What is a Matlab function?

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What 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, 5.6.1

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Basic 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 =

1

name 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.

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Three 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 field

refund amount

amount due

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Example: 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 (x

i ,y

i) 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 black

c m y r g b w k

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Linestyle can be any of the following:

solid dashed dotted dashed-dot no line

line line line line

- - - : -. none

and marker can be specified as:

plus asterisk point cross square diamond

+ * . x square diamond

Example:

>> x = -10 : .1 : 10;

>> y = sin(x);

>> plot(x,y,’m--square’); Figure Window

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Note: 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 Arguments

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>> x = pi / 4; % line 1

>> y = sin(x) ; % line 2

During 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.

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>> 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 =

5

Matlab’s built-in functions accept a wide variety of array sizes.

Example: The built-in function sum.

(see section 5.3)

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Users 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.

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Programming -

• 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.

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• Modular Programming

Break 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.

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1. Problem Definition

2. 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 Code

6. Run Code

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Write a function that converts a temperature in Fahrenheit to Celsius.



Use the fact that celsius = (fahr - 32) * 5/9

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Natural-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)

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4. Write the “Function" (Code)

(instruction sequence to be carried out by the computer)

Any sequence of Matlab commands can be put in a file.

The file suffix should end with a “.m”. The sequence of

commands will be executed (from the top of the file down,

command by command).

>> edit

to open the Matlab editor and create a new file. Then type

(and save) the following:

function celsius = F_to_C(fahr)

% This function converts Fahrenheit to Celsius.

celsius = (fahr -32)*5/9;

Click “File” and then “Save As” to name the file “F_to_C.m”.

Execute(call) the function in by typing “ F_to_C( temperature )”.

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If the program works correctly then it has no “bugs” so

bring the Matlab editor back up and close out the

Matlab program. Does the program work with only

scalar input or does it work with vector values? (see

next slide)

6. Run Code

Since two points determine a linear function we know

the function F_to_C works correctly.

Input is a vector [32 212]

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• prepared during development of a program, as

comments within the program and possible

additional documentation; e.g., manuals, etc.

• Use the “%” symbol to write a comment in a

program.

• You must put comments in your program describing

the function interface - i.e. input and output format.

• Also a general description of what the function

does.

Finally the programmer should identify himself /

herself.

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Improved documentation for the F_to_C function.

function celsius = F_to_C(fahr)

% function celsius = F_to_C(fahr)

% This function converts Fahrenheit to Celsius.

% input fahr can be a scalar or vector of temps in degree F

% output celsius is a scalar or vector of temps in degree C

% Programmer: Tom Gambill

% Date: 1/30/01

celsius = (fahr -32)*5/9;

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Write a function that computes the time for a falling object to hit the

ground.



Use the fact that height_t = height_0 + velocity_0* time + 1/2 * g * time* time,

where height_t is the height of the object at any given time (in seconds), g is the acceleration due to gravity, -9.8 m/s2. velocity_0 is the velocity at time = 0. Therefore to compute the time to impact, set height_t = 0 and solve for time. This equation (after doing some algebra)can be written as: 0 = -4.9 * time2 + velocity_0 * time + height_0 This is a quadratic formula in terms of the variable time.

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Natural-Language Algorithm

Initial values of height_0 and velocity_0 are provided

via the arguments when the function is called.

Solve quadratic formula for time

Quadratic formula has two solutions, select the

positive value as the result to be returned.

3. Develop Algorithm (processing steps to solve problem)

2. (continued)

The input arguments to the function consists of scalar values for height_0 and velocity_0 and the output is the exact time (in seconds) of contact with the ground.

Assumptions: No air resistance and time = 0 when object begins decent. (Also height_0 > 0 implicit)

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4. Write the “Function" (Code)

(instruction sequence to be carried out by the computer)

Use the Matlab editor to create a file “time_to_impact.m” .

function time = time_to_impact(height_0,velocity_0)

% function time = time_to_impact(height_0,velocity_0)

% Input: Two scalars height_0 (meters) and velocity_0 (meters/sec)

% Output: time to impact (sec) given initial height is

% height_0 and initial velocity is velocity_0.

% Programmer: Tom Gambill

% Date: 9/10//00

% Assumptions: No air resistance

% time = zero when object begins decent

% g = 9.8 is constant

p = [-4.9 , velocity_0, height_0];

time=roots(p);

time = max(time);

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Although the value of the function is assigned to the

variable time, when you execute the function you can assign

the value of the function to any variable.(see next slide)

6. Run Code

Note: The prefix of the Unix filename must be the same as

the name of the function. e.g. if the function name is

“time_to_impact” then the filename in Unix must be

“time_to_impact.m”. Also, don’t use the same name for a

function and a variable in your workspace.

(see the next slide for ways to “run” or execute the function)

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Body of the function

Note: One statement in the body of the function should be

of the form,

output_variable = expression;

function output_variable = function_name(input_variables)

% The line above is called the function definition line.

% Simple functions have only one output variable..

% A line that begins with a “%” symbol is called a comment.

% Comments are ignored by Matlab but necessary for humans.

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time_to_impact uses the built-in functions, roots, and max.

The function roots (see 5.6.1) computes all the roots of a

polynomial. In Matlab polynomials are represented by vectors.

e.g. the polynomial,

x2 - 1 is represented by

>> p = [1 0 -1]; % p is just a vector

To compute all the roots (x-values where p(x) = 0) of this

polynomial type,

>> roots(p)

ans =

-1

1

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From the previous slide,

-6+x+x2 is represented by

>> p = [1 1 -6]; % p is just a vector

To evaluate the polynomial p at x = 3 , x = 4 and x = 5

(that is to compute p(3), p(4), p(5) use the built-in Matlab

function polyval (see 5.2.2),

>> polyval(p , [3, 4, 5])

ans =

6 14 24

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The functions max or min compute the maximum or minimum

value of an array. These functions work on arrays and

vectors in a similar manner to the function sum (slide 2-13).

Example

>> vec1 = [-2 ; 3 ; 4] ;

>> vec2 = [-2 3 4] ;

Continued on next slide ...

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>> min(vec2)

ans =

-2

>> min(vec1)

ans =

-2

>> max(vec2)

ans =

4

>> max(vec1)

ans =

4

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A Matlab function is a sequence of Matlab

statements that are entered in a file. The first line

of the function called the function definition line

and has a specific format. A function is executed

whenever it occurs in a Matlab expression that is

executing in the Matlab environment.

Matlab function filenames end with the .m

extension and the filename must be the same as

the function name.

You create your own function by following a six

step design procedure.

Functions provide modular design.

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What is a Matlab function?