LINPACK_BENCH
The LINPACK Benchmark

LINPACK_BENCH is a FORTRAN77 program, using single or double precision, that 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 ).

Language	Precision	Type	Machine	Comment	MegaFLOPS
Fortran77	Single	Real	DHCP95 (Apple G5)	gfortran	221
Fortran77	Double	Real	DHCP95 (Apple G5)	gfortran	202

Usage:

linpack_bench_s

runs the single precision benchmark program and prints the timings.

linpack_bench_d

runs the double precision benchmark program and prints the timings.

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 FORTRAN90 version and a JAVA 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 FORTRAN77 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_S is the single precision version:

• linpack_bench_s.f, the source code.
• linpack_bench_s.csh, commands to compile and load the source code.
• linpack_bench_s_dhcp95_output.txt, the output from an Apple G5 named "DHCP95".

LINPACK_BENCH_D is the double precision version:

• linpack_bench_d.f, the source code.
• linpack_bench_d.csh, commands to compile and load the source code.
• linpack_bench_d_dhcp95_output.txt, the output from an Apple G5 named "DHCP95".

List of Routines:

This is the list of routines for the double precision version of the benchmark program. The single precision names are similar.

• MAIN drives the double precision LINPACK benchmark program.
• MATGEN generates a random matrix.
• DGEFA factors a real matrix.
• DGESL solves a real general linear system A * X = B.
• DAXPY adds a constant times one vector to another.
• DDOT computes the dot product of two vectors.
• DSCAL scales a vector.
• IDAMAX finds the index of the vector element of maximum absolute value.
• EPSLON estimates the unit roundoff.
• MM computes the matrix-matrix product A=B*C
• DMXPY computes the matrix-vector product y=A*x.
• RANDOM_VALUE returns a uniformly distributed random number between 0 and 1.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.