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

# include "r83v.h"

int main ( );
void r83v_cg_test ( );
void r83v_copy_test ( );
void r83v_cr_fa_test ( );
void r83v_cr_sl_test ( );
void r83v_cr_sls_test ( );
void r83v_dif2_test ( );
void r83v_fs_test ( );;
void r83v_gs_sl_test ( );
void r83v_indicator_test ( );
void r83v_jac_sl_test ( );
void r83v_mtv_test ( );
void r83v_mv_test ( );
void r83v_print_test ( );
void r83v_print_some_test ( );
void r83v_random_test ( );
void r83v_res_test ( );
void r83v_to_r8ge_test ( );
void r83v_to_r8vec_test ( );
void r83v_transpose_test ( );
void r83v_zeros_test ( );

void r8ge_to_r83v_test ( );

void r8vec_to_r83v_test ( );

void timestamp ( );

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

int main ( )

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

    r83v_test() tests r83v().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    16 February 2016

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "R83V_TEST\n" );
  printf ( "  C version\n" );
  printf ( "  Test the R83V library.\n" );

  r83v_cg_test ( );
  r83v_copy_test ( );
  r83v_cr_fa_test ( );
  r83v_cr_sl_test ( );
  r83v_cr_sls_test ( );
  r83v_dif2_test ( );
  r83v_fs_test ( );
  r83v_gs_sl_test ( );
  r83v_indicator_test ( );
  r83v_jac_sl_test ( );
  r83v_mtv_test ( );
  r83v_mv_test ( );
  r83v_print_test ( );
  r83v_print_some_test ( );
  r83v_random_test ( );
  r83v_res_test ( );
  r83v_to_r8ge_test ( );
  r83v_to_r8vec_test ( );
  r83v_transpose_test ( );
  r83v_zeros_test ( );

  r8ge_to_r83v_test ( );

  r8vec_to_r83v_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "r83v_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void r83v_cg_test ( )

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

    R83V_CG_TEST tests R83V_CG.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  double *b;
  double e_norm;
  int i;
  int n;
  double *r;
  double r_norm;
  int seed;
  double *x1;
  double *x2;

  printf ( "\n" );
  printf ( "R83_CG_TEST\n" );
  printf ( "  R83_CG applies CG to an R83 matrix.\n" );

  n = 10;
/*
  Let A be the -1 2 -1 matrix.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc ( n * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );

  r83v_dif2 ( n, n, a1, a2, a3 );
/*
  Choose a random solution.
*/
  seed = 123456789;
  x1 = r8vec_uniform_01_new ( n, &seed );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x1 );
/*
  Call the CG routine.
*/
  x2 = ( double * ) malloc ( n * sizeof ( double ) );
  for ( i = 0; i < n; i++ )
  {
    x2[i] = 1.0;
  }
  r83v_cg ( n, a1, a2, a3, b, x2 );
/*
  Compute the residual.
*/
  r = r83v_res ( n, n, a1, a2, a3, x2, b );
  r_norm = r8vec_norm ( n, r );
/*
  Compute the error.
*/
  e_norm = r8vec_norm_affine ( n, x1, x2 );
/*
  Report.
*/
  printf ( "\n" );
  printf ( "  Number of variables N = %d\n", n );
  printf ( "  Norm of residual ||Ax-b|| = %g\n", r_norm );
  printf ( "  Norm of error ||x1-x2|| = %g\n", e_norm );
/*
  Free memory.
*/
  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( r );
  free ( x1 );
  free ( x2 );

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

void r83v_copy_test ( )

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

    R83V_COPY_TEST tests R83V_COPY.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  double *b1;
  double *b2;
  double *b3;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_COPY_TEST\n" );
  printf ( "  R83V_COPY copies an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_indicator ( m, n, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V matrix A:" );

    b1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    b2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    b3 = ( double * ) malloc ( chi * sizeof ( double ) );
    r83v_copy ( m, n, a1, a2, a3, b1, b2, b3 );
    r83v_print ( m, n, b1, b2, b3, "  B = copy of A:" );

    free ( a1 );
    free ( a2 );
    free ( a3 );
    free ( b1 );
    free ( b2 );
    free ( b3 );
  }

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

void r83v_cr_fa_test ( )

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

    R83V_CR_FA_TEST tests R83V_CR_FA.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 February 2016

  Author:

    John Burkardt
*/
{
  double *a_cr;
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int i;
  int j;
  int n = 10;

  double *x;

  printf ( "\n" );
  printf ( "R83V_CR_FA_TEST:\n" );
  printf ( "  R83V_CR_FA factors an R83V matrix using cyclic reduction;\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  The matrix is NOT symmetric.\n" );
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
 
  for ( j = 0; j < n; j++ )
  {
    for ( i = i4_max ( 0, j - 1 ); i <= i4_min ( n - 1, j + 1 ); i++ )
    {
      if ( j == i - 1 )
      {
        a1[j] = ( double ) ( j + 1 );
      }
      else if ( j == i )
      {
        a2[j] = ( double ) ( 4 * ( j + 1 ) );
      }
      else if ( j == i + 1 )
      {
        a3[j-1] = ( double ) ( j + 1 );
      }
    }
  }

  r83v_print ( n, n, a1, a2, a3, "  The matrix:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x );
/*
  Factor the matrix.
*/
  a_cr = r83v_cr_fa ( n, a1, a2, a3 );
/*
  Solve the linear system.
*/
  x = r83v_cr_sl ( n, a_cr, b );

  r8vec_print ( n, x, "  Solution:" );

  free ( a_cr );
  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x );

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

void r83v_cr_sl_test ( )

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

    R83V_CR_SL_TEST tests R83V_CR_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 February 2016

  Author:

    John Burkardt
*/
{
  double *a_cr;
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int i;
  int j;
  int n = 10;
  double *x;

  printf ( "\n" );
  printf ( "R83V_CR_SL_TEST:\n" );
  printf ( "  R83V_CR_SL solves a linear system factored by R83V_CR_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  The matrix is NOT symmetric.\n" );
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
 
  for ( j = 0; j < n; j++ )
  {
    for ( i = i4_max ( 0, j - 1 ); i <= i4_min ( n - 1, j + 1 ); i++ )
    {
      if ( j == i - 1 )
      {
        a1[j] = ( double ) ( j + 1 );
      }
      else if ( j == i )
      {
        a2[j] = ( double ) ( 4 * ( j + 1 ) );
      }
      else if ( j == i + 1 )
      {
        a3[j-1] = ( double ) ( j + 1 );
      }
    }
  }

  r83v_print ( n, n, a1, a2, a3, "  The matrix:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x );
/*
  Factor the matrix.
*/
  a_cr = r83v_cr_fa ( n, a1, a2, a3 );
/*
  Solve the linear system.
*/
  x = r83v_cr_sl ( n, a_cr, b );

  r8vec_print ( n, x, "  Solution:" );

  free ( a_cr );
  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x );

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

void r83v_cr_sls_test ( )

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

    R83V_CR_SLS_TEST tests R83V_CR_SLS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 February 2016

  Author:

    John Burkardt
*/
{
  double *a_cr;
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int i;
  int j;
  int n = 5;
  int nb = 2;
  double *x;

  printf ( "\n" );
  printf ( "R83V_CR_SLS_TEST\n" );
  printf ( "  R83V_CR_SLS solves multiple linear systems A*x=b1:bn with R83V matrix\n" );
  printf ( "  using cyclic reduction, after factorization by R83V_CR_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Number of linear systems = %d\n", nb );
  printf ( "  Demonstrate multiple system solution method.\n" );
/*
  Set the matrix values.
*/
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
 
  r83v_dif2 ( n, n, a1, a2, a3 );

  r83v_print ( n, n, a1, a2, a3, "  System matrix:" );
/*
  Factor the matrix once.
*/
  a_cr = r83v_cr_fa ( n, a1, a2, a3 );
/*
  Set up the linear systems.
*/
  b = ( double * ) malloc ( n * nb * sizeof ( double ) );

  for ( j = 0; j < nb; j++ )
  {
    for ( i = 0; i < n; i++ )
    {
      b[i+j*n] = 0.0;
    }
  }

  j = 0;
  b[n-1+j*n] = ( double ) ( n + 1 );

  j = 1;
  b[0  +j*n] = 1.0;
  b[n-1+j*n] = 1.0;

  r8ge_print ( n, nb, b, "  RHS:" );
/*
  Solve the linear systems.
*/
  x = r83v_cr_sls ( n, a_cr, nb, b );

  r8ge_print ( n, nb, x, "  Solutions:" );

  free ( a_cr );
  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x );

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

void r83v_dif2_test ( )

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

    R83V_DIF2_TEST tests R83V_DIF2.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_DIF2_TEST\n" );
  printf ( "  R83V_DIF2 sets up an R83V second difference matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_dif2 ( m, n, a, b, c );

    r83v_print ( m, n, a, b, c, "  The R83V DIF2 matrix:" );

    free ( a );
    free ( b );
    free ( c );
  }

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

void r83v_fs_test ( )

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

    R83V_FS_TEST tests R83V_FS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    16 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int n = 10;
  double *x1;
  double *x2;

  printf ( "\n" );
  printf ( "R83V_FS_TEST\n" );
  printf ( "  R83V_FS factors and solves a linear system\n" );
  printf ( "  for an R83V matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );

  r83v_dif2 ( n, n, a1, a2, a3 );
/*
  Set the desired solution.
*/
  x1 = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x1 );

  r8vec_print  ( n, b, "  The right hand side:" );
/*
  Solve the linear system.
*/
  x2 = r83v_fs ( n, a1, a2, a3, b );

  if ( ! x2 )
  {
    printf ( "\n" );
    printf ( "  R83V_FS failed.\n" );
  }
  else
  {
    r8vec_print ( n, x2, "  Solution:" );
  }
/*
  Free memory.
*/
  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x1 );
  free ( x2 );

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

void r83v_gs_sl_test ( )

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

    R83V_GS_SL_TEST tests R83V_GS_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int i;
  int maxit = 25;
  int n = 10;
  double *x;

  printf ( "\n" );
  printf ( "R83V_GS_SL_TEST\n" );
  printf ( "  R83V_GS_SL solves a linear system using Gauss-Seidel\n" );
  printf ( "  iteration for an R83V matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );

  r83v_dif2 ( n, n, a1, a2, a3 );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x );

  r8vec_print  ( n, b, "  The right hand side:" );
/*
  Set the starting solution.
*/
  for ( i = 0; i < n; i++ )
  {
    x[i] = 0.0;
  }
/*
  Solve the linear system.
*/
  for ( i = 1; i <= 3; i++ )
  {
    r83v_gs_sl ( n, a1, a2, a3, b, x, maxit );

    r8vec_print ( n, x, "  Current estimated solution:" );
  }

  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x );

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

void r83v_indicator_test ( )

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

    R83V_INDICATOR_TEST tests R83V_INDICATOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_INDICATOR_TEST\n" );
  printf ( "  R83V_INDICATOR sets up an R83V indicator matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_indicator ( m, n, a, b, c );

    r83v_print ( m, n, a, b, c, "  The R83V indicator matrix:" );

    free ( a );
    free ( b );
    free ( c );
  }

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

void r83v_jac_sl_test ( )

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

    R83V_JAC_SL_TEST tests R83V_JAC_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  double *b;
  int i;
  int maxit = 25;
  int n = 10;
  double *x;

  printf ( "\n" );
  printf ( "R83V_JAC_SL_TEST\n" );
  printf ( "  R83V_JAC_SL solves a linear system using Jacobi iteration,\n" );
  printf ( "  for an R83V matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Iterations per call = %d\n", maxit );
/*
  Set the matrix values.
*/
  a1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  a2 = ( double * ) malloc (   n       * sizeof ( double ) );
  a3 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );

  r83v_dif2 ( n, n, a1, a2, a3 );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r83v_mv ( n, n, a1, a2, a3, x );

  r8vec_print  ( n, b, "  The right hand side:" );
/*
  Set the starting solution.
*/
  for ( i = 0; i < n; i++ )
  {
    x[i] = 0.0;
  }
/*
  Solve the linear system.
*/
  for ( i = 1; i <= 3; i++ )
  {
    r83v_jac_sl ( n, a1, a2, a3, b, x, maxit );

    r8vec_print ( n, x, "  Current estimated solution:" );
  }

  free ( a1 );
  free ( a2 );
  free ( a3 );
  free ( b );
  free ( x );

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

void r83v_mtv_test ( )

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

    R83V_MTV_TEST tests R83V_MTV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a_ge;
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  double *ax;
  double *ax_ge;
  int bhi;
  int chi;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83V_MTV_TEST\n" );
  printf ( "  R83V_MTV computes b=A'*x, where A is an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );

    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    seed = 123456789;
    r83v_random ( m, n, &seed, a1, a2, a3 );
    x = r8vec_indicator1_new ( m );
    ax = r83v_mtv ( m, n, a1, a2, a3, x );

    a_ge = r83v_to_r8ge ( m, n, a1, a2, a3 );
    ax_ge = r8ge_mtv ( m, n, a_ge, x );
    r8vec2_print ( n, ax, ax_ge, "  Product comparison:" );

    free ( a_ge );
    free ( a1 );
    free ( a2 );
    free ( a3 );
    free ( ax );
    free ( ax_ge );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83v_mv_test ( )

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

    R83V_MV_TEST tests R83_MV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *a_ge;
  int ahi;
  double *ax;
  double *ax_ge;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83V_MV_TEST\n" );
  printf ( "  R83V_MV computes b=A*x, where A is an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );

    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    seed = 123456789;
    r83v_random ( m, n, &seed, a, b, c );
    x = r8vec_indicator1_new ( n );
    ax = r83v_mv ( m, n, a, b, c, x );

    a_ge = r83v_to_r8ge ( m, n, a, b, c );
    ax_ge = r8ge_mv ( m, n, a_ge, x );
    r8vec2_print ( m, ax, ax_ge, "  Product comparison:" );

    free ( a );
    free ( a_ge );
    free ( ax );
    free ( ax_ge );
    free ( b );
    free ( c );
    free ( x );
  }
  return;
}
/******************************************************************************/

void r83v_print_test ( )

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

    R83V_PRINT_TEST tests R83V_PRINT.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_PRINT_TEST\n" );
  printf ( "  R83V_PRINT prints an R83V matrix.\n" );

  m = 5;
  n = 5;

  ahi = i4_min ( m - 1, n );
  bhi = i4_min ( m,     n );
  chi = i4_min ( m,     n - 1 );
  a = ( double * ) malloc ( ahi * sizeof ( double ) );
  b = ( double * ) malloc ( bhi * sizeof ( double ) );
  c = ( double * ) malloc ( chi * sizeof ( double ) );

  r83v_indicator ( m, n, a, b, c );

  r83v_print ( m, n, a, b, c, "  The R83V  matrix:" );

  free ( a );
  free ( b );
  free ( c );

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

void r83v_print_some_test ( )

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

    R83V_PRINT_SOME_TEST tests R83V_PRINT_SOME.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_PRINT_SOME_TEST\n" );
  printf ( "  R83V_PRINT_SOME prints some of an R83V matrix.\n" );

  m = 5;
  n = 5;

  ahi = i4_min ( m - 1, n );
  bhi = i4_min ( m,     n );
  chi = i4_min ( m,     n - 1 );
  a = ( double * ) malloc ( ahi * sizeof ( double ) );
  b = ( double * ) malloc ( bhi * sizeof ( double ) );
  c = ( double * ) malloc ( chi * sizeof ( double ) );

  r83v_indicator ( m, n, a, b, c );

  r83v_print_some ( m, n, a, b, c, 2, 2, 5, 4, "  Rows 2-5, Cols 2-4:" );

  free ( a );
  free ( b );
  free ( c );

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

void r83v_random_test ( )

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

    R83V_RANDOM_TEST tests R83V_RANDOM.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;
  int seed;

  printf ( "\n" );
  printf ( "R83V_RANDOM_TEST\n" );
  printf ( "  R83V_RANDOM sets up an R83V random matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    seed = 123456789;

    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_random ( m, n, &seed, a, b, c );

    r83v_print ( m, n, a, b, c, "  The R83V random matrix:" );

    free ( a );
    free ( b );
    free ( c );
  }

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

void r83v_res_test ( )

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

    R83V_RES_TEST tests R83V_RES.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *ax;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;
  double *r;
  int seed;
  double *x;

  printf ( "\n" );
  printf ( "R83V_RES_TEST\n" );
  printf ( "  R83V_RES computes b-A*x, where A is an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    seed = 123456789;
    r83v_random ( m, n, &seed, a, b, c );
    x = r8vec_indicator1_new ( n );
    ax = r83v_mv ( m, n, a, b, c, x );
    r = r83v_res ( m, n, a, b, c, x, ax );
    r8vec_print ( m, r, "  Residual A*x-b:" );

    free ( a );
    free ( ax );
    free ( b );
    free ( c );
    free ( r );
    free ( x );
  }

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

void r83v_to_r8ge_test ( )

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

    R83V_TO_R8GE_TEST tests R83V_TO_R8GE.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_TO_R8GE_TEST\n" );
  printf ( "  R83V_TO_R8GE copies an R83V matrix to an R8GE matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_indicator ( m, n, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V matrix A:" );

    a = r83v_to_r8ge ( m, n, a1, a2, a3 );
    r8ge_print ( m, n, a, "  R8GE version of A:" );

    free ( a );
    free ( a1 );
    free ( a2 );
    free ( a3 );
  }

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

void r83v_to_r8vec_test ( )

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

    R83V_TO_R8VEC_TEST tests R83V_TO_R8VEC.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_TO_R8VEC_TEST\n" );
  printf ( "  R83V_TO_R8VEC copies an R83V matrix to an R8VEC.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_indicator ( m, n, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V matrix A:" );

    a = r83v_to_r8vec ( m, n, a1, a2, a3 );
    r8vec_print ( ahi + bhi + chi, a, "  Vector version of A:" );

    free ( a );
    free ( a1 );
    free ( a2 );
    free ( a3 );
  }

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

void r83v_transpose_test ( )

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

    R83V_TRANSPOSE_TEST tests R83V_TRANSPOSE.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  double *b1;
  double *b2;
  double *b3;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_TRANSPOSE_TEST\n" );
  printf ( "  R83V_TRANSPOSE makes a transposed copy of an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_indicator ( m, n, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V matrix A:" );

    b1 = ( double * ) malloc ( chi * sizeof ( double ) );
    b2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    b3 = ( double * ) malloc ( ahi * sizeof ( double ) );
    r83v_transpose ( m, n, a1, a2, a3, b1, b2, b3 );
    r83v_print ( n, m, b1, b2, b3, "  B = copy of A:" );

    free ( a1 );
    free ( a2 );
    free ( a3 );
    free ( b1 );
    free ( b2 );
    free ( b3 );
  }

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

void r83v_zeros_test ( )

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

    R83V_ZEROS_TEST tests R83V_ZEROS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  int ahi;
  double *b;
  int bhi;
  double *c;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R83V_ZEROS_TEST\n" );
  printf ( "  R83V_ZEROS sets up an R83V zero matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a = ( double * ) malloc ( ahi * sizeof ( double ) );
    b = ( double * ) malloc ( bhi * sizeof ( double ) );
    c = ( double * ) malloc ( chi * sizeof ( double ) );

    r83v_zeros ( m, n, a, b, c );

    r83v_print ( m, n, a, b, c, "  The R83V zero matrix:" );

    free ( a );
    free ( b );
    free ( c );
  }

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

void r8ge_to_r83v_test ( )

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

    R8GE_TO_R83V_TEST tests R8GE_TO_R83V.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R8GE_TO_R83V_TEST\n" );
  printf ( "  R8GE_TO_R83V copies an R8GE matrix to an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    a = r8ge_indicator ( m, n );
    r8ge_print ( m, n, a, "  R8GE matrix A:" );

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );
    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r8ge_to_r83v ( m, n, a, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V copy of (some of ) matrix A:" );

    free ( a );
    free ( a1 );
    free ( a2 );
    free ( a3 );
  }

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

void r8vec_to_r83v_test ( )

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

    R8VEC_TO_R83V_TEST tests R8VEC_TO_R83V.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 February 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *a1;
  double *a2;
  double *a3;
  int ahi;
  int bhi;
  int chi;
  int i;
  int m;
  int n;

  printf ( "\n" );
  printf ( "R8VEC_TO_R83V_TEST\n" );
  printf ( "  R8VEC_TO_R83V copies an R8VEC to an R83V matrix.\n" );
  printf ( "  We check three cases, M<N, M=N, M>N.\n" );

  for ( i = 1; i <= 3; i++ )
  {
    if ( i == 1 )
    {
      m = 3;
      n = 5;
    }
    else if ( i == 2 )
    {
      m = 5;
      n = 5;
    }
    else if ( i == 3 )
    {
      m = 5;
      n = 3;
    }

    ahi = i4_min ( m - 1, n );
    bhi = i4_min ( m,     n );
    chi = i4_min ( m,     n - 1 );

    a = r8vec_indicator1_new ( ahi + bhi + chi );
    r8vec_print ( ahi + bhi + chi, a, "  R8VEC:" );

    a1 = ( double * ) malloc ( ahi * sizeof ( double ) );
    a2 = ( double * ) malloc ( bhi * sizeof ( double ) );
    a3 = ( double * ) malloc ( chi * sizeof ( double ) );

    r8vec_to_r83v ( m, n, a, a1, a2, a3 );
    r83v_print ( m, n, a1, a2, a3, "  R83V matrix:" );

    free ( a );
    free ( a1 );
    free ( a2 );
    free ( a3 );
  }

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

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
*/
{
# 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 );

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

  return;
# undef TIME_SIZE
}