Introduction to MATLAB

Transcription

1 CHEE MATLAB Tutorial Introduction to MATLAB Introduction In this tutorial, you will learn how to enter matrices and perform some matrix operations using MATLAB. MATLAB is an interactive program for numerical computation and data visualization. It is easy to use, yet very powerful. Entering Matrices Matlab has three main types of displays: the main command window, figure (plot) windows, and the file editor. For the moment we will concentrate on the command window, which is the primary means by which you will enter and manipulate data in the workspace. When you open MATLAB, the command window will appear with a prompt which looks like >>. The basic entity in MATLAB is the rectangular matrix (although there are many other data types as well!). Matrix elements can be either real or complex. Commas or spaces are used to separate elements within a row, while semicolons separate each row. Example: To enter a row vector (i.e. n matrix), say x >> x = [ 7 ] x = 7 and for a column vector y, we use a semicolon as the delimiter between each row: >> [; ; ; 7; ] 7 Transposing a row vector yields a column vector, and vise versa. The transpose command in MATLAB is the sign. >> x

2 7 There is a faster way to enter matrices or vectors that have a repeating pattern. For example, to create a vector z with elements from 0 to 40 with increments of (the default increment, if omitted, is ): >> z = 0 : : 40 z = To suppress printing, we can add a semicolon after any MATLAB command: >> w = 0 : : 40; The vector w is generated, but not printed in the command window (we can see in the workspace viewer that w was created). We can find the value of the third element in the w vector; >> w() ans = 0 Notice that a new variable, ans, was defined automatically. To enter a matrix, say A >> A = [ ; 4 6; 7 8 9] A = >> B = [ 4 ; 8; 4 7] B = Other useful commands for generating n m matrices include: zeros(n,m) ones(n,m) rand(n,m) eye(n) (matrix of uniform random numbers) (n n Identity matrix)

3 Some Matrix Operations. Addition and Subtraction Addition and subtraction of matrices are denoted by (+ and -). The operations are defined whenever the matrices have the same dimensions. For example: >> C = A + B C = Matrix Multiplication Multiplication of matrices is denoted by (*). The operation is defined whenever the inner dimensions of the two matrices are the same. >> D = A B D = Another example: >> E = : : 8 E = 8 >> F = A E F = Matrix Powers The expression xˆn raises the variable x to the n th power and is defined if x is a square matrix and n is a scalar. >> G = Bˆ G =

4 Matrix Inversion The inverse of a square matrix A is obtained by typing inv(a). Given a linear equation AX = B (A is a nonsingular square matrix) the solution is X = A B (=inverse of A multiplied by B). Suppose >> A = [ ; 6 4; 0 8]; and >> B = E ; We can find the solution in MATLAB by: >> X = inv(a) B X = Matrix Division There are two matrix division symbols in MATLAB, \ and /. If A is a nonsingular square matrix, then A \ B and B/A correspond to inv(a) B and B inv(a) respectively..6 Other useful operations/functions Element-by-element multiplication, division, and raising to some power can be done by preceeding the operator (*,/,^) by a period, i.e. (.*,./,.^) However, using this dot-notation requires that both operands have the same dimension. For example, let >> Y = [ ]; >> Z = Y.ˆY Z = 4 7 4

5 Other useful functions include: Determinant of matrix A >> det(a) Eigenvalues of A >> eig(a) 4 Plotting The basic plot command uses the syntax plot(x, y), where x is a column vector, and y is a matrix having the same number of rows as x. Each column in y will be plotted as a separate data series. >> plot((:),b) A new figure window should have opened containing the plotted data. We can also add titles, legends, etc to the plot: >> figure; plot((:),a); title( Sample plot ); ylabel( y axis );... xlabel( x axis ); legend( col, col, col, 0); (The figure command opens a new window, so that the previous plot is not overwritten). To learn more about plotting or any other commands, either explore the help browser or simply type help command-name. Notes. MATLAB has an extensive on-line help facility. For example to find help on exponential, type >> help exp. Command line editor The arrow keys on the keyboard can be used to edit misspelled commands or to recall previous command lines. e.g. suppose you enter X = in(a) C instead of X = inv(a) B. Rather then typing the whole command a second time, simply hit the up arrow key. The previous line will be displayed again and you can move the cursor over using the left arrow key until you can insert the missing v and change B to A.