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

# include "r8po.h"

int main ( );
void r8ge_to_r8po_test ( );
void r8po_det_test ( );
void r8po_dif2_test ( );
void r8po_fa_test ( );
void r8po_indicator_test ( );
void r8po_inverse_test ( );
void r8po_ml_test ( );
void r8po_mm_test ( );
void r8po_mv_test ( );
void r8po_print_test ( );
void r8po_print_some_test ( );
void r8po_random_test ( );
void r8po_sl_test ( );
void r8po_to_r8ge_test ( );
void r8po_zeros_test ( );
void timestamp ( );

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

int main ( )

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

    r8po_test() tests r8po().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    25 August 2022

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "r8po_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test r8po().\n" );

  r8ge_to_r8po_test ( );

  r8po_det_test ( );
  r8po_dif2_test ( );
  r8po_fa_test ( );
  r8po_indicator_test ( );
  r8po_inverse_test ( );
  r8po_ml_test ( );
  r8po_mm_test ( );
  r8po_mv_test ( );
  r8po_print_test ( );
  r8po_print_some_test ( );
  r8po_random_test ( );
  r8po_sl_test ( );
  r8po_to_r8ge_test ( );
  r8po_zeros_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "r8po_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void r8ge_to_r8po_test ( )

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

    R8GE_TO_R8PO_TEST tests R8GE_TO_R8PO.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    02 August 2015

  Author:

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

  printf ( "\n" );
  printf ( "R8GE_TO_R8PO_TEST\n" );
  printf ( "  R8GE_TO_R8PO converts an R8GE matrix to R8PO format.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );

  a = r8ge_random ( n, n, &seed );

  r8ge_print ( n, n, a, "  The random R8GE matrix A:" );

  b = r8ge_to_r8po ( n, a );

  r8po_print ( n, b, "  The R8PO matrix" );

  free ( a );
  free ( b );

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

void r8po_det_test ( )

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

    R8PO_DET_TEST tests R8PO_DET.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    29 July 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double det;
  int i;
  int j;
  int n = 4;
  double *r;

  printf ( "\n" );
  printf ( "R8PO_DET_TEST\n" );
  printf ( "  R8PO_DET computes the determinant of\n" );
  printf ( "  a symmetric positive definite matrix\n" );
  printf ( "  factored by R8PO_FA.\n" );
/*
  Set the matrix.
*/
  a = ( double * ) malloc ( n * n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      if ( j == i - 1 )
      {
        a[i+j*n] = - 1.0;
      }
      else if ( j == i )
      {
        a[i+j*n] = 2.0;
      }
      else if ( j == i + 1 )
      {
        a[i+j*n] = - 1.0;
      }
      else
      {
        a[i+j*n] = 0.0;
      }
    }
  }
  r8po_print ( n, a, "  Matrix A:" );
/*
  Factor the matrix.
*/
  r = r8po_fa ( n, a );
/*
  Compute the determinant.
*/
  det = r8po_det ( n, r );
 
  printf ( "\n" );
  printf ( "  Determinant of A = %g\n", det );

  free ( a );
  free ( r );

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

void r8po_dif2_test ( )

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

    R8PO_DIF2_TEST tests R8PO_DIF2.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 5;

  printf ( "\n" );
  printf ( "R8PO_DIF2_TEST\n" );
  printf ( "  R8PO_DIF2 sets the second difference matrix in R8PO format.\n" );

  a = r8po_dif2 ( n );

  r8po_print ( n, a, "  The R8PO DIF2 matrix:" );
 
  free ( a );

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

void r8po_fa_test ( )

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

    R8PO_FA_TEST tests R8PO_FA;

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 April 2013

  Author:

    John Burkardt
*/
{
  double *a;
  int i;
  int j;
  int k;
  int n = 5;
  double *r;

  printf ( "\n" );
  printf ( "R8PO_FA_TEST\n" );
  printf ( "  R8PO_FA factors a positive definite symmetric\n" );
  printf ( "  linear system,\n" );

  a = ( double * ) malloc ( n * n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      a[i+j*n] = ( double ) ( i4_min ( i + 1, j + 1 ) );
    }
  }

  r8po_print ( n, a, "  The matrix A:" );
/*
  Factor the matrix.
*/
  r = r8po_fa ( n, a );

  if ( r == NULL )
  {
    printf ( "\n" );
    printf ( "  Fatal error!\n" );
    printf ( "  R8PO_FA declares the matrix is singular!\n" );
    return;
  }
  r8ut_print ( n, n, r, "  The factor R (an R8UT matrix):" );
/*
  Compute the product R' * R.
*/
  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      a[i+j*n] = 0.0;
      for ( k = 0; k < n; k++ )
      {
        a[i+j*n] = a[i+j*n] + r[k+i*n] * r[k+j*n];
      }
    }
  }

  r8ge_print ( n, n, a, "  The product R' * R:" );

  free ( a );
  free ( r );

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

void r8po_indicator_test ( )

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

    R8PO_INDICATOR_TEST tests R8PO_INDICATOR.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 5;

  printf ( "\n" );
  printf ( "R8PO_INDICATOR_TEST\n" );
  printf ( "  R8PO_INDICATOR sets up an R8PO indicator matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
/*
  Set the matrix.
*/
  a = r8po_indicator ( n );

  r8po_print ( n, a, "  The R8PO indicator matrix:" );
 
  free ( a );

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

void r8po_inverse_test ( )

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

    R8PO_INVERSE_TEST tests R8PO_INVERSE.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    29 July 2015

  Author:

    John Burkardt
*/
{
# define N 4

  double a[N*N];
  double *a_inv;
  double *c;
  int i;
  int j;
  double *r;

  printf ( "\n" );
  printf ( "R8PO_INVERSE_TEST\n" );
  printf ( "  R8PO_INVERSE computes the inverse of\n" );
  printf ( "  a symmetric positive definite matrix\n" );
  printf ( "  factored by R8PO_FA.\n" );

  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", N );
/*
  Set the matrix.
*/
  for ( i = 0; i < N; i++ )
  {
    for ( j = 0; j < N; j++ )
    {
      a[i+j*N] = ( double ) ( i4_min ( i + 1, j + 1 ) );
    }
  }

  r8po_print ( N, a, "  Matrix A:" );
/*
  Factor the matrix.
*/
  r = r8po_fa ( N, a );
/*
  Compute the inverse.
*/
  a_inv = r8po_inverse ( N, r );

  r8po_print ( N, a_inv, "  Inverse matrix A_INV:" );
/*
  Check.
*/
  c = r8po_mm ( N, a, a_inv );

  r8po_print ( N, c, "  Product A * A_INV:" );

  free ( a_inv );
  free ( c );
  free ( r );

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

void r8po_ml_test ( )

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

    R8PO_ML_TEST tests R8PO_ML.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int i;
  int j;
  int n = 10;
  double *r;
  double *x;

  printf ( "\n" );
  printf ( "R8PO_ML_TEST\n" );
  printf ( "  R8PO_ML can compute A*x for an R8PO matrix A\n" );
  printf ( "  even after it has been factored by R8PO_FA.\n" );

  a = ( double * ) malloc ( n * n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      a[i+j*n] = ( double ) ( i4_min ( i + 1, j + 1 ) );
    }
  }
/*
  Set the desired solution.
*/
  x = r8vec_indicator1_new ( n );
/*
  Compute the corresponding right hand side.
*/
  b = r8po_mv ( n, a, x );
/*
  Factor the matrix.
*/
  r = r8po_fa ( n, a );

  if ( r == NULL )
  {
    printf ( "\n" );
    printf ( "  Fatal error!\n" );
    printf ( "  R8PO_FA declares the matrix is singular!\n" );
    return;
  }
/*
  Solve the linear system.
*/
  free ( x );
  x = r8po_sl ( n, r, b );
 
  r8vec_print ( n, x, "  Solution:" );
/*
  Set the desired solution.
*/
  free ( x );
  x = ( double * ) malloc ( n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    x[i] = 1.0;
  }
/*
  Compute the corresponding right hand side, using the factored matrix.
*/
  free ( b );
  b = r8po_ml ( n, r, x );
/*
  Solve the linear system.
*/
  free ( x );
  x = r8po_sl ( n, r, b );
 
  r8vec_print ( n, x, "  Solution:" );

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

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

void r8po_mm_test ( )

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

    R8PO_MM_TEST tests R8PO_MM.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    31 July 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  double *c;
  int i;
  int n = 5;

  printf ( "\n" );
  printf ( "R8PO_MM_TEST\n" );
  printf ( "  R8PO_MM computes the product of two\n" );
  printf ( "  symmetric positive definite matrices.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );
/*
  Set (the upper half of) matrix A.
*/
  a = r8po_zeros ( n );

  for ( i = 0; i < n; i++ )
  {
    a[i+i*n] = 2.0;
  }

  for ( i = 0; i < n - 1; i++ )
  {
    a[i+(i+1)*n] = -1.0;
  }

  r8po_print ( n, a, "  Matrix A:" );
/*
  Set (the upper half of) matrix B.
*/
  b = r8po_zeros ( n );

  for ( i = 0; i < n; i++ )
  {
    b[i+i*n] = ( double ) ( i + i + 1 );
  }

  for ( i = 0; i < n - 1; i++ )
  {
    b[i+(i+1)*n] = ( double ) ( i + i + 1 + 1 );
  }

  r8po_print ( n, b, "  Matrix B:" );
/*
  Compute the product.
*/
  c = r8po_mm ( n, a, b );

  r8po_print ( n, c, "  Product matrix C = A * B:" );

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

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

void r8po_mv_test ( )

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

    R8PO_MV_TEST tests R8PO_MV.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int i;
  int n = 5;
  double *v;
  double *w;

  printf ( "\n" );
  printf ( "R8PO_MV_TEST\n" );
  printf ( "  R8PO_MV computes the product of an R8PO matrix and a vector.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );

  a = r8po_zeros ( n );

  for ( i = 0; i < n; i++ )
  {
    a[i+i*n] = 2.0;
  }

  for ( i = 0; i < n - 1; i++ )
  {
    a[i+(i+1)*n] = -1.0;
  }

  r8po_print ( n, a, "  Matrix A:" );
/*
  Set the vector V.
*/
  v = r8vec_indicator1_new ( n );

  r8vec_print ( n, v, "  Vector V:" );
/*
  Compute the product.
*/
  w = r8po_mv ( n, a, v );

  r8vec_print ( n, w, "  Product w = A * v:" );

  free ( a );
  free ( v );
  free ( w );

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

void r8po_print_test ( )

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

    R8PO_PRINT_TEST tests R8PO_PRINT.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 5;

  printf ( "\n" );
  printf ( "R8PO_PRINT_TEST\n" );
  printf ( "  R8PO_PRINT prints an R8PO matrix.\n" );

  a = r8po_indicator ( n );

  r8po_print ( n, a, "  The R8PO matrix:" );
 
  free ( a );

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

void r8po_print_some_test ( )

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

    R8PO_PRINT_SOME_TEST tests R8PO_PRINT_SOME.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 10;

  printf ( "\n" );
  printf ( "R8PO_PRINT_SOME_TEST\n" );
  printf ( "  R8PO_PRINT_SOME prints some of an R8PO matrix.\n" );

  a = r8po_indicator ( n );

  r8po_print_some ( n, a, 2, 5, 6, 7, "  Rows 2-6, 5-7:" );
 
  free ( a );

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

void r8po_random_test ( )

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

    R8PO_RANDOM_TEST tests R8PO_RANDOM..

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 5;
  int seed = 123456789;

  printf ( "\n" );
  printf ( "R8PO_RANDOM_TEST\n" );
  printf ( "  R8PO_RANDOM computes a random positive definite\n" );
  printf ( "  symmetric matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );

  a = r8po_random ( n, &seed );

  r8po_print ( n, a, "  The random R8PO matrix:" );
 
  free ( a );

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

void r8po_sl_test ( )

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

    R8PO_SL_TEST tests R8PO_SL.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    02 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  double *b;
  int i;
  int n = 5;
  double *r;
  double *x;

  printf ( "\n" );
  printf ( "R8PO_SL_TEST\n" );
  printf ( "  R8PO_SL solves a linear system with R8PO matrix\n" );
  printf ( "  after it has been factored by R8PO_FA.\n" );

  a = r8po_zeros ( n );

  for ( i = 0; i < n; i++ )
  {
    a[i+i*n] = 2.0;
  }

  for ( i = 0; i < n - 1; i++ )
  {
    a[i+(i+1)*n] = -1.0;
  }

  r8po_print ( n, a, "  Matrix A:" );
/*
  Factor the matrix.
*/
  r = r8po_fa ( n, a );

  if ( r == NULL )
  {
    printf ( "\n" );
    printf ( "  R8PO_FA declares the matrix is singular!\n" );
    return;
  }
/*
  Set the right hand side.
*/
  b = r8vec_zeros_new ( n );
  b[n-1] = ( double ) ( n + 1 );
  r8vec_print ( n, b, "  Right hand side b:" );
/*
  Solve the linear system.
*/
  x = r8po_sl ( n, r, b );
 
  r8vec_print ( n, x, "  Solution x:" );
/*
  Free memory.
*/
  free ( a );
  free ( b );
  free ( r );
  free ( x );

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

void r8po_to_r8ge_test ( )

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

    R8PO_TO_R8GE_TEST tests R8PO_TO_R8GE.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 August 2015

  Author:

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

  printf ( "\n" );
  printf ( "R8PO_TO_R8GE_TEST\n" );
  printf ( "  R8PO_TO_R8GE converts an R8PO matrix to R8GE format.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );

  a = r8po_random ( n, &seed );

  r8po_print ( n, a, "  The random R8PO matrix:" );
 
  r8ge_print ( n, n, a, "  The random R8PO matrix (printed by R8GE_PRINT):" );

  b = r8po_to_r8ge ( n, a );

  r8ge_print ( n, n, b, "  The random R8GE matrix (printed by R8GE_PRINT):" );

  free ( a );
  free ( b );

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

void r8po_zeros_test ( )

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

    R8PO_ZEROS_TEST tests R8PO_ZEROS.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 August 2015

  Author:

    John Burkardt
*/
{
  double *a;
  int n = 5;

  printf ( "\n" );
  printf ( "R8PO_ZEROS_TEST\n" );
  printf ( "  R8PO_ZEROS returns a zeroed out R8PO matrix.\n" );
  printf ( "\n" );
  printf ( "  Matrix order N = %d\n", n );

  a = r8po_zeros ( n );

  r8po_print ( n, a, "  Matrix A:" );

  free ( a );

  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 );

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

  return;
# undef TIME_SIZE
}