INTRODUCTION TO MATLAB (MATrix LABoratory): INTUITIVE APPROACH

Transcription

1 M445 FALL 2012 INTRODUCTION TO MATLAB (MATrix LABoratory): INTUITIVE APPROACH MATLAB: Widely used in scientific community. Many powerful tools/constructs related to matrix manipulation, the corner stone of scientific computing. Variety of automatic checks for mistakes in programs. Integrated development environment. Visualization capabilities. Excellent documentation. No strong types. 1 A number of MATLAB tutorials (including university authored ones) may be found here: 2 1

2 Enter the following in the Command Window, press Enter after each line and observe the results: a=5 b=8; a b a + b c = a + b; c a*b b/a a^2 Note the role of semi colon at the end of the line! 3 Enter the following in the Command Window, press Enter after each line and observe the results: a b a = [1, 2; 3, 4] b = [ ] a*b inv(b) a*inv(b) a/b c = a\b inv(a)*b c(1,2) 4 2

3 One dimensional arrays (row and column vectors) and operations: a = [1, 2, 3, 4] b=[5; 4; 3; 2] a*b b*a b a*b a.*b a(2) a(1,2) size(a) length(a) c = [ ] a + c 5 One dimensional arrays (row and column vectors) and operations. Simple plotting in MATLAB. x= 0: 0.1:2; x y = exp(x); y plot(x,y) pi t = linspace(0,2*pi,20) z = sin(t) plot(t,z, r ) z1 = t.*sin(t) plot(t,z1, r ) xlabel( t ) zlabel( z(t) ) title( function ) 6 3

4 Arrays of characters: a = Hello b = World t = [a, b,!!! ]; disp(t) t c = x =1 x eval(c) 7 Simple plotting in MATLAB. 8 4

5 MORE on ARRAYS IN MATLAB Array: indexed sequence of values of the same type. Very convenient to store and manipulate large quantities of data. Example: How can we specify 10 variables of the same type having value 0? We can assign value zero to 10 variables, e.g., by typing: a1 = 0; a2 = 0; a3 = 0; a4 = 0; a5 = 0; a6 = 0; a7 = 0; a8 = 0; a9 = 0; a10 = 0; There exists a simpler way! 9 Enter the following in the Command Window, press Enter after each line and observe the results: N = 10 a =zeros(n,1) b = zeros(1,n) M = 5 a = 1:M b = 0:2:M+1 c = linspace(0,1,m) d = zeros(m) e = ones(m) r = rand(m) n = randn(m) 10 5

6 Saving the data, reading (loading) the data; elementary statistical operations: N = randn(100,1) save N.mat N load N.mat Nmean = mean(n) Nstd = std(n) hist(n) %array (column) of 100 normally %distributed random numbers %saving values of N in the file N.mat %reading the data from file N.mat %computing the mean of N %computing standard deviation of N %histogram of N 11 Let us now specify a two dimensional array (sign % identifies comments): p = [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12]; s = size(p) %size of the matrix p %display the matrix p(2,3) %display element of array P %display transposed matrix p.*p %element wise multiplication p*p %matrix multiplication p *p %matrix multiplication 12 6

7 WRITING PROGRAMS IN MATLAB Programs may be written using MATLAB editor and saved as files with.m suffix. To run the program, type the name of this program in MATLAB window (without suffix) and press Enter. Use the sign % at the beginning of comment lines. Do not forget to make comments in the programs (both for others sake and for your own convenience 13 Write the programs that follow, save them, run them and observe the results: You may also copy this program from the web site. This program is SIMPLEprogram1.m 14 7

8 Program with FOR loop: 15 Program with FOR loop: You may also copy this program from the web site. This program is FORprogram1.m 16 8

9 Program with IF statement: 17 Program with IF statement: You may also copy this program from the web site. This program is IFprogram1.m 18 9

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11 Program with nested IF statements: You may also copy this program from the web site. This program is nestedifprogram1.m 21 11