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

using namespace std;

# include "gegenbauer_polynomial.hpp"

int main ( );
void gegenbauer_alpha_check_test ( );
void gegenbauer_ek_compute_test ( );
void gegenbauer_integral_test ( );
void gegenbauer_polynomial_value_test ( );
void gegenbauer_ss_compute_test ( );
void gegenbauer_to_monomial_matrix_test ( );
void imtqlx_test ( );
void monomial_to_gegenbauer_matrix_test ( );
void r8_hyper_2f1_test ( );
void r8_uniform_ab_test ( );
double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] );
double *r8mat_mv_new ( int m, int n, double a[], double x[] );
void r8mat_print ( int m, int n, double a[], string title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, string title );
void r8poly_print ( int n, double a[], string title );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_polynomial_test() tests gegenbauer_polynomial().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 April 2024
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "gegenbauer_polynomial_test():\n";
  cout << "  C++ version.\n";
  cout << "  Test gegenbauer_polynomial().\n";

  gegenbauer_alpha_check_test ( );
  gegenbauer_ek_compute_test ( );
  gegenbauer_integral_test ( );
  gegenbauer_polynomial_value_test ( );
  gegenbauer_ss_compute_test ( );
  gegenbauer_to_monomial_matrix_test ( );

  imtqlx_test ( );

  monomial_to_gegenbauer_matrix_test ( );

  r8_hyper_2f1_test ( );
  r8_uniform_ab_test ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "gegenbauer_polynomial_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

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

void gegenbauer_alpha_check_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_alpha_check_test() tests gegenbauer_alpha_check().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    30 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  bool check;
  int n;
  int seed;

  cout << "\n";
  cout << "gegenbauer_alpha_check_test():\n";
  cout << "  gegenbauer_alpha_check() checks that ALPHA is legal;\n";
  cout << "\n";
  cout << "       ALPHA   Check?\n";
  cout << "\n";

  seed = 123456789;

  for ( n = 1; n <= 10; n++ )
  {
    alpha = r8_uniform_ab ( -5.0, +5.0, seed );
    check = gegenbauer_alpha_check ( alpha );
    cout << "  " << setw(10) << alpha
         << "       " << setw(1) << check << "\n";
  }

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

void gegenbauer_ek_compute_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_ek_compute_test() tests gegenbauer_ek_compute().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    20 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  int i;
  int n;
  int prec;
  double *w;
  double *x;

  prec = cout.precision ( );
  cout.precision ( 16 );

  alpha = 0.5;

  cout << "\n";
  cout << "gegenbauer_ek_compute_test():\n";
  cout << "  gegenbauer_ek_compute() computes a Gauss-Gegenbauer rule;\n";
  cout << "\n";
  cout << "  with ALPHA = " << alpha << "\n";
  cout << "  and integration interval [-1,+1]\n";
  cout << "\n";
  cout << "                  W               X\n";

  for ( n = 1; n <= 10; n++ )
  {
    cout << "\n";

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

    gegenbauer_ek_compute ( n, alpha, x, w );

    for ( i = 0; i < n; i++ )
    {
      cout << "          "
           << "  " << setw(14) << w[i]
           << "  " << setw(14) << x[i] << "\n";
    }
    delete [] w;
    delete [] x;
  }

  cout.precision ( prec );

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

void gegenbauer_integral_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_integral_test() tests gegenbauer_integral().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    14 June 2015
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  int n;
  int prec;
  double value;

  prec = cout.precision ( );
  cout.precision ( 16 );

  alpha = 0.25;

  cout << "\n";
  cout << "GEGENBAUER_INTEGRAL_TEST\n";
  cout << "  GEGENBAUER_INTEGRAL evaluates\n";
  cout << "  Integral ( -1 < x < +1 ) x^n * (1-x*x)^alpha dx\n";
  cout << "\n";
  cout << "         N         Value\n";
  cout << "\n";

  for ( n = 0; n <= 10; n++ )
  {
    value = gegenbauer_integral ( n, alpha );
    cout << "  " << setw(8)  << n
         << "  " << setw(24) << value << "\n";
  }

  cout.precision ( prec );
 
  return;
}
//****************************************************************************80

void gegenbauer_polynomial_value_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    GEGENBAUER_POLYNOMIAL_VALUE_TEST tests GEGENBAUER_POLYNOMIAL_VALUE.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  double *c;
  double fx;
  int m;
  int n;
  int n_data;
  double x[1];
  double xscalar;

  cout << "\n";
  cout << "GEGENBAUER_POLYNOMIAL_VALUE_TEST:\n";
  cout << "  GEGENBAUER_POLYNOMIAL_VALUE evaluates the Gegenbauer polynomial.\n";
  cout << "\n";
  cout << "       M     ALPHA         X           GPV    GEGENBAUER\n";
  cout << "\n";

  n_data = 0;

  for ( ; ; )
  {
    gegenbauer_polynomial_values ( n_data, m, alpha, xscalar, fx );

    if ( n_data == 0 )
    {
      break;
    }
//
//  Since GEGENBAUER_POLYNOMIAL_VALUE expects a vector input X, we have to
//  do a little "rewrapping" of the input.
//
    n = 1;
    x[0] = xscalar;
    c = gegenbauer_polynomial_value ( m, n, alpha, x );
    cout << "  " << setw(6) << m
         << "  " << setw(8) << alpha
         << "  " << setw(8) << x[0]
         << "  " << setw(12) << fx
         << "  " << setw(12) << c[m+0*(m+1)] << "\n";
    delete [] c;
  }

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

void gegenbauer_ss_compute_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_ss_compute_test() tests gegenbauer_ss_compute().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    10 June 2015
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  int i;
  int n;
  int prec;
  double *w;
  double *x;

  prec = cout.precision ( );
  cout.precision ( 16 );

  alpha = 0.5;

  cout << "\n";
  cout << "gegenbauer_ss_compute_test():\n";
  cout << "  gegenbauer_ss_compute() computes a Gauss-Gegenbauer rule;\n";
  cout << "\n";
  cout << "  with ALPHA = " << alpha << "\n";
  cout << "\n";
  cout << "                  W               X\n";

  for ( n = 1; n <= 10; n++ )
  {
    cout << "\n";

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

    gegenbauer_ss_compute ( n, alpha, x, w );

    for ( i = 0; i < n; i++ )
    {
      cout << "          "
           << "  " << setw(14) << w[i]
           << "  " << setw(14) << x[i] << "\n";
    }

    delete [] w;
    delete [] x;
  }

  cout.precision ( prec );

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

void gegenbauer_to_monomial_matrix_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    gegenbauer_to_monomial_matrix_test() tests gegenbauer_to_monomial_matrix().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    16 April 2024
//
//  Author:
//
//    John Burkardt
//
{
  double *A;
  double alpha;
  double *g;
  int i;
  int j;
  int n = 5;
  double *mono;

  cout << "\n";
  cout << "gegenbauer_to_monomial_matrix_test():\n";
  cout << "  gegenbauer_to_monomial_matrix() evaluates the matrix\n";
  cout << "  which converts Gegenbauer polyjomial coefficients\n";
  cout << "  to monomial coefficients.\n";
  
  alpha = 0.5;

  A = gegenbauer_to_monomial_matrix ( n, alpha );

  r8mat_print ( n, n, A, "  Gegenbauer to Monomial matrix G:" );

  g = new double[n];

  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      g[j] = 0.0;
    }
    g[i] = 1.0;
    mono = r8mat_mv_new ( n, n, A, g );
    cout << "\n";
    cout << "  Monomial form of Gegenbauer polynomial " << i << "\n";
    r8poly_print ( i, mono, "" );
    delete [] mono;
  }
  delete [] A;
  delete [] g;

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

void imtqlx_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    imtqlx_test() tests imtqlx().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 June 2015
//
//  Author:
//
//    John Burkardt.
//
{
  double angle;
  double d[5];
  double e[5];
  int i;
  double lam[5];
  double lam2[5];
  int n = 5;
  double qtz[5];
  double r8_pi = 3.141592653589793;
  double z[5];

  cout << "\n";
  cout << "IMTQLX_TEST\n";
  cout << "  IMTQLX takes a symmetric tridiagonal matrix A\n";
  cout << "  and computes its eigenvalues LAM.\n";
  cout << "  It also accepts a vector Z and computes Q'*Z,\n";
  cout << "  where Q is the matrix that diagonalizes A.\n";

  for ( i = 0; i < n; i++ )
  {
    d[i] = 2.0;
  }
  for ( i = 0; i < n - 1; i++ )
  {
    e[i] = -1.0;
  }
  e[n-1] = 0.0;
  for ( i = 0; i < n; i++ )
  {
    z[i] = 1.0;
  }
//
//  On input, LAM is D, and QTZ is Z.
//
  for ( i = 0; i < n; i++ )
  {
    lam[i] = d[i];
  }
  for ( i = 0; i < n; i++ )
  {
    qtz[i] = z[i];
  }

  imtqlx ( n, lam, e, qtz );

  r8vec_print ( n, lam, "  Computed eigenvalues:" );

  for ( i = 0; i < n; i++ )
  {
    angle = ( double ) ( i + 1 ) * r8_pi / ( double ) ( 2 * ( n + 1 ) );
    lam2[i] = 4.0 * pow ( sin ( angle ), 2 );
  }

  r8vec_print ( n, lam2, "  Exact eigenvalues:" );

  r8vec_print ( n, z, "  Vector Z:" );
  r8vec_print ( n, qtz, "  Vector Q'*Z:" );

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

void monomial_to_gegenbauer_matrix_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    monomial_to_gegenbauer_matrix_test() tests monomial_to_gegenbauer_matrix().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    24 April 2024
//
//  Author:
//
//    John Burkardt
//
{
  double alpha;
  double *G;
  double *Ginv;
  double *I;
  int n = 5;

  cout << "\n";
  cout << "monomial_to_gegenbauer_matrix_test():\n";
  cout << "  monomial_to_gegenbauer_matrix() evaluates the matrix\n";
  cout << "  which converts monomial polynomial coefficients\n";
  cout << "  to Gegenbauer coefficients.\n";
  
  alpha = 0.5;
  cout << "  Using parameter alpha = " << alpha << "\n";

  G = gegenbauer_to_monomial_matrix ( n, alpha );
  r8mat_print ( n, n, G, "  Gegenbauer to Monomial matrix G:" );

  Ginv = monomial_to_gegenbauer_matrix ( n, alpha );
  r8mat_print ( n, n, Ginv, "  Monomial to Gegenbauer matrix Ginv:" );

  I = r8mat_mm_new ( n, n, n, G, Ginv );
  r8mat_print ( n, n, I, "  I = G * Ginv:" );

  delete [] G;
  delete [] Ginv;
  delete [] I;

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

void r8_hyper_2f1_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    r8_hyper_2f1_test() tests r8_hyper_2f1().
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    09 February 2008
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  double c;
  double fx;
  double fx2;
  int n_data;
  double x;

  cout << "\n";
  cout << " R8_HYPER_2F1_TEST:\n";
  cout << "   R8_HYPER_2F1 evaluates the hypergeometric function 2F1.\n";
  cout << "\n";
  cout << "      A       B       C       X      ";
  cout << " 2F1                       2F1                     DIFF\n";
  cout << "                                     ";
  cout << "(tabulated)               (computed)\n";
  cout << "\n";

  n_data = 0;

  for ( ; ; )
  {
    hyper_2f1_values ( n_data, a, b, c, x, fx );

    if ( n_data == 0 )
    {
      break;
    }

    fx2 = r8_hyper_2f1 ( a, b, c, x );

    cout << "  " << setw(6)  << setprecision(2)  << a
         << "  " << setw(6)  << setprecision(2)  << b  
         << "  " << setw(6)  << setprecision(2)  << c  
         << "  " << setw(6)  << setprecision(2)  << x  
         << "  " << setw(24) << setprecision(16) << fx
         << "  " << setw(24) << setprecision(16) << fx2
         << "  " << setw(10) << setprecision(4)  << fabs ( fx - fx2 ) << "\n";
  }
  return;
}
//****************************************************************************80

void r8_uniform_ab_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    r8_uniform_ab_test() tests r8_uniform_ab().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    11 April 2007
//
//  Author:
//
//    John Burkardt
//
{
  double a;
  double b;
  double c;
  int i;
  int seed;

  b = 10.0;
  c = 25.0;
  seed = 17;

  cout << "\n";
  cout << "r8_uniform_ab_test():\n";
  cout << "  r8_uniform_ab() produces a random real in a given range.\n";
  cout << "\n";
  cout << "  Using range " << b << " <= A <= " << c << ".\n";
  cout << "\n";

  cout << "\n";
  cout << "      I       A\n";
  cout << "\n";
  for ( i = 0; i < 10; i++ )
  {
    a = r8_uniform_ab ( b, c, seed );
    cout << setw ( 6 )  << i << " "
         << setw ( 10 ) << a << "\n";
  }

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

double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] )

//****************************************************************************80
//
//  Purpose:
//
//    r8mat_mm_new() multiplies two matrices.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//    For this routine, the result is returned as the function value.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    18 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N1, N2, N3, the order of the matrices.
//
//    Input, double A[N1*N2], double B[N2*N3], the matrices to multiply.
//
//    Output, double R8MAT_MM_NEW[N1*N3], the product matrix C = A * B.
//
{
  double *c;
  int i;
  int j;
  int k;

  c = new double[n1*n3];

  for ( i = 0; i < n1; i++ )
  {
    for ( j = 0; j < n3; j++ )
    {
      c[i+j*n1] = 0.0;
      for ( k = 0; k < n2; k++ )
      {
        c[i+j*n1] = c[i+j*n1] + a[i+k*n1] * b[k+j*n2];
      }
    }
  }

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

double *r8mat_mv_new ( int m, int n, double a[], double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    r8mat_mv_new() multiplies a matrix times a vector.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//    For this routine, the result is returned as the function value.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    11 April 2007
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, N, the number of rows and columns of the matrix.
//
//    double A[M,N], the M by N matrix.
//
//    double X[N], the vector to be multiplied by A.
//
//  Output:
//
//    double R8MAT_MV_NEW[M], the product A*X.
//
{
  int i;
  int j;
  double *y;

  y = new double[m];

  for ( i = 0; i < m; i++ )
  {
    y[i] = 0.0;
    for ( j = 0; j < n; j++ )
    {
      y[i] = y[i] + a[i+j*m] * x[j];
    }
  }

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

void r8mat_print ( int m, int n, double a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    r8mat_print() prints an R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//    Entry A(I,J) is stored as A[I+J*M]
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 September 2009
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, the number of rows in A.
//
//    int N, the number of columns in A.
//
//    double A[M*N], the M by N matrix.
//
//    string TITLE, a title.
//
{
  r8mat_print_some ( m, n, a, 1, 1, m, n, title );

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

void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, string title )

//****************************************************************************80
//
//  Purpose:
//
//    r8mat_print_some() prints some of an R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    26 June 2013
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, the number of rows of the matrix.
//    M must be positive.
//
//    int N, the number of columns of the matrix.
//    N must be positive.
//
//    double A[M*N], the matrix.
//
//    int ILO, JLO, IHI, JHI, designate the first row and
//    column, and the last row and column to be printed.
//
//    string TITLE, a title.
//
{
# define INCX 5

  int i;
  int i2hi;
  int i2lo;
  int j;
  int j2hi;
  int j2lo;

  cout << "\n";
  cout << title << "\n";

  if ( m <= 0 || n <= 0 )
  {
    cout << "\n";
    cout << "  (None)\n";
    return;
  }
//
//  Print the columns of the matrix, in strips of 5.
//
  for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX )
  {
    j2hi = j2lo + INCX - 1;
    if ( n < j2hi )
    {
      j2hi = n;
    }
    if ( jhi < j2hi )
    {
      j2hi = jhi;
    }
    cout << "\n";
//
//  For each column J in the current range...
//
//  Write the header.
//
    cout << "  Col:    ";
    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(7) << j - 1 << "       ";
    }
    cout << "\n";
    cout << "  Row\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( ihi < m )
    {
      i2hi = ihi;
    }
    else
    {
      i2hi = m;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
//
//  Print out (up to) 5 entries in row I, that lie in the current strip.
//
      cout << setw(5) << i - 1 << ": ";
      for ( j = j2lo; j <= j2hi; j++ )
      {
        cout << setw(12) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }
  }

  return;
# undef INCX
}
//****************************************************************************80

void r8poly_print ( int n, double a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    r8poly_print() prints a polynomial.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    15 July 2015
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the dimension of A.
//
//    double A[N+1], the polynomial coefficients.
//    A(0) is the constant term and
//    A(N) is the coefficient of X^N.
//
//    string TITLE, a title.
//
{
  int i;
  double mag;
  char plus_minus;

  if ( 0 < title.length ( ) )
  {
    cout << "\n";
    cout << title << "\n";
  }
  cout << "\n";

  if ( n < 0 )
  {
    cout << "  p(x) = 0\n";
    return;
  }

  if ( a[n] < 0.0 )
  {
    plus_minus = '-';
  }
  else
  {
    plus_minus = ' ';
  }

  mag = fabs ( a[n] );

  if ( 2 <= n )
  {
    cout << "  p(x) = " << plus_minus
         << setw(14) << mag << " * x ^ " << n << "\n";
  }
  else if ( n == 1 )
  {
    cout << "  p(x) = " << plus_minus
         << setw(14) << mag << " * x\n";
  }
  else if ( n == 0 )
  {
    cout << "  p(x) = " << plus_minus
         << setw(14) << mag << "\n";
  }

  for ( i = n - 1; 0 <= i; i-- )
  {
    if ( a[i] < 0.0 )
    {
      plus_minus = '-';
    }
    else
    {
      plus_minus = '+';
    }

    mag = fabs ( a[i] );

    if ( mag != 0.0 )
    {
      if ( 2 <= i )
      {
        cout << "         " << plus_minus
             << setw(14) << mag << " * x ^ " << i << "\n";
      }
      else if ( i == 1 )
      {
        cout << "         " << plus_minus
             << setw(14) << mag << " * x\n";
      }
      else if ( i == 0 )
      {
        cout << "         " << plus_minus
             << setw(14) << mag << "\n";
      }
    }
  }

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

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    timestamp() prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    19 March 2018
//
//  Author:
//
//    John Burkardt
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}