ECE Lesson Plan - Class 1 Fall, 2001

Transcription

1 ECE Lesson Plan - Class 1 Fall, 2001 Software Development Philosophy Matrix-based numeric computation - MATrix LABoratory High-level programming language - Programming data type specification not required & no pointers - Yeah! Superb graphics provide excellent data visualization Toolboxes provide application specific functionality Just a few examples of how MATLAB is used in industry Signal generation RADAR/SONAR simulation Modeling and analysis of Digital Signal Processing models Complex mathematical computation Control Systems Modeling The 3 MATLAB Display windows - command - the command window is where MATLAB code executes and type in your functions - this window opens when you open MATLAB - by >> MATLAB or by clicking on the MATLAB icon - edit - please see Dr. Beale or lab assistant as to which editor you will be using - Or try File->New->M-file in the upper-left corner of your command window - this window is used to create and edit MATLAB (M-files) executable files - graphics - this window (or figure) is used to display plots or other images (our 3rd class) MATLAB assistance >> help help => Online help for MATLAB functions and M-files a.k.a. - the most often used word in the MATLAB kingdom. help lists all the primary help topics. There are many - the test is tomorrow. :-) Example: >> help more Each help topic is very large. To give you an idea, the last time I looked, the help files, in their entirety, consumed 211 Meg of memory. >> doc doc => Displays The MathWorks, Inc. HTML (Online) documentation. doc opens The MathWorks, Inc. Online Help Desk. doc function displays the HTML documentation for the MATLAB function named. 1

2 doc toolbox/function displays the HTML documentation for the specified toolbox function. >>lookfor lookfor => keyword search through all help entries. lookfor topic searches for the string topic in the first comment line of the help text and gives the user the opportunity to be vague. The MATLAB Workspace The workspace is the area of memory accessible from the MATLAB command line. (The command line, of course, can be found in the command window) Two commands, who and whos, show the current contents of the workspace. The who command gives a short list, while whos also gives size and storage information. Column Vectors A column vector is an m-by-1 matrix so the number of columns is always one. The number of rows can be any integer value except one. (If the number of rows is one and the number of columns is one then that single element is known as a scalar.) Matrices Informally, the terms matrix and array are often used interchangeably. More precisely, a matrix is a two-dimensional rectangular array of real or complex numbers. The linear algebraic operations defined on matrices have found applications in a wide variety of technical fields. MATLAB has dozens of functions that create different kinds of matrices. Row Vectors A row vector is an 1-by-n matrix so the number of rows is always one. The number of columns can be any integer value except one. Scalars Any single element or numerical value. Or said other way, any vector or matrix that has one row and one column. (Its size is equal to 1,1.) Square Matrices Any matrix that has the number of rows equal to the number of columns (m = n). cd cd => Changes working directory cd prints out the current directory. 2

3 cd directory sets the current directory to the one specified. On UNIX platforms, the character ~ is interpreted as the user's root directory. cd... changes to the directory above the current one. dir dir => Lists the specified directory listing. dir lists the files in the current directory. dir subdirectoryname lists the files in subdirectory. Use pathnames, wildcards, and any other options available in your operating system. more more => Control page output for command window. more on turns on the more function. more off turns off the more function. more(n) enables paging to occur over n number of lines. The return key will advance the printed text line-by-line. The space bar will advance the printed text page-by-page. The letter 'q' will turn off the more function and interrupt paging. quit quit => Terminates MATLAB The command window will disappear at the execution of this command. No example. (Class isn't over yet.) Beware - Using quit will not save the current workspace. The Percent Sign The Percent Sign (%) at the start of the line will create a comment out of that line. All text or executable code on that line will be ignored. Unlike some other languages, the comment symbol does not have to be at the end of the line as well. The Single Quote The Single Quote (') at the end of a variable assignment transposes the array or matrix. Each row becomes a column and each column becomes a row. Both occur in sequence so the first row becomes the first column, etc. So, consequently, the number of rows changes to the number of columns and the number of columns changes to the number of rows. Single quotes on either side of text creates a string of the characters inside the quotes. Double quotes should be used for apostrophe usage inside of single quotes. 3

4 Transpose Using the single quote after a variable to make row vectors into column vectors and column vectors into row vectors. Works with matrices as well, columns become rows and rows become columns. Examples: >> A = [ ; ; ; ] A = >> A' ans = who, whos >> doc who List a directory of variables currently in memory. Lists the current variables, their sizes, and whether they have nonzero imaginary parts. >> whos Variables MATLAB does not require any type declarations or dimension statements. When a new variable name is encountered, MATLAB automatically creates the variable and allocates the appropriate amount of storage. If the variable already exists, MATLAB changes its contents and, if necessary, allocates new storage. For example: >> Number_of_Students = 25; returns a 1-by-1 matrix (a.k.a. - a scalar) named Number_of_Students and stores the value 25 in its single element. Variable names consist of a letter, followed by any number of letters, underscores or digits. MATLAB uses only the first 31 characters of a variable name. This means that you have plenty of characters to provide variable names that are sensible. The best 4

5 programming skills allow the user to remember/understand what the variable names represent. Consider a program that consists of +4k lines of code and more than 50 variables. Now imagine this code was written by someone else and they just left the company (that employs you). Six months pass and you have been given the less than envious assignment of debugging this program. MATLAB is case sensitive; it distinguishes between uppercase and lowercase letters. The variables "A" and "a" are not the same variable. (Both of which are good examples variable names that do not represent themselves very well). To view the matrix assigned to any variable, simply enter in the variable name. ans The most recent answer and the default variable name. Syntax ans Description The ans variable is created automatically when no output argument is specified. Example: >> 2+2 will return ans = 4 The Semicolon The Semicolon (;) can be used to end rows of vectors or matrices. (Examples will be provided further into this lesson plan.) The semicolon can also be used to separate statements on the same line such as: >> Num_of_Students=50; Num_of_Teachers=12; It is used very often, however, to suppress the displaying of the variable in the command window. Consider a variable that contains 185 columns and rows (personal experience). To bring this variable into the MATLAB workspace without a semicolon would require MATLAB to display all 8,140,000 elements in this variable. The command window would scroll for a considerable time before completing this task. You will find that most of the time you will not need to see the variables' contents displayed as you generate them. 5

6 Colon : The colon is one of the most useful operators in MATLAB. It can create vectors, subscripts, and specify for-loop iterations. The colon operator uses the following rules to create regularly spaced vectors: j:k is the same as [j,j+1,...,k] j:k is empty if j > k j:i:k is the same as [j,j+i,j+2i,...,k] j:i:k is empty if i > 0 and j > k or if i < 0 and j < k where i,j, and k are all scalars. Below are the definitions that govern the use of the colon to pick out selected rows, columns, and elements of vectors, matrices, and higher-dimensional arrays: A(:,j) is the j-th column of A A(i,:) is the i-th row of A A(:,:) is the equivalent 2-dimensional array. For matrices this is the same as A. A(j:k) is A(j), A(j+1),...,A(k) A(:,j:k) is A(:,j), A(:,j+1),...,A(:,k) Examples: >> A = 1:4:90 A = Columns 1 through Columns 13 through Parentheses Parentheses can be used to indicate precedence in arithmetic expressions. Examples: >> B = (5+6) - (4-1) returns B = 8 >> C = 5+(6-4)-1 returns C = 6 6

7 They are also used to enclose arguments of functions in the usual way, which will be discussed in a later class, as well as to enclose subscripts of vectors and matrices. If X and V are vectors, then X(V) is [X(V(1)), X(V(2)),..., X(V(n))]. The components of V must be integers to be used as subscripts. An error occurs if any such subscript is less than 1 or greater than the size of X. Some examples are: X(3) is the third element of X. X([1 2 3]) is the first three elements of X. Subscripts The element in row i and column j of L is denoted by L (i, j). For example, suppose >> L = [ ; ; ; ], then L(4, 2) is the number in the fourth row and second column. For matrix L, L(4, 2) is 15. So it is possible to compute the sum of the elements in the fourth column of L by typing >>L(1, 4) + L(2, 4) + L(3, 4) + L(4, 4) Examples: >> L = [ ; ; ; ]; L = If you try to use the value of an element outside of the matrix, it is an error: >> T = L(4, 5) returns Index exceeds matrix dimensions >> G = L(3,3) G = 6 >> T = L(1:4,1) T =

8 >> D = L(2,:) D = It is also possible to refer to the elements of a matrix with a single subscript, L(k). This is the usual way of referencing row and columns vectors. But it can also apply to a fully two-dimensional matrix, in which case the array is regarded as one long column vector formed from the columns of the original matrix. So for Matrix "L", A(8) is another way of referring to the value 15 stored in A(4, 2). Square Brackets Square brackets are used in forming vectors and matrices. >> [ SQRT(-1)] is a vector with three elements separated by white spaces. >> [6.9, 9.64, sqrt(-1)] is the same thing except that commas have been used to separate the elements. >> [ ] and >> [ ] are not the same. The first has 3 elements, the second has 5. >> [ ; ] is a 2-by-3 matrix. The semicolon ends the first row. Vectors and matrices can be concatenated with [ ] brackets. [A B; C] is allowed if the number of rows of A equals the number of rows of B and the number of columns of A plus the number of columns of B equals the number of columns of C. This rule generalizes in a hopefully obvious way to allow fairly complicated constructions. Examples: >> A = [ ]; >> B = [ ]; >> C = [ ]; >> D = [A B; C] How many rows and how many columns does "D" contain? 8

9 ones Create an array of all ones. Syntax Y = ones(n) Y = ones(m,n) Y = ones([m n]) Description Y = ones(n) returns an n-by-n matrix of 1s. An error message appears if n is not a scalar. Y = ones(m,n) or Y = ones([m n]) returns an m-by-n matrix of ones. Examples >> A = ones(1,5) >> B = ones(3) >> C = ones([2 4]) zeros Create an array of all zeros. Syntax B = zeros(n) B = zeros(m,n) B = zeros([m n]) Description B = zeros(n) returns an n-by-n matrix of zeros. An error message appears if n is not a scalar. B = zeros(m,n) or B = zeros([m n]) returns an m-by-n matrix of zeros. Remarks The MATLAB language does not have a dimension statement--matlab automatically allocates storage for matrices. Nevertheless, most MATLAB programs execute faster if the zeros function is used to set aside storage for a matrix whose elements are to be generated one at a time, or a row or column at a time. The ones function could also be used for this purpose. Examples >> E = zeros(1,5) >> F = zeros(3) >> G = zeros([2 4]) 9

10 size Array dimensions Syntax Size_of_X = size(x) [m,n] = size(x) Description d = size(x) returns the sizes of the vector or matrix X as d. [m,n] = size(x) returns the size of matrix or vector X in variables m and n. The first representing the number of rows and the second representing the number of columns. Examples >> X = 0:12; >> [m, n] = size(x) returns m = n = 13 1 >> X = X'; >> size(x) returns ans = 13 1 length Length of vector Syntax length(x) n = length(x) Description 10

11 length(x) returns the greater of the two values returned by size(x) for nonempty arrays and 0 for empty arrays. If X is square, i.e., m=n, then length(x)returns the one value. Examples: >> A = 2:2:20; >> Length_of_A = length(a) Length_of_A = 10 >> X = 1:3:31; >> Length_of_X = length(x) Length_of_X = 11 diary Save session in a disk file Syntax diary diary filename diary off diary on Description The diary command creates a log of keyboard input and system responses. The output of diary is an ASCII file, suitable for printing or for inclusion in reports and other documents. diary, by itself, toggles diary mode on and off. diary filename writes a copy of all subsequent keyboard input and most of the resulting output (but not graphs) to the named file. If the file already exists, output is appended to the end of the file. diary off suspends the diary. diary on resumes diary mode using the current filename, or the default filename diary if none has yet been specified. Remarks The function form of the syntax, diary('filename'), is also permitted. Limitations You cannot put a diary into the files named off and on. Examples 11

12 >> diary Test1 >> X = 44 >> Y = [4; 5; 6] >> diary off >> dir % Test1 is now in your working subdirectory - notice that there is no extension. % Using the editor and open Test1. This is what you should see: X = 44 X = 44 Y = [4; 5; 6] Y = diary off % Now close Test1. Go back to the MATLAB Command Window and enter in the % following code. >> diary Test1 >> A = 15:-2:1 >> diary off % This will add the information generated above to Test1 as such: X = 44 X = 44 Y = [4; 5; 6] Y = diary off A = 15:-2:1 A = 12

13 diary off References: - The MathWorks, Inc. Online (Helpdesk) Documentation - Using MATLAB Version 5.0 by The MathWorks, Inc. - Getting Started with MATLAB Version 5.0 by The MathWorks, Inc. 13