PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 362-2What is a Matlab function?How does the plot function work?What Matlab functions are available to do Data Analysis?How can you create your own function ?Readings: Matlab by Pratap Chapters 2.4, 4.1, 4.2, 4.3, 5.2.2, 5.6.12-3Basic Mathematical Functions (see 3.2.4 in Pratap) However, since there are hundreds of Matlab functions, a useful tool is Matlab Helpdesk.Exponential Function>> exp(0) (exponential function ex)ans =1name argument parenthesis>> x = [-1 0 1];>> exp(x) ans =0.3679 1.0000 2.7183 ( [exp(-1), exp(0), exp(1)] )The exp function argument can be a scalar, vector or matrix.4Three forms of the use of a function in Matlab are:>> VAR = function_name(arg1,arg2, …);>> [VAR1,VAR2,...] = function_name(arg1,arg2, …);>> function_name(arg1,arg2, …);A Matlab function like a mathematical function is a rule where given a certain input or inputs, the rule tells you how to compute the output value or how to produce an effect (e.g. the plot function produces a figure). The inputs are called the “arguments” to the function.As an illustration, a function can be likened to the sequence of instructions on an income tax form(see next two slides).• The instructions must be followed in sequential order.• Fields (or boxes in the form represent variables). All variables in a function are local to that function. They cannot been seen by other users filling out other forms.• Fields in the form that must be filled in with information provided by the person whose tax is being computed are called parameters . The values entered in these fields, (like name , social security number),... are called input arguments. • If the taxpayer recieves a return this amount is always found in one specific field on the form, field 67a. This field is called an output variable.name fieldrefund amountamount due2-8Example: Plot the sine function using the built-in function “sin” .(see section 5.1)>> x = -10 : .1 : 10; % (remember ; suppresses output)>> y = sin(x); % x in radians>> plot(x,y);By default Matlab will connect the points (xi ,yi) with a straight line. A more general version of the plot command is:plot(x,y,’color_linestyle_marker’);where color is:cyan magenta yellow red green blue white blackc m y r g b w k2-9Linestyle can be any of the following:solid dashed dotted dashed-dot no lineline line line line- - - : -. noneand marker can be specified as:plus asterisk point cross square diamond+ * . x square diamondExample:>> x = -10 : .1 : 10;>> y = sin(x); >> plot(x,y,’m--square’);Figure Window2-11Note: the function plot can have a variable number of arguments. However, the order of placement of the arguments is significant. On an income tax form, if in field 7 wages, tips,... you typed in the number of dependents you would not expect to compute the true income tax.Example:>> plot(y,x); (may not give the same results as plot(x,y) )>> plot(’m--square’,x,y); (does not work)>> plot(x,y); plot x and y>> plot(x,y,’m--square’); plot x , y and a string >> y = sin(x+1); sin expression “x+1”Name of function Arguments2-12>> x = pi / 4; % line 1>> y = sin(x) ; % line 2During execution of the above lines, the mechanism for the call works this way:1) A copy of the value of the variable x is passed (by Matlab) to the code for the built-in function sin .2) The execution temporarily suspends (at line 2) while the code for the function sin executes.3) After the code in sin finishes executing, execution proceeds with line 2. The value (.7071…) that the sin function computes is returned to line 2 and replaces the expression shaded in yellow above.2-13>> vec1 = [-2 ; 3 ; 4] ;>> vec2 = [-2 3 4] ;>> sum(vec1) input is a 3 x 1 column vector and output is a scalar.ans =5>> sum(vec2) input is a 1 x 3 row vector and output is a scalar.ans =5Matlab’s built-in functions accept a wide variety of array sizes. Example: The built-in function sum.(see section 5.3)2-14Users can add to Matlab’s built-in functions by “programming” a function. A program in Matlab is either in the form of a script or a function.Programming a function is described in the Matlab book in Chapter 4.2 and scripts are described in Chapter 4.1.2-15Programming - • A process for obtaining a computer solution to a problem. • A computer program is a sequence of instructions that tell the computer what to do.2-16• Modular ProgrammingBreak complicated tasks up into pieces(functions).• Functions can “call” other functions.This means you don’t have to re-write the code for the function again and again.• Variables in Functions are “local”.All variables in the function are “ local ” by default. That means that if you have a variable in your workspace with the same name as the variable in a function, then assigning a value to the variable in the function has no affect on the variable in the workspace. That is, a function cannot accidentally change (destroy) the data in your workspace.2-171. Problem Definition2. Refine, Generalize, Decompose the problem definition(i.e., identify sub-problems, I/O, etc.)3. Develop Algorithm(processing steps to solve problem)4. Write the "Program" (Code)(instruction sequence to be carried out by the computer)5. Test and Debug the Code6. Run Code2-181. Problem Definition Write a function that converts a temperature in Fahrenheit to Celsius. 2. Refine, Generalize, Decompose the problem definition(i.e., identify sub-problems, I/O, etc.)Use the fact that celsius = (fahr - 32) * 5/92-19Natural-Language Algorithm The function “definition” should list one input variable named fahr and one output variable celsius. Compute the value of the celsius temperature and assign the value to a variable “celsius” The “function” mechanism of Matlab will automatically return the value in the variable celsius when the function is used (called) at the Matlab prompt.3. Develop Algorithm (processing steps to solve problem)2-204. Write the “Function"