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

# include "gegenbauer_polynomial.h"

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[], char *title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title );
void r8poly_print ( int n, double a[], char *title );
void timestamp ( );

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

int main ( )

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

    gegenbauer_polynomial_test() tests gegenbauer_polynomial().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 April 2024

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "gegenbauer_polynomial_test():\n" );
  printf ( "  C version.\n" );
  printf ( "  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.
*/
  printf ( "\n" );
  printf ( "gegenbauer_polynomial_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void gegenbauer_alpha_check_test ( )

/******************************************************************************/
/*
  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;

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

  seed = 123456789;

  for ( n = 1; n <= 10; n++ )
  {
    alpha = r8_uniform_ab ( -5.0, +5.0, &seed );
    check = gegenbauer_alpha_check ( alpha );
    printf ( "  %10.4f       %1d\n", alpha, check );
  }

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

void gegenbauer_ek_compute_test ( )

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

    gegenbauer_ek_compute_test() tests gegenbauer_ek_compute().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    19 November 2015

  Author:

    John Burkardt
*/
{
  double alpha;
  int i;
  int n;
  double *w;
  double *x;

  alpha = 0.5;

  printf ( "\n" );
  printf ( "gegenbauer_ek_compute_test():\n" );
  printf ( "  gegenbauer_ek_compute() computes a Gauss-Gegenbauer rule;\n" );
  printf ( "\n" );
  printf ( "  Abscissas X and weights W for a Gauss Gegenbauer rule\n" );
  printf ( "  with ALPHA = %f\n", alpha );
  printf ( "  Integration interval = [-1,+1]\n" );
  printf ( "\n" );
  printf ( "                  W               X\n" );

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

    w = ( double * ) malloc ( n * sizeof ( double ) );
    x = ( double * ) malloc ( n * sizeof ( double ) );

    gegenbauer_ek_compute ( n, alpha, x, w );

    for ( i = 0; i < n; i++ )
    {
      printf ( "  %2d  %24.16g  %24.16g\n", i, w[i], x[i]  );
    }

    free ( w );
    free ( x );
  }
  return;
}
/******************************************************************************/

void gegenbauer_integral_test ( )

/******************************************************************************/
/*
  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;
  double value;

  alpha = 0.25;

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

  for ( n = 0; n <= 10; n++ )
  {
    value = gegenbauer_integral ( n, alpha );

    printf ( "  %8d  %24.16g\n", n, value );
  }
 
  return;
}
/******************************************************************************/

void gegenbauer_polynomial_value_test ( )

/******************************************************************************/
/*
  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;

  printf ( "\n" );
  printf ( "GEGENBAUER_POLYNOMIAL_VALUE_TEST:\n" );
  printf ( "  GEGENBAUER_POLYNOMIAL_VALUE evaluates the Gegenbauer polynomial.\n" );
  printf ( "\n" );
  printf ( "       M     ALPHA         X           GPV    GEGENBAUER\n" );
  printf ( "\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 );
    printf ( "  %6d  %8.2f  %8.2f  %12f  %12f\n", m, alpha, x[0], fx, c[m+0*(m+1)] );
    free ( c );
  }

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

void gegenbauer_ss_compute_test ( )

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

    gegenbauer_ss_compute_test() tests gegenbauer_ss_compute().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    24 June 2008

  Author:

    John Burkardt
*/
{
  double alpha;
  int i;
  int n;
  double *w;
  double *x;

  alpha = 0.5;

  printf ( "\n" );
  printf ( "GEGENBAUER_SS_COMPUTE_TEST\n" );
  printf ( "  GEGENBAUER_SS_COMPUTE computes a Gauss-Gegenbauer rule;\n" );
  printf ( "\n" );
  printf ( "  Abscissas X and weights W for a Gauss Gegenbauer rule\n" );
  printf ( "  with ALPHA = %f\n", alpha );
  printf ( "\n" );
  printf ( "                  W               X\n" );

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

    w = ( double * ) malloc ( n * sizeof ( double ) );
    x = ( double * ) malloc ( n * sizeof ( double ) );

    gegenbauer_ss_compute ( n, alpha, x, w );

    for ( i = 0; i < n; i++ )
    {
      printf ( "  %2d  %24.16g  %24.16g\n", i, w[i], x[i]  );
    }

    free ( w );
    free ( x );
  }
  return;
}
/******************************************************************************/

void gegenbauer_to_monomial_matrix_test ( )

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

    gegenbauer_to_monomial_matrix_test() tests gegenbauer_to_monomial_matrix().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 April 2024

  Author:

    John Burkardt
*/
{
  double *A;
  double alpha;
  double *g;
  int i;
  int j;
  int n = 5;
  double *mono;

  printf ( "\n" );
  printf ( "gegenbauer_to_monomial_matrix_test():\n" );
  printf ( "  gegenbauer_to_monomial_matrix() evaluates the matrix\n" );
  printf ( "  which converts Gegenbauer polyjomial coefficients\n" );
  printf ( "  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 = ( double * ) malloc ( n * sizeof ( double ) );

  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 );
    printf ( "\n" );
    printf ( "  Monomial form of Gegenbauer polynomial %d\n", i );
    r8poly_print ( i, mono, "" );
    free ( mono );
  }
  free ( A );
  free ( g );

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

void imtqlx_test ( )

/******************************************************************************/
/*
  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];

  printf ( "\n" );
  printf ( "IMTQLX_TEST\n" );
  printf ( "  IMTQLX takes a symmetric tridiagonal matrix A\n" );
  printf ( "  and computes its eigenvalues LAM.\n" );
  printf ( "  It also accepts a vector Z and computes Q'*Z,\n" );
  printf ( "  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;
}
/******************************************************************************/

void monomial_to_gegenbauer_matrix_test ( )

/******************************************************************************/
/*
  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;

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

  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:" );

  free ( G );
  free ( Ginv );
  free ( I );

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

void r8_hyper_2f1_test ( )

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

    r8_hyper_2f1_test() tests r8_hyper_2f1().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    11 May 2012

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  double c;
  double fx;
  double fx2;
  int n_data;
  double x;

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

    printf ( "  %6f  %6f  %6f  %6f  %24.16g  %24.16g  %10.4g\n",
      a, b, c, x, fx, fx2, fabs ( fx - fx2 )  );
  }
  return;
}
/******************************************************************************/

void r8_uniform_ab_test ( )

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

    r8_uniform_ab_test() tests r8_uniform_ab().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    05 May 2006

  Author:

    John Burkardt
*/
{
  double a;
  double b;
  double c;
  int i;
  int seed;

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

  printf ( "\n" );
  printf ( "R8_UNIFORM_AB_TEST\n" );
  printf ( "  R8_UNIFORM_AB produces a random real in a given range.\n" );
  printf ( "\n" );
  printf ( "  Using range %f <= A <= %f.\n", b, c );
  printf ( "\n" );

  printf ( "\n" );
  printf ( "     I      A\n" );
  printf ( "\n" );
  for ( i = 0; i < 10; i++ )
  {
    a = r8_uniform_ab ( b, c, &seed );
    printf ( "  %4d  %10f\n", i, a );
  }

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

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

/******************************************************************************/
/*
  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:

    08 April 2009

  Author:

    John Burkardt

  Input:

    int N1, N2, N3, the order of the matrices.

    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 = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

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

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

/******************************************************************************/
/*
  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:

    15 April 2014

  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 = ( double * ) malloc ( m * sizeof ( double ) );

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

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

/******************************************************************************/
/*
  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:

    28 May 2008

  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.

    char *TITLE, a title.
*/
{
  r8mat_print_some ( m, n, a, 1, 1, m, n, title );

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

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

/******************************************************************************/
/*
  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.

    char *TITLE, a title.
*/
{
# define INCX 5

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

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );

  if ( m <= 0 || n <= 0 )
  {
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  (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;
    }

    fprintf ( stdout, "\n" );
/*
  For each column J in the current range...

  Write the header.
*/
    fprintf ( stdout, "  Col:  ");
    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "  %7d     ", j - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row\n" );
    fprintf ( stdout, "\n" );
/*
  Determine the range of the rows in this strip.
*/
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( m < ihi )
    {
      i2hi = m;
    }
    else
    {
      i2hi = ihi;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
/*
  Print out (up to) 5 entries in row I, that lie in the current strip.
*/
      fprintf ( stdout, "%5d:", i - 1 );
      for ( j = j2lo; j <= j2hi; j++ )
      {
        fprintf ( stdout, "  %14g", a[i-1+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

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

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

/******************************************************************************/
/*
  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.

    char *TITLE, a title.
*/
{
  int i;
  int m;
  double mag;
  char plus_minus;

  if ( 0 < strlen ( title ) )
  {
    printf ( "\n" );
    printf ( "%s\n", title );
  }
  printf ( "\n" );

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

  m = n;
  while ( a[m] == 0.0 )
  {
    m = m - 1;
  }

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

  mag = fabs ( a[m] );

  if ( 2 <= m )
  {
    printf ( "  p(x) = %c%g * x^%d\n", plus_minus, mag, m );
  }
  else if ( m == 1 )
  {
    printf ( "  p(x) = %c%g * x\n", plus_minus, mag );
  }
  else if ( m == 0 )
  {
    printf ( "  p(x) = %c%g\n", plus_minus, mag );
  }

  for ( i = m - 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 )
      {
        printf ( "         %c%g * x^%d\n", plus_minus, mag, i );
      }
      else if ( i == 1 )
      {
        printf ( "         %c%g * x\n", plus_minus, mag );
      }
      else if ( i == 0 )
      {
        printf ( "         %c%g\n", plus_minus, mag );
      }
    }
  }
  return;
}
/******************************************************************************/

void timestamp ( )

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

    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  Author:

    John Burkardt
*/
{
# define TIME_SIZE 40

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

  now = time ( NULL );
  tm = localtime ( &now );

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

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}