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

using namespace std;

# include "freefem_msh_io.hpp"

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

int ch_eqi ( char ch1, char ch2 )

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

void ffmsh_2d_data_example ( int v_num, int e_num, int t_num, double v_xy[],
  int v_l[], int e_v[], int e_l[], int t_v[], int t_l[] )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_DATA_EXAMPLE returns example FFMSH data.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    21 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int V_NUM, the number of vertices.
//
//    Input, int E_NUM, the number of boundary edges.
//
//    Input, int T_NUM, the number of triangles.
//
//    Output, double V_XY[2*V_NUM], vertex coordinates.
//
//    Output, int V_L[V_NUM], vertex labels.
//
//    Output, int E_V[2*E_NUM], edge vertices.
//
//    Output, int E_L[E_NUM], vertex labels.
//
//    Output, int T_V[3*T_NUM], triangle vertices.
//
//    Output, int T_L[T_NUM], triangle labels.
//
{
  int e_l_save[10] = {
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
  int e_v_save[2*10] = {
  11,  6,
   6,  4,
   4,  1,
   1,  2,
   2,  5,
   5,  9,
   9, 13,
  13, 15,
  15, 14,
  14, 11 };
  int t_l_save[18] = {
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
  int t_v_save[3*18] = {
     1,  3,  4,
     7,  2,  5,
     9,  7,  5,
     8,  6,  4,
    12,  8,  7,
    12, 11,  8,
     3,  1,  2,
     7,  3,  2,
     7,  8,  3,
     4,  3,  8,
     6,  8, 11,
    12,  7, 10,
    11, 12, 14,
    10,  9, 13,
    12, 10, 13,
     7,  9, 10,
    12, 13, 15,
    14, 12, 15 };
  int v_l_save[15] = {
    1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1 };
  double v_xy_save[2*15] = {
    -0.309016994375,  0.951056516295,
    -0.809016994375,  0.587785252292,
    -0.321175165867,  0.475528256720,
     0.309016994375,  0.951056516295,
    -1.000000000000,  0.000000000000,
     0.809016994375,  0.587785252292,
    -0.333333334358,  0.000000000000,
     0.237841829972,  0.293892623813,
    -0.809016994375, -0.587785252292,
    -0.321175165867, -0.475528259963,
     1.000000000000,  0.000000000000,
     0.206011327827, -0.391856835534,
    -0.309016994375, -0.951056516295,
     0.809016994375, -0.587785252292,
     0.309016994375, -0.951056516295 };

  i4vec_copy (    v_num, v_l_save,  v_l );
  r8mat_copy ( 2, v_num, v_xy_save, v_xy );
  i4vec_copy (    e_num, e_l_save,  e_l );
  i4mat_copy ( 2, e_num, e_v_save,  e_v );
  i4vec_copy (    t_num, t_l_save,  t_l );
  i4mat_copy ( 3, t_num, t_v_save,  t_v );

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

void ffmsh_2d_data_print ( string title, int v_num, int e_num, int t_num,
  double v_xy[], int v_l[], int e_v[], int e_l[], int t_v[], int t_l[] )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_DATA_PRINT prints FFMSH data.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string TITLE, a title.
//
//    Input, int V_NUM, the number of vertices.
//
//    Input, int E_NUM, the number of boundary edges.
//
//    Input, int T_NUM, the number of triangles.
//
//    Input, double V_XY[2*V_NUM], vertex coordinates.
//
//    Input, int V_L[V_NUM], vertex labels.
//
//    Input, int E_V[2*E_NUM], edge vertices.
//
//    Input, int E_L[E_NUM], vertex labels.
//
//    Input, int T_V[3*T_NUM], triangle vertices.
//
//    Input, int T_L[T_NUM], triangle labels.
//
{
  cout << "\n";
  cout << title << "\n";

  i4vec_print (              v_num, v_l,  "  Vertex labels:" );
  r8mat_transpose_print ( 2, v_num, v_xy, "  Vertex coordinates:" );
  i4vec_print (              e_num, e_l,  "  Edge labels:" );
  i4mat_transpose_print ( 2, e_num, e_v,  "  Edge vertices:" );
  i4vec_print (              t_num, t_l,  "  Triangle labels:" );
  i4mat_transpose_print ( 3, t_num, t_v,  "  Triangle vertices:" );

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

void ffmsh_2d_data_read ( string ffmsh_filename, int v_num, int e_num, int t_num,
  double v_xy[], int v_l[], int e_v[], int e_l[], int t_v[], int t_l[] )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_DATA_READ reads data from an FFMSH file.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string FFMSH_FILENAME, the FFMSH filename.
//
//    Input, int V_NUM, the number of vertices.
//
//    Input, int E_NUM, the number of boundary edges.
//
//    Input, int T_NUM, the number of triangles.
//
//    Output, double V_XY[2*V_NUM], vertex coordinates.
//
//    Output, int V_L[V_NUM], vertex labels.
//
//    Output, int E_V[2*E_NUM], edge vertices.
//
//    Output, int E_L[E_NUM], vertex labels.!
//
//    Output, int T_V[3*T_NUM], triangle vertices.
//
//    Output, int T_L[T_NUM], triangle labels.
//
{
  bool error;
  ifstream ffmsh_unit;
  int i1;
  int i2;
  int i3;
  int i4;
  int j;
  int length;
  double r1;
  double r2;
  string text;

  ffmsh_unit.open ( ffmsh_filename.c_str ( ) );

  if ( ! ffmsh_unit )
  {
    cerr << "\n";
    cerr << "FFMSH_2D_DATA_READ - Fatal error!\n";
    cerr << "  Could not open input file '" << ffmsh_filename << "\n";
    exit ( 1 );
  }
//
//  Read the sizes (again).
//
  getline ( ffmsh_unit, text );
  s_to_i4 ( text, length, error );
  text.erase ( 0, length );
  s_to_i4 ( text, length, error );
  text.erase ( 0, length );
  s_to_i4 ( text, length, error );
  text.erase ( 0, length );
//
//  Read Vertex X, Y, Label
//
  for ( j = 0; j < v_num; j++ )
  {
    getline ( ffmsh_unit, text );
    r1 = s_to_r8 ( text, length, error );
    text.erase ( 0, length );
    r2 = s_to_r8 ( text, length, error );
    text.erase ( 0, length );
    i1 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    v_xy[0+j*2] = r1;
    v_xy[1+j*2] = r2;
    v_l[j] = i1;
  }
//
//  Read Triangle V1, V2, V3, Label
//
  for ( j = 0; j < t_num; j++ )
  {
    getline ( ffmsh_unit, text );
    i1 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    i2 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    i3 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    i4 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    t_v[0+j*3] = i1;
    t_v[1+j*3] = i2;
    t_v[2+j*3] = i3;
    t_l[j] = i4;
  }
//
//  Read Edge V1, V2, Label
//
  for ( j = 0; j < e_num; j++ )
  {
    getline ( ffmsh_unit, text );
    i1 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    i2 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    i3 = s_to_i4 ( text, length, error );
    text.erase ( 0, length );
    e_v[0+j*2] = i1;
    e_v[1+j*2] = i2;
    e_l[j] = i3;
  }

  ffmsh_unit.close ( );

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

void ffmsh_2d_size_example ( int &v_num, int &e_num, int &t_num )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_SIZE_EXAMPLE returns sizes for the 2D example.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    21 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, int &V_NUM, the number of vertices.
//
//    Output, int &E_NUM, the number of boundary edges.
//
//    Output, int &T_NUM, the number of triangles.
//
{
  e_num = 10;
  t_num = 18;
  v_num = 15;

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

void ffmsh_2d_size_print ( string title, int v_num, int e_num, int t_num )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_SIZE_PRINT prints the sizes of an FFMSH.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    21 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string TITLE, a title.
//
//    Input, int V_NUM, the number of vertices.
//
//    Input, int E_NUM, the number of boundary edges.
//
//    Input, int T_NUM, the number of triangles.
//
{
  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  cout << "  Number of vertices = " << v_num << "\n";
  cout << "  Number of boundary edges = " << e_num << "\n";
  cout << "  Number of triangles = " << t_num << "\n";

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

void ffmsh_2d_size_read ( string ffmsh_filename, int &v_num, int &e_num,
  int &t_num )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_SIZE_READ reads sizes from a FFMSH file.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string FFMSH_FILENAME, the FFMSH filename.
//
//    Output, int &V_NUM, the number of vertices.
//
//    Output, int &E_NUM, the number of boundary edges.
//
//    Output, int &T_NUM, the number of triangles.
//
{
  bool error;
  ifstream ffmsh_unit;
  int length;
  string text;

  ffmsh_unit.open ( ffmsh_filename.c_str ( ) );

  if ( ! ffmsh_unit )
  {
    cerr << "\n";
    cerr << "FFMSH_SIZE_READ - Fatal error!\n";
    cerr << "  Could not open the input file '" << ffmsh_filename << "'.\n";
    exit ( 1 );
  }

  getline ( ffmsh_unit, text );
  v_num = s_to_i4 ( text, length, error );
  text.erase ( 0, length );
  t_num = s_to_i4 ( text, length, error );
  text.erase ( 0, length );
  e_num = s_to_i4 ( text, length, error );
  text.erase ( 0, length );

  ffmsh_unit.close ( );

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

void ffmsh_2d_write ( string ffmsh_filename, int v_num, int e_num, int t_num,
  double v_xy[], int v_l[], int e_v[], int e_l[], int t_v[], int t_l[] )

//****************************************************************************80
//
//  Purpose:
//
//    FFMSH_2D_WRITE writes FFMSH data to a file.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 December 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string FFMSH_FILENAME, the name of the file.
//
//    Input, int V_NUM, the number of vertices.
//
//    Input, int E_NUM, the number of boundary edges.
//
//    Input, int T_NUM, the number of triangles.
//
//    Input, double V_XY[2*V_NUM], vertex coordinates.
//
//    Input, int V_L[V_NUM], vertex labels.
//
//    Input, int E_V[2*E_NUM], edge vertices.
//
//    Input, int E_L[E_NUM], vertex labels.
//
//    Input, int T_V[3*T_NUM], triangle vertices.
//
//    Input, int T_L[T_NUM], triangle labels.
//
{
  ofstream ffmsh_unit;
  int j;
//
//  Open the file.
//
  ffmsh_unit.open ( ffmsh_filename.c_str ( ) );
//
//  Write the data.
//
  ffmsh_unit << v_num << "  "
             << t_num << "  "
             << e_num << "\n";

  for ( j = 0; j < v_num; j++ )
  {
    ffmsh_unit << v_xy[0+j*2] << "  "
               << v_xy[1+j*2] << "  "
               << v_l[j] << "\n";
  }

  for ( j = 0; j < t_num; j++ )
  {
    ffmsh_unit << t_v[0+j*3] << "  " 
               << t_v[1+j*3] << "  " 
               << t_v[2+j*3] << "  " 
               << t_l[j] << "\n";
  }

  for ( j = 0; j < e_num; j++ )
  {
    ffmsh_unit << e_v[0+j*2] << "  "
               << e_v[1+j*2] << "  "
               << e_l[j] << "\n";
  }

  ffmsh_unit.close ( );

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

void i4mat_copy ( int m, int n, int a1[], int a2[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_COPY copies one I4MAT to another.
//
//  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:
//
//    27 August 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, int A1[M*N], the matrix to be copied.
//
//    Output, int A2[M*N], the copy of A1.
//
{
  int i;
  int j;

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      a2[i+j*m] = a1[i+j*m];
    }
  }
  return;
}
//****************************************************************************80

void i4mat_transpose_print ( int m, int n, int a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_TRANSPOSE_PRINT prints 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:
//
//    31 January 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows in A.
//
//    Input, int N, the number of columns in A.
//
//    Input, int A[M*N], the M by N matrix.
//
//    Input, string TITLE, a title.
//
{
  i4mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

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

//****************************************************************************80
//
//  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:
//
//    15 October 2014
//
//  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, string TITLE, a title.
//
{
# define INCX 10

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

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

  if ( m <= 0 || n <= 0 )
  {
    cout << "\n";
    cout << "  (None)\n";
    return;
  }
//
//  Print the columns of the matrix, in strips of INCX.
//
  for ( i2lo = ilo; i2lo <= ihi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    if ( m < i2hi )
    {
      i2hi = m;
    }
    if ( ihi < i2hi )
    {
      i2hi = ihi;
    }
    cout << "\n";
//
//  For each row I in the current range...
//
//  Write the header.
//
    cout << "  Row: ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(6) << i - 1 << "  ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    j2lo = jlo;
    if ( j2lo < 1 )
    {
      j2lo = 1;
    }
    j2hi = jhi;
    if ( n < j2hi )
    {
      j2hi = n;
    }
    for ( j = j2lo; j <= j2hi; j++ )
    {
//
//  Print out (up to INCX) entries in column J, that lie in the current strip.
//
      cout << setw(5) << j - 1 << ":";
      for ( i = i2lo; i <= i2hi; i++ )
      {
        cout << setw(6) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }
  }

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

void i4vec_copy ( int n, int a1[], int a2[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_COPY copies an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    25 April 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vectors.
//
//    Input, int A1[N], the vector to be copied.
//
//    Input, int A2[N], the copy of A1.
//
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a2[i] = a1[i];
  }
  return;
}
//****************************************************************************80

void i4vec_print ( int n, int a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_PRINT prints an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    14 November 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, int A[N], the vector to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << setw(8) << i
         << ": " << setw(8) << a[i]  << "\n";
  }
  return;
}
//****************************************************************************80

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

//****************************************************************************80
//
//  Purpose:
//
//    MESH_BASE_ONE ensures that the element definition is one-based.
//
//  Discussion:
//
//    The ELEMENT_NODE array contains nodes indices that form elements.
//    The convention for node indexing might start at 0 or at 1.
//
//    If this function detects 0-based indexing, it converts to 1-based.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    18 October 2014
//
//  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;
  const int i4_huge = 2147483647;
  int node;
  int node_max;
  int node_min;
  int order;

  node_min = + i4_huge;
  node_max = - i4_huge;
  for ( element = 0; element < element_num; element++ )
  {
    for ( order = 0; order < element_order; order++ )
    {
      node = element_node[order+element*element_order];
      if ( node < node_min )
      {
        node_min = node;
      }
      if ( node_max < node )
      {
        node_max = node;
      }
    }
  }

  if ( node_min == 0 && node_max == node_num - 1 )
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ONE:\n" );
    printf ( "  The element indexing appears to be 0-based!\n" );
    printf ( "  This will be converted to 1-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 == 1 && node_max == node_num )
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ONE:\n" );
    printf ( "  The element indexing appears to be 1-based!\n" );
    printf ( "  No conversion is necessary.\n" );
  }
  else
  {
    printf ( "\n" );
    printf ( "MESH_BASE_ONE - 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;
}
//****************************************************************************80

void r8mat_copy ( int m, int n, double a1[], double a2[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_COPY copies one R8MAT to another.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    26 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, double A1[M*N], the matrix to be copied.
//
//    Output, double A2[M*N], the copy of A1.
//
{
  int i;
  int j;

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      a2[i+j*m] = a1[i+j*m];
    }
  }

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

void r8mat_transpose_print ( int m, int n, double a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 September 2009
//
//  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, string TITLE, a title.
//
{
  r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    07 April 2014
//
//  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, string TITLE, a title.
//
{
# define INCX 5

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int i2lo_hi;
  int i2lo_lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

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

  if ( m <= 0 || n <= 0 )
  {
    cout << "\n";
    cout << "  (None)\n";
    return;
  }

  if ( ilo < 1 )
  {
    i2lo_lo = 1;
  }
  else
  {
    i2lo_lo = ilo;
  }

  if ( ihi < m )
  {
    i2lo_hi = m;
  }
  else
  {
    i2lo_hi = ihi;
  }

  for ( i2lo = i2lo_lo; i2lo <= i2lo_hi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;

    if ( m < i2hi )
    {
      i2hi = m;
    }
    if ( ihi < i2hi )
    {
      i2hi = ihi;
    }

    inc = i2hi + 1 - i2lo;

    cout << "\n";
    cout << "  Row: ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(7) << i - 1 << "       ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";

    if ( jlo < 1 )
    {
      j2lo = 1;
    }
    else
    {
      j2lo = jlo;
    }
    if ( n < jhi )
    {
      j2hi = n;
    }
    else
    {
      j2hi = jhi;
    }

    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(5) << j - 1 << ":";
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        cout << setw(14) << a[(i-1)+(j-1)*m];
      }
      cout << "\n";
    }
  }

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

int s_len_trim ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 October 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, 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;

  n = s.length ( );

  while ( 0 < n )
  {
    if ( s[n-1] != ' ' && s[n-1] != '\n' )
    {
      return n;
    }
    n = n - 1;
  }

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

int s_to_i4 ( string s, int &last, bool &error )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4 reads an I4 from a string.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    21 October 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, a string to be examined.
//
//    Output, int &LAST, the last character of S used to make IVAL.
//
//    Output, bool &ERROR is TRUE if an error occurred.
//
//    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;

  last = 0;
  error = false;

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

  for ( ; ; )
  {
    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 = true;
        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 = true;
        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 = true;
    last = 0;
  }

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

double s_to_r8 ( string s, int &lchar, bool &error )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8 reads an R8 from a string.
//
//  Discussion:
//
//    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:
//
//    02 May 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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, bool &ERROR, is true if an error occurred.
//
//    Output, double S_TO_R8, the real 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;
  static double ten = 10.0;

  lchar = -1;
  error = false;

  nchar = s_len_trim ( s );
  r = 0.0;
  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 = true;
    return r;
  }
//
//  Number seems OK.  Form it.
//
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      rexp = pow ( ten, jsgn * jtop );
    }
    else
    {
      rexp = jsgn * jtop;
      rexp = rexp / jbot;
      rexp = pow ( ten, rexp );
    }

  }

  r = isgn * rexp * rtop / rbot;

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

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

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

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

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

  return;
# undef TIME_SIZE
}