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Computer Simulation Lab

Computer Simulation Lab. “Lecture 2”. Electrical and Computer Engineering Department SUNY – New Paltz. MATLAB fundamentals. · Desktop, Editing ·         V ariables, Operators, Expressions ·         V ectors ·         I nput / Output ·         R epetition ·         D ecision.

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Computer Simulation Lab

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  1. Computer Simulation Lab “Lecture 2” Electrical and Computer Engineering Department SUNY – New Paltz SUNY-New Paltz

  2. MATLAB fundamentals · Desktop, Editing ·        Variables, Operators, Expressions ·        Vectors ·        Input / Output ·        Repetition ·        Decision SUNY-New Paltz

  3. The MATLAB Desktop SUNY-New Paltz

  4. Integrated Development Environment (IDE) qCommand Window qCurrent Directory qCommand History qLaunch Pad qWorkspace SUNY-New Paltz

  5. Programs A collection of statements to solve a problem is called a program. Different Types of Languages: • Machine Language (Executable File) • Low-Level Languages (Assembly) • High-Level Languages (C, C++, Java, Basic, Fortran, etc.) • Script Languages ( PERL, MATLAB, PHP, etc.) SUNY-New Paltz

  6. Write a program! A Simple Program: Suppose you have $1000 saved in the bank. Interest is compounded at the rate of 9% per year. What will your bank balance be after one year? • 1. Get the data (initial balance and interest rate) into the program. • 2. Calculate the interest (9 per cent of $1000, i.e. $90). • Add the interest to the balance ($90 + $1000, i.e. $1090) • 4. Display the new balance SUNY-New Paltz

  7. C Language include <stdio.h> include <interest.h> define int interest, balance main{ balance = 1000; rate = 0.09; interest = rate * balance; balance = balance + interest; printf(“balance=%d”, balance); } SUNY-New Paltz

  8. MATLAB Program balance = 1000; rate = 0.09; interest = rate * balance; balance = balance + interest; disp( ’New balance:’ ); disp( balance ); SUNY-New Paltz

  9. Variables and the workspace A variable name (like balance) must comply with the following two rules: 1. It may consist only of the letters a–z, the digits 0–9 and the underscore ( _ ). 2. It must start with a letter. Valid: r2d2, pay_day Invalid:pay-day, 2a name$, _2a SUNY-New Paltz

  10. Case sensitivity • Different variables: • balance, BALANCE and BaLance • Camel Caps: • camelCaps • milleniumBug • dayOfTheWeek • Commands are all in lower case SUNY-New Paltz

  11. Examples of variables • interest=.09; • years=10; • delta=1.e-3; • email=‘doej@gmail.com’; • vect=[1 2 3 4 5]; • matx=[1 2 3; 4 5 6]; SUNY-New Paltz

  12. workspace • who: lists the names of all the variables in your workspace • whos: lists the size of each variable as well • ans: returns the value of the last expression evaluated but not assigned to a variable • Workspace • Name Size Bytes Class • balance 1x1 8 double array • interest 1x1 8 double array • rate 1x1 8 double array SUNY-New Paltz

  13. Arrays: vectors and matrices • Initializing vectors: explicit lists x = [1 3 0 -1 5] use spaces a = [5,6,7] use commas a = [1 2 3], b = [4 5], c = [a -b] x = [ ] • Initializing vectors: the colon operator x = 1:10 x = 1:0.5:4 x = 10:-1:1 x = 0:-2:-5 • linspace • linspace(0, pi/2, 10) SUNY-New Paltz

  14. ArraySubscripts • r = rand(1,7) This gives you a row vector of seven random numbers. • r(3) This will display the third element of r. The number 3 is the subscript. • r(2:4) This should give you the second, third and fourth elements. • r(1:2:7) • r([1 7 2 6]) • r([1 7 2]) = [ ] will remove elements 1, 7 and 2. SUNY-New Paltz

  15. Matrices • a = [1 2 3; 4 5 6] = 1 2 3 4 5 6 • a’ = 1 4 2 5 3 6 • A matrix can be constructed from column vectors of the same lengths: x = 0:30:180; table = [x’ sin(x*pi/180)’] = 0.0000 0.0000 30.0000 0.5000 60.0000 0.8660 90.0000 1.0000 120.0000 0.8660 150.0000 0.5000 180.0000 0.0000 SUNY-New Paltz

  16. Exercise Construct the following vectors and matrices: • A row vector of all odd numbers between –101 and 101 • A column vector of all numbers between –101 and 101 that are divisible by 3 • A matrix of 16 equally spaced angles between 0 and 2*pi along with sin(x) and cos(x) and tan(x). • A matrix of size 5x5 having random numbers between 0 and 1 for each element. SUNY-New Paltz

  17. Capturing output • diary filename • diary off SUNY-New Paltz

  18. Operators, Expressions, Statements • Arithmetic operations between two scalars • OperationAlgebraic formMATLAB • Addition a + b a + b • Subtraction a -b a - b • Multiplication a × b a * b • Right division a/b a / b • Left division b/a a \ b • Power aba ^ b SUNY-New Paltz

  19. Precedence of arithmetic operations PrecedenceOperator 1 Parentheses 2 Power, left to right 3 Multiplication and division, left to right 4 Addition and subtraction, left to right SUNY-New Paltz

  20. Exercise • Evaluate the following arithmetic expressions: • A= 2/4^2*2+1\4 • B=1/2^2*2/4 SUNY-New Paltz

  21. Arithmetic operations on arrays Arithmetic operators that operate element-by-element on arrays Operator Description .* Multiplication ./ Right division .\ Left division .^ Power Examples: a = [2 4 8]; 3 .* a = ? b = [3 2 2]; a .^ 2 = ? a .* b = ? a ./ b = ? SUNY-New Paltz

  22. Statements, Commands and Functions • Statements: s = u * t - g / 2 * t .^ 2; • Functions: sin(x), plot(x) • Commands: load, save, clear SUNY-New Paltz

  23. Vectorization of Formulae1- Case of Scalar A = 750; r = 0.09; n = 10; B = A * (1 + r) ^ n; disp( [A B] ) • 750.00 1775.52 SUNY-New Paltz

  24. Vectorization of Formulae2- Case of Mutiple Investment • A = [750 1000 3000 5000 11999]; • r = 0.09; • n = 10; • B = A * (1 + r) ^ n; • disp( [A’ B’] ) • 750.00 1775.52 • 1000.00 2367.36 • 3000.00 7102.09 • 5000.00 11836.82 • 11999.00 28406.00 SUNY-New Paltz SUNY-New Paltz

  25. Output • disp( variable ) {variable could be numerical or textual} • disp( ’Pilate said, ’’What is truth?’’’ ); • disp( [x y z] ) • disp( [’The answer is ’, num2str(x)] ); SUNY-New Paltz

  26. format • 1234567890 is displayed as 1.2346e+009 • mantissa is between 1 and 9.9999 • format short , format short e • format long , format long e • format long g, format short g • format compact • format hex • format rat • format bank SUNY-New Paltz

  27. Repeating with for for i = 1:5 disp(i) end • for index = j:m:k • for index = v (where v is any vector such as [2 3 8]) • Show the squares of all even numbers between 0 and 1000 for i=0:2:1000 disp([i i*i]) end SUNY-New Paltz

  28. Avoid Loops! s = 0; for n = 1:100000 s = s + n; end; n = 1:100000; s = sum( n ); Find x=1+1/2+1/3+1/4…. + 1/1000 SUNY-New Paltz

  29. Decisions if r > 0.5 disp( ’greater indeed’ ) end Relational operators Relational OperatorMeaning < less than <= less than or equal == equal ~= not equal > greater than >= greater than or equal SUNY-New Paltz

  30. Decisions if condition1 statementsA elseif condition2 statementsB elseif condition3 statementsC ... else statementsE end if condition statementsA else statementsB end SUNY-New Paltz

  31. Logical operators ‘~’ ‘&’ ‘ |’ if bal >= 5000 & bal < 10000 SUNY-New Paltz

  32. Nested if’s d = b^2 - 4*a*c; if a ~= 0 if d < 0 disp( ’Complex roots’ ) else x1 = (-b + sqrt( d )) / (2*a); x2 = (-b - sqrt( d )) / (2*a); end end SUNY-New Paltz

  33. Switch/Case d = floor(3*rand) + 1 switch d case 1 disp( ’That’’s a 1!’ ); case 2 disp( ’That’’s a 2!’ ); otherwise disp( ’Must be 3!’ ); end SUNY-New Paltz

  34. Switch/Case d = floor(10*rand); switch d case {2, 4, 6, 8} disp( ’Even’ ); case {1, 3, 5, 7, 9} disp( ’Odd’ ); otherwise disp( ’Zero’ ); end SUNY-New Paltz

  35. Complex numbers • z = 2 + 3*i • sqrt(2 + 3*i) • exp(i*pi) circle = exp( 2*i*[1:360]*pi/360 ); % select all points around a circle plot(circle) % is equivalent to: plot(real(y), imag(y)) axis equal a = [1+i, 2+2i; 3+3i, 4+4i] 1.0000 + 1.0000i 2.0000 + 2.0000i 3.0000 + 3.0000i 4.0000 + 4.0000i SUNY-New Paltz

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