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

int main ( int argc, char *argv[] );
double cpu_time ( );
double *matgen ( int m, int n, int *seed );
double mxm_ijk ( int n1, int n2, int n3, double b[], double c[] );
double mxm_ikj ( int n1, int n2, int n3, double b[], double c[] );
double mxm_jik ( int n1, int n2, int n3, double b[], double c[] );
double mxm_jki ( int n1, int n2, int n3, double b[], double c[] );
double mxm_kij ( int n1, int n2, int n3, double b[], double c[] );
double mxm_kji ( int n1, int n2, int n3, double b[], double c[] );
void timestamp ( );

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

int main ( int argc, char *argv[] )

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

    MAIN is the main program for MXM.

  Discussion:

    MXV computes a matrix-matrix product in a number of ways, and reports
    the elapsed CPU time.

    The multiplication carried out is

      A(1:N1,1:N3) = B(1:N1,1:N2) * C(1:N2,1:N3)

    where B and C are real double precision matrices whose entries
    are assigned randomly.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    08 October 2010

  Author:

    John Burkardt

  Usage:

    mxm n1 n2 n3

  Parameters:

    Command line argument, int N1, N2, N3, defines the number of
    rows and columns in the two matrices.
*/
{
  double *b;
  double *c;
  double cpu_seconds;
  int flop_count;
  double mflops;
  int n1;
  int n2;
  int n3;
  int seed;
  double time_estimate;

  timestamp ( );

  printf ( "\n" );
  printf ( "MXM:\n" );
  printf ( "  C version\n" );
  printf ( "  Compute matrix-matrix product A = B * C\n" );
/*
  Get N1.
*/
  if ( 1 < argc )
  {
    n1 = atoi ( argv[1] );
  } 
  else
  {
    printf ( "\n" );
    printf ( "  Enter N1, the number of rows in B.\n" );
    scanf ( "%d", &n1 );
  }
/*
  Get N2.
*/
  if ( 2 < argc )
  {
    n2 = atoi ( argv[2] );
  } 
  else
  {
    printf ( "\n" );
    printf ( "  Enter N2, the number of columns in B and rows in C.\n" );
    scanf ( "%d", &n2 );
  }
/*
  Get N3.
*/
  if ( 3 < argc )
  {
    n3 = atoi ( argv[3] );
  } 
  else
  {
    printf ( "\n" );
    printf ( "  Enter N3, the number of columns in C.\n" );
    scanf ( "%d", &n3 );
  }
/*
  Record the amount of work.
  Each of the N1 * N3 entries of A requires N2 multiplies and N2 adds.
*/
  flop_count = 2 * n1 * n2 * n3;

  printf ( "\n" );
  printf ( "  Matrix B is %d by %d\n", n1, n2 );
  printf ( "  Matrix C is %d by %d\n", n2, n3 );
  printf ( "  Matrix A will be %d by %d\n", n1, n3 );
  printf ( "\n" );
  printf ( "  Number of floating point operations = %d\n", flop_count );
  time_estimate = ( double ) ( flop_count ) / 2.6E+09;
  printf ( "  Estimated CPU time is %f seconds.\n", time_estimate );
/*
  Set B and C.
*/
  seed = 1325;
  b = matgen ( n1, n2, &seed );
  c = matgen ( n2, n3, &seed );
  printf ( "\n" );
  printf ( "  Method     Cpu Seconds       MegaFlopS\n" );
  printf ( "  ------  --------------  --------------\n" );
/*
  IJK
*/
  cpu_seconds = mxm_ijk ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  IJK     %14f  %14f\n", cpu_seconds, mflops );
/*
  IKJ
*/
  cpu_seconds = mxm_ikj ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  IKJ     %14f  %14f\n", cpu_seconds, mflops );
/*
  JIK
*/
  cpu_seconds = mxm_jik ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  JIK     %14f  %14f\n", cpu_seconds, mflops );
/*
  JKI
*/
  cpu_seconds = mxm_jki ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  JKI     %14f  %14f\n", cpu_seconds, mflops );
/*
  KIJ
*/
  cpu_seconds = mxm_kij ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  KIJ     %14f  %14f\n", cpu_seconds, mflops );
/*
  KJI
*/
  cpu_seconds = mxm_kji ( n1, n2, n3, b, c );

  if ( 0.0 < cpu_seconds )
  {
    mflops = ( double ) ( flop_count ) / cpu_seconds / 1000000.0;
  }
  else
  {
    mflops = -1.0;
  }

  printf ( "  KJI     %14f  %14f\n", cpu_seconds, mflops );
/*
  Deallocate arrays.
*/
  free ( b );
  free ( c );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "MXM:\n" );
  printf ( "  Normal end of execution.\n" );

  printf ( "\n" );
  timestamp ( );

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

double cpu_time ( void )

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

    CPU_TIME returns the current reading on the CPU clock.

  Discussion:

    The CPU time measurements available through this routine are often
    not very accurate.  In some cases, the accuracy is no better than
    a hundredth of a second.  

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    06 June 2005

  Author:

    John Burkardt

  Parameters:

    Output, double CPU_TIME, the current reading of the CPU clock, in seconds.
*/
{
  double value;

  value = ( double ) clock ( ) 
        / ( double ) CLOCKS_PER_SEC;

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

double *matgen ( int m, int n, int *seed )

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

    MATGEN generates a random matrix.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    09 October 2010

  Author:

    John Burkardt

  Parameters:

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

    Input, int *SEED, a seed for the random number
    generator.

    Output, double MATGEN[M*N], the matrix.
*/
{
  double *a;
  int i;
  int j;

  a = ( double * ) malloc ( m * n * sizeof ( double ) );
/*
  Set the matrix A.
*/
  for ( j = 0;j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      *seed = ( ( 3125 * *seed ) % 65536 );
      a[i+j*m] = ( *seed - 32768.0 ) / 16384.0;
    }
  }

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

double mxm_ijk ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_IJK computes A = B * C using FOR I, FOR J, FOR K loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    09 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( i = 0; i < n1; i++ )
  {
    for ( j = 0; j < n3; j++ )
    {
      for ( k = 0; k < n2; k++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

double mxm_ikj ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_IKJ computes A = B * C using FOR I, FOR K, FOR J loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    07 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( i = 0; i < n1; i++ )
  {
    for ( k = 0; k < n2; k++ )
    {
      for ( j = 0; j < n3; j++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

double mxm_jik ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_JIK computes A = B * C using FOR J, FOR I, FOR K loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    07 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      for ( k = 0; k < n2; k++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

double mxm_jki ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_JKI computes A = B * C using FOR J, FOR K, FOR I loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    07 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( j = 0; j < n3; j++ )
  {
    for ( k = 0; k < n2; k++ )
    {
      for ( i = 0; i < n1; i++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

double mxm_kij ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_KIJ computes A = B * C using FOR K, FOR I, FOR J loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    07 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( k = 0; k < n2; k++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      for ( j = 0; j < n3; j++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

double mxm_kji ( int n1, int n2, int n3, double b[], double c[] )

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

    MXM_KJI computes A = B * C using FOR K, FOR J, FOR I loops.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    07 October 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N1, N2, N3, define the orders of the
    matrices.

    Input, double B[N1*N2], C[N2*N3], the factor matrices.

    Output, double MXM_IJK, the elapsed CPU time.
*/
{
  double *a;
  double cpu_seconds;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( j = 0; j < n3; j++ )
  {
    for ( i = 0; i < n1; i++ )
    {
      a[i+j*n1] = 0.0;
    }
  }

  cpu_seconds = cpu_time ( );

  for ( k = 0; k < n2; k++ )
  {
    for ( j = 0; j < n3; j++ )
    {
      for ( i = 0; i < n1; i++ )
      {
        a[i+j*n1] = a[i+j*n1] + b[i+k*n1] * c[k+j*n2];
      }
    }
  }

  cpu_seconds = cpu_time ( ) - cpu_seconds;

  free ( a );

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

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

  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
}