Creating Arrays

1. Creating Arrays Creating scalars, vectors, matrices Ex. Plotting Graphs Ex. Conversion Table Ex. Plotting functions Ex. Use of matrices in real world

2. 1. Creating scalars • Assign a value to a variable (i.e. Hardcode) pressure = 10; %pascals temperature = 298; %kelvin • Store the result of an equation pressure = density*R*temperature; • Collect the return value of a function: age = input('Enter your age: '); distance = sind(angleDeg);

3. 2. Creating vectors • There are LOTS of ways to create vectors, based on three simple ideas: • The values in the vector are pre-defined. For example: [ 2 -5 4.4 -96.6] • The values have an addition pattern. For example: [10, 20, 30 ,…100] or [-10 -8 -6 -4 -2 0] • Or even, the total number of values is known! For example: 25 points evenly spaced from 0 to 100.

4. 2.1. row vector • Square brackets [] and commas • OR square brackets and white space 1 by 4 1 by 4

5. 2.1. column vector • Square brackets and semi-colons • Or a row vector transposed with the apostrophe 3 by 1 3 by 1

6. Trivia • What are the true statements? • y is a row vector • y is a column vector • y is a scalar • y contains 4 scalars • y is a 1 by 4 • y is a 4 by 1 • None of these

7. New operators… [] Use [] to tell MATLAB you are about to hardcode an array , Use a comma or white-space to create new columns ; Use semi-colons to create a new row ’ Use an apostrophe to transpose the array (caution if you are using imaginary numbers…) NO MATTER WHAT YOU DO: KEEP THE ARRAY RECTANGULAR!!!!!

8. y x y -7 -2 3 8 4 -7 3 -1 x Ex. Plotting graphs • In order to plot, MATLAB needs data points:

9. y x y -7 -2 3 8 4 -7 3 -1 x Ex. Plotting graphs • In order to plot, MATLAB needs data points:

10. y x y -7 -2 3 8 4 -7 3 -1 x Ex. Plotting graphs • In order to plot, MATLAB needs data points: MATLAB connects the dots!

11. y x y -7 -2 3 8 4 -7 3 -1 x Ex. Plotting graphs • In order to plot, MATLAB needs data points: x is an vector of data points y is another vector of data points …for the curious ones, to plot: clc clear x = [-7 -2 3 8]; y = [4 -7 3 -1]; plot(x,y); %plots y vs. x

12. y x y -7 3 -2 8 4 3 7 -1 x Ex. Plotting graphs • MATLAB plots in order of the data-points: clc clear x = [-7 3 -2 8]; y = [4 3 -7 -1]; plot(x,y); %plots y vs. x

13. 2.2. Patterns (addition only) • For addition pattern, no need to code a lot! The range operator Numbers are separated by +1

14. 2.2. Patterns, cont. • Add an increment to increase by a different amount than +1 An additional value in the middle specifies the increment (aka step-size). +3 +3 +3 +3 +3 +3 +3 +3 >32 

15. 2.2. Patterns, cont. • Create a decreasing pattern by using a negative increment! CAUTION: the beginning number must be > the end number. Here 10>3. Note: it works with fractional values. -2.5 -2.5 -2.5 < 3 

16. Pause… • Where has this logic been used before? k = 1:4:25

17. 2.2. Patterns, cont. • To use the apostrophe (single quote) and create a column vector: place brackets first … otherwise? (try it at home..) +3 >32 

18. Ex. Conversion table clc clear % create Celsius vector of data points Celsius = 0:10:100; %0 to 100 by inc. +10 % calculate Fahrenheit Fahrenheit = Celsius * 9/5 + 32; % create/show table <code not shown> EFFICIENT: MATLAB has a built-in loop that applies the formula to EACH element of the vector Celsius 1 line of code = 11 calculations! Fahrenheit is a ___ by ____.

19. 2.3. Specific amount of data points • Sometimes, the increment isn’t so important (or known) vs. HOW MANY points there are. • A built-in function called linspace() spaces elements linearly in an array. • What does this mean? • The distance between consecutive data points is a constant across the array.

20. Ex. Plotting sine • How many points would it take to plot correctly the sine function on the interval ? • 2 points? • 5 points? • 10 points? • 100 points? • 1,000,000?

21. Ex. Plotting sine • Why linearly spaced? These 9 points? Or These 9 points?

22. >>doc linspace<enter> linspace Generate linearly spaced vectors Syntax y = linspace(a,b)y = linspace(a,b,n) Description The linspace function generates linearly spaced vectors. It is similar to the colon operator ":", but gives direct control over the number of points. y = linspace(a,b) generates a rowvector y of 100 points linearly spaced between and including a and b. y = linspace(a,b,n) generates a row vector y of n points linearly spaced between and including a and b. For n < 2, linspace returns b.

23. Ex. Plotting sine clc clear %x coordinates angles = linspace(0, 2*pi, 9); %calculate y(x) = sin(x) y = sin(angles); %plot sine as a function of the angle plot(angles,y) Will 9 data points really be enough?

24. Ex. Plotting sine clc clear %x coordinates angles = linspace(0, 2*pi, 9); %calculate y(x) = sin(x) y = sin(angles); %plot sine as a function of the angle plot(angles,y) Will 9 data points really be enough?

25. Ex. Plotting sine clc clear %x coordinates angles = 0: :2*pi; %without linspace()? %calculate y(x) = sin(x) y = sin(angles); %plot sine as a function of the angle plot(angles,y) Remember 9 points…

26. 2.3. linspace(), cont. • MATLAB runs out of space to display? When MATLAB cannot display all the elements on one line, it simply indicates the column numbers for each line.

27. 2.3. linspace(), cont. • Transpose the return value of linspace() to create a column vector

28. 2.3. linspace(), cont. ?????? %no third argument Omitthe third argument uses a default of _______ data points!

29. 3. Creating Matrices • Simply a combination of all operators introduced with vectors! • Square brackets [ ] • Spaces or commas , , • Semi-colons ; • Apostrophes ‘ • Just keep in mind: only RECTANGULAR matrices

30. 3.1. Matrices: hard-coding • Use semi-colons to create new rows. • Good or bad? Why? 2 by 3 3 by 2

31. 3.2. Concatenating matrices • Assume variable a from the previous slide. Use it as a reference to create a new variable: “CONCATENATING” The art of “gluing” vectors and matrices together

32. Finish this code.. Concatenate! clc clear % create Celsius vector of data points Celsius = 0:10:100; %0 to 100 by inc. +10 % calculate Fahrenheit Fahrenheit = Celsius * 9/5 + 32; % create/show table table = _________________________

33. 3.3 Using colons • Combine ALL methods necessary JUST KEEP THE ARRAY RECTANGULAR

34. Creating arrays is great but… What to do with them???

35. Actual uses of Arrays

36. Basic functions on arrays CAUTION: A function will return different values depending on whether the argument is a vector or a matrix!

37. Ex. vector: Temperatures clc clear % engine temperature temps = [45.5,56.7,99.9,42,12,29]; % determine minimum,maximum,average temperature minTemp = min(temps) maxTemp = max(temps) avgTemp = mean(temps) Do not use min =, or max=…, or mean= … These keywords are reserved by MATLAB!

38. Ex. matrix: Scores clc clear % scores from playing. Col1 = player1, col2 = player2…etc. scores = [45,34,56; 67,3,45; 22,55,99]’; %transposed! % determine minimum,maximum,averagescores minScores= min(scores) ? maxScores= ______________ avgScores= ______________

39. Making Arrays We've just begun arrays – much more to follow (2 weeks total) Arrays frequently holds a large number of values, which is usually what data files contains. Matrices typically involve nested loops (although later we’ll see that this can sometimes be avoided…) Next time: using values inside the array (“referencing” them) changing arrays (inserting values/deleting values) learning the MATLAB array tools

40. Try it at home! • Create a vector for each category of this class (assignments, homework, quizzes, exams, extra credit… ). Find your minimum, maximum, average grade in each category. • Search into the sum() function, and calculate your grade using the weighted averages! – or wait till next time!