Introductory An MATLAB Tutorial for Engineers - Presented to UIC IEEE Student Chapter on Sept. 20, 2005 by Dr. Vladimir Goncharoff
Tutorial Topics 1. Brief description of MATLAB1
Short for "MATrix LABoratory" MATLAB refers to both a numerical computing environment and to its core programming language. Created by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it specializes in numerical computing, an optional toolbox interfaces with the Maple symbolic engine, making it a full computer algebra system. It is used by more than one million people in industry and academia and runs on most modern operating systems, including Windows, Mac OS, Linux and Unix. The current version is MATLAB 7.1 Service Pack 3. It is available for commercial use for approximately US$2000 and US$100 for an academic license with a limited set of Toolboxes. MATLAB was invented in the late 1970s by Cleve Moler, then chairman of the computer science department at the University of New Mexico. He designed it to give his students access to LINPACK and EISPACK without having to learn Fortran. It soon spread to other universities and found a strong audience within the applied mathematics community. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded The MathWorks in 1984 to continue its development. MATLAB was first adopted by control design engineers, Little's specialty, but quickly spread to many other domains. It is now also used in education, in particular the teaching of linear algebra and numerical analysis.
2. MATLAB as a command-line calculator
At the command prompt, type as you would on a scientific calculator (press Enter key instead of =): 2.3 - 5.6/0.13^2 log2(15) atan(pi/3) acosh(cosh(2.0)) sqrt(-13) -5/0 0/0
Note: MATLAB utilizes double precision calculations, comes with many built-in functions, supports complex numbers, has representations for and not-a-number. The MATLAB workspace may be used to store values using variable names (case-sensitive labels):
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X = 2.3 Y = 5.6; Z = 0.13; X - Y/Z^2 clear X
taken directly from the on-line encyclopedia wikipedia.com
Note: the = sign performs value assignment, a variable name is typed followed by the Enter key to see its value, a semicolon at the end of a line supresses the display of a variable's value after an assignment; more than one assignment per line is allowed; all calculations may be done using previously-defined variable names that are stored in memory until they are cleared.
MATLAB supports matrices and other multidimensional data types: A B C D [1, 2, 3.5, 7] [1-j 2+3*j j] [1, 2, 1; 3, 4, 5] [1 2 3 3 4 5]; X1 = eye(5) X2 = [zeros(4,4),ones(4,4)] X3 = [0:9] X4 = [15.2:-1:10] X5 = linspace(1,9,8) X6 = logspace(log10(1),log10(9),8) X_uniform = rand(3,4) X_normal = randn(1,1) = = = =
Note: commas or spaces are used to separate data in different columns, spaces or Crlf are used to separate data in different rows; matrices may be initialized to all 0's, all 1's, pseudorandom, identity matrix, as a linear/exponential sequence, etc., or to any specified set of coefficients.
MATLAB supports linear algebraic and scalar operations on matrix elements: A = [1, 2, 3.5, 7], sqrt(A) B = [1 2 3]' [1, 2] + [4, 5] X1 = rand(5,5), X2 = rand(5,5); X1*X2, X1.*X2 I = eye(5); I + fliplr(I) W = randn(4,4), Y = inv(W); v W*Y = [3; 2; 1], y = v', v*y 1./[4, 5] Z = rand(3,3), sum(Z), mean(Z), std(Z)
Note: to perform matrix multiplication the inner dimensions of the matrices must match; for most other matrix manipulations (add, subtract, product of corresponding coefficient values e.g.) the matrices must be of equal dimensions; most vector operations are repeated for each column.
One of the most powerful features of MATLAB is the variety of ways that one may refer to (index) the elements of a matrix: A = 2:9, A(3), A(2:4), A(A(1:3)) B = magic(5), B1 = B(1:2,4:5) C = rand(3,3), D = [C >.5], C*.D X7 = rand(2,2), X7(:), X7(:)' X8 = eye(4), reshape(X8,2,8) A = round(2*rand(4,4)), v = find(A~=2)', A(v)
Note: in MATLAB indexing begins with item 1 (not 0), as is normally done when writing row and column indexes for matrices.
3. MATLAB as a programming language
functions: function [output pars.] = function_name[input pars.]; .... ; return These are compiled the first time that they are called structured programming: for / while / if / elseif / else / end Loops should be avoided if matrix methods will do the same job automatic dimensioning of matrices On-the-fly memory space allocation slows execution time - preallocate space
Example: given array X that is a vector -- find a new vector Y where Y(n) = |X(n) - X(n+2)| .
Poor -- using a loop, no preallocation of memory space: function Y = diff2(X) for n = 1:(length(X)-2) Y(n) = abs(X(n+2)-X(n)); end return
Better -- using a loop, this time preallocating memory space for output array Y: function Y = diff2(X) nmax = length(X)-2; Y = X(1:nmax); for n = 1:nmax Y(n) = abs(X(n+2)-X(n)); end return
Best -- not using a loop: function Y = diff2(X) n1 = length(X); n2 = n1 - 2; Y = abs(X(3:n1)-X(1:n2)); return
MATLAB has built-in inefficiencies such as storing all values in double precision floating-point format (unless specified otherwise, which is a must for being able to efficiently handle large image files), needing to compile functions during the first call at run-time, etc. However, a MATLAB compiler is available for those who would like better performance. MATLAB is a good programming testbed, but probably not the ...