r8ut_prb.cpp

# include <cmath>
# include <cstdlib>
# include <iomanip>
# include <iostream>

using namespace std;

# include "r8ut.hpp"

int main ( );
void r8ge_to_r8ut_test ( );
void r8ut_det_test ( );
void r8ut_indicator_test ( );
void r8ut_inverse_test ( );
void r8ut_mm_test ( );
void r8ut_mtm_test ( );
void r8ut_mtv_test ( );
void r8ut_mv_test ( );
void r8ut_print_test ( );
void r8ut_print_some_test ( );
void r8ut_random_test ( );
void r8ut_sl_test ( );
void r8ut_slt_test ( );
void r8ut_to_r8ge_test ( );
void r8ut_zeros_test ( );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for R8UT_PRB.
//
//  Discussion:
//
//    R8UT_PRB tests the R8UT library.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    20 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "R8UT_PRB\n";
  cout << "  C++ version\n";
  cout << "  Test the R8UT library.\n";

  r8ge_to_r8ut_test ( );

  r8ut_det_test ( );
  r8ut_indicator_test ( );
  r8ut_inverse_test ( );
  r8ut_mm_test ( );
  r8ut_mtm_test ( );
  r8ut_mtv_test ( );
  r8ut_mv_test ( );
  r8ut_print_test ( );
  r8ut_print_some_test ( );
  r8ut_random_test ( );
  r8ut_sl_test ( );
  r8ut_slt_test ( );
  r8ut_to_r8ge_test ( );
  r8ut_zeros_test ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "R8UT_PRB\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void r8ge_to_r8ut_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8GE_TO_R8UT_TEST tests R8GE_TO_R8UT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a_ge;
  double *a_ut;
  int m = 5;
  int n = 4;
  int seed = 123456789;

  cout << "\n";
  cout << "R8GE_TO_R8UT_TEST\n";
  cout << "  R8GE_TO_R8UT converts an R8GE matrix to R8UT format.\n";

  a_ge = r8ge_random ( m, n, seed );

  r8ge_print ( m, n, a_ge, "  The random R8GE matrix:" );

  a_ut = r8ge_to_r8ut ( m, n, a_ge );

  r8ut_print ( m, n, a_ut, "  The R8UT matrix" );

  delete [] a_ge;
  delete [] a_ut;

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

void r8ut_det_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_DET_TEST tests R8UT_DET.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    18 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double det;
  int m = 5;
  int n = 5;
  int seed = 123456789;

  cout << "\n";
  cout << "R8UT_DET_TEST\n";
  cout << "  R8UT_DET computes the determinant or an R8UT matrix\n";

  a = r8ut_random ( m, n, seed );

  r8ut_print ( m, n, a, "  The matrix A:" );
//
//  Compute the determinant.
//
  det = r8ut_det ( n, a );

  cout << "\n";
  cout << "  Determinant is " << det << "\n";

  delete [] a;

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

void r8ut_indicator_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_INDICATOR_TEST tests R8UT_INDICATOR.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  int m = 5;
  int n = 4;

  cout << "\n";
  cout << "R8UT_INDICATOR_TEST\n";
  cout << "  R8UT_INDICATOR sets up an indicator matrix in R8UT format.\n";

  a = r8ut_indicator ( m, n );

  r8ut_print ( m, n, a, "  The matrix:" );

  delete [] a;

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

void r8ut_inverse_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_INVERSE_TEST tests R8UT_INVERSE.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *b;
  double *c;
  int i;
  int j;
  int n = 5;
  int seed = 123456789;

  cout << "\n";
  cout << "R8UT_INVERSE_TEST\n";
  cout << "  R8UT_INVERSE computes the inverse of an R8UT matrix\n";

  a = r8ut_random ( n, n, seed );

  r8ut_print ( n, n, a, "  The matrix A:" );
//
//  Compute the inverse matrix B.
//
  b = r8ut_inverse ( n, a );

  r8ut_print ( n, n, b, "  The inverse matrix B:" );
//
//  Check
//
  c = r8ut_mm ( n, a, b );

  r8ut_print ( n, n, c, "  The product A * B:" );

  delete [] a;
  delete [] b;
  delete [] c;

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

void r8ut_mm_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_MM_TEST tests R8UT_MM.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *c;
  int i;
  int j;
  int n = 5;

  cout << "\n";
  cout << "R8UT_MM_TEST\n";
  cout << "  R8UT_MM computes C=A*B for R8UT matrices.\n";

  a = r8ut_zeros ( n, n );
  for ( i = 0; i < n; i++ )
  {
    for ( j = i; j < n; j++ )
    {
      a[i+j*n] = 1.0;
    }
  }
  r8ut_print ( n, n, a, "  The matrix:" );

  c = r8ut_mm ( n, a, a );
  r8ut_print ( n, n, c, "  C = A * A:" );

  delete [] a;
  delete [] c;

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

void r8ut_mtm_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_MTM_TEST tests R8UT_MTM.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *c;
  int i;
  int j;
  int n = 5;

  cout << "\n";
  cout << "R8UT_MTM_TEST\n";
  cout << "  R8UT_MTM computes C=A'*B for R8UT matrices.\n";

  a = r8ut_zeros ( n, n );
  for ( i = 0; i < n; i++ )
  {
    for ( j = i; j < n; j++ )
    {
      a[i+j*n] = 1.0;
    }
  }
  r8ut_print ( n, n, a, "  The matrix:" );

  c = r8ut_mtm ( n, a, a );
  r8ge_print ( n, n, c, "  C = A' * A:" );

  delete [] a;
  delete [] c;

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

void r8ut_mtv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_MTV_TEST tests R8UT_MTV.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *b;
  int m = 5;
  int n = 4;
  double *x;

  cout << "\n";
  cout << "R8UT_MTV_TEST\n";
  cout << "  R8UT_MTV computes a product b=A'*x, where A is an R8UT matrix.\n";

  a = r8ut_indicator ( m, n );
  r8ut_print ( m, n, a, "  The matrix:" );

  x = r8vec_indicator1_new ( m );
  r8vec_print ( m, x, "  Vector x:" );

  b = r8ut_mtv ( m, n, a, x );
  r8vec_print ( n, b, "  Vector b:" );

  delete [] a;
  delete [] b;
  delete [] x;

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

void r8ut_mv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_MV_TEST tests R8UT_MV.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *b;
  int m = 5;
  int n = 4;
  double *x;

  cout << "\n";
  cout << "R8UT_MV_TEST\n";
  cout << "  R8UT_MV computes a product b=A*x, where A is an R8UT matrix.\n";

  a = r8ut_indicator ( m, n );
  r8ut_print ( m, n, a, "  The matrix:" );

  x = r8vec_indicator1_new ( n );
  r8vec_print ( n, x, "  Vector x:" );

  b = r8ut_mv ( m, n, a, x );
  r8vec_print ( m, b, "  Vector b:" );

  delete [] a;
  delete [] b;
  delete [] x;

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

void r8ut_print_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_PRINT_TEST tests R8UT_PRINT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    18 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  int m = 6;
  int n = 4;

  cout << "\n";
  cout << "R8UT_PRINT_TEST\n";
  cout << "  R8UT_PRINT prints a R8UT matrix.\n";

  a = r8ut_indicator ( m, n );

  r8ut_print ( m, n, a, "  The matrix:" );

  delete [] a;

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

void r8ut_print_some_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_PRINT_SOME_TEST tests R8UT_PRINT_SOME.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    18 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  int m = 4;
  int n = 6;

  cout << "\n";
  cout << "R8UT_PRINT_SOME_TEST\n";
  cout << "  R8UT_PRINT_SOME prints some of an R8UT matrix.\n";

  a = r8ut_indicator ( m, n );

  r8ut_print_some ( m, n, a, 0, 3, 2, 5, "  Some of the matrix:" );

  delete [] a;

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

void r8ut_random_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_RANDOM_TEST tests R8UT_RANDOM.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    18 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  int m;
  int n;
  int seed;

  m = 5;
  n = 4;
  seed = 123456789;

  cout << "\n";
  cout << "R8UT_RANDOM_TEST\n";
  cout << "  R8UT_RANDOM randomizes an R8UT matrix.\n";
  cout << "\n";
  cout << "  Matrix order M, N = " << m << ", " << n << "\n";

  a = r8ut_random ( m, n, seed );

  r8ut_print ( m, n, a, "  Matrix A:" );

  delete [] a;

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

void r8ut_sl_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_SL tests R8UT_SL.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *b;
  int i;
  int j;
  int n = 5;
  double *x;

  cout << "\n";
  cout << "R8UT_SL_TEST\n";
  cout << "  R8UT_SL solves a linear system A*x=b with R8UT matrix;\n";
  cout << "\n";
  cout << "  Matrix order N = " << n << " \n";

  a = new double[n*n];
  for ( i = 1; i <= n; i++ )
  {
    for ( j = 1; j <= n; j++ )
    {
      if ( i <= j )
      {
        a[i-1+(j-1)*n] = ( double ) j;
      }
      else
      {
        a[i-1+(j-1)*n] = 0.0;
      }
    }
  }

  r8ut_print ( n, n, a, "  The upper triangular matrix:" );
//
//  Set the desired solution.
//
  x = r8vec_indicator1_new ( n );
//
//  Compute the corresponding right hand side.
//
  b = r8ut_mv ( n, n, a, x );
//
//  Solve the linear system.
//
  delete [] x;
  x = r8ut_sl ( n, a, b );

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

  delete [] a;
  delete [] b;
  delete [] x;

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

void r8ut_slt_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_SLT tests R8UT_SLT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  double *b;
  int i;
  int j;
  int n = 5;
  double *x;

  cout << "\n";
  cout << "R8UT_SLT\n";
  cout << "  R8UT_SLT solves a linear system A'*x=b with R8UT matrix;\n";
  cout << "\n";
  cout << "  Matrix order N = " << n << " \n";

  a = new double[n*n];

  for ( i = 1; i <= n; i++ )
  {
    for ( j = 1; j <= n; j++ )
    {
      if ( i <= j )
      {
        a[i-1+(j-1)*n] = ( double ) j;
      }
      else
      {
        a[i-1+(j-1)*n] = 0.0;
      }
    }
  }

  r8ut_print ( n, n, a, "  The upper triangular matrix:" );
//
//  Set the desired solution.
//
  x = r8vec_indicator1_new ( n );
//
//  Compute the corresponding right hand side.
//
  b = r8ut_mtv ( n, n, a, x );
//
//  Solve the linear system.
//
  delete [] x;
  x = r8ut_slt ( n, a, b );

  r8vec_print ( n, x, "  Solution to transposed system:" );

  delete [] a;
  delete [] b;
  delete [] x;

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

void r8ut_to_r8ge_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_TO_R8GE_TEST tests R8UT_TO_R8GE.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a_ge;
  double *a_ut;
  int m = 5;
  int n = 4;
  int seed = 123456789;

  cout << "\n";
  cout << "R8UT_TO_R8GE_TEST\n";
  cout << "  R8UT_TO_R8GE converts an R8UT matrix to R8GE format.\n";

  a_ut = r8ut_random ( m, n, seed );

  r8ut_print ( m, n, a_ut, "  The random R8UT matrix:" );

  a_ge = r8ut_to_r8ge ( m, n, a_ut );

  r8ge_print ( m, n, a_ge, "  The R8GE matrix" );

  delete [] a_ge;
  delete [] a_ut;

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

void r8ut_zeros_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8UT_ZEROS_TEST tests R8UT_ZEROS.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 August 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  int m = 5;
  int n = 4;

  cout << "\n";
  cout << "R8UT_ZEROS_TEST\n";
  cout << "  R8UT_ZEROS returns zeroed out space for an R8UT matrix.\n";
  cout << "\n";
  cout << "  Matrix order M, N = " << m << ", " << n << "\n";

  a = r8ut_zeros ( m, n );

  r8ut_print ( m, n, a, "  Matrix A:" );

  delete [] a;

  return;
}