Introduction to MATLAB

1. Introduction to MATLAB MATLAB is all of the following: Computational environment Plotting software Programming language Typical applications: Calculations Engineering/Scientific programs Audio processing Image processing

2. % Scalars x = 1.23; y = pi; disp(x) format long disp(y) format short disp(y) 1.2300 3.141592653589793 3.1416

3. % Scalar arithmetic x = 3; y = 2; disp(x+y) % addition: + disp(x-y) % subtraction: - disp(x*y) % multiplication: * disp(x/y) % division: / disp(x^y) % power: ^ 5 1 6 1.5000 9

4. Exercise Hints: * (multiplication) ^ (raising to a power)

5. % vectors x = [1,2,3]; % row vector x = [1 2 3]; % commas can be replaced by spaces disp(x) disp(length(x)) disp(size(x)) y = [1;2;3]; % column vector disp(y) disp(size(y)) 1 2 3 3 1 3 1 2 3 3 1

6. % Transpose x = [1 2 3]; y = x'; % transpose of real vector x disp(y) z = y'; disp(z) 1 2 3 1 2 3

7. Exercise Hints: size() '(transpose)

8. % Concatenation of row vectors x = [1 2 3]; y = [4 5 6]; z = [x y]; % concatenate row vectors disp(z) z = cat(2,x,y); % concatenate by adding columns % this accomplishes the same thing as above disp(z) 1 2 3 4 5 6 1 2 3 4 5 6

9. % Concatenation of column vectors x = [1; 2]; y = [3; 4]; z = [x; y]; % concatenate column vectors disp(z) z = cat(1,x,y); % concatenate by adding rows % this accomplishes the same thing as above disp(z) 1 2 3 4 1 2 3 4

10. Exercise

11. MATLAB Documentation for sum sum Sum of array elements Syntax B = sum(A) B = sum(A,dim) My comments: A is a matrix, and dim is either 1 or 2. If A is a vector, then a scalar (the sum of all elements) results. If A is a matrix (with at least 2 rows and at least 2 columns), then either a row (dim = 1) or a column (dim = 2) vector results.

12. % sum function with vector argument x = [1 2 3 4]; % row vector disp(x) disp(sum(x)) y = [1; 2; 3]; % column vector disp(y) disp(sum(y)) 1 2 3 4 10 1 2 3 6

13. % The functions maximum and minimum x = [1 2 3]; % The functions maximum and minimum work equally well for % row and column vectors. disp(max(x)) disp(max(x')) disp(min(x)) disp(min(x')) 3 3 1 1

14. Exercise Create a column vector consisting of the whole numbers 0 to 10. Have MATLAB find the length of this vector, the sum of its elements, the maximum and minimum elements. Hints: length()sum() max() min()

15. % Create vectors with the functions zeros and ones x = zeros(1,5); disp(x) y = zeros(2,1); disp(y) y = ones(1,4); disp(y) 0 0 0 0 0 0 0 1 1 1 1

16. % Create row vectors with the colon operator a = 0:2:10; % start at 0, increment by 2, end at 10 disp(a) b = 0:5; % by default, increment by 1 disp(b) c = 0:-1:-5; disp(c) 0 2 4 6 8 10 0 1 2 3 4 5 0 -1 -2 -3 -4 -5

17. % Create row vectors with linspace and logspace x = linspace(0,1,5); % 5 values: 0 through 1 disp(x) y = logspace(0,4,5); % 5 values: 10^0 through 10^4 disp(y) 0 0.2500 0.5000 0.7500 1.0000 1 10 100 1000 10000

18. Exercise Hints: zeros()linspace()logspace()

19. % Vector input to built-in mathematical function x = linspace(0,pi,5); disp(x) y = sin(x); % because x is a vector, sin produces a vector disp(y) 0 0.7854 1.5708 2.3562 3.1416 0 0.7071 1.0000 0.7071 0.0000

20. % Basic plot x = linspace(0,4,41); y = sqrt(x); figure(1) plot(x,y,'-b') axis([0 4 0 2]) saveas(1,'basic','png')

21. % Bigger font size and thicker lines x = linspace(0,4,41); y = sqrt(x); figure(2); plot(x,y,'-b') axis([0 4 0 2]) set(gca,'FontSize',24) set(findobj(2,'LineWidth',0.5),'LineWidth',2) % thick lines saveas(2,'better','png')

22. Exercise Create a plot of the squaring function (). Experiment with different ranges for the axes. For example, you could start with: axis([0 2 0 4]) For this exercise, you needn’t worry about appearance. In other words, you don’t have to set font size or line thickness. Hint. Recall that we plotted square-root like this: x = linspace(0,4,41); y = sqrt(x); figure(2); plot(x,y,'-b') axis([0 4 0 2])

23. Color Specifiers

24. Line Style Specifiers

25. Exercise Create a plot of the common logarithm (base 10 logarithm), . In MATLAB the common logarithm function is log10. Experiment with using different line style specifiers and different colors. Hint. Recall that we plotted square-root like this: x = linspace(0,4,41); y = sqrt(x); figure(2); plot(x,y,'-b') axis([0 4 0 2])

26. % Two curves x = linspace(0,4,41); y = sqrt(x); z = x./2; figure(5); plot(x,y,'-k',x,z,'--b') % 2 curves on same axes axis([0 4 0 2]) set(gca,'FontSize',24) set(findobj(5,'LineWidth',0.5),'LineWidth',2) saveas(5,'curves','png')

27. Using an Index to Address Elements of an Array In the C/C++ programming language, an index starts at 0 and elements of an array are addressed with square brackets [∙]: 8 2 -3 7 -1 x[0] x[1] x[2] x[3] x[4] ↑ ↑ ↑ ↑ ↑ In MATLAB, an index starts at 1 and elements of an array are addressed with parentheses (∙): 8 2 -3 7 -1 x(1) x(2) x(3) x(4) x(5) ↑ ↑ ↑ ↑ ↑

28. Square Brackets in MATLAB In MATLAB, square brackets [∙]are used for building arrays, such as vectors, matrices, and three-dimensional arrays. For example, x = [1 2 3]; y = [4 5 6]; z = [x y]; % concatenate row vectors disp(z) 1 2 3 4 5 6

29. % Indices (spelling lesson: 1 index, 2 or more indices) x = zeros(1,5); x(1) = 8; % change element with index 1 (first element) disp(x) x(2:5) = 7; % change elements having indices 2 through 5 disp(x) y = 1:4; x(2:5) = y; disp(x) 8 0 0 0 0 8 7 7 7 7 8 1 2 3 4

30. Exercise