MXV
Matrix Vector Multiplication Timings

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

• FORIFORJ, nested FOR I, FOR J loops;
• FORJFORI, nested FOR J, FOR I loops;
• ASTARX, the MATLAB intrinsic matrix multiplication operator "A*X";

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  ASTARX

         10       10        100       1       0       1

         10      100       1000       3       1       8
        100       10       1000       1       1       9

         10    1,000     10,000       3       1       6
        100      100     10,000       2       2       8
       1000       10     10,000       1       1       8

         10   10,000    100,000       3       1       8
        100    1,000    100,000       3       3       9
      1,000      100    100,000       3       3      11
     10,000       10    100,000       0       0      18

         10  100,000  1,000,000       5       1      18
        100   10,000  1,000,000       3       4      24
      1,000    1,000  1,000,000       4       4      22
     10,000      100  1,000,000       0       0      23
    100,000       10  1,000,000       0       0      17
      

These timing results seem very poor. Surprisingly, the tic and toc functions in MATLAB seemed to produce more accurate and reliable timings than the cputime function, which seems to return values only to the nearest 1/100 of a second. Also, MATLAB really does not like to carry out explicit FOR loops. For large values of M or N, some of these loops had abysmal MegaFLOPS ratings.

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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LINPACK_BENCH, a MATLAB 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 MATLAB 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.

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

TIMER, MATLAB 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.m, the source code.

List of Routines:

• MAIN is the main program for MXV.
• MATGEN generates a random matrix A and vector X.
• MXV_ASTARX computes y = A * x, using the MATLAB A*X notation.
• 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 MALAB source codes.