Introduction to Matlab Programming with Applications

Size: px

Start display at page:

Download "Introduction to Matlab Programming with Applications"

さわいさし
5 years ago
Views:

1 Histogram ˆ The function hist(x) or histogram creates a histogram of x. ˆ By default, elements in x are organized into equally spaced bins between min(x) and max(x). ˆ You can specify the number of bins. clear; clc; 3 n = e5; nbins = e; 4 subplot(,, ); histogram(rand(, n), nbins) 5 subplot(,, ); histogram(randn(, n), nbins) Since R4a. Zheng-Liang Lu 3 / 57

2 Zheng-Liang Lu 4 / 57

3 Polar Coordinate Plot ˆ The function polar(θ, r) creates a polar coordinate plot of the angle θ versus the radius r. clear; clc; close all; 3 theta = :. : * pi; 4 subplot(,, ); 5 rho = cos(3 * theta); 6 polar(theta, rho, '--r'); 7 subplot(,, ); 8 rho = cos(theta).* sin(theta); 9 polar(theta, rho, '--b'); ˆ Try cartpol. Zheng-Liang Lu 5 / 57

4 Zheng-Liang Lu 6 / 57

5 Contours ˆ A contour plot displays isolines of Z by calling contour(x, Y, Z). ˆ Instead of using nested loops, you may use the function meshgrid which transforms the domain specified by vectors x and y into matrices X and Y. ˆ Then X and Y can be used for the evaluation of functions of f (X, Y ) by vectorization. clear; clc; close all; 3 x = linspace(- * pi, * pi); 4 y = linspace(, 4 * pi); 5 [X, Y] = meshgrid(x, y); 6 Z = sin(x) + cos(y); 7 figure; contour(x, Y, Z, 'showtext', 'on'); You may try contourf. Zheng-Liang Lu 7 / 57

6 Zheng-Liang Lu 8 / 57

7 Quiver (Velocity) Plot ˆ The function quiver(x, y, u, v) plots a vector (u, v) at the coordinate (x, y). clear; clc; close all; 3 [x, y, z] = peaks(); 4 [u, v] = gradient(z); 5 figure; hold on; grid on; 6 contour(x, y, z, ); 7 quiver(x, y, u, v); Zheng-Liang Lu 9 / 57

8 Zheng-Liang Lu 3 / 57

9 Mesh Plot ˆ The function mesh(x, Y, Z) draws a wireframe mesh with the color proportional to surface height, determined by Z. clear; clc; close all; 3 x = linspace(-,, 3); 4 y = x + pi / ; 5 z = zeros(length(x), length(y)); 6 for i = : length(x) 7 for j = : length(y) 8 z(i, j) = cos(x(i)) * sin(y(j)); 9 end end figure; mesh(x, y, z'); Zheng-Liang Lu 3 / 57

10 Zheng-Liang Lu 3 / 57

11 Surface Plot ˆ The function surf(x, Y, Z) plots the colored surface. ˆ Try meshz, meshc, surfc, and waterfall. ˆ Consider this equation z = xe (x +y ). clear; clc; close all; 3 x = linspace(-,, 5); 4 y = linspace(-,, 5); 5 [X, Y] = meshgrid(x, y); % form all x-y pairs 6 Z = X.* exp(-x.ˆ - Y.ˆ ); 7 surf(x, Y, Z); Zheng-Liang Lu 33 / 57

12 Zheng-Liang Lu 34 / 57

13 Exercise ˆ Consider sinc(r) = sin(r) R. ˆ There is a singularity at R =, which can be removed by replacing a zero with eps =.4 6. clear; clc; close all; 3 [X, Y] = meshgrid(linspace(-,, 5)); 4 R = sqrt(x.ˆ + Y.ˆ ); 5 R(R == ) = eps; % avoid the singularity 6 Z = sin(r)./ R; 7 surf(x, Y, Z); Zheng-Liang Lu 35 / 57

14 Zheng-Liang Lu 36 / 57

15 3D Line Plot ˆ The function plot3(x, y, z) plots a curve in 3-dimensional coordinate through the points (x, y, z). ˆ For example, clear; clc; close all; 3 figure; hold on; axis equal; grid on; 4 t = linspace(, * pi, ); 5 plot3(t.* sin(t), t.* cos(t), t); 6 plot3(t.* sin(t), t.* cos(t), -t, 'r'); Zheng-Liang Lu 37 / 57

16 Zheng-Liang Lu 38 / 57

17 Quiver in 3D ˆ The function quiver3(x, y, z, u, v, w) plots the vector (u, v, w) at the point (x, y, z). ˆ For example, clear; clc; close all; 3 figure; hold on; 4 x = - :. : ; 5 [X, Y] = meshgrid(x); 6 Z = X.* exp(-x.ˆ - Y.ˆ ); 7 [U, V, W] = surfnorm(x, Y, Z); 8 quiver3(x, Y, Z, U, V, W); 9 surf(x, Y, Z); grid on; Zheng-Liang Lu 39 / 57

18 Zheng-Liang Lu 4 / 57

19 More 3D Plots 3 ˆ Try pie3, stem3, fill3, polar3, bar3, ezmesh, and ezsurf. 3 See http: // Zheng-Liang Lu 4 / 57

20 Interpolation 5 ˆ Interpolation is a method of constructing new data points within the range of a discrete set of known data points. ˆ The function interp(x, v, xq) returns interpolated values of a D function at specific query points. 4 ˆ Optional parameters: nearest, linear, spline, pchip, and extrap. ˆ Note that x must be in ascending order. ˆ Try interp, interp3, interpn, and interpft. 4 See 5 See Zheng-Liang Lu 4 / 57

21 Example clear; clc; close all; 3 x = : 4 * pi; 4 y = sin(x).* exp(-x / 5); 5 xi = :. : 4 * pi; 6 y = interp(x, y, xi, 'nearest'); 7 y = interp(x, y, xi, 'linear'); 8 y3 = interp(x, y, xi, 'pchip'); 9 y4 = interp(x, y, xi, 'spline'); plot(x, y, 'o', xi, y, xi, y, xi, y3, xi, y4); legend('original', 'Nearest', 'Linear', 'Pchip',... 'Spline'); Zheng-Liang Lu 43 / 57

22 .8.6 Original Nearest Linear Pchip Spline Zheng-Liang Lu 44 / 57

23 Exercise 6 Original Spline Zheng-Liang Lu 45 / 57

24 clear; clc; close all; 3 x = [ 4 3 ]; 4 y = [ 4 5 ]; 5 n = length(x) - 6 t = : n; 7 tq = linspace(, n, ); 8 xx = interp(t, x, tq, 'spline'); 9 yy = interp(t, y, tq, 'spline'); plot(x, y, 'o', xx, yy, '-'); grid on; xlabel('x'); ylabel('y'); legend('spot', 'Spline'); ˆ You may try various interpolation methods. Zheng-Liang Lu 46 / 57

25 Surface Reconstruction ˆ In practice, we collect the data from experiments. ˆ One posterior analysis on these data points is to find the possible curves or surfaces to fit the observed data points. ˆ Let (x, y, z) be the data points. ˆ Then the function zq = griddata(x, y, z, xq, yq) interpolates the data points for the region specified by (xq, yq) to reconstructs the surface. Zheng-Liang Lu 47 / 57

26 Example clear; clc; close all; 3 x = 6 * rand(, ) - 3; 4 y = 6 * rand(, ) - 3; 5 z = peaks(x, y); % sample points in total 6 [xq, yq] = meshgrid(x, y); 7 zq = griddata(x, y, z, xq, yq, 'cubic'); 8 mesh(xq, yq, zq); hold on; 9 plot3(x, y, z, '.', 'markersize', 6); axis tight; ˆ Note that the resulting figure may be different when the program runs. Zheng-Liang Lu 48 / 57

27 Zheng-Liang Lu 49 / 57

28 3D Graph Viewpoint Specification ˆ The function view(az, el) sets the view angle from which an observer sees the current 3D plot. ˆ az: azimuth (horizontal) rotation ˆ el: vertical elevation ˆ Try some predetermined values for view. ˆ Also, you can use the button Rotate 3D of the figure. clear; clc; 3 peaks; 4 view([6, -5]); % degree 5 colorbar; % appends a colorbar to the current axes 6 colormap spring; % change the colormap Zheng-Liang Lu 5 / 57

29 Peaks y x -6 Zheng-Liang Lu 5 / 57

30 colormap 6 6 The colormap is parula as default since R5a. Zheng-Liang Lu 5 / 57

31 Animation ˆ Animation is a process of creating motion and shape change illusion by means of the rapid display of a sequence of static images that minimally differ from each other. ˆ Images are displayed in a rapid succession, usually 4, 5, 3, or 6 frames per second (aka fps). ˆ You may use the following functions for animation: drawnow comet comet3 movie getframe imframe frameim Flush pending graphics events immediately Make a -D comet plot Make a 3-D comet plot Play recorded movie frames Capture movie frames Convert image to movie frames Return image data associated with movie frames Zheng-Liang Lu 53 / 57

32 Example clear; clc; close all; 3 x = linspace(, 8 * pi, ); 4 figure; 5 h = plot(x, sin(x).* exp(-x / 5)); 6 axis([-inf inf - ]); grid on; 7 for i = : 5 8 y = sin(x - i / ).* exp(-x / 5); 9 set(h, 'ydata', y); drawnow; end Zheng-Liang Lu 54 / 57

33 Example clear; clc; close all; 3 r = linspace(, 4, 3); t = linspace(, * pi, 3); 4 [rr, tt] = meshgrid(r, t); 5 xx = rr.* cos(tt); yy = rr.* sin(tt); 6 zz = peaks(xx, yy); 7 n = ; 8 scale = cos(linspace(, * pi, n)); 9 figure('renderer', 'zbuffer'); for i = : n surf(xx, yy, zz * scale(i)); axis([-inf inf -inf inf ]); 3 M(i) = getframe; 4 end 5 cla 6 movie(m, 5); Zheng-Liang Lu 55 / 57

34 More Demonstrations for Animation ˆ Try lorenz, truss, and travel. Zheng-Liang Lu 56 / 57

35 GUI Design Tutorial ˆ See Prof. Roger Chang s slides. Zheng-Liang Lu 57 / 57

web05.dvi

web05.dvi 5 3 copyright c Tatsuya Kitamura / All rights reserved. 57 5 5. 3 MATLAB 3 line plot plot3 MAT plot Z Octave gnuplot splot gsplot OCT 3 splot plot3 MAT plot 5. 5. 5.3 plot 5. >> t=:pi/:*pi; >> plot3(t.*cos(t),t.*sin(t),t)