LINPACK_BENCH
The LINPACK Benchmark

LINPACK_BENCH is a MATLAB program which carries out the LINPACK Benchmark.

The LINPACK benchmark is a test problem used to rate the performance of a computer on a simple linear algebra problem.

The test problem requires the user to set up a random dense matrix A of size N = 1000, and a right hand side vector B which is the product of A and a vector X of all 1's. The first task is to compute an LU factorization of A. The second task is to use the LU factorization to solve the linear system

A * X = B.

The number of floating point operations required for these two tasks is roughly

ops = 2 * N*N*N / 3 + 2 * N * N,

mflops = ops / ( cpu * 1000000 ).

On a given computer, if you run the benchmark for a sequence of increasing values of N, the behavior of the MegaFLOPS rating will vary as you pass through three main zones of behavior:

• a rising zone, as both the local cache memory and the processor are not challenged.
• a flat zone, where the processor is challenged, that is, it is performing at top efficiency.
• a decaying zone, where the local cache memory is also challenged, that is the matrix is so large that the cache is not big enough to keep the necessary data close enough to the processor to keep it running at top speed.

Language	Precision	Type	Machine	Comment	MegaFLOPS
MATLAB	Double	Real	Prism		22
MATLAB	Double	Real	DHCP95 (Apple G95)		20
MATLAB	Double	Real	PC		9

Languages:

LINPACK_BENCH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a JAVA version and a MATLAB version.

Related Data and Programs:

LINPACK_D, a MATLAB library which supplies the solvers used by LINPACK_BENCH.

LINPACK_BENCH_BACKSLASH, a MATLAB program which measures the time taken by LINPACK to solve a particular linear system, and uses MATLAB's builtin "backslash" operator to do the solving.

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

MDBNCH, a FORTRAN77 program which is a benchmark code for a molecular dynamics calculation.

MEMORY_TEST, a MATLAB program which declares and uses a sequence of larger and larger vectors, to see how big a vector can be used on a given machine and compiler.

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, a MATLAB library which demonstrates how to measure CPU time or elapsed time.

Reference:

1. http://www.netlib.org/benchmark/1000s the LINPACK benchmark website (single precision).
2. http://www.netlib.org/benchmark/1000d the LINPACK benchmark website (double precision).
3. Jack Dongarra,
   Performance of Various Computers Using Standard Linear Equations Software, Technical Report CS-89-85,
   Electrical Engineering and Computer Science Department,
   University of Tennessee, 2008.
4. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
5. George Fishman,
   Multiplicative congruential random number generators with modulus 2**b: an exhaustive analysis for b = 32 and a partial analysis for b = 48,
   Mathematics of Computation,
   Volume 189, 1990, pages 331-344.
6. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• linpack_bench.m, the source code.

Examples and Tests:

• linpack_bench_dhcp95_output.txt, the output from DHCP95, an Apple G5, of about 20 MegaFLOPS.
• linpack_bench_pc_output.txt, the output from a PC, of about 9 MegaFLOPS.
• linpack_bench_prism_output.txt, the output from PRISM000, of about 22 MegaFLOPS.

You can go up one level to the MATLAB source codes.