COMPUTER PROGRAMMING

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COMPUTER PROGRAMMING

• Course code CE10082
• Recommended text-books any book about
  Fortran77/90 programming.
• Course length (contact hours) 15 hours
• Method of assessment Computing project

Course outline In this course you will learn
basic programming by Fortran 77 and Fortran 90.
The course will be run on an informal basis, and
will essentially be a teach yourself process,
under guidance. You will be given a series of
worksheets and a project to be completed during
the course, which must be handed in on-time.
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Course Content

• Section 1
• Introduction of the programming concept, learning
  about the computing resources and getting
  familiar with logging into the system in order to
  use Fortran 77 and Fortran 90, and compiling the
  Fortran routines.
• Section 2
• Learning how to write algorithms, preparing
  flowcharts, and learning basic features and rules
  of Fortran.
• Section 3
• Learning how to use the Fortran language by
  writing programs and running them.
• Section 4
• Learning some of the numerical computing methods
  to solve polynomial functions, integral and
  differential equations, and writing Fortran
  programs to do them.

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Why do we need to know how to program?
Not every problem a chemical engineer wishes to
solve has a ready-made PC package available that
can be bought off a shelf. E.g. computer
simulation of the growth of a silica film at an
air-water interface. Experimental observations-
time
Silica particles precipitate out at the water-air
interface
Individual particles aggregate into a fractal
cluster structure
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Computer Simulation
If we are able to write a computer program that
models the growth of the silica film we,
therefore, understand the system and can
experiment in-silico-
Image of real film
Simulated film
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The Programming Concept

• Computer programming is a bit like learning a
  foreign language - you have to learn the
  computers vocabulary and grammar (in the jargon
  it is called syntax).
• Unfortunately, unlike a human, a computer cannot
  guess what you are trying to say and only goes on
  just what you tell it.
• If your vocabulary or grammar has even the
  slightest mistake, it will not understand you.
• The computer will follow the instructions that
  you give it to the letter, even if you really
  meant it to do something else !
• Therefore you will need to develop a way of
  thinking that breaks down a task into smaller
  components that you are able to write down very
  precisely.

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Flow Diagrams and Programs
A program is a set of instructions telling the
computer to perform a set of operations in a
particular order. In order to convert a specific
task into a computer program it is often helpful
to construct a flow diagram for procedures
involved in the task. A flow diagram consists of
operations such as
Terminator
Yes
No
Decision e.g. xgt1 ?
Process e.g. x x1
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The Compilation Process The first step in testing
a program after it is written. The compiler
checks if the program is written correctly (the
syntax is correct). It wont spot mistakes that
are grammatically correct.
Compiler
Object code
Source code
Compilation of the code
Source code listing
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Writing Fortran Programs In principle you have
several options for where to write your FORTRAN
programs. You can use- 1) fbench.exe in the f77
folder on the G-drive 2) the vi editor, or
similar, on any UNIX computer, e.g. mary 3) some
PCs have other FORTRAN compilers (e.g. Force)
installed 4) UNIX workstations, such as SUNs and
SILICON GRAPHICS We will use option (1) or
(3). Your files will be stored in your home
directory. You can also keep copies on floppy.
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Basic UNIX commands
ls -list contents of current directory pwd -pr
esent working directory mkdir name -make new
directory (folder) rm name -remove file called
name rmdir name -remove directory called name cd
path/name -change directory to path/name cd
.. -go back to previous directory man
command -brings up on-line manual entry for
a particular command Program files must have a
name followed immediately by .f To compile a
program in file name.f type f77 -o name
name.f and to run the program type name
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Basic Programming

• Start program commands on at least column 7 (e.g.
  use tab) of whatever text editor is used.
• Do not exceed column 72 for each line of text.
• Start program with the name of the program
• PROGRAM NAME
• Next disengage any defaults for variable classes
• IMPLICIT NONE
• Text which is not a Fortran command must be
  indicated by either a C or ! character in the
  first column.
• ! comments
• It is helpful to use comments to both remind
  yourself, and tell any new reader of your
  program, what each bit of the program does.

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Data Types and Integer Constants

• Next you must declare the names and types of all
  the variables you intend to use in the program.
• Integer values are those that represent whole
  numbers only. The range of values possible
  depends on the computer but is typically from
  -232-1 to 232-1-1 for a typical machine.
• The declaration statement is as follows
• INTEGER NAME
• The second main type of numerical variable is
  called Real. Real numbers are stored in the
  computer as two components a mantissa ranging
  between 0.1 and 1.0, and an exponent that
  indicates the appropriate power of 10.
• E.g 0.5x105 0.5E5

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Data Types and Integer Constants

• Real numbers may be positive or negative, and
  always possess a decimal point.
• The limit of accuracy for Real variables is 7
  digits, with magnitudes in the range from 10-39
  to 1039.
• Declaration statements are of the form
• REAL NAME
• If more than 7 digits accuracy is required you
  can use a Double Precision constant, which is
  accurate up to 14-16 decimal places, depending on
  the machine.
• Instead of using E to denote the exponent you
  must use the letter D, e.g. 0.5D5
• Double precision numbers require longer
  computational time to do calculations.
• Declaration statements are of the form
• DOUBLE PRECISION NAME

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Simple Input/Output

• To input a value to a variable you use the Read
  statement.
• For example, to get the user to enter a value for
  the variable VARIABLE1 use
• READ, VARIABLE1
• When the computer reaches this command in a
  program it will sit and wait for the user to
  enter a value.
• To display the value of a variable, or to print
  some text we use the Print command
• For example
• PRINT, VARIABLE 1
• will print the value of VARIABLE1 on the screen,
  and
• PRINT,text
• will print the text between the inverted commas
  on the screen.

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Mathematical Operations
Note Using Reals 3.0/2.0 1.5 Using
Integers 3/2 1 Integer answer obtained
by truncation
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IFTHEN...ELSEENDIF
IF statements can be used to make
decisions e.g. IF(X.EQ.1) THEN -Note full
stops PRINT,HELLO ELSE
PRINT,GOODBYE ENDIF If you are asking more
than one question, or two questions about more
than one variable, you can use .AND. and .OR.
statements e.g. IF((X.EQ.1).AND.(Y.EQ.1))
THEN IF((X.EQ.1).OR.(Y.EQ.1)) THEN For
the logical parts of the statements EQ
equals NE not equal to GT greater
than GE greater than or equal to LT less
than LE less than or equal to
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DOENDDO
The DO statement is for carrying out loops. The
format of the statement is DO variablestart,
stop, step e.g. DO I1,10,1 The loop must be
finished with an ENDDO statement e.g. DO
I1,10,1 YYI ENDDO A slight variant is
the DO WHILE loop e.g. X1 Y1 DO WHILE
(X.LT.10) YYX XX1 ENDDO The DO
WHILE loop uses the same codes for less than
etc. as IF.
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FILE MANAGEMENT
Computer programs may be run in your absence.
You can get the computer to run a program
overnight and then output the data to a file
that you can pick up later, at your convenience.
You may also wish to use other peoples data in
your programs. To create a file separate to your
source code file use the following command OPEN
(UNIT1, FILEname,STATUSNEW) To add
something to the file use the WRITE
command e.g. WRITE(1,) NUMBER
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FILE MANAGEMENT
When you have finished using the file, close it
down using CLOSE(1) When you want to
retrieve data from an existing file, re-open
it OPEN(UNIT1, FILEname,STATUSOLD) and
read in the data contained therein
using READ(1,) NUMBER and dont forget to
close the file again, afterwards.
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PROGRAM VALIDATION

• When you have written a program it is important
  to check, not only that it compiles and runs, but
  also that it does the job it was designed to do!!
• This process is known as program validation.
• If the program is designed to solve a class of
  numerical problems, then use it to solve a
  particular special case where the solution is
  known analytically or can easily be done on a
  spreadsheet, and then check the answer from your
  program against the alternative method.
• If the program works in the simple case, we can
  have more confidence that it will work for a
  complex case we cant tackle by simpler means.

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Trapezium Rule
y
y0
y1
y3
y(x)
h
h
x
x1
x2
x3
(I) Divide integration region into strips of
width h (II) Approximate curve over each strip by
a straight line (III) Sum areas of resulting
trapezia - n strips means (n1)
function evaluations
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Simpsons Rule
y
A
B
C
yi-1
yi
yi1
y(x)
h
h
x
xi-1
xi
xi1
(I) Divide integral region into an even number of
strips, each of width h (II) Approximate curve
over two adjacent strips by a quadratic- interpola
tion through A, B, C
(III) Find area underneath interpolating curve
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Simpsons Rule
(IV) Sum
Note (1) Simpsons rule is exact for a
quadratic, by construction (2) Simpsons rule is
exact for a cubic too !
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Solving Differential Equations using Eulers
Method
y
Slope f(x0,y0)
Slope f(x1,y1)
y(x)
Start here
y0
y1
y3
h
h
x
x1
x2
x3
Approximate solution by a set of straight lines,
where the slopes are given by the differential
equation
In general
Equivalent to a Taylor expansion truncated after
the 1st derivative
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Modified Euler Method
yn
h
xn
xn1
Over the step xn,xn1 Euler uses yn/ f(xn,yn)
i.e. the slope at the start of the step. To
improve this, estimate the derivative at the end
of the step too, and take the average of the two
estimates. Estimate of derivative at xn is k1
f(xn,yn) Estimate of derivative at xn1 is
yn1 yn h/2(k1 k2)
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Example - Solving a Quadratic Equation by
Iteration

• Problem Write a program to solve a general
  quadratic equation by iteration.
• The general quadratic equation is given by
• For an iterative solution we must re-arrange the
  equation such that x alone occurs on one side of
  the equation

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Example - Solving a Quadratic Equation by
Iteration

• To solve by iteration we first select our initial
  guess for x.
• Then we insert this value of x into the rhs of
  the re-arranged quadratic to obtain our next
  value of x
• We repeat this process until (hopefully) x
  converges to one of the solutions of the
  quadratic.