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

using namespace std;

int main ( int argc, char *argv[] );
char ch_cap ( char ch );
bool ch_eqi ( char ch1, char ch2 );
int ch_to_digit ( char ch );
void chebyshev2_compute ( int order, double xtab[], double weight[] );
void chebyshev2_handle ( int order, char *output );
void dtable_close_write ( ofstream &output );
void dtable_data_write ( ofstream &output, int m, int n, double table[] );
void dtable_header_write ( char *output_filename, ofstream &output, int m, 
  int n );
void dtable_write ( char *output_filename, int m, int n, double table[], 
  bool header );
double r8_epsilon ( void );
bool s_eqi ( char *s1, char *s2 );
void timestamp ( void );
char *timestring ( void );

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

int main ( int argc, char *argv[] )

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for CHEBYSHEV2_RULE.
//
//  Discussion:
//
//    This program computes a standard Gauss-Chebyshev type 2 quadrature rule
//    and writes it to a file.
//
//    The user specifies:
//    * the ORDER (number of points) in the rule
//    * the OUTPUT option.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    01 March 2008
//
//  Author:
//
//    John Burkardt
//
{
  int order;
  char output[81];

  timestamp ( );
  cout << "\n";
  cout << "CHEBYSHEV2_RULE\n";
  cout << "  C++ version\n";
  cout << "\n";
  cout << "  Compiled on " << __DATE__ << " at " << __TIME__ << ".\n";
  cout << "\n";
  cout << "  Compute a Gauss-Chebyshev type 2 rule for approximating\n";
  cout << "\n";
  cout << "    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx\n";
  cout << "\n";
  cout << "  of order ORDER.\n";
  cout << "\n";
  cout << "  The user specifies ORDER and OUTPUT.\n";
  cout << "\n";
  cout << "  OUTPUT is:\n";
  cout << "\n";
  cout << "  \"C++\" for printed C++ output;\n";
  cout << "  \"F77\" for printed Fortran77 output;\n";
  cout << "  \"F90\" for printed Fortran90 output;\n";
  cout << "  \"MAT\" for printed MATLAB output;\n";
  cout << "\n";
  cout << "  or:\n";
  cout << "\n";
  cout << "  \"filename\" to generate 3 files:\n";
  cout << "\n";
  cout << "    filename_w.txt - the weight file\n";
  cout << "    filename_x.txt - the abscissa file.\n";
  cout << "    filename_r.txt - the region file.\n";
//
//  Get the order.
//
  if ( 1 < argc )
  {
    order = atoi ( argv[1] );
  }
  else
  {
    cout << "\n";
    cout << "  Enter the value of ORDER (1 or greater)\n";
    cin >> order;
  }

  cout << "\n";
  cout << "  The requested order of the rule is = " << order << "\n";
//
//  Get the output option or quadrature file root name:
//
  if ( 2 < argc )
  {
    strcpy ( output, argv[2] );
  }
  else
  {
    cout << "\n";
    cout << "  Enter OUTPUT (one of C++, F77, F90, MAT\n";
    cout << "  or else the \"root name\" of the quadrature files).\n";
    cin >> output;
  }

  cout << "\n";
  cout << "  OUTPUT option is \"" << output << "\".\n";
//
//  Construct the rule and output it.
//
  chebyshev2_handle ( order, output );

  cout << "\n";
  cout << "CHEBYSHEV2_RULE:\n";
  cout << "  Normal end of execution.\n";

  cout << "\n";
  timestamp ( );

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

char ch_cap ( char ch )

//****************************************************************************80
//
//  Purpose:
//
//    CH_CAP capitalizes a single character.
//
//  Discussion:
//
//    This routine should be equivalent to the library "toupper" function.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the character to capitalize.
//
//    Output, char CH_CAP, the capitalized character.
//
{
  if ( 97 <= ch && ch <= 122 ) 
  {
    ch = ch - 32;
  }   

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

bool ch_eqi ( char ch1, char ch2 )

//****************************************************************************80
//
//  Purpose:
//
//    CH_EQI is true if two characters are equal, disregarding case.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH1, CH2, the characters to compare.
//
//    Output, bool CH_EQI, is true if the two characters are equal,
//    disregarding case.
//
{
  if ( 97 <= ch1 && ch1 <= 122 ) 
  {
    ch1 = ch1 - 32;
  } 
  if ( 97 <= ch2 && ch2 <= 122 ) 
  {
    ch2 = ch2 - 32;
  }     

  return ( ch1 == ch2 );
}
//****************************************************************************80

int ch_to_digit ( char ch )

//****************************************************************************80
//
//  Purpose:
//
//    CH_TO_DIGIT returns the integer value of a base 10 digit.
//
//  Example:
//
//     CH  DIGIT
//    ---  -----
//    '0'    0
//    '1'    1
//    ...  ...
//    '9'    9
//    ' '    0
//    'X'   -1
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the decimal digit, '0' through '9' or blank are legal.
//
//    Output, int CH_TO_DIGIT, the corresponding integer value.  If the 
//    character was 'illegal', then DIGIT is -1.
//
{
  int digit;

  if ( '0' <= ch && ch <= '9' )
  {
    digit = ch - '0';
  }
  else if ( ch == ' ' )
  {
    digit = 0;
  }
  else
  {
    digit = -1;
  }

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

void chebyshev2_compute ( int order, double x[], double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    CHEBYSHEV2_COMPUTE computes a Gauss-Chebyshev type 2 quadrature rule.
//
//  Discussion:
//
//    The integration interval is [ -1, 1 ].
//
//    The weight function is w(x) = sqrt ( 1 - x^2 ).
//
//    The integral to approximate:
//
//      Integral ( -1 <= X <= 1 ) F(X)  sqrt ( 1 - x^2 )  dX
//
//    The quadrature rule:
//
//      Sum ( 1 <= I <= ORDER ) WEIGHT(I) * F ( XTAB(I) )
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    26 February 2008
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Philip Davis, Philip Rabinowitz,
//    Methods of Numerical Integration,
//    Second Edition,
//    Dover, 2007,
//    ISBN: 0486453391,
//    LC: QA299.3.D28.
//
//  Parameters:
//
//    Input, int ORDER, the order of the rule.
//    ORDER must be greater than 0.
//
//    Output, double X[ORDER], the abscissas.
//
//    Output, double W[ORDER], the weights.
//
{
  double angle;
  int i;
  double pi = 3.141592653589793;

  if ( order < 1 )
  {
    cout << "\n";
    cout << "CHEBYSHEV2_COMPUTE - Fatal error!\n";
    cout << "  Illegal value of ORDER = " << order << "\n";
    exit ( 1 );
  }

  for ( i = 0; i < order; i++ )
  {
    angle = pi * ( double ) ( order - i ) / ( double ) ( order + 1 );
    w[i] = pi / ( double ) ( order + 1 ) * pow ( sin ( angle ), 2 );
    x[i] = cos ( angle );
  }

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

void chebyshev2_handle ( int order, char *output )

//****************************************************************************80
//
//  Purpose:
//
//    CHEBYSHEV2_HANDLE handles the requested Gauss-Chebyshev type 2 rule.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    01 March 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int ORDER, the order of the rule.
//
//    Input, char *OUTPUT, specifies the output.
//    * "C++'", print as C++ code.
//    * "F77", print as FORTRAN77 code.
//    * "F90", print as FORTRAN90 code.
//    * "MAT", print as MATLAB code.
//    * file,  write files "file_w.txt", "file_x.txt", "file_r.txt" 
//      defining weights, abscissas, and region.
// 
{
  bool header;
  int i;
  char output_r[81];
  char output_w[81];
  char output_x[81];
  double *r;
  double *w;
  double *x;

  r = new double[2];
  w = new double[order];
  x = new double[order];

  r[0] = - 1.0;
  r[1] = + 1.0;

  chebyshev2_compute ( order, x, w );

  if ( s_eqi ( output, "C++" ) )
  {
    cout << "//\n";
    cout << "//  Weights W, abscissas X and range R\n";
    cout << "//  for a Gauss-Chebyshev type 2 quadrature rule.\n";
    cout << "//  ORDER = " << order << "\n";
    cout << "//\n";
    cout << "//  Standard rule:\n";
	cout << "//    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx\n";
	cout << "//    is to be approximated by\n";
	cout << "//    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).\n";
    cout << "//\n";

    for ( i = 0; i < order; i++ )
    {
      cout << "  w[" << i << "] = " 
           << setprecision(16) << w[i] << ";\n";
    }
    cout << "\n";
    for ( i = 0; i < order; i++ )
    {
      cout << "  x[" << i << "] = " 
           << setprecision(16) << x[i] << ";\n";
    }
    cout << "\n";
    for ( i = 0; i < 2; i++ )
    {
      cout << "  r[" << i << "] = " << r[i] << ";\n";
    }
   }
   else if ( s_eqi ( output, "F77" ) )
   {
    cout << "c\n";
    cout << "c  Weights W, abscissas X and range R\n";
    cout << "c  for a Gauss-Chebyshev type 2 quadrature rule.\n";
    cout << "c  ORDER = " << order << "\n";
    cout << "c\n";
	cout << "c  Standard rule:\n";
	cout << "c    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx\n";
	cout << "c    is to be approximated by\n";
	cout << "c    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).\n";
    cout << "c\n";

    for ( i = 0; i < order; i++ )
    {
      cout << "      w(" << i + 1 << ") = " 
           << setprecision(16) << w[i] << "\n";
    }
    cout << "\n";
    for ( i = 0; i < order; i++ )
    {
      cout << "      x(" << i + 1 << ") = " 
           << setprecision(16) << x[i] << "\n";
    }
    cout << "\n";
    for ( i = 0; i < 2; i++ )
    {
      cout << "      r(" << i + 1 << ") = " << r[i] << "\n";
    }
  }
  else if ( s_eqi ( output, "F90" ) )
  {  
    cout << "!\n";
    cout << "!  Weights W, abscissas X and range R\n";
    cout << "!  for a Gauss-Chebyshev type 2 quadrature rule.\n";
    cout << "!  ORDER = " << order << "\n";
    cout << "!\n";
	cout << "!  Standard rule:\n";
	cout << "!    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx\n";
	cout << "!    is to be approximated by\n";
	cout << "!    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).\n";
    cout << "!\n";

    for ( i = 0; i < order; i++ )
    {
      cout << "  w(" << i + 1 << ") = " 
           << setprecision(16) << w[i] << "\n";
    }
    cout << "\n";
    for ( i = 0; i < order; i++ )
    {
      cout << "  x(" << i + 1 << ") = " 
           << setprecision(16) << x[i] << "\n";
    }
    cout << "\n";
    for ( i = 0; i < 2; i++ )
    {
      cout << "  r(" << i + 1 << ") = " << r[i] << "\n";
    }
  }
  else if ( s_eqi ( output, "MAT" ) )
  {
    cout << "%\n";
    cout << "%  Weights W, abscissas X and range R\n";
    cout << "%  for a Gauss-Chebyshev type 2 quadrature rule.\n";
    cout << "%  ORDER = " << order << "\n";
    cout << "%\n";
	cout << "%  Standard rule:\n";
	cout << "%    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx\n";
	cout << "%    is to be approximated by\n";
	cout << "%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).\n";
    cout << "%\n";

    for ( i = 0; i < order; i++ )
    {
      cout << "  w(" << i + 1 << ") = " 
           << setprecision(16) << w[i] << ";\n";
    }
    cout << "\n";
    for ( i = 0; i < order; i++ )
    {
      cout << "  x(" << i + 1 << ") = " 
           << setprecision(16) << x[i] << ";\n";
    }
    cout << "\n";
    for ( i = 0; i < 2; i++ )
    {
      cout << "  r(" << i + 1 << ") = " << r[i] << ";\n";
    }
  } 
  else
  {
    sprintf ( output_w, "%s_w.txt", output );
    sprintf ( output_x, "%s_x.txt", output );
    sprintf ( output_r, "%s_r.txt", output );

    cout << "\n";
    cout << "  Creating quadrature files.\n";
    cout << "\n";
    cout << "  Root file name is     \"" << output   << "\".\n";
    cout << "\n";
    cout << "  Weight file will be   \"" << output_w << "\".\n";
    cout << "  Abscissa file will be \"" << output_x << "\".\n";
    cout << "  Region file will be   \"" << output_r << "\".\n";

    header = false;
            
    dtable_write ( output_w, 1, order, w, header );
    dtable_write ( output_x, 1, order, x, header );
    dtable_write ( output_r, 1, 2,     r, header );
  }
  
  delete [] r;
  delete [] w;
  delete [] x;

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

void dtable_close_write ( ofstream &output )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_CLOSE_WRITE closes a file to which a DTABLE was to be written.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream output, the output file stream.
//
{
  output.close ( );

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

void dtable_data_write ( ofstream &output, int m, int n, double table[] )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_DATA_WRITE writes data to a DTABLE file.
//
//  Discussion:
//
//    The file should already be open.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream &OUTPUT, a pointer to the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, double TABLE[M*N], the table data.
//
{
  int i;
  int j;
  char *s;

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << setprecision(16) << setw(24) << table[i+j*m] << "  ";
    }
    output << "\n";
  }

  output.close ( );

  return;
}
//****************************************************************************80
 
void dtable_header_write ( char *output_filename, ofstream &output, int m, 
  int n )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_WRITE writes the header of a DTABLE file.
//
//  Discussion:
//
//    The file should already be open.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *OUTPUT_FILENAME, the output filename.
//
//    Input, ofstream &OUTPUT, the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
{
  char *s;

  s = timestring ( );

  output << "#  " << output_filename << "\n";
  output << "#  created by dtable_write in table_io.C" << "\n";
  output << "#  at " << s << "\n";
  output << "#\n";
  output << "#  Spatial dimension M = " << m << "\n";
  output << "#  Number of points N =  " << n << "\n";
  output << "#  EPSILON (unit roundoff) = " << r8_epsilon ( ) << "\n";
  output << "#\n";

  delete [] s;

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

void dtable_write ( char *output_filename, int m, int n, double table[], 
  bool header )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_WRITE writes information to a DTABLE file.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *OUTPUT_FILENAME, the output filename.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, double TABLE[M*N], the table data.
//
//    Input, bool HEADER, is TRUE if the header is to be included.
//
{
  ofstream output;

  output.open ( output_filename );

  if ( !output )
  {
    cout << "\n";
    cout << "DTABLE_WRITE - Fatal error!\n";
    cout << "  Could not open the output file.\n";
    return;
  }

  if ( header )
  {
    dtable_header_write ( output_filename, output, m, n );
  }

  dtable_data_write ( output, m, n, table );

  dtable_close_write ( output );

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

double r8_epsilon ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_EPSILON returns the R8 roundoff unit.
//
//  Discussion:
//
//    The roundoff unit is a number R which is a power of 2 with the 
//    property that, to the precision of the computer's arithmetic,
//      1 < 1 + R
//    but 
//      1 = ( 1 + R / 2 )
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_EPSILON, the R8 round-off unit.
//
{
  double value;

  value = 1.0;

  while ( 1.0 < ( double ) ( 1.0 + value )  )
  {
    value = value / 2.0;
  }

  value = 2.0 * value;

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

bool s_eqi ( char *s1, char *s2 )

//****************************************************************************80
//
//  Purpose:
//
//    S_EQI reports whether two strings are equal, ignoring case.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S1, char *S2, pointers to two strings.
//
//    Output, bool S_EQI, is true if the strings are equal. 
//
{
  int i;
  int nchar;
  int nchar1;
  int nchar2;

  nchar1 = strlen ( s1 );
  nchar2 = strlen ( s2 );
  if ( nchar1 < nchar2 )
  {
    nchar = nchar1;
  }
  else
  {
    nchar = nchar2;
  }
//
//  The strings are not equal if they differ over their common length.
//
  for ( i = 0; i < nchar; i++ ) 
  {

    if ( ch_cap ( s1[i] ) != ch_cap ( s2[i] ) ) 
    {
      return false;
    }
  }
//
//  The strings are not equal if the longer one includes nonblanks
//  in the tail.
//
  if ( nchar < nchar1 ) 
  {
    for ( i = nchar; i < nchar1; i++ ) 
    {
      if ( s1[i] != ' ' ) 
      {
        return false;
      }
    } 
  }
  else if ( nchar < nchar2 ) 
  {
    for ( i = nchar; i < nchar2; i++ )
    {
      if ( s2[i] != ' ' ) 
      {
        return false;
      }
    } 
  }

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

void timestamp ( void )

//****************************************************************************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 GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

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

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

  cout << time_buffer << "\n";

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

char *timestring ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTRING returns the current YMDHMS date as a string.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 January 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, char *TIMESTRING, a string containing the current YMDHMS date.
//
{
# define TIME_SIZE 40

  const struct tm *tm;
  size_t len;
  time_t now;
  char *s;

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

  s = new char[TIME_SIZE];

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

  return s;
# undef TIME_SIZE
}