# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <string.h>
# include <time.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 );
int file_column_count ( char *filename );
int file_row_count ( char *filename );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
int i4_modp ( int i, int j );
int i4_wrap ( int ival, int ilo, int ihi );
int *i4mat_data_read ( char *input_filename, int m, int n );
void i4mat_header_read ( char *input_filename, int *m, int *n );
void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
void i4mat_write ( char *output_filename, int m, int n, int table[] );
void mesh_base_zero ( int node_num, int element_order, 
  int element_num, int element_node[] );
int r8_nint ( double x );
double *r8mat_data_read ( char *input_filename, int m, int n );
void r8mat_header_read ( char *input_filename, int *m, int *n );
void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
void r8mat_write ( char *output_filename, int m, int n, double table[] );
void s_blank_delete ( char *s );
int s_len_trim ( char *s );
int s_to_i4 ( char *s, int *last, int *error );
int s_to_i4vec ( char *s, int n, int ivec[] );
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 ( );

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

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

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

    MAIN is the main program for TRIANGULATION_NODE_TO_ELEMENT.

  Discussion:

    TRIANGULATION_NODE_TO_ELEMENT averages node values to an element value.

    This program is given a triangulation, along with the values of one or
    more data items associated with each node.

    It produces a file containing the average of the nodal values for 
    each element.

  Usage:

    triangulation_node_to_element ( 'prefix' )

    where

    * 'prefix'_nodes.txt contains the node coordinates;
    * 'prefix'_elements.txt contains the element definitions 
      (this file is optional, and if missing, the elements will be generated
      by the program);
    * 'prefix'_values.txt contains the nodal values.
    * 'prefix'_element_values will contain the averaged element data.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    08 April 2014

  Author:

    John Burkardt
*/
{
  int dim_num;
  char element_filename[255];
  int *element_node;
  int element_num;
  int element_order;
  double *element_value;
  char element_value_filename[255];
  int i;
  int j;
  int k;
  int ni;
  char node_filename[255];
  int node_num;
  double *node_xy;
  char prefix[255];
  int value_dim;
  char value_filename[255];
  int value_num;
  double *value;

  timestamp ( );
  printf ( "\n" );
  printf ( "TRIANGULATION_NODE_TO_ELEMENT:\n" );
  printf ( "  C version:\n" );
  printf ( "  Average nodal data to create element data.\n" );
  printf ( "\n" );
  printf ( "  This program expects three files:\n" );
  printf ( "  * prefix_nodes.txt,    node coordinates,\n" );
  printf ( "  * prefix_elements.txt, indices of nodes forming elements,\n" );
  printf ( "  * prefix_values.txt,   data values at nodes,\n" );
  printf ( "  and creates:\n" );
  printf ( "  * prefix_element_values.txt, averaged data at elements.\n" );
/*
  Get the filename prefix.
*/
  if ( argc <= 1 ) 
  {
    printf ( "\n" );
    printf ( "  Please enter the filename prefix.\n" );

    scanf ( "%s", prefix );
  }
  else 
  {
    strcpy ( prefix, argv[1] );
  }
/*
  Create the filenames.
*/
  strcpy ( node_filename, prefix );
  strcat ( node_filename, "_nodes.txt" );
  strcpy ( element_filename, prefix );
  strcat ( element_filename, "_elements.txt" );
  strcpy ( value_filename, prefix );
  strcat ( value_filename, "_values.txt" );
  strcpy ( element_value_filename, prefix );
  strcat ( element_value_filename, "_element_values.txt" );
/*
  Read the node data.
*/
  r8mat_header_read ( node_filename, &dim_num, &node_num );

  printf ( "\n" );
  printf ( "  Read the header of \"%s\".\n", node_filename );
  printf ( "\n" );
  printf ( "  Spatial dimension DIM_NUM = %d\n", dim_num );
  printf ( "  Number of nodes NODE_NUM  = %d\n", node_num );

  node_xy = r8mat_data_read ( node_filename, dim_num, node_num );

  printf ( "\n" );
  printf ( "  Read the data in \"%s\".\n", node_filename );

  r8mat_transpose_print_some ( dim_num, node_num, node_xy, 1, 1, dim_num, 5, 
    "  Portion of coordinate data from file:" );
/*
  Read the element data.
*/
  i4mat_header_read ( element_filename, &element_order, &element_num );

  printf ( "\n" );
  printf ( " Read the header of \"%s\".\n", element_filename );
  printf ( "\n" );
  printf ( "  Element order ELEMENT_ORDER = %d\n", element_order );
  printf ( "  Number of elements ELEMENT_NUM  = %d\n", element_num );

  element_node = i4mat_data_read ( element_filename, element_order, element_num );

  printf ( "\n" );
  printf ( "  Read the data in \"%s\".\n", element_filename );

  i4mat_transpose_print_some ( element_order, element_num, element_node, 1, 1, 
    element_order, 5, "  Portion of data read from file:" );
/*
  Read the node value data.
*/
  r8mat_header_read ( value_filename, &value_dim, &value_num );

  printf ( "\n" );
  printf ( "  Read the header of \"%s\".\n", value_filename );
  printf ( "\n" );
  printf ( "  Value dimension VALUE_DIM = %d\n", value_dim );
  printf ( "  Number of values VALUE_NUM  = %d\n", value_num );

  value = r8mat_data_read ( value_filename, value_dim, value_num );

  printf ( "\n" );
  printf ( "  Read the data in \"%s\".\n", value_filename );

  r8mat_transpose_print_some ( value_dim, value_num, value, 1, 1, value_dim, 5, 
    "  First 5 node values:" );
/*
  Detect and correct 1-based node indexing.
*/
  mesh_base_zero ( node_num, element_order, element_num, element_node );
/*
  Create the element values data.
*/
  element_value = ( double * ) malloc ( value_dim * element_num * sizeof ( double ) );

  for ( j = 0; j < element_num; j++ )
  {
    for ( i = 0; i < value_dim; i++ )
    {
      element_value[i+j*value_dim] = 0.0;
    }
  }

  for ( j = 0; j < element_num; j++ )
  {
    for ( i = 0; i < element_order; i++ )
    {
      ni = element_node[i+j*element_order];
      for ( k = 0; k < value_dim; k++ )
      {
        element_value[k+j*value_dim] = element_value[k+j*value_dim] 
          + value[k+ni*value_dim];
      }
    }
  }

  for ( j = 0; j < element_num; j++ )
  {
    for ( k = 0; k < value_dim; k++ )
    {
      element_value[k+j*value_dim] = element_value[k+j*value_dim] 
        / ( double ) ( element_order );
    }
  }
/*
  Write out the file.
*/
  r8mat_write ( element_value_filename, value_dim, element_num, element_value );

  printf ( "\n" );
  printf ( "  Element values written to '%s'\n", element_value_filename );
/*
  Free memory.
*/
  free ( element_node );
  free ( element_value );
  free ( node_xy );
  free ( value );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "TRIANGULATION_NODE_TO_ELEMENT:\n" );
  printf ( "  Normal end of execution.\n" );

  printf ( "\n" );
  timestamp ( );

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

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 MIT 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 255

  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 MIT 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 255

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

  row_num = 0;
  comment_num = 0;
  record_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_max ( int i1, int i2 )

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

    I4_MAX returns the maximum of two I4's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, are two integers to be compared.

    Output, int I4_MAX, the larger of I1 and I2.
*/
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

int i4_min ( int i1, int i2 )

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

    I4_MIN returns the smaller of two I4's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, two integers to be compared.

    Output, int I4_MIN, the smaller of I1 and I2.
*/
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

int i4_modp ( int i, int j )

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

    I4_MODP returns the nonnegative remainder of I4 division.

  Discussion:

    If
      NREM = I4_MODP ( I, J )
      NMULT = ( I - NREM ) / J
    then
      I = J * NMULT + NREM
    where NREM is always nonnegative.

    The MOD function computes a result with the same sign as the
    quantity being divided.  Thus, suppose you had an angle A,
    and you wanted to ensure that it was between 0 and 360.
    Then mod(A,360) would do, if A was positive, but if A
    was negative, your result would be between -360 and 0.

    On the other hand, I4_MODP(A,360) is between 0 and 360, always.

  Example:

        I         J     MOD  I4_MODP   I4_MODP Factorization

      107        50       7       7    107 =  2 *  50 + 7
      107       -50       7       7    107 = -2 * -50 + 7
     -107        50      -7      43   -107 = -3 *  50 + 43
     -107       -50      -7      43   -107 =  3 * -50 + 43

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    12 January 2007

  Author:

    John Burkardt

  Parameters:

    Input, int I, the number to be divided.

    Input, int J, the number that divides I.

    Output, int I4_MODP, the nonnegative remainder when I is
    divided by J.
*/
{
  int value;

  if ( j == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "I4_MODP - Fatal error!\n" );
    fprintf ( stderr, "  I4_MODP ( I, J ) called with J = %d\n", j );
    exit ( 1 );
  }

  value = i % j;

  if ( value < 0 )
  {
    value = value + abs ( j );
  }

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

int i4_wrap ( int ival, int ilo, int ihi )

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

    I4_WRAP forces an I4 to lie between given limits by wrapping.

  Example:

    ILO = 4, IHI = 8

    I   Value

    -2     8
    -1     4
     0     5
     1     6
     2     7
     3     8
     4     4
     5     5
     6     6
     7     7
     8     8
     9     4
    10     5
    11     6
    12     7
    13     8
    14     4

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 December 2012

  Author:

    John Burkardt

  Parameters:

    Input, int IVAL, an integer value.

    Input, int ILO, IHI, the desired bounds for the integer value.

    Output, int I4_WRAP, a "wrapped" version of IVAL.
*/
{
  int jhi;
  int jlo;
  int value;
  int wide;

  if ( ilo < ihi )
  {
   jlo = ilo;
   jhi = ihi;
  }
  else
  {
    jlo = ihi;
    jhi = ilo;
  }

  wide = jhi + 1 - jlo;

  if ( wide == 1 )
  {
    value = jlo;
  }
  else
  {
    value = jlo + i4_modp ( ival - jlo, wide );
  }

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

int *i4mat_data_read ( char *input_filename, int m, int n )

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

    I4MAT_DATA_READ reads the data from an I4MAT file.

  Discussion:

    An I4MAT is an array of I4's.

    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 MIT license. 

  Modified:

    28 May 2008

  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, int I4MAT_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];
  int *table;
  int *x;

  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    printf ( "\n" );
    printf ( "I4MAT_DATA_READ - Fatal error!\n" );
    printf ( "  Could not open the input file: \"%s\"\n", input_filename );
    return NULL;
  }

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

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

  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_i4vec ( 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 i4mat_header_read ( char *input_filename, int *m, int *n )
 
/******************************************************************************/
/*
  Purpose:

    I4MAT_HEADER_READ reads the header from an I4MAT file.

  Discussion:

    An I4MAT is an array of I4's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    28 May 2008

  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 ( "I4MAT_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 ( "I4MAT_HEADER_READ - Fatal error!\n" );
    printf ( "  FILE_ROW_COUNT failed.\n" );
    return;
  }

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

void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

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

    I4MAT_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.

  Discussion:

    An I4MAT is an MxN array of I4's, stored by (I,J) -> [I+J*M].

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 June 2005

  Author:

    John Burkardt

  Parameters:

    Input, int M, the number of rows of the matrix.
    M must be positive.

    Input, int N, the number of columns of the matrix.
    N must be positive.

    Input, int A[M*N], the matrix.

    Input, int ILO, JLO, IHI, JHI, designate the first row and
    column, and the last row and column to be printed.

    Input, char *TITLE, a title.
*/
{
# define INCX 10

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

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );
/*
  Print the columns of the matrix, in strips of INCX.
*/
  for ( i2lo = ilo; i2lo <= ihi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

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

  Write the header.
*/
    fprintf ( stdout, "  Row: " );
    for ( i = i2lo; i <= i2hi; i++ )
    {
      fprintf ( stdout, "%6d  ", i );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Col\n" );
    fprintf ( stdout, "\n" );
/*
  Determine the range of the rows in this strip.
*/
    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
/*
  Print out (up to INCX) entries in column J, that lie in the current strip.
*/
      fprintf ( stdout, "%5d: ", j );
      for ( i = i2lo; i <= i2hi; i++ )
      {
        fprintf ( stdout, "%6d  ", a[i-1+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

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

void i4mat_write ( char *output_filename, int m, int n, int table[] )

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

    I4MAT_WRITE writes an I4MAT file.

  Discussion:

    An I4MAT is an array of I4's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 June 2009

  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, int TABLE[M*N], the data.
*/
{
  int i;
  int j;
  FILE *output;
/*
  Open the file.
*/
  output = fopen ( output_filename, "wt" );

  if ( !output )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "I4MAT_WRITE - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the output file.\n" );
    exit ( 1 );
  }
/*
  Write the data.
*/
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      fprintf ( output, "  %d", table[i+j*m] );
    }
    fprintf ( output, "\n" );
  }
/*
  Close the file.
*/
  fclose ( output );

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

void mesh_base_zero ( int node_num, int element_order, int element_num, 
  int element_node[] )

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

    MESH_BASE_ZERO ensures that the element definition is zero-based.

  Discussion:

    The ELEMENT_NODE array contains nodes indices that form elements.
    The convention for node indexing might start at 0 or at 1.
    Since a C or C++ program will naturally assume a 0-based indexing, it is
    necessary to check a given element definition and, if it is actually
    1-based, to convert it.

    This function attempts to detect 1-based node indexing and correct it.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    08 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int NODE_NUM, the number of nodes.

    Input, int ELEMENT_ORDER, the order of the elements.

    Input, int ELEMENT_NUM, the number of elements.

    Input/output, int ELEMENT_NODE[ELEMENT_ORDER*ELEMENT_NUM], the element
    definitions.
*/
{
  int element;
  int node;
  int node_max;
  int node_min;
  int order;

  node_min = node_num + 1;
  node_max = -1;
  for ( element = 0; element < element_num; element++ )
  {
    for ( order = 0; order < element_order; order++ )
    {
      node = element_node[order+element*element_order];
      node_min = i4_min ( node_min, node );
      node_max = i4_max ( node_max, node );
    }
  }

  if ( node_min == 1 && node_max == node_num )
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ZERO:\n" );
    printf ( "  The element indexing appears to be 1-based!\n" );
    printf ( "  This will be converted to 0-based.\n" );
    for ( element = 0; element < element_num; element++ )
    {
      for ( order = 0; order < element_order; order++ )
      {
        element_node[order+element*element_order] =
          element_node[order+element*element_order] - 1;
      }
    }
  }
  else if ( node_min == 0 && node_max == node_num - 1 )
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ZERO:\n" );
    printf ( "  The element indexing appears to be 0-based!\n" );
    printf ( "  No conversion is necessary.\n" );
  }
  else
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ZERO - Warning!\n" );
    printf ( "  The element indexing is not of a recognized type.\n" );
    printf ( "  NODE_MIN = %d\n", node_min );
    printf ( "  NODE_MAX = %d\n", node_max );
    printf ( "  NODE_NUM = %d\n", node_num );
  }
  return;
}
/******************************************************************************/

int r8_nint ( double x )

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

    R8_NINT returns the nearest integer to an R8.

  Example:

        X         R8_NINT

      1.3         1
      1.4         1
      1.5         1 or 2
      1.6         2
      0.0         0
     -0.7        -1
     -1.1        -1
     -1.6        -2

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    05 May 2006

  Author:

    John Burkardt

  Parameters:

    Input, double X, the value.

    Output, int R8_NINT, the nearest integer to X.
*/
{
  int s;
  int value;

  if ( x < 0.0 )
  {
    s = - 1;
  }
  else
  {
    s = + 1;
  }
  value = s * ( int ) ( fabs ( x ) + 0.5 );

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

double *r8mat_data_read ( char *input_filename, int m, int n )

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

    R8MAT_DATA_READ reads the data from an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

    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 MIT 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 R8MAT_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 ( "R8MAT_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 r8mat_header_read ( char *input_filename, int *m, int *n )
 
/******************************************************************************/
/*
  Purpose:

    R8MAT_HEADER_READ reads the header from an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

  Licensing:

    This code is distributed under the MIT 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 ( "R8MAT_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 ( "R8MAT_HEADER_READ - Fatal error!\n" );
    printf ( "  FILE_ROW_COUNT failed.\n" );
    return;
  }

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

void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

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

    R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 August 2010

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A[M*N], an M by N matrix to be printed.

    Input, int ILO, JLO, the first row and column to print.

    Input, int IHI, JHI, the last row and column to print.

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

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

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

  for ( i2lo = i4_max ( ilo, 1 ); i2lo <= i4_min ( ihi, m ); i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

    inc = i2hi + 1 - i2lo;

    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row:" );
    for ( i = i2lo; i <= i2hi; i++ )
    {
      fprintf ( stdout, "  %7d     ", i - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Col\n" );
    fprintf ( stdout, "\n" );

    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "%5d:", j - 1 );
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        fprintf ( stdout, "  %14f", a[(i-1)+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

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

void r8mat_write ( char *output_filename, int m, int n, double table[] )

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

    R8MAT_WRITE writes an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 June 2009

  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 data.
*/
{
  int i;
  int j;
  FILE *output;
/*
  Open the file.
*/
  output = fopen ( output_filename, "wt" );

  if ( !output )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_WRITE - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the output file.\n" );
    exit ( 1 );
  }
/*
  Write the data.
*/
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      fprintf ( output, "  %24.16g", table[i+j*m] );
    }
    fprintf ( output, "\n" );
  }
/*
  Close the file.
*/
  fclose ( output );

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

void s_blank_delete ( char *s )

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

    S_BLANK_DELETE removes blanks and left justifies the remainder.

  Discussion:

    All TAB characters are also removed.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 July 2008

  Author:

    John Burkardt

  Parameters:

    Input/output, char *S, the string to be transformed.
*/
{
  char *get;
  char *put;
  char TAB = 9;

  put = s;
  get = s;

  while ( *get != '\0' )
  {
    if ( *get != ' ' && *get != TAB )
    {
      *put = *get;
      put = put + 1;
    }
    get = get + 1;
  }

  *put = *get;

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

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

int s_to_i4vec ( char *s, int n, int ivec[] )

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

    S_TO_I4VEC reads an I4VEC from a string.

  Licensing:

    This code is distributed under the MIT 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, int IVEC[N], the values read from the string.

    Output, int S_TO_I4VEC, 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++ )
  {
    ivec[i] = s_to_i4 ( s, &lchar, &error );

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

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

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 MIT 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 MIT 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 MIT license.

  Modified:

    16 September 2015

  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 word_num;
  char *t;

  word_num = 0;
  blank = 1;
  t = s;

  while ( *t )
  {
    if ( *t == ' ' || *t == '\n' )
    {
      blank = 1;
    }
    else if ( blank )
    {
      word_num = word_num + 1;
      blank = 0;
    }
    t++;
  }

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

void timestamp ( )

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

    24 September 2003

  Author:

    John Burkardt

  Parameters:

    None
*/
{
# 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
}