Lab of COMP 406 Introduction of Matlab (II) Graphics and Visualization

Lab of COMP 406 Introduction of Matlab (II) Graphics and Visualization Teaching Assistant: Pei-Yuan Zhou Contact: cspyzhou@comp.polyu.edu.hk Lab 2: 19 Sep., 2014 1

Review Find the Matlab under the folder 1. Y:\Win32\Matlab\R2012a 2. Double click it and open Matlab Or open Matlab on your computer 1. Click 'Start' 2. Click 'Run' 3. Input 'nalwin32' 4. Find the Matlab under the folder /Network Application Packages/Statistical & Mathematical/Matlab 2

Review Matrix and Array >>a = [1 2 3 4] / a=[1,2,3,4] >> a = [1 2 3; 4 5 6; 7 8 10] >>z = zeros(5,1) >>a / inv(a) / a*a / a.*a / a.^3 / a^3 Calling functions >>c=sin(a) >>max(a) % a is a vector Save workspace variables >>save myfile.mat >>load myfile.mat 3

Outline -Graphics and Visualization 2-D Plots 3-D Plots Sub-Plots Line Plots of a Chirp, Bar Plot of a Bell Shaped Curve Stairstep Plot of a Sine Wave, Errorbar Plot Stem Plot Scatter Plot Mesh, Surface (Surfacel), Contour, Quiverm Slice 4

Outline 2-D Plots 3-D Plots Sub-Plots Line Plots of a Chirp, Bar Plot of a Bell Shaped Curve Stairstep Plot of a Sine Wave, Errorbar Plot Stem Plot Scatter Plot Mesh, Surface (Surfacel), Contour, Quiverm Slice 5

Line Plots To create two-dimensional line plots, use the plot function. For example, plot the value of the sine function from 0 to 2π: x = linspace(0,2*pi); % 100 points from 0 to 2pi y = sin (x); % calculate sin(x) plot(x,y); 6

Line Plots X=linspace(0,2*pi); % 100 points from 0 to 2pi plot(x,sin(x),x,cos(x),x,xin(x)+cos(x)); % multiple lines 7

Line Plots x = 0:pi/100:2*pi; To add plots to an existing figure, use hold on. Until you use hold off or close the window, all plots appear in the current figure window. % from 0 to 2pi, the interval between two points is pi/100 y = sin(x); plot(x,y); hold on y2 = cos(x); plot(x,y2,'r--') legend('sin','cos') xlabel('x') title('plot of the Sine and Cosine Function') 8

Line Plots You can label the axes and add a title. title legend label 9

Line Plots By adding a third input argument to the plot function, you can plot the same variables using a green star line. x = 0:0.05:7; y=log(x); plot(x,y,'g*') xlabel('x') ylabel( log(x)') title('plot of the log Function') 10

Line Plots of a Chirp x = 0:0.05:5; y = sin(x.^2); plot(x,y); xlabel('time') ylabel('amplitude') plot(sin((0:0.05:5).^2)). 11

Bar Plot of a Bell Shaped Curve x = -3:0.2:3; bar(x,exp(-x.*x)); 12

Stairstep Plot of a Sine Wave x = 0:0.25:10; stairs(x,sin(x)); 13

Errorbar Plot x = -2:0.1:2; y = erf(x); e = rand(size(x))/10; errorbar(x,y,e); The errorbar function draws a line plot of x and y values and superimposes on each observation a vertical error bar 14

x = 0:0.1:4; y = sin(x.^2).*exp(-x); stem(x,y) Stem Plot 15

Scatter Plot x = -10:0.5:10; y = x.^3; scatter(x,y,'bx'); ylabel('x-axis'); xlabel('y-axis'); doc line, doc scatter, doc line_props 16

Exercise Plot two functions, cos(x)+sin(x) and exp(-x) for variable x in one figure. The value of x is from 0 to pi, and the interval between two points is 0.1. Use line format --* for function 1, and --o for function 2. Provide the figure a title, legends of two functions, and Labels for x-axis and y-axis 17

Exercise - answer x=0:0.1:2*pi; y1=sin(x)+cos(x); y2=exp(-x); plot(x,y1,'--*',x,y2,'--o'); xlabel('time'); ylabel('value of sin(x)+cos(x) and exp(-x)'); title('function Plots of "sin(x)+cos(x)" and "exp(-x)"'); legend('sin(x)+cos(x)','exp(-x)'); 18

Outline 2-D Plots 3-D Plots Sub-Plots Line Plots of a Chirp, Bar Plot of a Bell Shaped Curve Stairstep Plot of a Sine Wave, Errorbar Plot Stem Plot Scatter Plot Mesh, Surface (Surfacel), Contour, Quiverm Slice 19

3-D Plots Three-dimensional plots typically display a surface defined by a function in two variables, z = f (x,y). To evaluate z, first create a set of (x,y) points over the domain of the function using meshgrid. Then, create a surface plot. [X,Y] = meshgrid(-2:.2:2); Z = X.* exp(-x.^2 - Y.^2); surf(x,y,z) / mesh(x,y,z) Both the surf function and its companion mesh display surfaces in three dimensions. surf displays both the connecting lines and the faces of the surface in color. mesh produces wireframe surfaces that color only the lines connecting the defining points. 20

Mesh Plot of Peaks z = peaks(25); mesh(z); colormap(hsv); peaks is a function to produce a 25-by-25 matrix obtained by translating and scaling Gaussian distributions, which is useful for demonstrating MESH, SURF, PCOLOR, CONTOUR, etc mesh(z) plot the colored parametrix mesh defined by matrix z. colormap is a function that sets the colormap property of a figure. See also hsv, caxis, spinmap, brighten, rgbplot, figure, colormapeditor. 21

Mesh Plot of Peaks z = peaks(25); mesh(z); colormap(hsv); 22

Surface Plot of Peaks z = peaks(25); surf(z); colormap(jet); 23

Surface plot with shading of peaks z = peaks(25); surfl(z); shading interp; colormap(pink); 24

Contour Plot of Peaks z = peaks(25); contour(z,16); colormap(hsv); contour(z) is a contour plot of matrix Z treating the values in Z as heights above a plane. * contour(z,n), draws N contour lines, overriding the automatic value. 25

Quiver x = -2:.2:2; y = -1:.2:1; [xx,yy] = meshgrid(x,y); % meshgrid replicates the grid vectors x and y to produce the coordinates of a rectangular grid (xx,yy) zz = xx.*exp(-xx.^2-yy.^2); [px,py] = gradient(zz); quiver(x,y,px,py,2); Plots velocity vectors as arrows with components (px,py) at the points (x,y). *And automatically scales the arrows to fit within the grid and then stretches them by 2. Use 0 to plot the arrows without the automatic scaling. 26

Outline 2-D Plots 3-D Plots Sub-Plots Line Plots of a Chirp, Bar Plot of a Bell Shaped Curve Stairstep Plot of a Sine Wave, Errorbar Plot Stem Plot Scatter Plot Mesh, Surface (Surfacel), Contour, Quiverm Slice 28

[X,Y] = meshgrid(-2:.2:2); Subplot Z = X.* exp(-x.^2 - Y.^2);%3D function You can display multiple plots in different subregions of the same window using the subplot function. subplot(2,2,1); mesh(x); title('x'); % the plot for x-axis subplot(2,2,2); mesh(y); title('y'); % the plot for y-axis subplot(2,2,3); mesh(z); title('z'); % the plot for z-axis subplot(2,2,4); mesh(x,y,z); title('x,y,z'); % the plot for the 3D function The first two inputs to the subplot function indicate the number of plots in each row and column. The third input specifies which plot is active. 29

Subplot 30

Exercise t = 0:pi/2:4*pi; [X,Y,Z] = cylinder(5*sin(t)); Plot this 3-D function into four subplots for each axis and the function. 31

Answer t = 0:pi/2:4*pi; [X,Y,Z] = cylinder(5*sin(t)); subplot(2,2,1); mesh(x); title('x'); subplot(2,2,2); mesh(y); title('y'); subplot(2,2,3); mesh(z); title('z'); subplot(2,2,4); mesh(x,y,z); title('x,y,z'); 32

Try this example Plot six functions in one window/figure, and give the title of them x=[0,2pi], y1=sin(x); y2=cos(x); y3=sin(x)+cos(x); y4=exp(x); y5=log(x); y6=x.^3 33

Answer x=0:pi/10:2*pi; y1=sin(x); y2=cos(x); y3=sin(x)+cos(x); y4=exp(-x); y5=log(x); y6=x.^(1/3); subplot(2,3,1); plot(y1); title('sin(x)'); subplot(2,3,2); plot(y2); title('cos(x)'); subplot(2,3,3); plot(y3); title('sin(x)+cos(x)'); subplot(2,3,4); plot(y4); title('exp(x)'); subplot(2,3,5); plot(y5); title('log(x)'); subplot(2,3,6); plot(y6); title('x^1^/^3'); 34

Ex 1 Please add variable A and B to Matlab workspace Create A and B. What s the transpose of A? What s the result of (A+B+10)/3? Concatenate A and B horizontally, then vertically. Subtract the 2nd row vector from A. Please clear A and B from Matlab workspace. 35

Ex 1 Please add variable A and B to Matlab workspace A=[1 2 3 4; 5 6 7 8; 11 12 13 14; 15 16 17 18]; B=A+4*j What s the transpose of A? A What s the result of (A+B+10)/3? (A + B + 10)/3 Concatenate A and B horizontally, then vertically. [A, B] [A;B] Subtract the 2nd row vector from A. A(2, :); Please clear A and B from Matlab workspace. clear 36

Ex 2 Make some simple plots: y = cos(x), x [0, 2π] Try to make it smoother by making the step smaller Label X-axis and Y-axis Add a title Add a legend 37

Ex 2 Make some simple plots: y = cos(x), x [0, 2π] x = 0:2*pi; y = cos(x); plot(x,y) Try to make it smoother by making the step smaller x = 0:0.1: 2*pi; y = cos(x); plot(x,y) Add x-axis label x-axis and y-axis label y-axis xlabel( x-axis ) ; ylabel( Y-axis ); Add a title title( The plot for function cos(x) ); Add a legend legend( cos(x) ); 38

Ex 2 39

Ex 3 Make a more complicated plot y = e -0.4x sin x, x [0,2π] Label the axes, create a nifty title and legend. Type help plot and use the information you get to make another plot of just the unconnected data points. 40

Ex 3 Make a more complicated plot: y = e -0.4x sin x, x [0,2π] x = 0:0.01:2*pi; y = exp(-0.4*x).*sin(x); plot(x,y) Label the axes, create a nifty title and legend. xlabel( x-axis ); ylabel( y-axis ) title( y=exp(-0.4*x)sin(x) ); legend( y=exp(-0.4*x)sin(x) ); Type help plot and use the information you get to make another plot of just the unconnected data points. plot(x, y, : ) / plot (x,y, -- ) 41

Ex 3 Make a 3-dimensional plot of the helix x = sin t, y = cos t, z = t. Hint: Create the vectors t, x, y, and z, then use the command plot3(x,y,z). t = 0:0.01:2*pi; x = sin(t); y = cos(t); z = t; plot3(x, y, z); grid on; 42

What We have Learned? 1. 2-D Plot 2. 3-D Plot 3. Sub-Plot 43

Contact: cspyzhou@comp.polyu.edu.hk Lab 2: 19 Sep., 2014 44