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Today's Agenda● Introduce Matlab User Functions


What are Functions?

● Functions in MATLAB are similar to: ● functions in C● subroutines in FORTRAN and BASIC ● procedures in Pascal

● Building blocks of larger programs● Allows complex programs to be structured

and organized● Defined by MATLAB or created by user● Accept input values and return output values


Matlab's Built-In Functions:

● Elementary Functions

● Array Operations● Special Functions● Matrix Operations● Numerical Methods

● Data analysis functions

● Graphing Functions● Polynomial

Functions● Signal Processing

Functions


Using Elementary Functions● Math Format

y = f(x)

● MATLAB Format

output_variable = function_name (input_variable)

● Example

squareroot_of_number = sqrt (16)

Any name you choose(output value)

MATLAB function

number or variable(input value)


Matlab runs two types of programs:

1) SCRIPT files --- stand alone programs like you've been writing

2) FUNCTION files --- sub-programs intended to do a specific task and return the results to the program that called it


Matlab user-defined FUNCTIONS:

● First line designates it as a function● lists input values and returns output values

● Second line(s) are “prologue” to be printed in response to a help command

● Following lines complete the calculations

NOTE: All the variables are local variables, which means their values are only available within the function


Generic Function Examplefunction [output_variables] = function_name (input_variables);

% this is an example of a function

% input_variable and ouput_variable are both vectors

output_variables =input_variables .^ 2

● If only one output value the [ ] are optional● First line tells MATLAB "this is a function"● Prologue describes what the function does

● help function_name prints Prologue to screen● Calculations come after the Prologue● Must SAVE function in EDITOR with .m extension


Area of a Square Function

function [Asqr] = square(side)

% This function calculates the area of a square.

% Input variable (length of side) can be a scalar or vector

% Output variable will be a scalar or vector depending on input

[Asqr]=side.^2;

● output_variables = Asqr● function_name = square.m● input_variables = side


Calling a Function

In Command Window or Parent program type:

[output_variable]=function_name(input_variable)

Examples:

>> side=2

>> [Asqr]=square(side)

OR

>> Area=square(2)

OR

>> Asqr=square([1,2,4])


Area of a Square and Circle Function

function [Asqr,Acir] = square_circle(side,radius)

% This function calculates the area of a square and circle.

% Input variables can be a scalar or vector

% Input variables are length of square and radius of circle

% Output variable will be a scalar or vector depending on input

% Output variables are area of square and area of circle

[Asqr]=side.^2;

[Acir]=pi*radius.^2;


Calling this Function

● Variable names do NOT need to be the same as in the function

● Variables must be in same location and order

Example:

>> length=2

>> r=2

>> [Area1,Area2] = square_circle(33,65)

>> [surf_a_sq,surf_a_ci]=square_circle(length,r)


As a Team...● Write a "statistics' function that calculates

mean, min, max, stdev for a set of data● Name this function stat_pack.m● Test this function in your command window

using a simple data set● x=[1,2,3,4,5,6,7,8,9,10]


Stepwise Refinement

● Design Strategy used to break a large task into smaller tasks

● Continue to divide tasks until the tasks are relatively simple and have an obvious solution

● For example: plot a sine wave from 0 to 2*pi● Generate a vector x with elements between 0

and 2pi

● Evaluate yi=sin(x

i)

● Plot yi versus x

i


Program Modules

● Programs generally have a Main program which calls individual modules (user functions)

● Modules should be dedicated to 1 task ● Each module can be individually developed

and tested● Modules may be reused for other applications


As a Team

● Read the Glen Canyon Dam problem (LM p. 44)

● Plan your solution to the Glen Canyon Dam Monitoring Analysis.

● Break tasks to modules● List Input and Output parameters for each

module


Modules

● Main Program● flow_stats● daily_ave● weekly_ave● plot_data


main

● Main routine● Problem documentation● Tasks:

● Load the data into MATLAB matrix● Copy the data into a vector of times and a vector

of flow rates● Call other functions to calculate statistics and

output results


flow_stats● Input: hourly flow vector● Output: mean hourly flow, median hourly

flow, standard deviation of hourly flow

● Tasks:● Calculate mean, median, standard deviation hourly

flow for the entire year


daily_ave

● Input: hour vector, hourly flow vector● Output: day vector, average daily flow

vector● Tasks:

● Determine number of days in data set● Day vector = day of year● Daily ave = mean (flow hours (a:b) )


weekly_ave

● Input: hour vector, hourly flow vector● Output: week vector, weekly flow vector● Tasks:

● Determine number of weeks in data set● Week vector = day of year, middle of the week● Weekly ave = mean (hourly flow (a:b) )


plot_data

● Input: hour, hourly flow, day vector, daily flow, week vector, weekly flow

● Output: plot of flow rates and histogram● Tasks:

● Plot hourly data versus time● Plot histogram of hourly flow, with 20 bins● Plot daily data versus time as a line and weekly

data versus time as circle


Testing Your Code

● Test each module with a simple version of the problem, whose answers can be checked by hand calculations

● Display intermediate calculations by removing semicolons at the end of statements or adding or removing print statements

● Use MATLAB debugger


Team Homework ...Due: 13A

● Glen Canyon Dam Analysis (see handout)

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