w6 7 functions and functions file

8/2/2019 W6 7 Functions and Functions File

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KNJ2332Engineering Programming

Week 6 & 7

Functions and Functions File


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Outline

Elementary Mathematical Functions

User Defined FunctionsWorking with Data Files


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Elementary MathematicalFunctions

Exponentialexp(x)

sqrt(x)

Logarithmiclog(x)

log10(x)

Exponential; e x

Square root; x

Natural logarithm; ln x

Common (base 10) logarithm; log x = log10 x


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Complex Numberabs(x)

angle(x)conj(x)imag(x)real(x)

Absolute value.

Angle of a complex number.Complex conjugate.Imaginary part of a complex number.Real part of a complex number.


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Example : is a complex number .

Can be entered in MATLAB in different ways:

i35


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Numeric Functions

ceil(x)fix(x)

floor(x)round(x)sign(x)

Round to nearest integer toward . Round to nearest integer toward zero.

Round to nearest integer toward - . Round toward nearest integer.Signum function:

+1 if x > 0; 0 if x = 0; -1 if x < 0.


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Example:


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Trigonometric functions:

cos(x)

cot(x)

csc(x)

sec(x)

sin(x)

tan(x)

cosine; cos x .

cotangent; cot x .

cosecant; csc x .

secant; sec x .

sine; sin x .

tangent; tan x .


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acos(x)acot(x)acsc(x)asec(x)asin(x)

atan(x)atan2(y,x)

Inverse cosine; arccos x .

Inverse cotangent; arccot x .Inverse cosecant; arccsc x .

Inverse secant; arcsec x .Inverse sine; arcsin x .

Inverse tangent; arctan x .Four-quadrant inverse tangent.

Inverse Trigonometric Functions:


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Hyperbolic Functions:

Hyperbolic cosine

Hyperbolic cotangent.

Hyperbolic cosecant

Hyperbolic secant

Hyperbolic sine

Hyperbolic tangent

cosh(x)

coth(x)

csch(x)

sech(x)

sinh(x)

tanh(x)


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Inverse Hyperbolic Functions:

acosh(x)

acoth(x)

acsch(x)

asech(x)

asinh(x)

atanh(x)

Inverse hyperbolic cosine

Inverse hyperbolic cotangent

Inverse hyperbolic cosecant

Inverse hyperbolic secant

Inverse hyperbolic sine

Inverse hyperbolic tangent;


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Example:For x in the range 0 x 2 , confirm that

tan(2x) = 2 tan x/(1 - tan 2x)


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User-Defined Functions

Function file is another type of M-file.

Function files are useful when you need torepeat a set of commands several times.

Function files are commonly the building blocksof larger programs.


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The first line in a function file must begin with a function definitionline that has a list of inputs and outputs. This line distinguishes afunction M-file from a script M-file. Its syntax is as follows:

function [output variables] = name(input variables)

Note that the output variables are enclosed in square brackets,while the input variables must be enclosed with parentheses.

The function name should be the same as the file name in which itis saved (with the .m extension).


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Rules of naming user-defined functions are similar to namingvariables:

The function name must start with a letter.It can consists of letters, numbers and underscore.Reserved names cannot be used.Any length is allowed although long names are not goodprogramming practice.


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Example 1:


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Output from Example 1:


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Example 2:Create a function that computes the area and circumference of acircle, given its radius as input.


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User-Defined FunctionsOutput from Example 2:


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Example 3:Create a function that converts degrees to radians:


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A function may have no input arguments and nooutput list.

For example:


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Local Variables

The names of the input variables given in the function

definition line are local to that function.

This means that other variable names can be used when youcall the function.

All variables inside a function are erased after the functionfinishes executing, except when the same variable namesappear in the output variable list used in the function call.


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Global Variables

The global command declares certain variables global, andtherefore their values are available to the basic workspace andto other functions that declare these variables global.

The syntax to declare the variables a , x , and q isglobal a x q


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Global Variables

In general, it is not recommended to define globalvariables.

Because, it becomes available to other functions and can bechanged by those functions, unintentionally.


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Global Variables

Example of function with global variable:


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Some Applications of Functions

Finding the Zeros of a FunctionMinimizing a Function of One VariableMinimizing a Function of Several

VariablesDesign Optimization


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Finding the Zeros of a Function

Recall that we use the built-in functionroots to find the zeros of polynomialfunctions: 065213 23 x x x


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Finding the Zeros of a Function

For any function of a single variable, we canuse fzero function to find the zero.

The syntax is fzero (function, x0) where function is the name of the function

and x0 is a user-supplied guess for the zeroIt returns a value of x that is near x0 .


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Example: For function y = x +2e -x -3


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Minimizing a Function of One Variable

Function fminbnd finds the minimum of afunction of a single variable at certain xinterval.

Common syntax is fminbnd (function,x1, x2)where x1 and x2 is the lower and upperlimit of the interval.


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Example:For function y = 1 xe -x, find the value of x thatgives a minimum of y for 0 x 5.


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Minimizing a Function of Several Variables

The fminsearch function is used to find theminimum of a function of more than onevariable.

Common syntax isfminsearch (function, x0) where x0 is the vector that a user input basedon a guess.


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Example:For function , find the value of x andy that gives a minimum of f.

22 y x xe f

First define it in an M-file, using the vector x whose elements are x(1)=x and x(2)= y .

function f = f4(x)f = x(1).*exp(-x(1).^2-x(2).^2);

Suppose we guess that the minimum is near x = y = 0 :>>fminsearch (f4,[0,0]) ans =

-0.7071 0.000

Thus the minimum occurs at x = 0.7071, y = 0.


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Design Optimization

Design optimization is an approach that findways to improve engineering designs byformulating the mathematical equationsdescribing the minimization/ maximizationof the problem.

Examples, minimise energy consumption ordesign cost; maximize efficiency or productcapacity.


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Design Optimization

Example:A fenced enclosure has the followingmeasurement. An area A of 1600 ft 2 isrequired, and fencing cost is RM40/footfor the curved part and RM30/foot onthe straight sides. Determine the value of

R and L to minimize the total cost of thefence.

A = 1600 ft 2


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Design Optimization

A = 1600 ft 2


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Working with Data Files

Importing Spreadsheet Files

Some spreadsheet programs store data in the .wk1 format. You can use the commandM = wk1read(filename) to import this datainto MATLAB and store it in the matrix M.

The command A = xlsread (filename)

imports the Microsoft Excel workbook filefilename.xls into the array A. The command [A,B] = xlsread (filename) imports all numericdata into the array A and all text data into the cell array

B.


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The Import Wizard

To import ASCII data, you must know how the data in the fileis formatted.

For example, many ASCII data files use a fixed (or uniform)format of rows and columns.

(continued )


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The Import Wizard (continued)

For these files, you should know the following.

How many data items are in each row?

Are the data items numeric, text strings, or a mixture of

both types?

Does each row or column have a descriptive textheader?

What character is used as the delimiter, that is, thecharacter used to separate the data items in each row?The delimiter is also called the column separator .

(continued )


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You can use the Import Wizard to import many types of ASCII data formats, including data on the clipboard. Whenyou use the Import Wizard to create a variable in theMATLAB workspace, it overwrites any existing variable in theworkspace with the same name without issuing a warning.

The Import Wizard presents a series of dialog boxes in whichyou:

1. Specify the name of the file you want to import,2. Specify the delimiter used in the file, and3. Select the variables that you want to import.


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