matlab_intro_part3

Exercise 23. Plot the function y = sin(x) + x − x cos(x) in two separate figures for the intervals: 0 < x < 30 and −100 < x < 100. Add a title and axes description.
produces the dashed red line. The third argument of plot specifies the color (optional) and the line style. Table ?? shows a few possibilities, help plot shows all. To add a title, grid and to label the axes, one uses:
Symbol
r g b y m c k
Color
red green blue yellow magenta cyan black
Symbol
., o *
x, + -: -.
Line style
point, circle star
x-mark, plus solid line dash line dot line
−0.4
−0.6
−0.8
−1
0
0.5
1
1.5
2
2.5
Hale Waihona Puke 3The solid line is used by plot by default. It is possible to change the style and the color, e.g.:
>> x = 0:04:3; y = sin(5*x); >> plot(x,y,’r--’)
>> x = 0:10; >> y = 2.^x; >> plot(x,y) >> semilogy(x,y)
% this is the same as y = [1 2 4 8 16 32 64 128 256 512 1024] % to get a graphic representation % to make the y-axis logarithmic
4.2 Several functions in one figure
184-188 197-201
There are different ways to draw several functions in the same figure. The first one is with the command hold on. After this command, all functions will be plotted in the same figure until the command hold off is used. When a number of functions is plotted in a figure, it is useful to use different symbols and colors. An example is:
A second method to display a few functions in one figure is to plot several functions at the same time. The next commands will produce the same output as the commands in the previous example:
>> title(’Function y = sin(5*x)’);
>> xlabel(’x-axis’);
>> ylabel(’y-axis’);
>> grid
% remove grid by calling grid off
Exercise 22. Make a plot connecting the coordinates: (2, 6), (2.5, 18), (5, 17.5), (4.2, 12.5) and (2,12) by a line.
4 Visualization
Matlab can be used to visualize the results of an experiment. Therefore, you should define variables, each of them containing all values of one parameter to plot.
Exercise 24. Plot a circle with the radius r = 2, knowing that the parametric equation of a circle is [x(t), y(t)] = [r cos(t), r sin(t)] for t = [0, 2π].
>> x1 = 1:.1:3.1; y1 = sin(x1); >> plot(x1,y1,’md’); >> x2 = 1:.3:3.1; y2 = sin(-x2+pi/3); >> hold on >> plot(x2,y2,’k*-.’) >> plot(x1,y1,’m-’) >> hold off
4.1 Simple plots
With the command plot, a graphical display can be made. For a vector y, plot(y) draws the points [1, y(1)], 184 [2, y(2)], . . ., [n, y(n)] and connects them with a straight line. plot(x,y) does the same for the points
[x(1), y(1)], [x(2), y(2)], . . . , [x(n), y(n)]. Note that x and y have to be both either row or column vectors of the same length (i.e. the number of elements).
% coarse sampling
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.5
1
1.5
2
2.5
3
>> n = 25; >> x = 0:1/n:3; >> y = sin(5*x); >> plot(x,y)
% good sampling
1
0.8
0.6
0.4
0.2
0
−0.2
dash-dot line
Table 5: Plot colors and styles.
76-79
Exercise 17. Given the vectors x = [1 3 7], y = [2 4 2] and the matrices A = [3 1 6; 5 2 7], B = [1 4; 7 8; 2 2], determine which of the following statements will correctly execute (and if not, try to understand why) and provide the result:
Exercise 19. Let A = ones(6) + eye(6). Normalize columns of the matrix A so that all columns of the resulting matrix, say B, have the Euclidean norm (length) equal to 1. Then, find the angles between consecutive columns of the matrix B.
• x+y • x+A • x +y • A − [x y ] • [x; y] + A
• [x; y ] • [x; y] • A−3 • A+B • B +A
• B∗A • A. ∗ B • A.∗B • 2∗B • 2. ∗ B
• B./x • B./[x x ] • 2/A • ones(1, 3) ∗ A • ones(1, 3) ∗ B
The commands loglog, semilogx and semilogy are similar to plot, except that they use either one or two logarithmic axes.
Exercise 21. Type the following commands after predicting the result:
Exercise 18. Let A be a random 5 × 5 matrix, and b a random 5 × 1 vector. Given that Ax = b, try to find x (look at Table ??). Explain what is the difference between the operators \, / and the command inv. Having found x, check whether Ax − b is close to a zero vector.