MXV
Matrix Vector Multiplication Timings

MXV is a C++ program which sets up several matrix vector multiplication problems y=A*x, and carries them out using

• Nested FOR I, FOR J loops, A stored as a vector;
• Nested FOR J, FOR I loops, A stored as a vector;

The user is allowed to specify M and N, the number of matrix rows and columns.

Usage:

mxv m n

• m is the number of matrix rows;
• n is the number of matrix columns;

Sample Results:

          M        N       FLOP  FORIFORJ  FORJFORI

         10       10        100       7      13

         10      100      1,000      22      29
        100       10      1,000      14      31

         10    1,000     10,000      35      32
        100      100     10,000      23      33
      1,000       10     10,000      22      32

         10   10,000    100,000      18      26
        100    1,000    100,000      23      30
      1,000      100    100,000      23      32
     10,000       10    100,000      22      32

         10  100,000  1,000,000      17      33
        100   10,000  1,000,000       7      48
      1,000    1,000  1,000,000      17      33
     10,000      100  1,000,000      26      33
    100,000       10  1,000,000      22      31
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MXV is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LINPACK_BENCH, a C++ program which measures the time needed to factor and solve a "large" (N=1000) dense linear system of equations, and is used as a benchmark.

MATMUL, a FORTRAN90 program which is an interactive matrix multiplication benchmark program.

MXM, a C++ program which sets up a matrix multiplication problem A=B*C of arbitrary size, and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI orderings of the loops.

MXV_OPENMP, a C++ program which compares the performance of plain vanilla Fortran and the FORTRAN90 intrinsic routine MATMUL, for the matrix multiplication problem y=A*x, with and without parallelization by OpenMP.

SUM_MILLION, a C++ program which sums the integers from 1 to 1,000,000, as a demonstration of how to rate a computer's speed;

TIMER, C++ programs which demonstrate how to compute CPU time or elapsed time.

Reference:

1. John Burkardt, Paul Puglielli,
   Pittsburgh Supercomputing Center,
   MATMUL: An Interactive Matrix Multiplication Benchmark

Source Code:

• mxv.cpp, the source code.
• mxv.sh, commands to compile and link the source code.

List of Routines:

• MAIN is the main program for MXV.
• CPU_TIME returns the current reading on the CPU clock.
• MATGEN generates a random matrix A and vector X.
• MXV_FORIFORJ computes y = A * x, using FOR I, FOR J loops.
• MXV_FORJFORI computes y = A * x, using FOR J, FOR I loops.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.