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Intro to Matlab

Can be found at: http://www.cs.unc.edu/~kim/matlab.ppt. Intro to Matlab. Using scalar variables Vectors, matrices, and arithmetic Plotting Solving Systems of Equations. New Class--for Engineers. ENGR196.3 SPECIAL TOPICS: INTRODUCTION TO MATLAB

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Intro to Matlab

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  1. Can be found at: http://www.cs.unc.edu/~kim/matlab.ppt Intro to Matlab Using scalar variables Vectors, matrices, and arithmetic Plotting Solving Systems of Equations

  2. New Class--for Engineers • ENGR196.3 • SPECIAL TOPICS: INTRODUCTION TO MATLAB • Description:Fundamentals of MATLAB programming applied to problems in science and mathematics. Solving systems of equations, basic scripting, functions, vectors, data files, and graphics. (Credit course for grade or CR/NC)

  3. Drawbacks: Slow (execution) compared to C or Java Advantages: Handles vector and matrices very nice Quick plotting and analysis EXTENSIVE documentation (type ‘help’) Lots of nice functions: FFT, fuzzy logic, neural nets, numerical integration, OpenGL (!?) One of the major tools accelerating tech change Why use Matlab?

  4. Click on Help>Full Product Family Help: Check out Fuzzy Logic Genetic Algorithms Symbolic Math A tour of Matlab’s features

  5. Scalars • The First Time You Bring Up MATLAB • MATLAB as a Calculator for Scalars • Fetching and Setting Scalar Variables • MATLAB Built-in Functions, Operators, and Expressions • Problem Sets for Scalars

  6. 3-1 The First Time You Bring Up MATLAB Basic windows in MATLAB are: • Command - executes single-line commands • Workspace - keeps track of all defined variables • Command History - keeps a running record of all single line programs you have executed • Current Folder - lists all files that are directly available for MATLAB use • Array Editor - allows direct editing of MATLAB arrays • Preferences - for setting preferences for the display of results, fonts used, and many other aspects of how MATLAB looks to you

  7. 3-2 MATLAB as a Calculator for Scalars • A scalar is simply a number… • In science the term scalar is used as opposed to a vector, i.e. a magnitude having no direction. • In MATLAB, scalar is used as opposed to arrays, i.e. a single number. • Since we have not covered arrays (tables of numbers) yet, we will be dealing with scalars in MATLAB.

  8. 3-3 Fetching and Setting Scalar Variables • Think of computer variables as named containers. • We can perform 2 types of operations on variables: • we can set the value held in the container: x = 22 • we can look at the value held in the container: x

  9. The Assignment Operator (=) • The equal sign is the assignment operator in MATLAB. >> x = 22 places number 22 in container x • How about: >> x = x + 1 • Note the difference between the equal sign in mathematics and the assignment operator in MATLAB!

  10. Useful Constants • Inf infinity • NaN Not a number (div by zero) • eps machine epsilon • ans most recent unassigned answer • pi 3.14159…. • i and j Matlab supports imaginary numbers!

  11. Using the Command History Window

  12. 3-4 MATLAB Built-in Functions, Operators, and Expressions • MATLAB comes with a large number of built-in functions (e.g.. sin, cos, tan, log10, log, exp) • A special subclass of often-used MATLAB functions is called operators • Assignment operator (=) • Arithmetic operators (+, -, *, /, ^) • Relational operators (<, <=, = =, ~=, >=, >) • Logical operators (&, |, ~)

  13. Example – Arithmetic Operators Hint: the function exp(x) gives e raised to a power x

  14. Example – Relational and Logical Operators

  15. Vector Operations Chapter 5

  16. Vector Operations • Vector Creation • Accessing Vector Elements • Row Vectors and Column Vectors, and the Transpose Operator • Vector Built-in Functions, Operators, and Expressions

  17. Vectors and Matrices • Can be to command line or from *.m file scalar: x = 3 vector: x = [1 0 0] 2D matrix: x = [1 0 0; 0 1 0; 0 0 1] arbitrarily higher dimensions (don’t use much) • Can also use matrices / vectors as elements: • x = [1 2 3] • y = [ x 4 5 6]

  18. 2-D Plotting and Help in MATLAB Chapter 6

  19. 2-D Plotting and Help in MATLAB • Using Vectors to Plot Numerical Data • Other 2-D plot types in MATLAB • Problem Sets for 2-D Plotting

  20. 6-2 Using Vectors to Plot Numerical Data • Mostly from observed data - your goal is to understand the relationship between the variables of a system. • Determine the independent and dependent variables and plot: speed = 20:10:70; stopDis = [46,75,128,201,292,385]; plot(speed, stopDis, '-ro') % note the ‘-ro’ switch • Don’t forget to properly label your graphs: title('Stopping Distance versus Vehicle Speed', 'FontSize', 14) xlabel('vehicle speed (mi/hr)', 'FontSize', 12) ylabel('stopping distance (ft)', 'FontSize', 12) grid on

  21. Sample Problem – Plotting Numerical Data

  22. 3D Plotting • 3D plots – plot an outer product x = 1:10 y = 1:10 z = x’ * y mesh(x,y,z) Single quote ‘ means transpose (can’t cut and paste though…)

  23. IF block if (<condition>) <body> elseif <body> end WHILE block while (<condition>) <body> end Flow Constructs Conditions same as C, ( ==, >=, <=) except != is ~=

  24. FOR block for i = 1:10 <body> end SWITCH statement switch <expression> case <condition>, <statement> otherwise <condition>, <statement> end More Flow Constructs

  25. Other Language Features • Matlab language is pretty sophisticated • Functions Stored in a *.m file of the same name: function <return variable> = <function name>(<args>) <function body> • Structs • point.x = 2; point.y = 3; point.z = 4; • Even has try and catch (never used them)

  26. Solving Systems of Equations • Consider a system of simultaneous equations 3x + 4y + 5z = 32 21x + 5y + 2z = 20 x – 2y + 10z = 120 • A solution is a value of x, y, and z that satisfies all 3 equations • In general, these 3 equations could have 1 solution, many solutions, or NO solutions

  27. Using Matlab to Solve Simultaneous Equations • Set up the equation in matrix/vector form: A = [3 4 5; 21 5 2; 1 -2 10] u = [ x y z]’ b = [ 32 20 120]’ In other words, A u = b (this is linear algebra) = *

  28. The solution uses matrix inverse • If you multiply both sides by 1/A you get u = 1/A * b • In the case of matrices, order of operation is critical (WRONG: u = b/A ) • SO we have “Left division” u = A \ b (recommended approach) • OR use inv( ) function: u = inv(A) * b

  29. The solution >> u = A\b u = 1.4497 ( value of x) -6.3249 ( value of y) 10.5901 ( value of z) • You can plug these values in the original equation test = A * u and see if you get b

  30. Caution with Systems of Eqs • Sometimes, Matrix A does not have an inverse: • This means the 3 equations are not really independent and there is no single solution (there may be an infinite # of solns) • Take determinant det(A) if 0, it’s singular = *

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