Categories

ID #1124

How do I run the HPL test on a Bright Cluster?

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline;">How do I run the HPL test on a Bright Cluster?an>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">
an>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">What is HPL?an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Slightly rewording froman> an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">http://www.netlib.org/benchmark/hpl/:an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPLan>an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;"> is a software package that solves aan>an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-variant: normal; text-decoration: none; vertical-align: baseline;"> random, dense linearan>an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;"> system of equations with N unknowns, in double-precision arithmetic on distributed-memory computers. It then prints the estimated performance of the distributed-memory computer as the ratio between the number of effective floating point operations divided by the amount of time in seconds it an class="highlight">toan>ok an class="highlight">toan>  perform those operations.an>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">It can thus be regarded as a portable as well as freely available implementation of the High Performance Computing LINPACK Benchmark.an>



an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The algorithman>

 

  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Two-dimensional block-cyclic data distributionan>

  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;"> Right-looking variant of the LU facan class="highlight">toan>rization with row partial pivoting featuring multiple look-ahead depths an>

  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Recursive panel facan class="highlight">toan>rization with pivot search and column broadcast combined an>

  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Various virtual panel broadcast an class="highlight">toan>pologies an>

    • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">bandwidth reducing swap-broadcast algorithm an>

    • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">backward substitution with look-ahead of depth 1an>



an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The HPL algorithm is changeable and can be tuned via 17 parameters:an>



able style="border: none; border-collapse: collapse; width: 624px;">

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Nan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Problem sizean>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Pmapan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Process mappingan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">NBan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Blocking facan class="highlight">toan>ran>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">thresholdan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">for matrix validity testan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Pan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Rows in process gridan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Ndivan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Panels in recursionan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Qan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Columns in process gridan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Nbminan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Recursion san class="highlight">toan>pping criteriaan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Depthan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Lookahead depthan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Swapan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Swap algorithman>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Bcastsan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Panel broadcasting methodan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">L1, Uan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">an class="highlight">toan> san class="highlight">toan>re triangle of panelan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Pfactsan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Panel facan class="highlight">toan>rization methodan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Alignan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Memory  alignmentan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Rfactsan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Recursive facan class="highlight">toan>rization methodan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Equilibrationan>

 
able>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The parameters in the red cells are the most important tuning parameters, while the ones in the green cells are of somewhat lesser importance. The parameter space is huge and exploring the full parameter space is inefficient as there are more than a billion different combinations. If one considers only combination of the most important parameters the parameter space reduces an class="highlight">toan> 50,000 combinations.an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">There are several algorithms that aim at cutting the amount of time required for tuning, but they are beyond the scope of this article. However, it is worth mentioning that one does an class="highlight">notan> have an class="highlight">toan> use the maximal problem size in tuning. Early termination can be used an class="highlight">toan> cut down the time, and the fact that tuning algorithms perform well and seem an class="highlight">toan> be robust suggest that for a given architecture the amount of important parameters might be smaller than suggested above.an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The tuning parameters need an class="highlight">toan> be san class="highlight">toan>red in a file named HPL.dat. an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Setting the values of HPL.dat parametersan>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The problem size N should be set an class="highlight">toan> a large value but an class="highlight">notan> an class="highlight">toan>o large. The amount of computations scales as the cube of that number which means that doubling N requires eight times more computations. Values of the order of 1000-10,000 are reasonable for modern systems. Make sure that there is no paging occurring while executing the problem by monian class="highlight">toan>ring the an style="font-family: courier new,courier;">vmstatan>an>an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;"> command. A useful formula an class="highlight">toan> estimate the problem size is:an>

 

N = sqrt ( 0.75 * Number of Nodes * Minimum memory of any node / 8 )an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">
an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPL uses the block size NB for the data distribution as well as for the computational granularity.  Small values are better from a load balancing point of view, but an class="highlight">toan>o small values might limit performance. A value in the range [32,...,256] is good for modern systems with large values being more efficient for larger problem sizes. an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The process decomposition should be roughly square with P greater than or equal an class="highlight">toan> Q. The product PxQ should obviously match the number of processors/cores that are going an class="highlight">toan> be used for HPL. The most important facan class="highlight">toan>r that affects the selection of this parameter is the type of physical network with which the nodes of the cluster are interconnected. Flat grids  like 4x1, 8x1, 4x2, etc. are good for ethernet-based networks. an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The Rfact and Pfact values need experimentation, but for very large clusters both parameters can be set an class="highlight">toan> the right-looking part of the LU decomposition.
an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Once the panel facan class="highlight">toan>rization has been computed, this panel of columns is broadcast an class="highlight">toan> the other process columns. There are many possible broadcast algorithms, and the software currently offers 6 variants an class="highlight">toan> choose from. A brief an class="highlight">notan>e on some of these:

an>

  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Algorithm 2: Increasing-ring (modified) is the usually the best choicean>
  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Algorithm 4: Increasing-2-ring (modified) is usually a second choice.an>
  • an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Algorithm 5: an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Long (bandwidth reducing) - this can be a good choice fan>or systems with very fast nodes, but a very slow network.
    an>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">
A final recommendation is an class="highlight">toan> ensure that HPL is an class="highlight">notan> going an class="highlight">toan> use more than 80% of the memory available an class="highlight">toan> that system
an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">There are also a couple of web-based HPL.dat generaan class="highlight">toan>rs like the following:an>

an style="font-family: courier new,courier;"><a href="http://www.advancedclustering.com/faq/how-do-i-tune-my-hpldat-file.html">an style="font-size: 15px; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">http://www.advancedclustering.com/faq/how-do-i-tune-my-hpldat-file.htmlan>a>an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">A sample HPL.dat filean>

 

HPLinpack benchmark input file
Innovative Computing Laboraan class="highlight">toan>ry, University of Tennessee
HPL.out      output file name (if any)
6            device out (6=stdout,7=stderr,file)
1            # of problems sizes (N)
58464         Ns
1            # of NBs
168           NBs
0            PMAP process mapping (0=Row-,1=Column-major)
1            # of process grids (P x Q)
4            Ps
8            Qs
16.0         threshold
1            # of panel fact
2            PFACTs (0=left, 1=Crout, 2=Right)
1            # of recursive san class="highlight">toan>pping criterium
4            NBMINs (>= 1)
1            # of panels in recursion
2            NDIVs
1            # of recursive panel fact.
1            RFACTs (0=left, 1=Crout, 2=Right)
1            # of broadcast
1            BCASTs (0=1rg,1=1rM,2=2rg,3=2rM,4=Lng,5=LnM)
1            # of lookahead depth
1            DEPTHs (>=0)
2            SWAP (0=bin-exch,1=long,2=mix)
64           swapping threshold
0            L1 in (0=transposed,1=no-transposed) form
0            U  in (0=transposed,1=no-transposed) form
1            Equilibration (0=no,1=yes)
8            memory alignment in double (> 0)




an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Prerequisitesan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPL requires a distributed-memory system with a tuned implementation of the BLAS library and a working implementation of the MPI standard. The Bright Cluster Manager provides several modules of the OpenBLAS library tuned for different architectures as well as a general-purpose module (openblas/dynamic) that attempts an class="highlight">toan> auan class="highlight">toan>-detect the relevant architecture and use routines optimized for that particular system.an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The relevant modules can be loaded with the command below:an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">[user@myHeadNode ~]$ module load shared openmpi/gcc openblas/dynamic  hplan>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The other available tuned versions of OpenBLAS are:an>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- openblas/bulldozeran>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- openblas/istanbulan>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- openblas/nehaleman>

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- openblas/sandybridgean>

 

 

an style="color: #ff0000;">an class="highlight">Notan>e: OpenBLAS is available in Bright 6.1. Users of Bright 5.2 and 6.0 can choose between goan class="highlight">toan>BLAS and BLAS. In the latter case the HPL binary is called xhpl.blas.an>



an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Running HPL on a Bright clusteran>

 

 

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">an class="highlight">Toan> run HPL after loading the modules, the user needs an class="highlight">toan> issue the command:an>

 

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">mpiexec -machinefile nodes   xhpl | tee HPL.outan>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">If your cluster has InfiniBand, and you want an class="highlight">toan> see the performance difference between InfiniBand and Ethernet, you can do a run over Ethernet by issuing the following command:
an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">mpiexec -machinefile nodes  --mca btl ^openib  xhpl | tee HPL.outan>

 

an style="font-size: 15px; font-family: Arial; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Sample output:an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">================================================================================an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPLinpack 2.1  --  High-Performance Linpack benchmark  --   Ocan class="highlight">toan>ber 26, 2012an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Written by A. Petitet and R. Clint Whaley,  Innovative Computing Laboraan class="highlight">toan>ry, UTKan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Modified by Piotr Luszczek, Innovative Computing Laboraan class="highlight">toan>ry, UTKan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Modified by Julien Langou, University of Colorado Denveran>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">================================================================================an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">An explanation of the input/output parameters follows:an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">T/V    : Wall time / encoded variant.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">N      : The order of the coefficient matrix A.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">NB     : The partitioning blocking facan class="highlight">toan>r.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">P      : The number of process rows.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Q      : The number of process columns.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Time   : Time in seconds an class="highlight">toan> solve the linear system.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Gflops : Rate of execution for solving the linear system.an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">The following parameter values will be used:an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">N      :   79232an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">NB     :     128an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">PMAP   : Row-major process mappingan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">P      :       4an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Q      :       4an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">PFACT  :   Rightan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">NBMIN  :       4an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">NDIV   :       2an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">RFACT  :   Croutan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">BCAST  :  1ringMan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">DEPTH  :       1an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">SWAP   : Mix (threshold = 64)an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">L1     : transposed forman>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">U      : transposed forman>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">EQUIL  : yesan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">ALIGN  : 8 double precision wordsan>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">--------------------------------------------------------------------------------an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- The matrix A is randomly generated for each test.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- The following scaled residual check will be computed:an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">      ||Ax-b||_oo / ( eps * ( || x ||_oo * || A ||_oo + || b ||_oo ) * N )an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- The relative machine precision (eps) is taken an class="highlight">toan> be               1.110223e-16an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">- Computational tests pass if scaled residuals are less than                16.0an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">================================================================================an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">T/V                N    NB     P     Q               Time                 Gflopsan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">--------------------------------------------------------------------------------an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">WR11C2R4       79232   128     4     4            2311.44              1.435e+02an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPL_pdgesv() start time Wed Jan  2 21:53:09 2013an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">HPL_pdgesv() end time   Wed Jan  2 22:31:40 2013an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">--------------------------------------------------------------------------------an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)=        0.0034949 ...... PASSEDan>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">================================================================================an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">Finished      1 tests with the following results:an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">              1 tests completed and passed residual checks,an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">              0 tests completed and failed residual checks,an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">              0 tests skipped because of illegal input values.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">--------------------------------------------------------------------------------an>

 

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">End of Tests.an>

an style="font-size: 15px; font-family: courier new,courier; color: #000000; background-color: transparent; font-weight: normal; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline;">================================================================================an>



Tags: HPL

Related entries:

You cannot comment on this entry