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

# include "quadrature_golub_welsch.h"

int main ( );
void test01 ( );
void test02 ( );
void test03 ( );
void test04 ( );
void test05 ( );
void test06 ( );
void test07 ( );
void test08 ( );
void test09 ( );

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

int main ( )

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

    quadrature_golub_welsch_test() tests quadrature_golub_welsch().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "quadrature_golub_welsch_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test quadrature_golub_welsch().\n" );

  test01 ( );
  test02 ( );
  test03 ( );
  test04 ( );
  test05 ( );
  test06 ( );
  test07 ( );
  test08 ( );
  test09 ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "QWGW_TEST:\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void test01 ( )

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

    TEST01 tests QWGW for the Chebyshev Type 1 weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double a;
  double *aj;
  double b;
  double *bj;
  int j;
  double mu0;
  int n;
  const double pi = 3.141592653589793;
  double *w;
  double *x;
/*
  Set the quadrature interval and number of points.
*/
  a = -1.0;
  b = +1.0;
  n = 5;

  printf ( "\n" );
  printf ( "TEST01:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Chebyshev Type 1 weight w(x) = 1/sqrt(1-x^2).\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = [%g,%g]\n", a, b );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  bj[0] = 1.0 / 2.0;
  for ( j = 1; j < n - 1; j++ )
  {
    bj[j] = 1.0 / 4.0;
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = pi;
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test02 ( )

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

    TEST02 tests QWGW for the Chebyshev Type 2 weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double a;
  double *aj;
  double b;
  double *bj;
  int j;
  double mu0;
  int n;
  const double pi = 3.141592653589793;
  double *w;
  double *x;
/*
  Set the quadrature interval and number of points.
*/
  a = -1.0;
  b = +1.0;
  n = 5;

  printf ( "\n" );
  printf ( "TEST02:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Chebyshev Type 2 weight w(x) = sqrt(1-x^2).\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = [%g,%g]\n", a, b );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    bj[j] = 1.0 / 4.0;
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = pi / 2.0;
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test03 ( )

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

    TEST03 tests QWGW for the Gegenbauer weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double a;
  double *aj;
  double alpha;
  double b;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  Set the quadrature interval and number of points.
*/
  a = -1.0;
  b = +1.0;
  n = 5;
/*
  Set the weight function parameter.
*/
  alpha = 0.25;

  printf ( "\n" );
  printf ( "TEST03:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Gegenbauer weight w(x) = (1-x^2)^alpha.\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  ALPHA = %g\n", alpha );
  printf ( "  Interval = [%g,%g]\n", a, b );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = ( jr * ( 2.0 * alpha + jr ) ) 
      / ( 4.0 * pow ( alpha + jr, 2 ) - 1.0 );
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = tgamma ( alpha + 1.0 ) * tgamma ( 0.5 ) / tgamma ( alpha + 1.5 );
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test04 ( )

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

    TEST04 tests QWGW for the generalized Hermite weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double *aj;
  double alpha;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  The quadrature interval is (-oo,+oo).
  Set the number of points.
*/
  n = 5;
/*
  Set the weight function parameter.
*/
  alpha = 2.0;

  printf ( "\n" );
  printf ( "TEST04:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the generalized Hermite weight w(x) = |x|^alpha * exp(-x^2).\n" );
  printf ( "  ALPHA = %g\n", alpha );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = (-oo,+oo)\n" );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    if ( ( j % 2 ) == 0 )
    {
      bj[j] = ( jr + alpha ) / 2.0;
    }
    else
    {
      bj[j] = jr / 2.0;
    }
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = tgamma ( ( alpha + 1.0 ) / 2.0 );
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test05 ( )

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

    TEST05 tests QWGW for the generalized Laguerre weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double *aj;
  double alpha;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  The quadrature interval is [0,+oo).
  Set the number of points.
*/
  n = 5;
/*
  Set the weight function parameter.
*/
  alpha = 2.0;

  printf ( "\n" );
  printf ( "TEST05:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the generalized Laguerre weight w(x) = x^alpha * exp(-x).\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  ALPHA = %g\n", alpha );
  printf ( "  Interval = [0,+oo)\n" );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    jr = ( double ) ( j + 1 );
    aj[j] = alpha + 2.0 * jr - 1.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = jr * ( alpha + jr );
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = tgamma ( alpha + 1.0 );
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test06 ( )

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

    TEST06 tests QWGW for the Hermite weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double *aj;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  const double pi = 3.141592653589793;
  double *w;
  double *x;
/*
  The quadrature interval is (-oo,+oo).
  Set the number of points.
*/
  n = 5;

  printf ( "\n" );
  printf ( "TEST06:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Hermite weight w(x) = exp(-x^2).\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = (-oo,+oo)\n" );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = jr / 2.0;
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = sqrt ( pi );
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test07 ( )

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

    TEST07 tests QWGW for the Jacobi weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double a;
  double *aj;
  double alpha;
  double b;
  double beta;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  Set the quadrature interval and number of points.
*/
  a = -1.0;
  b = +1.0;
  n = 5;
/*
  Set the weight function parameters.
*/
  alpha = 0.25;
  beta = 0.75;

  printf ( "\n" );
  printf ( "TEST07:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Jacobi weight w(x) = (1-x^2)^alpha*(1+x)^beta\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  ALPHA = %g\n", alpha );
  printf ( "  BETA =  %g\n", beta );
  printf ( "  Interval = [%g,%g]\n", a, b );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    jr = ( double ) ( j + 1 );
    aj[j] = ( beta - alpha ) * ( beta + alpha ) 
      / ( alpha + beta + 2.0 * jr - 2.0 ) 
      / ( alpha + beta + 2.0 * jr );
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = 4.0 * jr * ( alpha + jr ) * ( beta + jr ) 
      * ( alpha + beta + jr ) 
      / ( pow ( alpha + beta + 2.0 * jr, 2 ) - 1.0 ) 
      / pow ( alpha + beta + 2.0 * jr, 2 );
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = pow ( 2.0, alpha + beta + 1.0 ) 
    * tgamma ( alpha + 1.0 ) * tgamma ( beta + 1.0 ) 
    / tgamma ( alpha + beta + 2.0 );
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test08 ( )

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

    TEST08 tests QWGW for the Laguerre weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double *aj;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  The quadrature interval is [a,+oo).
  Set the number of points.
*/
  n = 5;

  printf ( "\n" );
  printf ( "TEST08:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Laguerre weight w(x) = exp(-x).\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = [0,+oo)\n" );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    jr = ( double ) ( j + 1 );
    aj[j] = 2.0 * jr - 1.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = jr * jr;
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = 1.0;
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

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

void test09 ( )

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

    TEST09 tests QWGW for the Legendre weight.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    22 February 2014

  Author:

    John Burkardt
*/
{
  double a;
  double *aj;
  double b;
  double *bj;
  int j;
  double jr;
  double mu0;
  int n;
  double *w;
  double *x;
/*
  Set the quadrature interval and number of points.
*/
  a = -1.0;
  b = +1.0;
  n = 5;

  printf ( "\n" );
  printf ( "TEST09:\n" );
  printf ( "  Compute points and weights for Gauss quadrature\n" );
  printf ( "  with the Legendre weight w(x) = 1.\n" );
  printf ( "  Order N = %d\n", n );
  printf ( "  Interval = [%g,%g]\n", a, b );
/*
  Set the recursion coefficients.
*/
  aj = ( double * ) malloc ( n * sizeof ( double ) );
  bj = ( double * ) malloc ( n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    aj[j] = 0.0;
  }

  for ( j = 0; j < n - 1; j++ )
  {
    jr = ( double ) ( j + 1 );
    bj[j] = jr * jr / ( 4.0 * jr * jr - 1.0 );
  }
  bj[n-1] = 0.0;

  for ( j = 0; j < n; j++ )
  {
    bj[j] = sqrt ( bj[j] );
  }

  mu0 = 2.0;
/*
  Compute the points and weights.
*/
  x = ( double * ) malloc ( n * sizeof ( double ) );
  w = ( double * ) malloc ( n * sizeof ( double ) );

  sgqf ( n, aj, bj, mu0, x, w );

  r8vec_print ( n, x, "  Abscissas:" );
  r8vec_print ( n, w, "  Weights:" );
/*
  Free memory.
*/
  free ( aj );
  free ( bj );
  free ( w );
  free ( x );

  return;
}