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

# include "mpi.h"

int main ( int argc, char *argv[] );
char ch_cap ( char ch );
int ch_eqi ( char ch1, char ch2 );
int ch_to_digit ( char ch );
double *dtable_data_read ( char *input_filename, int m, int n );
void dtable_header_read ( char *input_filename, int *m, int *n );
int file_column_count ( char *input_filename );
int file_row_count ( char *input_filename );
int i4_div_rounded ( int a, int b );
int i4_huge ( void );
int i4_sign ( int i );
int s_len_trim ( char *s );
int s_to_i4 ( char *s, int *last, int *error );
double s_to_r8 ( char *s, int *lchar, int *error );
int s_to_r8vec ( char *s, int n, double rvec[] );
int s_word_count ( char *s );
void timestamp ( void );
void p28_f ( int dim_num, int point_num, double x[], double value[] );

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

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

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

    MAIN is the main program for QUAD_MPI.

  Discussion:

    Process 0 reads the name of a quadrature rule file, 
    reads the R, W and X files, and sends a subset of the W and X data
    to each process (including itself!).

    Process I evaluates F(X) at the assigned points and returns the
    weighted sum to Process 0.

    Process 0 adds up the contributions and reports the integral estimate.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    04 May 2008

  Author:

    John Burkardt
*/
{
  int dim;
  int dim_num;
  int dim_num2;
  int error;
  double *f_proc;
  int i;
  double integral;
  int last;
  int point;
  int point_num;
  int point_num_proc;
  int point_num2;
  int problem;
  int process;
  int process_id;
  int process_master = 0;
  int process_number;
  int process_remain;
  double quad;
  double quad_err;
  char quad_filename[81];
  double quad_proc;
  char quad_r_filename[81];
  char quad_w_filename[81];
  char quad_x_filename[81];
  double *r;
  char *region;
  int source;
  MPI_Status status;
  char *string;
  int tag;
  int target;
  int task_hi;
  int task_lo;
  int task_proc;
  int task_remain;
  double volume1;
  double *w;
  double *w_proc;
  double wtime_diff;
  double wtime_start;
  double wtime_stop;
  double *x;
  double *x_proc;
/*
  Initialize MPI.
*/
  MPI_Init ( &argc, &argv );
/*
  Get this processor's ID.
*/
  MPI_Comm_rank ( MPI_COMM_WORLD, &process_id );
/*
  Get the number of processors.
*/
  MPI_Comm_size ( MPI_COMM_WORLD, &process_number );

  if ( process_id == process_master )
  {
    timestamp ( );
    printf ( "\n" );
    printf ( "QUAD_MPI\n" );
    printf ( "  C version\n" );
    printf ( "\n" );
    printf ( "  Compiled on %s at %s\n", __DATE__, __TIME__ );
    printf ( "\n" );
    printf ( "  Estimate the integral of a function F(X)\n" );
    printf ( "  defined over a multidimensional domain\n" );
    printf ( "  using a quadrature rule stored in 3 files.\n" );
    printf ( "\n" );
    printf ( "  Use MPI to divide the computation among\n" );
    printf ( "  multiple processes.\n" );
    printf ( "\n" );
    printf ( "\n" );
    printf ( "  The parallel processing is carried out as follows,\n" );
    printf ( "  with process 0 playing the role of \"master\":\n" );
    printf ( "\n" );;
    printf ( "  Process 0:\n" );
    printf ( "\n" );
    printf ( "  * Reads 3 files defining a quadrature rule.\n" );
    printf ( "  * Divides the quadrature rule into PROC_NUM\n" );
    printf ( "    portions, sending one portion to each processor\n" );
    printf ( "    (including itself).\n" );
    printf ( "  * Carries out its portion of the computation\n" );
    printf ( "  * Collects and sums the contributions from\n" );
    printf ( "    other processes.\n" );
    printf ( "\n" );
    printf ( "  Process I:\n" );
    printf ( "\n" );
    printf ( "  * Receives one portion of the quadrature rule;\n" );
    printf ( "  * Carries out its portion of the computation\n" );
    printf ( "  * Sends its contribution to process 0.\n" );
/*
  Get the quadrature file root name:
*/
    if ( 1 < argc ) 
    {
      strcpy ( quad_filename, argv[1] );
    }
    else
    {
      printf ( "\n" );
      printf ( "QUAD_MPI:\n" );
      printf ( "  Enter the \"root\" name of the quadrature files.\n" );

      scanf ( "%s", quad_filename );
    }
/*
  Create the names of:
    the quadrature X file;
    the quadrature W file;
    the quadrature R file.
*/
    if ( 0 < s_len_trim ( quad_filename ) )
    {
      strcpy ( quad_x_filename, quad_filename );
      strcat ( quad_x_filename, "_x.txt" );
      strcpy ( quad_w_filename, quad_filename );
      strcat ( quad_w_filename, "_w.txt" );
      strcpy ( quad_r_filename, quad_filename );
      strcat ( quad_r_filename, "_r.txt" );
    }
    else
    {
      strcpy ( quad_x_filename, "x.txt" );
      strcpy ( quad_w_filename, "w.txt" );
      strcpy ( quad_r_filename, "r.txt" );
    }
/*
  Summarize the input.
*/
    printf ( "\n" );
    printf ( "QUAD_MPI: User input:\n" );
    printf ( "  Quadrature rule X file = \"%s\".\n", quad_x_filename );
    printf ( "  Quadrature rule W file = \"%s\".\n", quad_w_filename );
    printf ( "  Quadrature rule R file = \"%s\".\n", quad_r_filename );
/*
  Read the X file.
*/
    dtable_header_read ( quad_x_filename, &dim_num, &point_num );

    printf ( "\n" );
    printf ( "  Spatial dimension = %d\n", dim_num );
    printf ( "  Number of points  = %d\n", point_num );

    x = dtable_data_read ( quad_x_filename, dim_num, point_num );
/*
  Read the W file.
*/
    dtable_header_read ( quad_w_filename, &dim_num2, &point_num2 );

    if ( dim_num2 != 1 ) 
    {
      printf ( "\n" );
      printf ( "QUAD_MPI - Fatal error!\n" );
      printf ( "  The quadrature weight file should have exactly\n" );
      printf ( "  one value on each line.\n" );
      exit ( 1 );
    }

    if ( point_num2 != point_num )
    {
      printf ( "\n" );
      printf ( "QUAD_MPI - Fatal error!\n" );
      printf ( "  The quadrature weight file should have exactly\n" );
      printf ( "  the same number of lines as the abscissa file.\n" );
      exit ( 1 );
    }

    w = dtable_data_read ( quad_w_filename, 1, point_num );
/*
  Read the R file.
*/
    dtable_header_read ( quad_r_filename, &dim_num2, &point_num2 );

    if ( dim_num2 != dim_num )
    {
      printf ( "\n" );
      printf ( "QUAD_MPI - Fatal error!\n" );
      printf ( "  The quadrature region file should have the same\n" );
      printf ( "  number of values on each line as the abscissa file\n" );
      printf ( "  does.\n" );
      exit ( 1 );
    }

    if ( point_num2 != 2 )
    {
      printf ( "\n" );
      printf ( "QUAD_MPI - Fatal error!\n" );
      printf ( "  The quadrature region file should have two lines.\n" );
      exit ( 1 );
    }

    r = dtable_data_read ( quad_r_filename, dim_num, 2 );
/*
  Rescale the weights, and translate the abscissas.
*/
    volume1 = 1.0;
    for ( dim = 0; dim < dim_num; dim++ )
    {
      volume1 = volume1 * ( r[dim+1*dim_num] - r[dim+0*dim_num] );
    }
    volume1 = fabs ( volume1 );

    problem = 28;

    integral = pow ( 2.0 * atan ( 0.5 ), dim_num );
/*
  Map the abscissas to the [A,B] hypercube.
*/
    for ( point = 0; point < point_num; point++ )
    {
      for ( dim = 0; dim < dim_num; dim++ )
      {
        x[dim+point*dim_num] = ( x[dim+point*dim_num] - r[dim+0*dim_num] )
                             / ( r[dim+1*dim_num]     - r[dim+0*dim_num] );
      }
    }
  }
/*
  We have POINT_NUM tasks to carry out, and PROCESS_NUMBER processors.

  We assign tasks TASK_LO to TASK_HI to processor PROCESS.

  The master process BROADCASTS to all processes:

    DIM_NUM

  The master process SENDS to PROCESS:

    TASK_PROC = TASK_HI + 1 - TASK_LO;
    W(TASK_LO:TASK_HI)
    X(1:DIM_NUM,TASK_LO:TASK:HI)

  Process PROCESS RECEIVES the data, evaluates

    QUAD_PROC = sum ( TASK_LO <= TASK <= TASK_HI ) W(TASK) * F(X(:,TASK) )

  and SENDS QUAD_PROC back to the master process.

  While PROCESS 0 also does its share of the work, we don't allow it
  to SEND or RECEIVE messages to itself.

  PROCESS 0 sums up the values of QUAD_PROC to produce QUAD, 
  the estimate for the integral.
*/
  source = process_master;
  MPI_Bcast ( &dim_num, 1, MPI_INT, source, MPI_COMM_WORLD );

  if ( process_id == process_master )
  {
    task_hi = -1;

    task_remain = point_num;
    process_remain = process_number;

    for ( process = 0; process < process_number; process++ )
    {
      task_proc = i4_div_rounded ( task_remain, process_remain );

      process_remain = process_remain - 1;
      task_remain = task_remain - task_proc;

      task_lo = task_hi + 1;
      task_hi = task_hi + task_proc;

      if ( process == process_master )
      {
        point_num_proc = task_proc;

        w_proc = ( double * ) malloc ( point_num_proc * sizeof ( double ) );

        for ( point = 0; point < point_num_proc; point++ )
        {
          w_proc[point] = w[task_lo+point];
        }

        x_proc = ( double * ) malloc ( dim_num * point_num_proc * sizeof ( double ) );

        for ( point = 0; point < point_num_proc; point++ )
        {
          for ( dim = 0; dim < dim_num; dim++ )
          {
            x_proc[dim+point*dim_num] = x[dim+(point+task_lo)*dim_num];
          }
        }
      }
      else
      {
        target = process;
        tag = 1;
        MPI_Send ( &task_proc, 1, MPI_INT, target, tag, MPI_COMM_WORLD );

        target = process;
        tag = 2;
        MPI_Send ( w+task_lo, task_proc, MPI_DOUBLE, target, tag, MPI_COMM_WORLD );

        target = process;
        tag = 3;
        MPI_Send ( x+task_lo*dim_num, dim_num * task_proc, 
          MPI_DOUBLE, target, tag, MPI_COMM_WORLD );
      }
    }
    quad = 0.0;
  }
  else
  {
    source = process_master;
    tag = 1;

    MPI_Recv ( &point_num_proc, 1, MPI_INT, source, tag, MPI_COMM_WORLD, 
      &status );

    w_proc = ( double * ) malloc ( point_num_proc * sizeof ( double ) );

    source = process_master;
    tag = 2;

    MPI_Recv ( w_proc, point_num_proc, MPI_DOUBLE, source, tag, MPI_COMM_WORLD, 
      &status );

    x_proc = ( double * ) malloc ( dim_num * point_num_proc * sizeof ( double ) );
    source = process_master;
    tag = 3;

    MPI_Recv ( x_proc, dim_num * point_num_proc, MPI_DOUBLE, source, tag, 
      MPI_COMM_WORLD, &status );
  }
/*
  Each process evaluates the function at the abscissas.
*/
  f_proc = ( double * ) malloc ( point_num_proc * sizeof ( double ) );

  p28_f ( dim_num, point_num_proc, x_proc, f_proc );
/*
  Each process weights their points.
*/
  quad_proc = 0.0;
  for ( point = 0; point < point_num_proc; point++ )
  {
    quad_proc = quad_proc + w_proc[point] * f_proc[point];
  }

  printf ( "  Process %d contributes QUAD_PROC = %f\n", process_id, quad_proc );
/*
  Each process sends its value of QUAD_PROC to the master process, to
  be summed in QUAD.
*/
  MPI_Reduce ( &quad_proc, &quad, 1, MPI_DOUBLE, MPI_SUM, process_master,
  MPI_COMM_WORLD );

  free ( f_proc );
  free ( w_proc );
  free ( x_proc );
/*
  Compute the weighted estimate.
*/
  if ( process_id == process_master )
  {
    quad = quad / volume1;

    quad_err = fabs ( quad - integral );

    printf ( "\n" );
    printf ( 
      "  Prob   Dim      Points       Approx          Exact           Error      Time\n" );
    printf ( "\n" );

    printf ( "  %4d  %4d  %10d  %14e  %14e  %10e\n",
      problem, dim_num, point_num, quad, integral, quad_err );

    free ( r );
    free ( w );
    free ( x );

    printf ( "\n" );
    printf ( "QUAD_MPI:\n" );
    printf ( "  Normal end of execution.\n" );
    printf ( "\n" );
    timestamp ( );
  }
/*
  TERMINATE PARALLEL PROCESSING.
*/
  MPI_Finalize ( );

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

char ch_cap ( char ch )

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

    19 July 1998

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

int ch_eqi ( char ch1, char ch2 )

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

    CH_EQI is TRUE (1) if two characters are equal, disregarding case.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Parameters:

    Input, char CH1, CH2, the characters to compare.

    Output, int CH_EQI, is TRUE (1) if the two characters are equal,
    disregarding case and FALSE (0) otherwise.
*/
{
  int value;

  if ( 97 <= ch1 && ch1 <= 122 ) 
  {
    ch1 = ch1 - 32;
  } 
  if ( 97 <= ch2 && ch2 <= 122 ) 
  {
    ch2 = ch2 - 32;
  }     
  if ( ch1 == ch2 )
  {
    value = 1;
  }
  else
  {
    value = 0;
  }
  return value;
}
/******************************************************************************/

int ch_to_digit ( char ch )

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

    13 June 2003

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

double *dtable_data_read ( char *input_filename, int m, int n )

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

    DTABLE_DATA_READ reads the data from a DTABLE file.

  Discussion:

    The file is assumed to contain one record per line.

    Records beginning with the '#' character are comments, and are ignored.
    Blank lines are also ignored.

    Each line that is not ignored is assumed to contain exactly (or at least)
    M real numbers, representing the coordinates of a point.

    There are assumed to be exactly (or at least) N such records.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    27 January 2005

  Author:

    John Burkardt

  Parameters:

    Input, char *INPUT_FILENAME, the name of the input file.

    Input, int M, the number of spatial dimensions.

    Input, int N, the number of points.  The program
    will stop reading data once N values have been read.

    Output, double DTABLE_DATA_READ[M*N], the table data.
*/
{
# define LINE_MAX 255

  int error;
  char *got_string;
  FILE *input;
  int i;
  int j;
  char line[255];
  double *table;
  double *x;

  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    printf ( "\n" );
    printf ( "DTABLE_DATA_READ - Fatal error!\n" );
    printf ( "  Could not open the input file: \"%s\"\n", input_filename );
    return NULL;
  }

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

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

  j = 0;

  while ( j < n )
  {
    got_string = fgets ( line, LINE_MAX, input );

    if ( !got_string )
    {
      break;
    }

    if ( line[0] == '#' || s_len_trim ( line ) == 0 )
    {
      continue;
    }

    error = s_to_r8vec ( line, m, x );

    if ( error == 1 )
    {
      continue;
    }

    for ( i = 0; i < m; i++ )
    {
      table[i+j*m] = x[i];
    }
    j = j + 1;

  }

  fclose ( input );

  free ( x );

  return table;

# undef LINE_MAX
}
/******************************************************************************/
 
void dtable_header_read ( char *input_filename, int *m, int *n )
 
/******************************************************************************/
/*
  Purpose:

    DTABLE_HEADER_READ reads the header from a DTABLE file.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    04 June 2004

  Author:

    John Burkardt

  Parameters:

    Input, char *INPUT_FILENAME, the name of the input file.

    Output, int *M, the number of spatial dimensions.

    Output, int *N, the number of points.
*/
{
  *m = file_column_count ( input_filename );

  if ( *m <= 0 )
  {
    printf ( "\n" );
    printf ( "DTABLE_HEADER_READ - Fatal error!\n" );
    printf ( "  FILE_COLUMN_COUNT failed.\n" );
    *n = -1;
    return;
  }

  *n = file_row_count ( input_filename );

  if ( *n <= 0 )
  {
    printf ( "\n" );
    printf ( "DTABLE_HEADER_READ - Fatal error!\n" );
    printf ( "  FILE_ROW_COUNT failed.\n" );
    return;
  }

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

int file_column_count ( char *input_filename )

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

    FILE_COLUMN_COUNT counts the number of columns in the first line of a file.

  Discussion:

    The file is assumed to be a simple text file.

    Most lines of the file is presumed to consist of COLUMN_NUM words, separated
    by spaces.  There may also be some blank lines, and some comment lines,
    which have a "#" in column 1.

    The routine tries to find the first non-comment non-blank line and
    counts the number of words in that line.

    If all lines are blanks or comments, it goes back and tries to analyze
    a comment line.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Parameters:

    Input, char *INPUT_FILENAME, the name of the file.

    Output, int FILE_COLUMN_COUNT, the number of columns assumed 
    to be in the file.
*/
{
# define LINE_MAX 256

  int column_num;
  char *error;
  FILE *input;
  int got_one;
  char line[LINE_MAX];
/*
  Open the file.
*/
  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    column_num = -1;
    printf ( "\n" );
    printf ( "FILE_COLUMN_COUNT - Fatal error!\n" );
    printf ( "  Could not open the input file: \"%s\"\n", input_filename );
    return column_num;
  }
/*
  Read one line, but skip blank lines and comment lines.
*/
  got_one = 0;

  for ( ; ; )
  {
    error = fgets ( line, LINE_MAX, input );

    if ( !error )
    {
      break;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      continue;
    }

    if ( line[0] == '#' )
    {
      continue;
    }

    got_one = 1;
    break;

  }

  if ( got_one == 0 )
  {
    fclose ( input );

    input = fopen ( input_filename, "r" );

    for ( ; ; )
    {
      error = fgets ( line, LINE_MAX, input );

      if ( !error )
      {
        break;
      }

      if ( s_len_trim ( line ) == 0 )
      {
        continue;
      }

      got_one = 1;
      break;
    }
  }

  fclose ( input );

  if ( got_one == 0 )
  {
    printf ( "\n" );
    printf ( "FILE_COLUMN_COUNT - Warning!\n" );
    printf ( "  The file does not seem to contain any data.\n" );
    return -1;
  }

  column_num = s_word_count ( line );

  return column_num;

# undef LINE_MAX
}
/******************************************************************************/

int file_row_count ( char *input_filename )

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

    FILE_ROW_COUNT counts the number of row records in a file.

  Discussion:

    It does not count lines that are blank, or that begin with a
    comment symbol '#'.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Parameters:

    Input, char *INPUT_FILENAME, the name of the input file.

    Output, int FILE_ROW_COUNT, the number of rows found.
*/
{
# define LINE_MAX 256

  int bad_num;
  int comment_num;
  char *error;
  FILE *input;
  int i;
  char line[LINE_MAX];
  int record_num;
  int row_num;

  row_num = 0;
  comment_num = 0;
  record_num = 0;
  bad_num = 0;

  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    printf ( "\n" );
    printf ( "FILE_ROW_COUNT - Fatal error!\n" );
    printf ( "  Could not open the input file: \"%s\"\n", input_filename );
    return (-1);
  }

  for ( ; ; )
  {
    error = fgets ( line, LINE_MAX, input );

    if ( !error )
    {
      break;
    }

    record_num = record_num + 1;

    if ( line[0] == '#' )
    {
      comment_num = comment_num + 1;
      continue;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      comment_num = comment_num + 1;
      continue;
    }

    row_num = row_num + 1;
  }

  fclose ( input );

  return row_num;

# undef LINE_MAX
}
/******************************************************************************/

int i4_div_rounded ( int a, int b )

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

    I4_DIV_ROUNDED computes the rounded result of I4 division.

  Discussion:

    This routine computes C = A / B, where A, B and C are integers
    and C is the closest integer value to the exact real result.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    23 October 2007

  Author:

    John Burkardt

  Parameters:

    Input, int A, B, the number to be divided,
    and the divisor.

    Output, int I4_DIV_ROUNDED, the rounded result
    of the division.
*/
{
  int a_abs;
  int b_abs;
  int c;
  int c_abs;
  int c_s;

  if ( a == 0 )
  {
    c_abs = i4_huge ( );
    c_s = i4_sign ( b );
  }
  else
  {
    a_abs = abs ( a );
    b_abs = abs ( b );
    c_s = i4_sign ( a ) * i4_sign ( b );

    c_abs = a_abs / b_abs;

    if ( ( 2 * c_abs + 1 ) * b_abs < 2 * a_abs )
    {
      c_abs = c_abs + 1;
    }
  }

  c = c_s * c_abs;

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

int i4_huge ( void )

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

    I4_HUGE returns a "huge" I4.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Output, int I4_HUGE, a "huge" integer.
*/
{
  return 2147483647;
}
/******************************************************************************/

int i4_sign ( int i )

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

    I4_SIGN returns the sign of an I4.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    23 October 2007

  Author:

    John Burkardt

  Parameters:

    Input, int I, the integer whose sign is desired.

    Output, int I4_SIGN, the sign of I.
*/
{
  int value;

  if ( i < 0 ) 
  {
    value = -1;
  }
  else
  {
    value = 1;
  }
  return value;
}
/******************************************************************************/

int s_len_trim ( char *s )

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

    S_LEN_TRIM returns the length of a string to the last nonblank.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    26 April 2003

  Author:

    John Burkardt

  Parameters:

    Input, char *S, a pointer to a string.

    Output, int S_LEN_TRIM, the length of the string to the last nonblank.
    If S_LEN_TRIM is 0, then the string is entirely blank.
*/
{
  int n;
  char *t;

  n = strlen ( s );
  t = s + strlen ( s ) - 1;

  while ( 0 < n ) 
  {
    if ( *t != ' ' )
    {
      return n;
    }
    t--;
    n--;
  }

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

int s_to_i4 ( char *s, int *last, int *error )

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

    S_TO_I4 reads an I4 from a string.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Parameters:

    Input, char *S, a string to be examined.

    Output, int *LAST, the last character of S used to make IVAL.

    Output, int *ERROR is TRUE (1) if an error occurred and FALSE (0) otherwise.

    Output, int *S_TO_I4, the integer value read from the string.
    If the string is blank, then IVAL will be returned 0.
*/
{
  char c;
  int i;
  int isgn;
  int istate;
  int ival;

  *error = 0;
  istate = 0;
  isgn = 1;
  i = 0;
  ival = 0;

  while ( *s ) 
  {
    c = s[i];
    i = i + 1;
/*
  Haven't read anything.
*/
    if ( istate == 0 )
    {
      if ( c == ' ' )
      {
      }
      else if ( c == '-' )
      {
        istate = 1;
        isgn = -1;
      }
      else if ( c == '+' )
      {
        istate = 1;
        isgn = + 1;
      }
      else if ( '0' <= c && c <= '9' )
      {
        istate = 2;
        ival = c - '0';
      }
      else
      {
        *error = 1;
        return ival;
      }
    }
/*
  Have read the sign, expecting digits.
*/
    else if ( istate == 1 )
    {
      if ( c == ' ' )
      {
      }
      else if ( '0' <= c && c <= '9' )
      {
        istate = 2;
        ival = c - '0';
      }
      else
      {
        *error = 1;
        return ival;
      }
    }
/*
  Have read at least one digit, expecting more.
*/
    else if ( istate == 2 )
    {
      if ( '0' <= c && c <= '9' )
      {
        ival = 10 * (ival) + c - '0';
      }
      else
      {
        ival = isgn * ival;
        *last = i - 1;
        return ival;
      }

    }
  }
/*
  If we read all the characters in the string, see if we're OK.
*/
  if ( istate == 2 )
  {
    ival = isgn * ival;
    *last = s_len_trim ( s );
  }
  else
  {
    *error = 1;
    *last = 0;
  }

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

double s_to_r8 ( char *s, int *lchar, int *error )

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

    S_TO_R8 reads an R8 value from a string.

  Discussion:

    We have had some trouble with input of the form 1.0E-312.
    For now, let's assume anything less than 1.0E-20 is zero.

    This routine will read as many characters as possible until it reaches
    the end of the string, or encounters a character which cannot be
    part of the real number.

    Legal input is:

       1 blanks,
       2 '+' or '-' sign,
       2.5 spaces
       3 integer part,
       4 decimal point,
       5 fraction part,
       6 'E' or 'e' or 'D' or 'd', exponent marker,
       7 exponent sign,
       8 exponent integer part,
       9 exponent decimal point,
      10 exponent fraction part,
      11 blanks,
      12 final comma or semicolon.

    with most quantities optional.

  Example:

    S                 R

    '1'               1.0
    '     1   '       1.0
    '1A'              1.0
    '12,34,56'        12.0
    '  34 7'          34.0
    '-1E2ABCD'        -100.0
    '-1X2ABCD'        -1.0
    ' 2E-1'           0.2
    '23.45'           23.45
    '-4.2E+2'         -420.0
    '17d2'            1700.0
    '-14e-2'         -0.14
    'e2'              100.0
    '-12.73e-9.23'   -12.73 * 10.0**(-9.23)

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    24 June 2005

  Author:

    John Burkardt

  Parameters:

    Input, char *S, the string containing the
    data to be read.  Reading will begin at position 1 and
    terminate at the end of the string, or when no more
    characters can be read to form a legal real.  Blanks,
    commas, or other nonnumeric data will, in particular,
    cause the conversion to halt.

    Output, int *LCHAR, the number of characters read from
    the string to form the number, including any terminating
    characters such as a trailing comma or blanks.

    Output, int *ERROR, is TRUE (1) if an error occurred and FALSE (0)
    otherwise.

    Output, double S_TO_R8, the value that was read from the string.
*/
{
  char c;
  int ihave;
  int isgn;
  int iterm;
  int jbot;
  int jsgn;
  int jtop;
  int nchar;
  int ndig;
  double r;
  double rbot;
  double rexp;
  double rtop;
  char TAB = 9;

  nchar = s_len_trim ( s );
  *error = 0;
  r = 0.0;
  *lchar = -1;
  isgn = 1;
  rtop = 0.0;
  rbot = 1.0;
  jsgn = 1;
  jtop = 0;
  jbot = 1;
  ihave = 1;
  iterm = 0;

  for ( ; ; )
  {
    c = s[*lchar+1];
    *lchar = *lchar + 1;
/*
  Blank or TAB character.
*/
    if ( c == ' ' || c == TAB )
    {
      if ( ihave == 2 )
      {
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        iterm = 1;
      }
      else if ( 1 < ihave )
      {
        ihave = 11;
      }
    }
/*
  Comma.
*/
    else if ( c == ',' || c == ';' )
    {
      if ( ihave != 1 )
      {
        iterm = 1;
        ihave = 12;
        *lchar = *lchar + 1;
      }
    }
/*
  Minus sign.
*/
    else if ( c == '-' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
        isgn = -1;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
        jsgn = -1;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Plus sign.
*/
    else if ( c == '+' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Decimal point.
*/
    else if ( c == '.' )
    {
      if ( ihave < 4 )
      {
        ihave = 4;
      }
      else if ( 6 <= ihave && ihave <= 8 )
      {
        ihave = 9;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Exponent marker.
*/
    else if ( ch_eqi ( c, 'E' ) || ch_eqi ( c, 'D' ) )
    {
      if ( ihave < 6 )
      {
        ihave = 6;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Digit.
*/
    else if ( ihave < 11 && '0' <= c && c <= '9' )
    {
      if ( ihave <= 2 )
      {
        ihave = 3;
      }
      else if ( ihave == 4 )
      {
        ihave = 5;
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        ihave = 8;
      }
      else if ( ihave == 9 )
      {
        ihave = 10;
      }

      ndig = ch_to_digit ( c );

      if ( ihave == 3 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
      }
      else if ( ihave == 5 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
        rbot = 10.0 * rbot;
      }
      else if ( ihave == 8 )
      {
        jtop = 10 * jtop + ndig;
      }
      else if ( ihave == 10 )
      {
        jtop = 10 * jtop + ndig;
        jbot = 10 * jbot;
      }
    }
/*
  Anything else is regarded as a terminator.
*/
    else
    {
      iterm = 1;
    }
/*
  If we haven't seen a terminator, and we haven't examined the
  entire string, go get the next character.
*/
    if ( iterm == 1 || nchar <= *lchar + 1 )
    {
      break;
    }

  }
/*
  If we haven't seen a terminator, and we have examined the
  entire string, then we're done, and LCHAR is equal to NCHAR.
*/
  if ( iterm != 1 && (*lchar) + 1 == nchar )
  {
    *lchar = nchar;
  }
/*
  Number seems to have terminated.  Have we got a legal number?
  Not if we terminated in states 1, 2, 6 or 7!
*/
  if ( ihave == 1 || ihave == 2 || ihave == 6 || ihave == 7 )
  {
    *error = 1;
    return r;
  }
/*
  Number seems OK.  Form it.

  We have had some trouble with input of the form 1.0E-312.
  For now, let's assume anything less than 1.0E-20 is zero.
*/
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      if ( jsgn * jtop < -20 )
      {
        rexp = 0.0;
      }
      else
      {
        rexp = pow ( ( double ) 10.0, ( double ) ( jsgn * jtop ) );
      }
    }
    else
    {
      if ( jsgn * jtop < -20 * jbot )
      {
        rexp = 0.0;
      }
      else
      {
        rexp = jsgn * jtop;
        rexp = rexp / jbot;
        rexp = pow ( ( double ) 10.0, ( double ) rexp );
      }
    }

  }

  r = isgn * rexp * rtop / rbot;

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

int s_to_r8vec ( char *s, int n, double rvec[] )

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

    S_TO_R8VEC reads an R8VEC from a string.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    19 February 2001

  Author:

    John Burkardt

  Parameters:

    Input, char *S, the string to be read.

    Input, int N, the number of values expected.

    Output, double RVEC[N], the values read from the string.

    Output, int S_TO_R8VEC, is TRUE (1) if an error occurred and FALSE (0)
    otherwise.
*/
{
  int error;
  int i;
  int lchar;

  error = 0;

  for ( i = 0; i < n; i++ )
  {
    rvec[i] = s_to_r8 ( s, &lchar, &error );

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

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

int s_word_count ( char *s )

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

    S_WORD_COUNT counts the number of "words" in a string.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    30 January 2006

  Author:

    John Burkardt

  Parameters:

    Input, char *S, the string to be examined.

    Output, int S_WORD_COUNT, the number of "words" in the string.
    Words are presumed to be separated by one or more blanks.
*/
{
  int blank;
  int i;
  int word_num;

  word_num = 0;
  blank = 1;

  while ( *s ) 
  {
    if ( *s == ' ' )
    {
      blank = 1;
    }
    else if ( blank )
    {
      word_num = word_num + 1;
      blank = 0;
    }
    *s++;
  }

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

void timestamp ( void )

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

    24 September 2003

  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 );

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

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

void p28_f ( int dim_num, int point_num, double x[], double value[] )

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

    P28_F evaluates the integrand for problem 28.

  Dimension:

    N arbitrary.

  Region:

    0 <= X(1:DIM_NUM) <= 1

  Integrand:

    1 / product ( C(1:DIM_NUM)**2 + ( X(1:DIM_NUM) - Z(1:DIM_NUM) )**2 )

  Exact Integral:

    product ( (   arctan ( ( 1 - Z(1:DIM_NUM) ) / C(1:DIM_NUM) )
                + arctan (       Z(1:DIM_NUM)   / C(1:DIM_NUM) ) 
              ) / C(1:DIM_NUM)
            )

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    04 May 2008

  Author:

    John Burkardt

  Reference:

    Alan Genz,
    [Integral #2]
    A Package for Testing Multiple Integration Subroutines,
    in Numerical Integration: Recent Developments, Software
    and Applications,
    edited by Patrick Keast and Graeme Fairweather,
    D Reidel, 1987, pages 337-340,
    LC: QA299.3.N38.

    Thomas Patterson,
    [Integral #6],
    On the Construction of a Practical Ermakov-Zolotukhin 
    Multiple Integrator,
    in Numerical Integration: Recent Developments, Software
    and Applications,
    edited by Patrick Keast and Graeme Fairweather,
    D. Reidel, 1987, pages 269-290,
    LC: QA299.3.N38.

  Parameters:

    Input, int DIM_NUM, the dimension of the argument.

    Input, int POINT_NUM, the number of points.

    Input, double X[DIM_NUM*POINT_NUM], the evaluation points.

    Output, double VALUE[POINT_NUM], the function values.
*/
{
  int dim;
  int point;

  for ( point = 0; point < point_num; point++ )
  {
    value[point] = 1.0;
    for ( dim = 0; dim < dim_num; dim++ )
    {
      value[point] = value[point] 
        / ( 1.0 + ( x[dim+point*dim_num] - 0.5 ) * ( x[dim+point*dim_num] - 0.5 ) );
    }
  }
  return;
}