Basics of Supercomputing - Interdisciplinary | Innovativesbrandt/basics_of_supercomputing/L6... ·...

Day 4: OS 2010 - Course MT1

Basics of Supercomputing

Prof. Thomas Sterling

Pervasive Technology Institute

School of Informatics & Computing

Indiana University

Dr. Steven R. Brandt

Center for Computation & Technology

Louisiana State University

User Environments

http://www.csc.lsu.edu/


Getting Class Materials

• http://tinyurl.com/basics-of-supercomputing

• Email: [email protected]

2


http://tinyurl.com/basics-of-supercomputing






Day 4: OS 2010 - Course MT1 3

Opening Remarks: Where are We??

• The two ends: what we’ve covered so far

– From the top down:

• Models, methods, and means

• Parallel Programming Models: the 3 C’s:

– Capability (OpenMP), Capacity (Condor), Cooperative (MPI)

– From the bottom up:

• Enabling device technologies

• Micro architectures

• Parallel system architectures

– Performance as cross cutting theme

• We’re now at the system center:

– The Operating System

• It owns the computer

• It controls the applications

• It facilitates your needs but limits your access

• It protects you from others, and they from you



Topics

• Operating System Structures and Services

• Mass Storage and File I/O

• Visualization



User Environments

• Provide added facilities that support critical functionality

for supercomputer users

• The operating system provides many of the services for

managing basic computing resources and scheduling

jobs, processes, and threads

• File I/O provides the capability of persistent storage and

large scale data maintenance

• Visualization hardware and software creates images of

raw data for ease of understanding

5



Topics



• Visualization



Operating System

• What is an Operating System?

– A persistent program that controls the execution of application

programs

– An interface between applications and hardware

• Primary functionality

– Exploits the hardware resources of one or more processors

– Provides a set of services to system users

– Manages secondary memory and I/O devices

• Objectives

– Convenience: Makes the computer more convenient to use

– Efficiency: Allows computer system resources to be used in an

efficient manner

– Reliability: through protection between jobs

– Ability to evolve: Permit effective development, testing, and

introduction of new system functions without interfering with service

Source: William Stallings “Operating Systems: Internals and Design Principles (5th Edition)”



Layers of Computer System



Resources Managed by the OS

• Processor

• Main Memory

– volatile

– referred to as “main memory” or “primary storage”

• Also “physical memory” or “core”

• I/O modules

– secondary memory devices

– communications equipment

– terminals

• System bus

– communication among processors, memory, and I/O modules



Operating System Components: Overview

• Process Management: Creating and deleting user and system processes, suspending and resuming processes, mechanisms for process communication, process synchronization, & deadlock handling

• Memory Management: managing usage of memory, loading processes into memory, allocation and de-allocation of memory

• File Management: Creating and deleting files, creating and deleting directories, manipulating files and directories, mapping to secondary storage etc.

• I/O System Management: buffering, caching, spooling, general device driver interfaces, drivers for specific hardware devices

• Secondary Storage Management: Free space management, storage allocation, disk scheduling

• Networking: Communication drivers, protocols

• Protection & Security systems: Controlling access of programs, processes, or users to the resources defined by the computer system.

10



Operating System Services

• Operating system provides an environment to execute programs. Following are some of the services an Operating System provides :

• Program execution: ability to load a program into memory and execute the program. Program must be able to end execution normally or abnormally.

• I/O operations: help in input/output operations to a file or an I/O device.

• File System Manipulation: read, write, modify, create, delete files by name.

• Communication: facilitate exchange of information between processes through shared memory or message passing.

• Error detection and handling: Monitor for potential errors in CPU, memory hardware, I/O devices, external devices, potential errors in user programs such as access to illegal memory location etc.

11



Multiprogramming & Multitasking

• Multiprogramming needed for efficiency

– Single user cannot keep CPU and I/O devices busy at all times

– Multiprogramming organizes jobs (code and data) so CPU always has one to execute

– A subset of total jobs in system is kept in memory

– One job selected and run via job scheduling

– When it has to wait (for I/O for example), OS switches to another job

• Timesharing (multitasking) is logical extension in which CPU switches jobs so frequently that users can interact with each job while it is running, creating interactive computing

– Response time should be < 1 second

– Each user has at least one program executing in memory process

– If several jobs ready to run at the same time CPU scheduling

– If processes don’t fit in memory, swapping moves them in and out to run

– Virtual memory allows execution of processes not completely in memory

12



Multiprogramming and Multiprocessing



OS distribution in the Top 500 list

14



Linux History

• Initial version written by Linus Torvalds (Finland) in 1991

• Originally intended as a non-commercial replacement for the

Minix kernel

• Since then, a number of contributors continued to improve Linux

collaborating over the Internet under Torvalds’ control:

– Added many features available in commercial counterparts

– Optimized the performance

– Ported to other hardware architectures (Intel x86 and IA-64, IBM

Power, MIPS, SPARC, ARM and others)

• The source code is available and free (protected by the GNU

Public License)

• The current kernel version is 3.0.8 (see http://kernel.org)

• Today Linux can be found on plethora of computing platforms,

from embedded microcontrollers and handhelds, through

desktops and workstations, to servers and supercomputers

15



Linux Design

• Monolithic OS – All functionality stored mainly in a single block of code

– All components of the kernel have access to all internal data structures

and routines

– Changes require relinking and frequently a reboot

• Modular architecture – Extensions of kernel functionality (modules) can be loaded and

unloaded at runtime (dynamic linking)

– Can be arranged hierarchically (stackable)

– Overcomes use and development difficulties associated with monolithic

structure

16



Linux Kernel Components

17



Topics



• Visualization



• Storage capacity: 1 TB per drive

• Areal density: 132 Gbit/in2 (perpendicular recording)

• Rotational speed: 15,000 RPM

• Average latency: 2 ms

• Seek time

– Track-to-track: 0.2 ms

– Average: 3.5 ms

– Full stroke: 6.7 ms

• Sustained transfer rate: up to 125 MB/s

• Non-recoverable error rate: 1 in 1017

• Interface bandwidth:

– Fibre channel: 400 MB/s

– Serially Attached SCSI (SAS): 300 MB/s

– Ultra320 SCSI: 320 MB/s

– Serial ATA (SATA): 600 MB/s

Permanent Storage: Hard Disks

Review

19



Storage – SATA & Overview

• Serial Advanced Technology Attachment (SATA) is the most recent commodity hard disk standard.

• SATA uses serial buses as opposed to parallel buses used by ATA (or PATA) and SCSI.

• The cables attached to SATA drives are smaller and run faster (up to 600 MB/s).

• The Basic disk technologies remain the same across the three busses

• The platters in disk spin at variety of speeds, faster the platters spin the faster the data can be read off the disk and data on the far end of the platter will become available sooner.

• Rotational speeds range between 5400 RPM to 15000 RPM

• Faster the platters rotate, the lower the latency and higher the bandwidth.

20

PATA vs SATA



I/O Needs on Parallel Computers

• High Performance

– Take advantage of parallel I/O paths (where available)

– Support application-level data access and throughput needs

– Scalable with systems size and user number/needs

• Data Integrity

– Sanely deal with hardware and power failures

• Single Namespace

– All nodes and users “see” the same file systems

– Equal access from anywhere on the resource

• Ease of Use

– Whenever possible, a storage system should be accessible

in consistent way, in the same ways as a traditional UNIX-

style file systems

21

Ohio Supercomputer Center



Related Topics

• Hardware-based solutions

– RAID

• File systems commonly used in parallel computing

– NFS

– PVFS2

– Lustre

– GPFS

– pNFS

– Panasas

• Software I/O libraries (next topic)

– POSIX I/O

– MPI-IO

– NetCDF

– HDF5

22



RAID: Key Concepts

• RAID stands for Redundant Array of Inexpensive (or: Independent) Disks - term coined by David Patterson, Garth Gibson and Randy Katz

• Aims to achieve greater levels of performance, reliability, and/or larger volume sizes

• Several basic architectures, ranging from RAID 0 through RAID 6

• Groups of two or more disks are treated effectively as single large disks; performance of multiple disks is better than that of individual disks due to bandwidth aggregation and overlap of multiple accesses

• Using multiple disks helps store data in multiple places (redundancy), allowing the system to continue functioning in case of failures

• Both software (OS managed) and hardware (dedicated I/O cards) raid solutions available

– Hardware solutions are more expensive, but provide better performance without CPU overhead

– Software solutions provide better flexibility, but have associated computational overhead

23



RAID 5

• Striped set with distributed parity

• Requires at least 3 disks per array

• Similarly to RAID 0, data are distributed

across all the disks

• Parity information for each stripe is also

distributed across the disks, eliminating the

bottleneck of a single parity disk (RAID 4)

and equalizing the load across components

• Tolerates single disk failures; the missing

data block may be recomputed based on the

contents of the parity block and the data

blocks of the remaining disks in the same

stripe

• Write performance of RAID 5 is reduced due

to parity computation for every physical write

operation

24

http://www.drivesolutions.com/datarecovery/raid.shtml



Distributed File Systems

• A distributed file system is a file system that is stored locally on one system

(server) but is accessible by processes on many systems (clients)

• Multiple processes access multiple files simultaneously

• Other attributes of a DFS may include:

– Access control lists (ACLs)

– Client-side file replication

– Server- and client- side caching

• Some examples of DFSes:

– NFS (Sun)

– DCE/DFS (Transarc / IBM)

– CIFS (Microsoft)

– SSHFS (Fuse / SSH)

• Distributed file systems can be used by parallel programs, but they have

significant disadvantages:

– The network bandwidth of the server system is a limiting factor on performance

– To retain UNIX-style file consistency, the DFS software must implement some form

of locking which has significant performance implications

25




Distributed File System: NFS

• Popular means for accessing remote file systems in a local area network

• Based on the client-server model, the remote file systems may be “mounted” via NFS and accessed through the Linux Virtual File System (VFS) layer

• NFS clients cache file data, periodically checking with the original file for any changes

• The loosely-synchronous model makes for convenient, low-latency access to shared spaces

• NFS avoids the common locking systems used to implement POSIX semantics

• Most client implementations are open-source; many servers remain proprietary

26

NFS support via

VFS layer in Linux



Why NFS is bad for Parallel I/O

• Clients can cache data indiscriminately, and tend to do that at

arbitrary block boundaries

• When nearby regions of a file are written by different processes on

different clients, the result is undefined due to lack of consistency

control

• All file operations are remote operations; extensive file locking is

required to implement sequential consistency

• Communication between client and server typically uses relatively

slow communication channels, adding to performance degradation

• Inefficient specification (e.g., a read operation involves two RPCs;

one for look-up of file handle and second for reading of file data)

27



Parallel File Systems

• Parallel File System is one in which there are multiple servers as

well as clients for a given file system, equivalent of RAID across

several file systems.

• Multiple processes can access the same file simultaneously

• Parallel File Systems are usually optimized for high performance

rather than general purpose use, common optimization criterion

being :

– Large block sizes (≥ 64kB)

– Relatively slow metadata operations (eg. fstat()) compared to reads

and writes

– Special APIs for direct access and additional optimizations

• Examples of Parallel file systems include :

– GPFS (IBM)

– Lustre (Cluster File Systems/Sun)

– PVFS2 (Clemson/ANL)

28




Characteristics of Parallel File Systems

• Three Key Characteristics:

– Various hardware I/O data storage resources

– Multiple connections between these hardware

devices and compute resources

– High-performance, concurrent access to these I/O

resources

• Multiple physical I/O devices and paths ensure

sufficient bandwidth for the high performance

desired

• Parallel I/O systems include both the hardware

and number of layers of software

29

Storage Hardware

Parallel File System

Parallel I/O (MPI I/O)

High-Level I/O Library



Parallel File Systems: Hardware Layer

• I/O Hardware is usually comprised of disks, controllers,

and interconnects for data movement

• Hardware determines the maximum raw bandwidth and

the minimum latency of the system

• Bisection bandwidth of the underlying transport

determines the aggregate bandwidth of the resulting

parallel I/O system

• At the hardware level, data is accessed at the

granularity of blocks, either physical disk blocks or

logical blocks spread across multiple physical devices

such as in a RAID array

• Parallel File Systems :

– manage data on the storage hardware,

– present this data as a directory hierarchy,

– coordinate access to files and directories in a consistent

manner

• File systems usually provide a UNIX like interface,

allowing users to access contiguous regions of files

30

Storage Hardware






Parallel I/O: Library Layers (Review)

• Lower level interfaces may be provided by the

file system for higher-performance access

• Above the parallel file systems are the parallel

I/O layers provided in the form of libraries such

as MPI-IO

• The parallel I/O layer provides a low level

interface and operations such as collective I/O

• Scientific applications work with structured data

for which a higher level API written on top of

MPI-IO such as HDF5 or parallel netCDF are

used

• HDF5 and parallel netCDF allow the scientists

to represent the data sets in terms closer to

those used in their applications, and in a

portable manner

31

Storage Hardware






POSIX File Access API • Widespread standard

• Available on any UNIX-compliant platform – IBM AIX, HP HP-UX, SGI Irix, Sun Solaris, BSDi BSD/OS, Mac OS X, Linux,

FreeBSD, OpenBSD, NetBSD, BeOS, and many others

– Also: Windows NT, XP, Server 2003, Vista (through C runtime libraries)

• Simple interface: six functions from POSIX.1 (core services) provide practically all necessary I/O functionality – File open

– File close

– File data read

– File data write

– Flush buffer to disk

– Adjust file pointer (seek)

• Two interface variants, provide roughly equivalent functionality – Low-level file interface (file handles are integer descriptors)

– C stream interface (streams are represented by FILE structure; function names prefixed with “f”)

• But: no parallel I/O support

32



Problems with POSIX File I/O • Too simplistic interface

– Operates on anonymous sequences of bytes

– No preservation of type or information structure

– Cumbersome access to optimized/additional features (fcntl, ioctl)

– Designed for sequential I/O (even regularly strided accesses require multiple calls and may suffer from poor performance)

• Portability issues – Must use specialized reader/writer created for a particular application

– Compatibility checks dependent on application developers (possibility of undetected failures)

– No generic utilities to parse and interpret the contents of saved files

– Cross platform endianness and type representation problem if saving in binary mode

– Significant waste of storage space if text mode is used (for portability or readability of transferred data)

• Permit access only to locally mounted storage, or remote storage via NFS (which has its share of problems)

• Parallel and concurrent access issues – Lack of synchronization when accessing shared files from multiple nodes

– Atomic access to shared files may not be enforceable, has unclear semantics, or has to rely on the programmer for synchronization

– Uncoordinated access of I/O devices shared by multiple nodes may result in poor performance (bottlenecks)

– Additional performance loss due to suboptimal bulk data movement (e.g., no collective I/O)

– On the other hand, without sharing, the management of individual files (i.e. with at least one data file per I/O node) is complicated and tedious

33



MPI-IO Overview

• Initially developed as a research project at the IBM T. J. Watson

Research Center in 1994

• Voted by the MPI Forum to be included in MPI-2 standard (Chapter 9)

• Most widespread open-source implementation is ANL’s ROMIO,

written by Rajeev Thakur (http://www-unix.mcs.anl.gov/romio/ )

• Integrates file access with the message passing infrastructure, using

similarities between send/receive and file write/read operations

• Allows MPI datatypes to meaningfully describe data layouts in files

instead of dealing with unorganized streams of bytes

• Provides potential for performance optimizations through the

mechanism of “hints”, collective operations on file data, or relaxation

of data access atomicity

• Enables better file portability by offering alternative data

representations

34


http://www-unix.mcs.anl.gov/romio/




Topics



• Visualization



Goals of visualization

• Understand not the data but the underlying

phenomenon. Numbers are not enough.

• Computers produce too much data

• Bandwidth of human visual channel is high and large

portion of brain devoted to visual processing

• Well developed languages for visual communication

• Understanding of the phenomenon represented by the

data.

• Achieving compelling visual depictions.

36



Why Visualization ?

u =

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-15.04266 , -15.08206 , -15.2573 ,

…

…

…

v =

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-2.432707 , -2.797345 , -3.046965 , -3.053234 , -3.053234 , -3.023986 ,

-2.730067 , -2.301303 , -1.71073 , -0.9851491 , -0.1510314 , 0.7523372 ,

1.677023 , 2.615013 , 3.343748 , 3.86464 , 4.160915 , 4.184602 ,

3.966629 , 3.474625 , 3.016644 , 2.568788 , 2.165158 , 1.824501 ,

1.54189 , 1.360883 , 1.035977 , 0.6115122 , 0.06123456 , -0.5250472 ,

-1.146736 , -1.800962 , -2.367146 , -2.846602 , -3.223269 , -3.491419 ,

-3.655909 , -3.702413 , -3.745571 ,

-0.5370894 , -0.8362811 , -1.261836 , -1.431323 , -1.439548 , -1.197057 ,

-1.010797 , -0.8057232 , -0.6501509 , -0.4674788 , -0.2819314 ,

-0.1039538 , -0.003672248 , -0.03016879 , -0.08807017 , -0.2992798 ,

-0.6517226 , -1.04221 , -1.493191 , -1.87203 , -2.175377 , -2.407176 ,

-2.555969 , -2.599726 , -2.671768 , -2.712004 , -2.75505 , -2.75902 ,

-2.60304 , -2.328378 , -2.018466 , -1.671619 , -1.297618 , -0.9531922 ,

-0.6438362 , -0.3950594 , -0.1701427 , 0.01022664 , 0.1364522 ,

0.1747276 , 0.07895294 , -0.163308 , -0.3119612 , -0.4108411 ,

-0.4113753 , -0.4671833 , -0.514634 , -0.6230809 , -0.6598164 ,

-0.6212637 , -0.5786133 , -0.5099974 , -0.4389736 , -0.3768384 ,

-0.2941028 , -0.184191 , -0.06520332 , 0.04737541 , 0.222767 ,

0.4200633 , 0.4607859 , 0.3320421 , 0.3006737 , 0.07510712 ,

-0.07692574 , -0.2115855 , -0.2936291 , -0.2928487 , -0.292287 ,

-0.2969472 , -0.3166117 , -0.4137569 , -0.4247616 , -0.2855123 ,

-0.01641562 , 0.3228842 , 0.7352448 , 1.223382 , 1.67242 , 2.098369 ,

2.465089 , 2.82751 , 3.167285 , 3.493491 , 3.772224 , 4.01767 ,

4.227215 , 4.45173 , 4.692906 , 4.956936 , 5.272628 , 5.639721 ,

6.05663 , 6.525858 , 7.034393 , 7.579512 , 8.094472 , 8.572382 ,

9.010693 , 9.246994 , 9.600247 , 9.734415 , 9.818371 , 9.768746 ,

9.634361 , 9.467207 , 9.223889 , 8.935048 , 8.680677 , 8.465234 ,

8.293701 , 8.204026 , 8.200741 , 8.238729 , 8.27344 , 8.296266 ,

8.249908 , 8.143016 , 7.933974 , 7.620547 , 7.205623 , 6.692104 ,

6.073251 , 5.356821 , 4.704732 , 3.950881 , 3.223222 , 2.52102 ,

1.863057 , 1.214219 , 0.5855544 , -0.008720525 , -0.6155071 , -1.212232 ,

-1.798152 , -2.302297 , -2.713413 , -2.993824 , -3.092898 , -3.038303 ,

-2.847107 , -2.602939 , -2.127067 , -1.511888 , -0.7935675 ,

-0.009873301 , 0.8129019 , 1.657815 , 2.47968 , 3.274564 , 3.86061 ,

4.223564 , 4.421453 , 4.368874 , 4.113844 , 3.630303 , 3.202399 ,

2.802837 , 2.467391 , 2.162023 , 1.88674 , 1.675342 , 1.306858 ,

0.8053824 , 0.09287734 , -0.5250471 , -1.144472 , -1.850449 , -2.463693 ,

…

…

...

MM5 Data (Left)

MM5 Viz (Right) using Amira

37



Astrophysics

38



Uses of visualization

• Data exploration.

• Hypothesis testing.

• Steering of computation.

• Program/performance debugging.

• Presentation.

39



Data exploration

40



Hypothesis testing

• Promoters of statistical methods may use linear correlation coefficients to detect relationships between variables, which works wonderfully when there is a linear relationship between variables and when the data is free from anomalies.

• However, if the relationship is quadratic (or exponential, sinusoidal, etc.) a linear algorithm may fail to detect the relationship.

• Similarly, if there are data collection problems that add outliers or if there are discontinuities over the range (e.g. freezing or boiling points of water), then linear correlation may fail.

• A visual presentation is more likely to help researchers find such phenomena and suggest richer hypotheses.

41



Hypothesis testing

42



Steering of computation

• Understanding the atmospheric dispersion of reacting chemicals is one of the major scientific challenges in the world today.

• Scientists study the problem by constructing a numerical simulation of the dispersion, combining the expertise of the scientist in the physical processes involved, and the skill of numerical mathematicians in the numerical modeling of these processes.

• As part of the analysis, a scientist will want to explore different scenarios: varying the chimney height, varying the terrain, varying the emission rate and varying the wind direction.

• http://www.visualization.leeds.ac.uk/CovisaG/demo.html

43


http://www.visualization.leeds.ac.uk/CovisaG/demo.html


Steering of computation

• The IRIS Explorer application (shown on the right) provides a 'user friendly' interface to computational steering and visualization.

• This application allows the scientist to control the simulation, experiment with different wind directions and see the visualized results with or without the ground and chimney geometry displayed.

44



Program/performance debugging

• TAU was designed to improve parallel programming productivity by combining advances in parallel debugging, performance evaluation, and program visualization tools.

45



Presentation (GNU plots)

46



Prime Spiral

• A visualization example: Prime Numbers

• Sequence of numbers whose only factors are

themselves and 1: 2, 3, 5, 7, 11, 13, 17, 19, …

• Important for security / encryption

• We know what a prime number is, and how to determine

if a number is prime – but do we understand prime

numbers?

47



Prime Spiral in Vish

48



Topics

• Introduction

• Application of Visualization

• Challenges and Approaches

• GnuPlot

• Others

49



Scalability and large dataset

management

• Databases often store data on the terabyte scale. Simulation results are often several gigabytes in size.

• Software growth exceeds hardware growth. Hence, processing speed is limited.

• Visualization algorithms have to process huge amounts of data to generate visual representations. Delay should be minimum.

• Some have to filter the data in order to extract relevant information.

• Visualization algorithms should be scalable.

50



Challenges & Approaches

• High data dimensionality : – Understand relationship between the attributes or dimensions.

– Represent data with high dimensionality or multiple attributes accurately; e.g. representation of flow simulation data attributes that describe the flow like velocity, temperature, pressure, kinetic energy, etc.

– Representation becomes more complex if data is time-dependent.

• Time dependent data

– Questions asked about time-dependent data element

• does it exist, when, how long, where, how often, in what order?

– Challenges

• High-dimensional temporal data.

• Comparability of visualizations for time-frames.

51



Challenges & Approaches

• Cross-Platform Visualization:

– Large variety of hardware, operating systems and display

devices.

– User-friendly visualization tools must adapt to variable

environments.

• Other challenges include defining the audience, the

primary features in the visual depiction, appropriate

visual metaphors, user-friendly design, choosing

compelling visual representations and interactive/pre-

generated graphics

52



GnuPlot

• Portable command-line driven

– interactive data and function plotting utility

• for UNIX, IBM OS/2, MS Windows, DOS, Macintosh, VMS,

Atari and many other platforms.

– copyrighted but freely distributed.

– supported and under development since 1986.

53



GnuPlot

• Plots – 2D and 3D.

• Presentations – lines, points, boxes, contours, vector fields, surfaces, and

various associated text.

• Output – interactive screen terminals

– direct output to printers

– output to many types of file (eps, jpeg, LaTeX, pdf, png, postscript).

54



GnuPlot

• Newest version of GnuPlot is 4.4 (October 2010). Official

web site is http://www.gnuplot.info/ .

• Current version can be obtained at

– http://sourceforge.net/projects/gnuplot/

– several mirror sites you can find at the URL above.

• For a development version:

http://sourceforge.net/projects/gnuplot/

55


http://www.gnuplot.info/

http://sourceforge.net/projects/gnuplot/


GnuPlot

• “exec GnuPlot” shows a GnuPlot command line prompt "GnuPlot> ".

• exit or quit command terminates GnuPlot.

gnuplot> save "savefile.plt"

gnuplot> load "savefile.plt"

% gnuplot savefile.plt

The above command is in batch mode.

56



gnuplot

• 2 basic commands to plot a graph – plot: 2-dimensional graph.

– splot: 3-dimensional graph.

• To plot a function – use the plot/splot command

with a range of X-axis (or X and Y ranges for 3-dim. plot) and the function.

– you can omit the range parameters.

gnuplot> plot [0:5] sin(x)

gnuplot> plot sin(x)

57



gnuplot

• You can change the appearance of your plot by the set command.

gnuplot> help set

gnuplot> set xlabel "X-AXIS“

gnuplot> set ylabel "Y-AXIS"

gnuplot> set xrange [0:5]

gnuplot> set yrange [-2:2]

gnuplot> plot sin(x)

58



gnuplot

• Produces a graph in a Postscript format when “set

terminal postscript” command is given.

• If an output direction is not specified, the produced

Postscript data flow on your screen.

• The set output command changes the destination of

output.

gnuplot> help set

59



gnuplot

• You can use gnuplot as a calculator.

gnuplot> set xrange [-2*pi:2*pi]

gnuplot> a=0.5

gnuplot> print a

0.5

gnuplot> plot a*sin(x)

gnuplot> f(x)=a*sin(x)*cos(x)

• You can also define your

own function.

60



Alternative Styles

• The alternative to lines is points, steps or impulses.

gnuplot> plot “output.dat” using 1:2

with lines

61



Multicolumn Data

1 2 3 4

0.10 9.0484E-01 9.0484E-01 9.0484E-01

0.20 8.1873E-01 8.1871E-01 8.1875E-01

0.30 7.4082E-01 7.4074E-01 7.4091E-01

0.40 6.7032E-01 6.7010E-01 6.7059E-01

0.50 6.0653E-01 6.0606E-01 6.0714E-01

....

4.60 1.0052E-02 -7.0237E-02 5.7632E-01

4.70 9.0953E-03 -7.2510E-02 6.0325E-01

4.80 8.2297E-03 -7.4627E-02 6.3077E-01

4.90 7.4466E-03 -7.6597E-02 6.5886E-01

5.00 6.7379E-03 -7.8431E-02 6.8750E-01

62

gnuplot> set xlabel "x"

gnuplot> set ylabel "y=exp(-x)"

gnuplot> set title "Pade approximation"

gnuplot> plot "output.dat" using 1:2 title

"Analytical" with lines, \

>"output.dat" using 1:3 title "L=1, M=2"

with lines,\

>"output.dat" using 1:4 title "L=2, M=1"

with lines



gnuplot

• Graduations starts with 0, and the interval is 0.5.

– change graduations, use “set {x|y}tics” .

• Controlled by 3 optional numbers after “set tics” command.

– One number: increment.

– Two numbers: initial value and increment.

– Three: initial value, increment and final value.

• Draw small tics inside the interval with the set m{x|y}tics n where n is

the number of divisions.

63



gnuplot

• Draw a color-mapped 3D figure by setting pm3d.

gnuplot> set xrange [-2:2]

gnuplot> set yrange [-2:2]

gnuplot> set pm3d

gnuplot> splot exp(-x*x)*exp(-y*y)

64



gnuplot

• References:

• http://t16web.lanl.gov/Kawano/gnuplot/index-e.html

• http://www.gnuplot.info/

• http://www.duke.edu/~hpgavin/gnuplot.html

• http://sparky.rice.edu/~hartigan/gnuplot.html

• http://www.chemie.fu-berlin.de/chemnet/use/suppl/gpcard.html

• http://gnuplot.flexkb.net/wc.dll?gnu~HomeTopic

65


http://t16web.lanl.gov/Kawano/gnuplot/index-e.html



http://www.gnuplot.info/

http://www.duke.edu/~hpgavin/gnuplot.html

http://sparky.rice.edu/~hartigan/gnuplot.html

http://www.chemie.fu-berlin.de/chemnet/use/suppl/gpcard.html



http://gnuplot.flexkb.net/wc.dll?gnu~HomeTopic


OpenGL

• Hides the complexities of interfacing with different hardware graphics platforms from the user.

• Accepts primitives such as points, lines and polygons, and converts them into pixels via a graphics pipeline called OpenGL state machine.

• Issues primitives to the graphics pipeline, configures how the pipeline processes these primitives.

66



VTK – Visualization Toolkit

• A set of resources for

building scientific

visualization software

• A set of C++ libraries

• Open source

67



ParaView

• Visualization tool

for interactive data

exploration

• Built on VTK

• Open source

68



VisIt Visualization Tool

• Interactive

visualization and

graphical analysis tool

• More sophisticated /

advanced than

ParaView

• Uses VTK

• Open source

69



OpenDX • A programming

environment for data visualization and analysis

• Interactive visualization using a point and click interface.

• Visual and scripting language programming

70



VISH – The Visualization Shell

• Built on VTK

• Interactive

tool

• Highly

scriptable

• Open source

• A product of

LSU

• Written by

Werner

Benger

71


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