\n";
  cout << "  Order: N = (L+1)*(L+2)/2\n";

  for ( l = 0; l <= 5; l++ )
  {
    n = ( ( l + 1 ) * ( l + 2 ) ) / 2;

    w = new double[n];
    x = new double[n];
    y = new double[n];

    padua_point_set ( l, x, y );
    padua_weight_set ( l, w );
 
    if ( l == 0 )
    {
      p_max = l + 2;
    }
    else
    {
      p_max = l + 1;
    }

    legendre_2d_exactness ( a, b, n, x, y, w, p_max );

    delete [] w;
    delete [] x;
    delete [] y;
  }

  return;
}
//****************************************************************************80

void legendre_2d_set ( double a[], double b[], int nx, int ny, double x[], 
  double y[], double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    LEGENDRE_2D_SET: set a 2D Gauss-Legendre quadrature rule.
//
//  Discussion:
//
//    The integral:
//
//      integral ( a(2) <= y <= b(2) ) ( a(1) <= x <= b(1) ) f(x,y) dx dy
//
//    The quadrature rule:
//
//      sum ( 1 <= i <= n ) w(i) * f ( x(i),y(i) )
//
//    where n = nx * ny, the orders of the rule in the X and Y directions.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    31 May 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double A[2], B[2], the lower and upper integration
//    limits.
//
//    Input, int NX, NY, the orders in the X and Y directions.
//    NX and NY must be between 1 and 10.
//
//    Output, double X[N], Y[N], the abscissas.
//
//    Output, double W[N], the weights.
//
{
  int i;
  int j;
  int k;
  double *wx;
  double *wy;
  double *xx;
  double *yy;
//
//  Get the rules for [-1,+1].
//
  xx = ( double * ) malloc ( nx * sizeof ( double ) );
  wx = ( double * ) malloc ( nx * sizeof ( double ) );
  legendre_set ( nx, xx, wx );

  yy = ( double * ) malloc ( ny * sizeof ( double ) );
  wy = ( double * ) malloc ( ny * sizeof ( double ) );
  legendre_set ( ny, yy, wy );
//
//  Adjust from [-1,+1] to [A,B].
//
  for ( i = 0; i < nx; i++ )
  {
    xx[i] = ( ( 1.0 - xx[i] ) * a[0]   
            + ( 1.0 + xx[i] ) * b[0] ) 
            /   2.0;
    wx[i] = wx[i] * ( b[0] - a[0] ) / 2.0;
  }

  for ( j = 0; j < ny; j++ )
  {
    yy[j] = ( ( 1.0 - yy[j] ) * a[1]   
            + ( 1.0 + yy[j] ) * b[1] ) 
            /   2.0;
    wy[j] = wy[j] * ( b[1] - a[1] ) / 2.0;
  }
//
//  Compute the product rule.
//
  k = 0;
  for ( j = 0; j < ny; j++ )
  {
    for ( i = 0; i < nx; i++ )
    {
      x[k] = xx[i];
      y[k] = yy[j];
      w[k] = wx[i] * wy[j];
      k = k + 1;
    }
  }

  delete [] wx;
  delete [] wy;
  delete [] xx;
  delete [] yy;

  return;
}
//****************************************************************************80

void legendre_set ( int n, double x[], double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.
//
//  Discussion:
//
//    The integral:
//
//      Integral ( -1 <= X <= 1 ) F(X) dX
//
//    Quadrature rule:
//
//      Sum ( 1 <= I <= N ) W(I) * F ( X(I) )
//
//    The quadrature rule is exact for all polynomials through degree 2*N-1.
//
//    The abscissas are the zeroes of the Legendre polynomial P(N)(X).
//
//    Mathematica can compute the abscissas and weights of a Gauss-Legendre
//    rule of order N for the interval [A,B] with P digits of precision
//    by the commands:
//
//    Needs["NumericalDifferentialEquationAnalysis`"]
//    GaussianQuadratureWeights [ n, a, b, p ]
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    20 April 2010
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Milton Abramowitz, Irene Stegun,
//    Handbook of Mathematical Functions,
//    National Bureau of Standards, 1964,
//    ISBN: 0-486-61272-4,
//    LC: QA47.A34.
//
//    Vladimir Krylov,
//    Approximate Calculation of Integrals,
//    Dover, 2006,
//    ISBN: 0486445798.
//    LC: QA311.K713.
//
//    Arthur Stroud, Don Secrest,
//    Gaussian Quadrature Formulas,
//    Prentice Hall, 1966,
//    LC: QA299.4G3S7.
//
//    Stephen Wolfram,
//    The Mathematica Book,
//    Fourth Edition,
//    Cambridge University Press, 1999,
//    ISBN: 0-521-64314-7,
//    LC: QA76.95.W65.
//
//    Daniel Zwillinger, editor,
//    CRC Standard Mathematical Tables and Formulae,
//    30th Edition,
//    CRC Press, 1996,
//    ISBN: 0-8493-2479-3,
//    LC: QA47.M315.
//
//  Parameters:
//
//    Input, int N, the order.
//    N must be between 1 and 33 or 63/64/65, 127/128/129, 
//    255/256/257.
//
//    Output, double X[N], the abscissas.
//
//    Output, double W[N], the weights.
//
{
  if ( n == 1 )
  {
    x[0] = 0.000000000000000000000000000000;

    w[0] = 2.000000000000000000000000000000;
  }
  else if ( n == 2 )
  {
    x[0] = -0.577350269189625764509148780502;
    x[1] = 0.577350269189625764509148780502;

    w[0] = 1.000000000000000000000000000000;
    w[1] = 1.000000000000000000000000000000;
  }
  else if ( n == 3 )
  {
    x[0] = -0.774596669241483377035853079956;
    x[1] = 0.000000000000000000000000000000;
    x[2] = 0.774596669241483377035853079956;

    w[0] = 0.555555555555555555555555555556;
    w[1] = 0.888888888888888888888888888889;
    w[2] = 0.555555555555555555555555555556;
  }
  else if ( n == 4 )
  {
    x[0] = -0.861136311594052575223946488893;
    x[1] = -0.339981043584856264802665759103;
    x[2] = 0.339981043584856264802665759103;
    x[3] = 0.861136311594052575223946488893;

    w[0] = 0.347854845137453857373063949222;
    w[1] = 0.652145154862546142626936050778;
    w[2] = 0.652145154862546142626936050778;
    w[3] = 0.347854845137453857373063949222;
  }
  else if ( n == 5 )
  {
    x[0] = -0.906179845938663992797626878299;
    x[1] = -0.538469310105683091036314420700;
    x[2] = 0.000000000000000000000000000000;
    x[3] = 0.538469310105683091036314420700;
    x[4] = 0.906179845938663992797626878299;

    w[0] = 0.236926885056189087514264040720;
    w[1] = 0.478628670499366468041291514836;
    w[2] = 0.568888888888888888888888888889;
    w[3] = 0.478628670499366468041291514836;
    w[4] = 0.236926885056189087514264040720;
  }
  else if ( n == 6 )
  {
    x[0] = -0.932469514203152027812301554494;
    x[1] = -0.661209386466264513661399595020;
    x[2] = -0.238619186083196908630501721681;
    x[3] = 0.238619186083196908630501721681;
    x[4] = 0.661209386466264513661399595020;
    x[5] = 0.932469514203152027812301554494;

    w[0] = 0.171324492379170345040296142173;
    w[1] = 0.360761573048138607569833513838;
    w[2] = 0.467913934572691047389870343990;
    w[3] = 0.467913934572691047389870343990;
    w[4] = 0.360761573048138607569833513838;
    w[5] = 0.171324492379170345040296142173;
  }
  else if ( n == 7 )
  {
    x[0] = -0.949107912342758524526189684048;
    x[1] = -0.741531185599394439863864773281;
    x[2] = -0.405845151377397166906606412077;
    x[3] = 0.000000000000000000000000000000;
    x[4] = 0.405845151377397166906606412077;
    x[5] = 0.741531185599394439863864773281;
    x[6] = 0.949107912342758524526189684048;

    w[0] = 0.129484966168869693270611432679;
    w[1] = 0.279705391489276667901467771424;
    w[2] = 0.381830050505118944950369775489;
    w[3] = 0.417959183673469387755102040816;
    w[4] = 0.381830050505118944950369775489;
    w[5] = 0.279705391489276667901467771424;
    w[6] = 0.129484966168869693270611432679;
  }
  else if ( n == 8 )
  {
    x[0] = -0.960289856497536231683560868569;
    x[1] = -0.796666477413626739591553936476;
    x[2] = -0.525532409916328985817739049189;
    x[3] = -0.183434642495649804939476142360;
    x[4] = 0.183434642495649804939476142360;
    x[5] = 0.525532409916328985817739049189;
    x[6] = 0.796666477413626739591553936476;
    x[7] = 0.960289856497536231683560868569;

    w[0] = 0.101228536290376259152531354310;
    w[1] = 0.222381034453374470544355994426;
    w[2] = 0.313706645877887287337962201987;
    w[3] = 0.362683783378361982965150449277;
    w[4] = 0.362683783378361982965150449277;
    w[5] = 0.313706645877887287337962201987;
    w[6] = 0.222381034453374470544355994426;
    w[7] = 0.101228536290376259152531354310;
  }
  else if ( n == 9 )
  {
    x[0] = -0.968160239507626089835576203;
    x[1] = -0.836031107326635794299429788;
    x[2] = -0.613371432700590397308702039;
    x[3] = -0.324253423403808929038538015;
    x[4] = 0.000000000000000000000000000;
    x[5] = 0.324253423403808929038538015;
    x[6] = 0.613371432700590397308702039;
    x[7] = 0.836031107326635794299429788;
    x[8] = 0.968160239507626089835576203;

    w[0] = 0.081274388361574411971892158111;
    w[1] = 0.18064816069485740405847203124;
    w[2] = 0.26061069640293546231874286942;
    w[3] = 0.31234707704000284006863040658;
    w[4] = 0.33023935500125976316452506929;
    w[5] = 0.31234707704000284006863040658;
    w[6] = 0.26061069640293546231874286942;
    w[7] = 0.18064816069485740405847203124;
    w[8] = 0.081274388361574411971892158111;
  }
  else if ( n == 10 )
  {
    x[0] = -0.973906528517171720077964012;
    x[1] = -0.865063366688984510732096688;
    x[2] = -0.679409568299024406234327365;
    x[3] = -0.433395394129247190799265943;
    x[4] = -0.148874338981631210884826001;
    x[5] = 0.148874338981631210884826001;
    x[6] = 0.433395394129247190799265943;
    x[7] = 0.679409568299024406234327365;
    x[8] = 0.865063366688984510732096688;
    x[9] = 0.973906528517171720077964012;

    w[0] = 0.066671344308688137593568809893;
    w[1] = 0.14945134915058059314577633966;
    w[2] = 0.21908636251598204399553493423;
    w[3] = 0.26926671930999635509122692157;
    w[4] = 0.29552422471475287017389299465;
    w[5] = 0.29552422471475287017389299465;
    w[6] = 0.26926671930999635509122692157;
    w[7] = 0.21908636251598204399553493423;
    w[8] = 0.14945134915058059314577633966;
    w[9] = 0.066671344308688137593568809893;
  }
  else
  {
    cerr << "\n";
    cerr << "LEGENDRE_SET - Fatal error!\n";
    cerr << "  Illegal value of N = " << n << "\n";
    cerr << "  Legal values are 1 to 10\n";
    exit ( 1 );
  }
  return;
}
//****************************************************************************80

void padua_point_set ( int l, double x[], double y[] )

//****************************************************************************80
//
//  Purpose:
//
//    PADUA_POINT_SET sets the Padua points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    29 May 2014
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Marco Caliari, Stefano de Marchi, Marco Vianello,
//    Bivariate interpolation on the square at new nodal sets,
//    Applied Mathematics and Computation,
//    Volume 165, Number 2, 2005, pages 261-274.
//
//  Parameters:
//
//    Input, int L, the level.
//    0 <= L <= 10.
//
//    Output, double X[N], Y[N], the Padua points.
//
{
  if ( l == 0 )
  {
    x[ 0] =  0.000000000000000;
    y[ 0] =  0.000000000000000;    
  }
  else if ( l == 1 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;    
    x[ 1] = -1.000000000000000;
    y[ 1] =  1.000000000000000;    
    x[ 2] =  1.000000000000000;
    y[ 2] =  0.000000000000000;    
  }
  else if ( l == 2 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;    
    x[ 1] = -1.000000000000000;
    y[ 1] =  0.5000000000000001;
    x[ 2] =  0.000000000000000;
    y[ 2] = -0.4999999999999998;    
    x[ 3] =  0.000000000000000;
    y[ 3] =  1.000000000000000;    
    x[ 4] =  1.000000000000000;
    y[ 4] = -1.000000000000000;
    x[ 5] =  1.000000000000000;
    y[ 5] =  0.5000000000000001;    
  }
  else if ( l == 3 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;    
    x[ 1] = -1.000000000000000;
    y[ 1] =  0.000000000000000;
    x[ 2] = -1.000000000000000;
    y[ 2] =  1.000000000000000;    
    x[ 3] = -0.4999999999999998;
    y[ 3] = -0.7071067811865475;    
    x[ 4] = -0.4999999999999998;
    y[ 4] =  0.7071067811865476;    
    x[ 5] =  0.5000000000000001;
    y[ 5] = -1.000000000000000;    
    x[ 6] =  0.5000000000000001;
    y[ 6] =  0.000000000000000;    
    x[ 7] =  0.5000000000000001;
    y[ 7] =  1.000000000000000;    
    x[ 8] =  1.000000000000000;
    y[ 8] = -0.7071067811865475;    
    x[ 9] =  1.000000000000000;
    y[ 9] =  0.7071067811865476;    
  }
  else if ( l == 4 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;   
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.3090169943749473;    
    x[ 2] = -1.000000000000000;
    y[ 2] =  0.8090169943749475;    
    x[ 3] = -0.7071067811865475;
    y[ 3] = -0.8090169943749473;    
    x[ 4] = -0.7071067811865475;
    y[ 4] =  0.3090169943749475;
    x[ 5] = -0.7071067811865475;
    y[ 5] =  1.000000000000000;    
    x[ 6] =  0.000000000000000;
    y[ 6] = -1.000000000000000;   
    x[ 7] =  0.000000000000000;
    y[ 7] = -0.3090169943749473;    
    x[ 8] =  0.000000000000000;
    y[ 8] =  0.8090169943749475;    
    x[ 9] =  0.7071067811865476;
    y[ 9] = -0.8090169943749473;    
    x[10] =  0.7071067811865476;
    y[10] =  0.3090169943749475; 
    x[11] =  0.7071067811865476;
    y[11] =  1.000000000000000;    
    x[12] =  1.000000000000000;
    y[12] = -1.000000000000000;   
    x[13] =  1.000000000000000;
    y[13] = -0.3090169943749473;    
    x[14] =  1.000000000000000;
    y[14] =  0.8090169943749475;    
  }
  else if ( l == 5 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.4999999999999998;    
    x[ 2] = -1.000000000000000;
    y[ 2] =  0.5000000000000001;    
    x[ 3] = -1.000000000000000;
    y[ 3] =  1.000000000000000;    
    x[ 4] = -0.8090169943749473;
    y[ 4] = -0.8660254037844387;
    x[ 5] = -0.8090169943749473;
    y[ 5] =  0.000000000000000;   
    x[ 6] = -0.8090169943749473;
    y[ 6] =  0.8660254037844387;
    x[ 7] = -0.3090169943749473;
    y[ 7] = -1.000000000000000;   
    x[ 8] = -0.3090169943749473;
    y[ 8] = -0.4999999999999998;    
    x[ 9] = -0.3090169943749473;
    y[ 9] =  0.5000000000000001;
    x[10] = -0.3090169943749473;
    y[10] =  1.000000000000000;   
    x[11] =  0.3090169943749475;
    y[11] = -0.8660254037844387;
    x[12] =  0.3090169943749475;
    y[12] =  0.000000000000000;    
    x[13] =  0.3090169943749475;
    y[13] =  0.8660254037844387;    
    x[14] =  0.8090169943749475;
    y[14] = -1.000000000000000;    
    x[15] =  0.8090169943749475;
    y[15] = -0.4999999999999998;    
    x[16] =  0.8090169943749475;
    y[16] =  0.5000000000000001;
    x[17] =  0.8090169943749475;
    y[17] =  1.000000000000000;
    x[18] =  1.000000000000000;
    y[18] = -0.8660254037844387;    
    x[19] =  1.000000000000000;
    y[19] =  0.000000000000000;
    x[20] =  1.000000000000000;
    y[20] =  0.8660254037844387; 
  }
  else if ( l == 6 )
  {   
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;   
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.6234898018587335;    
    x[ 2] = -1.000000000000000;
    y[ 2] =  0.2225209339563144;    
    x[ 3] = -1.000000000000000;
    y[ 3] =  0.9009688679024191;    
    x[ 4] = -0.8660254037844387;
    y[ 4] = -0.9009688679024190;    
    x[ 5] = -0.8660254037844387;
    y[ 5] = -0.2225209339563143;    
    x[ 6] = -0.8660254037844387;
    y[ 6] =  0.6234898018587336;
    x[ 7] = -0.8660254037844387;
    y[ 7] =  1.000000000000000;
    x[ 8] = -0.4999999999999998;
    y[ 8] = -1.000000000000000;   
    x[ 9] = -0.4999999999999998;
    y[ 9] = -0.6234898018587335;    
    x[10] = -0.4999999999999998;
    y[10] =  0.2225209339563144;    
    x[11] = -0.4999999999999998;
    y[11] =  0.9009688679024191;    
    x[12] =  0.000000000000000;
    y[12] = -0.9009688679024190;    
    x[13] =  0.000000000000000;
    y[13] = -0.2225209339563143;
    x[14] =  0.000000000000000;
    y[14] =  0.6234898018587336;    
    x[15] =  0.000000000000000;
    y[15] =  1.000000000000000;
    x[16] =  0.5000000000000001;
    y[16] = -1.000000000000000;    
    x[17] =  0.5000000000000001;
    y[17] = -0.6234898018587335;    
    x[18] =  0.5000000000000001;
    y[18] =  0.2225209339563144;    
    x[19] =  0.5000000000000001;
    y[19] =  0.9009688679024191;    
    x[20] =  0.8660254037844387;
    y[20] = -0.9009688679024190;    
    x[21] =  0.8660254037844387;
    y[21] = -0.2225209339563143;    
    x[22] =  0.8660254037844387;
    y[22] =  0.6234898018587336;
    x[23] =  0.8660254037844387;
    y[23] =  1.000000000000000;    
    x[24] =  1.000000000000000;
    y[24] = -1.000000000000000;   
    x[25] =  1.000000000000000;
    y[25] = -0.6234898018587335;    
    x[26] =  1.000000000000000;
    y[26] =  0.2225209339563144;
    x[27] =  1.000000000000000;
    y[27] =  0.9009688679024191;
  }
  else if ( l == 7 )
  {    
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.7071067811865475;    
    x[ 2] = -1.000000000000000;
    y[ 2] =  0.000000000000000;   
    x[ 3] = -1.000000000000000;
    y[ 3] =  0.7071067811865476; 
    x[ 4] = -1.000000000000000;
    y[ 4] =  1.000000000000000;    
    x[ 5] = -0.9009688679024190;
    y[ 5] = -0.9238795325112867;    
    x[ 6] = -0.9009688679024190;
    y[ 6] = -0.3826834323650897;    
    x[ 7] = -0.9009688679024190;
    y[ 7] =  0.3826834323650898;    
    x[ 8] = -0.9009688679024190;
    y[ 8] =  0.9238795325112867;
    x[ 9] = -0.6234898018587335;
    y[ 9] = -1.000000000000000;   
    x[10] = -0.6234898018587335;
    y[10] = -0.7071067811865475;
    x[11] = -0.6234898018587335;
    y[11] =  0.000000000000000;   
    x[12] = -0.6234898018587335;
    y[12] =  0.7071067811865476;
    x[13] = -0.6234898018587335;
    y[13] =  1.000000000000000;   
    x[14] = -0.2225209339563143;
    y[14] = -0.9238795325112867;    
    x[15] = -0.2225209339563143;
    y[15] = -0.3826834323650897;    
    x[16] = -0.2225209339563143;
    y[16] =  0.3826834323650898;    
    x[17] = -0.2225209339563143;
    y[17] =  0.9238795325112867;
    x[18] =  0.2225209339563144;
    y[18] = -1.000000000000000;   
    x[19] =  0.2225209339563144;
    y[19] = -0.7071067811865475;
    x[20] =  0.2225209339563144;
    y[20] =  0.000000000000000;
    x[21] =  0.2225209339563144;
    y[21] =  0.7071067811865476;
    x[22] =  0.2225209339563144;
    y[22] =  1.000000000000000;   
    x[23] =  0.6234898018587336;
    y[23] = -0.9238795325112867;    
    x[24] =  0.6234898018587336;
    y[24] = -0.3826834323650897;    
    x[25] =  0.6234898018587336;
    y[25] =  0.3826834323650898;    
    x[26] =  0.6234898018587336;
    y[26] =  0.9238795325112867;
    x[27] =  0.9009688679024191;
    y[27] = -1.000000000000000;   
    x[28] =  0.9009688679024191;
    y[28] = -0.7071067811865475;
    x[29] =  0.9009688679024191;
    y[29] =  0.000000000000000;   
    x[30] =  0.9009688679024191;
    y[30] =  0.7071067811865476;
    x[31] =  0.9009688679024191;
    y[31] =  1.000000000000000;   
    x[32] =  1.000000000000000;
    y[32] = -0.9238795325112867;    
    x[33] =  1.000000000000000;
    y[33] = -0.3826834323650897;    
    x[34] =  1.000000000000000;
    y[34] =  0.3826834323650898;    
    x[35] =  1.000000000000000;
    y[35] =  0.9238795325112867; 
  }
  else if ( l == 8 )
  { 
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;   
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.7660444431189779;    
    x[ 2] = -1.000000000000000;
    y[ 2] = -0.1736481776669303;    
    x[ 3] = -1.000000000000000;
    y[ 3] =  0.5000000000000001;    
    x[ 4] = -1.000000000000000;
    y[ 4] =  0.9396926207859084;    
    x[ 5] = -0.9238795325112867;
    y[ 5] = -0.9396926207859083;    
    x[ 6] = -0.9238795325112867;
    y[ 6] = -0.4999999999999998;    
    x[ 7] = -0.9238795325112867;
    y[ 7] =  0.1736481776669304;    
    x[ 8] = -0.9238795325112867;
    y[ 8] =  0.7660444431189780;
    x[ 9] = -0.9238795325112867;
    y[ 9] =  1.000000000000000;
    x[10] = -0.7071067811865475;
    y[10] = -1.000000000000000;   
    x[11] = -0.7071067811865475;
    y[11] = -0.7660444431189779;    
    x[12] = -0.7071067811865475;
    y[12] = -0.1736481776669303;    
    x[13] = -0.7071067811865475;
    y[13] =  0.5000000000000001;    
    x[14] = -0.7071067811865475;
    y[14] =  0.9396926207859084;    
    x[15] = -0.3826834323650897;
    y[15] = -0.9396926207859083;    
    x[16] = -0.3826834323650897;
    y[16] = -0.4999999999999998;    
    x[17] = -0.3826834323650897;
    y[17] =  0.1736481776669304;    
    x[18] = -0.3826834323650897;
    y[18] =  0.7660444431189780;
    x[19] = -0.3826834323650897;
    y[19] =  1.000000000000000;    
    x[20] =  0.000000000000000;
    y[20] = -1.000000000000000;   
    x[21] =  0.000000000000000;
    y[21] = -0.7660444431189779;    
    x[22] =  0.000000000000000;
    y[22] = -0.1736481776669303;    
    x[23] =  0.000000000000000;
    y[23] =  0.5000000000000001;    
    x[24] =  0.000000000000000;
    y[24] =  0.9396926207859084;    
    x[25] =  0.3826834323650898;
    y[25] = -0.9396926207859083;    
    x[26] =  0.3826834323650898;
    y[26] = -0.4999999999999998;    
    x[27] =  0.3826834323650898;
    y[27] =  0.1736481776669304;    
    x[28] =  0.3826834323650898;
    y[28] =  0.7660444431189780;
    x[29] =  0.3826834323650898;
    y[29] =  1.000000000000000;
    x[30] =  0.7071067811865476;
    y[30] = -1.000000000000000;   
    x[31] =  0.7071067811865476;
    y[31] = -0.7660444431189779;    
    x[32] =  0.7071067811865476;
    y[32] = -0.1736481776669303;    
    x[33] =  0.7071067811865476;
    y[33] =  0.5000000000000001;    
    x[34] =  0.7071067811865476;
    y[34] =  0.9396926207859084;    
    x[35] =  0.9238795325112867;
    y[35] = -0.9396926207859083;    
    x[36] =  0.9238795325112867;
    y[36] = -0.4999999999999998;    
    x[37] =  0.9238795325112867;
    y[37] =  0.1736481776669304;    
    x[38] =  0.9238795325112867;
    y[38] =  0.7660444431189780;
    x[39] =  0.9238795325112867;
    y[39] =  1.000000000000000;    
    x[40] =  1.000000000000000;
    y[40] = -1.000000000000000;   
    x[41] =  1.000000000000000;
    y[41] = -0.7660444431189779;    
    x[42] =  1.000000000000000;
    y[42] = -0.1736481776669303;    
    x[43] =  1.000000000000000;
    y[43] =  0.5000000000000001;
    x[44] =  1.000000000000000;
    y[44] =  0.9396926207859084;   
  }
  else if ( l == 9 )
  { 
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;   
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.8090169943749473;    
    x[ 2] = -1.000000000000000;
    y[ 2] = -0.3090169943749473;    
    x[ 3] = -1.000000000000000;
    y[ 3] =  0.3090169943749475;
    x[ 4] = -1.000000000000000;
    y[ 4] =  0.8090169943749475;    
    x[ 5] = -1.000000000000000;
    y[ 5] =  1.000000000000000;   
    x[ 6] = -0.9396926207859083;
    y[ 6] = -0.9510565162951535;    
    x[ 7] = -0.9396926207859083;
    y[ 7] = -0.5877852522924730;
    x[ 8] = -0.9396926207859083;
    y[ 8] =  0.000000000000000;   
    x[ 9] = -0.9396926207859083;
    y[ 9] =  0.5877852522924731;    
    x[10] = -0.9396926207859083;
    y[10] =  0.9510565162951535;
    x[11] = -0.7660444431189779;
    y[11] = -1.000000000000000;   
    x[12] = -0.7660444431189779;
    y[12] = -0.8090169943749473;    
    x[13] = -0.7660444431189779;
    y[13] = -0.3090169943749473;    
    x[14] = -0.7660444431189779;
    y[14] =  0.3090169943749475;    
    x[15] = -0.7660444431189779;
    y[15] =  0.8090169943749475; 
    x[16] = -0.7660444431189779;
    y[16] =  1.000000000000000;   
    x[17] = -0.4999999999999998;
    y[17] = -0.9510565162951535;    
    x[18] = -0.4999999999999998;
    y[18] = -0.5877852522924730;
    x[19] = -0.4999999999999998;
    y[19] =  0.000000000000000;   
    x[20] = -0.4999999999999998;
    y[20] =  0.5877852522924731;    
    x[21] = -0.4999999999999998;
    y[21] =  0.9510565162951535;
    x[22] = -0.1736481776669303;
    y[22] = -1.000000000000000;   
    x[23] = -0.1736481776669303;
    y[23] = -0.8090169943749473;    
    x[24] = -0.1736481776669303;
    y[24] = -0.3090169943749473;    
    x[25] = -0.1736481776669303;
    y[25] =  0.3090169943749475;    
    x[26] = -0.1736481776669303;
    y[26] =  0.8090169943749475;
    x[27] = -0.1736481776669303;
    y[27] =  1.000000000000000;   
    x[28] =  0.1736481776669304;
    y[28] = -0.9510565162951535;    
    x[29] =  0.1736481776669304;
    y[29] = -0.5877852522924730;
    x[30] =  0.1736481776669304;
    y[30] =  0.000000000000000;   
    x[31] =  0.1736481776669304;
    y[31] =  0.5877852522924731;    
    x[32] =  0.1736481776669304;
    y[32] =  0.9510565162951535;
    x[33] =  0.5000000000000001;
    y[33] = -1.000000000000000;   
    x[34] =  0.5000000000000001;
    y[34] = -0.8090169943749473;    
    x[35] =  0.5000000000000001;
    y[35] = -0.3090169943749473;    
    x[36] =  0.5000000000000001;
    y[36] =  0.3090169943749475;    
    x[37] =  0.5000000000000001;
    y[37] =  0.8090169943749475;
    x[38] =  0.5000000000000001;
    y[38] =  1.000000000000000;   
    x[39] =  0.7660444431189780;
    y[39] = -0.9510565162951535;    
    x[40] =  0.7660444431189780;
    y[40] = -0.5877852522924730;
    x[41] =  0.7660444431189780;
    y[41] =  0.000000000000000;   
    x[42] =  0.7660444431189780;
    y[42] =  0.5877852522924731;    
    x[43] =  0.7660444431189780;
    y[43] =  0.9510565162951535;
    x[44] =  0.9396926207859084;
    y[44] = -1.000000000000000;   
    x[45] =  0.9396926207859084;
    y[45] = -0.8090169943749473;    
    x[46] =  0.9396926207859084;
    y[46] = -0.3090169943749473;    
    x[47] =  0.9396926207859084;
    y[47] =  0.3090169943749475;    
    x[48] =  0.9396926207859084;
    y[48] =  0.8090169943749475;
    x[49] =  0.9396926207859084;
    y[49] =  1.000000000000000;   
    x[50] =  1.000000000000000;
    y[50] = -0.9510565162951535;
    x[51] =  1.000000000000000;
    y[51] = -0.5877852522924730;    
    x[52] =  1.000000000000000;
    y[52] =  0.000000000000000;   
    x[53] =  1.000000000000000;
    y[53] =  0.5877852522924731;
    x[54] =  1.000000000000000;
    y[54] =  0.9510565162951535;    
  }
  else if ( l == 10 )
  {
    x[ 0] = -1.000000000000000;
    y[ 0] = -1.000000000000000;   
    x[ 1] = -1.000000000000000;
    y[ 1] = -0.8412535328311811;    
    x[ 2] = -1.000000000000000;
    y[ 2] = -0.4154150130018863;    
    x[ 3] = -1.000000000000000;
    y[ 3] =  0.1423148382732851;    
    x[ 4] = -1.000000000000000;
    y[ 4] =  0.6548607339452851;    
    x[ 5] = -1.000000000000000;
    y[ 5] =  0.9594929736144974;    
    x[ 6] = -0.9510565162951535;
    y[ 6] = -0.9594929736144974;    
    x[ 7] = -0.9510565162951535;
    y[ 7] = -0.6548607339452850;    
    x[ 8] = -0.9510565162951535;
    y[ 8] = -0.1423148382732850;    
    x[ 9] = -0.9510565162951535;
    y[ 9] =  0.4154150130018864;    
    x[10] = -0.9510565162951535;
    y[10] =  0.8412535328311812;
    x[11] = -0.9510565162951535;
    y[11] =  1.000000000000000;
    x[12] = -0.8090169943749473;
    y[12] = -1.000000000000000;   
    x[13] = -0.8090169943749473;
    y[13] = -0.8412535328311811;    
    x[14] = -0.8090169943749473;
    y[14] = -0.4154150130018863;    
    x[15] = -0.8090169943749473;
    y[15] =  0.1423148382732851;    
    x[16] = -0.8090169943749473;
    y[16] =  0.6548607339452851;    
    x[17] = -0.8090169943749473;
    y[17] =  0.9594929736144974;    
    x[18] = -0.5877852522924730;
    y[18] = -0.9594929736144974;    
    x[19] = -0.5877852522924730;
    y[19] = -0.6548607339452850;    
    x[20] = -0.5877852522924730;
    y[20] = -0.1423148382732850;    
    x[21] = -0.5877852522924730;
    y[21] =  0.4154150130018864;    
    x[22] = -0.5877852522924730;
    y[22] =  0.8412535328311812;
    x[23] = -0.5877852522924730;
    y[23] =  1.000000000000000;
    x[24] = -0.3090169943749473;
    y[24] = -1.000000000000000;   
    x[25] = -0.3090169943749473;
    y[25] = -0.8412535328311811;    
    x[26] = -0.3090169943749473;
    y[26] = -0.4154150130018863;    
    x[27] = -0.3090169943749473;
    y[27] =  0.1423148382732851;    
    x[28] = -0.3090169943749473;
    y[28] =  0.6548607339452851;    
    x[29] = -0.3090169943749473;
    y[29] =  0.9594929736144974;    
    x[30] =  0.000000000000000;
    y[30] = -0.9594929736144974;    
    x[31] =  0.000000000000000;
    y[31] = -0.6548607339452850;    
    x[32] =  0.000000000000000;
    y[32] = -0.1423148382732850;    
    x[33] =  0.000000000000000;
    y[33] =  0.4154150130018864;
    x[34] =  0.000000000000000;
    y[34] =  0.8412535328311812;    
    x[35] =  0.000000000000000;
    y[35] =  1.000000000000000; 
    x[36] =  0.3090169943749475;
    y[36] = -1.000000000000000;    
    x[37] =  0.3090169943749475;
    y[37] = -0.8412535328311811;    
    x[38] =  0.3090169943749475;
    y[38] = -0.4154150130018863;    
    x[39] =  0.3090169943749475;
    y[39] =  0.1423148382732851;    
    x[40] =  0.3090169943749475;
    y[40] =  0.6548607339452851;    
    x[41] =  0.3090169943749475;
    y[41] =  0.9594929736144974;    
    x[42] =  0.5877852522924731;
    y[42] = -0.9594929736144974;    
    x[43] =  0.5877852522924731;
    y[43] = -0.6548607339452850;    
    x[44] =  0.5877852522924731;
    y[44] = -0.1423148382732850;    
    x[45] =  0.5877852522924731;
    y[45] =  0.4154150130018864;    
    x[46] =  0.5877852522924731;
    y[46] =  0.8412535328311812;
    x[47] =  0.5877852522924731;
    y[47] =  1.000000000000000;
    x[48] =  0.8090169943749475;
    y[48] = -1.000000000000000;   
    x[49] =  0.8090169943749475;
    y[49] = -0.8412535328311811;    
    x[50] =  0.8090169943749475;
    y[50] = -0.4154150130018863;    
    x[51] =  0.8090169943749475;
    y[51] =  0.1423148382732851;    
    x[52] =  0.8090169943749475;
    y[52] =  0.6548607339452851;    
    x[53] =  0.8090169943749475;
    y[53] =  0.9594929736144974;    
    x[54] =  0.9510565162951535;
    y[54] = -0.9594929736144974;    
    x[55] =  0.9510565162951535;
    y[55] = -0.6548607339452850;    
    x[56] =  0.9510565162951535;
    y[56] = -0.1423148382732850;    
    x[57] =  0.9510565162951535;
    y[57] =  0.4154150130018864;    
    x[58] =  0.9510565162951535;
    y[58] =  0.8412535328311812;
    x[59] =  0.9510565162951535;
    y[59] =  1.000000000000000;    
    x[60] =  1.000000000000000;
    y[60] = -1.000000000000000;   
    x[61] =  1.000000000000000;
    y[61] = -0.8412535328311811;    
    x[62] =  1.000000000000000;
    y[62] = -0.4154150130018863;    
    x[63] =  1.000000000000000;
    y[63] =  0.1423148382732851;    
    x[64] =  1.000000000000000;
    y[64] =  0.6548607339452851; 
    x[65] =  1.000000000000000;
    y[65] =  0.9594929736144974;
  }
  else
  {
    cerr << "\n";
    cerr << "PADUA_POINT_SET - Fatal error!\n";
    cerr << "  Illegal value of L = " << l << "\n";
    cerr << "  Legal values are 1 through 10.\n";
    exit ( 1 );
  }

  return;
}
//****************************************************************************80

void padua_weight_set ( int l, double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    PADUA_WEIGHT_SET sets quadrature weights for the Padua points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    30 May 2014
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Marco Caliari, Stefano de Marchi, Marco Vianello,
//    Bivariate interpolation on the square at new nodal sets,
//    Applied Mathematics and Computation,
//    Volume 165, Number 2, 2005, pages 261-274.
//
//  Parameters:
//
//    Input, int L, the level.
//    0 <= L <= 10.
//
//    Output, double W[N], the quadrature weights.
//
{
  if ( l == 0 )
  {
    w[ 0] =    4.000000000000000E+00;
  }
  else if ( l == 1 )
  {
    w[ 0] =    1.000000000000000E+00;
    w[ 1] =    1.000000000000000E+00;
    w[ 2] =    2.000000000000000E+00;
  }
  else if ( l == 2 )
  {
    w[ 0] =   0.0E+00;
    w[ 1] =   0.6666666666666663E+00;
    w[ 2] =    2.222222222222222E+00;
    w[ 3] =   0.4444444444444444E+00;
    w[ 4] =   0.0E+00;
    w[ 5] =   0.6666666666666664E+00;
  }
  else if ( l == 3 )
  {
    w[ 0] =  -0.5555555555555480E-01;
    w[ 1] =   0.3333333333333331E+00;
    w[ 2] =  -0.5555555555555580E-01;
    w[ 3] =   0.8888888888888886E+00;
    w[ 4] =   0.8888888888888893E+00;
    w[ 5] =   0.2222222222222224E+00;
    w[ 6] =    1.333333333333333E+00;
    w[ 7] =   0.2222222222222220E+00;
    w[ 8] =   0.1111111111111109E+00;
    w[ 9] =   0.1111111111111112E+00;
  }
  else if ( l == 4 )
  {
    w[ 0] =  -0.8888888888888932E-02;
    w[ 1] =   0.8104919101110961E-01;
    w[ 2] =   0.6117303121111219E-01;
    w[ 3] =   0.3874097078666789E+00;
    w[ 4] =   0.6259236254666545E+00;
    w[ 5] =   0.5333333333333362E-01;
    w[ 6] =   0.7111111111111067E-01;
    w[ 7] =   0.9830822022444241E+00;
    w[ 8] =   0.5458066866444642E+00;
    w[ 9] =   0.3874097078666780E+00;
    w[10] =   0.6259236254666568E+00;
    w[11] =   0.5333333333333383E-01;
    w[12] =  -0.8888888888888703E-02;
    w[13] =   0.8104919101110968E-01;
    w[14] =   0.6117303121111135E-01;
  }
  else if ( l == 5 )
  {
    w[ 0] =  -0.1037037037037093E-01;
    w[ 1] =   0.5037037037036911E-01;
    w[ 2] =   0.5037037037037081E-01;
    w[ 3] =  -0.1037037037036947E-01;
    w[ 4] =   0.1876963678740801E+00;
    w[ 5] =   0.3460933466518654E+00;
    w[ 6] =   0.1876963678740763E+00;
    w[ 7] =   0.4514390511851724E-01;
    w[ 8] =   0.5541130536814713E+00;
    w[ 9] =   0.5541130536814728E+00;
    w[10] =   0.4514390511851834E-01;
    w[11] =   0.2804517802740705E+00;
    w[12] =   0.6376103570518378E+00;
    w[13] =   0.2804517802740683E+00;
    w[14] =   0.3189313191851883E-01;
    w[15] =   0.3288499092814910E+00;
    w[16] =   0.3288499092814925E+00;
    w[17] =   0.3189313191851956E-01;
    w[18] =   0.2074074074074123E-01;
    w[19] =   0.3851851851851849E-01;
    w[20] =   0.2074074074074051E-01;
  }
  else if ( l == 6 )
  {
    w[ 0] =  -0.3023431594858565E-02;
    w[ 1] =   0.1957267632451884E-01;
    w[ 2] =   0.2633929313290840E-01;
    w[ 3] =   0.1425431928029237E-01;
    w[ 4] =   0.1006383046329639E+00;
    w[ 5] =   0.2208900184526934E+00;
    w[ 6] =   0.1743144584714012E+00;
    w[ 7] =   0.1209372637943976E-01;
    w[ 8] =   0.1934996220710680E-01;
    w[ 9] =   0.3245064820875231E+00;
    w[10] =   0.4027058473592984E+00;
    w[11] =   0.1677234226317961E+00;
    w[12] =   0.1953319357827178E+00;
    w[13] =   0.4489633053035124E+00;
    w[14] =   0.3721824611057551E+00;
    w[15] =   0.2479213907785274E-01;
    w[16] =   0.1934996220710561E-01;
    w[17] =   0.3245064820875153E+00;
    w[18] =   0.4027058473592959E+00;
    w[19] =   0.1677234226317944E+00;
    w[20] =   0.1006383046329745E+00;
    w[21] =   0.2208900184526933E+00;
    w[22] =   0.1743144584714027E+00;
    w[23] =   0.1209372637944051E-01;
    w[24] =  -0.3023431594861990E-02;
    w[25] =   0.1957267632451757E-01;
    w[26] =   0.2633929313290797E-01;
    w[27] =   0.1425431928029198E-01;
  }
  else if ( l == 7 )
  {
    w[ 0] =  -0.3287981859413765E-02;
    w[ 1] =   0.1337868480725671E-01;
    w[ 2] =   0.2063492063491996E-01;
    w[ 3] =   0.1337868480725546E-01;
    w[ 4] =  -0.3287981859408898E-02;
    w[ 5] =   0.5949324721885513E-01;
    w[ 6] =   0.1306477599993571E+00;
    w[ 7] =   0.1306477599993581E+00;
    w[ 8] =   0.5949324721885061E-01;
    w[ 9] =   0.1263869091685831E-01;
    w[10] =   0.1979944935601103E+00;
    w[11] =   0.2832184784823740E+00;
    w[12] =   0.1979944935601143E+00;
    w[13] =   0.1263869091685747E-01;
    w[14] =   0.1221817987389771E+00;
    w[15] =   0.3150266070593529E+00;
    w[16] =   0.3150266070593440E+00;
    w[17] =   0.1221817987389802E+00;
    w[18] =   0.1771365352315134E-01;
    w[19] =   0.2490926964598258E+00;
    w[20] =   0.3408041116306980E+00;
    w[21] =   0.2490926964598291E+00;
    w[22] =   0.1771365352314976E-01;
    w[23] =   0.9646986307476696E-01;
    w[24] =   0.2557725606433917E+00;
    w[25] =   0.2557725606433927E+00;
    w[26] =   0.9646986307476431E-01;
    w[27] =   0.8649923133686802E-02;
    w[28] =   0.1062007918394705E+00;
    w[29] =   0.1505805844901012E+00;
    w[30] =   0.1062007918394705E+00;
    w[31] =   0.8649923133690016E-02;
    w[32] =   0.6355881462931014E-02;
    w[33] =   0.1405228180237514E-01;
    w[34] =   0.1405228180237651E-01;
    w[35] =   0.6355881462928496E-02;
  }
  else if ( l == 8 )
  {
    w[ 0] =  -0.1269841269835311E-02;
    w[ 1] =   0.6706089639041270E-02;
    w[ 2] =   0.1111455441352989E-01;
    w[ 3] =   0.1026455026455282E-01;
    w[ 4] =   0.4930678698742625E-02;
    w[ 5] =   0.3633146869162523E-01;
    w[ 6] =   0.8838322767333079E-01;
    w[ 7] =   0.9965911758463214E-01;
    w[ 8] =   0.6400185533755555E-01;
    w[ 9] =   0.4061629144893127E-02;
    w[10] =   0.6772486772485166E-02;
    w[11] =   0.1258344472781388E+00;
    w[12] =   0.1927501398511116E+00;
    w[13] =   0.1699470899470907E+00;
    w[14] =   0.6342599488133535E-01;
    w[15] =   0.8376332474107638E-01;
    w[16] =   0.2170841444607031E+00;
    w[17] =   0.2477307250801775E+00;
    w[18] =   0.1648098048612226E+00;
    w[19] =   0.1004771829779292E-01;
    w[20] =   0.1015873015872910E-01;
    w[21] =   0.1784328991205164E+00;
    w[22] =   0.2729409493576765E+00;
    w[23] =   0.2364021164021134E+00;
    w[24] =   0.8936689226256009E-01;
    w[25] =   0.8376332474107701E-01;
    w[26] =   0.2170841444607054E+00;
    w[27] =   0.2477307250801761E+00;
    w[28] =   0.1648098048612200E+00;
    w[29] =   0.1004771829779330E-01;
    w[30] =   0.6772486772485237E-02;
    w[31] =   0.1258344472781358E+00;
    w[32] =   0.1927501398511135E+00;
    w[33] =   0.1699470899470926E+00;
    w[34] =   0.6342599488133838E-01;
    w[35] =   0.3633146869162453E-01;
    w[36] =   0.8838322767332588E-01;
    w[37] =   0.9965911758463601E-01;
    w[38] =   0.6400185533755502E-01;
    w[39] =   0.4061629144888279E-02;
    w[40] =  -0.1269841269836355E-02;
    w[41] =   0.6706089639046927E-02;
    w[42] =   0.1111455441352761E-01;
    w[43] =   0.1026455026454956E-01;
    w[44] =   0.4930678698747173E-02;
  }
  else if ( l == 9 )
  {
    w[ 0] =  -0.1368606701945113E-02;
    w[ 1] =   0.4837977417140975E-02;
    w[ 2] =   0.8876308297144902E-02;
    w[ 3] =   0.8876308297143068E-02;
    w[ 4] =   0.4837977417150492E-02;
    w[ 5] =  -0.1368606701935084E-02;
    w[ 6] =   0.2425285860992349E-01;
    w[ 7] =   0.5727330842923516E-01;
    w[ 8] =   0.7008257906578071E-01;
    w[ 9] =   0.5727330842922034E-01;
    w[10] =   0.2425285860989794E-01;
    w[11] =   0.4659404339099723E-02;
    w[12] =   0.8354521980498550E-01;
    w[13] =   0.1370796991940044E+00;
    w[14] =   0.1370796991940248E+00;
    w[15] =   0.8354521980500107E-01;
    w[16] =   0.4659404339109654E-02;
    w[17] =   0.5564545640233619E-01;
    w[18] =   0.1524391996823315E+00;
    w[19] =   0.1877107583774149E+00;
    w[20] =   0.1524391996823176E+00;
    w[21] =   0.5564545640232402E-01;
    w[22] =   0.8186176158691754E-02;
    w[23] =   0.1295355639606716E+00;
    w[24] =   0.2061407656847711E+00;
    w[25] =   0.2061407656847630E+00;
    w[26] =   0.1295355639606894E+00;
    w[27] =   0.8186176158692687E-02;
    w[28] =   0.6234969028097752E-01;
    w[29] =   0.1730419031522391E+00;
    w[30] =   0.2169418247419051E+00;
    w[31] =   0.1730419031522361E+00;
    w[32] =   0.6234969028097048E-01;
    w[33] =   0.7506172839505762E-02;
    w[34] =   0.1142161960569350E+00;
    w[35] =   0.1802176663769002E+00;
    w[36] =   0.1802176663769038E+00;
    w[37] =   0.1142161960569279E+00;
    w[38] =   0.7506172839512260E-02;
    w[39] =   0.4031900987631698E-01;
    w[40] =   0.1142976211857364E+00;
    w[41] =   0.1413353845521477E+00;
    w[42] =   0.1142976211857414E+00;
    w[43] =   0.4031900987631700E-01;
    w[44] =   0.3239075586856897E-02;
    w[45] =   0.4317587564913915E-01;
    w[46] =   0.7015250533601934E-01;
    w[47] =   0.7015250533601930E-01;
    w[48] =   0.4317587564913908E-01;
    w[49] =   0.3239075586852207E-02;
    w[50] =   0.2550690557469151E-02;
    w[51] =   0.6084230077461027E-02;
    w[52] =   0.7421516754852508E-02;
    w[53] =   0.6084230077458821E-02;
    w[54] =   0.2550690557473353E-02;
  }
  else if ( l == 10 )
  {
    w[ 0] =  -0.6240762604463766E-03;
    w[ 1] =   0.2843227149025789E-02;
    w[ 2] =   0.5250031948150784E-02;
    w[ 3] =   0.5891746241568810E-02;
    w[ 4] =   0.4705736485964679E-02;
    w[ 5] =   0.2135354637732944E-02;
    w[ 6] =   0.1610939653924566E-01;
    w[ 7] =   0.4099595211758227E-01;
    w[ 8] =   0.5326500934654063E-01;
    w[ 9] =   0.4863338516658277E-01;
    w[10] =   0.2843474741781434E-01;
    w[11] =   0.1719619179693151E-02;
    w[12] =   0.2883769745121509E-02;
    w[13] =   0.5724711668876453E-01;
    w[14] =   0.9659872841640438E-01;
    w[15] =   0.1053210323353631E+00;
    w[16] =   0.8066212502628711E-01;
    w[17] =   0.2855765663647366E-01;
    w[18] =   0.3981286043310814E-01;
    w[19] =   0.1090390674981577E+00;
    w[20] =   0.1430169021081585E+00;
    w[21] =   0.1313686303763064E+00;
    w[22] =   0.7932850918298831E-01;
    w[23] =   0.4610696968783255E-02;
    w[24] =   0.5086495679684716E-02;
    w[25] =   0.9311356395361167E-01;
    w[26] =   0.1562320334111262E+00;
    w[27] =   0.1696057154254139E+00;
    w[28] =   0.1283581371975154E+00;
    w[29] =   0.4603059518094556E-01;
    w[30] =   0.4894888812994630E-01;
    w[31] =   0.1347281473526573E+00;
    w[32] =   0.1764193542601264E+00;
    w[33] =   0.1635037456303485E+00;
    w[34] =   0.9822749154565460E-01;
    w[35] =   0.5704840613923174E-02;
    w[36] =   0.5086495679679268E-02;
    w[37] =   0.9311356395362781E-01;
    w[38] =   0.1562320334111511E+00;
    w[39] =   0.1696057154253968E+00;
    w[40] =   0.1283581371975113E+00;
    w[41] =   0.4603059518094044E-01;
    w[42] =   0.3981286043311782E-01;
    w[43] =   0.1090390674981293E+00;
    w[44] =   0.1430169021081508E+00;
    w[45] =   0.1313686303763217E+00;
    w[46] =   0.7932850918299997E-01;
    w[47] =   0.4610696968790496E-02;
    w[48] =   0.2883769745110260E-02;
    w[49] =   0.5724711668875122E-01;
    w[50] =   0.9659872841642343E-01;
    w[51] =   0.1053210323353932E+00;
    w[52] =   0.8066212502626474E-01;
    w[53] =   0.2855765663644533E-01;
    w[54] =   0.1610939653928420E-01;
    w[55] =   0.4099595211758404E-01;
    w[56] =   0.5326500934649123E-01;
    w[57] =   0.4863338516656233E-01;
    w[58] =   0.2843474741784810E-01;
    w[59] =   0.1719619179720036E-02;
    w[60] =  -0.6240762604606350E-03;
    w[61] =   0.2843227149011163E-02;
    w[62] =   0.5250031948172295E-02;
    w[63] =   0.5891746241587802E-02;
    w[64] =   0.4705736485965663E-02;
    w[65] =   0.2135354637703863E-02;
  }
  else
  {
    cerr << "\n";
    cerr << "PADUA_WEIGHT_SET - Fatal error\n";
    cerr << "  Illegal value of L = " << l << "\n";
    cerr << "  Legal values are 0 through 10.\n";
    exit ( 1 );
  }

  return;
}