# 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
}