matab no2
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This document discusses matrices and matrix operations in MATLAB. It begins by defining what a matrix is and how they are represented in MATLAB. It then covers topics like defining matrices, accessing matrix elements, built-in matrix functions like diag, eye, and size, and matrix operations like addition, multiplication, and dot notation. The document ends by discussing M-files in MATLAB, including how to create script and function M-files, use comments, and provide examples.
![Defining matrices
>> A = [1 2 3; 4 5 6; 7 8 9];
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
and
>> A = [ 1 2 3
456
7 8 9 ];
Defines
A=
1
3
4
5
6
7
CECOS College of Engineering and IT
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8
9
March – July 2012](https://image.slidesharecdn.com/labno-140228005532-phpapp01/85/matab-no2-3-320.jpg)
![Matrix functions : Examples
>> a=[1 2 3;4 5 6;7 8 9]
a=
1
4
7
2
5
8
3
6
9
>> diag(a)
>> triu(a)
>> tril(a)
>> size(a)
>> length(a)
ans =
ans =
ans =
ans =
ans =
1
5
9
CECOS College of Engineering and IT
1
0
0
2
5
0
3
6
9
1
4
7
0
5
8
0
0
9
3
3
3
March – July 2012](https://image.slidesharecdn.com/labno-140228005532-phpapp01/85/matab-no2-6-320.jpg)
![Function M-files
User defined functions
These M-files start with a keyword, “function”
The first line of these files should look like
function[output variables]=functionName(input variables)
These files are saved with the funtionName.m as file name.
An example:
CECOS College of Engineering and IT
March – July 2012](https://image.slidesharecdn.com/labno-140228005532-phpapp01/85/matab-no2-18-320.jpg)
matab no2
- 1. Lab No.02 M-files and Matrix operations Designed by : Dawar Awan dawar@cecos.edu.pk CECOS College of Engineering and IT March – July 2012
- 2. Matrices MATLAB treats every thing as a matrix (check the Workspace) 1-by-1 matrices are interpreted as scalars Matrices with only one row or one column are known as vectors A matrix is a rectangular array of numbers. 1 9 2 6 7 8 3 5 1 8 2 4 A matrix with 3 rows, 4 columns, and 12 elements CECOS College of Engineering and IT March – July 2012
- 3. Defining matrices >> A = [1 2 3; 4 5 6; 7 8 9]; >> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; and >> A = [ 1 2 3 456 7 8 9 ]; Defines A= 1 3 4 5 6 7 CECOS College of Engineering and IT 2 8 9 March – July 2012
- 4. Accessing matrix elements The matrix element located in the i-th row and j-th column of “A” is referred to as, A(i,j) Try the following instruction and observe the change in “A” >> A(2,3) = 10 CECOS College of Engineering and IT March – July 2012
- 5. Some Built-in matrix functions Function Description diag eye magic ones rand triu tril zeros size length find : : : : : : : : : : : CECOS College of Engineering and IT returns diagonal elements as vector identity matrix magic square matrix of ones randomly generated matrix upper triangular part of a matrix lower triangular part of a matrix matrix of zeros Number of rows and columns in a matrix Length of an array find indices of some elements in array March – July 2012
- 6. Matrix functions : Examples >> a=[1 2 3;4 5 6;7 8 9] a= 1 4 7 2 5 8 3 6 9 >> diag(a) >> triu(a) >> tril(a) >> size(a) >> length(a) ans = ans = ans = ans = ans = 1 5 9 CECOS College of Engineering and IT 1 0 0 2 5 0 3 6 9 1 4 7 0 5 8 0 0 9 3 3 3 March – July 2012
- 7. Matrix functions : Examples >> eye(3) >> magic(3) >> rand(3) ans = ans = ans = 1 0 0 0 1 0 0 0 1 8 3 4 1 5 9 6 7 2 0.8147 0.9134 0.2785 0.9058 0.6324 0.5469 0.1270 0.0975 0.9575 >> ones(3) >> ones(3,2) >> zeros(3) >> zeros(3,2) ans = ans = ans = ans = 1 1 1 1 1 1 1 1 1 CECOS College of Engineering and IT 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 March – July 2012
- 8. Matrix functions : Examples >> rand(3,2) ans = 0.9649 0.9572 0.1576 0.4854 0.9706 0.8003 CECOS College of Engineering and IT March – July 2012
- 9. Matrix operations + * ^ ' / => => => => => => Addition Subtraction Multiplication Power Conjugate transpose Division To perform index by index operation, use dot (.) notation ./ .* .^ .' => => => => CECOS College of Engineering and IT Index by index division Index by index multiplication Index by index power Non conjugate transpose March – July 2012
- 10. Dot notation Observe the change in result due to the “dot” CECOS College of Engineering and IT March – July 2012
- 11. Examples/Exercise 1 4 7 C= B= A= 2 5 8 3 6 9 1 2 3 1 2 3 1 2 3 1 D= 2 1 2 2 1 2 1 Practice the following matrix operations A+B, A’, A*B, 2*A, A/2, A/B, A./B, C/D, C./D, C*D, C.*D, C^2, C.^2 CECOS College of Engineering and IT March – July 2012
- 12. Colon notation CECOS College of Engineering and IT March – July 2012
- 13. M - files M-files are script/text files containing MATLAB commands Script M-file Function M-file To make a script M-file, you need to open a file using the built-in MATLAB editor. There are two ways to accomplish it: 1. From file menu, click NEW 2. Type edit on command line CECOS College of Engineering and IT March – July 2012
- 14. M - files To save the M-file go to the “file” menu and click on “save”. The name should not contain spaces, should not start with a number and should not be same as any built-in function. The extension of this file should be “.m” CECOS College of Engineering and IT March – July 2012
- 15. M - files This code can now be executed in two ways 1. Write the name of file on command window (excluding “.m”) 2. Under the “debug” menu, click “Run” The variables used in the M-file will be maintained in the workspace and hence accessible from the command window. CECOS College of Engineering and IT March – July 2012
- 16. M - files Code written in M-file to calculate various parameters of a circle Check the values of the variables after running the M-file CECOS College of Engineering and IT March – July 2012
- 17. Comments While writing any code, it’s a good practice to write proper comments against each instruction. In MATLAB, any thing written after “%” is treated as a comment and is ignored by the compiler. CECOS College of Engineering and IT March – July 2012
- 18. Function M-files User defined functions These M-files start with a keyword, “function” The first line of these files should look like function[output variables]=functionName(input variables) These files are saved with the funtionName.m as file name. An example: CECOS College of Engineering and IT March – July 2012
- 19. Function M-files Calling this function from command window CECOS College of Engineering and IT March – July 2012
- 20. Function M-files Any comments after the first line becomes the help for that function Command window CECOS College of Engineering and IT March – July 2012
- 21. Tasks 1- Generate a vector of 50 elements having random values between 0 and 50. 2- Generate a vector, containing all the odd numbers between 0 and 100. 3- Create a function M-file that accepts two numbers and generates there sum, product and difference as output. 4- Use Cramer's rule to solve the following set of equations. 3x1 - 1x2 + 0x3 = 1 1x1 + 4x2 - 2x3 = 5 0x1 - 2x2 + 8x3 = 6 CECOS College of Engineering and IT March – July 2012