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

# include "r8pbu.h"

int main ( );
void r8pbu_cg_test ( );
void r8pbu_det_test ( );
void r8pbu_dif2_test ( );
void r8pbu_fa_test ( );
void r8pbu_indicator_test ( );
void r8pbu_ml_test ( );
void r8pbu_mv_test ( );
void r8pbu_print_test ( );
void r8pbu_print_some_test ( );
void r8pbu_random_test ( );
void r8pbu_res_test ( );
void r8pbu_sl_test ( );
void r8pbu_sor_test ( );
void r8pbu_to_r8ge_test ( );
void r8pbu_zeros_test ( );
void timestamp ( );

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

int main ( )

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

    r8pbu_test() tests r8pbu().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    25 August 2022

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "r8pbu_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test r8pbu().\n" );

  r8pbu_cg_test ( );
  r8pbu_det_test ( );
  r8pbu_dif2_test ( );
  r8pbu_fa_test ( );
  r8pbu_indicator_test ( );
  r8pbu_ml_test ( );
  r8pbu_mv_test ( );
  r8pbu_print_test ( );
  r8pbu_print_some_test ( );
  r8pbu_random_test ( );
  r8pbu_res_test ( );
  r8pbu_sl_test ( );
  r8pbu_sor_test ( );
  r8pbu_to_r8ge_test ( );
  r8pbu_zeros_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "r8pbu_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void r8pbu_cg_test ( )

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

    R8PBU_CG_TEST tests R8PBU_CG.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 50
# define MU 1

  double a[(MU+1)*N];
  double *b;
  int i;
  int j;
  double *r;
  double res_max;
  double *x;
  double *x_init;

  printf ( "\n" );
  printf ( "R8PBU_CG_TEST\n" );
  printf ( "  R8PBU_CG applies the conjugate gradient method\n" );
  printf ( "  to a symmetric positive definite banded\n" );
  printf ( "  linear system.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
/*
  Set the matrix values.
*/
  a[0+0*(MU+1)] = 0.0;
  for ( j = 1; j < N; j++ )
  {
    a[0+j*(MU+1)] = -1.0;
  }
  for ( j = 0; j < N; j++ )
  {
    a[1+j*(MU+1)] = 2.0;
  }

  r8pbu_print_some ( N, MU, a, 1, 1, 10, 10, "The symmetric banded matrix:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( N );
/*
  Compute the right hand side.
*/
  b = r8pbu_mv ( N, N, MU, a, x );
/*
  Set the approximate solution.
*/
  x_init = ( double * ) malloc ( N * sizeof ( double ) );
  for ( i = 0; i < N; i++ )
  {
    x_init[i] = 1.0;
  }
/*
  Call the conjugate gradient method.
*/
  free ( x );

  x = r8pbu_cg ( N, MU, a, b, x_init );

  r8vec_print_some ( N, x, 10, "  Solution:" );
/*
  Compute the residual, A*x-b
*/
  r = r8pbu_mv ( N, N, MU, a, x );

  res_max = 0.0;
  for ( i = 0; i < N; i++ )
  { 
    res_max = r8_max ( res_max, fabs ( r[i] - b[i] ) );
  }

  printf ( "\n" );
  printf ( "  Maximum residual = %g\n", res_max );

  free ( r );
  free ( x );
  free ( x_init );
 
  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_det_test ( )

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

    R8PBU_DET_TEST tests R8PBU_DET.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 10
# define MU 3

  double *a;
  double *a2;
  double *a_lu;
  double det;
  int info;
  int pivot[N];
  int seed = 123456789;

  printf ( " \n" );  
  printf ( "R8PBU_DET_TEST\n" );
  printf ( "  R8PBU_DET, determinant of a positive definite\n" );
  printf ( "  symmetric banded matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
/*
  Set the matrix.
*/
  a = r8pbu_random ( N, MU, &seed );

  r8pbu_print ( N, MU, a, "  The R8PBU matrix:" );
/*
  Copy the matrix into a general array.
*/
  a2 = r8pbu_to_r8ge ( N, MU, a );
/*
  Factor the matrix.
*/
  a_lu = r8pbu_fa ( N, MU, a );
  r8pbu_print ( N, MU, a_lu, "  The factored R8PBU matrix:" );
/*
  Compute the determinant.
*/
  det = r8pbu_det ( N, MU, a_lu );

  printf ( "\n" );
  printf ( "  R8PBU_DET computes the determinant = %g\n", det );
/*
  Factor the general matrix.
*/
  info = r8ge_fa ( N, a2, pivot );
  if ( info != 0 )
  {
    printf ( "\n" );
    printf ( "r8pbu_det_test(): Fatal error!\n" );
    printf ( "  r8ge_fa() returns nonzero value of info!\n" );
    exit ( 1 );
  }
/*
  Compute the determinant.
*/
  det = r8ge_det ( N, a2, pivot );

  printf ( "  R8GE_DET computes the determinant =  %g\n", det );

  free ( a );
  free ( a2 );
  free ( a_lu );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_dif2_test ( )

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

    R8PBU_DIF2_TEST tests R8PBU_DIF2.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 June 2016

  Author:

    John Burkardt
*/
{
# define N 5
# define MU 1

  double *a;

  printf ( " \n" );
  printf ( "R8PBU_DIF2_TEST\n" );
  printf ( "  R8PBU_DIF2 sets up an R8PBU second difference matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_dif2 ( N, N, MU );

  r8pbu_print ( N, MU, a, "  The R8PBU second difference matrix:" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_fa_test ( )

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

    R8PBU_FA_TEST tests R8PBU_FA.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 50
# define MU 1

  double *a;
  double *a_lu;
  double *b;
  int seed = 123456789;
  double *x;

  printf ( "\n" );
  printf ( "R8PBU_FA_TEST\n" );
  printf ( "  R8PBU_FA factors a matrix in R8PBU format.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
/*
  Set the matrix values.
*/
  a = r8pbu_random ( N, MU, &seed );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( N );
/*
  Compute the right hand side.
*/
  b = r8pbu_mv ( N, N, MU, a, x );
/*
  Factor the matrix.
*/
  a_lu = r8pbu_fa ( N, MU, a );
/*
  Solve the linear system.
*/
  free ( x );
  x = r8pbu_sl ( N, MU, a_lu, b );

  r8vec_print_some ( N, x, 10, "  Solution:" );

  free ( a );
  free ( a_lu );
  free ( b ); 
  free ( x );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_indicator_test ( )

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

    R8PBU_INDICATOR_TEST tests R8PBU_INDICATOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 5
# define MU 3

  double *a;

  printf ( " \n" );
  printf ( "R8PBU_INDICATOR_TEST\n" );
  printf ( "  R8PBU_INDICATOR sets up an R8PBU indicator matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_indicator ( N, MU );

  r8pbu_print ( N, MU, a, "  The R8PBU indicator matrix:" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_ml_test ( )

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

    R8PBU_ML_TEST tests R8PBU_ML.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 10
# define MU 3

  double *a;
  double *a_lu;
  double *b;
  double *b2;
  int seed = 123456789;
  double *x;

  printf ( "\n" );
  printf ( "R8PBU_ML_TEST\n" );
  printf ( "  R8PBU_ML computes A*x \n" );
  printf ( "  where A has been factored by R8PBU_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
/*
  Set the matrix.
*/
  a = r8pbu_random ( N, MU, &seed );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( N );
/*
  Compute the corresponding right hand side.
*/
  b = r8pbu_mv ( N, N, MU, a, x );
/*
  Factor the matrix.
*/
  a_lu = r8pbu_fa ( N, MU, a );
/*
  Now multiply the factored matrix times solution to get right hand side again.
*/
  b2 = r8pbu_ml ( N, MU, a_lu, x );

  r8vec2_print_some ( N, b, b2, 10, "  A*x and PLU*x" );

  free ( a );
  free ( a_lu );
  free ( b );
  free ( b2 );
  free ( x );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_mv_test ( )

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

    R8PBU_MV_TEST tests R8PBU_MV.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 June 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int mu = 2;
  int n = 5;
  int seed = 123456789;
  double *x;

  printf ( "\n" );
  printf ( "R8PBU_MV_TEST\n" );
  printf ( "  R8PBU_MV computes A*x where A is an R8PBU matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Upper bandwidth MU = %d\n", mu );
/*
  Set the matrix.
*/
  a = r8pbu_random ( n, mu, &seed );
  r8pbu_print ( n, mu, a, "  Matrix A:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
  r8vec_print ( n, x, "  Vector x:" );
/*
  Compute the right hand side.
*/
  b = r8pbu_mv ( n, n, mu, a, x );
  r8vec_print ( n, b, "  Product b=A*x:" );

  free ( a );
  free ( b ); 
  free ( x );

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

void r8pbu_print_test ( )

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

    R8PBU_PRINT_TEST tests R8PBU_PRINT.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 5
# define MU 3

  double *a;

  printf ( " \n" );
  printf ( "R8PBU_PRINT_TEST\n" );
  printf ( "  R8PBU_PRINT prints an R8PBU matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_indicator ( N, MU );

  r8pbu_print ( N, MU, a, "  The R8PBU indicator matrix:" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_print_some_test ( )

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

    R8PBU_PRINT_SOME_TEST tests R8PBU_PRINT_SOME.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 June 2016

  Author:

    John Burkardt
*/
{
# define N 9
# define MU 4

  double *a;

  printf ( " \n" );
  printf ( "R8PBU_PRINT_SOME_TEST\n" );
  printf ( "  R8PBU_PRINT_SOME prints some of an R8PBU matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_indicator ( N, MU );

  r8pbu_print_some ( N, MU, a, 3, 4, 7, 8, "  Row(3:7), Col(4:8):" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_random_test ( )

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

    R8PBU_RANDOM_TEST tests R8PBU_RANDOM.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 5
# define MU 3

  double *a;
  int seed = 123456789;

  printf ( "\n" );
  printf ( "R8PBU_RANDOM_TEST\n" );
  printf ( "  R8PBU_RANDOM sets a random R8PBU matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
  printf ( "\n" );
/*
  Set the matrix values.
*/
  a = r8pbu_random ( N, MU, &seed );

  r8pbu_print ( N, MU, a, "  The R8PBU random matrix:" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_res_test ( )

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

    R8PBU_RES_TEST tests R8PBU_RES.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 June 2016

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  double *e;
  int i;
  int mu = 2;
  int n = 5;
  double *r;
  int seed = 123456789;
  double *x;
  double *x2;

  printf ( "\n" );
  printf ( "R8PBU_RES_TEST\n" );
  printf ( "  R8PBU_RES computes the residual b-A*x where A is an R8PBU matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
  printf ( "  Upper bandwidth MU = %d\n", mu );
/*
  Set the matrix.
*/
  a = r8pbu_random ( n, mu, &seed );
  r8pbu_print ( n, mu, a, "  Matrix A:" );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
  r8vec_print ( n, x, "  Vector x:" );
/*
  Compute the right hand side.
*/
  b = r8pbu_mv ( n, n, mu, a, x );
  r8vec_print ( n, b, "  Product b=A*x:" );
/*
  Jostle the solution.
*/
  e = r8vec_uniform_01_new ( n, &seed );
  x2 = ( double * ) malloc ( n * sizeof ( double ) );
  for ( i = 0; i < n; i++)
  {
    x2[i] = x[i] + 0.01 * e[i];
  }
  r8vec_print ( n, x2, "  Approximate solution x2:" );
/*
  Compute the residual.
*/
  r = r8pbu_res ( n, n, mu, a, x2, b );
  r8vec_print ( n, r, "  Residual r = b-A*x2:" );
/*
  Free memory.
*/
  free ( a );
  free ( b );
  free ( e );
  free ( r ); 
  free ( x );
  free ( x2 );

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

void r8pbu_sl_test ( )

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

    R8PBU_SL_TEST tests R8PBU_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 50
# define MU 1

  double *a;
  double *a_lu;
  double *b;
  int seed = 123456789;
  double *x;

  printf ( "\n" );
  printf ( "R8PBU_SL_TEST\n" );
  printf ( "  R8PBU_SL solves a linear system factored by R8PBU_FA.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );
/*
  Set the matrix values.
*/
  a = r8pbu_random ( N, MU, &seed );
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( N );
/*
  Compute the right hand side.
*/
  b = r8pbu_mv ( N, N, MU, a, x );
/*
  Factor the matrix.
*/
  a_lu = r8pbu_fa ( N, MU, a );
/*
  Solve the linear system.
*/
  free ( x );
  x = r8pbu_sl ( N, MU, a_lu, b );

  r8vec_print_some ( N, x, 10, "  Solution:" );

  free ( a );
  free ( a_lu );
  free ( b ); 
  free ( x );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_sor_test ( )

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

    R8PBU_SOR_TEST tests R8PBU_SOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 50
# define MU 1

  double a[(MU+1)*N];
  double *b;
  double *b2;
  double eps;
  double err;
  int i;
  int itchk;
  int itmax;
  int j;
  int k;
  double omega;
  double pi = 3.14159265;
  double t;
  double *x;
  double x_init[N];

  printf ( "\n" );
  printf ( "R8PBU_SOR_TEST\n" );
  printf ( "  R8PBU_SOR, SOR routine for iterative\n" );
  printf ( "  solution of A*x=b.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Upper bandwidth MU = %d\n", MU );

  for ( k = 1; k <= 3; k++ )
  {
    if ( k == 1 )
    {
      omega = 0.25;
    }
    else if ( k == 2 )
    {
      omega = 0.75;
    }
    else
    {
      omega = 1.00;
    }
/*
  Set matrix values.
*/
    a[0+0*(MU+1)] = 0.0;
    for ( j = 1; j < N; j++ )
    {
      a[0+j*(MU+1)] = -1.0;
    }

    for ( j = 0; j < N; j++ )
    {
      a[1+j*(MU+1)] = 2.0;
    }
/*
  Set the desired solution.
*/
    x = ( double * ) malloc ( N * sizeof ( double ) );
    for ( i = 0; i < N; i++ )
    {
      t = pi * ( double ) ( i ) / ( double ) ( N - 1 );
      x[i] = sin ( t );
    }
/*
  Compute the right hand side.
*/
    b = r8pbu_mv ( N, N, MU, a, x );
/*
  Set the initial solution estimate.
*/
    for ( i = 0; i < N; i++ )
    {
      x_init[i] = 1.0;
    }
 
    itchk = 1;
    itmax = 8000;
    eps = 0.0001;

    free ( x );
    x = r8pbu_sor ( N, MU, a, b, eps, itchk, itmax, omega, x_init );
/*
  Compute residual, A*x-b
*/
    b2 = r8pbu_mv ( N, N, MU, a, x );
 
    err = 0.0;
    for ( i = 0; i < N; i++ )
    {
      err = r8_max ( err, fabs ( b2[i] - b[i] ) );
    }
 
    printf ( "\n" );
    printf ( "SOR iteration.\n" );
    printf ( "\n" );
    printf ( "  Relaxation factor OMEGA = %g\n", omega );

    r8vec_print_some ( N, x, 10, "  Solution:" );

    printf ( "\n" );
    printf ( "  Maximum error = %g\n", err );

    free ( b );
    free ( b2 );
    free ( x );
  }
 
  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_to_r8ge_test ( )

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

    R8PBU_TO_R8GE_TEST tests R8PBU_TO_R8GE.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2013

  Author:

    John Burkardt
*/
{
# define N 5
# define MU 3

  double *a;
  double *a_r8ge;

  printf ( " \n" );
  printf ( "R8PBU_TO_R8GE_TEST\n" );
  printf ( "  R8PBU_TO_R8GE converts an R8PBU  matrix to R8GE format.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_indicator ( N, MU );

  r8pbu_print ( N, MU, a, "  The R8PBU matrix:" );

  a_r8ge = r8pbu_to_r8ge ( N, MU, a );

  r8ge_print ( N, N, a_r8ge, "  The R8GE matrix:" );

  free ( a );
  free ( a_r8ge );

  return;
# undef MU
# undef N
}
/******************************************************************************/

void r8pbu_zeros_test ( )

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

    R8PBU_ZEROS_TEST tests R8PBU_ZEROS.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    03 June 2016

  Author:

    John Burkardt
*/
{
# define N 9
# define MU 3

  double *a;

  printf ( " \n" );
  printf ( "R8PBU_ZEROS_TEST\n" );
  printf ( "  R8PBU_ZEROS sets up an R8PBU zero matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
  printf ( "  Bandwidth MU = %d\n", MU );

  a = r8pbu_zeros ( N, MU );

  r8pbu_print ( N, MU, a, "  The R8PBU zero matrix:" );

  free ( a );

  return;
# undef MU
# undef N
}
/******************************************************************************/

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 );

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

  return;
# undef TIME_SIZE
}