LINPACK_BENCH
The LINPACK Benchmark

LINPACK_BENCH is a JAVA script, using double precision arithmetic, which carries out the LINPACK benchmark.

The LINPACK benchmark tests the speed of a computer on a particular computational task, namely the factorization of a large dense matrix, and the solution of a related linear system.

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 ).

Language	Precision	Type	Machine	Comment	MegaFLOPS
Java	Double	Real	DHCP95 (Apple G5)		227

Usage:

javac linpack_bench_d

compiles the benchmark program, creating "linpack_bench_d.class".

java linpack_bench_d

runs the compiled program "linpack_bench_d.class".

Related Data and Programs:

LINPACK is a FORTRAN90 library which supplies the solvers used by LINPACK_BENCH.

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

MATMUL is an executable FORTRAN90 program which is an interactive matrix multiplication benchmark program.

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

MEMORY_TEST is a FORTRAN90 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.

TIMER is a FORTRAN90 example 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. GS 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_d.java, the source code;

Examples and Tests:

• linpack_bench_d_dhcp95_output.txt, the output from DHCP95, an Apple G5;

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