Computer Programming in MATLAB

Transcription

1 Computer Programming in MATLAB Prof. Dr. İrfan KAYMAZ Engineering Faculty Department of Mechanical Engineering

2 Arrays in MATLAB; Vectors and Matrices Graphing

3 Vector Generation Before graphing plots in MATLAB, different vector generation methods will be presented here: 1. Method clc clear all for i=1:5 A(i)=i; end A 2. Method >> A=1:5 A = A =

4 Vector Generation clc clear all s=0; for i=1:2:7 s=s+1; A(s)=i; end A A = 1. Method >> A=1:2:7 A = 2. Method A=start:increment:end creates row vector x starting with start, counting by increment, ending at or before end.

5 Element-by-element If you want to execute any arithmetic operation element-by-element basis on arrays, 1. Method clc clear all A=[ ]; B=[ ]; s=0; for i=1:length(a) s=s+1; C(s)=A(s)*B(s); end C >> A=[ ]; >> B=[ ]; >> C=A.*B C = 2. Method C =

6 Vector Production The operations are sometimes called array operations, or element-byelement operations because the operations are performed element by element. For example, a.*b results in the following vector (sometimes called the array product): [a(1)*b(1) a(2)*b(2) a(3)*b(3)] a./b gives element-by-element division. Operator Description.* Multiplication./ Right division.\ Left division. ˆ Power

7 Graphing A picture, it is said, is worth a thousand words. MATLAB has a powerful graphics system for presenting and visualizing data, which is reasonably easy to use. Graphs (in 2-D) are drawn with the plot statement.

8 Example 1 Write a MATLAB program that computes the values of the following equation for x varying from 2 to 2 in increments of 1, and then plots the x and y data. y x 2 9x 20 x=1:20; y=x.^2-9*x-20; plot(x,y)

9 Plot Editing Commands Title the plot Label the axes title( text ) Labels top of plot with text in quotes. xlabel( text ) Labels horizontal (x) axis with text in quotes. ylabel( text ) Labels vertical (y) axis with text in quotes.

10 Example 2 x=1:1:20; y=x.^2-9*x-20; plot(x,y) title('variation of x.^2-9*x-20 equation wit x '); xlabel('x-axis'); ylabel('y-axis');

11 Multiple Plots It is possible to draw multiple plots on the same set of axes. The first way is to use plot with multiple arguments, e.g. plot(x1, y1, x2, y2, x3, y3,... )

12 Example 3 Write a MATLAB program that plots the variation of following equation and its deviation with t on the same set of axes. 2 y( t) 3t 5t 8 y ( t) 6t 5 t=0:1:20; y_1=t.^3-5*t+8; y_2=6*t-5; plot(t,y_1,t,y_2)

13 Example 4 Write a MATLAB program that plots the sin(x) and cos(x) variations on the same set of axes for x varying from 0 to 2*pi.

14 Plot Editing Commands Color, Markers and Line styles plot(x,y, ro: ) this command plots the variation of x and y with a red colored line, draws circles at the data points and joins the plotted points with dotted line Color, markers and Line styles can be specified by giving plot an additional argument following the complex variable name. This optional additional argument is a character string (enclosed in single quotes) consisting of characters from the following table:

15 Color, Marker, Style Color Marker Line Styles y: yellow + Plus sign - : continuous line m:magenta o Circle : : dotted line b:blue * Asterisk -. : dash-dot line r:red. Point -- : dash-dash line g:green w:white x Cross 'square' or ssquare k: black 'diamond' or ddiamond ^ Upward-pointing triangle v Downward-pointing triangle > Right-pointing triangle < Left-pointing triangle ' pentagram' or pfive-pointed star (pentagram) ' hexagram' or hsix-pointed star (hexagram) + Plus sign o Circle * Asterisk

16 legend To distinguish between plots on the graph, the legend command is used. This command has the form: legend( string1, string2, string3,...) It places a box on the plot, with the curve type for first curve labeled with the text string string1, the second curved labeled with the text string string2, and so on. The position of the curve can be controlled by adding a final integer position argument pos to the legend command. Values of pos and the corresponding positions are: 0 = Automatic best placement (least conflict with data) 1 = Upper right-hand corner (default) 2 = Upper left-hand corner 3 = Lower left-hand corner 4 = Lower right-hand corner -1 = To the right of the plot

17 Example 5 x=[0:pi/10:4*pi]; y1=sin(x); y2=cos(x); plot(x,y1,'b.:',x,y2,'b<-') xlabel('radians'); ylabel('function Value'); title('variation of sinx and its deviation') legend('sin(x)','cos(x)',-1)

18 Multiple Figures A subsequent plot command will draw a new graph in this same window. The figure command allows the creation of multiple plot windows, allowing the display of multiple graphs. The command: figure(n) where n is a positive integer, will create a window named Figure No. n. Subsequent plot commands will draw graphs in this window, known as the active window x=0:pi/30:2*pi; y1=sin(x); y2=cos(x); figure(1),plot(x,y1,'bo:') figure(2),plot(x,y2,'r*-')

19 subplot The subplot command allows you to split the graph window into subwindows. The possible splits are two subwindows (top and bottom or left and right) or four subwindows (two on top, two on the bottom). subplot(m,n,p): m by n grid of windows, with p specifying the current plot as the pth window.

20 Example 6 subplot(2,2,1) x=0:pi/30:2*pi; y1=sin(x); plot(x,y1) title('f(x)=sin(x)') subplot(2,2,2) y2=cos(x); plot(x,y2) title('f(x)=cos(x)') subplot(2,2,3) y3=tan(x); plot(x,y3) title('f(x)=tan(x)') subplot(2,2,4) y4=cot(x); plot(x,y4) title('f(x)=cot(x)')

21 Mutiple plots (hold) The second way is simply to use hold to keep the current plot on the axes. All subsequent plots are added to the axes until hold is released, either with hold off, or just hold, which toggles the hold state. x=0:pi/30:2*pi; y1=sin(x); plot(x,y1,'k*:') hold y2=exp(2*sin(x)); plot(x,y2,'ro--') legend('sin(x)','\bf{e}^{2*sin(x)}')

22 Example 7 Write a MATLAB program that plots the following graphs by using 500 points for x varying from -2pi to 2pi (-2 π x 2 π)

23 Figure 1 Figure 2 Figure 3