Vmesto Zakladok

TORQUE is an open source resource manager providing control over batch jobs and distributed compute nodes. Basically, one can setup a home or small office Linux cluster and queue jobs with this software. A cluster consists of one head node and many compute nodes. The head node runs the torque-server daemon and the compute nodes run the torque-client daemon. The head node also runs a scheduler daemon.

Installation

Note: Although TORQUE is a very powerful queuing system, if the goal of the cluster is solely to increase compilation throughput, distcc is a much easier and elegant solution.

Install the torque package found in the AUR.

Must haves

/etc/hosts

Make sure that /etc/hosts on all of the boxes in the cluster contains the hostnames of every PC in the cluster. Example, cluster consists of 3 PCs, mars, phobos, and deimos.

192.168.0.20   mars
192.168.0.21   phobos
192.168.0.22   deimos

Firewall configuration (if installed)

Be sure to open TCP for all machines using TORQUE.
The pbs_server (server) and pbs_mom (client) by default use TCP and UDP ports 15001-15004. pbs_mom (client) also uses UDP ports 1023 and below if privileged ports are configured (the default).

NFS

Technically, one does not need to use NFS but doing so simplifies the whole process. An NFS share either on the server or another machine is highly recommended to simplify the process of sharing common build disk space.

Setup

Server (head node) configuration

Follow these steps on the head node/scheduler.
Edit /var/spool/torque/server_name to name the head node. It is recommended to match the hostname in /etc/hostname for simplicity's sake.
Create and configure the torque server:

# pbs_server -t create
PBS_Server localhost.localdomain: Create mode and server database exists,
do you wish to continue y/(n)?y

A minimal set of options are provided here. Adjust the first line substituting "mars" with the hostname entered in /var/spool/torque/server_name:

qmgr -c "set server acl_hosts = mars"
qmgr -c "set server scheduling=true"
qmgr -c "create queue batch queue_type=execution"
qmgr -c "set queue batch started=true"
qmgr -c "set queue batch enabled=true"
qmgr -c "set queue batch resources_default.nodes=1"
qmgr -c "set queue batch resources_default.walltime=3600"
qmgr -c "set server default_queue=batch"

It may be of interest to keep finished jobs in the queue for a period of time.

qmgr -c "set server keep_completed = 86400"

Here, 86400 sec = 24 h after which point, the job will be auto removed from the queue. One can see the full log of jobs removed from the queue with the -f switch on qstat:

qstat -f

Verify the server config with this command:

# qmgr -c 'p s'

Edit /var/spool/torque/server_priv/nodes adding all compute nodes. Again, it is recommended to match the hostname(s) of the machines on the LAN. The syntax is HOSTNAME np=x gpus=y properties

HOSTNAME=the hostname of the machine
np=number of processors
gpus=number of gpus
properties=comments

Only the hostname is required, all other fields are optional.
Example:

mars np=4
phobos np=2
deimos np=2

Note:

One can run both the server and client on the same box.
Re-running pbs_server -t create may delete this nodes file.

Restart the server and the new options are sourced.

Client (compute node) configuration

Follow these steps on each compute node in the cluster.

Note: If running both the server and client on the same box, be sure to complete these steps as well for that machine as well as other pure clients on the cluster.

Edit /var/spool/torque/mom_priv/config to contain some basic info identifying the server:

$pbsserver      mars          # note: this is the hostname of the headnode
$logevent       255           # bitmap of which events to log

Restart the server and client(s)

That should be it. Restart the server and the client: torque-server torque-node.

Verifying cluster status

To check the status of the cluster, issue the following:

$ pbsnodes -a

Each node if up should indicate that it is ready to receive jobs echoing a state of free. If a node is not working, it will report a state of down.
Example output:

mars
     state = free
     np = 4
     ntype = cluster
     status = rectime=1308479899,varattr=,jobs=0.localhost.localdomain,state=free,netload=1638547057,
gres=,loadave=2.69,ncpus=4,physmem=8195892kb,availmem=7172508kb,totmem=8195892kb,
idletime=24772,nusers=1,nsessions=5,sessions=1333 1349 1353 1388 9095,
uname=Linux mars 2.6.39-ck #1 SMP PREEMPT Sat Jun 18 14:19:01 EDT 2011 x86_64,opsys=linux
     mom_service_port = 15002
     mom_manager_port = 15003
     gpus = 2

phobos
     state = free
     np = 2
     ntype = cluster
     status = rectime=1308479933,varattr=,jobs=,state=free,netload=1085755815,
gres=,loadave=2.84,ncpus=2,physmem=4019704kb,availmem=5753552kb,totmem=6116852kb,
idletime=7324,nusers=2,nsessions=6,sessions=1565 1562 1691 1716 1737 1851,
uname=Linux phobos 2.6.37-ck #1 SMP PREEMPT Sun Apr 3 17:16:35 EDT 2011 x86_64,opsys=linux
     mom_service_port = 15002
     mom_manager_port = 15003
     gpus = 1

deimos
     state = free
     np = 2
     ntype = cluster
     status = rectime=1308479890,varattr=,jobs=2.localhost.localdomain,state=free,netload=527239670,
gres=,loadave=0.52,ncpus=2,physmem=4057808kb,availmem=3955624kb,totmem=4057808kb,
idletime=644,nusers=1,nsessions=1,sessions=865,
uname=Linux deimos 2.6.39-ck #1 SMP PREEMPT Sat Jun 11 12:36:21 EDT 2011 x86_64,opsys=linux
     mom_service_port = 15002
     mom_manager_port = 15003
     gpus = 1

Queuing jobs

Queuing to the cluster is accomplished via the qsub command.
A trivial test is to simply run sleep:

$ echo "sleep 30" | qsub

Check the status of the queue via the qstat command described below. At this point, the work will have a status of "Q" which means queued. To start it, run the scheduler:

# pbs_sched

One can modify the torque-server systemd daemon to activate pbs_sched at boot.
Another usage of qsub is to name a job and queue a script:

$ qsub -N x264 /home/facade/bin/x264_HQ.sh

Note: STDOUT and STDERR for a queued job will be logged by default in the form text files corresponding to the respective outputs pid.o and pid.e and will be written to the path from which the qsub command was issued.

Another example can use a wrapper script to make and queue work en mass automatically.

Checking job status

qstat is used to check work status.

$ qstat

Job id                    Name             User            Time Use S Queue
------------------------- ---------------- --------------- -------- - -----
13.localhost               generic-i686.pbs facade         00:05:06 R batch          
14.localhost               atom-i686.pbs    facade         00:03:09 R batch          
15.localhost               core2-i686.pbs   facade         00:01:02 R batch          
16.localhost               k7-i686.pbs      facade                0 Q batch          
17.localhost               k8-i686.pbs      facade                0 Q batch          
18.localhost               k10-i686.pbs     facade                0 Q batch          
19.localhost               p4-i686.pbs      facade                0 Q batch          
20.localhost               pentm-i686.pbs   facade                0 Q batch          
21.localhost               ...ic-x86_64.pbs facade                0 Q batch          
22.localhost               atom-x86_64.pbs  facade                0 Q batch          
23.localhost               core2-x86_64.pbs facade                0 Q batch          
24.localhost               k8-x86_64.pbs    facade                0 Q batch          
25.localhost               k10-x86_64.pbs   facade                0 Q batch

Append the -n switch to see which nodes are doing which jobs.

$ qstat -n

localhost.localdomain:
405.localhost.lo     facade  batch    i686-generic       3035     1   0    --  01:00 C 00:12
   mars/3+mars/2+mars/1+mars/0
406.localhost.lo     facade  batch    i686-atom          5768     1   0    --  01:00 C 00:46
   phobos/1+phobos/0
407.localhost.lo     facade  batch    i686-core2        22941     1   0    --  01:00 C 00:12
   mars/3+mars/2+mars/1+mars/0
408.localhost.lo     facade  batch    i686-k7           10152     1   0    --  01:00 C 00:12
   mars/3+mars/2+mars/1+mars/0
409.localhost.lo     facade  batch    i686-k8           29657     1   0    --  01:00 C 00:12
   mars/3+mars/2+mars/1+mars/0
410.localhost.lo     facade  batch    i686-k10          16838     1   0    --  01:00 C 00:12
   mars/3+mars/2+mars/1+mars/0
411.localhost.lo     facade  batch    i686-p4           25340     1   0    --  01:00 C 00:46
   deimos/1+deimos/0
412.localhost.lo     facade  batch    i686-pentm        12544     1   0    --  01:00 R 00:20
   phobos/1+phobos/0
413.localhost.lo     facade  batch    x86_64-generic     4024     1   0    --  01:00 C 00:13
   mars/3+mars/2+mars/1+mars/0
414.localhost.lo     facade  batch    x86_64-atom       19330     1   0    --  01:00 C 00:13
   mars/3+mars/2+mars/1+mars/0
415.localhost.lo     facade  batch    x86_64-core2       2146     1   0    --  01:00 C 00:13
   mars/3+mars/2+mars/1+mars/0
416.localhost.lo     facade  batch    x86_64-k8         17234     1   0    --  01:00 R 00:11
   mars/3+mars/2+mars/1+mars/0
417.localhost.lo     facade  batch    x86_64-k10          --      1   0    --  01:00 Q   -- 
    --

This tutorial deals with a few multivariate techniques including clustering and principal components. We begin with a short introduction to generating multivariate normal random vectors.

Multivariate normal distributions

We'll start off by generating some multivariate normal random vectors. There are packages that do this automatically, such as the mvtnorm package available from CRAN, but it is easy and instructive to do from first principles.

Let's generate from a bivariate normal distribution in which the standard deviations of the components are 2 and 3 where the correlation between the components is -1/2. For simplicity, let the mean of the vectors be the origin. We need to figure out what the covariance matrix looks like.

The diagonal elements of the covariance matrix are the marginal variances, namely 4 and 9. The off-diagonal element is the covariance, which equals the correlation times the product of the marginal standard deviations, or -3:

sigma <- matrix(c(4,-3,-3,9),2,2)
   sigma

We now seek to find a matrix M such that M times its transpose equals sigma. There are many matrices that do this; one of them is the transpose of the Cholesky square root:

M <- t(chol(sigma))
   M %*% t(M)

We now recall that if Z is a random vector and M is a matrix, then the covariance matrix of MZ equals M cov(Z) M^t. It is very easy to simulate normal random vectors whose covariance matrix is the identity matrix; this is accomplished whenever the vector components are independent standard normals. Thus, we obtain a multivariate normal random vector with covariance matrix sigma if we first generate a standard normal vector and then multiply by the matrix M above. Let us create a dataset with 200 such vectors:

Z <- matrix(rnorm(400),2,200) # 2 rows, 200 columns
   X <- t(M %*% Z)

The transpose above is taken so that X becomes a 200x2 matrix, since R prefers to have the columns as the vector components rather than the rows. Let us now plot the randomly generated normals and find the sample mean and covariance.

plot(X)
   Xbar <- apply(X,2,mean)
   S <- cov(X)

We can compare the S matrix with the sigma matrix, but it is also nice to plot an ellipse to see what shape these matrices correspond to. The car package, which we used in the EDA and regression tutorial, has the capability to plot ellipses. You might not need to run the install.packages function below since this package may already have been installed in the previous tutorial. However, the library function is necessary.

install.packages("car",lib="V:/")
   library(car,lib.loc="V:/")

To use the ellipse function in the car package, we need the center (mean), shape (covariance), and the radius. The radius is the radius of a circle that represents the "ellipse" for a standard bivariate normal distribution. To understand how to provide a radius, it is helpful to know that if we sum the squares of k independent standard normal random variables, the result is (by definition) a chi-squared random variable on k degrees of freedom. Thus, for a standard bivariate normal vector, the squares of the radii should be determined by the quantiles of the chi-squared distribution on 2 degrees of freedom. Let us then construct an ellipses with radius based on the median of the chi-squared distribution. Thus, this ellipse should contain roughly half of the points generated. We'll also produce a second ellipse, based on the true mean and covariance matrix, for purposes of comparison.

ellipse(Xbar, S, sqrt(qchisq(.5,2)))
   ellipse(c(0,0), sigma, 
      sqrt(qchisq(.5,2)), col=3, lty=2)

Vmesto Zakladok

September 3, 2014

Torque configuration on Archlinux

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