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

# include "mgs.h"

int main ( );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
int i4_uniform ( int a, int b, int *seed );
int r4_nint ( float x );
void r4mat_delete ( float **a, int m, int n );
float **r4mat_new ( int m, int n );
void r4mat_uniform ( int m, int n, float b, float c, int *seed, float **r );
void timestamp ( );

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

int main ( )

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

    MAIN is the main program for MGS_TEST.

  Discussion:

    MGS_TEST tests the MGS library.

  Modified:

    07 November 2011

  Author:

    John Burkardt
*/
{
  float **a;
  float **a_qr;
  float **a_save;
  float a_hi = 10.0;
  float a_lo = -10.0;
  float diff;
  int i;
  int j;
  int k;
  int m;
  int n;
  float **q;
  float **r;
  int seed = 123456789;
  int test;

  timestamp ( );
  printf ( "\n" );
  printf ( "MGS_TEST:\n" );
  printf ( "  C version\n" );
  printf ( "  Test cases for MGS.\n" );
  printf ( "\n" );

  for ( test = 1; test <= 4; test++ )
  {
    m = i4_uniform ( 1, 20, &seed );
    n = i4_uniform ( 1, 20, &seed );

    a = r4mat_new ( m, n );
    a_qr = r4mat_new ( m, n );
    a_save = r4mat_new ( m, n );
    q = r4mat_new ( m, n );
    r = r4mat_new ( n, n );

    r4mat_uniform ( m, n, a_lo, a_hi, &seed, a );

    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        a_save[i][j] = a[i][j];
      }
    }

    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        q[i][j] = 0.0;
      }
    }

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

    mgs ( m, n, a, r, q );

    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        a_qr[i][j] = 0.0;
        for ( k = 0; k < n; k++ )
        {
          a_qr[i][j] = a_qr[i][j] + q[i][k] * r[k][j];
        }
      }
    }
    diff = 0.0;
    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        diff = diff + pow ( a_save[i][j] - a_qr[i][j], 2 );
      }
    }
    diff = diff / sqrt ( ( float ) ( m * n ) );

    printf ( "  %2d  %2d  %14.6g\n", m, n, diff );

    r4mat_delete ( a, m, n );
    r4mat_delete ( a_qr, m, n );
    r4mat_delete ( a_save, m, n );
    r4mat_delete ( q, m, n );
    r4mat_delete ( r, n, n );
  }
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "MGS_TEST:\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

int i4_max ( int i1, int i2 )

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

    I4_MAX returns the maximum of two I4's.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, are two integers to be compared.

    Output, int I4_MAX, the larger of I1 and I2.
*/
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

int i4_min ( int i1, int i2 )

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

    I4_MIN returns the smaller of two I4's.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, two integers to be compared.

    Output, int I4_MIN, the smaller of I1 and I2.
*/
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

int i4_uniform ( int a, int b, int *seed )

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

    I4_UNIFORM returns a scaled pseudorandom I4.

  Discussion:

    The pseudorandom number should be uniformly distributed
    between A and B.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    12 November 2006

  Author:

    John Burkardt

  Reference:

    Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Springer Verlag, pages 201-202, 1983.

    Pierre L'Ecuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley Interscience, page 95, 1998.

    Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom
    Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.

    Peter Lewis, Allen Goodman, James Miller
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, pages 136-143, 1969.

  Parameters:

    Input, int A, B, the limits of the interval.

    Input/output, int *SEED, the "seed" value, which should NOT be 0.
    On output, SEED has been updated.

    Output, int I4_UNIFORM, a number between A and B.
*/
{
  int k;
  float r;
  int value;

  if ( *seed == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "I4_UNIFORM - Fatal error!\n" );
    fprintf ( stderr, "  Input value of SEED = 0.\n" );
    exit ( 1 );
  }

  k = *seed / 127773;

  *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

  if ( *seed < 0 )
  {
    *seed = *seed + 2147483647;
  }

  r = ( float ) ( *seed ) * 4.656612875E-10;
/*
  Scale R to lie between A-0.5 and B+0.5.
*/
  r = ( 1.0 - r ) * ( ( float ) ( i4_min ( a, b ) ) - 0.5 )
    +         r   * ( ( float ) ( i4_max ( a, b ) ) + 0.5 );
/*
  Use rounding to convert R to an integer between A and B.
*/
  value = r4_nint ( r );

  value = i4_max ( value, i4_min ( a, b ) );
  value = i4_min ( value, i4_max ( a, b ) );

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

int r4_nint ( float x )

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

    R4_NINT returns the nearest integer to an R4.

  Example:

        X         R4_NINT

      1.3         1
      1.4         1
      1.5         1 or 2
      1.6         2
      0.0         0
     -0.7        -1
     -1.1        -1
     -1.6        -2

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    05 May 2006

  Author:

    John Burkardt

  Parameters:

    Input, float X, the value.

    Output, int R4_NINT, the nearest integer to X.
*/
{
  int s;
  int value;

  if ( x < 0.0 )
  {
    s = - 1;
  }
  else
  {
    s = + 1;
  }
  value = s * ( int ) ( fabs ( x ) + 0.5 );

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

void r4mat_delete ( float **a, int m, int n )

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

    R4MAT_DELETE frees the memory set aside by R4MAT_NEW.

  Discussion:

    This function releases the memory associated with an array that was 
    created by a command like
      float **a;
      a = r4mat_new ( m, n );

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    11 September 2011

  Author:

    John Burkardt

  Parameters:

    Input, float **A, the array.

    Input, int M, N, the number of rows and columns.
*/
{
  int i;

  for ( i = 0; i < m; i++ )
  {
    free ( a[i] );
  }

  free ( a );

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

float **r4mat_new ( int m, int n )

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

    R4MAT_NEW sets up a float matrix of the desired dimensions.

  Discussion:

    A declaration of the form
      float **a;
    is necesary.  Then an assignment of the form:
      a = r4mat_new ( m, n );
    allows the user to assign entries to the matrix using typical
    2D array notation:
      a[2][3] = 17;
      y = a[1][0];
    and so on.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    11 September 2011

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Output, float **R4MAT_NEW, the array.
*/
{
  float **a;
  int i;

  a = ( float ** ) malloc ( m * n * sizeof ( float * ) );

  for ( i = 0; i < m; i++ )
  {
    a[i] = ( float * ) malloc ( n * sizeof ( float ) );
  }
  return a;
}
/******************************************************************************/

void r4mat_uniform ( int m, int n, float b, float c, int *seed, float **r )

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

    R4MAT_UNIFORM returns a scaled pseudorandom R4MAT.

  Discussion:

    This routine implements the recursion

      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
      u = seed / ( 2^31 - 1 )

    The integer arithmetic never requires more than 32 bits,
    including a sign bit.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    23 April 2008

  Author:

    John Burkardt

  Reference:

    Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673,
    LC: QA76.9.C65.B73.

    Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom
    Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, December 1986, pages 362-376.

    Pierre L'Ecuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley, 1998,
    ISBN: 0471134031,
    LC: T57.62.H37.

    Peter Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, Number 2, 1969, pages 136-143.

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, float B, C, the limits of the pseudorandom values.

    Input/output, int *SEED, the "seed" value.  Normally, this
    value should not be 0.  On output, SEED has 
    been updated.

    Output, float **R, a matrix of pseudorandom values.
*/
{
  int i;
  int i4_huge = 2147483647;
  int j;
  int k;

  if ( *seed == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R4MAT_UNIFORM - Fatal error!\n" );
    fprintf ( stderr, "  Input value of SEED = 0.\n" );
    exit ( 1 );
  }

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = *seed / 127773;

      *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

      if ( *seed < 0 )
      {
        *seed = *seed + i4_huge;
      }

      r[i][j] = b + ( c - b ) * ( float ) ( *seed ) * 4.656612875E-10;
    }
  }

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

void timestamp ( void )

/******************************************************************************/
/*
  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 GNU LGPL license. 

  Modified:

    24 September 2003

  Author:

    John Burkardt

  Parameters:

    None
*/
{
# 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
}