BIL106 E Introduction to Scientific & Engineering Computing

BIL106EIntroduction to

Scientific & Engineering ComputingHüseyin TOROS, Ph.D.

Istanbul Technical University Faculty of Aeronautics and Astronautics Dept. of Meteorological Engineering

Voice: 285 31 27E-mail: [email protected]

http://atlas.cc.itu.edu.tr/~torosAn important fraction of our interaction will be via e-mail

Useful Pages:http://www.be.itu.edu.tr/ http://atlas.cc.itu.edu.tr/~toros/bil106e.htmhttp://atlas.cc.itu.edu.tr/~F90/mainindex.htmlhttp://www.fortran.com/ http://www.foldoc.org (Free OnLine Dictionary of Computing)F Compiler: Read this first, Full installer (3.4Mb): win95nt.exeFor more information syllabus_F

07/26/09Introduction to Scientific & Engineering Computing 1

History of ComputersThe first computers were people! That is, electronic computers (and the earlier mechanical computers) were given this name because they performed the work that had previously been assigned to people. "Computer" was originally a job title: it was used to describe those human beings (predominantly women) whose job it was to perform the repetitive calculations required to compute such things as navigational tables, tide charts, and planetary positions for astronomical almanacs. Imagine you had a job where hour after hour, day after day, you were to do nothing but compute multiplications. Boredom would quickly set in, leading to carelessness, leading to mistakes. And even on your best days you wouldn't be producing answers very fast. Therefore, inventors have been searching for hundreds of years for a way to mechanize (that is, find a mechanism that can perform) this task.

07/26/09 2Introduction to Scientific & Engineering Computing

The abacus was an early aid for mathematical computations. Its only value is that it aids the memory of the human performing the calculation. A skilled abacus operator can work on addition and subtraction problems at the speed of a person equipped with a hand calculator (multiplication and division are slower). The abacus is often wrongly attributed to China. In fact, the oldest surviving abacus was used in 300 B.C. by the Babylonians.


ELECTRONİC NUMERİCAL INTEGRATOR AND COMPUTER

1st large scale electronic digital computerdesigned and constructed at the Moore School of

Electrical Engineering of the University of Pennsylvaniasince 1920s, faculty had worked with Aberdeen Proving

Ground’s Ballistics Research Laboratory (BRL)


INSPİRATİON AND PERSPİRATİON UNİTE

1943 Mauchly and Eckert prepare a proposal for the US Army to build an Electronic Numerical Integratorcalculate a trajectory in 1 second

May 31, 1943 Construction of ENIAC starts1944 early thoughts on stored program

computers by members of the ENIAC teamJuly 1944 two accumulators working


ACCUMULATOR(28 VACUUM TUBES)


ENIAC AT MOORE SCHOOL, UNİVERSİTY OF PENNSYLVANİA


EARLY THOUGHTS ABOUT STORED PROGRAM COMPUTİNG

January 1944 Moore School team thinks of better ways to do things; leverages delay line memories from War research

September 1944 John von Neumann visits Goldstine’s meeting at Aberdeen Train Station

October 1944 Army extends the ENIAC contract to include research on the EDVAC and the stored-program concept

Spring 1945 ENIAC working wellJune 1945 First Draft of a Report on the

EDVAC: Electronic Discrete Variable Automatic Computer


MANCHESTER MARK I (1948)

MANCHESTER MARK I (1948)

Freddy Williams and Tom KilburnDeveloped an electrostatic memoryPrototype operational June 21, 1948 and

machine to execute a stored programMemory: 32 words of 32 bits eachStorage: single Williams tube (CRT)Fully operational: October 1949Ferranti Mark I delivered in February 1951


EDSAC

Maurice Wilkes, University Mathematical Laboratory, Cambridge University

Moore School LecturesElectronic Delay Storage Automatic Calculator, EDSAC

operational May, 1949J. Lyons Company and the LEO, Lyons Electronic Office,

operational fall 1951


NATİONAL PHYSİCAL LABORATORY

Alan TuringAutomatic Computing Engine (ACE)Basic design by spring, 1946Harry Huskey joins projectPilot ACE working, May 10, 1950English Electric: DEUCE, 1954Full version of ACE at NPL, 1959



MAİNFRAME COMPUTERS

REMİNGTON RAND UNIVAC43 UNIVACs were delivered to government and

industry Memory: mercury delay lines: 1000 words of 12

alphanumeric charactersSecondary storage: metal oxide tapeAccess time: 222 microseconds (average)Instruction set: 45 operation codesAccumulators: 4Clock: 2.25 Mhz


19511951 UNİVACUNİVACTypical 1968 prices—EX-cluding maintenance & support!

IBM 701 (DEFENSE CALCULATOR)Addition time: 60 microsecondsMultiplication: 456 microsecondsMemory: 2048 (36 bit) words using Williams

tubesSecondary memory:

Magnetic drum: 8192 wordsMagnetic tape: plastic

Delivered: December 1952: IBM World Headquarters (total of 19 installed)


SECOND GENERATİON (1958-1964)1958 Philco introduces TRANSAC S-2000

first transistorized commercial machineIBM 7070, 7074 (1960), 7072(1961)1959 IBM 7090, 7040 (1961), 7094 (1962)1959 IBM 1401, 1410 (1960), 1440 (1962)FORTRAN, ALGOL, and COBOL are first standardized

programming languages


THİRD GENERATİON (1964-1971)

April 1964 IBM announces the System/360solid logic technology (integrated circuits)family of “compatible” computers

1964 Control Data delivers the CDC 6600nanosecondstelecommunicationsBASIC, Beginners All-purpose Symbolic

Instruction Code


FOURTH GENERATİON (1971- )

Large scale integrated circuits (MSI, LSI)Nanoseconds and picosecondsDatabases (large)Structured languages (Pascal)Structured techniquesBusiness packages


DİGİTAL EQUİPMENT CORPORATİON(MİNİ-COMPUTERS)ASSABET MİLLS, MAYNARD, MA

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FLİPCHİP

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PDP-8, FİRST MASS-PRODUCED MİNİ

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PDP-11 (1970)

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INTEL

Noyce, Moore, and Andrew Grove leave Fairchild and found Intel in 1968focus on random access memory (RAM) chips

Question: if you can put transistors, capacitors, etc. on a chip, why couldn’t you put a central processor on a chip?

Ted Hoff designs the Intel 4004, the first microprocessor in 1969 based on Digital’s PDP-8


MİCROCOMPUTERS

MİCROCOMPUTERS

Ed Roberts founds Micro Instrumentation Telemetry Systems (MITS) in 1968

Popular Electronics puts the MITS Altair on the cover in January 1975 [Intel 8080]

Les Solomon’s 12 year old daughter, Lauren, was a lover of Star Trek. He asked her what the name of the computer on the Enterprise was. She said “ ‘computer’ but why don’t you call it Altair because that is where they are going tonight!”


ALTAİR 8800 COMPUTER

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INTEL PROCESSORS


MICROPROCESSOR YEAR SPEED WORD LENGTH

TRANSISTORS

MIPS

Intel 4004 1969 108 KHz 4-bit 2,300 .06Intel 8008 1972 200 KHz 8-bit 3,500 .06Intel 8080 1974 2 MHz 8-bit 6,000 .64Intel 8086 1978 4.47 MHz 16-bit 29,000 .66Intel 8088 1981 4.47 MHz 16-bit 29,000 .75Intel 80286 1982 12 MHz 16-bit 134,000 2.66Intel 80386 1985 16-33 MHz 32-bit 275,000 4 Intel 80486 (i486) 1989 20-100 MHz 32-bit 1.2 Million 70Intel 80586 (Pentium) 1993 75-200 MHz 32-bit 3.3 Million 126 -

203Intel Pentium Pro 1995 150-200

MHz32-bit 5.5 Million 300

Intel Pentium MMX 1997 166-233 MHz

32-bit 4.5 Million -

Intel Pentium II 1997 233-450 MHz

32-bit 7.5 Million -

Intel Pentium III 1999 450-933 MHz

32-bit Over 9.5 Million

-

Intel Itanium Processor 2000 1 GHz 64-bit 15,000,000

1,200


Computer Processing SpeedComputer processing speed depends on a variety of factors. Three of the most important factors are:

•Word length (the number of bits that can be processed at one time by the microprocessor)•Cycle Speed (how fast individual events are processed, measured in Megahertz)•Data Bus Width (determines how much data can be transferred between the CPU and memory)

•Other factors Include:•RAM (amount of available random access memory)•Disk Access Speed (speed that data can be read from hard disk)•Code Efficiency (how efficiently the computer code has been designed)

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What is a computer?

İnputProcessingOutputstorage.

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The computer is an automatic device thatperforms calculationsmakes decisions has capacity for storing instantly recalling vast amount of information

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Computer system – A collection of related components that are designed to work together.A system includes hardware and software.

Hardware Software

What is a computer System?

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Introduction to Scientific & Engineering Computing

What is a computer?

Hardware

• Processor

• Memory

• I/O units (Input/Output Units)

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How does a computer work?

• Executes very simple instructions.

• Executes them incredibly fast.

• Must be programmed: it is the software, i.e., the programs, that characterize what a computer actually does.

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Computer StructureComputer Structure

Input Devices

Output Devices

ControlUnit

Arithmetic-Logic Unit

Main Memory

External Memory

CPU = Central Processing Unit

Major Components of a computing system


Computer StructureRegisters are a set of special high-speed memory locations within the CPUAccess speed within the register is thousands of times faster than access speed in RAM

MEMORY MEASUREMENTThe memory unit of a computer is two-state devices. Then it is natural to use a binary scheme (using only the two binary digits {bits} 0 and 1 to represent information in a computer). Bytes = 8 BitsMemory is commonly measured in bytes, and a block of 210 = 1024 bytes = 1 K1MB=1024 K=1024 . 210 = 210 . 210 = 220 = 1,048,576 bytes. or 220 . 23 = 223 = 8,384,608 bits.



What is a computer program?

• The computer program characterizes what a computer actually does.

• A program (independently of the language in which it is written) is constituted by two fundamental parts: • A representation of the information (data) relative to

the domain of interest.• A description of how to manipulate the

representation in such a way as to realize the desired functionality: operations.

• To write a program both aspects have to be addressed.


A list of instructions that are grouped together to accomplish a task or tasks. The instructions, called machine code or assembly code consist of things like reading and writing memory, arithmetic operations, and comparisons.

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Program


• Every program must be translated into a machine language that the computer can understand.

• This translation is performed by compilers, interpreters, and assemblers.

• When you buy software, you normally buy an executable version of a program.

• This means that the program is already in machine language -- it has already been compiled and assembled and is ready to execute.

Program


•While easily understood by computers, machine languages are almost impossible for humans to use because they consist entirely of numbers. •Programmers, therefore, use either a high-level programming language or an assembly language. An assembly language contains the same instructions as a machine language, but the instructions and variables have names instead of being just numbers.• Programs written in high-level languages are translated into assembly language or machine language by a compiler. Assembly language programs are translated into machine language by a program called an assembler. •Every CPU has its own unique machine language. Programs must be rewritten or recompiled, therefore, to run on different types of computers.

Program


Compiler

A program that translates source code into object code. The compiler derives its name from the way it works, looking at the entire piece of source code and collecting and reorganizing the instructions. Thus, a compiler differs from an interpreter, which analyzes and executes each line of source code in succession, without looking at the entire program. The advantage of interpreters is that they can execute a program immediately. Compilers require some time before an executable program emerges. However, programs produced by compilers run much faster than the same programs executed by an interpreter.


Every high-level programming language (except strictly interpretive languages) comes with a compiler. In effect, the compiler is the language, because it defines which instructions are acceptable. Because compilers translate source code into object code, which is unique for each type of computer, many compilers are available for the same language. For example, there is a FORTRAN compiler for PCs and another for Apple Macintosh computers. In addition, the compiler industry is quite competitive, so there are actually many compilers for each language on each type of computer. More than a dozen companies develop and sell C compilers for the PC.

Compiler

Source Program(High-level language)

Compiler Object Program(machine language)

Compilation errorsRun-time

errorsSteps of execution of a Fortran program


Interpreter•A program that executes instructions written in a high-level language. There are two ways to run programs written in a high-level language. The most common is to compile the program; the other method is to pass the program through an interpreter. •An interpreter translates high-level instructions into an intermediate form, which it then executes. In contrast, a compiler translates high-level instructions directly into machine language. Compiled programs generally run faster than interpreted programs. The advantage of an interpreter, however, is that it does not need to go through the compilation stage during which machine instructions are generated. This process can be time-consuming if the program is long. The interpreter, on the other hand, can immediately execute high-level programs. For this reason, interpreters are sometimes used during the development of a program, when a programmer wants to add small sections at a time and test them quickly. In addition, interpreters are often used in education because they allow students to program interactively. •Both interpreters and compilers are available for most high-level languages. However, BASIC and LISP are especially designed to be executed by an interpreter. In addition, page description languages, such as PostScript, use an interpreter. Every PostScript printer, for example, has a built-in interpreter that executes PostScript instructions.


Programing Language

A programming language that is once removed from a computer's machine language. Machine languages consist entirely of numbers and are almost impossible for humans to read and write. Assembly languages have the same structure and set of commands as machine languages, but they enable a programmer to use names instead of numbers. Each type of CPU has its own machine language and assembly language, so an assembly language program written for one type of CPU won't run on another. In the early days of programming, all programs were written in assembly language. Now, most programs are written in a high-level language such as FORTRAN or C. Programmers still use assembly language when speed is essential or when they need to perform an operation that isn't possible in a high-level language.

Why we use a programming language ?The main reason for learning a programming language is to use the computer to solve

• scientific• engineering problems



Taught in three versions:Fortran (F)CMatlab


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Programming language

• Basic skills for scientific/engineering problem solving using computers:• Data structures and algorithms

• Programming skills in a (standard) language• Skills for integrating the computing chain:

?????????????????• Analyze Program Run Visualize


Engineering simulation of the natural/artificial systems

Build a conceptual quantitative model (most of the time,

write down the appropriate equations) Formulate a solution to these equations using numerical methods

Data structures + algorithms Program these data structures and algorithms in a language Run the program and analyze its output using

visualization techniques



Scientific & Engineering problems

???


•Flowcharts are often used to graphically represent algorithms. •In mathematics, computing, linguistics, and related subjects, an algorithm is a finite sequence of instructions, an explicit, step-by-step procedure for solving a problem, often used for calculation and data processing. •It is formally a type of effective method in which a list of well-defined instructions for completing a task, will when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end-state. •The transition from one state to the next is not necessarily deterministic; some algorithms, known as probabilistic algorithms, incorporate randomness.

solving a problem : Algorithm - Flowcharts


Write out the problem statement. Include information on what you are to solve, and consider why you need to solve the problem.


A simple flowchart representing a process for dealing with a broken lamp.


A simple flowchart for computing factorial N (N!)

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Kavak Ağacı ile Kabak Ulu bir kavak ağacının yanında bir kabak filizi boy göstermiş. Bahar ilerledikçe bitki kavak ağacına sarılarak yükselmeye başlamış. Yağmurların ve güneşin etkisiyle müthiş bir hızla büyümüş ve neredeyse kavak ağacı ile aynı boya gelmiş. Bir gün dayanamayıp sormuş kavağa: -Sen kaç ayda bu hale geldin ağaç? -On yılda, demiş kavak. -On yılda mı? Diye gülmüş ve çiçeklerini sallamış kabak. -Ben neredeyse iki ayda seninle aynı boya geldim bak! -Doğru, demiş kavak. Günler günleri kovalamış ve sonbaharın ilk rüzgârları başladığında kabak üşümeye sonra yapraklarını düşürmeye, soğuklar arttıkça da aşağıya doğru inmeye başlamış. Sormuş endişeyle kavağa: -Neler oluyor bana ağaç? -Ölüyorsun, demiş kavak. -Niçin? -Benim on yılda geldiğim yere, iki ayda gelmeye çalıştığın için.

Çalışmadan emek harcamadan gelinen nokta başarı sayılmaz. Kolay kazanılan, kolay kaybedilir. Her işte alın teri ve emek şarttır.


!!program checkinteger::M,N,Fprint*,”Please enter full number for N? N>1”read*,NM=1F=1do if (M==N) then print*,”M=“,M,” N=“,N,” F=“,F exit else M=M+1 F=F*M cycle endifenddoend program check


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Programming and Problem SolvingProgramming and Problem SolvingProgram-development process consists of at least five steps:1) Problem analysis and specification

The first stage in solving the problem is to analyze the problem and formulate a precise specification of it

2) Data organization and algorithm designDetermine how to organize and store the data in the problem.Develop procedures to process the data and produce the

required output. These procedures are called algorithms.

3) Program codingCoding is the process of implementing data objects and

algorithms in some programming language.A Simple program begins with the

PROGRAM, and ends with the END PROGRAM statements


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Programming and Problem SolvingProgramming and Problem Solving4) Execution and testing

This is the checking step that the algorithm and program are correct.

Compile (produce an object file) {compile-time errors} + run {run-time

errors}: IMPORTANT!! Logic errors that arise in the design of the algorithm or in the coding of the program are very hard to find.

5) Program maintenanceIn real world applications, programs need to

modify to improve their performance.


Bazı şeyler paylaşıldıkça küçülür,

BİLGİ ve SEVGİise

paylaşıldıkça büyür


Algoritma ve Akış Diyagramları

Algoritma sözcüğü Ebu Abdullah Muhammed bin Musa el Harezmi adındaki İran’lı alimden gelmiştir. El Harezmi 9. yüzyılda cebir alanındaki çalışmalarını kitaba dökerek matematiğe çok büyük bir katkı sağlamıştır. Hazırladığı bu “Hisab el-cebir ve el-mukabala” kitabı dünyanın ilk cebir kitabı ve aynı zamanda ilk algoritma kitabı olma özelliğini kazanmıştır.

Algoritma, çözülmesi gereken bir problemin belirli kurallar ve mantık çerçevesinde adım adım çözülerek yazıya dökülmesi işlemidir. Algoritmalar sonlu ve kesin ifadelerle birlikte kullanılmalıdır. Aksi takdirde sonu belirlenmemiş ve/veya kesin ifadeler kullanılmamış algoritmalar yazılırsa sonsuz döngü, kilitlenme gibi istenmeyen bir takım hatalar ortaya çıkacaktır.

http://www.ozgurlukicin.com/atolye/algoritma-ve-akis-diyagramlari/

Yazar: Mehmet PEKGENÇ

Algoritma Neden Gereklidir?

Aslında algoritmalar her zaman hayatımızın bir parçası olmuştur. Çoğu insan her gün birtakım işlerini algoritma yoluyla yaptıkları halde bunun farkında değildir. Örneğin, çay demlemek, yemek yapmak, işe gitmek, araba sürmek gibi işlemlerde normal şartlar altında belli bir sıralama takip edilmektedir. Kısacası yapacağımız tüm işlemlerde yapılması ve/veya yapılmaması gereken kurallar dizisi olacaktır. Bu yüzden tüm programcılar bu kuralları atlamadan hatasız bir şekilde program oluşturmaya çalışırlar. Bunu başarabilmeleri için birkaç saat ya da gün ayırarak bu işlem basamaklarını oluşturmak zorundadırlar. Eğer algoritma oluşturmadan program yazılırsa, daha sonra yazılan yüzlerce ve/ veya binlerce kod arasından hata bulmak neredeyse imkansızdır. Fakat elimizin altında belli bir sırada işlem basamakları olduğu sürece hangi programlama dilinde yazarsak yazalım programımız hatasız olacaktır.

Özellikle bilgisayar programcılığı okuyan arkadaşlarımızın arasında rastladığım kadarıyla çoğu, bu durumu göz ardı etmektedir. Ne kadar çok programlama dili bilirsek o kadar iyi program yazabiliriz düşüncesine sahipler. Unutulmamalıdır ki eğer bir soruna matematiksel ya da mantıksal bir çözüm getiremiyorsak programlama dili bilmemizinde bir anlamı yoktur.Programcılar algoritmaların dışında bir de akış diyagramları kullanmaktadırlar.

Akış Diyagramı Neden Gereklidir?

Algoritmanın daha iyi anlaşılabilmesi için yazı yerine akış diyagramları kullanılmaktadır. Bunu kullanmanın diğer bir önemli yanı da oluşturulan her algoritmanın herkesin anladığı dili yansıtmasıdır. Aksi halde algoritmalar, yazıldığı dili (Türkçe, İngilizce vb.) bilmeyen diğer bir kişi tarafından anlaşılır olmayacaktır. Bu yüzden uluslararası standart sembollerle tüm algoritmaların yazıldıkları dillerden bağımsız hale getirilmesi gerekmektedir.

Bunun için akış diyagramları hayatımıza girmiştir. Konunun daha iyi anlaşılması açısından şu örneği verebiliriz. Trafik lambalarında renk ve/veya şekil yerine DUR, BEKLE ya da GEÇ yazması bizim için anlamlıdır ancak yabancılar için hiçbir anlam ifade etmemektedir. Trafik lambalarında yazı yerine KIRMIZI, YEŞİL gibi renk kodlarının kullanılması tüm dünyada bu işaretleri anlaşılır kılmıştır. Bu yüzden algoritmaları akış diyagramları ile sembolize etmek projenizin uluslararası anlaşılırlığını artıracaktır

Algoritmanın Özellikleri

Etkinlik: Algoritma oluştururken dikkat etmemiz gereken özelliklerden biri etkinliktir. Bu özelliğin sağlanabilmesi için oluşturulan algoritmalarda işlem tekrarı olmamasına dikkat edilmelidir. Diğer bir işlem ise oluşturulan algoritmanın gerekirse diğer algoritmalar içinde kullanılmasını sağlıyor.

Kesinlik: Kullanılan değerler her zaman kesin ifadeler içermelidir.

Sonluluk: Her algoritmanın bir sonu vardır. Ne kadar işlem ya da döngü olursa olsun algoritmanın uygun bir adımda sonlandırılması gerekir.

Giriş/Çıkış: Tüm algoritmaların giriş ve çıkış verileri olmak zorundadır. Çıkış verilerinin kesinlikle doğru olmasına dikkat edilmelidir. Çünkü, çıkışverileri başka bir algoritmanın giriş verisi olarak kullanılabiliyor.

Performans: Performans değeri, algoritmanın ne kadar tekrar ettiği, uyguladığı işlemler, çalışma süresi gibi işlemlere göre belirlenir. Eğer oluşturulan algoritmada performans ihtiyacı varsa saydığım bu tür özelliklere dikkat edilmesi gerekiyor. Eğer bu tip sorunlar varsa tekrar incelenerek düzeltilmesi gerekir.

Örnek Algoritma...

Yeni başlayan arkadaşlara örnek oluşturması için 1’den 100’e kadar olan tam sayıların aritmetik ortalamasını hesaplayan bir algoritma ve akış diyagramını yapalım. Bunun için öncelikle 1’den 100’e kadar olan sayıların toplamına ihtiyacımız olacaktır. Sonrasında bu toplamın 100’e bölünmesiyle ortalama elde edilecektir. Burada toplam için (n*n+1) /2 ne güne duruyor dediğinizi duyar gibiyim. :) Tabiki toplamı bulmak için Gauss yöntemini kullanabiliriz ancak anlatmaya çalıştığımız şey algoritma kurmayı göstermek olduğundan biz uzun yolu seçiyoruz.

Bu anlattıklarımız ışığında algoritmamız aşağıdaki gibi olacaktır.

BaşlaSayac=1 : Toplam=0 : Aritmetik_Orta=0Eğer Sayac=100 ise Git 6Toplam=Toplam+SayacSayac=Sayac+1 : Git 3Aritmetik_Orta=Toplam/100Aritmetik_Orta değerini yazDur.

Ayrıca anlaşılırlığını artırmak için akış diyagramını çizdiğimizde oluşacak diyagram ise aşağıdaki gibidir.

Algoritmanın programlama dillerinden bağımsız olmasının yanında işletim

sistemlerinden de bağımsız olduğunu unutmayınız. Programcılığın başlangıcından

itibaren, hayatınızın sonuna kadar devam edecek ve değişmeyecek tek gerçek aslında algoritmadır. Bu yüzden programcılığa yeni

başlayan ya da başlayacak olan arkadaşlara algoritma ile iyi geçinmelerini tavsiye ederim.

Konu ile ilgili görüş ve önerilerinizi Özgürlükİçin forumlarına bekliyorum.

http://www.ozgurlukicin.com/atolye/algoritma-ve-akis-diyagramlari/

Yazar: Mehmet PEKGENÇ

BIL106 E Introduction to Scientific & Engineering Computing

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Transcript of BIL106 E Introduction to Scientific & Engineering Computing