Introduction to Computational Modeling

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1 Introduction to Computational Modeling Lecture 1 : Introduction to UNIX and Fortran Instructor : Cedric Weber Course : 4CCP1000

2 General informations Ø Lecture: Thursday, 9-10am Ø Practice: K3.16 (25C), 10am- 13pm Ø Schedule Ø First term: 10 Lectures, 10 practice sessions Ø 1h Lecture / 3h practice Ø Lecture : short overview of the theory and context Ø Practice : programming hands- on Ø Office : 4.02D Ø Office hours : Monday pm / Tuesday am Ø Website : keats.kcl.ac.uk Ø cedric.weber@kcl.ac.uk Ø Examination 1 Ø 1) A set of problems to be solved in the computer room (3h), codes and answers collected at the end of the examination and marked Ø Last week of December Ø 2) A 10 page report where a set of problems is solved and presented Ø After the Christmas break Ø Contributes 25% to the final grade of the Laboratory module Ø Computers Ø Your KCL login Ø To reset it : kclpword.kcl.ac.uk 2

3 Schedule Class/Week Chapter Topic Milestones 1 Monte Carlo UNIX system / Fortran 2 Monte Carlo Fibonacci sequence 3 Monte Carlo Random variables 4 Monte Carlo Central Limit Theorem 5 Monte Carlo Monte Carlo integration Milestone 1 6 Differential equations The Pendulum 7 Differential equations A Quantum Particle in a box 8 Differential equations The Tacoma bridge Milestone 2 9 Linear Algebra System of equations 10 Linear Algebra Matrix operations Milestone 3 3

Buckle up Lecture: Theory historical context : ~20 min Programming : ~30 min The lecture is merely an overview of the topic covered by the

the practice session you can ask the TA any questions or help to get through the problems 70% 60% 50% 40% Learning curve I expect from you to :

write your questions down and contact me or the TA to go through those points 30% 20% 10% 0% In each lecture we will add one or a few programming

4 Buckle up Lecture: Theory historical context : ~20 min Programming : ~30 min The lecture is merely an overview of the topic covered by the practice session 100% 90% 80% You will be confused until ~Week 5 and really wonder what we are doing, that s to be expected with programming In the practice session you can ask the TA any questions or help to get through the problems 70% 60% 50% 40% Learning curve I expect from you to : Solve problems during practice sessions Go through the lecture notes before the lecture starts Spend ~1h on the lecture notes after the lecture, write your questions down and contact me or the TA to go through those points 30% 20% 10% 0% In each lecture we will add one or a few programming features, and see how they can be used to solve important problems in Physics and Maths week 1 week 2 week 3 week 4 week 5 week 6 week 7 week 8 week 9 week 10 4

5 Reading list / Literature For the Theory For the Programming Numerical Analysis, 2 nd ed., Timothy Sauer Modern Fortran explained, Metcalf, Reid, Cohen, Oxford Available at the KCL library 5

6 Part 1 : UNIX/Linux Operative system 6

networking capabilities Ø Available for laptops, servers, Ø Lightweight : does not require

7 What is Unix/Linux? 7 Ø Multi- tasking, multi- user architecture Ø Stability, portability and powerful networking capabilities Ø Available for laptops, servers, Ø Lightweight : does not require state of the art Ø Open- source (=free) : Ø Open office Ø firefox explorer Ø Mozzila Ø = microsoft office = internet = outlook Ø Remote access (work from home, supercomputers )

8 Linux File system Ø Files are contained in directories Ø Directories follow a tree structure Ø The source directory is denoted / Ø The path to a given directory is denoted by its location in the tree : / book / chapter / page / Ø Means the directory page is contained in the directory chapter, itself contained in the directory book Ø Your personal file are contained in Ø /home/ your_login / Ø An equivalent shorthand notation is : ~/ /etc/ /opt/ /usr/ /home/your_login/ [ = ~/ ] /home/. /tmp/ /scratch/ Ø You can access your files from any computers in the computer room(shared file system) 8

Getting started with Linux Ø You will be first prompted to enter your login Ø Once your credentials entered, you will access a desktop session, with various menus Ø Find and open the program terminal

9 Getting started with Linux Ø You will be first prompted to enter your login Ø Once your credentials entered, you will access a desktop session, with various menus Ø Find and open the program terminal in utilities 9 Ø You can open/close programs and execute commands from the terminal Ø Example : Ø to display the files in this directory, type ls, and press enter Ø A list of your files and directories will be shown Ø To enter the directory tmp : Ø Type cd tmp, press enter

10 File system navigation To navigate through directories cd [space] name_of_directory cd change your location in the file tree from the current directory to the new directory name_of_directory bring you back to your home directory (~/). This is equivalent to : cd ~/ cd [space].. goes one directory up in the tree ls list the content of name_of_directory pwd gives back the position in the file tree Important : if you hit the tab key and entered the first half of a command or directory name, the second half will be auto- completed 10

11 Directory operation File/directory operations mkdir [space] name_of_directory creates a directory with name name_of_directory rm [space] - r [space] name_of_directory deletes this directory and all its content cp [space] r [space] name_of_directory [space] name_of_target Copies the directory and content File operation cp [space] file [space] file_copy copies the files named file to a file named file_copy rm [space] file_to_erase erases the file named file_to_erase 11

12 Account management To manage your UNIX account : quota will give you the amount of disk space that you can use. top displays the list of running processes, the left column is a job/ process identifier (PID number) kill - 9 PID stops a running calculation. PID is the job identifier obtained by top If you wish to stop or exit a running calculation, press CTRL and C at the same time, or CTRL and D 12

13 Nedit / Gedit : opens a text editor program in window mode. Type in the terminal : gedit& Gnuplot : opens a plotting tool in terminal mode. Once in this program, you can plot functions. Step 1, type: f(x)=x*x*3, hit enter Step 2, type: p f(x), enter. The function will be displayed. Plotting interval: To plot the function from x=- 3 to x=+3, Step 2, type: p [- 3:3][] f(x), hit enter. File content plotting: to plot the content of the file name_of_file, which has as its first column the x coordinates, and as a second column the y coordinates, Step 2, type: p [- 3:3][] name_of_file To produce an output file of the plot, type: Set term postscript Set output name_of_the_file.ps rep Text editor, simple plotting tool Once finished, type exit to return to the terminal To display the produced graphics, type in the terminal: gv name_of_the_file.ps Type in the terminal: gnuplot xmgrace: in the terminal, type: xmgrace name_of_file to display a two column file Type in the terminal: xmgrace& 13

14 Ø What does programming mean? Ø 1) Write a series of specific instructions (e.g. a scientific calculation) in a given language (programming) Ø 2) Transform these instructions into a program that the computer can execute (compilation) Ø 3) Execute this program (execution) Ø 4) Obtain results (numbers, plot) as a result of this scientific calculation (post- processing) STEP 1 : With a text editor, write a series of instruction (programming) Ø Fortran programming language Ø Modern programming language with Python and C Ø Syntax is convenient for scientific applications Ø Fast and efficient Ø open- source compiler : gfortran Ø Large number of available scientific libraries Ø Increasing number of functionalities and continuously updated/improved versions 14 STEP 2 : Transform the text into a program (compilation) STEP 3 : execute the program (execution)

15 Part 2 : Fortran Programming 15

end program Ø Ø Ø Instructions are executed from the top to the bottom, one by one When executing your software, the computer executes all

16 What is a program? Ø A program is a list of instructions Ø Each line contains one instruction 1. Program something 2. instruction 1 3. instruction instruction 3 5. end program Ø Ø Ø Instructions are executed from the top to the bottom, one by one When executing your software, the computer executes all the lines until it reaches the end program instruction Vertical axis can be thought of as a timeline Ø The program starts at the first line, and ends at the last line Ø Each instruction has a very precise syntax, every coma, space, is important. 16

17 The Hello program 1. program hello 2. write(*,*) hi there! 3. end program 1. program hello 2.! This is just a notice 3. write(*,*) hi there! Ø Ø Ø Ø Ø program / end program define the scope of the series of instructions that constitute the program In between these two lines, you can add the instructions that you want to execute, the program stops at line 3 A name is given to the program scope, in this case hello. Write(*,*) is a programming command : it displays on your screen the text given as an argument, so here the string of characters hi there. The text shown on the display by write(*,*) is given within quotes. This allows the computer to differentiate this string of characters from the rest of your program 4. end program Ø Line starting with an exclamation mark are not taken into account by the program. They can be used to add some notes or reminder for yourself. Those are called comments 17

18 Spot the mistake 1. program hello write(*,*) 2 4.! write(*,*) 1 5. write(*,*) 2 6. write(*,*) 3 Ø If I want to display 1,2,3, where is the mistake in the program? What do I need to change? 7. end program 18

Compilation 1) write your program with any text editor (the hello program) 2) save it to a file, the filename can be anything, but should end with the extension f90 : myprogram.

19 Compilation 1) write your program with any text editor (the hello program) 2) save it to a file, the filename can be anything, but should end with the extension f90 : myprogram.f90 3) open a terminal, and type : gfortran [space] myprogram.f90 4) Gfortran is a command (compiler) that converts the text to an executable software/program, the program is now called a.out 5) to execute your program, type in the terminal :. / a.out 6) If you modify the text/series of instructions in myprogram.f90, you need to compile again, obtain a new program, and execute it again 19

20 Optional : Linking and executable name You can also change the name of the obtained program (instead of getting a.out) by specifying the additional option o to the compiler : In the terminal, type : gfortran [space ] o [space ] progname.out [space ] myprogram.f90 If any errors in your code (syntax, misspells, typos, conceptual problems), your will receive a list of errors. Correct your code and try to compile again This will produce the executable prog_name.out To run your program, write in the terminal:./progname.out 20

21 Variables We want to perform some calculations with the computer, and for this we need to store the result of an operation in the memory. A variable is a location in the memory where you can store the result of an addition, subtraction etcetera. We could denote this location with a number (or an address), but it is more convenient to just give it a name (variable). There are different types of variables in Fortran : integer : whole numbers, positive and negative real : rational numbers (floating point numbers) Single precision Double precision character : a string of character (text) hello I am here 21

can you write this in terms of 0 and 1?" Question 2 : How would I represent -130?

22 Integer / real representation Both integer and real are stored in the computer s memory in the binary basis (in terms of 0 and 1) Integers are decomposed in powers of 2 : Sign bit 130 = = 2^7 + 2^1 " Question 1 : How can you write this in terms of 0 and 1?" Question 2 : How would I represent -130? " Question 3 : How many bytes if 32 bits? " 0" 0" 0" 1" 0" bit 0" 0" 0" 0" 1" 0" 2^31" 2^30" 2^29".." 2^7" 2^6" 2^5" 2^4" 2^3" 2^2" 2^1" 2^0" Byte / octet 22

The single precision real number is represented as follows:" A constant shift is commonly applied to exp, so it runs from -127 to +128" Largest number : 2 128 =3.4 x 10 38 smallest number : 2-127 =5.

23 The single precision real number is represented as follows:" A constant shift is commonly applied to exp, so it runs from -127 to +128" Largest number : =3.4 x smallest number : =5.8 x " Representation of Floating Number ( 1) s 2 exp mantissa Variable Definition Number of bits s" sign" 1" exp" Exponent between 0-255" 8" mantissa" Coded as : m 1 (2-1 ) + m 2 (2-2 ) + + m 23 ( 2-23 )" 23" Only the 7-8 digits after the coma are significant in single precision" Example, is obtained with : " s=0; sign=-1 0 " "exp=0; exp=2 0 "m 1 =1; mantissa=2-1" 23

24 Using variables Left side : variable type Right side : variable names (your choice) Block of Variable declarations 1. program testingvariables" 2. Real(8) ":: " var1" 3. Integer(4) ":: " var2,var3" Integer à integer(4) Execution Block of the program 4. var1 = 1.10" 5. write(*,*) "var1 " 6. var2 = 2 " 7. write(*,*) "var2" 8. end program" 24 Floating Single precision à real(4) Floating Double precision à real(8) You can t declare a variable in the execution block & all variables need to be declared

25 Spot the 3 mistakes Block of Variable declarations Execution Block of the program 1. program testingvariables" 2. Integer(4) " ":: " var2" " " 3. write(*,*) "var2" 4. var2 = 2 " 5. real(8) " " ":: " var4" 6. var4 = 1.10" 7. write(*,*) "var4 " 8. var2 = 2 " 9. write(*,*) "var3" 10. end program" 25

26 Variable Assignment 1. var1 = 1" 2. var1 = 2*var1 + 1" 3. write(*,*) var1 " Even more confusing!! Remember : 1. Line (2) is not an equation 2. Line are executed one by one from the top down to the bottom. 3. At Line (2), the computer first evaluates all the operation contained on the right hand side, and obtains a numerical result 4. This numerical result is stored in the variable appearing on the left hand side, which is assigned a new value = [Fill in] 26

27 Basic operations var1 = " Extremely confusing!! This operation is not an equation It is a multi- step process : 1. The computer always first carries out all the operation contained on the right hand side, and obtains a numerical result 2. This numerical result is stored in the variable appearing on the left hand side, which is assigned a new value Basic operations : addition: substraction: division: multiplication: to the power n: to the power 1/n: a+b a- b a/b a*b a**n a**(1.0/2.0) Priorities: Elements in brackets are done first Powers are done before multiplications Multiplications are done before additions If any doubt, use a bracket 27

28 Example Block of Variable declarations Execution Block of the program 1. program testingvariables" 2. Integer(4) " ":: " var1" " 3. var1 = 1" 4. write(*,*) var1 " 5. var1= var1 + 2 " 6. write(*,*) var1 " 7. Var1= var1 * 2 " 8. Write(*,*) var1" 9. end program" Questions : 1) How many outputs displayed? [Fill in] 2) Write them here : [Fill in] 28

29 Operations with different types Type are conserved during operations, so if i and j are integers, i/j is also an integer (floored down) i = 2/3 will give i=0 i = 4/3 will give i=1 Integers involved in floating operations are automatically converted Example : a = 10.0 / 3, 3 is converted internally to 3.0 Warning: some ambiguous cases exists, and will give different results on different compilers, such as : 10.0 * 2 / 3 Why is it ambiguous? To avoid any confusion, integer can be transformed to real numbers with the function dble 10.0 * dble(2)/dble(3) is equivalent to 10.0 * 2.0/ a = 2.0 * b / dble(i), where a,b, are real numbers and i is an integer

30 Operations mixing different types Integer(4) ":: var2" Real(8) ":: var1" var1 = var2 / 2 " If var1 is a floating number and var2 an integer, and they appear in the same operation, we need to convert var2 to a floating number Integer to floating type conversion : Simply insert dble( ) around var2, this will transform var2 from an integer to a floating number var1 = dble(var2) / 2 " Warnings : Integer divisions are floored down Example : var2 = 1 / 2 will give the value zero to the variable var2 To distinguish integer values from floating values, we always append explicitly a coma to floating point numbers Example : var1 = 1.0 / 2.0 [and not var1 = 1 ] 30

31 Available functions for double precision floating numbers 1. program testop 2. real(8) :: a, b 3. a=sin(2.0) 4. b=cos( a ) 5. write(*,*) b=, b 6. end program Functions readily available in Fortran:" Trigonometric functions:" " "à sin(x), cos(x), tan(x)" Inverse functions:" " "à asin(x),acos(x),atan(x)" Hyperbolic functions: " " "à sinh(x),cosh(x),tanh(x)" units of x are radians above" Absolute value:" " "à abs(x)" Exponentials:" " "à exp(x)" Square root:" " "à Sqrt(x)" 31

32 Practice in K3.16 / 25 C 1 st Floor - Kings Building 32

Computational modeling

Computational modeling Lecture 3 : Random variables Theory: 1 Random variables Programming: 1 Implicit none statement 2 Modules 3 Outputs 4 Functions 5 Conditional statement Instructor : Cedric Weber Course