INTRODUCTION TO MATLAB by. Introduction to Matlab

Transcription

1 INTRODUCTION TO MATLAB by Mohamed Hussein Lecture 5 Introduction to Matlab More on XY Plotting Other Types of Plotting 3D Plot (XYZ Plotting)

2 More on XY Plotting Other XY plotting commands are axis ([xmin xmax ymin ymax]) - sets the minimum and maximum limits of x & y axes fplot( fhandle, [xmin xmax ]) - Performs a plotting based on a given function which is handle by fhandle plot (y) - Plot the value of y against its indices or plots the imaginary values against real values if y having complex values More on XY Plotting (cont.) The graph y = 3x 3 5x 2 + 2x -10 can be plotted using the following two lines of commands >> y (3 *x^3 5 *x^2 + 2 *x 10) >> fplot (y, [-10 10]) We can also plot a data against its indices using plot (y) >> y = [ ]; plot (y) or imaginary numbers against real number >> y = [-2-2i -1-i 0 1+ i 2+2i ]; plot (y)

3 More on Plot Enhancement Beside changing the lines color and marking, labelling the plot axes etc., there are more commands that can help user producing presentable figure gtext ( text ) - place the text at mouse clicked position text (x,y, text ) - place the text at coordinates x,y legend ( legtxt1, legtxt2, ) - creates legend text for each graph s line subplot (m,n,p) - divide a Figure windows into an array of m n plots, p is the position of the subplot within the plot array figure (no.) - creates or bring into focus Figure with the specified number. More on XY Plotting (cont.) Try the followings: >> t = [0:100]; >> x =10 * (1 exp (-t /15 )); y = 12*(1-exp(-t /6)); z= 20*(1-exp(-t /8)); >> figure (5) >> subplot (2,3, 1); plot (t, x) >> subplot (2,3,3); plot (t, y) >> subplot (2,3,5); plot (t, z)

4 Exercise Based on the previous example, write a script to produce the following plot Other Types of Plotting There some specilaised plot command type cater various type of graphs bar (x,y) - creates a bar chart of y versus x loglog (x,y) - creates a plot of log y versus log x plotyy (x1,y1,x2,y2) - creates a plot with two y axes, y1 axis on the left and y2 axis on the right polar (θ, r, type ) - creates a polar plot from the polar coordinates θ and r. type specifies type of data markers and colors.

5 Other Types of Plotting (cont.) There some specilaised plot command type cater various type of graphs semilog x(x,y) - creates a plot of of y versus log x semilogy (x,y) - creates a plot of log y versus x stairs (x, y) - creates a stairs plot of y versus x stem (x, y) - creates a stem plot of y versus x Polar Plot and 3D Plot Try the followings: >> freq = [0 :0.2 :100]; >> gain = 1./ sqrt ( ((1 + (0.5 * freq).^2).* (1 + (0.25 * freq).^2))); >> phase = -( atan (0.5 * freq )) (atan ( 0.25 * freq)); >> polar (phase, gain, r - - ) >> t = 0: pi /50 : 10 * pi; >> plot3 (sin (t), cos (t), t) >> title ( Helix Plot ), xlabel ( sine t ), ylabel ( cosine (t ) ), zlabel ( t )

6 Polar Plot and 3D Plot Mesh and Surface Plots Matlab defines a mesh surface by the z- coordinates of points above a rectangular grid in the x-y plane. The result looks like a fishing net with the knots at the data points. Mesh plots are useful for visualising large matrices or plotting functions of two variables.

7 Mesh and Surface Plots (cont.) The first step in generating the mesh plot of a function, z = f(x, y), is to generate X and Y matrices consisting of repeated rows and columns, respectively, for some range of the variables x and y. Matlab provides the function meshrig. [X,Y]=meshgrid(x,y) creates matrix X, whose rows are copies of the vector x, and matrix Y, whose columns are copies of the vector y. Mesh and Surface Plots (cont.) >> x = -7.5:0.5:7.5 >> y = x; >> [X,Y] = meshgrid(x,y); X and Y are a pair of matrices representing a rectangular grid of points in the x-y plane. >> r = sqrt(x.^2 + Y.^2) + eps; >> Z = sin(r)./r; The matrix r contains the radius of each point in [X,Y] - the distance from each point to the centre of the matrix, which is the origin (0, 0). Adding eps prevents dividing by zero.

8 >> mesh(x,y,z) Mesh and Surface Plots (cont.) A surface plot looks like the mesh plot, except that the spaces between the lines (called patches) are filled in. Matlab provides the function surf.

9 >> surf(x,y,z) Peaks Function Matlab provides the function peaks. Peaks is a function of two variables, obtained by translating and scaling Gaussian distributions, which is useful for demonstrating mesh, surf, pcolor, and contour.

10 >> mesh(peaks) >> title('mesh plot of the peaks function') >> [x,y,z] = peaks; >> contour(x,y,z,20) % generate 20 2-D contours

11 >> [x,y,z] = peaks; >> contour3(x,y,z,20) % generate 20 3-D contours >> axis([ ]) % adjust scale

12 Another interesting way to visualise contour information is to use color for representing height. The pcolor function maps heights to a set of colours and presents the same information as the contour plot at the same scale. >> z = peaks; >> pcolor(z) >> title('peaks: pseudocolour plot')

13 We can also combine pseudocolour and contour plots of the peaks function. >> [x,y,z] = peaks; >> colormap(hot) % select a set of colours >> pcolor(x,y,z) % generate the plot >> shading flat % remove the grid lines >> hold on >> contour(x,y,z,20,'k') % plot 20 contour lines >> hold off Combined pseudocolour and contour plots

14 >> mesh(peaks(20) + 7) % coarse mesh, shifted up; >> hold on >> pcolor(peaks(20)) % add a pseudocolour plot >> hold off >> title('mesh with hidden on') >> hidden off >> title('mesh with hidden off')

15 >> colormap(gray) >> surfl(peaks), shading interp