MATLAB – A Computational Methods By Rohit Khokher Department of Computer Science, Sharda University, Greater Noida, India MATLAB – A Computational Methods

Outline of the Talk 1 Introduction 2 Array and Files 3 Programming in Matlab 4 Importing and Exporting Data 5 Plots

MATLAB – A Computational Methods Introduction MATLAB is a program for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory. MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation.

MATLAB – A Computational Methods Contd… MatLab : Matrix Laboratory Numerical Computations with matrices Every number can be represented as matrix Why Matlab? User Friendly (GUI) Easy to work with Powerful tools for complex mathematics

MATLAB – A Computational Methods Contd… Workspace Command History Command Window

MATLAB – A Computational Methods Array and Function Files MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored. Vectors are special forms of matrices and contain only one row OR one column. Scalars are matrices with only one row AND one column MATLAB Matrices

MATLAB – A Computational Methods Contd… A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows: » a_value=23 a_value = 23

MATLAB – A Computational Methods Contd… A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas): » rowvec = [12, 14, 63] rowvec =

MATLAB – A Computational Methods Contd… A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons): » colvec = [13 ; 45 ; -2] colvec =

MATLAB – A Computational Methods Contd… A matrix can be created in MATLAB as follows (note the commas AND semicolons): » matrix = [1, 2, 3 ; 4, 5,6 ; 7, 8, 9] matrix =

MATLAB – A Computational Methods Contd… a vectorx = [ ] x = transposey = x.’ y = a matrixx = [1 2 3; 5 1 4; ] x =

MATLAB – A Computational Methods Contd… x(i,j) subscription whole row y=x(2,3) y = 4 y=x(3,:) y = y=x(:,2) y = whole column

MATLAB – A Computational Methods Files Use predefined functions or write your own functions Reside on the current directory or the search path –add with File/Set Path Use the Editor/Debugger to edit, run MatLab Files (.m)

MATLAB – A Computational Methods Contd… Reading Data from files MATLAB supports reading an entire file and creating a matrix of the data with one statement. >> load mydata.dat;% loads file into matrix. % The matrix may be a scalar, a vector, or a % matrix with multiple rows and columns. The % matrix will be named mydata. >> size (mydata)% size will return the number % of rows and number of % columns in the matrix >> length (myvector)% length will return the total % no. of elements in myvector

MATLAB – A Computational Methods Programming in MATLAB MATLAB Variable Names Variable names ARE case sensitive Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer) Variable names must start with a letter followed by letters, digits, and underscores.

MATLAB – A Computational Methods Contd… To get started, type one of these commands: A simple program » a=5; » b=a/2 b = »

Computational Methods MATLAB Contd… MATLAB symbols >>prompt...continue statement on next line,separate statements and data %start comment which ends at end of line ;(1)suppress output (2)used as a row separator in a matrix :specify range

Computational Methods MATLAB Contd… MATLAB Math & Assignment Operators OperatorSymbolSyntax Power ^ or.^a^ba.^b Multiplication * or.*a*ba.*b Division or / or./ \ or.\ a/b b\a a./b b.\a NOTE: 56/8 = 8\56

Computational Methods MATLAB Contd... - (unary) + (unary) OperatorSymbolSyntax Addition +a + b Subtraction -a - b Assignment =a = b (assign b to a )

MATLAB – A Computational Methods Contd… MATLAB Relational Operators MATLAB supports six relational operators. OperatorSymbol Less Than< Less Than or Equal<= Greater Than> Greater Than or Equal>= Equal To== Not Equal To~=

MATLAB – A Computational Methods Contd… MATLAB Logical Operators MATLAB supports three logical operators. OperatorSymbolPrecedence not~% highest precedence and&% equal precedence with or or |% equal precedence with and

Computational Methods MATLAB Contd… A for loop in MATLAB for i = 1:1:100 temp(1,i)=0; end A while loop in MATLAB while x <= 10 % execute these commands end

Computational Methods MATLAB Contd… Scalar - Matrix Addition » a=3; » b=[1, 2, 3;4, 5, 6] b = » c= b+a% Add a to each element of b c =

Computational Methods MATLAB Contd… Scalar - Matrix Multiplication » a=3; » b=[1, 2, 3; 4, 5, 6] b = » c = a * b % Multiply each element of b by a c =

Computational Methods MATLAB Importing and Exporting Data Importing Data into the Workspace The first step in analyzing data is to import it into the MATLAB workspace. See the topics under Importing Data for detailed information about supported data formats and the functions.Importing Data When you work with time series data, use the Time Series Tools GUI (tstool) to import the data and create timeseries objects. The Time Series Tools Import Wizard makes it easy to import or define a time vector for your data.tstool

Computational Methods MATLAB Contd… Exporting Data from the Workspace When you analyze your data, you might create new variables or modified imported variables. You can export variables from the MATLAB workspace to various file formats, both character-based and binary. You can, for example, create HDF and Excel files containing your data,

MATLAB – A Computational Methods Plots A plot is any graphic display you can create within a figure window. Plots can display tabular data, geometric objects, surface and image objects, and annotations such as titles, legends, and colorbars. Figures can contain any number of plots. Each plot is created within a 2-D or a 3-D data space called an axes.

Computational Methods MATLAB Contd… Plotting with MATLAB There are commands in MATLAB to "annotate" a plot to put on axis labels, titles, and legends. For example: >> % To put a label on the axes we would use: >> xlabel ('X-axis label') >> ylabel ('Y-axis label') >> % To put a title on the plot, we would use: >> title ('Title of my plot')

MATLAB – A Computational Methods Contd… x = 0:pi/100:2*pi; y = sin(x); plot(x,y) xlabel('x = 0:2\pi') ylabel('Sine of x') title('Plot of the Sine Function')

MATLAB – A Computational Methods Contd… Types of 2-D Graphs Line Graphs Bar Graphs Area Graphs Direction Graphs Radial Graphs Scatter Graphs

MATLAB – A Computational Methods Contd… 3-D Plots Here are some examples of surface plots in MATLAB. Mesh Plot of Peaks z=peaks(25); mesh(z); Colormap(hsv) Surface Plot of Peaks z=peaks(25); surf(z); colormap(jet); Contour Plot of Peaks z=peaks(25); contour(z,16); colormap(hsv)

MATLAB – A Computational Methods Applications of Matlab  Linear Algebra  Solving a linear system  Gaussian elimination  finding eigenvalues and eigenvectors  Matrix factorization  Curve Fitting and Interpolation  Polynomial curve fitting on the fly  Least squares curve fitting  Interpolation  Data Analysis and Statistics  Numerical Integration  Ordinary Differential Equations  Nonlinear Algebraic Equations  Graphs ( 2 D and 3 D)

MATLAB – A Computational Methods Contd… 3-D Plots Here are some examples of surface plots in MATLAB. Mesh Plot of Peaks z=peaks(25); mesh(z); Colormap(hsv) Surface Plot of Peaks z=peaks(25); surf(z); colormap(jet); Contour Plot of Peaks z=peaks(25); contour(z,16); colormap(hsv)

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