Scientific Computing with MATLAB 2. Graphics for Research & Publication

Transcription

1 Scientific Computing with MATLAB 2. Graphics for Research & Publication Dra. K.-Y. Daisy Fan Department of Computer Science Cornell University Ithaca, NY, USA UNAM IIM 2012

2 Monte Carlo Approximation of Throw N darts L L/2 Sq. area = N = L L Circle area = N in = L 2 /4 = 4 N in / N 3

3 Monte Carlo with N darts on L-by-L board N= ; L= ; hits= 0; for k = 1:N % Throw kth dart x = rand(1)*l L/2; y = rand(1)*l L/2; % Count it if it is in the circle if sqrt(x^2+y^2) <= L/2 hits = hits + 1; end end mypi = 4*hits/N; 4

4 2-d array: matrix r c An array is a named collection of like data organized into rows and columns A 2-d array is a table, called a matrix Two indices identify the position of a value in a matrix, e.g., mat(r,c) refers to component in row r, column c of matrix mat Array index starts at 1 Rectangular: all rows have the same #of columns 5

5 Creating a matrix Built-in functions: ones, zeros, rand E.g., g, zeros(2,3) (,)gives a 2-by-3 matrix of 0s Build a matrix using square brackets, [ ], but the dimension must match up: [x y] puts y to the right of x [x; y] puts y below x [4 0 3; 5 1 9] creates the matrix [4 0 3; ones(1,3)] gives [4 0 3; ones(3,1)] doesn t work

6 What will A be? A= [0 0] A= [A ones(2,1)] A= [ ; A A] 7

7 % Given an nr-by-nc matrix M. % What is A? for r= 1: nr for c= 1: nc A(c,r)= M(r,c); end end 9

8 X-Y Plot The basic command is plot(a,b) which draws a line connecting the points (a(1),b(1)),(1) (a(2),b(2)),(2), (a(n),b(n)), ( ) )) where n is the length of vectors a and b. Can add format specifications. E.g., plot(a,b, *r ) draws red asterisks (*) at the data points instead of draws red asterisks (*) at the data points instead of using a line 11

9 Color Options White Black Red Blue Green Yellow Magenta Cyan w k r b g y m c 12

10 Making an x-y plot a= [ ]; % x-coords b= [ ]; % y-coords plot(a, b, -* ) x-values (a vector) y-values (a vector) 6 5 Line/marker format

11 Making a figure with plot figure % start a new graphics window hold on % hold subsequent plot commands in current axes plot(a,b) plot(c,d) hold off % subsequent plot command refreshes axes-- % erase previous items close % close graphics window 14

12 Trajectory of a projectile golf ball Without air resistance (drag), the trajectory of a golf ball in flight is a parabola. What is the effect of drag? Relevant equations for simulating the golf ball in flight: 15

13 Trajectory of a projectile golf ball Without air resistance (drag), the trajectory of a golf ball in flight is a parabola. What is the effect of drag? Relevant equations for simulating the golf ball in flight: 16

14 Trajectory of a projectile golf ball Without air resistance (drag), the trajectory of a golf ball in flight is a parabola. What is the effect of drag? Relevant equations for simulating the golf ball in flight: 17

15 Simulate a golf ball in flight Simulation begins at t = 0 and position (0,0) Simulation ends when the ball lands (y 0) or when maximum simulation time is reached Plot the trajectory See the given file golfball.m for the skeleton program, including given constant and parameters 18

16 Simulate a golf ball in flight Simulation begins at t = 0 and position (0,0) Simulation ends when the ball lands (y 0) or when maximum simulation time is reached Plot the trajectory See the given file golfball.m for the skeleton program, including given constant and parameters 19

17 Simulate flight for different friction coefficient values Modify golfball to show the trajectories in one plot for different values of the friction coefficient: k = 0,.02,,.08 21

18 Some format commands to use with plot close all % close all graphics windows axis equal % same scaling for x, y axes axis off % hide axes axis on % show axes xlabel( text for labeling x-axis ) ylable( text for labeling y-axis ) title( text for plot title at top center ) hold on % hold subsequent plot commands in current axes hold off % subsequent plot command refreshes axes-- % erase previous items 22

19 Draw a single line segment a= 0; % x-coord of pt 1 b= 1; % y-coord of pt 1 c= 5; % x-coord of pt 2 d= 3; % y-coord of pt 2 plot([a c], [b d], -* ) x-values (a vector) y-values (a vector) Line/marker format 23

20 Making an x-y plot with multiple graphs (lines) My graphs graph 1 name graph 2 name 4 a= [ ]; 3.5 b= [ ]; f= [ ]; g= [ ]; plot(a,b,'-*',f,g,'c') legend('graph 1 name', 'graph 2 name') xlabel('x values') ylabel('y values') title('my graphs', 'Fontsize',14) y values x values See also plotcomparison.m 25

21 Simulate flight for different friction coefficient values Modify golfball to show the trajectories in one plot for different values of the friction coefficient: k = 0,.02,,.08 Note: Can create or lengthen a vector, e.g., x = 3.1; % x is scalar 3.1 x(4) = 2; % x is vector [ ] 26

22 Demonstrate commonly used 2-d graphics 27

23 Files for tomorrow: df / UNAM_IIM2012/popMexicoByStates.xlsx A JPEG photo file, color or grayscale 39