Introduction

1. Introduction

2. >> t = 0:0.01:1 >> y = 2*pi*t >> x = sin(y) >> plot(t,x,t,y) >> w = x'*x >> surf(w)

3. Intro • MATLAB: Special Purpose Computer Program Optimized to perform engineering and scientific calculations • Implements the MATLAB programming language • Has an extensive library of predefined functions

4. Advantages and disadvantages • Advantages: • Easy to use • Interpreted, not compiled • Integrated editor/debugger • Platform Independence • Works on Windows, Linux, Unix, and MacIntosh • Many predefined functions • E.g., arithmetic mean, standard deviation, median, etc. • Disadvantages: • Interpreted, not compiled • May execute more slowly

5. Command Window • In command window, can type: • area=pi*2.5^2 • If line is too long , can add … to end of line to continue it on the next line • E.g., • x1 = 1 + ½ + 1/3 + ¼ + 1/5 + 1/6 • x1 = 1 + ½ + 1/3 + ¼ …+ 1/5 + 1/6 • Note the space between ¼ and …!

6. Edit/Debug Window • Can create new Matlab files or modify existing ones • Created automatically when you create a new M-file or open an existing one • Select Home • Select New->Script (for scripts (nonfunctions)) • In edit window, type:%This m-file calculates the area of a circle.%and displays the result.radius = 2.5;area = pi * 2.5^2;string = [‘The area of the circle is ‘ num2str(area)];disp(string); • Save file as calc_area.m • Run by typing calc_area in Command Window • Select New->Function for functions

7. Figure Windows • Used to display MATLAB graphics • Can be a two- or three-dimensional plot of data, an image, or a GUI • Write program to plot sin x: • %sin_x.m: This M-file calculates and plots the %function sin(x) for 0 <= x <= 6.x = 0:0.1:6y = sin(x)plot (x,y) • Save as sin_x.m and type sin_x into Command Window

8. Getting Help in MATLAB • Use the Help Browser • ? Icon in desktop toolbar • Type "helpwin” in Command Window • Type “help” or “help” followed by function name in Command Window • “help” -displays a list of possible help topics • “help” function – displays help for that function • “lookfor” command • Searches summaries of each function for a match • Helpful in finding a function you don’t know the name of • E.g., suppose you wanted to find a function that takes the inverse of a matrix. • There’s no function called “inverse” • Do “lookfor inverse” • Get: • INVHILB Inverse Hilbert Matrix • ACOS Inverse cosine • ACOSH Inverse Hyperbolic cosine • ACOT Inverse Cotangent • ACSC Inverse cosecant • ACSCH Inverse Hyperbolic secant • ASIN Inverse sine • ASINH Inverse Hyperbolic sine • ATAN Inverse Tangent • Etc.

9. Other Useful Commands • “demo” in command window (or select demos from the start button • Gives you demos of MATLAB’s capabilities • “clc” in command window • Clears content of command window • “clf” in command window • Clears content of figure window • “clear” in command window • Clears content of workspace • Good idea to avoid variables in one program affecting results in another program • Abort command (Ctrl-C) • Stops a running program • Good for infinite loops • “!” – sends commands to operating system and they are executed as if they’re typed into the operating system’s command prompt • Lets you embed op sys commands into MATLAB programs • “diary” filename • Once typed, all input and most output will be echoed into the diary file. • Helps find problems • To stop: type “diary off” • To continue: type “diary on”

10. Matlabvs Python • Python Functions: def func(x): """ Summary of this function goes here Detailed explanation goes here """ return(x*x) • Matlab function [y] = func( x ) %Summary of this function goes here %Detailed explanation goes here y = x*x end

11. Python vsMatlab Python: def func(): inp = input('would you like to continue?') totalcost = 0 while (inp =='yes'): totalcost = totalcost + 3 inp = input('Would you like to buy something else?') return(totalcost) Matlab: function [totalcost ]= func() inp = input('would you like to continue?','s'); totalcost = 0; while (strcmpi(inp,'yes') == 1) totalcost = totalcost + 3; inp = input('Would you like to buy something else?','s'); end end

12. Python Vs Matlab arr = [3, 2, 8, 1, 4, 7, 9] k = len(arr) print(k) total = 0 for i in range (0,k): total = total + arr[i] print(total); Matlab: arr = [3 2 8 1 4 7 9] k = length(arr); disp(k) total = 0; for i=1:k %Note where loop starts!!! total = total + arr(i); end disp(total)

13. Matlabvs Python arr = [3, 2, 8, 1, 4, 7, 9] k = length(arr) print(k) total = 0 for i in range (0,k,2): total = total + arr[i] print(total); Matlab: arr = [3 2 8 1 4 7 9] k = length(arr); disp(k) total = 0 for i=1:2:k %Note where loop starts!!! total = total + arr(i); end disp(total);

14. Vectors In Matlab • A vector is a list of numbers expressed as a 1 dimensional array. • A vector can be n×1 or 1×n. • Columns are separated by commas (or spaces): h= [1, 2, 3] • Rows are separated by semicolons: v = [1; 2; 3]

15. Matrices in Matlab Columns • A matrix is a two dimensional array of numbers. • For example, this is a 4×3 matrix: • m=[3.0, 1.8, 3.6; 4.6, -2.0, 21.3; 0.0, -6.1, 12.8; 2.3, 0.3, -6.1] Rows

16. Defining (or assigning) arrays • An array can be defined by typing in a list of numbers enclosed in square brackets: • Commas or spaces separate numbers. • A = [12, 18, -3] or A = [12 18 -3] • Semicolons indicate a new row. • B = [2, 5, 2; 1, 1, 2; 0, -2, 6] • 12 18 -3 • 2 5 2 • 1 1 2 • 0 -2 6

17. Array vs. Matrix Operations • Example: x = [2,1; 3,4] y = [5,6; 7,8] 2 1 5 6 3 4 7 8 z = x .* y results in [ 10, 6 21, 32] this is array multiplication z = x * y results in [ 17, 20; 43, 50] this is matrix multiplication So, do NOT forget the dot if you want to do array operations! (.* ./ .^)

18. Matrix vs Array Multiplication • Multiply a .* b 10 15 4 36 • a * b 20 50 20 42 • b * c 11 16 • b .* c error • b * d • error • b .* d • error a = [ 10 5 2 9 ] b = [ 1 3 2 4 ] c = [ 2 3 ] d = [ 2 3 ]

19. Defining arrays continued C = 12 18 -3 • 2 5 2 • 1 1 2 • 0 -2 6 • D = [C, C] • D = • 12 18 -312 18 -3 • 2 5 22 5 2 • 1 1 21 1 2 • 0 -2 60 -2 6 You can define an array in terms of another array: A = [12, 18, -3] B = [2, 5, 2; 1, 1, 2; 0, -2, 6] C = [A; B];

20. Creating Zeros & Ones arrays • E = • 0 0 0 0 0 • 0 0 0 0 0 • 0 0 0 0 0 • F = • 1 1 1 • 1 1 1 • Create an array of zeros: E = zeros (3,5) • Create an array of ones: F=ones(2,3) Note: Placing a single number inside either function will return an n × n array. e.g. ones(4) will return a 4 × 4 array filled with ones.

21. Retrieving Values in an Array • Index – a number used to identify elements in an array • Retrieving a value from an array:G = [1, 2, 3; 4, 5, 6; 7, 8, 9] G(2,1) G(3,2) • 1 2 3 • 4 5 6 • 7 8 9 • ans = 4 • ans = 8

22. Changing Values in an Array • You can change a value in an element in an array with indexing: A = [12, 18, -3] • You can extend an array by defining a new element: • Notice how undefined values of the array are filled with zeros • A = • 12 5 -3 • A = • 12 5 -3 0 08

23. Colon Operator • Colon notation can be used to define evenly spaced vectors in the form: first : last • The default spacing is 1, so to use a different increment, use the form: first : increment : last • The numbers now increment by 2 (Note: if we are incrementing by 1, we don’t need to specify) • H = • 1 2 3 4 5 6 • I = • 1 3 5 7 9 11

24. Extracting Data with the Colon Operator • The colon represents an entire row or column when used as an array index in place of a particular number. • G = • 1 2 3 • 4 5 6 • 7 8 9 • ans = • 1 • 4 • 7 • ans = • 3 • 6 • 9 • ans = • 4 5 6

25. Extracting Data with the Colon Operator Continued • The colon operator can also be used to extract a range of rows or columns: • G = • 1 2 3 • 4 5 6 • 7 8 9 • G = • 4 5 6 • 7 8 9 • ans = • 2 3

26. Manipulating Arrays • The transpose operator, an apostrophe, changes all of an array’s rows to columns and columns to rows. • (how would you recreate J’?) J = 1 3 7 ans = 1 3 7

27. function [ct] = BiSe(ls,n ) flag = 0; a = 1; b = length(ls); ct = 0; while (a <= b) && (flag == 0) x = floor((b - a)/2 + a); ct = ct + 1; if (ls(x) == n) %prints out the value of n, yep, and the value in ct fprintf('%d yep, %d counts \n',n,ct); flag = 1; elseif (ls(x) > n) b = x - 1; elseif (ls(x) < n) a = x + 1; end end if (flag == 0) %prints out the value of n, nope, and the value in ct fprintf('%d nope, %d counts \n',n,ct); end end

28. Your job: • Write an algorithm (a detailed step-by-step description) of how you'd sort a list: ls = [32 1 6 88 63 23 45 26 2 17 82 9 4 42]

29. Functions in Matlab • Selection Sort: function SS( arr) for i = 1:length(arr) smallest = i for j = i+1:length(arr) if arr(j) < arr(smallest) smallest = j; end end temp = arr(smallest); arr(smallest) = arr(i); arr(i) = temp; end disp(arr) End

30. Function 2 • Bubble Sort: • function BuS( arr) • k = length(arr)-1; • flag = true; • while (k > 1) && (flag == true) • flag = false; • for i=1:k • if arr(i) > arr(i+1) • m = arr(i); • arr(i) = arr(i+1); • arr(i+1) = m; • flag = true; • end • end • k = k-1; • end • disp(arr); • end

31. Function 3 • Insertion Sort: function IS(arr) for i = 1:length(arr) largest = arr(i); j = i – 1; while (j > 0) && (arr(j) > largest) arr(j + 1) = arr(j); j = j – 1; end arr(j+1) = largest; end disp(arr) end

32. Making a class of students (in Python)? class Student(object): def __init__(self, lastname, firstname, testscores, labscores): self.lastname = lastname self.firstname = firstname self.testave = self.calcave(testscores) self.labave = self.calcave(labscores) def calcave(self,scores): tot = 0 for x in scores: tot += x return(tot//len(scores)) def printstudent(self): strvar = ""; strvar += self.firstname + " " + self.lastname + ": " strvar += "Test: " + str(self.testave); strvar += " Lab: " + str(self.labave); return(strvar) liststu = [Student("baker","tom",[99,77,82],[88,89,93,92,91]), Student("abbey","steven",[75,86,96],[82,76,88,91,93]), Student("lawrence","sarah",[99,92,93],[85,77,72,65,22]), Student("miller","john",[22,27,45],[77,78,66,72,12]), Student("jones","tina",[94,99,97],[99,98,99,96,91])] for x in liststu: print (x.printstudent())

33. Sorting on Last name: def sortstudentslname(liststu): #is this a method or a function? for i in range(len(liststu)): smallstudent = liststu[i].lastname smallindex = i for j in range(i+1,len(liststu)): if liststu[j].lastname < smallstudent: smallstudent = liststu[j].lastname smallindex = j temp = liststu[i] liststu[i] = liststu[smallindex] liststu[smallindex] = temp return(liststu) liststu = [Student("baker","tom",132,88), Student("abbey","steven",122,96), Student("lawrence","sarah",144,85),Student("miller","john",132,92), Student("jones","tina",128,94)] for x in liststu: print (x.printstudent()) liststu = sortstudentslname(liststu) for x in liststu: print (x.printstudent()) Which sorting method is this one – how does it work?