University:
Boston University
Course:
CAS MA 511 | Introduction to Analysis I
Academic year:

2019
Views:

58

Pages:

15
Author:

Clint W.

 Line plot  Bar graph  Surface plot  Contour plot  MATLAB tutorial on 2D, 3D visualization tools as well as other graphics packages available in our tutorial series. >> t = 0:pi/100:2*pi; >> y = sin(t); >> plot(t,y) >> xlabel(‘t’); >> ylabel(‘sin(t)’); >> title(‘The plot of t vs sin(t)’); >> y2 = sin(t-0.25); >> y3 = sin(t+0.25); >> plot(t,y,t,y2,t,y3) % make 2D line plot of 3 curves >> legend('sin(t)','sin(t-0.25)','sin(t+0.25',1) Generally, MATLAB’s default graphical settings are adequate which make plotting fairly effortless. For more customized effects, use the get and set commands to change the behavior of specific rendering properties. >> hp1 = plot(1:5) % returns the handle of this line plot >> get(hp1) % to view line plot’s properties and their values >> set(hp1, ‘lineWidth’) % show possible values for lineWidth >> set(hp1, ‘lineWidth’, 2) % change line width of plot to 2 >> gcf % returns current figure handle >> gca % returns current axes handle >> get(gcf) % gets current figure’s property settings >> set(gcf, ‘Name’, ‘My First Plot’) % Figure 1 => Figure 1: My First Plot >> get(gca) % gets the current axes’ property settings >> figure(1) % create/switch to Figure 1 or pop Figure 1 to the front >> clf % clears current figure >> close % close current figure; “close 3” closes Figure 3 >> close all % close all figures >> x = magic(3); % generate data for bar graph >> bar(x) % create bar chart >> grid % add grid for clarity • Many MATLAB utilities are available in both command and function forms. • For this example, both forms produce the same effect: • >> print –djpeg mybar % print as a command • >> print('-djpeg', 'mybar') % print as a function • For this example, the command form yields an unintentional outcome: • >> myfile = 'mybar'; • >> print –djpeg myfile • >> print('-djpeg', myfile) % myfile is defined as a string % as a command, myfile is treated as text % as a function, myfile is treated as a variable % i.e., ‘mybar’ is passed into print • Other frequently used utilities that are available in both forms are: • save, load >> Z = peaks; >> surf(Z) % generate data for plot; peaks returns function values % surface plot of Z Try these commands also: >> shading flat >> shading interp >> shading faceted >> grid off >> axis off >> colorbar >> colormap(‘winter’) >> colormap(‘jet’) >> Z = peaks; >> contour(Z, 20) % contour plot of Z with 20 contours >> contourf(Z, 20); % with color fill >> colormap('hot') % map option >> colorbar % make color bar • Integration of cosine from 0 to π/2. • Use mid-point rule for simplicity. b m a i 1  cos( x)dx    a ih a ( i 1) h m cos( x )dx   cos(a  (i  12 )h)h i 1 mid-point of increment cos(x) h ; % range ; % # of increments ; % increment % integration with for-loop tic m = 100; a = 0; % lower limit of integration b = pi/2; % upper limit of integration h = (b – a)/m; % increment length integral = 0; % initialize integral for i=1:m x = a+(i-0.5)*h; % mid-point of increment i integral = integral + cos(x)*h; end toc h a X(1) = a + h/2 b X(m) = b - h/2 % integration with vector form tic m = 100; a = 0; % lower limit of integration b = pi/2; % upper limit of integration h = (b – a)/m; % increment length x = a+h/2:h:b-h/2; % mid-point of m increments integral = sum(cos(x))*h; toc h a X(1) = a + h/2 b X(m) = b - h/2 % integration with for-loop tic m = 100; % number of intervals a = 0; % lower limit of integration b = pi/2; % upper limit of integration integral = midpoint(a, b, m, @cos); % integrand determined at runtime toc function int = midpoint(a, b, m, fct) h = (b – a)/m; % increment length int = 0; % initialize int for i=1:m x = a+(i-0.5)*h; % mid-point of increment i int = int + fct(x)*h; end end h a X(1) = a + h/2 b X(m) = b - h/2 1. Write a program (with editor) to generate the figure that describe the integration scheme we discussed. (Hint: use plot to plot the cosine curve. Use bar to draw the rectangles that depict the integrated value for each interval. Save as plotIntegral.m 2. Compute the cosine integrals, from 0 to pi/2, using 10 different increment sizes (10, 20, 30, . . . , 100). Plot these 10 values to see how the solution converges to the analytical value of 1. a = 0; b=pi/2; % lower and upper limits of integration m = 8; % number of increments h = (b-a)/m; % increment size x= a+h/2:h:b-h/2; % m mid-points bh = bar(x,cos(x),1,'c'); % make bar chart with bars full width (1) and cyan (‘c’) hold % all plots will be superposed on same figure x = a:h/10:b; % use more points at which to evaluate cosine f = cos(x); % compute cosine at x ph = plot(x,f,'r'); % plots x vs f, in red % Compute integral with different values of m to study convergence for i=1:10 n(i) = 10+(i-1)*10; h = (b-a)/n(i); x = a+h/2:h:b-h/2; integral(i) = sum(cos(x)*h); end figure % create a new figure plot(n, integral)